Thesis Latt

University of Lüneburg Department of Civil Engineering Water Resources Management in Tropical and Sub-tropical Regions

Presented to

The Department of Civil Engineering as a partial Fulfilment for the

Degree of Master of Science in

Water Resources Management

(M Sc. W.R.M)

First Supervisor : Prof. Dr. Ing. H. Wittenberg Second Supervisor : Prof. Dr. Ing. A. Töppe

Submitted by

Zaw Zaw Latt Matriculation Nr. 158204

February, 2006

University of Lüneburg Department of Civil Engineering Water Resources Management in Tropical and Sub-tropical Regions

Presented to

The Department of Civil Engineering as a partial Fulfilment for the

Degree of Master of Science in

Water Resources Management

(M Sc. W.R.M)

First Supervisor : Prof. Dr. Ing. H. Wittenberg Second Supervisor : Prof. Dr. Ing. A. Töppe

Submitted by

Zaw Zaw Latt Matriculation Nr. 158204

Lüneburg University

Germany

February, 2006

i

DECLARATION

Herewith I would like to declare that I have prepared the M.Sc. thesis with the title of “ Low

Flow Analysis of Chindwin River in Myanmar ” myself without using any other sources and

references except those which are listed as the references for my thesis. Initiation of the

proposed subject is originated from my interest. Different kinds of ideas, thoughts and the

correct approach to the study come from my supervisors who kindly contributed to my

thesis.

Zaw Zaw Latt

Matriculation No.158204

Lüneburg University, Campus Suderburg

Germany

February, 2006

ii

ACKNOWLEDGEMENT

Firstly I wish to express sincere gratitude to my first supervisor Prof. Dr. -Ing. H Wittenberg

and second supervisor Prof. Dr. –Ing. A Töppe for their kind acceptance to supervise my

thesis. Then my deep appreciation is due to their enthusiastic instructions, fruitful criticisms

and indispensable guidance throughout the preparation of my thesis.

I offer my grateful thanks to U Kyaw San Win, director general of the Irrigation Department,

Ministry of Agriculture and Irrigation, Myanmar for his impressive recommendation to me to

study the postgraduate course in Germany.

I am also indebted to the associate professor, Daw Cho Cho from the Yangon

Technological University and U Tin Oo, deputy director of Hydrology Branch under the

Irrigation Department, Ministry of Agriculture and Irrigation for their logical supports and

great encouragement.

Then my kind gratitude goes to Daw Htay Htay Win, deputy director of Irrigation

Technology center for her encouragement and continuous supports during period of the

field study in Myanmar.

I am deeply grateful to all professors who have given the excellent lectures during the

postgraduate course in Lüneburg University, Germany.

In writing this thesis, I wish to acknowledge the lasting influence of my teachers and

colleagues for their interests, assistance and helpful manners which give me great strength

to carry out my thesis.

I would like to thank to the following organizations which provided me with information that

eventually was included in the paper: the Irrigation Department, the Department of

Meteorology and Hydrology, and the Water Resource Utilization Department

Besides I also want to express my deep appreciation to DAAD for the financial support

through which I could have a chance to study and stay in Germany.

Last but not least, I would like to express my indebted thanks to my parents and younger

sister for their forbearance, love and sharing of my stresses and burdens.

iii

ABSTRACT A study of drought conditions is intended to help assess future storage conditions and

impact on water resources management. So many hydrologists have systematically carried

out on the extraction and diagnosis of the hydrologic drought characteristics so far.

As an introduction brief information on water resources in Myanmar and some important

facts of the study area are mentioned to have a clear vision on the thesis. Before starting

the analysis, hydrologic data tests of collected stream flows are carried out in order to

detect the possible errors. Collected daily discharges are found to be consistent,

homogeneous and free from outliers. In this paper the analysis is statistically attempted for

streamflow drought characteristic of Chindwin river, Myanmar at Monywa gauging station.

There are three main portions of analysis to determine the low flow indices.

Firstly the probability of each stream flow calculated by the plotting position is used to draw

the low flow duration curve through which low flow index of the stream can be theoretically

expressed in terms of a percentile value of the study period. Drought discharge is

interpreted as EFQ90 which has the exceedance probability of 90% of the period.

Comparing the shape of the lower half of the curve, the changes of low flow condition in the

stream are traced with the time.

For water resources planning it is also important to extract and assess low flow recession

which aims at the characterizing the falling limb of the hydrograph, from which the

recession indices are derived by linear and no-linear storage functions. Here the

construction of the master recession curve based on the analytical expression is proposed

and applied to the study area. Then shapes of the curves are expressed in quantitative

manner i.e. in terms of recession constants. Non-linear storage provides the best fit for

groundwater contribution.

Then frequency curves for different time reaches are analyzed to check the change of

lower half of the curves which show the tendency of low flow occurrence of the stream.

Observed frequency curve for the whole study period is fitted by distribution functions. After

testing the goodness of fit, Pearson III is found to be the best fit for observed data and low

flow values given by the best suited distribution function and drought discharge, 7Q10 are

interpreted.

In accordance with the available data, impacts on low flow such as climate impact and land

use impact are analyzed and have been proved to have the relation with the low flow

indices obtained in the study.

According to overall performances, all low flow indices indicate that stream flow has

suffered more seasonal and man-made impacts especially during the last 10-year interval,

1995-2004.

iv

ZUSAMMENFASSUNG

Es ist eine Studie der Bedingungen bei einer Dürre geplant, welche bei der Abschätzung

von künftigen Wasserspeicherungen und die Auswirkung auf die Wasserwirtschaft helfen

soll. Bislang haben sehr viele Hydrologen systematisch die Charakteristiken einer Dürre

ausgearbeitet und diagnostiziert.

Zur Einführung wird eine kurze Information über das Wasservorkommen in Myanmar

gegeben und es werden einige wichtigen Fakten über das Untersuchungsgebiet erläutert,

um einen klaren Überblick über die Masterarbeit zu bekommen. Vor Beginn der Analyse

werden die hydrologischen Tests des gesammelten Wassers unterzogen, um mögliche

Fehler zu entdecken. Die täglich gesammelten Abflüsse werden dabei als konsistent,

homogen und frei von Ausreißern befunden. In dieser Arbeit wird eine statistische Analyse

der Dürre-Charakteristik der Wasserströmung des Chindwin-Flusses in Maynmar bei der

Monywa-Messstation versucht. Es gibt drei Hauptbereiche der Analyse, um die

Niedrigwasserindizes zu bestimmen.

Als erstes wird von jeden Durchfluss die Wahrscheinlichkeit, berechnet durch die

Zeichenposition, benutzt, um die Niedrigwasserdauerlinie zu zeichnen. Durch diese lässt

sich der Niedrigwasserindex des Stroms ausdrücken, der theoretisch durch den

durchschnittlichen Wert der Studiendauer ausgedrückt werde kann. Der

Trockenheitsabfluss wird als EFQ90 interpretiert, welche die Überschreitung der

Eintrittswahrscheinlichkeit von 90 % der Zeitperiode hat. Durch das Vergleichen der

Formen der unteren Hälften der Kurven wird die NiedrigwassersBedingung des Stromes im

Laufe der Zeit verfolgt.

Zur Planung der Wasserwirtschaft ist es auch wichtig die Trockenwetterganglinie

abzuschätzen und zu extrahieren, welche den Zweck hat, den fallenden Zeiger des

Hydrographen zu charakterisieren. Von diesen werden die Recession-Indizes durch lineare

und nicht-lieare Speichersfunktionen abgeleitet. An dieser Stelle wird eine Meister-

Recession-Kurve basierend auf dem analytischen Ausdruck aufgestellt, konstruiert und auf

das Untersuchungsgebiet angewendet. Nicht-lineare Speichersfunktionen liefern den

besten Anpassung für der Grundwasserabfluss.

Es werden dann Häufigkeitskurven für verschiedene Zeiten analysiert um die

Veränderungen der unteren Hälften der Kurven zu überprüfen. Diese zeigen die Tendenz

des Niedrigwasser-Ereignises des Stromes. Die beobachtete Häufigkeitskurve der

gesamten Untersuchungsperiode wird durch Verteilungsfunktionen gefittet. Nachdem der

Fit auf gute Qualität getestet wurde, wurde Pearson III als der beste Anpassung für die

beobachteten Daten befunden. Die Niedrigflusswerte, gegeben durch die bestangepassten

Verteilungsfunktionen und der Dürre-Abflüsse, werden als 7Q10 interpretiert.

v

In Übereinstimmung mit den verfügbaren Daten werden Einflüsse von Klima und

Landnutzung auf den Niedrigwasser analysiert. Es wird überprüft, ob sie eine Beziehung

zu den Niedrigfluss-Indizes haben, die mit dieser Arbeit aufgestellt wurden.

In der Gesamtbetrachtung zeigt sich, dass alle Niedrigstrom-Indizes darauf hindeuten,

dass die Strömung sehr viel mehr jahreszeitliche und menschengemachte Einflüsse zeigt,

besonders in dem 10-Jahres-Intervall von 1995 bis 2004.

vi

TABLE OF CONTENTS

DECLARATION………………………………………………………………………………… i ACKNOWLEDGEMENT……………………………………………………………………….. ii ABSTRACT……………………………………………………………………………………… ii ZUSAMMENFASSUNG……………………………………………………………………….. iv

LIST OF FIGURES……………………………………………………………………………... x

LIST OF TABLES………………………………………………………………………………. xii LIST OF APPENDICES……………………………………………………………………….. xiv

LIST OF ABBREVIATIONS…………………………………………………………………… xv

EXECUTIVE SUMMERY……………………………………………………………………… xvi

Chapter 1. Introduction……………………………………………………………… 1 1.1 Country Profile………………………………………………………………….. 1

1.2 Administrative Units……………………………………………………………. 3

1.3 Socio-economic Features……………………………………………………... 3

1.4 Climate…………………………………………………………………………... 3

1.4.1 Major seasons……………………………………………………………… 3

1.4.2 General description……………………………………………………….. 4

1.5 Classification of Rainfall……………………………………………………….. 9

1.6 Current Water Resources Management Activities………………………….. 9

1.7 Irrigation and drainage………………………………………………………….10

1.8 Institutional Environment………………………………………………………. 11

1.9 Background Problems in Water Sector……………………………………….12

Chapter 2. Description of the Study………………………………………………. 13 2.1 Introduction……………………………………………………………………… 13

2.2 General Description……………………………………………………………. 13

2.3 Objectives of the Study…………………………………………………………16

2.4 Scope of the Study……………………………………………………………...17

2.5 Available Data…………………………………………………………………...17

2.6 Methodology……………………………………………………………………..18

2.6.1 Materials…………………………………………………………………….. 18

2.6.2 Method………………………………………………………………………. 18

Chapter 3. Literature Review……………………………………………………….. 20 3.1 Introduction……………………………………………………………………… 20

vii

3.2 Flow Duration Curve Analysis………………………………………………… 20

3.3 Recession Curve Analysis…………………………………………………….. 22

3.3.1 Linear Storage……………………………………………………………… 22

3.3.2 Non-linear Storage………………………………………………………… 23

3.4 Low Flow Frequency Analysis…………………………………………………24

3.4.1 Selection of Data Series ………………………………………………….. 25

3.4.2 Concepts of Statistic and Probability…………………………………….. 25

3.4.3 Properties of Statistical Distribution……………………………………… 26

3.4.4 Return Period, Frequency, and Risk…………………………………….. 26

3.4.5 Plotting Position……………………………………………………………. 26

3.4.6 Frequency Factor………………………………………………………….. 27

3.4.7 Continuous Probability Distributions…………………………………….. 28

3.4.8 Three-Parameter Lognormal Distribution ………………………………. 28

3.4.8.1Determination of Frequency Factor………………………………. 28

3.4.9 Pearson Type III Distribution……………………………………………… 29

3.4.9.1 Determination of Frequency Factor………………………………. 29

3.4.10 Extreme Value Type III Distribution…………………………………….. 29

3.4.10.1 Determination of Frequency Factor……………………………… 30

3.4.11 Test for Goodness of Fit………………………………………………… 30

3.4.11.1 Method of Least Squares………………………………………… 30

Chapter 4. Water Resources in Myanmar ……………………………………….. 32

4.1 Water Resources Availability…………………………………………………. 32

4.1.1 General………………………………………………………………………32

4.1.2 Surface Water……………………………………………………………… 32

4.1.2.1 Major River Basins and Water Resources……………………….. 33

4.1.3 Ground Water………………………………………………………………. 36

4.1.4 Non- Conventional Water Resources …………………………………… 37

4.2 Water Quality…………………………………………………………………… 37

4.2.1 Surface Water……………………………………………………………… 37

4.2.2 Ground Water……………………………………………………………… 38

4.3 National Water Sector Context……………………………………………….. 38

4.4 Water Resource Utilization and Challenges………………………………… 39

4.5 Water-Related Response Indicators…………………………………………. 40

4.6 Trends in Water Management………………………………………………… 40

Chapter 5. Outline of the Chindwin River Basin………………………………… 42

viii

5.1 Region under the Study……………………………………………………….. 42

5.2 Topography…………………………………………………………………….. 45

5.3 General Climate ……………………………………………………………….. 46

5.4 Land Use and land cover……………………………………………………… 46

5.5 Soil Type and Basin Characteristics…………………………………………. 48

5.6 Water Utilization…………………………………………………………………49

Chapter 6. Data Description and Analysis of Collected Data………………… 50 6.1 Description of Collected Data Series………………………………………… 50

6.2 Determination of Statistical Parameters of the collected Data Set……….. 52

6.3 Analysis of Collected Data Series……………………………………………. 52

6.3.1 Test for Independence and Stationary………………………………….. 53

6.3.1.1 Result of the Test…………………………………………………… 53

6.3.2 Test for Homogeneity and Stationary…………………………………… 54

6.3.2.1 Result of the Test……………………………………………………. 55

6.3.3 Test for Outliers……………………………………………………………. 55

6.3.3.1 Result of the Test…………………………………………………… 56

6.4 Summary Result of Data Test………………………………………………… 57

6.5 Main Activities of Low Flow Analysis in the Region………………………… 57

Chapter 7. Duration Curve Analysis………………………………………………. 59 7.1 Introduction……………………………………………………………………… 59

7.2 Use of the Duration Curve…………………………………………………….. 59

7.3 Study Area and Data………………………………………………………….. 60

7.4 Percentiles from the Flow Duration Curve……………………………………60

7.5 Evaluation of Flow Duration Curves………………………………………….. 63

7.6 Flow Duration Curve for the Entire Study Period…………………………… 65

Chapter 8. Recession Curve Analysis…………………………………………….. 66 8.1 Introduction……………………………………………………………………… 67

8.2 Study Area and Data……………………………………………………………67

8.3 Determination of Master Recession Curves………………………………… 67

8.3.1 Master Recession Curves for every 10-year Period…………………… 68

8.3.1.1 Determination of Recession Constant by Simple Averaging ….. 69

8.3.1.1.1 Linear Storage…………………………………..………….. 69

8.3.1.1.2 Non-linear Storage……………………………..…………... 71

8.3.1.1.3 Verification of Master Recession Curves……. ………… 73

ix

8.3.1.2 Determination of Average K fitted by Matching Strip Method….. 74

8.3.1.2.1 Linear Storage………………………………. …………….. 76

8.3.1.2.2 Non-linear Storage…………………………..……………... 77

8.3.1.2.3 Verification of Master Recession Curves........................ 78

8.3.2 Evaluation of Master Recession Curves…………………………..…… 80

Chapter 9. Low Flow Frequency Analysis……………………………………….. 82 9.1 Introduction……………………………………………………………………… 82

9.2 Study Area and Data………………………………………………………….. 82

9.3 Mean Annual Minimum Flow………………………………………………….. 83

9.4 Plotting Position of Average Low Flows……………………………………... 83

9.4.1 Frequency Curves of 15-Year Time Reaches………………………….. 84

9.4.2 Frequency Curves of 10-Year Time Reaches………………………….. 86

9.5 Fitting of Low Flow Frequency Curve by Distribution Functions………….. 88

9.5.1 Three-Parameter Lognormal Distribution............................................. 89

9.5.2 Pearson Type III Distribution……………………………………………… 89

9.5.3 Extreme Value Type III distribution………………………………………. 90

9.5.4 Selection of Distribution Function………………………………………… 91

9.5.5 Test for Goodness of Fit…………………………………………………... 91

9.5.5.1 Method of Least Squares............................................................. 92

9.5.6 Result of Expected Low Flows by best fitted Distribution……………… 93

Chapter 10. Miscellaneous Approaches……………………………………........ 95 10.1 Introduction............................................................................................... 95

10.2 Mass Curve Analysis................................................................................ 95

10.3 Impacts on Low Flow…………………………………………………………. 97

10.3.1 Impact of Climate Change……………………………………………… 97

10.3.2Impact of Land-Use Change……………………………………………. 101

Chapter 11. Discussion, Recommendation and Conclusion…………………. 104

11.1 General………………………………………………………………………… 104

11.2 Discussion……………………………………………………………………... 104

11.3 Recommendation……………………………………………………………... 107

11.4 Conclusion…………………………………………………………………….. 109

REFERENCES……………………………………………………………………………….. 110 APPENDICES…………………………………………………………………………………... 112

x

LIST OF FIGURES Figure 1.1 Location Map of Myanmar

Figure 1.2 Map of Myanmar

Figure 1.3 Mean Daily Maximum Temperatures during the hot Season

Figure 1.4 Mean Daily Minimum Temperatures during the cold Season

Figure 1.5 Isohyetal Map of Myanmar

Figure 2.1 Propagation of Drought through the Hydrological Cycle

Figure 4.1 Major Drainage Basins of Myanmar

Figure 5.1 Chindwin River joining to Ayeyarwaddy River

Figure 5.2 Location of the Chindwin Basin

Figure 5.3 Chindwin Basin Map

Figure 5.4 Transportation by Small Boat in Chindwin River

Figure 5.5 Irrigation Development along the Chindwin River by Direct Pumping

Figure 6.1 Location of the gauging Station

Figure 6.2 Annual Low Flows ( 7-day minimum) of the Data Set

Figure 6.3 Derivation of Low Flow characteristics

Figure 7.1 Duration Curve for the period of 1975-1984



Figure 7.4 Comparison of flow duration curves for every 10-year period

Figure 7.5 Comparison of tail Portions of Duration Curves

Figure 7.6 Flow Duration curve for entire Period (1975-2004)

Figure 8.1 Recession constants for the period of 1975-1984



Figure 8.4 Master Recession Curves (Linear Storage) using arithmetic mean of K

Figure 8.5 Master Recession Curves (Nonlinear Storage) using arithmetic mean of a

Figure 8.6 Verification MRC by simple arithmetic Mean (1975-1984)



Figure 8.9 Positioning of recession curves (1975-1984)



Figure 8.12 Master Recession Curves (Linear)

Figure 8.13 Master Recession Curves (Nonlinear)

Figure 8.14 Verification of MRC by positioning of integrated Recessions (1975-1984)


xi


Figure 9.1 Low flow analysis with empirical return periods

Figure 9.2 Low Flow Frequency Curves for first and second half of the Data Length

Figure 9.3 Low Flow Frequency Curves for each 10-year period of the Data Length

Figure 9.4 Fitting of Low Flow Frequency Curve by three distribution functions

Figure 9.5 Low Flow Frequency Curve of Chindwin River by Pearson III

Figure 10.1 Mass Curve of Cumulative Min Q

Figure 10.2 Mass Curve of Cumulative Max Q

Figure 10.3 Mass Curve of Cumulative Flow Volume

Figure 10.4 Mean Annual Rainfall in Chindwin Basin

Figure 10.5 Mean Annual Temperature of Chindwin Basin (Monywa Station)

Figure 10.6 Annual Rainfall and Annual Average Low Flow (NM7Q)

Figure 10.7 Mean Annual Temperature and Annual Average Low Flow (NM7Q)

Figure 10.8 Mean monthly Temperature of Recession Periods

Figure 10.9 Mean Temperatures of Recession Periods in every 10-year Interval

Figure 10.10 Comparison of Regional Mean Annual Temperatures

Figure 10.11 Yearly Irrigation Development in Chindwin Basin

Figure 10.12 Cumulative Irrigation Development in Chindwin Basin

xii

LIST OF TABLES Table 1.1 Climatological Data of states and Divisions in Myanmar (1992-2001

Average)

Table 2.1 Condition of the available Data Type and Length

Table 4.1 Annual Surface and Groundwater Potential in Myanmar

Table 5.1 Area portion of Land Use and Land Cover

Table 5.2 Major Soil Classification of the Chindwin Basin

Table 5.3 Basin Characteristics of the Chindwin Catchment

Table 6.1 7-day minimum discharge for each year in the collected data series

Table 6.2 Statistical Parameters of data set of NM7Q

Table 6.3 Result of Independence Test

Table 6.4 Result of Homogeneity Test

Table 6.5 kN Values for Outlier test

Table 6.6 Result of Outlier Test

Table 6.7 Summery Result of the Data Test

Table 7.1 Calculation of a daily FDC for Chindwin River at Monywa Station

Table 7.2 Streamflow Values Corresponding to EFQ90

Table 7.3 Exceedance Frequencies corresponding to actual drought discharge

Table 8.1 Recession constants for each Year (linear)

Table 8.2 Average Recession Constants by Linear Storage

Table 8.3 Factor a of Nonlinear Storage

Table 8.4 Average factor a of Nonlinear Storage

Table 8.5 Master Recession Constants by Linear Storage

Table 8.6 Master Recession Constants by Nonlinear Storage

Table 9.1 Average minimum flows arranged in decreasing order

Table 9.2 Annual average low flow and return period in the first 15-year reach

Table 9.3 Annual average low flow and return period in the second 15-year reach

Table 9.4 Annual average low flows and return periods in the first 10-year reach

Table 9.5 Annual average low flows and return periods in the second 10-year reach

Table 9.6 Annual average low flows and return periods in the third 10-year reach

Table 9.7 Drought Discharge (7Q10) for each Period

Table 9.8 Expected Low Flows given by 3-Parameter Lognormal Distribution

Table 9.9 Expected Low Flows given by Pearson Type III Distribution

Table 9.10 Expected Low Flows given by Extreme Value Type III Distribution

Table 9.11 Standard errors of selected distributions for different return periods

Table 9.12 Expected Low flows given by best fitted distribution (Pearson III)

Table 10.1 Standard Deviation (Std.Dev.) Values of Collected Meteorological Data

xiii

Table 10.2 Correlation Coefficient Matrix

Table 11.1 Summary of Drought Characteristics and Indices for water Resources and

Drought Assessment

xiv

LIST OF APPENDICES

Appendix- A Basic Information Table.1 Various Agencies and Departments engaged in Water Use Sector

Table.2 Major Government Organizations engaged in Groundwater Extraction

Table.3 Irrigation Area Development of Myanmar Since 1962

Table.4 Irrigation Development in Chindwin Basin (ha) (as of Sagaing Division)

Appendix- B Maps of the Study Area, Chindwin Watershed Map.1 Soil Erodibility Factor (K) & Soil Map of Chindwin Watershed Area(1990)

Map.2 Land Cover Map of Chindwin Watershed (1990)


Map.4 Rainfall Isohyetal Map of Chindwin Baisn with Rainfall Stations

Appendix- C Meteorological and Hydrological Data Used in the Study Table.1 Mean Daily Discharge of Chindwin River ( Monywa Station )

Table.2 Mean Annual Temperature of Different Stations (°C)

Table.3 Mean Monthly Temperature of Chindwin Basin ( Monywa station )

Table.4 Annual Rainfall of Chindwin Basin

Fig.1 Hydrograph of Chindwin River at Monywa Station

Appendix- D Frequency Factors and Useful Tables for Distribution Functions

Table.1 Frequency Factors for 3-Parameter Lognormal Distribution

Table.2 Frequency Factors for Pearson Type III Distribution

Table.3 Useful Data of Gamma Function

Table.4 Parameter α, Aα and Bα for Extreme Value Type III Distribution

Table.5 Frequency Factors for Extreme Value Type III Distribution

xv

LIST OF ABBREVIATIONS DWC Development in Water Science

DMH Department of Meteorology and Hydrology

EF Exceedance Probability

EFQ90 Discharge having Exceedance Probability of 90 % of the Time

EV III Extreme Value Type III Distribution

FAO Food and Agriculture Organization

FDC Flow Duration Curve

GDP Gross Domestic Product

ha Hectare

ID Irrigation Department

LN(3) 3-Parametr Logmormal Distribution

MOAI Ministry of Agriculture and Irrigation

MRC Master Recession Curve

m.s.l Mean Sea Level

NCEA National Commission for Environment Affairs

NM1Q Annual Minimum Flow

NM7Q 7-Day Average Annual Minimum Flow



POT Peaks-over-a-Threshold

PDF Probability Distribution Function

Std Dev Standard Deviation

UN United Nations

UNDP United Nations Development Programme

U.S.G.S United States Geological Survey

WMO World Meteorological Organization

7Q10 Average 7-day Minimum Flow with a Return Period of 10 Year

xvi

EXECUTIVE SUMMERY This study primarily aims to carry out the low flow analysis of Chindwin river at Monywa

gauging station by the determination of low flow indices such as flow duration curve,

recession and frequency curve. Besides the study tries to find out the possible correlation

between these indices and the seasonal and land use changes in the region as well.

This study is divided into eleven chapters which tell not only the main analysis but also

some relevant information about the water resources in the region.

Chapter 1 describes the country profile giving the information on geographical location,

socioeconomic condition, climate, water resources, irrigation development and major

institutions engaged in water sector of the country.

Before the main analysis start, required quantitative coverage of the principles and

methods to be followed in the study are described in literature review, chapter 2.

Chapter 3 contains the explanation of the study, necessary to provide the objectives of the

study, methodology used including materials and methods and available data type and

length as well.

Then to have an overview of the water resources availability, chapter 4 is included at this

early stage to expose the readers to the information on water resources potential in

Myanmar.

And explanation about the study area such as location, topography, general climate,

chatchment characteristics, land cover and land use and water utilization conditions can be

seen in chapter 5. These two chapters, 4 and 5, dwell on both water related fundamentals

and situation of the area.

After giving the necessary information of the region, collected hydrological data namely

mean daily discharges are tested and analysed in chapter 6 to check whether they are

consistent and homogeneous ones or not and to detect the outliers of the sample.

In coming chapters, determination of three main low flow indices is mentioned. Chapter 7

deals with preparation of low flow duration curves through which drought discharges of

Chindwin river in terms of percentile values of the period are investigated.

One important index, master recession curves for different 10-year intervals are created

and master recession curve constants are determined in chapter 8 using simple averaging

and matching strip method. Then master recession curves are fitted by both linear and

nonlinear storage equations.

After that, chapter 9 contains the preparation of low flow frequency curves for different time

reaches using the plotting position method. Then observed frequency curve is fitted by

distribution functions so that expected low flow can be predicted using best fit distribution.

Chapter 10 constitutes the miscellaneous approaches using the available information of the

region. Mass curves are drawn to see the consistency of the data. And impacts on low

xvii

flows are analysed based on annual rainfall, mean annual temperature and irrigation

development data of the area in order to find the correlation between these impacts and

low flow indices obtained in previous chapters.

Finally discussion for the overall result, recommendation for the study and conclusion on

work done and further study are mentioned in chapter 11.

Chapter 1. Introduction Mtr. Nr. 158204

1

M.Sc Thesis Low Flow Analysis of Chindwin River

Chapter 1. Introduction

1.1 Country Profile The Union of Myanmar is geographically situated in Southeast Asia between latitudes 09°

32' N and 28° 31' N and longitudes 92° 10' E and 101° 11' E. The total land area is 261,

228 square miles (676,577 sq. km). It stretches for 582 miles (936 km) from east to west

and 1275 miles (2051 km) from north to south. The length of continuous frontier is 3900

miles (6286 km), sharing 2227 km with China, 2099 km with Thailand, 1453 km with India,

272 km with Bangladesh and 235 km with Laos respectively. The coast line extends from

the mouth of Nat River in the West to Kawthaung in the South and measures about 2230

km.

Location

Latitude: 9°32´ - 28°31´ Longitude: 92°10´ - 101°11´

Land frontier: With Thailand 2099km. With Laos 235 km With China 2227 km With Bangladesh 272 km With India 1453 km

Sea frontier: Rakhine coastline 713 km Delta coastline 438 km

Fig 1.1 Location of Myanmar ( Source: MOAI )

Tanintharyi coastline 1078 km


2


Fig 1.2 Map of Myanmar (source : http://www.pbase.com/rovebeetle/image/41479890)

The country is topographically divided into four regions. The eastern Shan Plateau is a

highland region averaging 900 meters in height and merging with the Dawna range and the

Tnintharyi Yoma towards the Isthmus of Kra. The central belt spans the valleys of the

Ayeyarwaddy, Chindwin and Sittoung rivers with a mountainous region in the north and a

vast, low-lying delta in the south that covers an area of 25900 sq. km. It produces almost

all the nation’s rice. The western mountain belt, also known as Rakhine mountains, is a

series of ridges that originate in the northern mountain area and extend southward to the

south-western corner. The Rakhine coastal strip is a narrow, predominantly alluvial, belt

lying between the Rakhine mountains and the Bay of Bengal. In some places the strips

disappears as the mountain spurs reach the sea. Offshore, there are hundreds of islands,

many of which are cultivated.

In 2004, the total population was calculated at 49.9 millions inhabitants. With a population

density of 68 inhabitants/km², Myanmar is well below the level of other countries in south

and Southeast Asia. The population growth rate is estimated at 1.3 percent. About


3


63 percent of the total labor force is engaged in agriculture, and 70 percent in the primary

sector, including livestock, fisheries and forestry.

1.2 Administrative Units

Myanmar is divided administratively into States and Divisions which are now in 17 numbers

in total and state/divisions are sub-divided into 64 districts which are further divided into

324 townships. Townships are also further subdivided into 13,759 village-tracts. The

village-tract is basic administrative unit which is made up of one or more villages

depending upon the size of population in each village. Statistics are collected usually on

village tract basis. Each village tract is under the charge of a committee which is directly

supervised by Township Peace and Development Council. The administrative bodies are

an integral part of the agricultural statistics system and it has to give necessary assistance

to the collection, compilation and in maintaining records at the village tract level.

1.3 Socio-economic Features

Union of Myanmar is basically an agricultural country with about 75 percent of the

population residing in rural areas. The agriculture sector provides about 72 percent of the

total labour force and contributes 36 percent of GDP and 35 percent of total foreign export

earnings (FAO).

1.4 Climate

1.4.1 Major Seasons

Most of Myanmar enjoys a tropical climate. Temperatures in Mandalay, in central Myanmar

is average 20 °C (68 °F) in January and 29 °C (85 °F) in July. Temperature in Yangon, on

the delta, is average 25 °C (77 °F) in January and 27 °C (80 °F) in July. Myanmar has

three seasons namely rainy season or monsoon, cool season or winter and hot season or

summer.

The rainy season lasts from late May to October. Rainfall varies greatly from region to

region. For example, the Mandalay area receives only about 760 mm (30 inches) of rain a

year. The Taninthayi Coast, however, is drenched with over 5100 mm (200 inches). The

heavy rainfall is brought by seasonal winds called monsoons, which sweep North-Eastward

from the Indian Ocean.

The cool season runs from late October to mid-February. Temperatures are lowest at this

time, though the climate remains tropical throughout most of Myanmar.


4


The hot season lasts from late February to about mid-May. During this season,

temperatures often top 38 °C (100 °F) in many parts of Myanmar.

1.4.2 General Description

Because of its diversity of relief, there are many striking contrasts in the meteorology

conditions of different parts of Myanmar. In the central part of the country an area lies with

an average annual rainfall of 1000 mm while certain parts of the coastal regions have an

annual average rainfall of 5000 mm. The mean maximum temperature of over 40°C

(100°F) is observed in central Myanmar areas during the months of March and April and a

mean minimum temperature of 5°C (40°F) to 10°C (50°F) is found in the northern part of

Myanmar during January and February.

Except for the northern highlands and, to a lesser degree, parts of the Shan plateau,

temperatures are high all year, and the cold season is cool only by comparison with the hot

season. The mean annual temperature of the country as a whole is about 27°C (80°F), but

there is a considerable variation between different parts of the country. In the lowlands

during the wet season the humidity is constantly high, and the temperature may reach

38°C (100°F) or more. Here also there is comparatively little noticeable change from day to

day, even though the cold season does bring some relief. In the Shan Plateau

temperatures are significantly lower than those in the lowlands, making it the nation’s most

pleasant area for habitation. Many peaks in higher elevations of the northern mountains are

snowcapped.

The most striking feature of the meteorology of Myanmar is the alteration of seasons

known as the monsoon. Strictly speaking monsoons are seasonal winds whose directions

reverse twice during the year. Lying within the tropics and the great Asiatic continent to the

north and the wide expanse of the Indian ocean to the south, Myanmar furnishes one of the

best examples of a monsoon country. During the winter months of the year from December

to February the general flow is from the north or north-west in the northern parts and from

the north-east in the rest of the country. In this season the air over the country is mainly of

continental origin and hence of low humidity and low temperature and the season is known

as the north-east or winter monsoon season.

In the summer, months of May to October the general flow of wind is from the

opposite direction, from sea to land, with a tropical maritime origin, and the season is one

of much humidity, cloudiness and rain. The direction of winds in the Bay of Bengal and the

Adman sea is south-westerly and season is named the south-west or summer monsoon

season.


5


Between these two principal seasons are the transition seasons of the hot and dry weather

months; March, April and May and the retreating monsoon months of October and

November. It is noteworthy that most storms which make landfall on Myanmar coasts occur

in these transition seasons.

Table 1.1 Climatological Data of states and Divisions in Myanmar (1992-2001 Average)

Temperature (°C) State/Division Annual Rainfall

(mm) Mean Max.Temp Mean Min.Temp

Mean Relative

Humidity (%)

Kachin 2146 29.5 18.25 76.7

Kayah 1020 29.2 17 69.5

Kayin 3990 32.9 22.8 77.5

Chin 1675 22.2 12.5 72.4

Sagaing 1705 31.4 19.8 74.6

Tanintharyi 4830 31.9 22.4 79.8

Bago 2245 33.2 21.5 74.2

Magway 1063 33.2 19.3 69.8

Mandalay 1084 31.5 19.4 70.2

Mon 5399 32.1 20.7 77.9

Rakhine 5263 31.2 21.3 79.1

Yangon 2903 32.9 21.7 76.8

Shan 1354 27.8 15.3 71.2

Ayarwaddy 2988 32 22.7 70.2

(Source : DMH)


6


(Source : United Nations Publication, 1996)

Fig 1.3 Mean Daily Maximum Temperatures during the hot season


7


(Source : United Nations Publication, 1996)

Fig 1.4 Mean Daily Minimum Temperatures during the cold season


8


Fig 1.5 Isohyetal Map of Myanmar

(Source: MOAI)


9


1.5 Classification of Rainfall

The precipitation of the various parts of the country is classified into three groups.

R3. There is sufficient rainfall for crop production during the rainy season and the

rainfall pattern is normally uni-modal. There is no dry spell during the rainy

season. This pattern occurs in Rakhine, Mon, northern part of Kachin State,

Ayeyarwady and Tanintharyi Division, which receive over 2500 mm of rainfall.

R4. There is sufficient rainfall for crop production during the rainy season and three

months of period of continuous summer season (or) at least three months of no

rain during a year. During the rainy season, a dry spell may occur, or excessive

rainfall and flood. The rainfall pattern is normally uni-modal. This pattern occurs

in Chin, Kachin, Kayah, Shan state and Bago-Yoma hill which receive from

1000 to 2500 mm.

R5. The amount of rainfall varies year by year and the rainfall pattern is in most

years bi-modal. This pattern occurs in the dry zone including Mandalay,

Magwe and southern part of Sagaing Division which receives under the 1000

mm of rainfall.

1.6 Current Water Resources Management Activities

Myanmar is endowed with abundant water resources, with available yearly surface and

ground water of about 1 082 km3 and 495 km3 respectively. The bulk of the water resources

is used for agriculture (about 91 percent of total consumption). Numerous irrigation facilities

have been implemented during the present decade for irrigation and water supply to

develop rural and urban areas. Several government agencies and departments are

engaged independently in using both surface and ground water, but the extent and type of

water use differ.

Long taken for granted, water must be seen as a finite resource that has to be used

rationally. As population and economic activities grow, water demand increases rapidly. Up

to now, there have been no water-sharing policies and riparian rights and environmental

impact assessment have not been defined in the country.

The rising water requirements of the country's rapidly expanding urban and industrial

centers and the contamination by pollutants from industrial, municipal and agricultural

effluents (the latter associated with the uncontrolled use of pesticides and fertilizers) have

lead to the decreasing availability of freshwater. Moreover, salinity intrusion has been

reported in the inland areas along the tidal reaches of the Ayeyarwaddy river system, and


10


monitoring of the Ayeyarwaddy in the dry zone shows excessive pollution, particularly in

summer. All of this calls for the integrated management and planning of water resources

and higher investment in water conservation and resources protection, as well as the

promotion of healthy behavior among users.

Protection and restoration of the watersheds are planned and carried by the Ministry of

Forestry. The rapid construction of irrigation facilities such as dams, reservoirs, weirs and

river pumping stations may lead to contamination and depletion of water resources rapidly.

As the water supply agencies established various facilities according to their own policies

and practices and as they were as a result uncoordinated, in 1990 the government

established the National Commission for Environmental Affairs, comprising all concerned

departments' representatives, to offer systematic guidance in environmental management.

Water conservation was seen as a key area to be addressed and laws and regulations to

prevent water-related environmental degradation were seen as being essential.

With the increase of population and a greater need for water for economic activities, there

is increasing pressure on groundwater extraction. Control and management of groundwater

is therefore necessary. Unrestricted groundwater extraction could result in land subsidence

and saltwater intrusion. Besides, in order to ensure the recharge of groundwater aquifers,

surface water has to be managed along with groundwater in an integrated way.

Traditional water management systems can no longer meet the requirements of the market

economy. Thus, the water management system must be reformed soon, and the function

of the management agency strengthened. An important problem for water resource

planning is insufficient information and data on watershed resources.

1.7 Irrigation and Drainage

Irrigation water storage projects have been identified and constructed on smaller rivers and

streams. Dry zone areas received more benefit by these projects during the monsoon

season while stored water for dry season cropping is the primary advantage. Although the

cost of these projects are relatively high, they can produce benefits in specific areas

creating opportunities for crop diversification towards cash crops and for helping regional

development objectives such as water supply, greening of arid areas by reforestation, soil

conservation etc.

Diversion schemes are given less priority given that the major dry zone potentials have

been exploited. Such projects are being constructed in hilly areas while the modernization

and rehabilitation of existing works has also been carried out. Modernization prevents

further deterioration and loss of command in the existing irrigated areas.


11


Land reclamation, flood protection and drainage projects present in Ayeyarwaddy Delta to

enhance paddy production. In the upper and middle area of delta that were previously

subject to flooding and also areas of lower delta that previously suffered from tidal inflows,

water logging and salt intrusion could be reclaimed.

In dry zone of Myanmar, safe drinking water is scarce and deep tube wells are seen to be

expensive both in drilling and operation and maintenance. Therefore rural water supply will

be provided from existing dams and also from the ones which are in plan to be constructed

in future. The flow will be conveyed to the villages by gravity.

Because of the rainfall and hydrological pattern of the country, the need for irrigation is

highest in the central dry zone, while the delta is more concerned with drainage and flood

protection problems.

Dam construction and irrigation network implementation were accelerated in the 1960s,

1970s and after 1990 irrigation development significantly increased (Figure 1.6). Now

irrigation expansion has been significant (up 200 percent) since 1990 to the year 2004.

0

0.5

1

1.5

2

2.5

1962

1964

1966

1968

1970

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

Year

Irrig

ated

Are

a ( M

illio

n Ha

)

Fig 1.6 Irrigation Developments in Myanmar

1.8 Institutional Environment

The major institutions involved in water resources management are as follows:

The Ministry of Agriculture and Irrigation (MOAI) is the main ministry involved in water

resources through its various departments :

(i)The Water Resources Utilization Department, which is responsible for groundwater use

(for both irrigation and rural water supply), irrigation by pumping in rivers, and the

development of sprinkler and micro-irrigation;


12


(ii) The Irrigation Department (ID), which is responsible for O&M of irrigation works,

construction of new projects, and investigation, design and implementation of proposed

projects, as long as surface water is used;

(iii) The Settlement and Land Records Department, which is responsible for collecting

agricultural statistics and land administration;

(iv) The Agricultural Planning Department, which is in charge of planning, monitoring and

evaluation of all agricultural projects, including irrigation and drainage projects.

The Meteorology and Hydrology Department (DMH) of the Ministry of Transport is in

charge of collecting hydrological and meteorological data, while the Irrigation Department

has also its own hydrological network. Hydropower generation is supervised by the

Myanmar Electric Power Enterprise, within the Ministry of Energy.

Detailed list of water related agencies in Myanmar is shown in Appendix-A

1.9 Background Problems in Water Sector Although Myanmar is rich in water resources, less than 10% of the fresh water resources is

used for development of country at present mainly for agriculture sector, the situation calls

for a proper water resource management and strong policy for sustainable development of

the country’s economy and conservation of nature and environment for future generation.

At present a number of government agencies engaged in water sector have different water

pricing policies and less coordination. There is no apex body for overall management of

water resources of the country in cooperation with both the public and private sectors.

Therefore there is an urgent need to carry out water conservation with appropriate

management and planning practice in view of the rapid changes in the socio-economic

development of the country and also for protection of water related environment

degradation.

Present organizational arrangements at both national and provincial levels generally

support the achievement of the nation’s policies but the current institutional problems in the

water sector is mainly relates to lack of coordination and collaboration between agencies

within the sector and with those of other sectors and loose line of communication and

coordination between the national agencies and authorities.

Others weakness in water sector are limited manpower, scarcity of financial resources, lack

of appropriate monitoring facilities, proper and systematic upkeep of records, regular

monitoring and surveillance of water quality and finally lack of technical know-how on water

management techniques.

.

Chapter 2. Description of the Study 13 Mtr.No.158204


Chapter 2. Description of the Study 2.1 Introduction Water- the most fundamental and indispensable resource of the world. History has shown

how vulnerable regions all over the world are to severe and prolonged droughts, which

have caused major social, economic and environmental problems. Increasing demand for

water, following a growing global population and extensive use of water for irrigation and

industry, has raised the awareness of our vulnerability to drought. Any deficit or limitation in

water supply will be most critical in drought periods, and competing water needs may be

the cause of conflicts. Current global change scenarios suggest that the magnitude,

frequency and impacts of extreme drought events could increase due to mankind, through

climate and large-scale changes in vegetation. A prerequisite for sound water management

is a thorough understanding of drought, considered by many to be the least understood of

all major natural hazards (Wilhite, 2000a).

Low flow investigations for the Chindwin river has traditionally used hydrologically based

flow indices and exceedance percentiles to recommend low flow and instream conditions

for the stream. Flow indices have been used extensively and are considered appropriate at

the planning level of water resource development.

The low flow estimate is arguably the most important factor determining the adequacy of

water quality protection provided by a discharge permit, because it is the quantitative link

between the stream standards that protect designated uses and the permit limits that

regulate effluent quality. If the low flow estimate is high relative to conditions that occur in

the future, it increases the risk that aquatic life, or another designated use of the water,

may not receive adequate protection. If the estimate is too low, it increases the probability

that more money will be invested in treatment than is necessary to protect designated

uses.

2.2 General Description

The primary cause of a drought is the lack of precipitation over a large area and for an

extensive period of the time, called a meteorological drought. This water deficit propagates

through the hydrological cycle and gives rise to different types of droughts. Combined with

high evaporation rates a soil water deficiency might cause a soil moisture drought to

develop. The term agricultural drought is used when soil moisture is insufficient to support

crops. Subsequently groundwater recharge and stream will be reduced and a hydrological

drought may develop. A reduced recharge leads to lower groundwater heads and storage.

The relationship between the types of droughts is illustrated in Fig 2.1.



Fig 2.1 Propagation of Drought through the Hydrological Cycle (Modified from Stahl, 2001)

(Source: DWS 48)

Natural Climate Variability

Persisting anticyclonic

pressure systems

Low / no precipitation High temperature, wind

speed, radiation, low

humidity etc.

Precipitation deficiencyIncreased evaporation

and transpiration

Soil water deficiency Plant water stress,

reduced biomass

and yield

Streamflow Deficiency Depletion of

groundwater reservoir

Meteorological Situation

Meteorological Drought

Soil Moisture Drought

Hydrological Drought



The general definition of drought as “a sustained and regional extensive occurrence of

below average natural water availability” implies that both the time and spatial aspect of the

drought are considered. The definition is relative in the sense that the concept of a drought

refers to a certain threshold that distinguishes a drought event from a non-drought

situation, and the event has thus a beginning and an end. Key aspects of a drought include

its duration, severity, time of occurrence and spatial event. Streamflow drought

characteristics are obtained from the time series of discharge, observed or simulated, and

encompass both low flow and deficit characteristics. A time series of low flow characteristic

can, for instance, be the lowest observed streamflow each year, i.e. the annual minimum

series. Low flow characteristics are particularly suitable for characterizing the hydrological

regime, i.e. the seasonal variation in streamflow, but consider only one feature of the event,

the drought severity. A method that simultaneously characterizes streamflow drought in

terms of severity and duration is the threshold level method, which defines droughts as a

period during which the flow is below a certain threshold level. Time series of observed

groundwater level and derived time series of groundwater discharge and recharge are

used for characterizing groundwater drought.

Based on time series of hydrological drought characteristics, corresponding indices (single

values) can be derived, for example the mean annual minimum flow or the mean annual

deficit duration. As droughts are regional in nature and critical drought condition occur

when there is an extreme shortage of water for long durations over large areas, a drought

study often includes the spatial extent of the drought as a measure of the severity of the

drought.

Whereas high flows lead to floods, sustained low flows can lead to drought. Drought has

had severe and sometimes catastrophic effects on vital activities of people. Drought is a

chronic problem which has caused distress, economic loses and degradation of the

environment. There is no single region where drought has not affected people’s activities in

one way or another, at one time or another. Depending on the flood severity, effects are

often site specific; whereas droughts are generalized to an entire area or region.

In practice, a drought refers to a period of unusually low water supplies, regardless of water

demand. The regions most subject to droughts are those with the greatest variability in

annual rainfall. Studies have shown that regions where the variance coefficient of annual

rainfall exceeds 0.35 are more likely to have frequent droughts. Low annual rainfall and

high annual rainfall variability are typical of arid and semiarid regions. Therefore these

regions are more likely to be prone to droughts. The severe of droughts can be established

by measuring (1) the deficiency in rainfall and runoff, (2) the decline of soil moisture, and

(3) the decrease in groundwater levels.



For a long time, the statistical analysis of low water discharge has been neglected in favor

of flood flow. One reason for this negligence might be the fact that flood events are

spectacular and dangerous. Only the increasing use of river water for agriculture, municipal

and industrial purposes has shown that possible damages of low water period is

comparable with the damage caused by flood events. Therefore many efforts have been

made in the last few years to describe low water discharges by deterministic and statistical

procedures. Now it is very easy to get various Satellite data. Then using those data, many

hydrologists and meteorologists have so far presented effective and interesting research

results for the global water balance and climate change and so on. On the other hand a

statistical analysis on regional low flow has lively been carried out using the observation

data from the earth.

The adequacy of stream flow to meet requirements for disposal of liquid waste, and for

municipal or industrial supplies, supplemental irrigation, and maintenance of suitable

conditions for aquatic life is commonly evaluated in terms of low flow characteristic (Riggs,

1980). Certain of these low flow characteristic are useful as variables in regional draft-

storage studies, as the basis for forecasting seasonal low flows, and indicators of the

amount of ground water flow to the stream. Since the water resources situation will be

increasingly tight in future, water resources planners need the effective hydrologic

information in the source area of a river through the statistical and/or runoff analysis. And

then it is particularly required to provide an effective water resources management in

gauged or ungauged.

According to Riggs, low flow characteristics at a gauging station may be described by

frequency curves of annual or seasonal minimum flows, by duration curves, and by base-

flow recession curves.

2.3 Objectives of the Study

The main objective of the study is to give a brief explanation of water resources in

Myanmar and to extract and discuss the low flow characteristic of Chindwin river basin at

the selected site through low flow indices obtained from the analysis and then to find the

possible relations between these indices and climate and land use impacts on low flows in

the study area.

To attain this main goal, it is necessary to get following sub-objectives. They are;

(1) To investigate the low flow condition using flow duration curve.

(2) To determine the master recession curves



(3) To prepare low flow frequency curves and to predict the expected low flows using

frequency analysis

(4) To find the link between above low flow indices and impacts of climate and land

use.

2.4 Scope of the Study

A study of the drought conditions in the river reaches is intended to help assess future

storage conditions and impact on water resources management. So many hydrologists and

irrigation engineers have systematically carried out on the extraction and diagnosis of the

hydrologic drought characteristics so far.

The study describes hydrological drought conditions defined by the available water

resources in the Chindwin catchment. The main scope is to provide a comprehensive

understanding of processes and estimation methods for streamflow drought. It is

accompanied by computational details, general discussions and possible limitation for

application of a particular methodology. The regional aspect of low flow characteristics are

studied using daily streamflow series in the region.

In this paper, before the main analysis hydrologic data tests were carried out to see the

reliability of the collected data and then three kinds of analysis were performed. In order to

encourage a wise use low flow indices are determined by the use of duration curves and

frequency curves and then drought discharges are expressed in terms of EFQ90 and 7Q10.

The lower ends of the frequency and duration curves are useful expressions of the low flow

characteristics of the stream. Secondly analysis for a master recession curve constants are

determined because it became apparent that the recession constant of a master depletion

curve may be defined as the total index of low flow characteristics.

The study also concludes with impacts of climate and large changes of vegetation in the

region which may cause high potential of low flow occurrence.

2.5 Available Data

Relevant data of the study are collected from Monywa gauging station which is situated at

the most downstream portion of the basin area.



Table 2.1 Condition of the available Data Type and Length

Collected Data Type and Period

Station Latitude Longitude

Elevation

from m.s.l

(m)

Daily

Discharge

(m3/s)

Mean

Annual

Rainfall

(mm)

Mean

monthly &

Annual

Temperature

(°C)

Monywa 22° 06’ N 95° 08’ E 73.32 1975-2004 1975-2005 1975-2005

Here mean annual rainfall is obtained from the average value of six gauging stations in the

catchment area. And the daily discharge and mean monthly temperature are collected from

the specific gauging station, namely Monywa station.

2.6 Methodology

To attain the main objective of this paper, the study is carried out based on the following

materials and methods.

2.6.1 Materials

In this study daily mean discharges are used to determine the low flow characteristic of

Chindwin river. Mean annual rainfall and mean monthly temperature of the basin are used

to find out the causes and the relevance of the result as decisive factors which are normally

considered in drought study of the area.

2.6.2 Methods

To perform a research work available data is much of importance. So, required

hydrological and meteorological data are collected.

Frequent visit to the offices concerned was conducted to have the information of the study

area. And discussion with staff personal plays a vital role for this paper.

Preparation of maps showing selected site and observation station are also supporting

factors for this study.

Testing of collected data set was required to get consistent and homogenous ones for the

analysis.



Then flow duration curves are drawn to give an identification of the severity of low flow for

different probabilities in terms of percent of the time and drought discharges, EFQ90s are

determined. Then master depletion curves are constructed both by linear and non-linear

storage to identify the low flow index.

Low flow frequency curves are drawn using plotting position to check of the changes of low

flow conditions for different time intervals and to find the drought discharge 7Q10 (average

annual minimum flow with a return period of 10 year).

Method of low flow frequency analysis is also applied to fit the observed frequency curve

based on collected time series hydrologic data using frequency factor method in the

assessment of the probability of occurrence of droughts of different return periods.

Testing of goodness of fit for selected probability distribution function has been done using

least square (standard errors) method.

Finally the results obtained are judged and discussed comparing with the annual rainfall,

temperature and irrigation development data of the region.

Chapter 3. Literature Review 20 Mtr.No.158204


Chapter 3. Literature Review 3.1 Introduction

The long-duration periods of low discharges are usually called droughts. In the hydrological

literature no uniform definition of drought periods has yet been established. This results

from the fact that, in general, the term in question may be defined depending upon the aim

of the investigation. Usually, a drought is assumed to be the period in which the natural

river discharges are lower than those needed for water supply or other water management

activity.

Some analysis of low flow is necessary before a stream can be used as a reliable source of

water supply. If the minimum flow of record far exceeds the proposed demand, further

analysis may not be necessary, but if once or twice during the period of record the flow was

less than the proposed demand, further analysis should be made to see if the anticipated

deficiencies in flow are too serious to be tolerated.

Low flow frequency analysis and flow duration curves are the two simplest methods used in

making such analysis. If the deficiency is likely to be too great too frequently, storage must

be provided to hold high flow for release during drought periods. Although detailed analysis

of storage requirements is necessary for design, reconnaissance planning can often be

facilitated by draft-storage curve based on low flow frequency analysis.

In addition to analysis of low flows for generalization water supply on a duration or

frequency basis, there are also situations in which the flow of a particular stream may be

extrapolated on a time scale. This extrapolation amounts to extension of the hydrograph

during periods of little or no rain. In a way, this operation corresponds to forecasting, but it

is more of a projection, or sort of projections, based on certain outlooks or specified

assumptions such as no rain, or some other amount of rain for the ensuing month or other

period.

3.2 Flow Duration Curve Analysis

The flow duration curve is believed to have been first used by the American engineers

Clemens Herschel and John R. Fremann from early 1880 to 1890. It is most frequently

used for determining water-supply potentials in planning and design of the water resources

projects, particularly the hydropower plants.

When the values of a hydrologic event are arranged in order of their descending

magnitude, the percent of time for each magnitude to be equaled or exceeded can be

computed. A plotting of the magnitudes as or ordinates against the corresponding percents



of time as abscissas results in a so-called duration curve. If the magnitude to be plotted is

the discharge of a stream, the duration curve is known as a flow duration curve.

In a statistical sense, the duration curve is a cumulative time series, displaying the relative

duration of various magnitudes. The slope of the duration curve depends greatly on the

observation period used in the analysis. The mean daily data will yield a much steeper

curve than annual data as the latter tend to group and smooth of the variations in the

shorter-interval daily data.

Typical flow duration curve may be considered to represent the hydrograph of the average

year with its flow arranged in order of magnitude. According to the different requirements in

the analysis, duration curve may be modified and developed. It should be noted that the

chronological sequence of events is completely masked in a duration curve.

The shape of a flow duration curve may change with the length of record. This property can

be used to extend the flow information on a given stream for which short-term records are

available and for which simultaneous and long-term records are available on at least on

adjacent stream which is believed to be under similar hydrologic conditions. By comparing

the flow duration curves constructed of the short-term record of the given stream and of the

corresponding short-period record on the adjacent stream, the flow duration curve for the

long-period record of the adjacent stream can be proportionally adjusted to produce an

approximate flow duration curve for the given stream for the corresponding long-period

record. (Handbook of applied hydrology, Chow)

Flow duration curves of daily discharge show the percent of time that the flow of a stream

is greater than given amounts regardless of continuity in time. The computation process is

simply a tallying of data in convenient class intervals. The duration curve of stream flow will

generally plot nearly as a straight line if logarithmic probability paper. This type of paper

gives equal plotting accuracy at all discharges so that differences in low flow characteristics

can be discerned. Such differences often have hydrological significance.

Flow duration curves are sometimes based on weekly or monthly discharge to simplify the

tallying process in which case the resulting curve represents the percentage of weeks or

months rather than the percentage of time. Such curves are less useful than the daily

duration curve. Duration curves of yearly discharge, however, have considerable value in

appraising the yearly variation in flow. (WMO, Guide to hydrological practices)



3.3 Recession Curve Analysis

The statistical and/or hydrological methods have been applied to deal successfully with the

low flow recession characteristics of the stream flow. As for hydrological methods, two

ways have been carried out by many hydrologists so far.

One method examines low flow runoff through the long time rainfall runoff analysis using

the runoff model, and another obtains the hydrological information from the analysis for a

low flow recession curve.

The former needs the stream flow, precipitation and evapotranspiration data for a long time

which were observed with a high accuracy.

The latter, the master depletion curve method is used to provide a model of flow from

groundwater storage. Based on this, it can be used to identify a point on the recession

where direct runoff ends and base flow begins; however, it also provides a model of the

recession limb.

3.3.1 Linear Storage

The procedure requires measured storm hydrographs for a good number of storm events

covering a wide range of volumes and for seasons of the year. The procedure is as follows:

1. Using a log q versus time-axis system, plot the recession curves for each storm

event on separate pieces of tracing paper.

2. On a master sheet having a log q versus time-axis system (semi log paper), plot the

recession for the storm event having the smallest values of log q.

3. Using the recession curve with the next smallest range of log q values, position the

tracing paper such that the curve appears to extend along a line coincident with the

recession of the first event plotted.

4. Continue this process using successively larger log q recession until all storm

events are plotted.

5. construct a master depletion curve that extends through the recession of the

observed storm events and fit a mathematical model to the master depletion curve;

the following linear functional form often provides a reasonable fit to the data:

qt = q0 e –Kt ( Eq 3.1)

In which qt is the discharge at time t, q0 is the discharge at time t = 0, and K is a fitting

coefficient. The value of K can be determined using any two points of the master depletion



curve. Letting one point be q0 , then making a natural-logarithm transformation of Equation

(3.1 ) and solving for K yields

K = t

qlnqln t0 − ( Eq 3.2)

Where t is the time at which discharge qt is recorded. If sufficient scatter is evident in the

recession line, then least squares can be used to estimate K. If the value of q0 is set, then

the least squares estimator of K is

K =

∑

∑

=

=

−

n

1i

2i

n

1it0i

t

)qlnq(lnt ( Eq 3.3)

In which n is the number of pairs of (qi,ti) points on the recession.

3.3.2 Non-Linear Storage

Linear relation is hardly expected in the nature and can only be the approximate solution.

Non linear storage equation is given by

S = a Qb ( Eq 3.4)

For S in m3 and Q in m3/s, the factor a has the dimension m3-3bsb. If the volumes are

expressed in depth units (i.e. volume per unit area) and the time step is a day (d), then s is

in mm, Q in mm/d and a will be in mm1-bdb.The exponent b is dimensionless. The

commonly used single linear reservoir is a special case with b = 1. However, analyses of

observed flow recession of numerous rivers in different hydrological regimes yielded values

b <1 with a typical value of b ≈ 0.5 ( Wittenberg, 1994, 1999; Wittenberg and Sivapalan,

1999; Aksoy and Wittenberg, 2001). This finding is confirmed by theoretical derivation (

Werner and Sundquist, 1951; Schoeller, 1962) for unconfined aquifers. The recession of

the nonlinear reservoir for b ≠ 1 is described by equation (3.5) for an initial value Qo.

Qt = Qo [ ] )1/(11)1(

1 −−−

+ bb

o tab

Qb ( Eq 3.5)

The coefficient a can be determined from the outflow data Q of the recessions and is given

by

a = ∑∑

−

∆+

)QQ(2

t)QQ(b

tb

0

to ( Eq 3.6)



The coefficient a and b can be determined for observed recession by hydrographs by an

iterative least-squares method ( Wittenberg, 1994, 1999).

3.4 Low Flow Frequency Analysis

The primary objective of frequency analysis is to relate the magnitude of extreme events to

their frequency of occurrence through the use of probability distribution ( Chow et al., 1988

). Data observed over an extended period of time in a river system are analyzed in

frequency analysis. The flow data are considered to be stochastic and may even be

assumed that the flows have not been affected by natural or manmade changes in the

hydrological regime in the system.

Partially treated wastewater is commonly discharged into streams and rivers where it mixes

with the existing flow. Natural processes improve the overall quality of the total flow. During

the periods of low flow the volume of wastewater may be too large to be safely discharged

without reducing the quality of water below established water-quality standards. When

evaluating sites for the suitability of a manufacturing or commercial business, it is important

to assess the probability that the stream will almost always have sufficient flow to meet the

need for discharging wastewater. Such probabilities are estimated using a low flow

frequency analysis at the site.

While instantaneous maximum discharges are used for flood frequency analyses, low flow

frequency analyses usually specify a flow duration (for example, 7-day). The instantaneous

discharge is used with high flows because damage often occurs even if the site inundated

only for a very short period of the time. This may not be true for low flow because high

pollution concentrations over very short periods of time may not be damaging to the

aquatic life of the stream. Thus, the duration such as seven days or one month, is specified

in establishing the policy.

One difference between low flow and flood frequency analysis is that the data for low flow

analysis consists of annual events that have the lowest average flow of the required

duration D during each water record. Thus the records of flow for each water year are

evaluated to find the period of D days during which the average flow was the lowest; these

annual values are used as the sample data. The record of n years is then evaluated using

frequency analysis.

Once the data record has been collected, the procedure for making a low flow frequency

analysis is quite similar to that used for flood frequency analysis. The major differences are

listed here:



1. Instead of using the exceedance probability scale, the non-exceedance scale

(that is, the scale at the bottom of the probability paper) is used to obtain

probabilities. The non-exceedance scale is important because the T-year event

is the value that will not be exceeded.

2. The data are ranked from low to high, with the smallest sample magnitude

associated with a Weibull probability of 1/(n+1) and the largest magnitude

associated with a probability of n/(n+1); any other plotting position formula in

place of the Weibull. However the plotting position probabilities are non-

exceedance probabilities.

3.4.1 Selection of Data Series

The complete record of stream flows at a given station is called the complete duration

series. To perform a flood frequency analysis, it is necessary to elect a flood series, i.e., a

sample of flood events extracted from the complete duration series.

There are two types of flood series: (1) the partial duration series and (2) the extreme value

series. The partial duration (or peaks-over-a threshold (POT) series consists of floods

whose magnitude is greater than a certain base value. When the base value is such that

the number of events in the series is equal to the number of years of record, the series is

called an annual exceedance series.

In the extreme value series, every year of record contributes one value to the extreme

value series, either the maximum value (as in the case of flood frequency analysis) or the

minimum value (as in the case of low-flow frequency analysis). The former is the annual

maxima series; the latter is the annual minima series.

The annual exceedance series takes into account all extreme events above a certain base

value, regardless of when they occurred. However the annual maxima or minima series

considers only one extreme event per yearly period.

3.4.2 Concepts of Statistic and Probability

Frequency analysis uses random variables and probability distributions. A random variable

follows a certain probability distribution. A probability distribution is a function that

expresses in mathematical terms the relative chance of occurrence of each of all possible

outcomes of the random variable.



3.4.3 Properties of Statistical Distribution

The properties of statistical distributions are described by the following measures: (1)

central tendency, (2) variability, and (3) skewness. Statistical distributions are described in

terms of moments. The first moment describes central tendency, the second moment

describes variability, and the third moment describes skewness. Higher-order moments are

possible but are seldom used in practical applications.

3.4.4 Return Period, Frequency, and Risk

The time elapsed between successive peak flows exceeding a certain flow Q is a random

variable whose mean value is called the return period T ( or recurrence interval ) of the flow

Q. The relationship between probability and return period is the following:

P(Q) = T1

( Eq 3.7)

In which P(Q) is the probability of exceedance of Q, or frequency. The terms frequency and

return period are often used interchangeably, although strictly speaking, frequency is the

reciprocal of return period. A frequency of 1/T, or one in T years, corresponds to a return

period of T years.

The probability of nonexceedance P (Q) is the complementary probability of the probability

of exceedance P (Q), defined as

P (Q) = 1- P (Q) = 1- T1

(Esq. 3.8)

The probability of nonexceedance in n successive years is

P(Q) = ( 1-T1

)n ( Eq 3.9)

Therefore, the probability, or risk, that Q will occur at least once in n successive years is

R = 1 - P(Q) = 1 - ( 1-T1

)n (Eq 3.10)

3.4.5 Plotting Positions

Frequency distributions are plotted using probability papers. One of the scales on a

probability paper is a probability scale; the other is either arithmetic or logarithmic scale.

Normal and extreme value probability distributions are most often used in probability

papers.



For plotting purposes, the probability of an individual event can be obtained directly from

the flood series. For a series of n annual maxima, the following ratio holds:

Nx

= 1n

m+

(Eq 3.11)

In which x = mean number of exceedances; N = number of trials; n = number of values in

the series; and m = the rank of descending values, with largest equal to 1.

Since return period T is associated with x = 1. Eq.(3.7) can be expressed as follows:

T1

= P = 1n

m+

(Eq 3.12)

In which P = exceedance probability. Eq. (3.12) is known as the Weibull plotting position

formula. This equation is commonly used in hydrologic applications, particularly for

computing plotting positions for unspecified distributions.

In computing plotting positions, when the ranking of values is in descending order (from

highest to lowest); P is the probability of exceedance, or the probability of a value being

greater than or equal to the ranked value. When the ranking values is in ascending order

(from lowest to highest), P is the probability of nonexceedance, or the probability of a value

being less than or equal to the ranked value.

3.4.6 Frequency Factor

Any value of a random variable may be represented in the following form:

x = x + ∆ x (Eq 3.13)

In which x = value of random variable; x = mean of the distribution, and ∆ x = departure

from the mean, a function of return period and statistical properties of the distribution. This

departure from the mean can be expressed in terms of the product of the standard

deviation s and a frequency factor K such that ∆ x = Ks. The frequency factor is a function

return period and probability distribution to be used in the analysis. Therefore Eq. (3.13)

can be written in the following form:

x = x + Ks (Eq 3.14)

Above equation is proposed by Chow as a general equation for hydrologic frequency

analysis. For any probability distribution, a relationship can be determined between

frequency factor and return period. This relationship can be expressed in analytical terms,

in the form of tables, or by K-T curves. In using the procedure, the statistical parameters

are first determined from the analysis of the flood series. For a given return period, the

frequency factor is determined from the curves or tables and the flood magnitude

computed by Eq. (3.14)



3.4.7 Continuous Probability Distributions

A continuous probability distribution is referred to as a probability density function (PDF). A

PDF is an equation relating probability, random variable, and parameters of the distribution.

Selected PDFs useful in engineering hydrology are described in this paper.

3.4.8 Three-Parameter Lognormal Distribution

Just as the lognormal distribution represents the normal distribution of the logarithms of the

variable x, so the 3-Parameter Lognormal represents the normal distribution of the

logarithms of the reduced variable (x-a): where a is a lower boundary. The probability

density distribution is given by:

P(x) = ∏σ− 2)ax(

1

y

exp { }⎥⎥⎦

⎤

⎢⎢⎣

⎡µ−−

σ− 2

y2y

)axlog(2

1 (Eq 3.15)

Where µy and σy are the form and scale parameters, shown later to be the variance of the

logarithms of (x-a).

Sangal and Biswas (1970) suggested a procedure to estimate the parameters of LN(3)

distribution in which only the mean, median and the standard deviation of the data are

used.

3.4.8.1 Determination of Frequency Factor

Frequency factor for LN(3) distribution is given by the following equation:

K = { } { }

2

22

2/122

z

0.12/)z1ln(t.)z1ln(exp −⎥⎦⎤

⎢⎣⎡ +−+

(Kite ) (Eq 3.16)

Where z1 and z2 represent the coefficients of variation of the distributions x and x-a then

Z1 = σ/µ (Eq 3.17)

Z2 = σ/( µ-a) (Eq 3.18)

From which a = µ (1-z1/ Z2) = µ - σ/ Z2 (Eq 3.19)

The value of z1 can be computed directly from the observed events. Since the second and

third moments of the distribution (x-a) do not contain terms in a, the value of z2 can be

obtained from the relationship

Ү1 = 3 Z2 + Z23 (Eq 3.20)



Where Ү1 is the coefficient of skewness of the distribution x. The solution of this equation is

Z2 = 3/1

3/21ωω−

(Eq 3.21)

ω = 2

)4( 2/1211 +γ+γ−

(Eq 3.22)

t = )W00131.0W1893.0W14328.11(

)W01033.0W80285.05255.2(W32

2

+++++−

(Eq 3.23)

W = [ ln T2 ]1/2 (Eq 3.24)

The procedure is then to compute the mean µ, standard deviation σ and coefficient of skew

Ү1 of observed events x.

3.4.9 Pearson Type III Distribution

The probability distribution of the Pearson type III distribution is of the form

P(x) = 1/α Γ(β) . [(x-γ)/ α] β-1 e - [ (x- γ)/ α] (Eq 3.25)

Where α, β and γ are parameters to be defined and Γ(β) is the Gamma function.


To find the frequency factor K for different values of skewness coefficient, compute the

value of

W = [ ln T2 ]1/2 where T = 1/P (Eq 3.26)

Y = )W00131.0W1893.0W14328.11(

)W01033.0W80285.05255.2(W32

2

+++++−

(Eq 3.27)

K = Y+(Y2-1). γ/6 +1/3(Y3-6Y).3 γ 2/36 -(y2-1). γ 3/216 +y. (γ /6)4 +1/3. (γ /6)5 (Eq 3.28)

3.4.10 Extreme Value Type III Distribution

The cumulative probability distribution is given by

P(x) = expα

⎭⎬⎫

⎩⎨⎧

γ−βγ−

−x

(Eq 3.29)



and the probability density function is

p(x) = γ−β

α1

x−α

⎭⎬⎫

⎩⎨⎧

γ−βγ−

.

α

⎭⎬⎫

⎩⎨⎧

γ−βγ−

−x

e (Eq 3.30)

where α is a scale parameter equal to the order of the lowest derivative of the probability

function that is not zero at x= Y, β is the characteristic drought ( a location or central value

parameter) and Y is the lower limit to x.


The frequency is given by

K = Aα + Bα [ { -ln (1-1/T) } 1/α -1 ] (Eq 3.31)

This expression is dependent only upon the return period T and the coefficient of skew Y1

of the recorded events. If two new variable are defined Aα and Bα, such that Aα is the

standardized difference between the characteristics value and the mean and Bα is the

standardized difference between the lower limit and the characteristic value.

Bα = { Γ(1+2/α) - Γ2(1+1/ α) } -1/2 (Eq 3.32)

Aα = { 1- Γ(1+1/ α) } Bα (Eq 3.33)

α = 1/ { a1 + a2ү1+a3 ү12+a4 ү1

3+a5 ү14 } (Eq 3.34)

where a1 = 0.2777757913 a4 = -0.0013038566

a2 = 0.3132617714 a5= -0.0081523408

a3 = 0.0575670910

So Aα and Bα can be computed above Gamma function equations. This polynomial is

valid for a range of ү1 from -1.02 to 2.00.

3.4.11 Test for Goodness of Fit

The choice of distributions to be used in flood frequency analysis has been a topic of

interest for a long time. Hazen (1914) looked at this question in the context of storage

design for municipal water supply. The two most commonly used tests of goodness of fit

are the chi-square test and the Kolmogorov-Smirnov test (Kite, 1977). An additional check

on goodness of fit may be made by computing the sum of squares of differences between

observed and computed event magnitudes. It is known as the method of least squares

which find the standard errors of the distribution.



3.4.11.1 Method of Least Squares

A method of comparing the fit of different distributions to a data sample is to compute the

sum of squares of the differences between calculated and observed discharges. Bobee

and Robitaille used this method to compare calculated discharges at 2, 5, 10, 20, 50 and

100-year return periods with discharges at the same return periods interpolated (or

extrapolated) from the recorded data.

The standard error is given by

SEj = [j

n

1i

2ii

mn

)YX(

−

−∑= ]1/2 (Eq 3.35)

Where Xi = recorded events

Yi = event magnitudes computed from jth probability distribution

N = number of events

mj = number of parameters estimated for the jth distribution.

Chapter 4. Water Resources in Myanmar 32 Mtr.No.158204


Chapter 4. Water Resources in Myanmar 4.1 Water Resources Availability

4.1.1 General

Although the country is generally blessed with abundant water, this resource is poorly

distributed both in space and time. The heavy rains during the south-west monsoon and

the torrential downpours associated with sudden storms lead to sustained flooding in wetter

areas and to flash floods in the drier parts or in places where steep mountain torrents

overflow. Such flood can do immense damage, eroding river banks, sometimes washing

away whole section of towns or villages, and at other times forming huge sandbanks that

impede navigation. Flash floods may also cause serious erosion of valuable agricultural

land.

During the dry season, on the other hand, scarcity of water becomes a problem over much

of the country. A depth as little as 1.5 m is not uncommon in the Ayeyarwaddy river

occurring low water, and 1 m in the Chindwin river; this create considerable difficulties for

navigation.

Thus, while in parts of the country the scarcity of water makes it imperative that water is

used to its maximum potential, elsewhere flood control and the protection of inhabited

places and cultivated lands are of vital importance.

4.1.2 Surface Water

Myanmar has five major and over 80 minor rivers. There are two major and seven minor

lakes in the country.

The major drainage lines in Myanmar are from north to south. The Ayeyarwaddy with its

major tributary, the Chindwin, is the largest and the most important river in Myanmar,

having a catchment area of 404000 km2 stretching into the northern mountains, which are

the eastern extension of the Himalayan range. In the upper delta region at Pyay, the mean

annual inflow for the period 1966 to 1994 is recorded as 12000 m3/sec but this average

makes a variation from 1600 m3/sec at the end of the dry season to more than 16000

m3/sec at the peak of the monsoon. The maximum discharge ever recorded at Pyay station

was 50460 m3/sec and the minimum ever recorded was 1148 m3/sec.

The Sittaung is a much smaller river with a catchment of about 35000 km2.It rises in the

Shan highland and Bago Yoma and flows southwards between Bago Yama and Shan



escarpment. Its average flow is about 1300 m3/sec but in the dry season it falls somewhere

around 55 m3/sec.

The Thanlwin (Salween) has a catchment of about 285900 km2, part of which is outside

Myanmar. Its average flow is somewhat more than 7000 m3/sec.

In addition to these three major drainage systems described above, there are some smaller

with independent catchments such as Bago river near Yangon, the streams draining the

western slopes of Rakhine Yoma and those draining the Tanintharyi region.

There are few lakes in Myanmar. The largest is Inle lake which in the past covered 259 km2

in a basin area of the Shan Plateau. It is the residue of a larger water body that is still

shrinking and the present area covers 155 km2. Drained by a tributary of Thanlwin river, it

abounds in fish and is surrounded by every fertile paddies and a cluster of farm village. It is

also a much favored recreation spot. Other lakes and ponds are formed by parts of

abandoned rivers courses in upper Myanmar, or are formed by the remaining of marshes

of the delta.

4.1.2.1 Major River Basins and Water Resources

The assessment of water resources potential in Myanmar, on the basic of planning units

corresponding to its (8) regions of river basins are indicated as in Table 4.1.

The north-south direction of Myanmar's mountain ranges is reflected in the flow of its major

rivers, of which two are international rivers.

- the Ayeyarwady and Chindwin river basin, which is almost entirely located in

Myanmar and drains 58 percent of the territory;

- the Sittoung River basin, which is also entirely located in Myanmar to the east of

the Ayeyarwady, drains 5.4 percent of the territory;

- the Thanlwin (Salween) River basin, which drains 18.4 percent of the territory,

mainly from the Shan plateau in the east of the country. The river comes from

China and after entering the country forms the border with Thailand for about

110 km;

- the Mekong River basin, which drains 4.2 percent of the territory in the far east

and forms the border with Lao PDR. The Mekong River has 2 percent of its

catchment area in Myanmar.

- the Rakhine (Arakan) coastal basin in the west draining into the Bay of Bengal;

- the Tanintharyi (Tenasserim) coastal basin in the south draining into the Andaman

Sea.



Fig 4.1 Major Drainage Basins of Myanmar (Source : MOAI)



Table 4.1 Annual Surface and Groundwater Potential in Myanmar

Sr

No Name of Principal River Basin

Catchment

Area

for each

stretch

(000’ sq-km)

Average

Esti.

Annual

Surface

Water (km3)

Estimated

Groundwater

Potential

(km3)

1 Chindwin River 115.30 227.920 57.578

2 Upper Ayeyarwady River (up to its

confluence with Chindwin River) 193.30 141.293 92.599

3 Lower Ayeyarwady River (from confluence

with Chindwin to its mouth) 95.60 85.800 153.249

4 Sittoung River 48.10 81.148 28.402

5 Rivers in Rakhine State 58.30 139.245 41.774

6 Rivers in Tanintharyi Division 40.60 130.927 39.278

7 Thanlwin River (from Myanmar boundary to

its mouth) 158.00 257.918 74.779

8 Mekong River (within Myanmar territory) 28.60 17.634 7.054

Total 737.80 1081.885 494.713

Source: Ministry of Agriculture and Irrigation, Irrigation Department, Water Resources

Utilization Department.

The inflow from other countries is estimated at 128.2 km³/year and includes: 20 km³/year

from India, 68.7 km³/year (Yuan Yiang) and 31.3 km³/year (Lancang) from China, and

8.2 km³/year from Thailand. The total surface water produced internally (total runoff minus

inflow from other countries) is estimated at 953.9 km³/year. The Mekong River forms the

border with Lao PDR over 170 km, from which 36.815 km³/year can theoretically be

considered as an additional external resource.



4.1.3 Ground Water

There is plenty of groundwater in the non-hilly areas of the country. No accurate and

comprehensive data about the depths, locations and sizes of the aquifers have as yet been

compiled. However, there is a severe shortage of water during the three months from mid-

February to mid-May. There may even be a drought at the end of May if the rains do not

come.

The main aquifers are described below, in decreasing order of importance.

(i) Alluvial aquifers

These are the most important and most explored aquifers located along the

Shan escarpment and western mountains ranges of the central Cenozoic belt which

supply fresh potable water. Pumping test data show that the permeability is about

10 m3/s. Ground water is mostly of the sodium bicarbonate type.

The older alluvia are deposited directly on Irrawaddian or Peguan formations

and located away from present river courses at an elevation of 25 to 45 m above

river level. In the Ayeyarwaddy delta area, the alluvia are believed to be 30 to 100

m thick. In the lower delta area, the chance of obtaining good potable water from

shallow aquifers is poor. However in deep tube-wells, the underlying Irrawaddian

aquifer produced good potable water.

(ii) Irrawaddian Series

Next to the alluvium, the Irrawddian is from good aquifers. Ground water is

generally fresh, with high discharges, but occasionally slightly saline. Ground water

should be classified as of the sodium bicarbonate type.

(iii) Peguan Series

The Peguans underlay the Irrawaddians and are not good aquifers. The sandy

units supply small amount of water. The water quality is poor and is most cases not

potable owing to higher salt content.

(iv) Tanintharyi, Shan highland and northern mountains Regions

In these areas lime stones and metamorphic rocks are found. Wells drilled in the

lime stones region produce good, though hard, water. In the metamorphic rocks the

quality of water is good, but storage conditions may be poor.

Towns and villages located on granites and gneisses depend largely on springs and

streams. Groundwater is found in highly weathered and fractured zones, and the

yield is small though the quality is excellent.



(v) Western mountain folded belt

In this sparsely populated region domestic water supply comes from streams and

springs. Water quality is good.

(vi) Rakhine Coastal Plain

The alluvial deposits from poor aquifers and saline water encroachment are limiting

water extraction.

In recent years, groundwater demand has increased in the country for such multiple uses

as rural and urban domestic use and industrial and irrigation use. In this connection,

groundwater quality management plays a major role in the sustainable development and

use of groundwater resources.

According to the records, the first tube well of Myanmar was drilled in 1889. In Myanmar,

groundwater exploration, exploitation, control and management tasks are mainly

undertaken by the government sector. The major government organizations, division and

authorities concerned with groundwater development are listed in Appendix-A.

4.1.4 Non- Conventional Water Resources

Non-conventional water resources generally refer to those additional water resources

made available through desalinization of sea water or brackish water, artificial rain created

by cloud seeding, and recycling of waste water (domestic, industrial and irrigation) after it

has passed through appropriate treatment processes that approve the quality of recycled

water to the standard required by the respective water users. In view of the availability of

adequate fresh raw water resources and in view of the lack of technology and financial

resources in Myanmar to introduce treatment processes that would enable recycled water

to be used, non-conventional water resources in Myanmar are almost negligible.

4.2 Water Quality

4.2.1 Surface Water

The water quality in the rivers of Myanamr is reported to be deteriorating gradually,

particularly with regard to turbidity. The main reason for this is that the suspended solids

load of the rivers is increasing progressively as a result of deforestation and other

development activities in the catchment areas. It is supported that the country’s forest are

being denuded at the rate of 2.1 % per year, which is affecting water quality as well as the

environment. For example, Fugyi reservoir, which is a part of the water supply system for

Yangon city, is already being affected by the increasing silt inflow into the reservoir and



UNDP assistance has been sought to implement appropriate catchment management. A

sedimentation problem is also affecting other hydraulic structures in the country, including

the many irrigation facilities in use. The rates of soil erosion are reported to be highest over

the Bago Yoma area, reaching as high as 2 tons/km2.

The effects of agricultural chemicals on water quality have not so far been recognized

because of a lack of monitoring of chemical parameters. However, it appears that the

consumption of fertilizers in Myanmar is relatively modest at present, totaling about

165,000 tons in 1990/91. It is also reported that salinity intrusion has reached well into the

inland areas along the tidal lower reaches of the Ayeyarwaddy river system. A maximum

chloride content of 1000 mg/l has been observed in the river at Pathein, Mawlamyinegyun

and Thabawchaung during the dry season.

4.2.2 Groundwater

In the dry zone hydrological studies quoted above, studies of groundwater chemistry

indicate that the shallow groundwater is of low to moderate salinity (1000-2000

microseimens/cm) mainly of a sodium bicarbonate type in all areas. Although there is little

variation in the degree of salinity in the vertical direction (i.e. with depth), there are some

variations in the horizontal direction (i.e. laterally).

4.3 National Water Sector Context

Water basin characteristics in Myanmar are quite variable due to the differences in

physiographic feature. The principal water resources flowing separately in the country

comprise eight major river basins and their tributaries. All rivers, with the exception of

Thanlwin, located within the Myanmar territory can be nationally owned water assets. Their

drainage areas are widely spread over the country, endowing with about 1082 km3 per

annum from drainage area of about 737629 km2 (284800 sq.miles). The monthly

distribution of the flow of the rivers closely follows the pattern of rainfall, about 80% during

the rainy season (May-October) and 20% in the dry season (November-April).

There are about (200) gauging stations under irrigation department for water level

recording and also for discharge measurement. Total of about (70) hydrological stations

are installed along Ayeyarwaddy, Chindwin, Myitnge, Sittoung, Thanlwin, Bago and

Kalandan rivers since 1965 by department of Meteorology and Hydrology (DMH). DMH has

about 30 discharge stations, 20 sediment discharge stations on main rivers and main

tributaries and also about 15 water quality stations on rivers of Ayeyarwaddy catchment



area for measuring discharge and sediment flows and monitoring salt intrusion. These

measuring data are valuable for National Planning related with water management.

The ministry of forestry is responsible for the rehabilitation and conservation of forest and

the watersheds and for keeping stability of environment, to develop the social and

economic conditions of the nation, especially for rural people.

For all environmental matters, the national commission for environmental affairs (NCEA)

was formed in February, 1990 and the environmental conservation committee was also

formed in March, 2004 with the aim to carry out the environmental conservation activities in

the country effectively and systematically.

4.4 Water Resource Utilization and Challenges

Myanmar is an agricultural country. It bounds in abundance of water resources. The

agricultural sector is the most basic economic of the state as well as the main livelihood of

the rural areas, since the rural people represent about 70% of the nation’s population. The

development program for agriculture, livestock breeding and fisheries sectors are also

included.

Total numbers of irrigation facilities are amounted to (176) from 1988 to end of June, 2005.

Dams and reservoirs are providing irrigation water over one million hectares of farm land.

In addition to dams, river water pumping stations, underground water tapping stations and

small dams have been built throughout the nations. A total of (271) river pumping projects

have been implemented and irrigating about (0.12) million hectares of cultivated land. In

addition completed (7478) tube wells could have been provided to irrigate (0.036) million

hectares of farm lands.

There are some tributaries originated from the western hill region and southern part of the

country which constitutes around 10% in terms of catchment area and surface runoff.

Hydropower potential of these tributaries has a considerable amount. The total generated

power is being estimated as 390MW and that is almost 1% of potential generated power in

the country. The development of the electrical power projects are being implemented

wherever possible in the nation to fulfill its electricity needs.

Groundwater withdrawal for domestic, industrial and irrigation usage, as per Myanmar

Agriculture Sector Review Report (2004), stands at (2.86 km3). Despite enormity of

groundwater potentials that amounted to 495 km3, availability of groundwater in both

quantity and quality restricts to alluvial and Ayeyarwaddian aquifers which however further

often limited by recently findings of sporadic contamination of health injurious chemicals,



arsenic in particular, especially in the part of Ayeyarwaddy delta, Sittoung valley, western

coastal area and Inlay lake region.

There are several problems faced by the water sector. These include unusual rainfall

patterns in some years, flood and drought in some of the main agricultural areas of country,

the impact of shifting cultivation, forest degradation and conflict of interests for

management within the sectors and lack of co-ordination within agencies. The most

important challenges include, to strengthen the legal framework for an effective and

harmonious integration of water resources management, (1) development and protection

activities into the socio economic development process of the country, (2) to enhance and

consolidate the existing systems, (3) to operate, maintain and rehabilitate facilities safely,

reliably and efficiently and (4) to prioritize the capacity building needs so as to enhance

organizational capacity and effectiveness of the water resources coordination system.

4.5 Water-Related Response Indicators

(i) Sustainable use of water resources

(ii) Implementation of schemes to provide adequate drainage and ensuring proper

maintenance; improving water management practices, particularly discouraging over-

watering; improving maintenance of canals and on-farm ponds and reducing seepage

from water courses; undertaking soil reclamation schemes.

(iii) Increased cultivation of salt-tolerant crops, or water intensive crops

(iv) Review of policies about the pricing of irrigation water or of energy for water pumping.

4.6 Trends in Water resources Management

Within the framework of its irrigation policy, MOAI has decided to undertake:

(i) the construction of new reservoirs and dams;

(ii) the rehabilitation of existing reservoirs and networks of both government and

private sectors, in order to upgrade the storage capacity and allow for an efficient

delivery of irrigation water;

(iii) the development of flood protection by embankment, and irrigation expansion

after flood recession;

(iv) the development of pump irrigation;

(v) the development of an efficient use of groundwater for irrigation.

The official target for irrigation development is to irrigate 25 percent of cultivated areas

before 2000, which is realistic regarding the ongoing and planned projects. Concerning the



flood protected areas, no target has been fixed by the Government although some 400

000 ha in the delta are in need of reclamation.

All new projects related to dam construction are now multipurpose projects and include

flood control, town water supply, hydroelectricity and irrigation. The priority for multipurpose

projects with hydropower is an indicator of the expanding demand for energy.

Chapter 5. Outline of the Chindwin River Basin 42 Mtr.No.158204


Chapter 5. Outline of the Chindwin River Basin 5.1 Region under the Study

Among the four major rivers, the Chindwin is the third largest river in the country. The

Chindwin basin occupies almost the entire North Western part of Myanmar. It is significant

for the development of the country as a whole and especially the area in the river basin is

rather great. The Chindwin with its tributaries is practically the most convenient way of

communication within the basin, and it also communicates the basin with the main

economically developed areas of the country. The Chindwin basin is located in upper

Sagaing Division, where Meteorological & Hydrological data are available at the stations

along this river, such as Monywa, as shown in Figure 5.3.

The source of Chindwin

radiates from the Kachin

plateau. The second highest

mountain in Myanmar,

Saramali with the elevation of

3826 m, is also located on the

upper Chindwin catchment

area. Since it passes through

the mountainous region there

are numerous streams, flowing

into the Chindwin river.

These streams are small tributaries of the Chindwin river. The large tributaries of Chindwin

river are U Yu and Myittha, where U Yu, flows into Chindwin near Homalin and Myittha

near Kalewa (Phyu Oo Khin 1998).

Chindwin river collects its head waters in the northern Sagaing division, and flows into the

Ayeyarwaddy river between Mandalay and Bagan. The double deckers sail up to Maw

Leik; beyond that only the smaller motor boats would go. In the dry season (February to

May) the large boats may go only up to Kale Wa. The Chindwin basin is the second busiest

river for navigation and thousands of cultivated lands are inside the catchmnet area. Thus

socio-economic condition of the region relies on its water resources.

Chindwin River Ayeyarwaddy River

Fig 5.1 Chindwin River joining to Ayeyarwaddy River

(Source: http://earth.google.com)



Fig 5.2 Location of the Chindwin Basin (Source: Ni Lar Aye, 2001)



Fig 5.3 Chindwin Basin Map with Discharge Observation Station

(Source: Ni Lar Aye, 2001)

Gauging Station



5.2 Topography

The Chindwin river in its upper reaches is known as the Tanai Hka, and rises near the

Ayeyarwaddy watershed in the Kachin hills in lat. 25º 40’ N. and long. 97º E., flowing

almost due north until it enters the south-east corner of the Hukawng valley. In the

Hukawng valley it is joined by two important tributaries, the Taron and the Tawan Hka from

the north. After leaving the valley it descends rapidly through a gorge with frequent rapids

and waterfalls until it enters Singkaling Kanti, whence it preserves a general southerly

course to its junction with the Ayeyarwaddy some ten miles north-east of Pakokku.

Six kilometers (Four miles) below Homalin the Chindwin receives an important tributary on

the left bank-the U Yu river, which rises in the Myintkyina district and is the famous

repository of part of the valuable Myanmar jade. On the right bank it receives the Yu at Yu-

wa and the Myittha at Kalewa, from which it receives the drainage of the Chin hills. The

main stream is navigable by light vessels as far as Pantha throughout the year; in the rainy

season the vessels ply up to

Homalin. The basin of

Chindwin river is, in general, a

mountainous forested terrain

with the only exception of its

lowest southern part which is

a vast plain. The highest

mountains are to be found to

the West and North of the

basin where they reach 300m

and more.

From the East the watershed passes a mountain chain of 1000m–1500m high. The source

of the river, which in its upper reaches before entering the Hukawng Valley, bears the

name of Tanai Hka, flowing at the height of about 2100m, then within the distance of

130km it goes down to the height of 210m and enters the Hukawng Valley. There it

receives several tributaries, gets the name of Chindwin and on the whole of its flow of

1000km down to its confluence with the Ayeyarwaddy has a gradient of 137m. After

confluence with Myittha, the Chindwin enters a spacious plain that extends as far as the

Ayeyarwaddy.

Fig 5.4 Transportation by Small Boat in Chindwin River

(Source: http://www.pbase.com/rovebeetle/image/41479890)



5.3 General Climate

Myanmar has the effects of monsoon in different parts of the country. The major

contribution of rainfall in the Chindwin basin is from rainfall over the catchment. The heavy

rainfalls are generally caused by monsoon trough and strong monsoon. Amount of rainfall

decreases from upstream to downstream of the basin according to the isohyetal map of

Chindwin basin (Appendix-B). The monthly and annual maximum amounts of rainfalls over

the catchment are about 686 mm and 2455 mm respectively. Maximum mean annual

temperature at Monywa station is 29°C whereas the minimum mean annual temperature

amounts to 25°C. Both rainfall and temperature vary in the whole basin. The lower part of

the Chindwin basin is situated in the dry zone of Myanmar. Dry zone comprises Lower

Sagaing, Mandalay and Magway Divisions and has an area of about 54,390 km2 (21,000

square miles) or about 10 per cent of the country.. There are altogether 13 districts and 57

townships in the Dry Zone. The Dry Zone suffers intense heat of monthly temperature

ranging from minimum of 10°C in the cool months to maximum of above 40°C in dry

months. Annual rainfall varies between 500mm and 1000mm.

5.4 Land Use and Land Cover

For the land use purpose, six major classes are defined as follows;

(a) Good Forest (closed Forest)

This includes Moist Forest (M), Semi-Indaing (Id), Dry Forest (DF), Hill Forest (H),

High Indaing (In), Mixed Deciduous Forest (MDF), Moist Forest with Bamboo (M/B),

Bamboo Breaks of Rakhine Yoma and Forest Plantations (Pt). Good means good

vegetation cover for Dry Zone management. Some areas may not be good for

Forest Management (timber production).

(b) Degraded Forest

This includes Scrub Forest (Sc), Scrub with Grassland (Sc/Gr), Scrub with Bamboo

(Sc/B) and Grass land (Gr). Some area needs only natural regeneration methods.

(c) Shifting Cultivation

This includes Shifting Cultivation (Sh), Shifting cultivation with Bamboo (Sh/B), and

Scrub land affected with Shifting Cultivation (Sc/Sh).



(d) Agriculture

This includes Permanent Agriculture (Af), Agriculture with vegetative bunds (Af/B),

Ya cultivation (Y), Alluvial Island Cultivation (Al) and Homestead Gardens (At).

(e) Water

This includes open water, lakes and major irrigation systems.

(f) Others

This includes Swamp areas (Um), Sand (S) and Settlements (Ui).

Land use maps are shown in Appendix-B. The Chindwin river basin is contributed mainly

by tertiary continental sediments. Among them more frequently found are sand-stones of

different hardness, less frequent are clay with gypseous veins, shales and lime-stones.

The width of the river varies from 91m (300 ft) to 3048m (10,000 ft). Chindwin catchment

area covers 97516 sq. km (Ni Lar Aye, 2001). The Chindwin basin has approximately

50000 ha (120, 000 acres) of cultivated land. About 90% of the basin is thickly covered by

valuable species of wood. (Phyu Oo Khin 1998).

Table 5.1 Area portion of Land Use and Land Cover (U Tin New & U Khin Soe, 2004)

Name of

Sub-basin L U&C(C.F) (%) L U&C(D.F) (%) L U&C(S.C) (%) L U&C(A.L) (%) L U&C(o) (%)

Hkamti 48.435 29.627 3.050 18.755 0.133

Homalin 46.38 35.95 2.26 14.97 0.43

Mawlaik 47.385 37.976 1.331 12.830 0.478

Kalewa 53.53 29.99 1.59 14.47 0.41

Monywa 51.618 29.302 1.375 17.171 0.534

Where,

L U&C(C.F) = Closed Forest Type (%)

L U&C(D.F) = Degraded Forest Type (%)

L U&C(S.C) = Shifting Cultivation (%)

L U&C(A.L) = Agriculture Land (%)

L U&C(o) = Other Type (%)

Lower part of the Chindwin basin is situated in the dry zone of Myanmar. The Dry Zone is a

vast semi-arid low land between two higher regions, the Shan plateau on the East and the



Rakhine Yoma and Chin hills on the west. Two major rivers, the Ayeyarwady and the

Chindwin flow through the Dry Zone from North to South connecting it to the Deltaic region

in the South. The original vegetation of central Dry Zone is described as Savannah

woodland which consisted deciduous trees and a ground flora composed of different

species of grass. Dry zone greening department has implemented forest plantation in the

dry zone since 1995.

5.5 Soil Type and Basin Characteristics

The area portions (km2) of different soil classification for five sub-basins of Chindwin

catchment are shown in Table 5.2. The basin characteristic of Chindwin catchment are

taken from the topographical map of Myanmar land map and shown in Table 5.3.

Table 5.2 Major Soil Classification of the Chindwin Basin (U Tin New & U Khin Soe, 2004)

Soil Type

Basin

Meadow

Alluvial

Soil

(clay)

Red Brown

Forest Soil

(silty clay)

Chin Hill

Complex

Soil (Sand &

Gravel)

Savanna

Soil (Sandy

Silt)

Red &

Yellow

Earth (Silt)

Hkamti 21015 6425

Homalin 25514 11555

Mawlaik 31133 31943 358

Kalewa 33688 40508 10080

Monywa 34357 48346 10080 1640 2292

Table 5.3 Basin Characteristics of the Chindwin Catchment (U Tin New & U Khin Soe,

2004)

Discharge

Station

P

(km) A (km2) L

(km)

Ls

(km)

Dd

(km/ km2)

Sequ Sbavg B

Hkamti 2148 27440 347 5726 0.21 0.0013 0.104 0.49

Homalin 2923 37070 546 8237 0.22 0.0002 0.122 0.48

Mawlaik 4985 63438 766 14173 0.22 0.0004 0.188 0.47

Kalewa 6437 84419 825 17774 0.21 0.0003 0.121 0.43

Monywa 7609 97516 1046 20791 0.21 0.0003 0.114 0.43



Where,

P = Perimeter of Catchment

A = Catchment Area

L = Length of River

Ls = Total Length of streams in the Catchment

Dd = Drainage Density ( Ls/A )

Sequ = Equivalent Slope of the river

Sbavg = Average Slope of the basin

B = Soil Factor

5.6 Water Utilization

According to the available information, there is only one weir in Chindwin catchment (as of

Sagaing Division) and it provides about 1400 ha. It might be assumed that there were

some cultivated areas by local farmers with their own traditional ways without using the

water from the government projects. These are hardly be achieved and the cultivated area

provided by the irrigation projects which are totally managed by the government. Since

1990, the irrigation schemes have gained momentum not only in the study area but also

through out the country. From 1996, pumping irrigation projects were introduced by Water

Resource Utilization Department along the Chindwin river only for agriculture purpose.

Irrigation development both by reservoir and direct pumping from Chindwin river are shown

in Appendix-A. Ground water extraction like drilling tube wells plays a vital role for rural

water supply and agriculture purpose. This information hardly can be monitored.

0

1000

2000

3000

4000

5000

6000

7000

1996 1997 1998 1999 2000 2001 2002 2003 2004Year

Pum

ping

Irrig

atio

n (h

a)

Fig 5.5 Irrigation Development along the Chindwin River by Direct Pumping

Chapter 6. Data Description and Analysis of Collected Data 50 Mtr.No.158204


Chapter 6. Data Description and Analysis of Collected Data 6.1 Description of Collected Data Series For drought study, it needs annual minimum flow and to be random variables. If other

climatic parameters are available, the study is more efficient. According to Shaw (1984), at

least 20 years of data should be obtained in order to achieve reliable results. There may

be gaps in the low flow data series.

However, Mutreja (1986) noted that theoretically there is no requirement of continuous

record of annual minimum series. Hence, if annual minimum flows of some years are

missing, it is not a problem and it is unnecessary to fill the missing data or discard the

broken data from further analysis. U.S.G.S restricted about the magnitude of low flow that

there is no lower stream flow level of 0.05 ft3/s (0.0014 m3/s) below which any

measurement is reported as a zero (Maung Aung Moe).

In this study, Chindwin river is selected as a case area. It is a perennial stream and impact

of its water resource reflects the country’s socio-economic condition. Here mean daily

discharges were collected for 30-years ( 1975-2004) at Monywa station which is the most

downstream portion of the river.

Hence these discharges cover

the whole basin. There are six

rainfall gauging stations in the

Chindwin catchment (Appendix-

B). Mean annual rainfall of the

chindwin basin which is average

value of these six stations and

mean monthly temperature of

Monywa station were available

for 31 years (1975-2005).

All data have been provided by the department of Meteorology and Hydrology and shown

in Appendix-C.

In the duration curve analysis and in the determination of master recession curve, collected

daily discharges are used. For frequency analysis low water discharge of 1-day minimum

can be wrong because of short-lived human actions. Thus 7-day minimum discharges

(NM7Q) are used in the analysis to avoid the errors.

Gauging Station

Chindwin river

Fig 6.1 Location of the gauging Station

(Source: http://earth.google.com)



First NM1Q, NM7Q, NM14Q and NM30Q of each year are calculated using moving

average method from the collected data series and NM7Q is shown in Table 6.1. And then

required statistical parameters are calculated for the data test and shown in Table 6.2.

Table 6.1 7-day minimum discharge for each year in the collected data series

Year NM7Q

(m3/s) Year

NM7Q

(m3/s) Year

NM7Q

(m3/s)

1975 715,6 1985 622.3 1995 685.3

1976 905 1986 595.6 1996 636.3

1977 800.6 1987 669.4 1997 463.3

1978 676.4 1988 614.1 1998 768.4

1979 539.3 1989 788.6 1999 500.9

1980 759.7 1990 913.1 2000 673.3

1981 795.7 1991 865.7 2001 535.3

1982 654.6 1992 1047 2002 689.9

1983 668.6 1993 998.7 2003 774.4

1984 608.4 1994 658.1 2004 612.6

Annual Low Flows (NM7Q)

0

200

400

600

800

1000

1200

1970 1975 1980 1985 1990 1995 2000 2005 2010Year

NM

7Q (m

3/s)

Fig 6.2 Annual Low Flows ( 7-day minimum) of the Data Set



6.2 Determination of Statistical Parameters of the collected Data Set Statistical parameters such as mean, standard deviation and skewness coefficient are

determined by following equations.

Mean, x = ∑=

n

1ixi /n (Eq 6.1)

Standard deviation, σ = √ (∑xi2 – (∑xi2)/n ) / (n-1) (Eq 6.2)

Skewness coefficient, ү = ( n2 ∑xi3 – 3n ∑xi ∑xi2+ 2 (∑xi)3) / (n(n-1) (n-2) σ3 ) (Eq

6.3)

Table 6.2 Statistical Parameters of data set of NM7Q

Natural Value Logarithmic Value

Station Data

Length Mean x

(m3/s)

Std. Dev

(m3/s)

Skewness

coefficientMean y

Standard.

Deviation

Skewness

coefficient

Monywa 30 707.8733 139.4771 0.646802 6.54404 0.19343 0.13903

6.3 Analysis of Collected Data Series The low water discharge can be influenced by short-lived isolated events and longer lasting

or even continuous actions in the drainage area (inhomogeneous data). It is also possible

that the data are wrong because of errors in the discharge measurements, etc.

Considering short-lived alterations, the extreme low water discharge have to be checked

with regard to disturbances by

- Temporary hold back in reservoirs

- Unusual situations at intakes and effluents

Other circumstances have no longer lasting or continuous influence, for instance:

- newly given or expired rights for intake and effluents,

- river training at the observed river or its tributaries,

- construction of sewage water treatment plants.

It is always useful to visit the examined gauging station and to try to find out possible

influences upon the measured values brought about by the surrounding area. The

observation period should comprise at least 20-30 years.

Two basic assumptions in statistical flood frequency analysis are the independence and

stationary of the data series. In addition, the assumption that the data come from the same

distribution (homogeneity) is made.



In this study, three types of test, namely independence and stationary test, homogeneity

test and outliers test are carried out especially for frequency analysis to check the reliability

of collected data series and to reduce the possible errors.

6.3.1 Test for Independence and Stationary

Given a sample of size N, the Wald-Wolfowitz (1943) (W-W) test is used to test for

the independence of a data set and to test for the existence of trends in it. For a data set

x1, x2, x3,…….., xN the statistic R is calculated from Eq. 6.4.

R = ∑−

=

1N

1ixi xi+1 + x1 xN (Eq 6.4)

When the elements of the sample are independent, R follows a normal distribution with

mean and variance given by Eqs. 6.5 and 6.6,

R = 1N

)ss( 22

1

−

− (Eq 6.5)

var (R) = )2N)(1N(

)s2sss4s4s(R1Nss 4

2231

21

4124

22

−−−++−

+−−−

(Eq 6.6)

where sr = Nm’r and m’r is the rth moment of the sample about the origin.

The statistic u = (R-R )/(var (R))1/2 is approximately normally distributed with mean zero and

variance unity and is used to test the hypothesis of independence at significance level α, by

comparing the statistic u with the standard normal variate uα/2 corresponding to a

probability of exceedance α/2.

6.3.1.1 Result of the Test Standard Deviation of the data series = 139.4771

R = 27532386

S1= Nm1' = 21236.2 , S12 = 450976190.4 , S1

4= 2.034x1017

S2 = Nm2' = 15596702 , S22 = 2.432 x 1014

S3 = Nm3 = 1.19x1010

S4 = Nm4' = 9.40x1012

R = 15013086

var (R) = 9.8x109



Table 6.3 Result of Independence Test

Station Statistic u

Critical u

at the significance level

(α = 5%)

Conclusion Remark

Monywa 0.035739 ± 1.96 Accept Considering both sides

of distribution function

The test value u = 0.035739 is less than the critical value at 5% significance level u0.025 =

1.96. Thus we can accept the hypothesis of independence and stationary. So the chindwin

river data at Monywa station are concluded to be independent and stationary at the 5%

significance level.

6.3.2 Test for Homogeneity and Stationary In this test two samples of size p and q with p≤ q are compared. The combined data set of

size N = p + q is ranked in increasing order. The Mann-Whitney (1947) test considers the

quantities V and W in Eqs. 6.7 and 6.8.

V = R - 2

))1P(P( + (Eq 6.7)

W = pq – V (Eq 6.8)

R is the sum of the ranks of the elements of the first sample (size p) in the combined series

(size N), and V and w are calculated from R, p and q. V represents the number of times an

item in sample 1 follows an item in sample 2 in the ranking. Similarly, w can be computed

for sample 2 following sample 1. The Mann-Whitney statistics U is defined by the smaller of

V and W. When N>20 and p,q >3 and under the null hypothesis that two samples came

from the same population, U is approximately normally distributed with mean U= 2

pq and

variance var(U),

Var(U) = [)1N(N

pq−

] [12

NN3 −- ∑ T ] (Eq 6.9)

Where T = ( J3 – J )/12 and J is the number of observations tied at a given rank. T is

summed over all groups of tied observations in both samples of size p and q.

The statistic u = ( U - U)/ [var(U)]1/2 is used to test the hypothesis of homogeneity at

significance level α by comparing it with the standard normal variate for that significance

level.



6.3.2.1 Result of the Test The data set was divided into two sets each length of p = 15, q = 15.

Calculated parameters and result are as follows;

R = 224

V = 119

W = 106

U = 106 ( smaller value of V and W )

U= 112.5

Var(U) =581.25

Table 6.4 Result of Homogeneity Test

Station Statistic u

Critical u

at the significance level

(α = 5%)

Conclusion Remark

Monywa -0.269607 ± 1.96 Accept Considering both sides

of distribution function

Since the modulus value of statistic u for homogeneity test is less than the critical values at

5% significant level u0.025 = 1.96, the Chindwin river data at Monywa station can be

considered to be homogeneous and stationary at 5% significant level.

6.3.3 Test for Outliers An outlier is an observation that deviates significantly from the bulk of the data, which may

be due to errors in data collection, or recording, or due to Natural causes. The presence of

outliers in the data causes difficulties when fitting a distribution to the data. Low and high

outliers are both possible and have different effect on the analysis. The Grubbs and Beck

(1972) test (G-B) may be used to detect outliers. In this test the quantities xH and xL are

calculated by using Eqs. (6.10) and (6.11).

xH = exp ( x + kNs ) (Eq 6.10)

xL = exp ( x - kNs ) (Eq 6.11)

where x and s are the mean and standard deviation of the natural logarithms of the

sample, respectively, and kN is the G-B statistic tabulated for various sample sizes and

significance levels by Grubbs and Beck (1972). At the 10% significance level, the following

approximation proposed by Pilon et al. (1985) is used, where N is the sample size.



kN = -3.62201+ 6.28446N1/4 – 2.49835N1/2 + 0.491436N3/4 – 0.037911N (Eq 6.12)

Calculated kN values using above equation are given for different sample size (N) in Table

6.5.

Tanble 6.5 kN vues for Outlier test (Source: A.R. Rao and K.H. Hamed, 2000)

Sample

Size N kN

Sample

Size N kN

Sample

Size N kN

Sample

Size N kN

10 2.036 23 2.448 36 2.639 49 2.760

11 2.088 24 2.467 37 2.650 50 2.768

12 2.134 25 2.486 38 2.661 55 2.804

13 2.175 26 2.502 39 2.671 60 2.837

14 2.213 27 2.519 40 2.682 65 2.866

15 2.247 28 2.534 41 2.692 70 2.893

16 2.279 29 2.549 42 2.700 75 2.917

17 2.309 30 2.563 43 2.710 80 2.940

18 2.335 31 2.577 44 2.719 85 2.961

19 2.361 32 2.591 45 2.727 90 2.981

20 2.385 33 2.604 46 2.736 95 3.000

21 2.408 34 2.616 47 2.744 100 3.017

22 2.429 35 2.628 48 2.753 110 3.049

Sample values greater than xH are considered to be high outliers, while those less than xL

are considered to be low outliers.

6.3.3.1 Result of the Test By using equations (6.10), (6.11) and statistical parameter of NM7Q data series, calculated

values of QH and QL for the selected are given in Table 6.6.

Table 6.6 Result of Outlier Test

Computed Value (m3/s) Observed Value (m3/s) Station N kN

QH QL Max NM7Q Min NM7Q

Monywa 30 Years 2.563 1141.175 423.382 1047 m3/s 463.3



By comparing the computed values and observed maximum and minimum NM7Q, it is

found that the computed QH is higher than the observed Max NM7Q and the computed QL

is lower than observed Min NM7Q. There is no high or low outliers in the data set. It is to

be considered as a freedom of outliers at 10% significance level.

6.4 Summary Result of Data Test According to the results of the tests mentioned above, the final conclusion can be

summarized that the hypothesis is acceptable at the 5 % significance level for

independence and homogeneity tests and at the 10% significance level for outlier test. So

further analyses continue in coming chapters. Summery results of data tests are shown in

Table 6.7.

Table 6.7 Summery Result of the Data Test

Station Data Length Data Test Result Remark

Independence Accept At 5% significance level

Homogeneity Accept At 5% significance level Monywa 30 Years

Outlier Accept At 10% significance level

6.5 Main Activities of Low Flow Analysis in the Region To be able to quantify the latter drought characteristics for the Chindwin river, it is

necessary to define a threshold level below which the flow or groundwater is regarded as

being in a drought situation. The derivation of hydrological drought characteristics,

including time series and indices, can be expressed by considering a time series of daily

streamflow or groundwater recharge, levels or discharge and main activities for the

determination of low flow indices are illustrated in Fig 6.3. These describe the low flow

regime of a river. They can be an index obtained using the whole time series of flow

directly in its derivation.



Select a Low Flow Index (Percentile from FDC)

100

1000

10000

100000

0 10 20 30 40 50 60 70 80 90 100Exceedance F requency ( %)

Select Annual Minimum Flows

0

5000

10000

15000

20000

25000

30000

0 500 1000 1500 2000 2500 3000 3500 4000

Time Step (day)

Dai

ly D

isch

arge

(m3/

s)

Select Recession Portions

0

5000

10000

15000

20000

25000

30000

0 500 1000 1500 200

Time Step (day)

Dai

ly Q

(m3/

s)

I I III

Original Time Series of Observation

0

5000

10000

15000

20000

25000

30000

0 500 1000 1500 2000 2500 3000 3500 4000

Time Step (day)D

aily

Dis

char

ge (m

3/s)

Calculate a low flow index from the time series

Calculate a low flow index from MRC

Examples of Indices

I. Period of record EFQ90 II. 7Q10 III. MRC Constant

Fig 6.3 Derivation of Low Flow characteristics (Modified from DWS 48)

Chapter 7. Duration Curve Analysis 59 Mtr.No.158204


Chapter 7. Duration Curve Analysis 7.1 Introduction The flow duration curve (FDC) of daily flows is a cumulative frequency curve that shows

the percent of time a specified discharge has been equaled or exceeded during a given

period, and has been used as a useful tool for various water resources problems. The flow

duration curve shows the statistical distribution of daily mean stream flows for a period of

years, and the lower end of that curve is a useful expression of the low flow characteristics

of the stream. A flow duration curve characterizes the ability of the basin to provide flows of

various magnitudes. Information concerning the relative amount of time that flows past a

site are likely to equal or exceed a specified value of interest is extremely useful for the

planning of hydraulic structures.

The shape of a flow-duration curve in its upper and lower regions is particularly significant

in evaluating the stream and basin characteristics. The shape of the curve in the high-

flow region indicates the type of flood regime the basin is likely to have, whereas, the

shape of the low-flow region characterizes the ability of the basin to sustain low flows

during dry seasons. A very steep curve (high flows for short periods) would be expected

for rain-caused floods on small watersheds. Snowmelt floods, which last for several days,

or regulation of floods with reservoir storage, will generally result in a much flatter curve

near the upper limit. In the low-flow region, an intermittent stream would exhibit periods of

no flow, whereas, a very flat curve indicates that moderate flows are sustained throughout

the year due to natural or artificial streamflow regulation, or due to a large groundwater

capacity which sustains the base flow to the stream.

Low flow analysis for Chindwin river has made extensive use of single flow indices or

exceedance (flow duration) percentiles, which are the second most widely used

hydrological environmental flow method, after the Tennant method (Tharme, 2003). The

exceedance percentile Q90 can be interpreted as the drought discharge which can be

expected to be exceeded 90% of the time.

7.2 Use of the Duration Curve Low flow percentiles can be selected from the flow duration curve to determine the low flow

index sometimes known as low flow statistic, measure, parameter and variable in the

literature. The lower end of the duration curve is an expression of low flow characteristics

of a stream, but it provides less information than a low flow frequency curve, because the

duration curve applies to the period of record rather than to a year. Nevertheless, frequent



request for duration curves indicate that they are used as a tool in water related studies.

Low flow percentiles from flow duration curve are used in various water management

applications such as water supply, hydropower and irrigation planning and design,

discharge permits, river and reservoir sedimentation studies and water transfer and

withdrawals. Furthermore, station data for any period can be economically arranged in

duration form by the computer, and tabular expression of values from the duration curve

requires only one line per station in a report. The period or periods selected for

computation of duration for a given station should correspond to the period of natural flow

or to a period that represents particular conditions imposed on the basin.

7.3 Study Area and Data Although the country is generally blessed with abundant water, this resources is poorly

distributed both space and time. The heavy rains during the southwest monsoon and the

torrential downpours associated with sudden storms lead to sustained flooding in the wetter

areas and to flash floods in the drier parts or in place where steep mountain torrents

overflow.

During the dry season, on the other hand, scarcity of water becomes a problem over much

of the country. A depth of as little as 1 m, providing 640 m3/s of river flow, is not uncommon

in the Chindwin river and this creates considerable difficulties for navigation (UN reports).

This might be especially for the navigation by light boat in the river and this value indicates

the most minimum requirement of water level in the river.

Based on the collected data series during 1975 to 2004, the estimation of flow duration

curve is applied for different time reaches in order to detect possible changes of low flow

characteristics with time and to define the low flow index as well.

7.4 Percentiles from the Flow Duration Curve In order to trace the changes of low flow pattern, flow duration curves for every 10-year

periods were drawn and studied the tail portion of the duration curves which show the low

flow indices of the period. Daily streamflow data of each 10-year period at Monywa station

are used here to construct a flow duration curve based on a daily time step, ∆t = 1 day. The

total number of ∆t interval is then N = 3653 days for 1975-1984 interval and 1985-2004

interval. Between 1985 and 1994, the total number of days is 3652. Then the flow duration

curves were constructed according to following steps (Developments in Water Science,

48).



(a) The rank, m of each value is calculated, which means that if the list is sorted, the

rank will be its position. Here the series is sorted in descending order and the mth

largest value has the rank m (i.e the largest value has rank 1).

(b) The exceedance frequency, EFQm is calculated as EFQm = m/N which gives as

estimate of the empirical exceedance frequency of the mth largest event. EFQ

designates here the observed frequency when the flow Q, is larger than the flow

value with rank m, Qm.

(c) The FDC was tabulated corresponding to the values of streamflows ( Q in m3/s)

and exceedance frequency (EFQmth in %). Table 7.1 lists the first seven flow

values for sample expression. The sorted table columns are then plotted. The

ordinate axis was here logarithmic.

(d) Values for a particular frequency, for example the 90-percentile (Q90), can be

obtained as the value of Q corresponding to the largest value of EFQm that is less

than or equal to the value of EFQm sought for. Corresponding values are shown in

Table 7.2

Table 7.1 Calculation of a daily FDC for Chindwin River at Monywa Station

Data, 10-year series Calculation of Flow Duration Curve

Rank, m Streamflow (m3/s) Exceedance frequency = m/N *100 (%)

1 27300 0.0273

2 26750 0.0547

3 26450 0.0821

4 26050 0.1095

5 25750 0.1369

6 25700 0.1642

7 25200 0.1916

This percentile value is used to define the drought discharge in the study area. Detail

specification to select the appropriate percentile could not found and it is normally taken

97%, 95% and 90%. Here theoretical drought discharge of Chindwin basin are described

as the flow value corresponding to the largest value of EFQ90 that is less than or equal to

the value of EFQ90.

The flow duration curve (FDC) plots the empirical cumulative frequency of streamflow as a

function of the percentage of time that the streamflow is exceeded. As such, the curve is

constructed by ranking the data, and for each value of the frequency of exceedance is

computed. The empirical FDCs of the river Chindwin at Monywa station for each 10-year



interval are shown in Fig 7.1, 7.2 and 7.3. FDCs represent the streamflow variability of a

catchment. Both high and low flows are included. To improve the readability of the curve,

streamflow is often plotted on a logarithmic scale. It is also common to let the abscissa

scale be based on the normal probability distribution. But here normal scale was used in

the figures to express the percentiles.

Duration Curve (1975-1984)

100

1000

10000

100000

0 10 20 30 40 50 60 70 80 90 100

Exceedance Frequency (%)

Q (m

3/s)

Fig 7.1 Duration Curve for the period of 1975-1984


100

1000

10000

100000

0 10 20 30 40 50 60 70 80 90 100


Q (m

3/s)





100

1000

10000

100000

0 10 20 30 40 50 60 70 80 90 100


Q (m

3/s)


Table 7.2 Streamflow values corresponding to EFQ90

First 10 years

1975-1984

Second 10 years

1985-1994

Third 10 years

1995-2004

EFQm (%) Drought

Discharge (m3/s)

EFQm (%) Drought

Discharge (m3/s)

EFQm (%) Drought

Discharge (m3/s)

90 769 90 785 90 712

7.5 Evaluation of Flow Duration Curves Flow duration curves for each interval are then compared in order to evaluate the patterns

of low flows conditions according to the period. Especially lower parts are to be checked.

Here three FDC for each interval are drawn and shown in Fig 7.4. In order to see clearly

the patterns of tail portions of FDCs, Fig 7.5 is more helpful.



Comparison of Duration Curves

100

1000

10000

100000

0 10 20 30 40 50 60 70 80 90 100


Q (m

3/s)

75-84

85-94

95-04

Fig 7.4 Comparison of flow duration curves for every 10-year period

0

200

400

600

800

1000

1200

1400

1600

2150 2350 2550 2750 2950 3150 3350 3550No of Days

Dis

char

ge (m

3 /s)

(75-84)

(85-94)

(95-04)

Fig 7.5 Comparison of tail Portions of Duration Curves

According the flow duration curve, it is clearly seen that tail portion of the flow duration

curve during 1995 and 2004 is quite lower than the other two duration curves. That shows

the same condition of the result from the percentile value, EFQ90 of each interval. It reflects

the steeper recession due to impacts on low flow in the stream. Information on actual



drought discharge of the area, 640 m3/s could be found from the graph and its exceedance

frequencies are shown in Table 7.3.

Table 7.3 Exceedance Frequencies corresponding to actual drought discharge

First 10 years

1975-1984

Second 10 years

1985-1994

Third 10 years

1995-2004

Drought Discharge

(m3/s) EFQm (%)

Drought Discharge

(m3/s) EFQm (%)

Drought Discharge

(m3/s) EFQm (%)

640 97 640 98 640 95

According to table 7.3, actual minimum requirement requires less percentile in the last

period, meaning the value of low flow index decreases.

7.6 Flow Duration Curve for the Entire Study Period For the wide use in water resource planning, flow duration curve for the whole study period,

1975-2004 is prepared and selected percentiles can be interpreted as low flow index.


100

1000

10000

100000

0 10 20 30 40 50 60 70 80 90 100


Q (m

3/s)

Fig 7.6 Flow Duration curve for entire Period (1975-2004)

According to the above FDC, the critical depth for the river, 640 m3/s is relevant to the

EFQ97 and theoretical drought discharge EFQ90 is 757 m3/s which is the low flow index of

the stream by FDC analysis.

Chapter 8. Recession Curve Analysis 66 Mtr.No.158204


Chapter 8. Recession Curve Analysis 8.1 Introduction The gradual depletion of water stored in a catchment during periods with little or no

precipitation is reflected in the shape of the recession curve, i.e. the falling limb of

hydrograph. The duration of the decline is referred to as the recession period, and a

recession segment is a selected part of the recession curve. The time resolution is

commonly in the order of days.

The stream hydrograph falling limb during the non-rainfall period is short in the temperate

zone, so that it is difficult to evaluate appropriately low flow characteristics by using only

one recession curve. Then the smooth curve constructed by linking the end part of the low

flow hydrograph, which is generally called a master recession curve, is usually applied in

order to evaluate the low flow characteristics.

The recession curve describes in an integrated manner how different factors in the

catchment influence the generation of flow in dry weather periods. It has therefore proved

useful in many areas of water resources management; in low flow forecasting of gauged

rivers, as an index of drainage rate in rainfall-runoff models, as an index of catchment

storage in regional regression models, in hydrograph analysis for separation of different

flow components and in frequency analysis for estimating lowflow indices.

The flow recessions in the baseflow component of a runoff hydrograph is considered to

describe the depletion of the groundwater reservoir. However baseflow is not the only

outflow from the saturated zone of a catchment. Evapotranspiration flux by water

consumption of vegetation or from river plains, capillary rise to vadose zone and

groundwater abstractions will significantly influence the shape of flow recession curves (

Wittenberg).

Flow recessions of rivers in most hydrological regimes show significant seasonal variation,

falling slower in winter and faster during summer (Weisman, 1977; Tallaksen, 1995; Moore,

1997; Wittenberg and Sivapalan, 1999). The inter-seasonal difference is mainly attributed

to evapotranspiration flux from the ground water and especially to seasonally varying water

uptake by deep-rooted trees.

Normally there are three seasons in Myanmar namely rainy season, winter and the

summer. Almost all of continuous recessions of hydrograph without any disturbance are

found in the later part of winter and earlier part of the summer. So according to situation it

is a little bit difficult to extract the recessions in winter and summer. Only one recession for

each year is usually picked up although it is known that recession properties can vary

according to the seasonal variation.



At present the country’s policy focus on the cultivation of second crop namely summer

paddy. So major source of irrigation undoubtedly rely on the stream flow which has

naturally emerged during the dry season. Recession flows of the rivers are not only low but

also decreasing gradually. Consequently depleted flow at any moment of the growing

season is required to know in advance so as to plan properly for the second crops.

This section will find out the characteristics of master recession curves of every 10 years

and patterns of low flow changes during the study period are checked. The result is

believed to help the irrigation engineers in the field to enable forecasting the possible

stream flows and condition of low flows at any period of the dry season.

8.2 Study Area and Data In Myanmar, the irrigation department manages to measure the water levels or discharges

regarding with the streams or rivers that are likely to be diverted or on which reservoirs are

constructed. DMH measures large streams and rivers for the purposes of meteorological

and hydrological forecast. On the other hand there is a lack of technical know-how or labor

or budget to measure the flow data in order to make the hydrologic analysis for water

resources planning and management or forecasting the flows on specific time during the

dry season in which no one can measure the flow data. Understanding the low flow

characteristics of the streams or rivers plays an important role especially for the irrigation

and navigation purposes which are the critical factors and affect to the socio-economic

conditions of the Chindwin river basin.

Daily stream flows measured by the DMH were utilized for the analysis. Normally there is

no specific restriction to define the water year in Myanmar and records are usually used

according to calendar year. But here, daily stream flows are managed in water year for

recession analysis so that recession effects after the rains could not be separated. Actual

data length is 30 years which starts in 1975 and ends in 2004. But after separating the

yearly record according to the water year, data length remains 29 years, starting in 1975

and ending in 2003. Here water year starts in the middle of June and ends in the mid June

of coming year.

.

8.3 Determination of Master Recession Curves Several methods have developed to construct a master recession curve for a catchment

from a set of shorter recessions. A major problem is the high variability encountered in the

recession rate of individual segments, which represent different stages in the outflow

process. In addition, seasonal variation in the recession rate adds to the variability. The

master recession methods try to overcome the problem by constructing a mean recession



curve. The most commonly used techniques are the matching strip and the correlation

method.

In the matching strip method (Toebes & Strang 1964) individual segments are plotted and

adjusted horizontally until they overlap. The master recession is then constructed as the

mean line by best eye fit through the set of common lines. The method permits a visual

control of irregularities in the recession curve, but as it is based on a subjective fit it might

telescope or contract the true recession.

In the correlation method (Langbein, 1938) the discharge at one time interval is plotted

against the discharge one time interval later and a curve fitted to the data points. If the

recession rate follows an exponential decay, a straight line results and the slope of the line

equals to the recession parameter k.

Several recession parameters can be calculated from the set of recession segments. It is

therefore necessary to combine the information contained in the recession behavior of the

individual segments to be able to identify and parameterize the characteristics recession

behavior of the catchment. This can be done by constructing a master recession curve, or

by obtaining averages vales of the recession parameters from the set of individual

recession segments. If it is assumed that there are n segments, one from each recession

period, then the j recession parameters can be obtained either from the master recession

curve or for each of the n segments. In the latter case a mean value can be calculated to

represent average catchment conditions.

.

8.3.1 Master Recession Curves for every 10-year Period The recession limb of the discharge hydrograph if no recharge is taking place is termed as

the recession curve. This curve represents the diminishing discharge from storage, and

that component consists of surface flow, interflow and base flow. Barnes defined the base

flow as the discharge into the stream system from storage in the ground at or below the

ground level.

An individual recession limb in the temperate zone is a short term event. Thus, in the

temperate zone, in order to assess low flow characteristics in a catchment, it is necessary

to combine an individual recession limb during the period of record. Here three master

recession curves, for the period of 1975-84, 1985-94 and 1995-03, are drawn first to

examine the conditions of the changes of recession patterns during the recorded length of

29 years. The curve which can be constructed by combining the individual yearly recession

limb is termed the master recession curve.



8.3.1.1 Determination of Recession Constant by Simple Averaging 8.3.1.1.1 Linear Storage Firstly recession constant (k) of each year are determined by using the relation Qt = Qo

exp(-kt) which is liner storage equation. It is suitable for groundwater storage contribution

and has been applied for the most lowest parts of the falling limbs of each hydrograph.

Firstly the relation Qt = Qo exp(-t/k) is transformed into simple form y = a + b.x. Here y is

lnQ0, a is lnQt, x= t and b=(y-a)/x. Then recession constant, k is equal to 1/b in days. Q is in

m3/s, t and k are in days. Recession constants for each period are then drawn in

decreasing order and master recession curve constants for each period are determined

from the best fit line of calculated recession constants of each period as shown in Fig 8.1,

8.2 and 8.3. This value obtained from this way is almost same as the arithmetic average of

the recession constants. Master recession curves (MRC) for the proposed three periods

were drawn using average recession constants and shown in Fig 8.4.

The calculated k values and average k for each period are shown in table 8.1 and table

8.2.

Table 8.1 Recession constants for each Year (linear)

Year K (days) Year K (days) Year K (days)

1975 128.383 1985 166.746 1995 155.041

1976 149.56 1986 121.049 1996 102.149

1977 194.503 1987 131.705 1997 146.485

1978 160.742 1988 127.977 1998 114.649

1979 164.022 1989 125.626 1999 106.859

1980 182.728 1990 134.016 2000 104.295

1981 133.402 1991 132.914 2001 96.6784

1982 169.251 1992 187.322 2002 109.341

1983 133.957 1993 199.294 2003 123.38

1984 148.286 1994 150.98



y = -7.1226x + 195.66

0

50

100

150

200

250

0 2 4 6 8 10 12No of k

Rece

ssio

n C

onst

ant,

k

Fig 8.1 Recession constants for the period of 1975-1984

y = -8.4173x + 194.06

0

50

100

150

200

250

0 2 4 6 8 10 12No of k

Rec

essi

on C

onst

ant,

k


y = -6.8736x + 152.02

020406080

100120140160180

0 2 4 6 8 10No of k

Rec

essi

on C

onst

ant,

k




Table 8.2 Average Recession Constants by Linear Storage

Period Average K (days) Linear Reservoir Equation

1975-1984 156.4815 Qt = Q0.exp(-∆t/156.48)

1985-1994 147.7628 Qt = Q0.exp(-∆t/147.76)

1995-2003 117.653 Qt = Q0.exp(-∆t/117.65)

Master Recession Curves (Linear)

0

200

400

600

800

1000

1200

1400

0 20 40 60 80 100 120 140Time Step (day)

Dis

char

ge (m

3/s)

M RC(75-84)

M RC(85-94)

M RC(95-03)

Fig 8.4 Master Recession Curves (Linear Storage) using arithmetic mean of K

8.3.1.1.2 Non-Linear Storage

The recession of non linear reservoir is described by Qt = Qo [ ] )1/(11)1(

1 −−−

+ bb

o tab

Qb.

Taking 0.5 as the value b, the factor a is determined for each recorded year. Then average

values for each 10-year interval are determined.

Table 8.3 Factor a of Nonlinear Storage

Year a (m3-3bsb) Year a (m3-3bsb) Year a (m3-3bsb)

1975 8982.635 1985 9152.384 1995 8384.035

1976 9527.531 1986 8099.347 1996 5526.07

1977 11768.06 1987 7600.866 1997 9735.731



1978 8800.729 1988 8018.535 1998 7300.286

1979 9946.61 1989 8615.39 1999 7038.592

1980 12789.63 1990 8513.39 2000 7419.669

1981 8161.268 1991 10413.7 2001 7106.65

1982 9609.714 1992 12465.39 2002 7937.687

1983 7257.283 1993 11343.65 2003 7359.071

1984 8483.052 1994 9193.001

Table 8.4 Average factor a of Nonlinear Storage

Period Average a

(m3-3bsb)

Average a

(mm1-bdb) Non-Linear Storage Equation

1975-1984 9532.651 32.43 Qt = Qo [ ] 25.0

5.0*651.95325.0

1 −+ tQo

1985-1994 9341.616 31.78 Qt = Qo [ ] 25.0

5.0*616.93415.0

1 −+ tQo

1995-2003 7534.199 25.63 Qt = Qo [ ] 25.0

5.0*199.75345.0

1 −+ tQo

Master Recession Curves (Non Linear)

0

200

400

600

800

1000

1200

1400

0 20 40 60 80 100 120 140

Time Step(days)

Dis

char

ge (m

3/s) M RC(75-84)

M RC(85-94)

M RC(95-03)

Fig 8.5 Master Recession Curves (Non-linear Storage) using arithmetic mean of a



8.3.1.1.3 Verification of Master Recession Curves

The master recession flow curves obtained above are verified with the selected years

whose k values are a little bit close to the average ones of each period.

Observed and Calculated Recessions (1975-1984)

0

200

400

600

800

1000

1200

1400

1600

0 10 20 30 40 50 60 70 80Time Step (day)

Dis

char

ge (m

3/s) Observed

(76)

Linear

Nonlinear

Fig 8.6 Verification MRC by simple arithmetic Mean (1975-1984)


840

860

880

900

920

940

960

980

1000

1020

0 5 10 15 20 25 30Time Step (day)

Dis

char

ge (m

3/s) Observed

(94)

Linear

Nonlinear





0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 10 20 30 40 50 60Time Step (day)

Dis

char

ge (m

3/s) Observed

(00)

Linear

Nonlinear


According to the result fitted by above method is quite different from the observed ones

because this is just an approximation of average k value for MRC and was the first trial of

approach to define the master recession constant. It is clearly seen that this simple

average value of k does not provide the reasonable result and fit well to the observed data.

8.3.1.2 Determination of Average K fitted by Matching Strip Method

In this section the matching strip method is applied to position the integrated recession

portions of the specific duration. First recession parts of each hydrograph having the

smallest values of discharge are plotted. Using the recession curve with the next smallest

values, the curves are positioned such that it appears to extend a long a line coincident

with the recession of the first event plotted. This process is continued using successively

larger magnitude recessions until all storm events are plotted. Then master depletion curve

that comes from the average values of storm event with every time step and extend

through the recessions of the observed storm events was constructed. In the positioning of

last 10-year interval, year 1995 and 1996 were omitted as their recession portions have

many disturbances and they are difficult to be fitted.

Here three master recession curves for each 10-year interval are prepared using above

method as shown in Fig 8.9, 8.10 and 8.11. Finally the obtained master recession curves

are fitted both by linear and non-linear storage equations.



0

200

400

600

800

1000

1200

1400

1600

0 20 40 60 80 100 120 140 160

Time Step (day)

Dis

char

ge (m

3/s)

1978

1983

1982

1984

1979

1981

1977

1976

1980

1975

Fig 8.9 Positioning of recession curves (1975-1984)

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 20 40 60 80 100 120 140

Time Step(day)

Dis

char

ge (m

3/s)

1985

1987

1993

1994

1986

1988

1990

1989

1992

1991




0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 20 40 60 80 100 120 140 160

Time Step (day)

disc

harg

e (m

3/s)

2003

1995

2000

1996

1998

2002

1999

1997

2001


8.3.1.2.1 Linear Storage

The linear storage model is given by S = k.Q, where S is storage, Q is discharge and k is in

time unit. This assumption is approximately applicable in the nature e.g. Groundwater or

Retention of the catchment. The hydrograph of the linear storage is expressed by the

exponential function: Qt = Qo. exp (-t/k) where k is recession constant in days.

Master recession constants for each 10-year interval are calculated using linear relation

and then master recession curves for each interval are prepared using calculated

recession constants.

Table 8.5 Master Recession Constants by Linear Storage

Period Master Recession Constant. K

(days) Linear Reservoir Equation

1975-1984 157.949 Qt = Q0.exp (-∆t/157.949)

1985-1994 134.202 Qt = Q0.exp (-∆t/134.202)

1995-2003 113.3361 Qt = Q0.exp (-∆t/113.3361)



0

200

400

600

800

1000

1200

1400

0 20 40 60 80 100Time Step (day)

Dis

char

ge (m

3/s)

!975-1984

1985-1994

1995-2003

Fig 8.12 Master Recession Curves (Linear)

8.3.1.2.2 Non-Linear Storage

The conventional exponential function of the linear reservoir (Maillet, 1905) is still widely

used to describe flow recession. However, the analysis of observed flow recession of rivers

shows that the value of the “reservoir constant” or “recession constant” is not constant, but

increasing generally with falling flow (e.g. Wittenberg, 1994; Moore, 1997). Consequently ,

a non linear storage-outflow relationship ( Schoeller, 1962; Wittenberg, 1994) is applied in

all case studies for the upper aquifers involved in the annual water cycle: S = a Qb where S

is storage, a and b are factors. And the recession of non linear reservoir is described by Qt

= Qo [ ] )1/(11)1(

1 −−−

+ bb

o tab

Qb.

The factor ”a” for each 10-year interval were calculated using above non linear relation

taking the factor “b” 0.5 and then master recession curves for each interval were prepared

using calculated recession constants.



Table 8.6 Master Recession Constants by Nonlinear Storage

Period Factor a

(m3-3bsb)

Factor a

(mm1-bdb) Nonlinear Reservoir Equation

1975-1984 9485.87 32.27 Qt = Qo [ ] 25.0

5.0*87.94855.0

1 −+ tQo

1985-1994 8694.58 29.58 Qt = Qo [ ] 25.0

5.0*58.86945.0

1 −+ tQo

1995-2003 7322.08 24.91 Qt = Qo [ ] 25.0

5.0*08.73225.0

1 −+ tQo

0

200

400

600

800

1000

1200

1400

0 20 40 60 80 100Time Step (day)

Dis

char

ge (m

3/s)

!975-1984

1985-1994

1995-2003

Fig 8.13 Master Recession Curves (Nonlinear)

8.3.1.2.3 Verification of Master Recession Curves The master recession flow curves theoretically obtained above are verified with the

corresponding observed master recession curves which represent the average value of

each time step from the observed data of the years selected for different periods.




400

600

800

1000

1200

1400

1600

0 20 40 60 80 100 120 140 160

Time Step (day)

Dis

char

ge (m

3/s)

Observed(75-84)

Linear

Non-Linear

Fig 8.14 Verification of MRC by positioning of integrated Recessions (1975-1984)


400

600

800

1000

1200

1400

1600

1800

2000

0 20 40 60 80 100 120 140

Time Step (day)

Dis

char

ge (m

3/s)

Observed(85-94)

Linear

Non-Linear





400

600

800

1000

1200

1400

1600

1800

2000

0 20 40 60 80 100 120 140

Time Step (day)

Dis

char

ge (m

3/s)

Observed(95-03)

Linear

Non-Linear


By comparing the observed master recession curves with the calculated ones given by

both linear and nonlinear reservoir equations, it is found that nonlinear reservoir provides

the best fit result to the observed storm events and it is more likely close to the actual

groundwater contribution in nature.

Ground water flow and hence stream flow in rivers appears more related to storage

properties and subsurface hydraulics rather than to concentration times and pathway of the

surface watershed (Wittenberg).

8.3.2 Evaluation of Master Recession Curves No matter how both storage equations fit to the observed value, the dominant change of

recession curves’ pattern can be clearly found that flow recessions decreased gradually

according to the time. It is evident that parameter k and a fitted to different discharge

ranges of the recession curves do not remain constant but decrease systematically with the

decrease of stream flow with respect to the different time interval in the study period.

Then according the condition of master recession curves, it can be easily seen that ground

water contribution of the Chindwin Basin is gradually decreased with the time since 1984

and rapidly dropped during last interval between 1995 and 2003. So it is very dominant that

low flow recession characteristic of the last period (1995-2003) is the lowest during the

recorded data length. It is likely to be suffered much by a big impact of water resources or

seasonal variations during this interval. In this section, only the change of the low flow



patterns in terms of ground water contribution is mainly focused rather than to predict the

exact MRC constant as precise as possible.

Variability as well as less reliability of the result could be remarked as the followings:

(a) If the stream flow is gauged carefully and consistently with the standard form and

the regime of the above the gauging station is not disturbed, then the result could

be found more reliable.

(b) The method applied to determine the MRC constant is based on just taking the

recessions of each year by seeing the hydrograph without making base flow

separation to define the actual turning points.

(c) Collected data length is not so much and determination of the MRC constant is

applied only for each 10-year interval as well.

Chapter 9. Low Flow Frequency Analysis 82 Mtr.No.158204


Chapter 9. Low Flow Frequency Analysis 9.1 Introduction For water resource management and planning it is of vital importance to asses how likely

or probable it is that an extremely hydrological event may occur. Frequency analysis is one

of the most common and earliest applications of statistics within hydrology. It involves (a)

definition of the hydrological event and extreme characteristics to be studied, (b) selection

of the extreme events and probability distribution to describe the data, (c) estimation of the

parameters of the distribution, and (d) estimation of extreme events or design values for a

given problem. The procedure is straightforward, but the uncertainty of the estimated

extreme values depends strongly on the sample size and the basic assumptions of the

model adopted. Hydrological time series typically range between 20 and 50 years, and thus

hydrological design often requires extrapolation beyond the range of observations. One of

the main purpose frequency analyses is to find the most suitable probability distribution to

describe the data in question.

In the study of hydrologic drought, different techniques have to be adopted for study of

surface water deficit and ground water deficit. The surface water aspect of drought studies

is essentially related to the stream flow. The objective of low flow frequency analysis of

Chindwin river is to investigate the characteristic of low flows and to predict the expected

low flow occurrences with the different return periods using different probability

distributions.

In this chapter, firstly plotting of average annual minimum flows such as NM1Q, NM7Q,

NM14Q and NM30Q with empirical return periods is carried out for the whole recorded

period namely 30 years. And frequency curves are drawn and analyzed for different time

reaches such as 15-year and 10-year periods to study the condition of low flow in each

interval.

Finally the plotting position of 7-d low flow frequency curve is fitted by distribution functions

and the best fit one is derived using method of least square which provides least standard

errors of the selected distributions. Then expected low flows are estimated using different

distribution functions. A flow index, such as the 7Q10 flow can be interpreted as the 7-day

low flow with a 10-year return period, using daily discharge data.

9.2 Study Area and Data In the country low flow frequency analysis is somehow left to take account into

consideration while some hydrologic studies regarding to the flood in Chindwin river are

mostly carried out. So low flow frequency analysis of Chindwin river at Monywa station is



focused in this section. Daily stream flows (m3/s) from Monywa station are firstly collected

and managed. Then average minima series are used for the study. For low flow frequency

analysis, average annual 7-day minimum flows (NM7Q) are used rather than 1-day

minimum flows (NM1Q) in order to avoid the possible errors.

9.3 Mean Annual Minimum Flow One of the most frequently applied low flow indices is derived from a series of the annual

minima of the n-day average flow. In its simplest form this would be the mean annual 1-day

flow, hence the average of the annual minimum value. For n>1, the method consists of

deriving a hydrograph whose values are not simply daily flows but are average flows over

the previous n-days or alternatively the previous n/2 days and the coming n/2 days. The

derived data can thus be regarded as the outcome of passing a moving average filter of n-

day duration through the daily data. Here mean annual minimum discharges such as 1-

day, 7-day, 14-day and 30-day are derived and listed in Table 9.1.

9.4 Plotting Position of Average Low Flows The different minimum average flows, such as 1-day, 7-day, 14-day, 30-day, are

determined using moving average method in Excel and arranged in decreasing order for

different return periods T = (n+1)/(n+1-m) with the largest sample magnitude with m=1 and

the smallest sample magnitude with m=n (H. Wittenberg).

Table 9.1 Average minimum flows (m3/s) arranged in decreasing order

Rank NM1Q NM7Q NM14Q NM30Q Return Period, T (Year) Log T 1 1039 1047 1082 1146 1.03 0.014 2 981 998.7 1022 1085 1.07 0.029 3 907 913.1 927.2 982.4 1.11 0.044 4 895 905 925.4 981.6 1.15 0.06 5 852 865.7 884 914.7 1.19 0.076 6 798 800.6 827.9 868.1 1.24 0.093 7 790 795.7 811.6 843.8 1.29 0.111 8 783 788.6 803 840.3 1.35 0.13 9 744 774.4 799.4 816.4 1.41 0.149

10 736 768.4 790.7 809.3 1.48 0.169 11 723 759.7 785.1 802.9 1.55 0.19 12 711 715.6 728.4 784.8 1.63 0.213 13 684 689.9 720.4 763.3 1.72 0.236 14 672 685.3 701.7 738.1 1.82 0.261 15 672 676.4 687.7 731.2 1.94 0.287 16 660 673.3 687.5 716.4 2.07 0.315 17 654 669.4 684.9 716.1 2.21 0.345



18 650 668.6 682.5 693.1 2.38 0.377 19 646 658.1 676.6 691.7 2.58 0.412 20 632 654.6 657.9 669.7 2.82 0.45 21 617 636.3 650.1 667.3 3.10 0.491 22 613 622.3 629.7 654.1 3.44 0.537 23 610 614.1 626.2 652.9 3.88 0.588 24 608 612.6 624.6 652 4.43 0.646 25 601 608.4 621.8 637.2 5.17 0.713 26 591 595.6 613.8 631.2 6.20 0.792 27 530 539.3 565.8 605.5 7.75 0.889 28 512 535.3 550.4 591.1 10.33 1.014 29 480 500.9 515.8 565.7 15.50 1.19 30 440 463.3 484.8 542.4 31.00 1.491

Low flow analysis w ith emperical TChindwin river at Monywa station (1975-2004)

0

300

600

900

1200

1.00 10.00 100.00Return period T (year)

Ave

rage

ann

ual l

ow fl

ow Q

(m3/

s)

NM 1Q

NM 7Q

NM 14Q

NM 30Q

Fig 9.1 Low flow analysis with empirical return periods

9.4.1 Frequency Curves of 15-Year Time Reaches Here two frequency curves of NM7Q are developed for first 15-year reach and second 15-

year reach of the collected data series which have the data length of 30 year, from 1975 to

2004 so that low flow patterns during these periods are examined.

First 15-year reach, from 1975 to 1989, and second 15-year reach, from 1990 to 2004, are

separately drawn and analyzed.

Annual minimum low flow data for first 15-year reach are arranged in decreasing order and

corresponding return periods are calculated. Table 9.2 shows the low flows and their return

periods in the first half of the data length.



Table 9.2 Annual average low flow (m3/s)and return period in the first 15-year reach

Rank

(m) NM7Q T (Year) Log T

Rank

(m) NM7Q T (Year) Log T

1 905 1.067 0.028 9 668.6 2.286 0.359

2 800.6 1.143 0,058 10 654.6 2.667 0.426

3 795.7 1.231 0.09 11 622.3 3.2 0.505

4 788.6 1.333 0.125 12 614.1 4 0.602

5 759.7 1.455 0.163 13 608.4 5.333 0.727

6 715.6 1.6 0.204 14 595.6 8 0.903

7 676.4 1.778 0.25 15 539.3 16 1.204

8 669.4 2 0.301

Then annual minimum low flow data for the second 15-year reach are arranged in

decreasing order and respective return periods are calculated. Table (9.3 ) shows the low

flows and their return periods in the second half of the data length.

Table 9.3 Annual average low flow (m3/s)and return period in the second 15-year reach

Rank m NM7Q T (Year) Log T Rank

m NM7Q T (Year) Log T

1 1047 1.067 0.028 9 673.3 2.286 0.359

2 998.7 1.143 0.058 10 658.1 2.667 0.426

3 913.1 1.231 0.09 11 636.3 3.2 0.505

4 865.7 1.333 0.125 12 612.6 4 0.602

5 774.4 1.455 0.163 13 535.3 5.333 0.727

6 768.4 1.6 0.204 14 500.9 8 0.903

7 689.9 1.778 0.25 15 463.3 16 1.204

8 685.3 2 0.301

After that, plotting of these data for two time reaches are drawn and analyzed to see the

changes of low flow condition which might have suffered by the environmental impact in

the basin area. Plotting positions for both time reaches are shown in Fig 9.2.



Low Flow Frequency Curves for ach 15-year Period

0

200

400

600

800

1000

1200

1 10 100Return Period T (Year)

NM

7Q (m

3/s)

NM 7Q(75-89)

NM 7Q(90-04)

Fig 9.2 Low Flow Frequency Curves for first and second half of the Data Length

According to the graph, low flows in the second 15-year period are more likely to decrease

with return periods especially after the return period of 4-year.

9.4.2 Frequency Curves of 10-Year Time Reaches Apart from the analysis in section 9.4.1, frequency curves of NM7Q for 10-year interval are

prepared to have a clearer picture of the changes of low flows. Data length of 30 years was

divided into three portions namely first interval (1975-1984), second interval (1985-1994)

and third one (1995-2004). Then annual NM7Qs are arranged in decreasing order and

corresponding return periods are determined by using plotting position. Drought

discharges, 7Q10, are also determined as the low flow indices to be compared.

Table 9.4 Annual average low flows (m3/s)and return periods in the first 10-year reach

Rank

(m) NM7Q

Return Period, T

(Year) Log T

1 905 1.1 0.041 2 800.6 1.222 0.087 3 795.7 1.375 0.138 4 759.7 1.571 0.196 5 715.6 1.833 0.263 6 676.4 2.2 0.342 7 668.6 2.75 0.439 8 654.6 3.667 0.564 9 608.4 5.5 0.74

10 539.3 11 1.041



Table 9.5 Annual average low flows (m3/s)and return periods in the second 10-year reach

Rank

(m) NM7Q

Return Period, T

(Year) Log T

1 1047 1.1 0.041

2 998.7 1.222 0.087

3 913.1 1.375 0.138

4 865.7 1.571 0.196

5 788.6 1.833 0.263

6 669.4 2.2 0.342

7 658.1 2.75 0.439

8 622.3 3.667 0.564

9 614.1 5.5 0.74

10 595.6 11 1.041

Table 9.6 Annual average low flows (m3/s)and return periods in the third 10-year reach

Rank

(m) NM7Q

Return Period, T

(Year) Log T

1 774.4 1.1 0.041

2 768.4 1.222 0.087

3 689.9 1.375 0.138

4 685.3 1.571 0.196

5 673.3 1.833 0.263

6 636.3 2.2 0.342

7 612.6 2.75 0.439

8 535.3 3.667 0.564

9 500.9 5.5 0.74

10 463.3 11 1.041

Table 9.7 Drought Discharge (7Q10) for each Period

Period 1975-1984 1985-1994 1995-2004

7Q10 (m3/s) 551.86 598.96 470.14



Low Flow Frequency Curves for ach 10-year Period

0

200

400

600

800

1000

1200

1 10 100Return Period (Year)

NM

7Q (m

3/s) NM 7Q

(75-84)

NM 7Q(85-94)

NM 7Q(95-04)

Fig 9.3 Low Flow Frequency Curves for each 10-year period of the Data Length

Drought discharge (7Q10) values and the pattern of curves provide clearer picture and

indicated the same low flow characteristic like other analysis showing the tendency of low

flow occurrence is the highest in the last period.

9.5 Fitting of Low Flow Frequency Curve by Distribution Functions Low flow frequency curves may be fitted mathematically by assuming a theoretical

frequency distribution of the data. Here curve fitting is carried out only for Low flow

frequency curve (NM7Q) of the whole period, 30 years, obtained from plotting position.

Statistical parameters of the NM7Q series are shown below.

Mean = 707.8733 m3/s

Standard Deviation = 139.4771 m3/s

Skewness = 0.646802

Frequency factor method for low flow analysis is X = X - K. γ ( H. Wittenberg) Where

X = Minimum flow

X = Mean of the data series

K = frequency factor γ = Skewness coefficient

According to Kite (1970), three distributions are suitable for the analysis of minimum events

such as low flows. They are:

(i) Three-Parameter Lognormal Distribution

(ii) Pearson Type III Distribution



(iii) Extreme Value Type III Though all three functions are suitable, the results can show considerable differences.

Thus it is strictly recommended to calculate with all three functions.

9.5.1 Three-Parameter Lognormal Distribution Here frequency factor for 3-Parameter Lognormal distribution can be calculated by

following equation.

K = { } { }

2

22

2/122

z

0.12/)z1ln(t.)z1ln(exp −⎥⎦⎤

⎢⎣⎡ +−+

Z2 = 3/1

3/21ωω−

ω = 2

)4( 2/1211 +γ+γ−

Ү1 is the coefficient of skew. Frequency factors for 3-Parameter Lognormal distribution are shown in Appendix-D. Note

that at Ү1=0 the frequency factor k is zero for all return periods. The 3-Parameter

Lognormal is thus not a suitable distribution for use with data samples having skews

approaching zero.

Then the expected low flows are calculated using frequency factor methods. The results

obtained by the distribution are given in table 9.8.

Table 9.8 Expected Low Flows given by 3-Parameter Lognormal Distribution

Return Period (Year)

2 5 10 20 50 100

k -0.0231 0.55362 0.90383 1.18127 1.50166 1.72015

Chindwin River at Monya Station Discharge

(m3/s) 698.25 624.505 583.597 553.106 519.865 498.354

9.5.2 Pearson Type III Distribution To find the frequency factor K for different values of skewness coefficient, compute the

value of

W = [ln T2]1/2 where T = 1/P



Y=W – (2.5255+0.80285.W+0.01033.W2) / (1+1.14328.W+0.1893.W2+0.00131.W3)

K = Y+(Y2-1). γ/6 +1/3(Y3-6Y).3 γ 2/36 -(y2-1). γ 3/216 +y. (γ /6)4 +1/3. (γ /6)5

where γ is skewness coefficient of the sample.

The Frequency factor values for Pearson type III are shown in Appendix-D. Then the

minimum flows with different return periods are given in table 9.9.

Table 9.9 Expected Low Flows given by Pearson Type III Distribution


1.01 2 5 10 20 50 100

k -1.815 -0.114 0.7912 1.3324 1.8163 2.4012 2.815


(m3/s) 961.01 723.76 597.51 522.03 454.53 372.95 315.14

9.5.3 Extreme Value Type III Distribution Droughts are analyzed by the asymptotic theory of smallest values of a limited statistical

variate. The theory of extreme value is also an appropriate tool for the analysis of droughts

which are defined as the annual minima of low flows. Shaw (1994) demonstrated that the

extreme value type III distribution of the smallest value is one of the most reliable and it is

recommended for the assessment of the frequency of annual minimum flows.

Frequency factor for EV III distribution is given by

K = Aα+Bα [ { -ln (1-1/T) } 1/α -1 ] and

Bα = { Γ(1+2/α) - Γ2(1+1/ α) } -1/2

Aα = { 1- Γ(1+1/ α) } Bα

Aα and Bα are the function of Gamma and the Gamma function is given by Appendix-D.

Parameter α, Aα and Bα for EV III distribution tabulated as a function of the sample

coefficient of skewness and frequency factors for different skewness are given in

Appendix-D. The calculated minimum flow data by EV III distribution are given in table

9.10.

Table 9.10 Expected Low Flows given by Extreme Value Type III Distribution


2 5 10 20 50 100

k -0.1252 -0.8923 -1.2015 -1.4042 -1.5758 -1.6598


(m3/s) 690.415 583.417 540.285 512.024 488.084 476.363



Graphical display of the results obtained by three distribution functions is also useful to see

approximately the best fit function and to judge the patterns of the frequency curves.

0

200

400

600

800

1000

1200

1 10 100

Return Period ( Yr )

Q (m

3/s)

Pearson EV III Lognormal Observed

Fig 9.4 Fitting of Low Flow Frequency Curve by three distribution functions

9.5.4 Selection of Distribution Function Relatively short return periods that do not greatly exceed the length of hydrological records

have often been sufficient in low flow design. This has led to a rather unrestricted use of

various distributions. Such an approach may give acceptable results if a prediction of

drought indices with a low return period is required. The estimates of events with higher

return periods will, however, always depend on the behavior of the tail of the fitted

distribution. The more parameters a distribution has, the better it will adapt to the data

sample, but the lower reliability of the estimate of the parameters will be. It is generally

recommended that the distribution has no more than three parameters ( Matalas, 1963 ).

Different goodness-of-fit test can be used for selection of a proper distribution functions.

9.5.5 Test for Goodness of Fit In the previous portions of this chapter attempts are made to fit a number of frequency

functions to each of the distribution of a sample of hydrological data. The question asked

and left without answer at the end of each attempt is whether the fit has been satisfactory

or not. The answer to this question is obtained by performing a test of goodness of fit which



is a mean of judging the credibility of a hypothesis concerning the population from which

the individuals of a sample are drawn.

Graphical methods are an efficient way to judge whether the fitted distribution appears

consistent with the data. The plots can be judged merely by visual inspection, or statistical

tests such as analytical goodness-of- fit criteria can be used to estimate whether a

departure, i.e. the difference between the ordered observations and the estimated quantile

from a theoretical distribution function, is statistically significant. Several measures are

available. Here least squares (Standard error) test is performed for the selection

distribution functions used in the previous analysis.

9.5.5.1 Method of Least Squares This method is to compare the standard errors of each distribution by computing the sum of

squares of the differences between calculated and observed discharge. According to Kite,

it is recommended that return periods of 2, 5, 10, 20, 50 and 100-years are enough to

check for low flows.

The standard error is given by

SEj = [j

n

1i

2ii

mn

)YX(

−

−∑= ]1/2

Where Xi = recorded events

Yi = event magnitudes computed from jth probability distribution

n = number of events

mj = number of parameters estimated for the jth distribution.

Here n is 6 ( six events at return periods of 2, 5, 10, 20, 50 and 100-year) and the mj is the

3 as the parameters estimated for the distributions are mean, standard deviation and the

skewness. The results are given in the table 9.11.



Table 9.11 Standard errors of selected distributions for different return periods

Return Period Observed Value, Yi Difference (Xi - Yi)2

(Year) LN(3) Pearson III EV III

Recorded Value,Xi LN(3) Pearson

III EV III

2 698.25 723.768 690.415 674.97 541.9584 2381.24 238.557

5 624.505 597.519 583.417 609.36 229.371 140.209 673.039

10 583.597 522.034 540.285 535.81 2283.597 189.778 20.0256

20 553.106 454.533 512.024 489.98 3984.892 1256.49 485.938

50 519.865 372.957 480.084 417.21 10538.05 1958.33 3953.14

100 498.354 315.147 476.363 295.92 40979.52 369.678 32559.7

Sum 58557.39 6295.73 37930.4

Standard Error 139.7109 45.8102 112.443

(Units of both observed and recorded values are in m3/s.)

According the ranking of the distributions by order of least standard error, Pearson type III

distribution provides the best fitting of distribution for the recorded data and the 3-

parameter lognormal distribution is the least fitted one.

9.5.6 Result of Expected Low Flows by best fitted Distribution According to the test for goodness of fit, Pearson type III is the best fit for the collected data

set and the low flow values given by this distribution will be used for future water resource

planning and management.

Table 9.12 Expected Low flows given by best fitted distribution (Pearson III)


1.01 2 5 10 20 50 100

k -1.815 -0.114 0.7912 1.3324 1.8163 2.4012 2.8157


(m3/s) 961.01 723.77 597.52 522.03 454.53 372.96 315.15



Low Flow Frequency Curve of Chindwin River by Pearson III

0

200

400

600

800

1000

1200

1 10 100Return Period (year)

Dis

char

ge (m

3/s)

Fig 9.5 Low Flow Frequency Curve of Chindwin River by Pearson III

Chindwin river has a critical water level of 1m providing 640 m3/s at which navigation is

impossible. According to the low flow frequency curve of Chindwin river, critical minimum

discharge 640 m3/s will occur once four years. Theoretically recommended drought

discharge, 7Q10 for the stream is found to be 522 m3/s. Minimum requirement for

navigation in the Chindwin river at Monywa station is higher than the theoretical drought

discharge during the period of the study.

3.7

640

522

Chapter 10. Miscellaneous Approaches 95 Mtr.No.158204


Chapter 10. Miscellaneous Approaches 10.1 Introduction

In the previous chapters the focus was on the low flow analysis based on the collected

daily discharge series. And some results have come out to see the low flow characteristics

of the Chindwin river basin especially at the Monywa gauging station. Besides it would be

more preferable to detect the possible influences on low flows in the river as much as

possible with the available information such as annual rainfall, mean annual temperature

and irrigation development in the study area which are probably relevant to the results

obtained by the previous analyses. Finally the relation between the low flow indices and the

changes of the condition in the area during the study period can be closely discussed and

evaluated.

10.2 Mass Curve Analysis

Cumulative annual data series are plotted against the time to see the trend of the curve

through which the changes of low flow patterns can be traced. Here three mass curves are

drawn for annual low flow and annual maximum flow and flow volume.

0

5000

10000

15000

20000

25000

1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Cum

ulat

ive

Min

Q (m

3/s)

S1=708.06

S2=646

Fig 10.1 Mass Curve of Cumulative Min Q



0

100000

200000

300000

400000

500000

600000

700000

1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Cum

ulat

ive

Max

Q (m

3/s)

Fig 10.2 Mass Curve of Cumulative Max Q

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Cum

ulat

ive

Volu

me

(m3.

109 )

Fig 10.3 Mass Curve of Cumulative Flow Volume

According the graphical presentation, it showed that mass curves of annual maximum and

flow volume indicated that there is almost no inconsistency of the data. But mass curve of

annual low flow series reflected that there was a change of trend after 1992 during the

entire study period. Especially in the later part of the study period, the possibility of lower

flows become strong as the slope of the curve deviates lower than the trend after 1992.



10.3 Impacts on Low Flow

10.3.1 Impact of Climate Change

In many regions climate change affects precipitation, temperature and potential

evapotranspiration having an effect on meteorological drought. There is a strong

interrelation between climate and the hydrological system. A change in one of the systems

will therefore induce a change in the other (Kundzewicz, 2002). Understanding the link

between the past and current droughts and climate and atmospheric circulation is therefore

not only a perquisite to understanding past drought characteristics and predicting the next

drought, it is similarly important for the assessment of the impact of climate change on the

characteristic of drought.

1000

1200

1400

1600

1800

2000

2200

2400

2600

2800

1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Rai

nfal

l (m

m) Annual

Rainfall

Average

Fig 10.4 Mean Annual Rainfall in Chindwin Basin

25.5

26

26.5

27

27.5

28

28.5

29

29.5

1970 1975 1980 1985 1990 1995 2000 2005 2010

Year

Tem

pera

ture

(°C

)

M eanAnnualTemp

Average

Fig 10.5 Mean Annual Temperature of Chindwin Basin (Monywa Station)



Annual rainfall and mean annual temperature are analyzed to see some relations with the

low flow occurrence in the region. Annual rainfall is the average of the seven rainfall

stations in the basin and mean annual temperature represents only Monywa station. Their

properties are checked with the standard deviation values.

Table 10.1 Standard deviation (Std.Dev.) Values of Collected Meteorological Data

Period Data Type

1975-1984 1985-1994 1995-2005

Std. Dev. of Annual Rainfall (mm) 149.3 237.0 155.1

Std. Dev. of Mean Annual Temperature (°C) 0.440 0.604 0.573

Thus collected meteorological data is found to have the smallest variation in the period of

1975-1984 and highest variation in the middle one, 1984-1995.

Annual rainfall and mean annual temperature data are then plotted accompanying with the

annual average low flow data (NM7Q). Also moving average data of annual rainfall series

are plotted. Here annual low flow data are picked up and the average low flows are

calculated according to the calendar year and all annual low flows occur in the later part of

the summer which is normally between March and May. So annual low flow of a year is the

effect of climate in the previous year. That’s why annual low flow data are plotted one year

backward to have a more correlation with meteorological condition of the area.

0

500

1000

1500

2000

2500

3000

1970 1975 1980 1985 1990 1995 2000 2005

Year

Rai

nfal

l (m

m)

0

300

600

900

1200

1500

NM

7Q (

m3/

s)

AnnualRainfall

7-YearAverage

NM 7Q

Fig 10.6 Annual Rainfall and Annual Average Low Flow (NM7Q)



0

200

400

600

800

1000

1200

1970 1975 1980 1985 1990 1995 2000 2005

Year

Ann

ual L

ow fl

ow (m

3/s)

)

25.5

26

26.5

27

27.5

28

28.5

29

29.5

30

Mea

n A

nnua

l Tem

pera

ture

(°C

)

NM7QTemp

Fig 10.7 Mean Annual Temperature and Annual Average Low Flow (NM7Q)

Here the pictures indicates that less low flows usually occurred during the time of high

temperature and less rainfall whereas the high low flows usually happen when temperature

decreased and rainfall increased. Interrelation between the annual low flows and

meteorological condition of the region is expressed by the correlation coefficients.

Table 10.2 Correlation Coefficient Matrix

Rainfall Temperature NM7Q

Rainfall 1.0 -0.681 0.655

Temperature -0.681 1.0 -0.763

Annual rainfall data is moderately related with mean annual temperature and annual low

flows whereas mean annual temperature is a little bit strongly related with annual low flows.

Here correlation coefficients are determined based on the moving average (7-year) data

rather than yearly data.

Then recession portions for each year are picked up and also checked. It is found that they

usually occur in the period which is normally between the month of December and March.

Mean monthly temperatures of these periods in which most recessions occurred are

determined for each 10-year interval and displayed in Fig 10.8



20

21

22

23

24

25

26

0 2 4 6 8 10 12

Time Step (year)

Mea

n M

onth

ly T

empe

ratu

re in

Rec

essi

on

Perio

ds (°

C)

1975-1984

1985-1994

1995-2004

Fig 10.8 Mean monthly Temperature of Recession Periods

22

23

24

25

1975-1984 1985-1994 1995-2004Time Interval

Mea

n M

onth

ly T

empe

ratu

re

(°C

)

Fig 10.9 Mean Temperatures of Recession Periods in every 10-year Interval

Mean monthly temperatures of yearly recession portions in the last period (1995-2004) are

clearly higher than that of other two periods although it is a little bit difficult to say the higher

one between the periods of 1975-1984 and 1985-1994. Then mean monthly temperatures

of the whole periods in which the recessions occurred were checked and shown in Fig

10.9. Mean temperatures of the first 10-year recession period (1975-1984) and second 10-

year period (1985-1994) are nearly the same and the mean temperature of the last 10-year

recession period (1995-2004) is the highest one. Above observations reflect the impact of

climate change on low flow conditions in the stream especially in the last 10-year interval of

the study period.



Moreover trend of climate change in the neighboring regions are checked to see whether

the climate change in the study area is related to regional change or not. Here mean

annual temperatures of Yangon (the capital of Myanmar), Bangkok (the capital of Thailand)

and New Deli (the capital of India) are analyzed.

20

22

24

26

28

30

32

1994 1996 1998 2000 2002 2004 2006Year

Mea

n A

nnua

l Tem

pera

ture

(°C

)

Yangon

New Deli

Bangkok

Chindw in

Fig 10.10 Comparison of Regional Mean Annual Temperatures

The trend of temperature change in Chindwin basin is similar to that of neighboring area,

especially quite similar to the trend of Yangon station. Correlation coefficient between

Chindwin basin and Yangon shows 0.8 which is meant that there has a somehow strong

relation. The trend of temperature change in study area is moderately related with that of

Bangkok due to the correlation coefficient, 0.54. It is found that there is a least relation

between the study area and New Deli because of the correlation coefficient, 0.14. It may

happen due to high variation of mean annual temperature in New Deli. But it can be

generally said that there has a increasing trend of temperature change in the region

according to the graph.

10.3.2 Impact of Land-Use Change

Population growth has led to extensive land-use change. Firstly, land cover contributes to

the amount of moisture in the atmosphere affecting precipitable water. Secondly, land-use

change influences interception, potential evapotranspiration, rooting depth and partitioning

between the overland flow and soil infiltration. All these processes have an influence on

actual evapotranspiration and recharge and finally groundwater response and streamflow

(Calder, 1992). It is likely that land-use change affects water tables and streamflows, thus

affecting hydrological drought.



0

2000

4000

6000

8000

10000

12000

1962

-89

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

Year

Year

ly Ir

rigat

ed A

rea

(ha)

Fig 10.11 Yearly Irrigation Development in the Chindwin Basin

Although the construction of dams and other irrigation facilities has been started especially

in the central Myanmar, the number of structures is very few and represents for the specific

area and does not cover the whole country. After 1990, the construction of dams,

reservoirs and other structures and projects related to the water supply for various

purposes has gained momentum through the country. There is no doubt that the amount of

cultivated area has increased with the high potential of water availability from those

completed hydraulic structures. As a result, much amount evapotranspiration from these

cultivated areas lower the groundwater level continuously causing the faster (steeper)

recessions and finally may lead to streamflow drought.

0

10000

20000

30000

40000

50000

60000

1962

-89

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

Year

Cum

ulat

ive

Irrig

ated

Are

a (h

a)

Fig 10.12 Cumulative Irrigation Development in the Chindwin Basin



In Myanmar the statistics normally shows the progress of irrigation development in local

wise and it does not provide the irrigation development in terms of river basin area.

Chindwin river basin is located mostly in the upper Sagaing division. Here the increase of

cultivated areas provided by reservoirs in Sagaing division is assumed and considered as

of the Chindwin basin for an easy way to determine the cultivated area. Pumping irrigation

projects along the Chindwin river can be found and considered altogether. Detail list of

Irrigation development is shown in Appendix-A.

According to the Fig 10.11, the agriculture did not play a vital role in the area till 1989. Then

irrigation sector had a progress which amount to 27% of the total cultivated area during the

period of 1989-1994. The irrigation in the last period, 1995-2004, gives the high peak and

covers about 70% of the total irrigated area. That situation clearly shows that much amount

of evapotranspiration can be lost in this period compare to other periods and finally the

large change in land use may lead to the lowering the groundwater table.

Chapter 11. Discussion, Recommendation and Conclusion 104 Mtr.No.158204


Chapter. 11 Discussion, Recommendation and Conclusion 11.1 General

Large basins without human influence hardly exist. This fact imposes constraints on

drought analysis. Human activities make the multifaceted relationship between

meteorological and hydrological droughts even more complicated. They may enhance

natural hydrological drought. For instance, a soil moisture drought in a semi-arid region

requires additional irrigation. This water may come from surface water, and the abstraction

of water implies low reservoir levels or streamflow enhancing surface water drought.

Irrigation water can also be abstracted from groundwater leading to low water tables and

reduced groundwater discharge. This may enhance an already existing groundwater

drought and also contribute to surface water drought.

Human activities can cause drought. Groundwater abstractions for domestic and industrial

use are a well-known example of such an environmental change. These permanent

abstractions lead to lowering of water tables and reduce groundwater discharge. A

hydrological drought can even develop, which would not have shown up without

abstractions. Construction of a reservoir could also induce development of stream flow

drought downstream of the dam. Some human activities are meant to reduce water excess,

but unintentionally they continue to drought development. An example is land drainage.

Like groundwater abstractions, land drainage causes permanently lower water tables

making the region more susceptible to drought.

11.2 Discussion

Downstream portion of the Chindwin basin is located in the dry zone of the country

whereas the upper most portion of the basin has the much amount of rainfall and relatively

less temperature. Meteorologists monitor the extent and severity of drought in terms of

rainfall deficiencies. Agriculturists rate the impact on soil moisture, hydrologists compare

runoff rate and sociologists define it on social expectations and perceptions. This study is

indicating that discharge rate over the basin is in decreasing state with respect to the time.

Although the hydrologic data tests provided reasonably consistent and homogeneous

according to the result, some disturbances or errors are found during the recession periods

without rain. It might occur due to human errors regarding to the measuring techniques.

From duration curve and frequency curve drought discharges such as EFQ90 and 7Q10 are

interpreted and then percentile value of the period and return period for the critical depth of

the stream especially for navigation are determined. This minimum requirement of water



depth is relevant to the value of EFQ97 which is expected to be equal or exceeded 97 % of

the study period. Furthermore from the frequency analysis, best fit distribution was Pearson

III distribution especially between return periods of 2 and 100 years. Using Pearson III

distribution, low flow frequency curve for Chindwin river at Monywa station can be drawn

and critical depth, 1m for navigation is expected to occur once four years. In the

preparation of frequency curve logarithmic scale is used rather than probability scale.

In the recession curve analysis non-linear function is found to be more relevant with the

actual ground water contribution. Recession property has decreased with the time and in

the last 10-year interval recession curves are significantly lower than that of other periods.

According to the study these indices have indicated the same picture of the low flow

condition of the Chindwin basin that the tendency of low flow occurrence has increased

gradually with the time and the occurrence of the low flow is the lowest in the last 10-year

interval (between 1995-2004) of the whole study period which start in 1975 and ends in

2004. Then these results are necessarily to be checked with other available information in

the study area so that possible reasons or correlations could be found.

Flow recession properties are subject to seasonal variation and changes due to

evapotranspiration and other fluxes and abstraction from ground water. Impacts of seasons

like meteorological changes and other influences on flow recessions are described to meet

the result of the analyses in the previous chapters. Here impact of climate change and land

use change, especially development of the cultivated area are mainly focused relevant to

the results of the study.

Meteorological data such as annual rainfall of the basin area and mean annual temperature

of the Monywa gauging station are observed. Climatic change during the study period is

found that there was a decrease in rainfall and increase in temperature especially after the

90’s causing the corresponding low flows in the same year. The result shows that the

pattern in changes of annual low flows is generally similar to the change in annual

precipitation and temperature. Especially in the last 10-year interval of the study period, the

mean temperature increased rapidly. As a result regional warming encourages the high

potential evapotranspiration. That situation can lower the groundwater level and might lead

to the high possibility of low flow occurrence in the stream. That picture coincides the

results obtained from the determination of low flow indices.

Irrigation development could also be a critical factor because much amount of

evapotranspiration is lost during the irrigation season. Intensification of irrigation with

pumped ground water could also be a reason for this change. It is sure that the country has

rapidly gained momentum in the construction of irrigation facilities such as dams,

reservoirs, pumping irrigation projects etc. throughout the country for agriculture purpose



since 1990. From 1962 to 1989 the irrigation development in the region indicates only 3%

of the total cultivated area of the Chindwin basin. Then agriculture sector has increased

gradually during the middle period 1989-1994 giving the amount of 27% of the net

cultivated area. In the last 10-year period, from 1995 to 2004, the cultivated area in the

region has reached the peak figure which constitutes 70% of the total cultivated area.

There was a change or progress in vegetation of the area. This situation might show that

the enormous amount of surface and/or groundwater is maintained and extracted in the

basin and the potential of groundwater reservoir contribution has decreased. On the other

hand, up to year 2004 total amount of cultivated are about 50000 ha (500 km2) which is

only 0.43% of the catchment area, 115300 km2. So this irrigation development could not

strongly affect to the steeper low flows in the region.

Annual deforestation rate of Chindwin basin was roughly estimated and it showed only

about 1 % between 1990 and 1995. It can not affect the low flow occurrence. Reforestation

program hast started since 1995 in the dry zone of Myanmar which also cover the lower

part of the Chindwin basin. It surely affect the high evaporation loss and lead to the lower

stream flows. But exact contribution of the reforestation rate in the area could not be

analyzed due to the lack of information.

Besides there may be other man-made impacts which can be taken into consideration for

low flows studies such as impact of surface water control, impact of groundwater

abstraction and impact of urbanization. Here these impacts could not be analyzed due to

the lack of information and but could be discussed theoretically.

Many rivers, lakes and reservoirs have been modified to serve various purposes, such as

improving navigation, reducing floods, energy production, enhancing low flows, supplying

drinking water, providing wildlife habitat, and increasing the possibilities for recreation.

Many of these modifications may affect streamflow drought. Reservoirs have an important

effect on the streamflow hydrograph.

Groundwater abstractions may initiate or enhance hydrological drought. Abstraction leads

to lower water tables and consequently to lower spring yields and groundwater flow to

streams. It may cause both groundwater and streamflow droughts.

Emigration from rural to urban areas has occurred everywhere, and still continues in most

developing countries. The provision of water supply, sanitations and drainage are key

elements of the urbanization process. Urbanization also involves a huge demand for water.

This water may be supplied from aquifers beneath the city and its surroundings or it may

be imported from other catchments at a distance. Where groundwater is abstracted in or

near the city it influences hydraulic heads of aquifers beneath the city and water tables in

superficial layers.



As a whole, there are three indices obtained in this study for characterizing low flow

regimes and droughts. These indices show their properties themselves to express different

aspects of drought. As a result, the high potential of low flow occurrence in Chindwin river

at Monywa station could happen due to the high seasonal variation and rapid increase of

cultivated area in the region through which much evapotranspiration are lost from

groundwater storage.

11.3 Recommendation

The study is carried out for the determination of low flow indices using mean daily

discharge. The most significant low flows occur during the period of last 10-year interval.

Concerning with the analysis, following activities are recommended to be implemented.

For duration curve and frequency analysis the probability scale should be used in graphical

presentation so that better frequency curves are obtained with all possible information.

In recession analysis, base flow separation should be carried out to know the turning points

of the recession and in order to determine also the base flow index and the groundwater

storage if necessary.

The curves representing the recession flows are derived both from linear and nonlinear and

then the calculated recessions given by the nonlinear reservoir is found to be close to the

actual occurrence of groundwater contribution. Master recession constant for the whole

recorded length, 30 year, should also be determined as an index of low flow and for a short

forecasting of dry weather flow.

Since the recession property varies with the seasonal changes, flow recession analysis

should be carried out in the very different seasons if possible, i.e. in the winter as well as in

the summer whose mean temperature difference is quite distinct. In fact it was the first

approximation of the depletion flows at only one gauging site and result may be regarded

as the preliminary assumption regarding to the precise master recession constant.

Other gauging stations i.e. all sub basins of the Chindwin catchment should also be

conducted by same analyses in order to know how the results are fitted and to find the

interrelations between low flow indices of all stations in the basin.

Since all the analyses mainly based on the basic records collected at the Monywa gauging

station, accuracy of the results virtually lies on the reliability of that basic information. In

presence of this problem, more reliable and accurate flow data are recommended to

collect. Constructive criticism followings the finding at the fields would be complimentary to

further processing for more accurate presentations.



Moreover all possible impacts should be found out and analyzed in order to detect all

possible causes for drought in the stream flows. Besides types of vegetation, deforestation

and reforestation should be examined in all sub basins so that severity of drought situation

can be monitored with time and space.

Due to the high temperature, only low water demanding crops should be introduced in the

area to reduce the evapotranspiration losses which may lead to the high ground water

abstraction.

This study will be helpful to the sustainable development of socio-economic condition in the

region in order to protect and preserve the environment including soil and water resources

and to provide the basic water demand of the region.

Finally the present way is anyhow believed to give basic methodology for the low flow

analysis in the region and to provide useful information for proper planning of water

resources management activities.

Usefulness of low flow indices obtained in this study for future water resources

management and planning in the region is summarized in the following table.

Table 11.1 Summary of drought Characteristics and Indices for water Resources and

Drought Assessment (Gustard et al; 1992) (Source : DWS 48)

Regime Measure Property Described Data Employed Applications

Flow Duration

Curve

Proportion of time a

given flow is exceeded

Daily flows or

flows averaged

over several days,

weeks or months

General regime

definition; licensing

abstractions (water

right) or effluents

(discharge consents);

hydropower design

Annual Minima

Series of

Frequency curve

Proportion of years in

which the mean

discharge ( of a given

duration) is below a

given magnitude

Annual minimum

flows –daily or

averaged over

several days

Drought return period;

preliminary design of

major schemes; first

step in some

storage/yield analysis

Recession

Indices

Rate of decay of

hydrograph

Daily flows during

dry periods

Short-term forecasting;

hydrogeological

studies; modeling



11.4 Conclusion

This master thesis explores the low flow characteristics of the Chindwin river at Monywa

gauging station. Moreover the study tried to find the some correlations between the

obtained low flow indices and natural and human impact on hydrological drought. But it

does not try to explain how operational water management might to prevent (proactive

approach) or to mitigate (reactive approach) drought. Human activities certainly affect

water quality as well as water quantity. Concentration of many critical water-quality

constituents, such as nutrients and dissolved oxygen, are related to discharge. Soluble

pollutants often show a negative correlation with discharge, whereas for dissolved oxygen

it is the opposite implying that drought leads to poor water quality. Thus this impact on

water quality will be a big issue for further study in the country.

Still non-climatic changes may have a greater impact on the natural system than climate

change. Dams, diversions and abstraction of surface water, change in land use, extensive

use of irrigation, but also industrial discharge to river, can greatly modify the quantity and

quality of streamflow. Yet despite, or rather because of, all those possible influences to the

hydrological cycle, the understanding of the natural drought phenomenon and its

meteorological and hydroclimatological causes are essential for a considerate

management of our limited water resources now and in the future.

REFERENCES 110 Mtr.No.158204


REFERENCES

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Technology,1964.

2. Deutsches IHP/OHP-Nationalkomitee “Statistical Analysis in Hydrology”, Material

prepared for training courses, A contribution to the Hydrological Operational

Multipurpose Subprogramme (HOMS) of WMO, Sonderheft 2, Koblenz 1986.

3. Haan, C.T “Statistical Methods in Hydrology”, Third printing 1982.

4. Jensen, Jürgen “Über Instationäre Entwicklungen der Wasserstände an der

Nordseeküste”, 31. October, 1985.

5. Kite, G.W. “Frequency and Risk Analyses in Hydrology”, Water Resources

Publication,1977.

6. Khin Cho Cho Shein and Ohn Gyaw “A Study of Agroclimatological Phenomenon

in the Dry Zone”, J. Myan. Acad. Tech. 3(1), 1-16, 2003.

7. McCuen, Richard H “Hydrologic Analysis and Design”, Second Edition, 1998.

8. Maung Aung Moe “ Drought Studies on the selected Rivers in Myanmar”,

December, 1998

9. Ministry of Agriculture and Irrigation, Union of Myanmar “ Draft on Strategic Plan

of Integrated Water Resources Management in Myanmar”, September, 2004.

10. Ni Lar Aye “ Flood Regionalization using Rainfall and Basin Characteristics of

Catchments”, June, 2001.

11. Ponce, Victor Miguel “Engineering Hydrology, Principles and Practices”, 1989

12. Phyu Oo Khin and Ohn Gyaw “ Assessment of Water Availability In Chindwin

Catchment”, J. Myan. Acad. Tech. 1.31-41, 2001

13. Ramachandra Rao, A. and Khaled, H. Hamed “Flood Frequency Analysis”,

2000.

14. Sugiyama, Hironobu “Analysis and Extraction Low Flow Recession

Characteristics”, Joint Seminar on Practical Application in Hydrology on 3 and 4

March, 1996, Irrigation Technology Centre.

15. Sugiyama, Hironobu “Hydrologic Drought Characteristics of the Upstream

Reaches of the Mae Klong River”, Workshop on Sustainable Development of

Agricultural, Infrastructure and organizational Management of Chao Phraya and

Mae Klong Basin, Bankok, October 30, 1998.

16. Tallaksen, L.M. and Van Lanen, Henny A.J “Hydrological Drought, Processes

and Etimation Methods for Streamflow and Groundwater”, Development in Water

Science 48, 2004.

REFERENCES 111 Mtr.No.158204


17. Tin Maung (Executive Engineer, Hydrology Section, Irrigation Department)

“Forecasting of Dry Season Flow through Recession Flow Curves”, October 1987.

18. United Nations, Economic and Social Commission for Asia and the Pacific

“Assessment of water Resources and Water Demand by User Sectors in

Myanmar”, United Nations Publication, 1996.

19. U.S Geological Survey, Reston, VA.,Water Resources DIV “Computer Program

for Describing the Recession of Ground-Water Discharge and For Estimating

Mean Ground-Water Recharge and Discharge from Streamflow Records-Update”,

Water Resources Investigation Report 98-4148,1998.

20. U Tin Ngwe & U Khin Soe, “Case Study on Floddplain Management in Myanmar“,

28. April, 2004.

21. Wittenberg, Hartmut and Sivapalan, M “Watershed Groundwater Balance

Estimation using Streamflow Recession Analysis and Baseflow Seperation”,

Journal of Hydrology 219 (1999) 20-33.

22. Wittenberg, Hartmut “ Effects of Season and Man-made Changes on Baseflow

and Flow Recession: Case Studies”, Hydrological Processes,17,2113-2123

(2003).

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Interviewed Persons: 1. Daw Tin Yi, Staff Officer, Department of Meteorology and Hydrology

2. Daw Cho Cho Naing, Assistant Director, Water Resource Utilization Department

Web Sites used : 1. http://www.fao.org/ag/agl/swlwpnr/reports/y_ta/z_mm/mm.htm

2. http://www.fao.org/ag/agl/aglw/aquastat/countries/myanmar/index.stm

3. http://www.fao.org/documents/show_cdr.asp?url_file=/docrep/008

/ae546e/ae546e00.htm

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9. http://earth.google.com

Appendix-A Basic Information 112 Mtr.No.158204


Appendix- A Basic Information Table.1 Various Agencies and Departments engaged in Water Use Sector

Agency/Department Ministry/City/Other Duty and function

Irrigation Department Agriculture & Irrigation Provision of irrigation water to farmland

Water Resources Utilization Department Agriculture & Irrigation Pump irrigation and rural

water supply Directorate of Water

Resources and Improvement of River

System

Transport River training and navigation

Myanmar Electric Power Enterprise Electric Power Electric power generation

Department of Hydroelectric Power Electric Power Hydropower generation

Factories under the Ministry of Industry Industry (1) and Industry (2) Industrial use

Myanmar Fishery Enterprise Livestock, Breeding & Fishery Fishery works

City Development Committee Yangon/Mandalay City water supply and

sanitation

Department of Development Affairs

Progress of Border Areas & National Races and Development Affairs

Domestic and rural water supply and sanitation

Private users UN agencies, NGOs & private entrepreneurs

Domestic water supply navigation & fisheries

Department of Meteorology and

Hydrology Transport Water assessment of main

rivers

Forest Department Forestry Reforestation and conservation of forest

Public Works Construction Domestic & industrial water supply and sanitation

Department of Human Settlement and Housing

Development Construction Domestic water supply

Department of Health Health Environmental health, water

quality assessment and control

Central Health Education Bureau Dept. of Health

Planning Health

Social mobilization, health promotion, behavior

research Yangon Technological

University Science and Technology Training and research

(Source:

http://www.fao.org/documents/show_cdr.asp?url_file=/docrep/008/ae546e/ae546e00.htm)



Table.2 Major Government Organizations engaged in Groundwater Extraction

Ministry Organization/Department Division/Section Nature of Responsibility

Agriculture and Irrigation

Agriculture Mechanization Department

Rural Water Supply Division

Rural domestic water supply

Agriculture and Irrigation Irrigation Department Drilling Division Irrigation for

Agriculture Purpose

Health General Affairs Department

Environmental Sanitation

Department

Provision, Supervision and management of

urban water supply and sanitation

services Progress of

Border Areas & National Races

and Development Affairs

Department of Development Affairs

Township Development

Domestic and rural water supply and

sanitation

City Development Committee Yangon/Mandalay

Municipal water supply and sanitation

Construction Department of Human

Settlement and Development

Urban water supply and

Sanitation division

Planning of urban water supply and sanitation works

Construction Public Works Water and Sanitation Division

Construction of urban water supply

and sanitation works. Water

supply to government owned

building

(Source: United Nations Publication, 1996)



Table.3 Irrigation Area Development of Myanmar Since 1962

Year Irrigated

Area (million ha)

Year Irrigated

Area (million ha)

Year Irrigated

Area (million ha)

1962 0.54 1977 0.95 1992 1.0 1963 0.57 1978 0.995 1993 1.1 1964 0.77 1979 1.025 1994 1.34 1965 0.795 1980 1.0 1995 1.56 1966 0.8 1981 1.08 1996 1.76 1967 0.785 1982 1.03 1997 1.56 1968 0.79 1983 1.005 1998 1.59 1969 0.81 1984 1.06 1999 1.69 1970 0.815 1985 1.08 2000 1.84 1971 0.82 1986 1.06 2001 1.91 1972 0.89 1987 1.065 2002 1.99 1973 0.895 1988 1.0 2003 1.97 1974 0.99 1989 1.015 2004 2.11 1975 0.995 1990 1.005 1976 0.998 1991 1.0

(Source: http://www.fao.org/ag/agl/aglw/aquastat/countries/myanmar/index.stm

http://www.myanmar.gov.mm/ministry/agri/statistics.htm )

Table.4 Irrigation Development in Chindwin Basin (ha) (as of Sagaing Division)

Year Pumping Reservoir Total Cumulative 1962-89 - 1416 1416 1416

1990 - - - 1416 1991 - - - 1416 1992 - 10399 10399 11815 1993 - 506 506 12321 1994 - - - 12321 1995 - 607 607 12928 1996 1141 4815 5956 18884 1997 2736 - 2736 21620 1998 506 4856 5362 26982 1999 5906 - 5906 32888 2000 304 - 304 33192 2001 4047 3237 7284 40476 2002 - - - 40476 2003 - 4102 4102 44578 2004 1214 2469 3683 48261

(Source: Irrigation Technology Center & Water Resource Utilization Department)

Appendix-B Maps of The Study Area 115 Mtr.No.158204


Appendix- B Maps of the Study Area, Chindwin Watershed


Map.1 Soil Erodibility Factor (K) & Soil Map of Chindwin Watershed Area (1990)




Map.4 Rainfall Isohyetal Map of Chindwin Baisn with Rainfall Stations

Appendix-C Meteorological and Hydrological Data 119 Mtr.No.158204


Appendix- C Meteorological and Hydrological Data Used in the Study Table.1 Daily Mean Discharge of Chindwin river (m3/s) Station - Monywa

1975 JAN FEB MAR APL MAY JUN JUL AUG SEP OCT NOV DEC 1 1523 1028 971 814 908 1544 9441 13890 8077 6603 6112 22842 1497 1028 961 809 934 1720 10109 14590 7668 6280 6638 22363 1450 1023 945 808 940 1816 10953 14913 7418 6112 5665 22094 1394 1023 935 799 857 1904 11697 16223 7468 5748 5313 21535 1371 1023 926 792 791 2512 12347 17410 9004 5422 5073 21506 1341 1016 921 784 785 2803 12563 17760 9888 5561 4853 21277 1300 1005 916 778 795 3150 12640 17200 10440 6000 4753 20708 1258 995 911 778 814 3080 12523 15823 11663 6232 4780 20339 1219 992 907 777 838 2725 11890 14123 14600 7420 4700 1997

10 1188 985 900 775 857 2396 11770 12283 12940 12690 4520 196311 1160 979 897 769 862 2444 11750 11077 16147 11757 4016 191512 1142 974 892 763 857 2754 11580 10650 16557 13310 3817 188313 1138 966 887 749 877 2977 11500 12337 15803 15430 3764 181614 1130 961 882 743 900 3038 11707 12970 14757 16357 3840 180015 1123 961 877 739 934 2717 12303 12700 13267 16657 4142 177616 1113 961 872 733 952 2560 13123 12170 12490 16790 4034 173617 1105 961 867 727 931 4023 13710 11107 11603 16590 3796 173618 1100 955 862 721 919 7735 13930 10270 10737 16407 3796 173619 1090 959 857 721 905 10364 13960 11027 10353 16200 3727 172520 1078 994 852 715 895 11087 13867 10170 9983 15510 3535 170921 1067 1013 847 715 887 10940 13523 9412 9792 14040 3321 168022 1059 1023 842 713 887 10087 13853 8443 9963 12340 3094 163723 1054 1021 838 711 887 8165 14267 8424 10200 11117 2968 159524 1054 1016 833 713 885 6580 14600 8605 10817 10152 2838 157325 1054 1000 833 735 963 5598 14923 9898 10850 7610 2676 155726 1049 990 828 771 1168 6059 15040 10467 10713 6612 2592 151227 1047 985 828 795 1350 7893 14793 10383 9962 5960 2500 147328 1044 976 823 825 1256 9260 14300 10350 8616 5554 2468 145629 1044 - 819 859 1373 10257 13917 9621 7627 5307 2396 145030 1044 - 819 884 1435 9688 13430 9669 7218 5353 2364 143531 1033 - 814 - 1439 - 13610 9051 - 5805 - 1422

1976 JAN FEB MAR APL MAY JUN JUL AUG SEP OCT NOV DEC

1 1413 1103 1064 955 1147 1375 8823 11280 10563 7102 2652 18432 1407 1095 1047 974 1113 1409 9488 11637 10440 6024 2504 18533 1396 1082 1030 974 1085 1501 10623 12427 10897 5466 2268 19254 1388 1074 1007 971 1064 1717 11687 10797 10069 5453 2177 19845 1366 1069 985 969 1044 2055 12410 11100 9099 5495 2100 20576 1345 1067 976 964 1026 2147 12997 11240 8359 5635 2043 20877 1332 1062 971 940 1011 2682 13380 11903 8252 5429 1976 20678 1322 1078 966 935 1000 3197 13847 12460 8567 5539 1936 20279 1317 1107 966 935 1085 3169 14613 12660 8270 5347 1907 1920

10 1309 1113 966 932 1145 3145 15480 12760 8177 4713 1864 183711 1294 1125 966 916 1162 3976 16290 12500 7768 4500 1840 164812 1281 1122 957 914 1185 6888 17140 12560 7343 4022 1821 157613 1268 1122 962 908 1188 9574 17857 12540 6952 3785 1792 151814 1258 1128 985 905 1247 11367 18297 12730 6802 3291 1771 148815 1247 1118 990 902 1298 12203 18983 13413 6480 3173 1749 145016 1236 1105 999 895 1343 12543 20800 13577 5835 3274 1717 141817 1224 1097 1018 895 1450 12873 22340 13150 6184 3228 1688 138618 1206 1074 1038 1433 1383 13040 23700 13190 6802 3159 1661 136419 1193 1066 1088 2067 1428 13010 25000 13320 6852 3178 1645 134120 1182 1081 1157 2057 1377 12940 25700 13620 6718 3169 1627 1313



21 1175 1044 1180 1792 1390 12780 26450 13770 6537 3905 1584 129422 1167 1039 1130 1651 1356 12047 25750 14053 6248 6319 1557 128123 1158 1033 1105 1501 1396 10620 25200 14610 6048 6752 1544 127024 1147 1028 1075 1415 1428 8861 22627 14997 6360 6546 1528 126225 1135 1023 1058 1326 1733 7752 21250 15230 7593 5211 1512 124926 1130 1044 1011 1262 1688 6794 19173 15453 8227 4034 1499 123627 1130 1069 966 1243 1563 6635 17390 14980 8385 3561 1488 122428 1125 1064 963 1224 1467 6743 15410 14200 8185 3113 1473 121129 1125 1072 957 1204 1424 7635 13253 13070 8880 2898 1739 119830 1117 - 938 1183 1384 8381 11707 12027 8118 2772 1835 118831 1108 - 937 - 1347 - 11280 11480 - 2708 - 1178


1 1170 981 867 798 1130 1484 6668 12203 20390 7743 2740 15952 1170 979 855 800 1113 1390 6993 12833 23127 7093 2680 15763 1165 976 847 809 1087 1364 7335 13690 23663 6885 2825 15654 1160 971 842 800 1052 1409 7235 14323 23213 6546 2949 15415 1155 968 839 798 1033 1685 7218 14863 21550 5905 2828 15286 1150 966 867 851 1020 3049 7402 15227 19213 5483 2760 15287 1145 964 1013 882 1011 4244 7927 15687 16670 5100 2672 15208 1138 961 1092 907 1002 4440 8330 16123 14940 4733 2500 15059 1135 959 1088 940 995 4262 8681 16257 14310 4967 2213 1488

10 1128 952 973 950 996 4070 9023 15253 14997 5591 2140 147511 1118 945 938 1113 1096 3775 9308 14070 15260 6489 2692 146212 1108 940 929 1213 1208 3497 9602 12883 15343 5914 2680 146213 1100 934 908 1349 1234 3263 9811 11470 14683 5307 2576 143914 1095 928 890 1386 1288 3187 9963 10173 14047 4900 2276 142615 1090 923 875 1302 1351 3131 10690 9089 12660 4540 2147 140516 1085 921 864 1247 1473 3173 11893 8265 11850 4208 1941 140517 1078 916 844 1201 1533 3247 12170 8068 9869 3856 2070 140518 1069 913 841 1306 1571 3332 11860 8738 9536 3572 2037 140519 1062 911 835 1272 1728 3792 11977 9688 9887 3331 2010 140520 1052 907 826 1256 1974 4190 11573 10707 10410 2898 2007 140521 1049 907 820 1234 2408 4448 11390 11480 10860 2856 2003 139222 1044 907 816 1226 2808 4727 11687 12120 10450 3075 1979 139223 1039 902 812 1217 2797 4853 12213 12200 11833 3252 1957 139224 1031 897 806 1206 2636 5269 12850 12110 12627 3024 1947 139225 1025 894 805 1200 2324 6104 13050 11873 12587 2837 1931 137326 1020 890 805 1190 2147 7485 13070 11967 12440 2764 1880 133927 1011 884 805 1178 2053 8077 12970 11870 11787 2700 1824 129228 1000 872 805 1168 1947 7852 12273 11637 10793 2652 1763 126029 995 - 800 1155 1877 7285 11407 11170 9841 2600 1720 120730 989 - 800 1145 1672 6718 11170 12803 8833 2536 1680 117231 983 - 799 - 1552 - 11500 17027 - 2544 - 1142


1 1105 897 805 693 690 2206 14873 10710 7302 7743 2212 15212 1073 892 805 689 702 1972 15610 10660 7985 7093 2180 14923 1049 887 803 685 699 1901 16120 10710 8576 6885 2060 14374 1041 882 800 682 688 1928 16153 11067 8064 6546 1955 14075 1042 877 800 681 687 1944 16120 11367 7310 5905 1923 13796 1057 870 798 681 690 1912 16160 12317 7135 5483 1920 13607 1078 867 796 680 681 1864 16347 12720 6902 5100 1885 13528 1067 865 794 678 681 1904 15767 12830 6643 4733 1848 13229 1052 860 791 674 681 2536 15620 12997 7843 4967 1829 1294

10 1039 857 788 672 681 2742 15223 13130 8994 5591 1827 128111 1026 855 787 672 678 3297 14600 13297 10717 6489 1848 124512 1021 852 785 681 687 3412 14123 13660 10960 5914 1797 122613 1013 850 784 692 703 3641 13450 14110 10212 5307 1757 121914 1005 847 780 703 751 4940 11890 14753 9317 4900 1723 1211



15 997 845 779 707 769 6352 10181 15197 9755 4540 1709 119816 992 842 778 713 772 6504 8785 14853 10049 4208 1677 118017 992 841 778 723 791 6224 7677 14160 9612 3856 1664 116318 987 838 776 743 831 6008 7027 13710 9042 3572 1632 114819 985 836 773 751 1064 5525 7610 12573 8294 3331 1597 113520 979 833 765 721 1150 5353 8836 11160 7435 2898 1576 113221 974 831 755 708 1223 5213 10690 10153 7327 2856 1536 113022 971 828 747 699 1341 5093 12437 9707 7085 3075 1518 112523 964 828 743 692 1497 5033 12700 9555 6256 3252 1492 111824 959 826 739 686 1629 4840 12940 8317 7852 3024 1454 110825 952 822 735 680 1616 6942 12783 7360 8671 2837 1443 109826 942 819 725 677 1712 9537 12337 6685 8766 2764 1437 109227 935 814 714 673 3484 11270 11707 6264 9051 2700 1467 108028 924 809 708 672 4034 12370 10527 5880 10532 2652 1573 106729 919 - 702 672 3444 13517 10190 5789 11593 2600 1592 105130 911 - 698 675 2917 14277 10487 6088 11077 2536 1571 104431 902 - 695 - 2484 - 11110 6224 - 2544 - 1035


1 1028 797 692 631 626 641 2198 13110 11367 13390 2796 14662 1015 794 686 634 638 616 2388 13310 11967 14083 2748 15033 1005 792 680 634 634 596 4091 13227 12400 12157 2624 16164 997 789 678 634 627 566 7861 12987 12593 11740 2492 16535 983 787 675 634 618 557 9974 12433 12617 10390 2376 16246 979 782 674 636 616 542 10807 12327 12607 9460 2276 15687 971 780 667 637 605 532 10900 12327 12907 9336 2208 15658 953 778 661 641 600 530 10096 12460 13557 9821 2150 15929 940 776 657 644 597 534 8814 12390 14697 10657 2097 1624

10 929 775 653 656 596 544 7802 12247 15800 11603 2030 164011 926 769 647 675 637 545 6810 11430 16987 12253 1984 159212 919 769 637 757 664 548 6216 10012 18073 12597 1936 151413 913 769 631 780 673 571 6064 8405 18813 12927 1896 146914 908 765 626 788 672 599 6112 7160 18840 13160 1869 141315 904 757 623 787 668 658 6256 6190 18303 13230 1832 137916 894 751 620 710 660 742 6589 6256 17800 13183 1800 135417 885 749 614 690 645 1051 7143 6810 17113 12873 1776 133418 875 743 611 658 631 1499 7627 6852 16393 11840 1744 130219 869 739 607 635 613 1696 7927 6384 15413 10031 1712 128320 862 735 604 626 581 1744 8052 6072 14150 8131 1680 125821 857 731 601 625 572 1744 7918 6152 12440 6353 1648 123222 852 727 598 625 568 1885 8127 7493 10590 4847 1589 121723 847 727 595 621 565 2027 9127 8880 8956 4365 1571 120224 842 725 589 631 569 2147 10430 10182 7627 4070 1589 119225 836 719 585 637 601 2150 11187 11057 6571 3775 1587 117726 830 713 582 637 658 2000 11707 11520 6088 3497 1560 116827 823 709 579 634 717 2100 12120 12337 5883 3295 1531 116028 819 703 579 644 771 2236 12410 11643 6720 3117 1535 115529 812 - 582 650 733 2392 13040 11210 7710 2973 1488 114530 805 - 602 629 695 2328 12850 10980 10883 2847 1475 114031 800 - 611 - 667 - 12950 11190 - 2800 - 1125


1 1135 907 790 789 877 1148 5220 11530 11387 13080 4753 15952 1132 904 793 784 877 1103 5220 11943 11667 12617 4124 15763 1128 895 803 779 955 1158 5153 12150 10807 13403 3866 15494 1123 887 803 816 1030 1323 5730 12627 10087 14717 3753 15215 1118 882 794 869 1083 1584 6368 13217 10440 17023 3636 14966 1110 882 799 973 1025 1765 6480 13640 10510 18720 3540 14867 1105 877 828 971 968 1845 5745 13940 10727 24250 3439 14628 1093 872 844 955 968 1887 5781 14037 9962 26750 3321 1443



9 1083 870 844 921 992 1771 6465 14083 8785 27300 3220 142010 1074 867 870 879 1013 2107 8523 14467 7685 26050 3173 140311 1072 865 898 833 1030 3636 9108 14830 7435 23600 3071 137912 1069 862 964 799 1047 4347 9460 14997 7293 20540 2893 136213 1062 857 1054 795 1086 4833 8633 15040 6827 18040 2740 134914 1056 852 1059 784 1198 5020 8557 15053 6320 16307 2392 133015 1047 847 996 783 1381 5437 9308 15110 5952 15320 2209 131316 1037 842 983 779 1490 7277 10430 15020 5752 13187 2153 129617 1028 838 974 755 1494 8085 11407 15010 6680 9858 2100 127018 1018 833 959 723 1435 7702 11800 15320 8500 8369 2060 125319 1005 828 940 729 1390 7468 12203 15727 8975 7435 2011 124020 994 823 919 765 1373 8747 12430 16197 8529 7435 1976 122821 985 819 897 821 1343 9583 12843 16640 7810 7310 1907 121522 974 814 879 905 1247 10670 13260 17177 7810 7160 1800 120223 968 809 846 955 1192 11013 13837 17600 7710 6877 1752 119224 957 805 816 1007 1150 11490 14147 16907 7860 6120 1736 118225 952 800 790 1033 1135 11633 14193 15917 8994 5819 1736 117226 945 798 790 975 1204 9860 14007 15273 9536 5774 1720 116227 935 795 790 938 1226 8410 13557 14433 9536 5613 1677 115328 924 795 790 929 1226 7677 12730 13743 10240 5495 1608 114829 919 793 790 924 1162 6035 11017 13123 11750 5307 1608 114230 916 - 790 902 1130 5140 10780 12617 13070 5153 1608 113231 911 - 788 - 1226 - 11033 11747 - 4893 - 1125


1 1115 976 838 852 973 1369 9099 11323 11697 4010 1520 11332 1110 971 826 855 939 1485 9917 11687 12273 3834 1501 11203 1105 971 817 862 900 2685 10647 12647 12420 3572 1486 11104 1100 966 808 870 877 3029 11417 13453 12400 3657 1464 10985 1090 966 802 870 859 3166 12087 14110 12367 3540 1454 10876 1085 961 798 857 842 3497 12687 14320 11693 3577 1430 10787 1080 955 795 855 831 3599 13297 14133 11313 3551 1405 10618 1074 950 793 852 826 3668 13793 13440 10743 3476 1403 10449 1069 950 790 852 825 3333 14277 12793 10247 3300 1416 1039

10 1064 945 791 847 841 3005 14743 12277 9944 3038 1439 103311 1059 942 801 847 845 2700 14940 11677 9678 2815 1418 102312 1057 940 819 862 838 2464 14720 11117 9678 2656 1386 101613 1052 937 838 951 828 2436 14397 11407 9441 2408 1354 100414 1049 935 850 1059 816 2396 13803 12130 9707 2528 1362 99215 1044 931 835 1123 803 2764 12903 12120 10183 2588 1377 98716 1044 931 826 1132 797 2616 11790 11447 10730 2492 1352 98117 1039 926 819 1095 793 2624 10817 10750 11220 2564 1322 97418 1033 926 816 1059 790 2828 10713 9953 11100 2612 1281 96619 1028 921 842 1025 874 2776 11623 9004 10743 2320 1277 96420 1023 918 882 1013 842 2842 12523 8443 10002 2213 1264 96121 1023 916 919 1021 806 2796 13267 8306 9545 2143 1258 95522 1020 910 934 1016 796 2712 13940 8234 8433 2020 1300 95023 1018 899 934 1016 801 2528 14540 9222 7393 1928 1336 95024 1013 890 921 1069 969 2616 14923 9726 6265 1923 1383 94525 1007 884 902 1085 1183 2796 14927 9773 5591 1888 1369 94026 1005 875 899 1085 1157 2784 14127 9355 5561 1808 1285 93527 1000 864 907 1080 1228 3133 12980 9355 5395 1749 1225 93128 997 852 907 1074 1195 5505 11923 10059 5067 2051 1195 92629 992 - 900 1054 1157 7735 11190 10663 4747 1675 1170 91930 983 - 887 1023 1152 8673 11020 10990 4374 1645 1145 91131 979 - 867 - 1182 - 11150 11130 - 1576 - 907


1 899 778 733 662 874 775 13783 16997 10191 8928 1989 11952 890 778 733 668 892 773 14180 20913 9564 11000 1907 1183



3 879 778 745 667 872 757 14297 23013 9365 12153 1856 11784 869 775 757 661 862 759 14517 22977 9194 11987 1957 11685 860 775 763 656 852 816 14070 21213 8899 10983 1805 11526 849 775 751 656 817 894 15723 19333 7820 10657 1760 11437 845 775 725 659 828 956 12737 17667 7821 9460 1707 11288 841 775 704 665 846 1004 12067 14353 7802 8947 1691 11129 836 775 699 669 860 976 11950 14370 6977 8258 1651 1103

10 828 769 696 673 867 1100 11437 14197 7227 7485 1603 109311 828 769 693 683 910 1198 10910 12770 7702 7060 1560 108312 823 769 693 705 1009 1431 10190 12077 7410 6685 1528 107113 819 769 690 747 1009 2499 10048 12017 7168 5113 1496 106114 814 769 689 784 1018 3631 10637 11997 6993 4593 1484 104915 809 769 687 795 1064 5130 12100 11800 6777 4274 1503 103516 805 769 684 814 1018 7535 11653 11430 6627 3875 1536 102517 800 769 681 823 952 8237 11870 10753 7052 3513 1664 101818 800 769 678 811 1018 7318 12007 10130 8093 3305 1803 101119 798 769 675 777 1081 6104 11633 8983 9564 3094 1808 99920 797 769 672 769 1122 8754 11003 7868 10627 2940 1701 98321 794 769 668 757 1090 11140 10087 9869 11140 2802 1970 97422 793 763 668 780 1063 11580 8652 11067 11553 2672 1864 96423 790 761 665 795 997 11347 8842 11623 11860 2504 1768 96124 790 757 662 800 950 10740 9194 11333 11900 2532 1725 95525 790 751 659 809 918 10343 9583 11747 11377 2420 1693 95026 788 745 659 819 870 9754 10287 12420 10163 2484 1656 94527 785 739 655 833 836 10060 11843 13610 9260 2296 1624 94528 783 739 653 847 816 12100 11933 13973 8078 2200 1234 94029 781 - 653 852 801 12977 12790 13070 7318 2180 1206 93430 778 - 653 857 786 13360 13557 12277 6918 2170 1200 92431 778 - 650 - 783 - 14627 11357 - 2100 - 916


1 911 780 654 1201 1215 1128 5347 11343 10290 9536 3817 17392 900 778 662 1140 1193 1113 5273 12350 12887 8690 3535 17153 910 769 680 1086 1215 1108 5073 13940 13557 7643 3364 16724 892 763 695 1039 1399 1088 5140 16177 13880 6745 3159 16245 887 757 704 983 1587 1067 5761 17600 13543 6064 2987 15926 884 751 712 971 1589 1160 6336 18517 12750 6464 2814 15767 880 745 721 952 1576 1320 7460 18787 11683 5605 2712 15578 872 739 733 900 1811 1424 8168 18080 10647 6742 2668 15319 867 733 755 904 2125 1561 8261 17267 9792 10667 2612 1490

10 862 727 801 916 2404 1755 8500 15997 9365 11450 3455 147311 855 751 825 926 2540 2219 8510 15997 9080 11417 4596 145412 847 778 806 924 2312 2368 8202 14250 8994 10740 5643 143513 842 777 785 935 2133 2608 7302 12250 9659 9868 6152 141614 833 771 761 1052 1949 2656 6685 10523 9878 9460 6050 138815 826 763 743 1236 1891 2328 6392 10041 9697 10193 5353 135116 819 755 747 1285 1781 2173 6000 9564 10597 9821 4491 133917 814 743 776 1485 1749 2127 5539 9175 11953 9412 4353 131518 814 731 788 1723 1632 2728 5107 8491 12937 9678 3873 129219 809 716 783 1885 1536 2813 4507 7943 13000 8426 3174 127220 809 711 771 1891 1486 2769 4807 7735 12863 7193 2879 125621 805 706 765 1819 1418 3066 4860 7418 13133 8485 2680 123822 805 703 791 1765 1366 3236 4840 7077 13370 9308 2492 122123 800 696 844 1728 1313 3164 4967 7002 13370 8595 2344 120624 798 694 911 1675 1277 3150 5621 6384 13133 8093 2195 120025 798 688 1013 1550 1251 3192 7799 6465 13030 7168 2080 119326 797 675 1177 1409 1201 3332 9926 7652 12803 6032 2011 118327 792 665 1643 1283 1197 3412 11190 8467 12183 5687 1952 117328 788 656 1733 1217 1177 3465 11480 8918 11533 5260 1880 116829 787 - 1803 1307 1152 4280 11323 9232 10923 4893 1797 1160



30 784 - 1768 1251 1132 5273 11160 9688 10153 4613 1701 116031 783 - 1709 - 1140 - 11160 9982 - 3938 - 1189


1 1270 939 725 616 664 2220 10837 16490 13520 5767 2728 12642 1354 907 713 613 697 2705 10963 17270 15370 5133 2644 12303 1403 872 709 619 719 4308 11477 17620 17870 4827 2600 12114 1384 849 706 622 739 5949 11953 17393 21587 4987 2552 12005 1328 838 706 614 725 6272 12080 16723 22637 4880 2476 11886 1279 831 704 609 710 5127 12100 16623 21700 4840 2416 11737 1232 823 702 601 719 4124 12410 16167 19007 4820 2332 11578 1185 823 699 601 747 3609 12680 16007 13531 4680 2356 11459 1143 820 697 604 773 3065 12927 15970 14163 4428 2332 1133

10 1125 817 694 610 778 2628 13213 15477 12957 4268 2296 112011 1107 814 689 620 783 2775 13610 14757 12863 4286 2256 110712 1092 809 683 634 785 3213 13833 13360 12650 4136 2167 110013 1076 809 678 668 800 3225 14093 12883 12267 4052 2130 108814 1059 805 676 715 825 3263 14663 10773 11800 5149 2113 108015 1049 800 672 726 811 3711 15217 9963 11427 5333 2090 106716 1039 800 668 700 822 3944 15840 10190 11170 4987 2050 105717 1026 802 663 685 841 4232 16790 10363 10777 4607 2017 104918 1011 817 660 668 860 4640 15067 11243 10670 4401 1973 104419 994 825 658 663 862 7657 20430 11210 11067 4292 1933 104220 981 822 654 672 921 11107 21773 9800 11477 4040 1893 103921 979 819 649 668 1004 13240 21477 8994 12037 4255 1837 103322 969 826 642 661 1076 14227 19827 9678 12220 4853 1779 104723 959 823 636 650 1235 14697 18543 9992 12380 5027 1739 104924 950 802 633 640 1601 15080 17403 9897 12440 5200 1680 105925 943 793 631 632 1977 15207 16123 10363 12097 5307 1637 104926 967 778 628 651 2284 14937 15193 10430 11180 5120 1595 103227 1007 765 625 643 2147 14123 14480 10797 10003 4529 1539 100628 1014 753 622 633 1920 13237 14193 11353 8747 3969 1473 98129 992 743 622 636 1856 12120 14373 11407 7543 3551 1401 96930 966 - 622 649 1939 11437 14650 11457 6482 3181 1326 95531 950 - 620 - 2140 - 15343 12180 - 2898 - 945


1 932 771 693 644 802 6008 12080 17143 14277 12820 2732 14182 924 771 690 641 809 5717 13027 17640 13280 13277 2636 13983 918 763 683 637 820 4369 14100 18070 12170 12573 2572 13754 910 757 677 634 838 3695 14813 19413 11097 12150 2520 13545 902 749 672 634 852 3223 15103 18623 10460 11437 2444 13326 895 745 667 631 872 3249 15123 16423 10817 9945 2392 13137 887 745 662 634 884 4979 15033 14550 11603 8766 2364 12948 882 739 659 640 862 8848 14733 13193 12480 7910 2340 12729 877 745 656 644 836 11190 14527 12327 12840 7627 2296 1262

10 870 745 656 641 814 11057 14490 11373 12990 6529 2252 124911 860 741 657 641 798 10777 14793 11127 14847 6112 2216 123012 857 749 656 644 798 11087 15683 11337 15580 5708 2197 121313 852 757 653 641 795 11020 16757 11170 16127 5287 2167 119714 845 757 650 641 802 10650 17690 10840 15353 4800 2137 119015 839 749 648 656 809 10267 18203 10610 14983 4292 2107 118016 835 741 644 674 801 9640 18243 10440 15130 4112 2077 117317 828 741 641 686 795 8994 19080 10133 15183 4441 2040 116318 823 741 644 698 788 8500 19007 9507 14540 4627 1955 114819 819 733 648 712 772 9450 18023 8918 13400 4793 1933 113820 814 739 653 751 747 11480 17123 8823 12330 4547 1893 113521 808 733 654 817 761 12450 16183 8500 11407 4753 1869 112522 800 727 649 880 786 12907 15433 9507 10086 4467 1845 111323 797 718 640 916 851 13070 14827 10617 10012 4112 1808 1103



24 794 709 633 950 952 13430 14033 11427 9897 3902 1771 109525 790 706 627 980 1190 12883 13590 12213 9336 3728 1725 109026 788 703 620 976 1447 11707 13857 12707 9849 3572 1669 108327 786 703 616 934 1791 10480 13970 13390 10107 3535 1635 107228 786 699 613 887 2843 9650 14287 14420 10152 3487 1592 106429 783 - 618 846 4185 9964 14730 14623 11850 3327 1484 105930 780 - 629 808 5087 11047 15283 14803 11767 3145 1428 105431 778 - 639 - 5621 - 15893 14793 - 3019 - 1046


1 1037 852 715 674 1013 703 6320 11303 12060 6088 3155 15732 1031 847 712 664 931 678 7027 10920 11760 7143 3010 15283 1021 841 709 658 895 658 7227 11293 11520 6192 2879 15014 1007 831 705 652 857 640 6793 12007 11460 6160 2712 14625 1007 822 698 641 847 625 5901 12873 11417 6855 2564 14396 1013 814 693 628 862 613 5133 14647 11250 9279 2440 14287 1018 809 690 622 882 600 4947 14333 10880 10387 2324 14418 1013 805 687 618 919 593 6150 13690 10860 11730 2264 13779 1005 800 684 612 926 591 9517 12193 10747 12430 2201 1364

10 990 798 681 610 926 599 10360 10269 11563 12770 2293 134511 979 798 678 610 898 599 8842 8657 12553 13473 2668 132612 971 795 677 611 872 594 7860 7660 13980 14163 3508 130713 959 795 675 613 852 593 7143 6613 14910 14720 3663 129414 942 794 672 616 842 631 6400 5650 15420 15147 3561 128115 928 791 672 629 877 720 5435 5060 15157 14983 3396 126216 918 787 671 634 1004 727 4860 4600 14610 14217 3080 124917 916 782 668 634 1123 787 4329 4800 13803 13527 2811 123618 914 777 668 634 1113 793 4124 5510 13277 11903 2624 122419 911 769 668 634 1061 843 4853 5620 12917 10520 2444 121120 911 763 668 636 1039 915 7495 6024 13350 9194 2272 119821 907 757 668 637 1007 940 11290 6572 14440 8027 2123 118822 907 751 665 646 990 1011 12607 8072 13840 7135 1976 118323 907 745 666 747 949 1354 13000 8985 12863 6368 1832 117824 907 739 682 970 907 2195 13660 9260 11750 5598 1723 117325 907 737 705 1092 867 2884 14287 9669 10407 5027 1672 116826 904 733 719 1110 836 3609 13963 10607 8947 4733 1653 116327 897 727 733 1105 808 4112 13390 11560 7685 4359 1637 115828 890 721 733 1120 793 4507 13100 11943 6977 4004 1621 115329 880 - 720 1128 783 4540 13390 12010 6192 3780 1608 115030 870 - 698 1097 769 5007 13400 12020 5277 3551 1600 114731 860 - 684 - 737 - 12360 11860 - 3343 - 1143


1 1133 872 765 788 783 664 4993 12037 16017 13837 2584 16002 1130 867 755 761 779 665 5080 14707 16373 14397 2484 15683 1123 867 743 739 773 681 4940 14697 16523 15020 2352 15284 1118 867 733 716 780 724 4880 14900 16990 15517 2232 15015 1113 867 733 703 803 788 5120 14247 16940 15727 2137 14756 1108 867 731 695 852 824 7119 15980 16640 15957 2073 14507 1103 870 725 689 885 1068 9023 16690 16390 15647 2007 14358 1100 884 719 678 892 1390 10550 17123 16290 14970 1968 14229 1093 913 714 671 860 4746 11583 17240 16207 14023 1936 1409

10 1088 924 711 669 850 8731 12100 17190 16113 16200 1888 139611 1080 926 708 708 845 10363 12493 17357 15857 10446 1901 138412 1074 924 705 718 847 10580 12977 17023 16093 9412 1885 137113 1071 918 700 767 872 10191 13300 17590 16167 7993 1869 135814 1066 908 697 780 882 9754 13567 18297 15890 7043 1853 134515 1061 892 696 790 875 9830 13810 18487 14867 6280 1840 133216 1052 880 693 809 857 10517 13900 18430 14353 5708 1832 132017 1042 865 693 826 833 10950 13860 18023 13383 5280 1824 1307



18 1031 855 693 828 809 10797 13880 17457 12937 4913 1832 129419 1021 845 693 823 788 10307 13890 17273 12917 4513 1949 128120 1011 831 694 834 743 9564 13900 16873 13517 4172 1995 127021 1000 817 700 879 711 8643 13607 17240 13793 3950 1941 124922 990 801 707 894 702 8260 13227 18107 13513 3748 1880 123823 979 790 709 894 686 8424 12440 18787 13280 3551 1813 123224 969 784 709 865 674 8366 11803 19787 13440 3385 1797 122625 959 779 713 830 667 7110 12627 19497 13567 3231 1760 121926 945 773 723 808 661 5987 13600 17773 13070 3155 1741 121927 931 769 735 785 660 5247 13907 15997 12387 3103 1725 121528 911 769 749 765 672 5409 14397 15227 12463 2996 1696 120629 899 - 779 771 678 5327 14947 15300 12997 2847 1664 120030 890 - 795 779 678 5167 15170 15780 13380 2756 1632 118031 880 - 800 - 673 - 15147 15957 - 2680 - 1160


1 1140 865 710 727 706 2368 11613 18970 16607 5716 4700 18722 1120 855 719 721 703 2408 10323 21663 17107 6232 4304 19603 1100 845 721 715 703 2860 9241 23713 17423 6743 3968 20174 1080 836 717 712 710 3122 8193 24600 17540 6893 3700 20375 1059 826 715 708 709 3625 8230 25050 17440 7052 3492 20906 1039 819 759 702 702 3551 9118 23650 17107 6344 3359 20607 1018 812 799 695 699 3679 9783 21213 16940 6040 3192 21578 997 805 809 690 699 3497 10077 17543 16673 6024 3038 21909 987 800 794 681 706 3284 10267 14777 16257 6184 2870 2160

10 981 798 780 668 715 3085 10733 12417 16080 6048 2736 212711 976 794 775 657 711 2968 11397 13400 15943 6448 2612 192512 971 789 771 651 696 3024 11943 13320 15903 7152 2512 176513 966 784 785 645 687 3066 12480 12937 15970 7685 2436 172814 961 779 797 631 687 3424 13050 12670 16307 7527 2360 167215 955 773 788 625 702 3636 13587 12607 16163 7927 2308 162416 950 761 776 622 706 3615 14063 12500 16210 8975 2260 157917 945 749 753 616 694 4010 14527 13037 16107 9165 2212 157318 1044 739 743 610 708 4371 14263 13320 15567 9051 2163 150919 935 733 731 612 801 4807 14037 13350 14647 9669 2206 149420 931 727 721 613 944 5053 13420 13037 13037 10090 2404 149421 926 721 714 613 1347 5187 12087 12317 11283 10343 2412 148822 921 715 708 616 1488 5187 10820 12500 10450 11480 2556 147723 921 712 702 619 1462 5220 10317 12307 8776 12327 2660 147324 916 709 695 637 1450 5327 9840 11890 7377 12163 2560 146725 916 706 704 665 1471 6026 9469 12263 6449 11687 2476 142626 911 706 739 723 1696 8571 10258 12813 5731 10820 2372 140027 907 714 757 757 2481 10777 11387 13473 5253 9536 2252 138628 900 712 751 761 3122 12110 13133 14123 5080 8100 2143 136029 890 709 745 735 3061 12760 13950 14817 5013 6985 1947 134530 880 - 739 717 2791 12470 14603 15413 5213 5917 1880 133231 872 - 733 - 2544 - 15593 15970 - 5133 - 1313


1 1302 1052 1110 882 1013 1744 3914 13793 8085 12587 7152 20702 1283 1042 1115 889 1028 1536 4004 16567 8018 11750 6376 20203 1258 1031 1110 899 1095 1424 4821 17873 8690 10597 5881 19844 1243 1021 1105 904 1180 1392 6571 19717 9336 9850 5591 19525 1234 1011 1100 907 1302 1377 7235 20877 9441 8918 5167 19336 1232 1000 1093 908 1477 1709 8306 21963 9127 8909 4727 19177 1224 992 1080 913 1549 1755 9650 22413 8652 8899 4390 18888 1211 981 1059 918 1522 1645 10807 21177 9488 9004 4148 18569 1198 976 1054 921 1437 1645 11347 19010 10562 10807 3962 1824

10 1188 971 1042 910 1352 1685 11790 17090 11307 13157 3812 179711 1180 966 1031 902 1251 1859 11730 15170 10963 12990 3636 1768



12 1177 961 1021 911 1178 1907 11800 13663 10950 13247 3487 173613 1173 959 1011 921 1105 1885 11997 12637 10413 13570 3337 170414 1168 955 1000 914 1069 1851 12553 11873 9564 13580 3192 167215 1160 995 997 897 1170 1840 12203 11250 8861 13513 3103 165316 1157 1037 992 877 1145 1805 11920 10550 8286 13497 2991 163717 1148 1044 985 855 1080 1757 12047 10343 8481 13190 2870 162418 1138 1041 981 827 1019 1723 12307 10477 9289 13130 2764 159219 1128 1035 969 800 990 2203 12360 10950 9327 12367 2672 156020 1122 1033 959 788 954 3404 12150 10920 8985 11727 2604 154121 1115 1028 948 783 1059 4780 11667 10963 9593 12027 2536 152522 1110 1028 938 786 976 5532 11357 12710 10097 13380 2488 151223 1105 1026 929 791 981 5664 10857 13433 10297 13870 2440 148824 1100 1023 919 791 1083 5355 10089 13730 10230 14650 2392 146225 1095 1018 913 788 1285 4920 8985 13257 9821 15220 2364 144826 1090 1032 910 793 1322 4288 7735 12577 9498 14830 2320 143527 1085 1062 902 900 1422 3684 6613 11250 9374 13483 2272 142228 1080 1085 899 997 1597 3321 5665 9877 10232 12080 2213 141129 1076 - 894 1007 1613 3391 5020 8795 11560 10473 2150 139030 1071 - 889 1016 1744 3771 5449 8018 12607 9279 2110 137731 1066 - 885 - 1819 - 10984 7927 - 8164 - 1364


1 1354 1049 990 932 2140 2204 17023 17873 8871 12907 3572 18032 1347 1044 987 942 2190 2516 16490 18660 8322 13277 3471 17763 1341 1044 981 952 2143 3117 17007 20430 8227 13870 3396 17414 1334 1039 992 966 1923 3131 18057 20127 8110 14720 3279 17255 1326 1033 1013 983 1813 3167 18323 18393 8795 15363 3131 16966 1315 1030 1054 999 1744 3647 18350 16890 8709 15113 3010 16647 1300 1030 1127 1021 1645 3844 17823 14527 8135 14770 2996 16358 1288 1039 1180 1005 1560 4940 17073 12617 7743 14587 3075 16249 1275 1046 1158 1021 1494 7110 16307 10940 7660 14647 3173 1627

10 1262 1054 1125 1075 1443 8365 16307 9926 8265 15137 3192 163211 1249 1054 1115 1122 1392 8890 16957 9412 8633 15207 3216 162412 1236 1049 1118 1168 1360 9327 17407 8956 8614 14973 3353 160813 1213 1046 1127 1190 1296 9697 17473 8766 8453 14707 3264 157614 1190 1044 1127 1202 1223 9669 17007 8966 8135 13860 3038 154915 1170 1039 1090 1192 1221 9507 16490 9327 7718 12840 2884 153316 1150 1031 1035 1183 1471 9450 16290 9926 7518 12183 2728 151817 1138 1021 1007 1272 1821 9355 16290 10260 7418 10950 2588 149418 1128 1011 995 1661 1635 8852 16407 10380 8844 9869 2500 146919 1118 1000 979 1968 1430 8152 16523 10360 12730 8985 2404 145620 1108 990 969 1800 1464 7968 16840 10230 13950 8043 2320 145621 1098 979 950 1497 1744 8431 17307 10113 14183 7285 2236 145022 1090 971 932 1392 2353 10001 17707 9574 13690 6727 2160 144323 1085 966 924 1375 2500 11500 18073 8766 13320 6144 2110 145224 1080 968 916 1443 2249 12513 18597 7993 12957 5693 2060 146225 1074 978 911 1557 2026 13933 19490 7343 13133 5160 2053 145626 1069 987 908 1640 1997 14887 19790 7110 12450 4820 1984 144127 1064 990 907 1821 2186 16233 19033 7160 12037 4547 1952 142428 1059 997 908 1909 2592 16873 18350 8037 11613 4298 1907 139829 1054 - 918 1984 2732 17223 17857 9431 11440 4064 1864 137330 1054 - 929 2060 2552 17390 17657 9631 11637 3879 1837 135831 1049 - 926 - 2300 - 17723 9279 - 3732 - 1345


1 1332 1105 985 852 932 2018 10420 14847 13550 11107 6453 23442 1309 1098 974 862 950 2295 10477 12967 12130 10597 7410 23163 1296 1088 955 877 999 2508 10983 11973 11077 9850 8633 22724 1296 1080 943 889 1218 2724 11293 12327 10203 8985 9070 22325 1302 1074 935 897 1619 3068 11460 13503 9241 8093 8599 2208



6 1309 1071 932 914 1811 3887 11873 14170 9754 8198 7085 21877 1315 1069 931 923 2029 4166 12573 14480 10220 9070 6272 21508 1315 1076 929 940 2130 4873 13503 15080 10280 10373 5620 21109 1322 1085 928 980 2160 5517 14157 15553 10117 11077 5100 2087

10 1328 1087 934 1142 2476 5343 14670 16283 10667 10993 4807 206711 1328 1097 947 1371 2760 4913 15263 17023 11013 11417 4346 203012 1322 1107 957 1443 2800 5608 15940 17457 11207 11643 4094 199713 1296 1110 966 1441 3021 6464 16973 17873 10980 12050 3861 198114 1277 1105 971 1409 4945 6569 17957 18073 12100 12153 3700 196515 1251 1095 966 1337 5627 6001 19070 18090 13143 13690 3540 194916 1236 1088 947 1236 4987 5532 20580 18133 13890 13587 3364 193317 1224 1078 940 1185 4445 5671 21703 19563 13390 13880 3207 191718 1211 1067 940 1155 3679 6032 22563 22077 12450 14443 3099 190119 1198 1054 937 1135 3290 6433 23327 23400 11697 14937 3052 188820 1192 1046 935 1108 3057 7218 24550 23203 11057 15340 2963 186921 1187 1039 931 1069 2963 8842 25300 21737 10470 15767 2884 185922 1178 1037 924 1028 2773 10473 25500 19527 10060 15740 2810 183723 1168 1030 919 988 2520 11170 25400 17890 10390 15063 2740 182124 1160 1023 914 959 2304 11290 24800 16740 11263 13790 2692 180525 1153 1020 908 929 2205 11087 24100 15363 12820 12223 2640 178926 1143 1011 902 907 2177 10920 23800 13443 12307 10172 2572 177627 1133 1004 892 902 2120 11117 22187 12840 11797 8757 2524 176028 1128 995 880 897 2037 11260 20277 13257 11580 7302 2476 174929 1117 - 870 892 1952 11033 18550 14043 11490 6652 2436 177130 1110 - 862 915 1872 10633 17473 14503 11490 6400 2392 177331 1110 - 857 - 1885 - 16243 14687 - 5984 - 1760


1 1749 1432 1294 1499 1217 1795 10078 12430 9327 8073 5207 19682 1733 1424 1290 1462 1204 1680 10323 12020 8652 9469 4760 19733 1717 1420 1298 1437 1193 1576 10340 11963 8002 10040 4420 19524 1701 1413 1315 1405 1185 1494 10507 11240 7527 9431 4334 19205 1685 1405 1330 1362 1180 1450 10830 10447 6539 8880 3968 19016 1669 1400 1334 1334 1173 1418 10757 10430 5753 8785 3812 18857 1653 1398 1326 1315 1163 1384 10610 10213 5613 8472 3599 18728 1637 1405 1313 1300 1157 1347 10420 10163 5693 8110 3391 18649 1624 1418 1300 1290 1150 1313 10550 10193 5635 7110 3227 1856

10 1616 1437 1277 1290 1147 1272 10930 10030 5341 6120 3085 183211 1605 1450 1262 1281 1142 1294 12020 10230 5047 5504 2982 180012 1589 1437 1249 1268 1133 1354 13173 10087 4800 5073 2921 176813 1573 1422 1236 1256 1127 1366 14253 10070 4780 5173 2842 173614 1557 1409 1224 1243 1117 1362 14277 9954 4840 4987 2792 168815 1541 1396 1211 1230 1095 1341 13310 9621 5060 4660 2764 163516 1525 1384 1200 1217 1074 1317 12587 9108 5895 5140 2716 159717 1514 1371 1195 1204 1049 1336 11863 8643 7318 5422 2640 156018 1507 1360 1200 1195 1039 1426 12253 8160 7585 6527 2524 152819 1501 1362 1204 1190 1049 1568 13257 7810 7610 8795 2416 151220 1494 1371 1200 1185 1054 1691 13983 7727 7718 9583 2336 149921 1488 1356 1193 1180 1047 1773 14110 7735 7560 9849 2268 148622 1482 1345 1183 1201 1039 1792 14140 7427 7002 10620 2197 147323 1475 1332 1173 1251 1049 1779 14060 7043 6943 10848 2140 146024 1469 1320 1163 1264 1128 1723 13773 6777 6482 11200 2100 144325 1469 1309 1153 1256 1461 1731 13527 7110 6637 10920 2063 143526 1475 1304 1150 1251 1896 1848 13290 9431 6345 10203 2050 143027 1482 1307 1157 1245 1968 2207 13017 10827 6176 8580 2007 142428 1473 1315 1190 1240 1987 4152 12637 11180 7027 7052 1976 141829 1462 1307 1249 1234 2027 7368 12853 12523 7702 6304 1971 140930 1456 - 1388 1230 1963 9222 13110 11590 7768 5851 1971 139631 1450 - 1488 - 1893 - 12503 10133 - 5569 - 1384




1 1371 1158 1377 1326 1049 1824 7160 10507 17940 5367 4773 16082 1358 1152 1326 1460 1049 1808 6216 10390 18597 6329 4753 15763 1347 1147 1270 1480 1049 2100 5532 10360 19523 7643 4397 15524 1339 1143 1230 1413 1073 2652 5473 10747 20427 8290 3699 15215 1326 1140 1193 1375 1082 2821 6925 11167 20763 9118 2968 15056 1315 1133 1165 1322 1087 2926 10937 12090 21027 10108 2865 14927 1309 1123 1145 1270 1100 3186 12400 12873 20690 10390 2788 14808 1304 1117 1125 1207 1152 3620 13413 13000 19717 10533 2712 14569 1296 1110 1105 1147 1238 4034 13753 13100 18970 10563 2644 1430

10 1290 1105 1093 1108 1405 4136 14680 13503 17340 10133 2596 141611 1283 1100 1083 1076 1821 4250 15100 13780 16590 9450 2540 140312 1277 1095 1076 1051 2336 4340 15100 13980 14920 8323 2488 139013 1270 1092 1071 1033 2372 4160 14743 14373 13380 7752 2440 137714 1264 1088 1069 1028 2153 4675 14287 14517 12337 7418 2400 135815 1258 1085 1064 1023 1997 5503 13703 14540 11687 6935 2344 133416 1253 1080 1059 1023 1840 4980 13050 14157 11387 6336 2296 130917 1249 1074 1054 1028 1725 5007 12243 13350 10380 5992 2248 128318 1245 1069 1049 1051 1637 5687 10873 12647 9146 6016 2180 125819 1260 1066 1044 1097 1547 5783 9393 12297 8002 6248 2100 123220 1309 1064 1039 1133 1498 5153 8510 11830 7352 6136 2033 120621 1350 1079 1031 1148 1613 5315 8210 11610 7077 6096 1968 119322 1360 1142 1013 1150 1944 8895 7993 11540 6643 6224 1904 117823 1350 1240 995 1152 2050 10850 7785 11490 6852 5976 1840 116324 1320 1349 983 1153 2047 11180 7610 11830 7568 5525 1784 115225 1281 1416 981 1130 1931 11170 8395 12427 7277 5160 1755 114326 1251 1422 990 1110 1856 10960 9127 13360 6653 5007 1736 113327 1226 1416 1009 1085 1779 10497 9917 14470 6088 4880 1720 112328 1203 1403 1020 1064 1701 9984 10723 15133 5664 4740 1699 111329 1188 - 1039 1057 1653 9118 11477 15993 5388 4448 1672 110330 1178 - 1098 1052 2428 8152 11590 16673 5220 4142 1640 109331 1168 - 1162 - 2134 - 10913 17507 - 3841 - 1085


1 1080 862 809 987 828 837 9973 11830 12967 4947 1733 11202 1067 857 814 993 819 887 9678 11447 12027 4613 1661 11123 1052 857 809 1055 843 919 9175 10587 11583 4389 1621 10924 1042 854 809 1097 867 990 9575 10123 11047 4493 1568 10825 1013 849 806 1108 995 1002 11580 10087 10200 4533 1514 10746 1007 847 800 1118 1237 1009 12160 9764 8317 4807 1494 10697 1007 841 798 1105 1183 1016 11343 9270 7185 4747 1478 10698 1007 838 794 1042 1158 1071 10013 9279 6296 4641 1430 10649 1002 835 786 978 1085 1160 8581 9127 6668 4540 1396 1051

10 1002 838 785 905 1045 1296 7960 8316 6482 4653 1364 103711 997 838 785 860 978 1379 8077 8871 6440 5255 1319 102812 997 831 779 839 907 1411 8135 8956 6320 4880 1298 102813 997 828 785 814 864 1411 8202 8928 6596 4403 1279 102514 992 823 787 793 838 1707 7993 9118 7847 4382 1253 102115 992 819 789 777 817 1936 8719 10077 8295 4395 1234 101816 987 814 785 755 812 1963 11417 10800 7893 4567 1226 101817 987 809 779 721 828 2532 11943 11313 7210 4587 1221 101318 981 805 773 707 826 4320 10703 12017 7018 4214 1219 101319 981 800 763 695 833 5935 9822 12500 5863 3732 1213 100720 976 798 753 682 816 6677 8728 12257 5087 3417 1213 100921 916 796 755 674 798 6743 8185 11600 4827 3024 1208 101322 911 793 745 665 788 7018 8370 10747 4973 2755 1188 101323 910 791 745 659 782 8118 7927 10357 5147 2568 1157 101324 902 793 751 657 771 8709 7652 10703 5467 2448 1143 100725 897 793 772 654 773 9355 7435 10437 6000 2312 1133 1007



26 892 797 814 652 774 9944 7252 11007 6096 2198 1128 100027 887 799 892 646 780 10430 7293 11957 6064 2087 1117 99428 882 805 904 681 785 10420 8450 12357 5944 2013 1115 98329 926 - 874 782 798 10031 10250 12530 5649 1936 1115 97830 872 - 850 822 808 9830 11357 12400 5320 1867 1122 96831 867 - 914 - 817 - 11717 12923 - 1800 - 963


1 957 814 780 687 759 1439 12640 12210 7168 17857 2380 24282 948 811 779 685 788 1343 12760 11570 6544 17107 2424 21103 940 809 778 684 796 1268 13110 11357 6328 16067 2424 19014 935 806 772 684 795 1285 13523 10943 7468 14680 2332 17605 931 805 769 684 786 1330 13813 10420 8842 13257 2400 15846 928 802 765 686 791 1362 14130 9851 9526 11667 2548 15237 923 799 759 687 839 1347 14683 8778 10460 10420 2692 14948 921 798 749 689 894 1364 15203 7852 10650 9441 2708 14679 918 796 743 690 907 1522 15593 8327 10503 10610 2548 1435

10 911 794 737 692 895 1998 15943 8842 9802 11303 2201 141411 902 793 731 693 899 2807 16390 9042 10760 11430 2087 138412 894 791 723 693 954 4305 16940 9175 11457 10697 2001 135413 884 790 721 695 1025 6112 17340 9355 10483 9441 2060 132414 877 787 721 696 1135 6328 17640 9889 9621 8263 2163 129215 872 784 721 696 1160 5762 17690 10833 9089 7185 2253 123016 867 783 719 698 1093 5353 17557 12677 8481 6370 2276 119017 862 781 715 696 1035 5193 17457 13783 8110 5759 2063 115518 859 780 713 693 1016 5227 17290 14303 7768 5234 2009 113319 852 779 710 700 994 5725 17240 14837 6918 4753 1949 110020 852 778 709 708 1732 6580 17540 15340 7468 4494 1837 106421 852 778 708 714 10150 7560 18443 15460 7027 4040 1784 104222 852 776 705 721 10893 8135 19490 15400 6561 3743 1784 102623 847 775 703 721 7710 8662 20427 15273 6529 3993 1760 100524 842 771 699 727 6737 9070 19940 15147 8567 4196 1715 99725 842 769 699 733 5376 9555 19120 14633 13640 3764 1653 99026 842 769 697 739 4078 10287 17707 13977 14180 3668 1608 97927 839 775 694 735 3107 10703 16690 13317 14563 3391 2329 96928 836 779 692 729 2432 10860 15817 11977 16340 3057 3529 95929 826 - 690 727 1999 11003 15027 10427 16890 2789 3497 94730 819 - 690 735 1760 12130 14137 9270 18007 2672 2893 93831 819 - 688 - 1563 - 13277 8198 - 2468 - 928


1 914 715 644 796 679 966 9336 10890 8060 8643 2137 12642 905 713 647 845 709 1448 10993 10210 8384 7568 2197 12383 887 710 650 1116 739 2501 11757 10740 9983 6802 2256 12174 870 707 655 1362 773 2787 12253 12660 11067 6827 3233 11985 860 705 665 1396 776 2496 12543 13183 10923 7068 4640 11836 850 700 665 1249 784 2254 12700 12440 10550 9070 4418 11687 841 697 662 1120 795 1986 12770 11480 9612 9868 3939 11588 826 694 657 1005 799 1880 12917 10440 8785 9156 3353 11439 819 691 660 929 797 1640 13267 9887 8529 7627 2945 1130

10 816 688 668 885 1078 1608 13483 9897 8052 6885 2732 110811 809 686 665 838 1405 1763 13570 9973 7618 7118 2572 109712 805 684 663 806 1317 1837 13650 10307 7277 7835 2408 108313 800 682 657 788 1313 1789 13400 10787 6943 7543 2253 106714 799 679 650 749 1441 1803 13130 11180 6088 6652 2050 105615 798 675 648 721 1448 1736 13070 12470 5274 5503 1941 104116 795 673 645 712 1426 1619 13217 13607 4967 4793 1848 102617 794 672 644 705 1540 1475 13120 13807 6264 4184 1773 101618 791 668 639 698 1981 1371 13170 12950 9699 3830 1707 100019 785 666 634 694 2143 1298 13170 11790 11047 3519 1645 992



20 783 662 631 691 2057 1240 13203 11063 10050 3208 1592 98521 780 660 641 683 1872 1202 13390 11487 8966 2954 1544 97422 779 659 660 676 1683 1241 13763 11987 7993 2769 1509 96423 776 656 687 669 1519 1398 14217 12170 9175 2604 1473 95724 771 653 753 659 1390 1787 14863 11963 10777 2452 1416 94725 763 651 767 649 1322 2396 15340 11583 11873 2316 1388 93826 757 650 753 642 1266 2644 15647 10880 12213 2201 1371 92827 751 648 765 627 1170 3408 16007 10933 12267 2097 1341 91928 745 647 775 623 1083 5753 15957 10114 11760 2050 1320 91129 739 645 791 617 1021 7052 15013 9384 10983 2020 1300 90530 729 - 813 637 966 7752 13503 8814 10010 2087 1281 89031 721 - 826 - 943 - 12020 8189 - 2110 - 879


1 1006 760 592 898 509 1209 6072 9824 8912 20200 2744 16252 996 752 587 906 504 1058 5243 9280 9813 20200 2636 16123 986 744 579 882 504 1038 4635 9032 9336 19440 2600 15934 974 739 576 840 557 1026 4512 8680 9392 18157 2540 15855 968 731 568 787 571 1014 5479 8520 9576 16333 2460 15696 962 723 563 736 576 1016 6731 8672 9953 14257 2387 15407 954 712 555 701 541 1006 7504 9984 12103 12280 2333 15118 942 704 547 675 509 962 8688 10977 14243 11827 2290 14899 932 701 536 648 496 968 9801 10560 14077 10887 2217 1473

10 926 696 528 640 475 928 10807 10227 13140 9408 2163 144911 920 688 523 648 459 1004 11610 10037 11333 8816 2140 142512 906 688 515 640 445 1026 12593 10773 9341 7696 2117 140713 892 680 507 627 440 1038 13970 12473 8048 6936 2097 138814 886 680 499 616 445 1032 15507 13897 7840 6327 2153 138015 876 672 491 632 483 1036 16800 14067 7191 5896 2147 137516 868 672 488 640 504 1087 18057 13957 7376 5506 2203 138317 860 669 483 632 477 1409 18890 15037 8176 5120 2233 142018 850 664 480 637 451 1783 19393 15670 8240 4773 2193 139919 842 656 472 603 507 2123 19637 16090 8384 4491 2103 136920 836 651 472 584 555 2672 19780 16800 8416 4219 2023 132421 830 643 469 560 603 2972 19790 16947 8512 4000 1940 128922 824 632 464 552 608 3524 19693 16613 8416 3797 1892 128123 816 624 464 560 627 4656 19517 15900 8960 3624 1865 126824 806 616 475 568 741 4869 19190 14663 9995 3476 1820 126325 800 611 509 579 910 4821 18627 12823 11620 3344 1785 126026 792 608 624 568 1083 5123 17720 11677 12153 3204 1748 125227 787 600 728 573 1151 5878 16083 10760 13393 3112 1713 124128 776 600 818 552 1263 6116 14123 10807 17540 3024 1681 122829 771 - 886 536 1447 6269 12103 10463 18990 2996 1665 121230 768 - 940 517 1441 6320 11177 9683 19623 2900 1641 118531 760 - 922 - 1319 - 10240 9144 - 2788 - 1169


1 1156 1040 856 1143 1172 3292 12923 12803 14413 5884 3845 20302 1145 1028 886 1204 1177 3256 13440 12400 14567 5698 3484 20073 1129 1018 918 1223 1156 2860 13787 12107 14990 5332 3284 19774 1121 1008 918 1183 1086 2608 13740 11863 15887 4848 3108 18935 1108 996 874 1109 1050 2620 13640 11770 17067 4379 2960 17996 1100 986 836 1040 1002 3020 13550 11967 18227 4005 2872 17247 1094 968 816 978 968 3360 13460 12307 18957 3765 2760 16558 1092 944 797 930 966 3388 13610 13210 19223 3556 2632 16209 1086 930 792 902 938 3072 14123 13897 19477 3392 2488 1580

10 1082 922 784 882 930 2928 14470 14303 19573 3284 2401 154811 1078 912 776 870 890 2892 14783 14817 19583 3144 2317 152112 1076 904 771 858 848 2988 14977 15230 19320 3084 2260 149513 1070 894 763 822 818 4550 15157 15527 18703 3124 2180 1487



14 1064 886 760 804 834 6606 15503 15530 17960 3164 2130 146015 1064 878 760 781 878 7360 15887 15250 16373 3060 2070 142816 1058 858 768 768 970 7273 16347 15370 14280 3268 2027 141217 1052 846 781 757 1028 6826 16920 15900 13537 3248 1973 139318 1046 838 824 792 1012 6496 17440 16307 10119 3364 1940 137719 1040 828 842 834 998 6149 17800 16533 8336 3384 1897 136720 1036 824 836 892 1028 5386 17960 16693 7108 3220 1881 135321 1034 820 830 910 1183 4928 17987 16987 6797 3164 1849 134522 1030 812 822 920 1465 4816 17947 17413 6379 2924 1833 133223 1024 806 814 928 2221 5115 17907 17720 6147 2972 1823 131324 1022 802 801 944 3404 5716 17787 17800 5698 3751 1809 129525 1028 800 773 944 3500 6908 17320 17493 5428 6287 1812 128126 1038 792 760 948 3296 8256 16720 17000 5608 7464 1833 126327 1046 806 736 964 3028 9555 16047 16360 5524 7592 1857 124928 1056 820 760 1006 2736 10927 15430 15673 5214 6885 1937 123929 1064 - 892 1062 2410 11940 14773 15180 5959 5806 1983 122030 1062 - 1026 1112 2592 12360 14087 14773 6077 4891 2010 120931 1052 - 1066 - 3076 - 13403 14543 - 4235 - 1199


1 1188 958 787 605 520 7608 13740 18637 19767 6657 5956 18442 1177 948 784 600 512 8888 14137 17173 21127 5908 5554 18153 1169 934 776 597 512 9605 14523 14940 21217 5494 5115 17804 1156 926 773 592 493 9544 14787 12573 20130 5019 5109 17535 1137 932 768 584 480 9248 15013 11413 19540 4928 5530 17246 1121 912 765 595 499 8480 15120 10103 18937 4624 6184 16897 1113 908 760 613 501 7119 15120 9088 18360 4357 5536 16638 1098 904 755 616 509 5716 14977 8416 17640 3973 5172 16369 1092 898 749 608 568 4757 14533 9176 16733 3629 4437 1609

10 1086 894 733 600 595 4107 13813 9456 15890 3524 3787 159111 1078 890 720 584 621 3536 12877 9472 14363 3524 3524 157512 1074 884 712 576 797 3364 11897 9749 13093 3856 3312 156413 1068 878 704 573 850 3212 10903 10050 11960 3835 3120 157714 1064 868 704 565 954 3096 10293 10783 11087 5110 2952 157515 1056 860 696 560 1140 2960 10540 11590 10337 4896 2820 159316 1052 854 688 560 1241 3108 11050 12110 9707 4768 2700 157717 1046 848 680 565 1255 3444 11443 13093 9376 5215 2604 155918 1038 844 675 563 1231 4309 11667 13873 9368 5602 2500 153519 1030 880 669 579 1161 5560 13423 14867 9320 5824 2420 152420 1022 834 664 565 1113 6313 13033 15443 9539 6613 2340 150021 1018 828 656 557 1148 6249 13717 16020 11327 7856 2270 146822 1008 822 648 552 1215 5794 14340 16267 11593 8592 2200 143623 1004 816 640 544 1324 6319 14903 16163 10677 8736 2150 140424 998 812 640 544 1391 7458 15550 15683 10557 8288 2100 137725 994 806 632 539 1503 8672 15900 15023 9877 7592 2060 135626 988 804 629 536 1444 9941 16227 14350 9328 6848 2020 132927 980 800 624 536 1508 11527 16627 15093 8760 6009 1977 130328 974 792 621 528 2160 12193 17293 15623 7968 6143 1940 128929 974 - 613 528 5063 13020 17947 15877 7656 5914 1892 127330 968 - 608 528 7115 13537 18563 17013 7488 5968 1863 126031 964 - 608 - 7528 - 18870 18713 - 5944 - 1252


1 1239 982 818 789 741 3973 11607 12887 10218 10069 4880 19432 1223 990 804 776 741 4048 11977 12817 12960 14807 5115 19573 1201 992 784 760 776 4005 12150 12560 16220 16420 4843 19044 1180 1004 776 752 858 3760 12247 12220 17507 17533 4448 18525 1164 1026 768 744 992 3631 12397 11927 18080 18443 4080 18206 1153 1032 773 744 1209 3536 12190 11440 17360 18603 3701 18097 1140 1036 784 733 1324 3324 11870 11387 15623 18267 3424 1791



8 1129 1024 792 725 1436 3164 11320 11537 13740 17533 3232 17679 1116 1010 792 712 1636 3136 10903 11600 12457 16487 3096 1732

10 1108 1000 802 704 1780 3124 10580 11630 11753 14810 2976 170011 1098 986 812 696 1745 3052 11060 11687 11120 12957 2888 167912 1086 976 818 691 1641 3501 12813 11657 10337 10927 2828 165213 1076 962 816 683 1543 4400 13980 12053 11077 9400 2768 162314 1070 962 810 680 1460 5353 14340 12330 12623 8432 2700 160415 1070 956 810 717 1364 8304 14270 12273 12937 7337 2556 158516 1058 950 812 755 1284 9901 13833 12160 13190 6701 2456 156117 1050 942 818 826 1215 11323 13237 11957 14133 6108 2360 154818 1040 928 818 862 1156 11973 13127 11713 16960 5746 2290 153519 1036 912 826 844 1111 12133 13680 11600 18520 5494 2200 151620 1028 900 838 818 1064 12647 14123 11750 18253 5284 2177 150321 1022 886 854 797 1034 12547 14197 12370 18013 5040 2160 148422 1016 874 872 771 1113 11993 13947 13670 17493 4821 2130 146023 1010 860 884 728 1295 11253 13547 14110 16680 4683 2073 144924 1010 854 896 688 1809 10487 13140 13943 15960 4416 2043 143125 1004 842 880 659 2073 9509 12890 13297 14927 4149 2000 140926 998 842 872 632 2193 9771 12830 12470 13333 3931 1960 139127 992 836 872 651 2492 10090 12873 11827 11887 3829 1930 137728 986 830 882 675 2592 10347 12767 10101 10507 3909 1920 136429 980 824 858 688 2303 11047 12720 9016 9539 4037 1910 135630 974 - 830 720 2800 11387 12637 8032 8784 4315 1910 134331 976 - 806 - 3636 - 12693 8512 - 4608 - 1329


1 1316 1046 870 600 544 1583 6090 10167 12630 6159 4480 20372 1308 1044 862 592 544 1973 7640 10613 11623 5890 4965 19703 1292 1040 858 592 536 2431 10073 11120 10720 6196 5374 19174 1276 1036 854 587 528 2544 11893 11823 9699 6973 5374 18815 1271 1034 848 589 536 2688 11603 12547 9200 7251 5320 18576 1255 1028 860 600 544 2764 10337 13570 9408 9184 5029 18257 1244 1026 884 608 544 2988 9509 13893 9739 10900 4528 18018 1231 1022 888 608 619 3932 8752 13897 10507 11283 4123 17779 1215 1018 866 608 810 5500 8392 12173 11137 11273 3787 1751

10 1204 1012 836 600 906 6351 8000 10337 10327 11167 3468 172111 1188 1004 812 600 914 7520 7488 9040 9835 10583 3372 170812 1180 1000 789 600 912 8304 8024 7632 10180 10497 3556 168913 1172 994 771 608 942 8472 8968 6665 10560 9793 3492 167114 1169 982 757 608 1006 7648 9739 7049 11107 9168 3376 164115 1159 976 736 600 1121 6899 9792 6467 11073 9304 3204 162516 1151 968 720 581 1471 6584 9584 6966 10460 9573 3068 160417 1140 964 717 568 1743 6701 10112 7159 10187 8976 2964 158818 1132 958 707 563 1860 6716 11007 6540 9627 8408 2780 156919 1124 950 696 555 1809 6584 11723 6203 9528 7816 2632 155120 1116 938 688 541 1684 6650 11947 6481 9480 7688 2520 152921 1105 930 683 520 1577 6577 11510 7504 9685 7632 2520 150822 1094 922 672 512 1428 6044 10880 8000 9931 7196 2476 149223 1088 916 656 520 1321 5770 10680 7408 9536 6965 2420 147124 1082 908 648 539 1284 6459 11173 6936 9272 6606 2397 145225 1076 900 648 560 1217 7816 11880 6819 8400 5884 2340 143326 1068 892 637 584 1185 8592 11460 7952 7720 5362 2297 142027 1064 886 624 605 1159 7808 10453 9192 7221 5077 2213 140428 1064 878 616 592 1140 7077 9648 10015 6936 4811 2167 139629 1058 - 616 565 1193 6193 9528 11400 6613 4555 2120 137730 1052 - 608 557 1212 5596 9845 12837 6313 4267 2090 136131 1046 - 600 - 1364 - 9877 13393 - 4315 - 1345




1 1332 1092 890 744 836 1883 6287 18900 8320 8136 2648 16232 1321 1127 890 739 824 1788 5584 18870 7488 7832 2496 16093 1305 1151 890 728 800 1815 5506 18840 7068 8808 2452 15934 1289 1172 884 720 781 1836 6317 18543 6613 9336 2432 15805 1273 1156 878 725 760 1788 7244 18273 5986 9488 2373 15646 1257 1137 876 771 752 1748 7472 17813 5350 9016 2290 15407 1244 1113 872 816 749 1660 7320 16933 4971 8032 2220 15248 1233 1094 866 832 755 1641 7648 15733 4944 7280 2187 15009 1220 1086 862 830 789 1729 8536 14050 4939 6496 2177 1489

10 1220 1070 854 828 862 1721 9008 12227 5443 5710 2167 146811 1212 1058 848 812 926 1705 9600 11090 8176 4955 2097 144912 1201 1058 840 792 956 1761 10350 9866 10153 4320 2043 143313 1193 1046 830 768 936 1825 10933 10793 10227 3947 1987 141714 1183 1038 830 749 926 1836 11603 14050 8984 3631 1950 140115 1177 1026 826 736 910 1807 11543 16550 7479 3508 1927 138816 1164 1006 828 723 902 1772 11723 18593 5614 3488 1900 138017 1156 986 816 720 922 1880 12027 20037 4667 3480 1892 136418 1156 960 804 712 980 2163 12170 22437 4613 3909 1884 134019 1148 942 812 704 1345 2852 12080 23957 4688 3925 1884 131620 1140 930 789 696 1777 3767 11527 23167 5321 3600 1879 130021 1132 920 781 696 1748 4901 11020 20397 4965 3456 1857 129222 1121 914 787 704 1700 5818 10433 19840 5196 3372 1828 128423 1108 908 768 701 1735 6335 10647 19537 5848 3312 1804 127324 1100 908 779 696 1655 7287 11640 19203 5968 3384 1783 126025 1092 918 752 688 1617 9251 12767 18453 6951 3576 1743 125226 1082 902 755 672 1505 10707 14077 17347 7199 3548 1703 124427 1076 896 744 672 1439 10590 15443 15177 8128 3384 1687 123628 1076 896 736 704 1596 9999 16057 12997 8544 3324 1663 122829 1076 - 728 768 1983 8544 17333 11860 10047 3304 1647 122830 1076 - 728 824 2110 7150 18370 10211 9120 3124 1644 122031 1074 - 736 - 2033 - 18820 9152 - 2868 - 1212


1 1204 980 922 830 994 1428 9877 9499 7688 6064 3544 17722 1196 974 920 824 1022 1417 10793 12780 8760 6437 3396 17563 1191 968 914 818 1010 1401 11720 14530 10017 6105 3288 17004 1183 968 914 806 1028 1460 12913 15057 11267 5956 3200 16475 1169 958 908 800 992 1793 13943 14783 11720 6320 3132 15936 1153 956 906 792 962 1983 14733 14400 11870 6533 3012 15567 1132 956 902 792 962 2073 15517 13763 12423 6591 2892 15488 1116 956 902 781 966 2330 16467 12603 12687 6936 2756 15299 1108 938 902 776 1000 2183 17387 11150 12233 7384 2692 1511

10 1100 948 896 765 1040 2193 18000 9563 12077 7209 2632 149211 1100 944 890 752 1052 2896 18340 8512 12273 6848 2560 147612 1094 944 890 763 1060 4187 18447 7680 11833 6393 2512 146513 1084 944 888 792 1070 4773 18380 7480 11193 6028 2456 144914 1082 944 884 814 1058 4944 18153 7632 11157 6159 2416 142515 1078 938 878 832 1044 5072 18027 7688 9780 7079 2363 140916 1076 950 878 834 1040 5083 18107 7848 9120 7688 2300 138817 1070 956 872 818 1064 5083 18230 7992 8240 7736 2247 137218 1064 956 866 797 1066 5404 18330 8200 7552 7400 2207 136119 1058 956 864 779 1106 5788 18197 9176 7090 6841 2140 134020 1052 952 854 763 1343 5836 17840 10163 7456 6215 2093 132921 1052 944 854 744 1308 6279 17253 11150 7568 5548 2040 132122 1046 938 848 763 1220 6687 16327 12017 7424 5452 2000 130823 1040 932 840 814 1247 6247 15710 11693 7400 5416 1973 129224 1034 932 836 848 1257 6120 15037 11077 8328 4944 1933 127625 1028 932 830 908 1444 6870 14160 9983 8488 4901 1887 1284



26 1022 932 832 986 1500 6848 13450 8960 8384 4923 1847 128727 1012 926 818 1030 1543 6364 12790 8344 7672 5266 1828 129228 1002 926 848 1086 1500 6379 12473 7696 6929 4827 1812 128429 994 - 844 1052 1495 7792 11507 7054 6577 4336 1796 127630 992 - 836 1014 1468 9016 10027 6591 6217 3968 1788 126531 986 - 830 - 1428 - 9056 6863 - 3744 - 1249


1 1228 950 760 611 1601 3040 10603 18917 7848 8240 3484 16972 1212 944 760 624 1495 2856 9328 17773 8128 7856 3312 16653 1196 942 752 648 1412 2664 8624 16343 8840 7840 3176 16524 1172 936 749 704 1324 2544 7904 14160 9523 7568 3044 16365 1161 932 741 712 1236 2524 7576 12387 10040 7039 2908 16256 1156 928 736 712 1156 2460 7856 11687 10163 6767 2784 16017 1156 926 728 691 1099 2572 7592 11163 10740 6379 2672 15778 1148 920 720 680 1058 2868 6863 10823 11563 6797 2540 15409 1145 918 712 664 1044 3877 7127 11500 12313 9325 2456 1513

10 1132 912 704 669 1020 4928 7624 12800 13437 11177 2370 149711 1121 908 696 691 1000 4960 9264 13693 13993 12103 2293 146012 1105 904 688 709 978 5279 10990 13403 14793 13043 2230 142813 1092 896 688 787 952 6031 12373 12923 16403 13570 2170 141714 1080 888 680 810 930 7068 13910 12233 17773 13813 2090 139615 1068 880 680 814 892 6701 15410 11353 17840 13653 2060 137716 1056 878 672 824 944 6082 16627 10123 18160 13043 2040 136117 1046 870 672 840 944 5800 17787 9653 18027 11880 2030 134818 1040 862 664 892 902 5452 18583 10349 17453 10707 2010 133219 1034 852 656 1046 1127 5104 18830 12007 16427 9963 1990 132120 1028 844 648 1500 1931 5040 18810 11487 15720 9408 1980 130021 1020 834 648 2223 2448 5560 18713 11230 14400 8880 1960 128922 1010 826 640 2988 3316 7802 18530 10440 13357 8192 1933 126523 1008 816 640 3468 4741 10293 18607 9248 12207 7325 1887 124124 998 802 632 3376 5596 11563 18893 8424 10880 6569 1852 121725 992 800 624 2992 5190 12073 19423 7688 9921 5800 1799 120426 990 792 624 2724 4496 12130 19660 6958 9392 5245 1764 119327 980 784 616 2293 3781 11987 19730 6921 9432 4789 1740 117228 974 779 613 2063 3408 12143 19617 6775 9528 4453 1732 116129 972 768 608 1877 3428 12010 19570 6643 9248 4192 1724 114030 962 - 608 1687 3328 11603 19550 6555 8912 3920 1708 113231 960 - 608 - 3212 - 19470 7157 - 3717 - 1124

(Source :Department of Meteorology and Hydrology) Table 2. Mean Annual Temperature of Different Stations (°C)

Year Station

1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

Yangon 27.42 27.64 28.42 27.27 27.17 27.34 27.75 27.63 27.63 28 New

Deli/Palam 23.92 24.69 26.13 25.52 25.55 27.88 26.76 26.23 26.15

Bangkok 28.63 29.43 29.62 28.48 28.79 29 29.22 29.23 29.34 29.13 (Source: http://tutiempo.net/en/Climate/asia.htm)



Table.3 Monthly Mean Temperature of Chindwin Basin at Monywa Station (°C)

STATION : MONYWA

YEAR JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC1975 20.6 23.5 27.8 31.7 31.4 29.6 28.9 28.6 28 27.9 23.8 19.4 1976 20.1 23 26.8 31.1 30 29.8 29.8 29.1 29.5 27.3 25.5 20.5 1977 20 23.5 28.4 29.1 29.4 31 30.4 28.8 27.9 25.8 24.8 21.5 1978 23 23.7 26.5 31 31 30 28.7 29.2 28.2 27.5 25 22.1 1979 21.1 23.7 27.4 32 34.6 32 30.5 29.5 29.5 28.2 27 21.7 1980 21 21.5 28.5 33 32.6 29.8 30 30.2 28.9 26.6 25.9 22.5 1981 21.4 24.5 26.8 28.7 31.1 29 30.1 30 29.9 28.7 24.8 21.1 1982 21 22.8 27 30.7 32.9 30.5 31.5 29.8 29.9 28.9 25.1 21.8 1983 20.2 23.7 26.9 30.8 32.8 32.1 32.3 30.4 30 27.7 23.7 20 1984 20.1 24.2 27 31.3 30.7 29 30 29.5 29 28 24.3 22.2 1985 21 22 28.3 31.6 31.2 30 30.1 29.7 29.2 29 24.3 22 1986 21.4 24.2 27.7 31.2 32.9 32 31.1 29.6 28.6 27.6 24.5 21.6 1987 21.4 23.7 25 30.4 32.7 31 31.1 29.6 29.2 28.3 26 21 1988 22.1 24.3 28.4 32.2 32.6 29.6 32 30.5 30.1 28.8 23.5 22.4 1989 19.5 23.1 27.5 30.5 32 30.3 30.3 29.3 29.6 27.7 24.2 20.7 1990 21.5 23.8 26.4 30.6 31.2 31.3 30.8 31.1 28.8 28.8 26.9 21.9 1991 20.4 23.6 29.6 30.8 31.6 28.9 30.5 29.8 28.9 27.2 23 20.1 1992 19.2 21 26.9 31.7 31.5 26.1 29.9 29.2 28.4 26 22.7 18.2 1993 19.2 22.9 26.9 30.3 30.5 29.8 31.6 30.2 28.2 27.6 24.7 22.8 1994 22.3 23.6 27.5 31.4 33.4 30.9 30.7 29.7 29.3 28.2 24.8 20.9 1995 21.5 23.9 26.8 31 32.5 32.1 30.6 30 29.1 28.5 25.1 15.7 1996 21.5 24 27.4 30.3 31.6 29.7 30.1 28.9 28.6 27.5 25.4 23.8 1997 20.9 22.8 28.3 29.4 32.8 32 30.7 30.3 29.7 28.3 26 22.6 1998 22 24.7 27.9 31.3 32.7 33 31.9 31.8 29.8 29.4 26.5 23.1 1999 21.9 26.2 28.5 32.6 29.9 31.4 31.5 29.9 29.5 28 24.4 20.8 2000 20.9 22.5 25.8 30.7 29 29.9 30.2 30.5 28.5 27.2 23.9 20.9 2001 21 24.5 27.9 32.1 30.1 30.3 30.7 30.4 30.4 28.2 25.3 22.8 2002 22 25.7 28.9 32.1 31 31.6 31.2 29.1 29.2 28.9 25.6 22.1 2003 21.2 24.6 27.9 32.1 30.8 30.3 31.6 31.1 30.2 29.2 25.9 23.6 2004 22.3 24.7 29.5 30.6 32 30.3 30.7 31.3 29 28.8 26.1 22.9 2005 22.4 26.2 28.8 32.4 33.3 31.9 31.6 30.9 29 29 25.8

" * " data not available (Source :Department of Meteorology and Hydrology)



Table.4 Annual Rainfall of Chindwin Basin

Year Rainfall (mm) Year Rainfall (mm)

1968 2268 1987 2409

1969 1855 1988 2496.9

1970 2149 1989 2293.4

1971 2285 1990 2427

1972 1479 1991 2542.6

1973 2252 1992 2023.4

1974 2077 1993 2048.6

1975 2208 1994 1969.6

1976 2115 1995 2362.1

1977 2328 1996 2206

1978 2184 1997 2258.6

1979 1897 1998 2004.4

1980 2350 1999 2221.3

1981 1980 2000 2032

1982 2271 2001 1855.2

1983 2228 2002 2036.5

1984 2301 2003 1968.5

1985 2346 2004 2152

1986 1902 2005 1327

(Source :Department of Meteorology and Hydrology)



Fig.1 Hydrograph of Chindwin River at Monywa Station

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Hydrograph 1974 - 1985



Appendix-D Frequency Factors and Useful Tables 139 Mtr.No.158204


Appendix- D Frequency Factors and Useful Tables for Distribution Functions

Table.1 Frequency Factors for 3-Parameter Lognormal Distribution Cumulative Probability, P (%)

50 80 90 95 98 99

Corresponding Return Period, T (year) Coefficient of Skew, γ

2 5 10 20 50 100

-1.00 0.1495 -0.7449 -1.3156 -1.8501 -2.5294 -3.0333

-0.80 0.1241 -0.7700 -1.3201 -1.8235 -2.4492 -2.9043

-0.60 0.0959 -0.7930 -1.3194 -1.7894 -2.3600 -2.7665

-0.40 0.0654 -0.8131 -1.3128 -1.7478 -2.2631 -2.6223

-0.20 0.0332 -0.8296 -1.3002 -1.6993 -2.1602 -2.4745

0.00 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.20 -0.0332 0.7449 1.3156 1.8501 2.5294 3.0333

0.40 -0.0654 0.7700 1.3201 1.8235 2.4492 2.9043

0.60 -0.0959 0.7930 1.3194 1.7894 2.3600 2.7665

0.80 -0.1241 0.8131 1.3128 1.7478 2.2631 2.6223

1.00 -0.1495 0.8296 1.3002 1.6993 2.1602 2.4745 (Source: G.W Kite “Frequency and Risk Analyses in Hydrology”, 1977) Table.2 Frequency Factors for Pearson Type III Distribution

Cumulative Probability, P (%)

50 80 90 95 98 99


2 5 10 20 50 100

0.0 0.0000 0.8416 1.2816 1.6448 2.0537 2.3264

0.1 -0.0167 0.8363 1.2917 1.6728 2.1070 2.3997

0.2 -0.0333 0.8303 1.3009 1.6996 2.1595 2.4727

0.3 -0.0499 0.8234 1.3089 1.7254 2.2112 2.5453

0.4 -0.0664 0.8157 1.3159 1.7501 2.2619 2.6172

0.5 -0.0828 0.8072 1.3218 1.7735 2.3117 2.6884

0.6 -0.0990 0.7980 1.3267 1.7958 2.3603 2.7588

0.7 -0.1151 0.7880 1.3304 1.8168 2.4078 2.8283

0.8 -0.1310 0.7773 1.3330 1.8366 2.4541 2.8968

0.9 -0.1467 0.7659 1.3345 1.8551 2.4991 2.9641

1.0 -0.1621 0.7537 1.3349 1.8723 2.5428 3.0303

(Source: G.W Kite “Frequency and Risk Analyses in Hydrology”, 1977)



Table.3 Useful Data of Gamma function, Γ (α) = (α -1 ) ! α Γ (α) α Γ (α) α Γ (α) α Γ (α)

1.00 1.0000 1.26 0.90440 1.52 0.88704 1.78 0.92623 1.02 0.98884 1.28 0.90072 1.54 0.88818 1.80 0.93138 1.04 0.97844 1.30 0.89747 1.56 0.88964 1.82 0.93685 1.06 0.96874 1.32 0.89464 1.58 0.89142 1.84 0.94261 1.08 0.95973 1.34 0.89222 1.60 0.89352 1.86 0.94869 1.10 0.95135 1.36 0.89018 1.62 0.89592 1.88 0.95507 1.12 0.94359 1.38 0.88854 1.64 0.89864 1.90 0.96177 1.14 0.93642 1.40 0.88726 1.66 0.90167 1.92 0.96877 1.16 0.92980 1.42 0.88636 1.68 0.90500 1.94 0.97610 1.18 0.92373 1.44 0.88581 1.70 0.90864 1.96 0.98374 1.20 0.91817 1.46 0.88560 1.72 0.91258 1.98 0.99171 1.22 0.91311 1.48 0.88575 1.74 0.91683 2.00 1.00000 1.24 0.90852 1.50 0.88623 1.76 0.92137

(Source: Wittenberg “Hydrologie Vorlesungsunterlagen”, 2004)

Table.4 Parameter α, Aα and Bα for Extreme Value Type III Distribution

Coefficient of Skew,Ү α Aα Bα -1.00 65.63043 0.44760 52.24465 -0.90 26.26360 0.44229 21.47978 -0.80 16.30207 0.43629 13.68443 -0.70 11.73785 0.42952 10.10381 -0.60 9.10978 0.42193 8.03409 -0.50 7.39676 0.41343 6.67757 -0.40 6.18962 0.40397 5.71462 -0.30 5.29236 0.39350 4.99218 -0.20 4.59923 0.38198 4.42770 -0.10 4.04809 0.36938 3.97273 0.00 3.59997 0.35571 3.59692 0.10 3.22914 0.34098 3.28029 0.20 2.91791 32523 3.00911 0.30 2.65366 0.30851 2.77366 0.40 2.42717 0.29089 2.56682 0.50 2.23149 0.27246 2.38329 0.60 2.06133 0.25334 2.21910 0.70 1.91253 0.23367 2.07116 0.80 1.78181 0.21360 1.93718 0.90 1.66654 0.19329 1.81524 1.00 1.56457 0.17291 1.70391

(Source: G.W Kite “Frequency and Risk Analyses in Hydrology”, 1977)



Table.5 Frequency Factors for Extreme Value Type III Distribution

Cumulative Probability, P (%)

50 80 90 95 98 99


2 5 10 20 50 100

-1.0 0.1567 -0.7329 -1.3134 -1.8641 -2.5680 -3.0889

-0.90 0.1446 -0.7501 -1.3215 -1.8546 -2.5232 -3.0089

-0.80 0.1321 -0.7666 -1.3282 -1.8430 -2.4766 -3.9282

-0.70 0.1189 -0.7825 -1.3332 -1.8294 -2.4280 -2.8465

-0.60 0.1051 -0.7977 -1.3366 -1.8134 -2.3771 -2.7634

-0.50 0.0906 -0.8122 -1.3382 -1.7950 -2.3239 -2.6788

-0.40 0.0754 -0.8258 -1.3379 -1.7741 -2.2683 -2.5928

-0.30 0.0595 -0.8385 -1.3356 -1.7506 -2.2103 -2.5055

-0.20 0.0428 -0.8502 -1.3313 -1.7245 -2.1502 -2.4172

-0.10 0.0255 -0.8607 -1.3248 -1.6960 -2.0881 -2.3282

0.00 0.0075 -0.8699 -1.3161 -1.6650 -2.0244 -2.2390

0.1 -0.0110 -0.8778 -1.3053 -1.6318 -1.9595 -2.1500

0.2 -0.0300 -0.8842 -1.2923 -1.5966 -1.8938 -2.0619

0.3 -0.0493 -0.8891 -1.2773 -1.5595 -1.8277 -1.9752

0.4 -0.0689 -0.8923 -1.2603 -1.5210 -1.7616 -1.8902

0.5 -0.0885 -0.8939 -1.2415 -1.4812 -1.6961 -1.8075

0.6 -0.1081 -0.8938 -1.2209 -1.4405 -1.6315 -1.7275

0.7 -0.1275 -0.8921 -1.1989 -1.3992 -1.5682 -1.6506

0.8 -0.1466 -0.8888 -1.1757 -1.3578 -1.5068 -1.5770

0.9 -0.1651 -0.8840 -1.1515 -1.3165 -1.4473 -1.5071

1.0 -0.1829 -0.8777 -1.1266 -1.2757 -1.3903 -1.4409 (Source: G.W Kite “Frequency and Risk Analyses in Hydrology”, 1977)

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