Post on 24-Mar-2021
Examensarbete vid Institutionen för geovetenskaper ISSN 1650-6553 Nr 242
Usability of Standard Monitored Rainfall-Runoff Data in Panama,
Juan Diaz River Basin
Usability of Standard MonitoredRainfall-Runoff Data in Panama,Juan Diaz River Basin
José Eduardo Reynolds Puga
José Eduardo Reynolds Puga
Uppsala universitet, Institutionen för geovetenskaperExamensarbete D, 15 hp i HydrologiISSN 1650-6553 Nr 242Tryckt hos Institutionen för geovetenskaper, Geotryckeriet, Uppsala universitet, Uppsala, 2012.
Water resources demand and natural disasters related to hydro meteorological events have increased the interest in hydrological studies in Panama. Runoff estimations are important for effective water resources management in any catchment, but the limited quantity and quality of the available hydrological and meteorological data in Panama make it hard for researchers to come to conclusive statements that can help in good planning. This issue has to be addressed, but meanwhile, the challenge is to try to understand the hydrological processes occurring in any catchment with the available data.
The relationship between rainfall and runoff in the Juan Diaz River basin is not well understood and its fast response due to high rainfall intensities in the area is a concern in the community and authorities. The meteorological and hydrological data in the Juan Diaz River basin are also limited. The main objective of this thesis was to establish how well the Juan Diaz River basin can be hydrologically represented by records of the available instrumentation. This was performed with a hydrological, WASMOD, and a statistical model, linear multiple regression. Both models simulated daily and monthly runoff for a period of 21 years. For the long term water balance, a graph showing discharge against rainfall data was plotted in the yearly scale to establish a relationship between the two variables.
Precipitation records from an active meteorological station, which was the closest to the basin from the ones with available records, were used in this study to estimate the areal mean precipitation of the basin, since nowadays there are no active meteorological stations within the basin.
It was not possible to represent the Juan Diaz River basin well with the two models in the daily and monthly resolution. Uncertainties in the precipitation input and in the discharge output data were considered to be the reasons for the poor simulations. That said, it can be stated that the available instrumentation at this point is not sufficient for modeling. In the long term water balance, the instrumentation can be used for water estimations, but care has to be taken if this approach is used since the limited quantity of data in this scale were scattered around the predictions.
Efforts have to be made to encourage decision makers to increase the available instrumentation in the Juan Diaz River basin, in order to make accurate simulations or forecasting that will better support water resources management.
Examensarbete vid Institutionen för geovetenskaper ISSN 1650-6553 Nr 242
Usability of Standard Monitored Rainfall-Runoff Data in Panama,
Juan Diaz River Basin
José Eduardo Reynolds Puga
Copyright © José Eduardo Reynolds Puga och Institutinen för geovetenskaper, Luft‐, vatten –och
landskapslära, Uppsala Universitet.
Tryckt hos Institutionen för geovetenskaper, Geotryckeriet, Uppsala universitet, Uppsala, 2012
ABSTRACT
USABILITY OF STANDARD MONITORED RAINFALL‐RUNOFF DATA IN PANAMA,
JUAN DIAZ RIVER BASIN.
Reynolds, J., Department of Earth Science, Uppsala University, Villavägen 16, SE−752 36,
Uppsala, Sweden.
Water resources demand and natural disasters related to hydro meteorological events have
increased the interest in hydrological studies in Panama. Runoff estimations are important
for effective water resources management in any catchment, but the limited quantity and
quality of the available hydrological and meteorological data in Panama make it hard for
researchers to come to conclusive statements that can help in good planning. This issue has
to be addressed, but meanwhile, the challenge is to try to understand the hydrological
processes occurring in any catchment with the available data.
The relationship between rainfall and runoff in the Juan Diaz River basin is not well
understood and its fast response due to high rainfall intensities in the area is a concern in
the community and authorities. The meteorological and hydrological data in the Juan Diaz
River basin are also limited. The main objective of this thesis was to establish how well the
Juan Diaz River basin can be hydrologically represented by records of the available
instrumentation. This was performed with a hydrological, WASMOD, and a statistical model,
linear multiple regression. Both models simulated daily and monthly runoff for a period of 21
years. For the long term water balance, a graph showing discharge against rainfall data was
plotted in the yearly scale to establish a relationship between the two variables.
Precipitation records from an active meteorological station, which was the closest to the
basin from the ones with available records, were used in this study to estimate the areal
mean precipitation of the basin, since nowadays there are no active meteorological stations
within the basin.
It was not possible to represent the Juan Diaz River basin well with the two models in the
daily and monthly resolution. Uncertainties in the precipitation input and in the discharge
output data were considered to be the reasons for the poor simulations. That said, it can be
stated that the available instrumentation at this point is not sufficient for modeling. In the
long term water balance, the instrumentation can be used for water estimations, but care
has to be taken if this approach is used since the limited quantity of data in this scale were
scattered around the predictions.
Efforts have to be made to encourage decision makers to increase the available
instrumentation in the Juan Diaz River basin, in order to make accurate simulations or
forecasting that will better support water resources management.
Keywords: Juan Diaz, WASMOD, Linear Multiple Regression, Available Instrumentation
RESUMEN
USABILIDAD DE REGISTROS TÍPICOS DE LLUVIA‐ESCORRENTÍA MONITOREADOS
EN PANAMÁ, CUENCA DEL RÍO JUAN DÍAZ
Reynolds, J., Departamento de Ciencias de las Tierra, Universidad de Uppsala, Villavägen 16,
SE−752 36, Uppsala, Suecia.
La demanda de recursos hídricos y la ocurrencia de desastres naturales relacionados con eventos
hidro‐meteorologicos han incrementado el interés de estudios hidrológicos en Panamá.
Estimaciones de escorrentía son importantes para el manejo efectivo de los recursos hídricos en
cualquier cuenca, pero la calidad y cantidad limitada de registros hidrológicos y meteorológicos
en Panamá hacen difícil a los investigadores llegar a conclusiones contundentes que puedan
ayudar a una buena planificación. Este problema debe ser abordado, pero entretanto, el reto es
tratar de entender los procesos hidrológicos que ocurren en las cuencas con los registros
disponibles.
La relación lluvia‐escorrentía en la cuenca del Río Juan Díaz no se entiende completamente y su
rápida respuesta debido a las lluvias de alta intensidad en el área es una preocupación en la
comunidad y en las autoridades. Los registros meteorológicos e hidrológicos en la cuenca del Río
Juan Díaz son limitados. El objetivo principal de esta tesis fue establecer que tan bien se podía
representar hidrológicamente la cuenca del Río Juan Díaz con los registros disponibles de la
instrumentación existente hoy en día en la misma. Esto se realizo con un modelo hidrológico,
WASMOD, y con un modelo estadístico, regresión lineal múltiple. Ambos modelos simularon
escorrentía diaria y mensual por un período de 21 años. Para el balance hídrico a largo plazo, se
graficaron en la escala anual los datos de caudal contra los datos de precipitación para
establecer una relación entre ambas variables.
Registros de precipitación de una estación meteorológica activa, la cual era la más próxima a la
cuenca de las estaciones con registros disponibles, fueron utilizados en este estudio para estimar
la precipitación promedio areal de la cuenca, dado que hoy en día no hay ninguna estación
meteorológica activa dentro de la misma. En la escala diaria y mensual, no fue posible
representar bien la cuenca del Río Juan Díaz con los dos métodos seleccionados. Incertidumbres
en los datos de entrada y salida fueron consideradas las razones de las pobres simulaciones.
Dicho lo anterior, se puede concluir que la instrumentación existente en la cuenca hoy en día no
es suficiente para su modelación hidrológica. En el balance hídrico a largo plazo, la
instrumentación existente podría usarse pero cuidado debe tenerse si esta aproximación es
utilizada ya que la cantidad limitada de datos en esta escala estaba dispersa alrededor de las
predicciones.
Esfuerzos tienen que hacerse para alentar a los tomadores de decisiones en Panamá para
aumentar la instrumentación existente en la cuenca del Río Juan Díaz, para así poder hacer la
misma posible para predicciones que servirán para una mejor planificación de sus recursos.
Palabras Claves: Juan Díaz, WASMOD, Regresión Lineal Múltiple, Instrumentación Existente.
REFERAT
ANVÄNDBARHET AV TILLGÄNGLIGA ÖVERVAKNINGSDATA FÖR NEDERBÖRD
OCH VATTENFÖRING I JUAN DIAZ‐FLODENS AVRINNINGSOMRÅDE, PANAMA
Reynolds, J., Institutionen för geovetenskaper, Uppsala Universitet, Villavägen 16, 752 36
Uppsala
Behovet av vattenresurser och den höga frekvensen av hydrometeorologiska naturkatastrofer har
ökat intresset för hydrologiska studier i Panama. Vattenföringsuppskattningar är viktiga för en
effektiv vattenförvaltning i varje avrinningsområde men den begränsande mängden och kvalitén på
hydrologiska och meteorologiska data i Panama gör det svårt för forskare att dra meningsfulla
slutsatser som underlag för en god vattenförvaltning. Detta problem måste adresseras och under
tiden är forskningens utmaning att klarlägga så mycket som möjligt av ett avrinningsområdes
hydrologiska egenskaper utifrån tillgängliga data.
Förhållandet mellan nederbörd och avrinning i Juan Diaz‐flodens avrinningsområde är otillräckligt
känt och det snabba svaret på intensiv nederbörd i området är ett samhällsproblem. Meteorologiska
och hydrologiska data är begränsade i Juan Diaz‐flodens avrinningsområde. Huvudsyftet med detta
examensarbete var att fastställa hur väl den hydrologiska regimen i Juan Diaz‐flodens
avrinningsområde kunde förstås med tillgängliga data från befintliga mätstationer. Studien
genomfördes med hjälp av en hydrologisk modell, WASMOD, och en statistisk modell, linjär multipel
regression. Båda modellerna simulerade dagliga och månatliga vattenföringar för en 21‐årsperiod.
Avrinningsområdets långsiktiga vattenbalans beräknades med ett diagram där flerårsmedelvärden av
vattenföring ritades upp mot flerårsmedelvärden av nederbörd.
Det fanns inga aktiva väderstationer inom avrinningsområdet och nederbördsmätningar från den
aktiva väderstation med tillgängliga data som låg närmast användes för att skatta nederbördens
arealmedelvärde.
Det gick inte att representera Juan Diaz‐flodens dagliga eller månatliga vattenföringsdynamik på ett
tillfredställande sätt med de två modellerna. Osäkerheten hos nederbördsindata och
vattenföringsdata för kalibrering ansågs vara orsak till de dåliga simuleringarna. De nuvarande
hydrologiska och meteorologiska mätstationerna räcker inte för att modellera denna dynamik.
Nuvarande mätdata kan användas för att fastställa avrinningsområdets vattenbalans över flera år
men även denna är osäker med stor spridning av värdena.
Det behövs insatser för att övertala beslutsfattare att utöka befintliga mätprogram för Juan Diaz‐
flodens avrinningsområde om vattenförvaltningen inom området skall kunna grundas på tillförlitliga
hydrologiska beräkningar.
Nyckelord: Juan Diaz‐floden, WASMOD, linjär multipel regression, befintliga mätstationer
CONTENTS
LIST OF FIGURES........................................................................................................................1
LIST OF TABLES..........................................................................................................................3
1. INTRODUCTION.....................................................................................................................5
2. STUDY AREA AND METHODS................................................................................................7
2.1. Study Area.....................................................................................................................7
2.1.1. Generalities..........................................................................................................7
2.2. Literature Review and Methodology...........................................................................9
2.2.1. Description of the Hydrological Model..............................................................10
2.2.1.1. WASMOD.............................................................................................11
2.2.1.2. Input Data............................................................................................11
2.2.1.3. WASMOD Model Structure..................................................................11
2.2.1.4. Evapotranspiration Losses...................................................................12
2.2.1.5. Slow Flow Component.........................................................................15
2.2.1.6. Fast Flow Component..........................................................................15
2.2.1.7. Routing Routine of Fast Flow Component...........................................16
2.2.1.8. Calculated Runoff and Water Balance.................................................16
2.2.2. Linear Multiple Regression Analysis...................................................................17
2.3. Available Data..............................................................................................................18
2.3.1. Meteorological Data...........................................................................................18
2.3.2. Hydrological Data...............................................................................................20
2.3.3. Historical Flood Records.....................................................................................23
3. DATA PREPARATION...........................................................................................................24
3.1. Precipitation................................................................................................................24
3.1.1. Quality Control of the Precipitation Data...........................................................24
3.1.2. Estimation of Missing Precipitation Data...........................................................26
3.1.3. Double Mass Analysis.........................................................................................28
3.1.4. Precipitation as Input Data.................................................................................29
3.2. Potential Evapotranspiration......................................................................................32
3.2.1. Estimation of Missing Pan Evaporation Data.....................................................32
3.2.2. Quality Control of Potential Evapotranspiration Data.......................................32
3.3. Temperature................................................................................................................33
3.3.1. Estimation of Missing Temperature Data...........................................................33
3.4. Relative Humidity........................................................................................................33
3.4.1. Estimation of Missing Relative Humidity Data...................................................33
3.5. Observed Discharge.....................................................................................................34
3.5.1. Quality Control of Observed Discharge Data.....................................................34
3.6. Flood Dates Registered................................................................................................40
3.6.1. Quality Control of the Flood Records.................................................................40
4. MODEL QUALITY..................................................................................................................41
4.1. WASMOD Calibration and Quality of the Simulations..............................................41
5. RESULTS...............................................................................................................................43
5.1. WASMOD Simulations.................................................................................................43
5.2. Linear Multiple Regression..........................................................................................47
5.3. Long Term Rainfall‐Runoff Relationship.....................................................................53
6. DISCUSSION.........................................................................................................................54
7. CONCLUSIONS.....................................................................................................................56
ACKNOWLEDGEMENTS...........................................................................................................57
REFERENCES.............................................................................................................................58
ANNEX A. List of Equations used in this thesis for the WASMOD system
(snow free catchment) ......................................................................................................61
ANNEX B. Annual Potential Evapotranspiration Map created by ETESA, 1971−2002...........62
1
LIST OF FIGURES
Figure 1. Location of the Juan Diaz River Basin (Map Source: ETESA, 1999)…….………………...…7
Figure 2. WASMOD Model Structure for a Snow Free Catchment.
Modified from Frevert and Singh (2002)………..……………….………..………………………………….11
Figure 3. Budyco Diagram (Sivapalan, 2001)…………………………………………………………………..……14
Figure 4. Flood Prone Areas due to the Juan Diaz River. Map created with
information from documents of ETESA (1999) and SINAPROC (2005)……………………..……20
Figure 5. Location of meteorological and hydrological stations with available
records located within and outside the Juan Diaz River basin..…………..…………….............21
Figure 6. Summary of the available data from the different stations within
and outside the Juan Diaz River basin on a yearly time scale……..….………………………..……21
Figure 7. Number of Floods Registered per Year in the Juan Diaz Township….……………..…….23
Figure 8. Double mass plot between precipitation records of the Tocumen
meteorological station and the other 6 stations with available records.……….……………..28
Figure 9. Elevation ranges of the Juan Diaz River basin at the discharge station.
Map Source: USGS (2011)……………………..………………………………………………….......…………...30
Figure 10. The long term accumulated precipitation registered
(from 1985 till 2000) at meteorological stations with available
records versus the elevation in which these are located.……………………………………………..31
Figure 11. Observed Monthly Discharge ‐Juan Diaz and
Monthly Precipitation‐Tocumen 1985−2005………………..…………………..……………………….…35
Figure 12. Observed Daily Discharge‐Juan Diaz and Daily Precipitation‐Tocumen
Aug−Dec 2005.…………………………………….…………………………………………………………………….…36
Figure 13. Observed Daily Discharge‐Juan Diaz and Daily Precipitation‐Tocumen
April−Dec 1991.…………………………………………………………………………………………………………….36
Figure 14. Observed Daily Discharge‐Juan Diaz and Daily Precipitation‐Tocumen
Jun−Dec 1986.…………………………………..……………………………..……………………………………….…37
Figure 15. Observed Daily Discharge‐Juan Diaz and Daily Precipitation‐Tocumen.
A corresponds to the period between May−Dec 1995.
B corresponds to the period between May−Dec 1998.
C corresponds to the period between May−Dec 1999….……………………..…………………….…38
2
Figure 16. Observed Daily Discharge‐Juan Diaz and Daily Precipitation‐Tocumen
May−Dec 2003.………………………………………………………………………………………………………….…39
Figure 17. Observed discharge and rainfall recorded during flood dates from
1985 till 2005………..……………………………………………………………………….………………………….…40
Figure 18. Observed versus Calculated Daily Runoff / WASMOD ‐ Juan Diaz.
A corresponds to the period between May−Dec 1989.
B corresponds to the period between May−Dec 1990. ………..……………………………………...43
Figure 19. Observed versus Calculated Daily Runoff / WASMOD ‐ Juan Diaz.
A corresponds to the period between May−Dec 1999.
B corresponds to the period between May−Dec 2005……………………………………………….…44
Figure 20. Observed versus Calculated Monthly Runoff / WASMOD ‐ Juan Diaz
(1988−2005)…………………………………………………………………………………………………………………45
Figure 21. Observed versus Estimated Daily Runoff
/ Linear Multiple Regression ‐ Juan Diaz (1999)…………………………..……….……………………...47
Figure 22. Observed versus Estimated Daily Runoff
/ Linear Multiple Regression ‐ Juan Diaz
A corresponds to the period between May−Dec 1986.
B corresponds to the period between May−Dec 1995.
C corresponds to the period between May−Dec 2005…………………………..……………………..48
Figure 23. Observed versus Estimated Monthly Runoff / Linear Multiple Regression
‐ Juan Diaz (1985−2005)……………………………………………….……………………………………………...50
Figure 24. Observed versus Estimated Daily Runoff / Linear Multiple Regression ‐ Soil Moisture Proxy (total rainfall of the 30 previous days) ‐ Juan Diaz. A corresponds to the period between May−Dec 1986. B corresponds to the period between May−Dec 1989. C corresponds to the period between May−Dec 1998…………………….……………………………52
Figure 25. Observed Yearly Runoff versus Yearly Rainfall Data…………………..………………….……53
3
LIST OF TABLES
Table 1. Summary of the available daily precipitation records of the
meteorological stations located once within the Juan Diaz River basin…….………………….18
Table 2. Summary of the available daily precipitation records of the
meteorological stations located in the neighboring basins of the
Juan Diaz River basin…………………………………………………………………………………………………….19
Table 3. Distance in kilometers between meteorological and
hydrological‐stations…………………………………………………………………………………………………….22
Table 4. Percentage difference between the annual precipitation of the
station with the missing record and the annual precipitation of the
three closest stations with available data………………………………………………..…………………..27
Table 5. The long term accumulated precipitation registered
(from 1985 till 2000) at meteorological stations with available records
and the elevation in which these are located…..…………………………………………………………..31
Table 6. Long term runoff coefficient………………….……………………………………………………………...39
Table 7. Best model parameter set obtained from manual calibration……………………..…………42
Table 8. Values of objective functions applied to the calculated runoff by WASMOD from 1985−2005…………………………………..………………………………………….……..46
Table 9. Values of objective functions applied to the estimated runoff
by linear multiple regression from 1985 to 2005……..…………………………………………………..49
Table 10. Values of objective functions applied to the estimated runoff
by linear multiple regression when an approximation of soil moisture
was added as independent variable. Estimation performed on a daily
scale from 1985−2005……………………………………………………………………………………………….…51
4
5
1. INTRODUCTION
Accurate runoff estimation is one of the biggest challenges (if not the biggest) in hydrological
modeling. This information is essential for effective water resources management, e.g., for
urban planning, flood risk assessment, water supply, irrigation, long term water balance.
According to the World Meteorological Organization (Arcia, 2006), the country of Panama is
one of the nations with small water scarcity problems (second in Central America). It has 52
watersheds and close to 500 rivers (350 flowing to the Pacific coast and 150 flowing to the
Caribbean coast). The mean annual volume of water generated by the precipitation events in
the whole country is around 224 thousand million cubic meters (ANAM, 2004), but less than
10% is used.
Many sectors in the country, such as hydropower, inter‐oceanic navigation, agriculture and
human consumption, are dependent on water resources, but its misuse and lack of
protection threaten its availability. According to The National Authority of Environment
(ANAM, 2004), Panama has a surface area capable for irrigation of close to 1,870 km2, but
due to the uneven spatial and temporal distribution of rainfall, surface runoff for irrigation is
only used on 717 km2. This means, that there is a water deficit on almost 62% of the areas
capable for irrigation. According to the National Census of 2010 (INEC, 2010), Panama has
close to 3.5 million habitants. In 2006, around 11 % of the population of the country lacked
drinking water supplies, and only a group of between 27% and 35% got drinking water
continuously (Arcia, 2006).
All this is happening in a country that is growing fast, that projects the drinking water
demand to double in the next 30 years (ANAM, 2004) and that projects the expansion of the
Panama Canal by 2014, which will demand more water in order to permit the traffic of more
ships through it.
To complicate matters even more, Panama has one of the highest rainfall intensities in the
world (Hoyos, 2011), making it vulnerable to flood events. Panama District, where Panama
City (the main city) is located, has close to 450,000 habitants (INEC, 2010) and is
experiencing an accelerated expansion. In the whole country, Panama District is considered
to be the zone with the highest flood risk (McKay, 2004).
The township with the biggest surface area and with the most habitants living within
Panama District is Juan Diaz (36 km2 and close to 100 thousand habitants, according to the
National Census of 2010). The flood events that occur in the Juan Diaz Township and in some
neighboring townships are mainly caused by an accelerated urbanization growth and
planning that is not taking the flood risk into consideration. Next to the principal river of this
area, in the lower part of the basin, landfills have been carried out to establish housing
projects. This has decreased the hydraulic capacity of the river, increasing the risk for
flooding. Previous studies have been made in the Juan Diaz River, mostly focused on
6
hydraulic aspects and frequency analysis of its records. According to some studies, the
riverbed can handle runoffs that occur on average every 2.33 to 5 years (CALTEC, 2010;
ETESA, 1999).
All of the above have increased the interest in hydrological studies, but the limited quantity
(and quality) of the available hydrological and meteorological data makes it hard for
researchers to come to conclusive statements that can support good planning.
Back in 1999, ETESA (a Panamanian energy company), in coordination with SINAPROC
(National System of Civil Protection), put in practice a system for real time forecasting of
floods in the Juan Diaz River basin, in which its meteorological and hydrological network was
increased, but due to the regular occurrence of the events and because the system was not
solving the problem, stakeholders and participants lost their interest, and presently the
records obtained from those stations (nowadays inactive) are not available (or were lost).
Despite the system is no longer in practice, a learning feedback should be made of this
project in order to apply (or not) the lessons learned from it in any new flood forecasting
system that will be implemented in the country.
The issue of limited quantity of data has to be addressed, but meanwhile the challenge is to
try to understand the hydrological processes occurring in any catchment with the available
data.
The relationship between rainfall and runoff in the Juan Diaz River basin is not well
understood, and its fast response due to high rainfall intensities in the area is a concern in
the community and authorities, but little efforts have been made to solve this flood problem
and to solve the actual and upcoming water supply problem. By understanding the
hydrological processes occurring in this basin, plans can be developed for better flood risk
management or for better use of this water resource. The main objective of this thesis was
to establish how well the Juan Diaz River basin can be hydrologically represented by records
of the available instrumentation.
From the main objective, this study had the following specific objectives:
1. To find a relationship between rainfall and runoff from the available data of the
basin in the daily and monthly resolution and in the long term.
2. To determine if the available instrumentation is sufficient for modeling.
2. STU
2.1. ST
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8
Climatologically speaking, Panama has two precipitation regimes, the Pacific regime and the
Atlantic regime. These two are mainly caused by the yearly migration of the Intertropical
Convergence Zone (ITCZ), by the semi‐permanent anti‐cyclone from the North Atlantic, by
Panama's proximity to both the Atlantic and Pacific Oceans, and by the topography of the
area, which results in a high spatial variation of the rainfall. These two precipitation regimes
are limited by the continental divide. At the same time, two well defined climate seasons are
distinguished in Panama: the dry season that begins in January (when the ITCZ is south of
Panama) and finishes in April, and the wet season that starts in May (when the ITCZ is
moving north of Panama) and finishes in December. When the ITCZ is established, there is a
secondary dry season where the rain decreases between July and August. By the end of
August, beginning of September, the ITCZ starts moving south generating the rains with the
highest intensities of the rainy season. Normally, September and October are the rainiest
months (ATIES, 1996; ETESA, 1999).
The Juan Diaz River basin is found in the Pacific regime, where the weather that prevails is
arid, and that is characterized by abundant rainfall events normally occurring between the
evening and early night time hours. In the Pacific regime, between 85% and 93% of the
annual rainfall happens during the wet season (UNESCO, 2008).
The average temperature of the basin is around 27 OC. The minimum and maximum
temperatures of the basin are around 24 OC and 32 OC respectively. The average relative
humidity of the basin is around 79% (information based on records from 1985 to 2005
belonging to the Tocumen meteorological station. Records provided by ETESA).
Generally, the rainfalls of the basin are convective and orographic. According to ETESA
(1999), the annual mean precipitation of the upper part of the basin (above 300 m above sea
level) and the lower part of the basin are 3,200 mm/annual and 2,000 mm/annual,
respectively. The Cerro Azul meteorological station, once an active station within the Juan
Diaz River basin located at an elevation of 660 m above sea level, registered a mean annual
precipitation of 4,256 mm from 1976 till 1985 (McKay, 2004), with high records in 1979
(5,065 mm), 1980 (6,861 mm) and 1981 (8,423 mm).
The geology of the basin is variable. The oldest rocks of the basin are of sedimentary origin
and are composed of marine sandstone, alluvium, limestone, lavas and shale (ATIES, 1996).
The rocks of the central upper part of the basin are composed of limestone, basalt, lavas,
tuffs and agglomerates, while the rocks on the bottom part of the basin are composed of an
unconsolidated material and alluviums. In the northwestern and western part of the basin,
the "Panama Formation" can be found, which is composed by strata of agglomerates and by
andesitic tuffs, inter spread with alluvial conglomerates. The high permeability of the
"Panama Formation" makes a high volume of precipitation to drain into the groundwater
storage (ATIES, 1996). Meanwhile in the northern and northeastern part of the basin,
substrate igneous of lavas and tuffs of basalt and andesite, spaced by bodies of diorites and
dacites can be found.
9
2.2. LITERATURE REVIEW AND METHODOLOGY
Different disciplines, such as hydrology and civil engineering, are interested in the amount of
runoff generated in a basin due to a given pattern of precipitation (Cedeño, 1997).
Many studies have been made with the purpose of developing a relation between
precipitation, evaporation and runoff, but the variability of many other factors that affect
these processes, such as precedent rainfall, soil moisture, infiltration, make it hard to
understand the runoff responses to each rainfall event (Cedeño, 1997; Hoyos, 2011).
To establish how well the Juan Diaz River basin can be hydrologically represented by the
available data, one hydrological model and a statistical method were applied. Both methods
were performed in daily and monthly time steps in an attempt to find a relationship
between rainfall and runoff in both resolutions from the available data of the basin. For the
long term water balance, a graph showing discharge against rainfall data was also plotted in
the yearly scale to establish a relationship between the two variables.
10
2.2.1. DESCRIPTION OF THE HYDROLOGICAL MODEL
A hydrological model is a simplified version of the processes that take place in a catchment.
Unfortunately, most of these hydrological processes are complex and if we plan to
understand some of the aspects occurring in a catchment, it is necessary to simplify the
description of some of them (Xu, 2010a).
If most of these hydrological processes occurring in a catchment are well understood, the
effects or impacts caused by changes can be determined. Another and one of the most
important objectives in hydrological modeling is to forecast floods and runoff volumes to
asses future spatial and temporal distribution of water resources in a catchment.
There are many hydrological models available, but the choice of the best model depends on
the problem, objectives and available data (Haan, 1982).
A conceptual model applies physical laws but in a simplified form (Xu, 2010a). This type of
model is mostly used for understanding rainfall‐runoff processes (Hoyos, 2011), and it is also
well known for modeling with limited information (Morales, 2010).
In terms of spatial variability of the inputs, outputs, or parameters, lumped models treat the
catchment as a homogenous whole. Lumped models use average values of the catchment
characteristics that affect the runoff volume. These models are mostly used for flood
forecasting, water resources assessment, dam‐reservoir design and operation (Xu, 2010a).
For this study, the Water And Snow balance MODeling system (WASMOD) was chosen.
WASMOD is a conceptual lumped model used for streamflow simulations from both
snowmelting and rainfall. This model was chosen because it has been used for water balance
investigations, as well as for river flow forecasting in countries with widely diverging climates
and soil characteristics. Another reason this model was chosen, was because of the flexibility
of its equations and its input requirements.
2.2.1.1
The WA
For this
catchme
only 4 p
2.2.1.2
The WA
potentia
observe
precipit
2.2.1.3
The sch
catchme
the eva
storage
evapotr
routing
1. WASMO
ASMOD syst
s study, sin
ent, the mo
parameters
2. INPUT D
ASMOD sys
al evapotra
ed daily (or
tation and p
3. WASMO
heme of the
ents, all the
potranspira
, smt, as
ranspiration
routine wa
Fig
OD
tem has 3 t
nce the Ju
odel will sim
were used.
DATA
stem accep
anspiration,
r monthly)
potential ev
OD MODE
e model for
e precipitat
ation losses
active ra
n, et, to the
s added to
gure 2. WAS
M
to 7 param
uan Diaz Ri
mulate the
ts different
temperatu
discharge f
vapotranspir
EL STRUCT
r a snow fre
ion, pt, is ra
s, et. The re
ainfall. Lat
fast flow co
the fast flow
MOD Model
Modified from
11
meters, depe
iver basin
streamflow
t combinat
ure and rel
for calibrat
ration were
TURE
ee catchme
ainfall, rt. O
emainder of
ter, the s
omponent,
w compone
l Structure fo
m Frevert an
ending on t
is characte
ws generate
ions of dai
ative humid
tion. For th
e used as in
ent is show
ne part of t
f rainfall co
soil moistu
ft, and to t
ent to distri
or a Snow Fr
nd Singh (200
the climate
erized by b
d only from
ly (or mon
dity as inpu
his study, d
put data for
wn in Figure
this rainfall
ontributes t
ure storag
he slow flow
bute it in ti
ree Catchme
02).
e of the stu
being a sn
m rainfall; th
nthly) preci
ut data, alo
daily (and m
r the mode
e 2. For this
contribute
to the soil m
ge contrib
w compone
me.
ent.
dy area.
ow free
herefore
pitation,
ong with
monthly)
l.
s type of
s first to
moisture
utes to
ent, st. A
12
2.2.1.4. EVAPOTRANSPIRATION LOSSES
The actual evapotranspiration losses, et, "describes all the processes by which liquid water at
or near the land surface becomes atmospheric water vapor under natural conditions" (Xu,
2010a). The evaporation loss is one of the water‐balance least understood components
because of its complex processes and difficulty to measure (Jones, 1997).
The actual evapotranspiration reaches its maximum value when the water supply to plants
and soil surface is unlimited. This unlimited water supply is called potential
evapotranspiration, ept. This last one is approximately equivalent to the evaporation that
will occur from a big surface of water, such as a lake (Cedeño, 1997).
The WASMOD system considers two factors to calculate the actual evapotranspiration
losses, et : daily (or monthly) potential evapotranspiration, ept, and the available water, wt,
during a day (or a month) t. The actual evapotranspiration is a function of the two factors
just mentioned (Frevert and Singh, 2002).
The available water during a day (or month) t is defined by equation (1).
……………………………………………………………….............................................(1)
where
wt: available water during a day (or month) t,
pt: total rainfall during a day (or month) t,
smt‐1: available storage from the previous day (or month) t. It is an approximation of the
wetness of the soil. For every time step, this has to be greater than or equal to 0.
The relationship between actual evapotranspiration, et, potential evapotranspiration, ept,
and the available water, wt, during a day (or month) t can be better understood by the
following statements:
et increases with ept and wt
et = 0 when wt = 0 or ept = 0
et <= ept, and et <= wt
et = ept when wt = ∞
In this study, potential evapotranspiration was unavailable. In principle, it can be estimated
from net radiation, wind, temperature and humidity, or by a measurement that relates the
previous variables, such as pan evaporation.
In practice it is very common to estimate lake evaporation by measuring pan evaporation.
Pan evaporation consists of measuring the daily difference of the water level from an iron
pan, which is positioned around 0.20 m above the ground surface on a small plinth. This pan
evaporation measured is higher than the evaporation that occurs from a lake surface. This is
13
caused by radiation and heat changes effects. Pan evaporation has to be adjusted with a
correction factor (Cedeño, 1997). This correction factor is not constant in time, and its
variation depends on the type of pan, climate and location of the measurement (Jones,
1997). Normally this factor varies from 0.5 and 1.0 (Xu, 2010a), but specific correction
factors may have to be found by calibration for any given situation.
The pan used in the country of Panama is the US NWS Class A pan. It consists of a cylinder
with a diameter of 1.22 m, and a height of 0.25 m. For this type of pan, the correction factor
is between 0.60 and 0.80 (Jones, 1997).
After choosing the correction factor, some long term water balance considerations have to
be checked. The long term sum of potential evapotranspiration, Ep, plus the long term sum
of the observed discharge, Q, should be larger or much larger than the long term sum of
precipitation, P (Xu, 2010a). This is because the long term sum of actual evapotranspiration,
E, plus the long term sum of the observed discharge, Q, should be equal to the long term
sum of precipitation, P (Sivapalan, 2001); and the long term sum of actual
evapotranspiration, E, should be smaller than the long term sum of potential
evapotranspiration, Ep (Xu, 2010a). The above can be resumed by the following statements:
Ep + Q >> P
E + Q = P
E < Ep
To calculate actual evapotranspiration, the WASMOD system uses two equations. One for
energy limited systems and the other for water limited systems. Water limited systems refer
to those where the actual evapotranspiration is controlled by the available rainfall in it; it
doesn't matter how high the potential evapotranspiration is (Sivapalan, 2001). These
systems are characterized by low annual precipitation, by infiltration events that barely wet
the vegetation root zone and by transpiration processes limited by the water availability in
the soil (Guswa, 2005). Water limited systems are found in arid climates. Energy limited
systems are the opposite of water limited systems. In other words, if water is plentiful, then
the system is energy limited. Energy limited systems are found in humid climates.
One way to determine if the system is water limited or energy limited is by the Budyko
diagram (Figure 3), which represents the ratio of the long term evapotranspiration losses
divided by the long term precipitation (E/P) as a function of the long term potential
evapotranspiration divided by the long term precipitation (Ep/P). "E/P is a measure of annual
water balance", meanwhile "Ep/P is a measure of the climate" (Sivapalan, 2001). Ep/P values
above 1 represents water limited systems, while Ep/P values below 1 represents energy
limited systems.
In this s
an ener
m
where
a4: is th
lim
the
study, the s
rgy limited s
min
he paramet
ited system
e greater the
Figu
system is an
system is de
1
ter that de
m, a4 is cons
e actual eva
ure 3. Budyco
n energy lim
efined by eq
, ,
termines th
strained by
apotranspir
14
o Diagram (S
mited syste
quation (2):
………………
he actual e
0 <= a4 <=
ration losses
Sivapalan, 20
em. The equ
:
…………………
evapotransp
1. The sma
s will be.
001).
uation that
…….............
piration los
ller the valu
WASMOD
..................
sses. For an
ue of param
uses for
.......(2)
n energy
meter a4,
15
2.2.1.5. SLOW FLOW COMPONENT
The slow flow component depends on the available storage in the catchment during the day
(or month) t in study. The slow flow component is defined by equation (3):
…………………………………………………………………........................................(3)
where
a5: is a positive parameter, which controls the fraction of the runoff that represents the base
flow. A high value of a5 produces a greater fraction of base flow. The latter is expected
to be the case in forest areas and in areas with sandy soil (Frevert and Singh, 2002).
b1: is a positive parameter related to the slow flow component. Since this parameter is highly
correlated to a5, it takes standard values (e.g., 0, 0.5, 1 or 2). For arid regions, b1 is fixed
to 0.5 or 1.
2.2.1.6. FAST FLOW COMPONENT
The fast flow component depends on the active rainfall, nt, on the soil moisture storage, smt,
and on the physical characteristics of the catchment that are reflected in the parameters.
The active rainfall is defined by equation (4):
1 , ……………………………………………………………........................(4)
where
rt: is rainfall
The fast flow is defined by equation (5):
………………………………………………………………....................................(5)
where
a6: is a positive parameter, which controls the fraction of the runoff that represents the fast
flow. The higher the degree of urbanization, the average basin slope and the drainage
density, then higher the parameter a6 should be. Lower values of this parameter are
expected in forest areas (Frevert and Singh, 2002).
b2: is a positive parameter related to the fast flow component. Since this parameter is highly
correlated to a6, this one is fixed to 1 or 2.
16
2.2.1.7. ROUTING ROUTINE OF THE FAST FLOW COMPONENT
A routing routine parameter was introduced to the fast flow component to distribute it in
time. This parameter gives a sense of the response time of any basin (Morales, 2010). The
routing routine applied in this study is explained by equations (6 to 8) (Westerberg, 2010):
……………………………………………………………………….......................................(6)
………………………………………………………………………………...................................(7)
……………………………………………………………………….....................................(8)
where
sct: is the routing storage for the day (or month) t
rft: is the routed fast flow component for the day (or month) t
Rf: is a positive parameter, which controls the fraction of the routing storage that represents
the direct runoff of a day (or month) t. Rf is constrained by 0 <= Rf <= 1.
2.2.1.8. CALCULATED RUNOFF AND WATER BALANCE
The calculated daily (or monthly) runoff is defined by equation (9):
…………………………………………………………………………….......................................(9)
where
dt: calculated runoff for a day (or month) t.
The soil moisture storage at the end of the day (or month) t is updated by the water balance
equation (10), which is:
max , 0 ……………………………………………….................(10)
17
2.2.2. LINEAR MULTIPLE REGRESSION ANALYSIS
The statistical method used to find a relationship between rainfall and runoff was the linear
multiple regression. The general objective of the linear multiple regression is to learn about
the relationship between several independent variables and a dependent variable (Xu,
2010b). This method is utilized to predict one variable with the knowledge of others. The
linear multiple regression estimates a linear equation of the form:
∗ ∗ … . . ∗ …………………………………………...........(11)
where
Y: dependent variable
X1, X2,..Xp: independent variables
A, b1, b2…bp: regression coefficients
The regression coefficients represent the contribution of each independent variable to
predict the dependent variable.
The dependent variable was the total (or calculated) runoff, and the independent variables
were precipitation, potential evapotranspiration, relative humidity and temperature for a
day (or month) t. In this method, the whole data series was used to predict the dependent
variable.
Additional linear multiple regressions were performed to study the runoff responses to
accumulated rainfall events. In this approach, an approximation of soil moisture was added
to the independent variables set to predict the observed discharge records. This
approximation of soil moisture for each day t was assumed to be the accumulated value of
previous rainfall events (for example: the total rainfall of the previous 3, 5, 10 or 30 days).
The whole data series was used in this approach to predict the dependent variable.
18
2.3. AVAILABLE DATA
2.3.1. METEOROLOGICAL DATA
Back in the beginning of the 70s, until the late 90s, the Juan Diaz River basin used to have
two active meteorological stations within it: "Cerro Azul" and "Las Cumbres". Nowadays,
there are no active meteorological stations within the basin.
From these two stations, ETESA provided daily precipitation records. A summary of those
rainfall records is shown in Table 1.
TABLE 1. Summary of the available daily precipitation records of the meteorological stations
located once within the Juan Diaz River basin.
Station Latitude Longitude Elevation (m.a.s.l.)
Period of Available Data (years)
Cerro Azul 9° 10´ 00" N 79° 25´ 00" W 660 1993−1998 *1 Las Cumbres 9° 05´ 00" N 79° 32´ 00" W 200 1985−1997 *2
ETESA also provided daily precipitation records of other meteorological stations located in
neighboring basins: "Hato Pintado*3", "Tocumen*4", "Utive*5", "Loma Bonita*5" and "Altos de
Pacora*5", all of which are active stations except the Utive station. A summary of the rainfall
records obtained from these five (5) stations is shown in Table 2. All the stations mentioned
in this section are (or were) rain gauge stations, where only one daily measurement of the
amount of rainfall is (or was) taken on each station at 7:00 a.m.
*1: With missing data in 1995, 1997 and 1998 (92% of the daily data from 1993−1998 were available).
*2: With missing data in 1995 and 1997 (99% of the daily data from 1985−1997 were available).
*3: Belongs to a hydrographical basin located between the Caimito and Juan Diaz Rivers.
*4: Belongs to a hydrographical basin located between the Juan Diaz and Pacora Rivers.
*5: Belongs to the hydrographical basin of the Pacora River.
19
TABLE 2. Summary of the available daily precipitation records of the meteorological stations
located in the neighboring basins of the Juan Diaz River basin.
Station Latitude Longitude Elevation (m.a.s.l.)
Period of Available Data (years)
Hato Pintado 9° 00´ 00" N 79° 31´ 00" W 45 1987−2003 *1 Tocumen 9° 03´ 56" N 79° 23´ 31" W 14 1985−2005 *2 Utive 9° 09´ 00" N 79° 20´ 00" W 80 1985−1999 *3 Loma Bonita 9° 10´ 00" N 79° 15´ 00" W 100 1985−2003 *4 Altos de Pacora 9° 14´ 44" N 79° 20´ 59" W 850 1985−2002 *5
The Tocumen station is the only active station that measures several types of meteorological
parameters. Besides the precipitation records, records of three other parameters were
obtained from the Tocumen station for this study: pan evaporation, relative humidity and
temperature. The available daily records of these three parameters were from 1985 till
2005.
For every year, at least one daily pan evaporation datum was missing. 93% of the daily pan
evaporation data from 1985−2005 of the Tocumen sta on were available.
The daily relative humidity records were complete in the years 1985, 1987, 1994 and 1999.
For the rest of the years, at least one daily relative humidity record was missing. 97% of the
daily relative humidity data from 1985−2005 of the Tocumen sta on were available.
In 11 out of the 21 years of available daily temperature data, there was at least one missing
datum. 98% of the daily temperature data from 1985−2005 of the Tocumen station were
available.
*1: With missing data in 1987 (97% of the daily data from 1987−2003 were available).
*2: Also available in hourly scale from 1986 until 2005.
*3: With missing data in 1989 and 1994 (99% of the daily data from 1985−1999 were available).
*4: With missing data in 1992, 1994, 1997, 2002 and 2003 (96% of the daily data from 1985−2003 were available).
*5: With missing data in 1986, 1987, 1992, 1996, 1997, 1998, 1999, 2001 and 2002 (94% of the daily data from 1985−2002 were available).
2.3.2. H
Nowada
location
from w
upstrea
The elev
102 km
the Juan
ETESA a
missing
87% of t
Every da
each da
Figure 4
h
w
HYDROLO
ays, there is
n of this sta
here the Ju
m from wh
vation posi2 (area high
n Diaz River
also provide
data from
the daily da
aily record
ay.
4. Flood Pro
hydrological
with informa
OGICAL DA
s only one a
tion is 9° 0
uan Diaz Ri
ere the floo
tion of the
hlighted in o
r basin.
ed daily reco
1985 till 19
ata from 19
correspond
one Areas d
l station and
ation from d
ATA
active hydro
3´ 00" N an
iver begins
od prone ar
hydrologica
orange in F
ords of this
987, also in
85 till 2005
ds to the ave
ue to the Ju
d the light bl
documents o
20
ological sta
nd 79° 26´ 0
in Cerro A
reas begin (
al station is
Figure 5), a
s station fro
1994, 1995
were availa
erage hourl
uan Diaz Ri
lue areas re
of ETESA (199
tion within
00" W, appr
Azul and it
Figure 4).
s 8 m above
nd for this
om 1985 till
5 and from
able.
ly discharge
ver. The re
present the
99) and SINA
the Juan D
roximately 1
is situated
e sea level.
study, this
2005. Thes
2000 till 20
e from 00:00
d dot repre
flood prone
APROC (2005
Diaz River ba
17 km dow
at less tha
This statio
area is ref
se daily reco
005. For th
0 till 24:00
esents the J
e areas. Map
5).
asin. The
nstream
an 1 km
n covers
ferred as
ords had
is study,
hours of
uan Diaz
p created
Figure 5
a
Figure 6
D
As it ca
records
station
1980
. Location of
and outside
6. Summary
Diaz River ba
an be seen
available w
that had th
19
P ‐ Cerro P ‐ Hato PP ‐ UtiveP ‐ Altos d
f meteorolog
the Juan Dia
of the avail
asin on a yea
in Figure
were Cerro
e same yea
985
AzulPintado
de Pacora
gical and hy
az River basi
lable data fr
arly time sca
6, the met
Azul and T
ars of availa
1990
21
drological st
in.
rom the diff
ale.
teorological
ocumen re
ble records
1995
tations with
ferent statio
l stations w
spectively.
s as the Juan
2000
P ‐ Las CumP, Pan EvaP ‐ Loma BQ ‐ Juan D
available re
ons within a
with the sh
The latter w
n Diaz statio
20
mbresp, Temp, HumBonitaiaz
ecords locate
and outside
hortest and
was the on
on.
005
m ‐ Tocumen
ed within
the Juan
longest
ly active
2010
22
TABLE 3. Distance in kilometers between meteorological and hydrological‐stations
Cerro Azul
*1
Las Cumbres
*1
Hato Pintado
*1
Tocumen*2
Utive*1
Loma Bonita
*1
Altos de
Pacora*1
Juan Diaz
*1
Cerro Azul*1 ‐ 17.30 21.41 11.53 9.30 18.33 11.23 13.14
Las Cumbres*1
17.30 ‐ 9.83 17.26 24.89 33.67 28.44 13.20
Hato Pintado*1
21.41 9.83 ‐ 15.52 26.30 33.60 33.82 10.72
Tocumen*2 11.53 17.26 15.52 ‐ 11.19 18.05 23.82 4.91
Utive*1 9.30 24.89 26.30 11.19 ‐ 9.20 10.53 15.54
Loma Bonita*1
18.33 33.67 33.60 18.05 9.20 ‐ 14.98 23.01
Altos de Pacora*1
11.23 28.44 33.82 23.82 10.53 14.98 ‐ 23.32
Juan Diaz*3 13.14 13.20 10.72 4.91 15.54 23.01 23.32 ‐
From Table 3, it can be seen that the closest meteorological station to the Juan Diaz
hydrological station is the Tocumen station (4.91 km).
*1: Rain gauge station.
*2: Meteorological station, which measures several types of meteorological parameters.
*3: Discharge station.
23
2.3.3. HISTORICAL FLOOD RECORDS
The historical flood records of the Juan Diaz Township were obtained from the SINAPROC
data‐base. As a complement of the SINAPROC records, additional flood days were added
according to other documents of ETESA and other articles (McKay, 2004), where the last had
flood dates that are not registered in the first one.
The historical flood records are from 1978 till 2009. In that period, there were 56 flood
events recorded in the Juan Diaz Township. From those 56 events, 6 were recorded from
1978 till 1990, 27 were recorded from 1993 till 2000, and 23 were recorded from 2004 till
2009. At first sight of Figure 7, it can be stated that the flood records are incomplete because
there are few events before 1990 (this could be attributed to the fact that SINAPROC started
to work as an entity at the beginnings of the 80s), additional to the last, there are no flood
events in 1991, 1992, 1994, 1999 and from 2001 till 2003. For this thesis, the flood records of
interest were from 1985 till 2005.
Figure 7. Number of Floods Registered per Year in the Juan Diaz Township
0
1
2
3
4
5
6
7
8
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
Number of Floods Registered
Time in Years
24
3. DATA PREPARATION
Uncertainties in any model prediction result from errors in input data, errors in output data
(data for model calibration), errors in parameters, and errors in model structure (Xu, 2010a;
Refsgaard and Storm, 1996).
One way to reduce errors in the input and output data is by performing quality control to the
available data.
3.1. PRECIPITATION
Precipitation is the largest quantity in the hydrological cycle (Xu, 2010a). Previous studies
have shown that errors in precipitation data are more (if not the most) important than
errors in other input variables (Westerberg, 2009).
3.1.1. QUALITY CONTROL OF THE PRECIPITATION DATA
Quality control of the precipitation data started with a visual data inspection along with
some considerations for each case.
All the daily precipitation records were plotted to identify extreme rainfall events (daily
values greater than 100 mm), as well as the monthly precipitation records were plotted to
identify seasonality.
For extreme rainfall events recorded in each station, some considerations were taken in
order to consider if those events actually happened. First, the average precipitation of the 3
closest stations to the one who recorded the extreme rainfall on that day was calculated. If
the average precipitation of that day from these three stations was below 20 mm, the
extreme rainfall event was removed. This was the consideration with the highest weight to
remove extreme rainfall events.
Another consideration taken to check extreme rainfall events was to check if there was any
precipitation registered (on the same station) in previous days to this extreme event, as well
as the day of the week in which this event occurred (e.g., Monday, Tuesday, ...Sunday). This
was done to check if the extreme rainfall event registered on that day was not an
accumulation of rainfall events that occurred in previous days (e.g., it could be the case that
the observer was absent to register the precipitation records for various days, and when the
observer came back to register the rainfall records, the observer could have registered for
one day the accumulated precipitation of the previous days when he or she was absent). For
this study, all the cases when the extreme rainfall event had no precipitation on the previous
days, the average precipitation of the three closest stations to the one who recorded the
extreme rainfall event was above 20 mm, therefore no extreme rainfall event was removed
due to this consideration.
25
Frequency of recurrence for every month was also checked. Values were flagged if there
were more than 10 values (or integer numbers) repeated within a month, which is highly
unlikely.
Sequence dry days longer than eight (8) were checked if they happened during the rainy
season.
Quality control was more extensive for the Tocumen meteorological station since hourly
records were also available. For effects of comparison, for every day a daily precipitation
value was calculated by doing the sum of the hourly precipitation records from 00:00 till
24:00.
When the accumulated hourly precipitation record (AHPR) was different to the observed
daily precipitation record (ODPR) of any given day, some considerations were taken to
choose one or the other.
Rounding errors were found in some days when comparing the AHPR to the ODPR (e.g., on
one case the ODPR was 10.8 mm and the AHPR was 1.8 mm). This type of errors may be
cause by incorrectly readings of the glasses. In these cases, the AHPR were chosen.
There were days where the ODPR was lower than the AHPR, but not by a significance
amount (e.g., on one case the ODPR was 3.7 mm and the AHPR was 4.3 mm). This could be
explained by imprecise measurements due to water spillage, wetting, evaporation or
imperfections on the equipment. In these cases, the AHPR were also chosen.
There were sequences of days in which the ODPR and the AHPR did not match, but when
comparing the accumulated precipitation of both during those days, both sums were the
same (or very close). This could be the case that the observer was absent to register the
daily records for some days and he (or she) distributed what he read on the day he came
back in the days he was absent. In these cases, the AHPR were also chosen.
There were days where the ODPR was too high compared to the AHPR, or vice versa (e.g., on
one case the ODPR was 48.2 mm and the AHPR was 0.00 mm). In these cases, a comparison
with the records of the other meteorological stations was performed on those days (similar
to the one done to check if the extreme rainfall events happened). If the precipitation
records of the other meteorological stations in that given day were considerably high (above
20 mm in average), then the highest value between the ODPR and the AHPR was chosen; if
not, then the lowest one was chosen. The days, in which there was not a clear pattern in
which value to choose, were flagged.
26
3.1.2. ESTIMATION OF MISSING PRECIPITATION DATA
In addition to the errors mentioned above, missing data in the precipitation records also had
to be dealt with (see Tables 1 and 2); because of the absence of observer or due to technical
problems of the equipment.
To estimate missing and removed precipitation data (during the quality control), the
Arithmetic Mean Method with a correction factor was used. This method consists of the
simple arithmetic mean of the daily precipitation records of the three closest stations (with
available records) to the one where the record is missing, plus a correction factor. This
correction factor was used when the annual precipitation of at least one of these three
stations differed more than 10% from the annual precipitation of the station with the
missing record (Cedeño, 1997). As it can be seen in Table 4, the previous was the case for all
the years. The Arithmetic Mean Method with a correction factor used in this study is defined
by equation (12).
................................................................................(12)
where
P: estimated daily precipitation of the station with the missing record.
Pa, Pb, Pc: daily precipitation of the three closest stations to the one where the daily
precipitation record is missing.
N: Annual accumulated precipitation of the station with the missing record(s). When more
than the half of the records in a year was missing, the value of N was estimated. First, an
annual average was estimated with the annual records of this station that had no missing
data. The percentage of contribution by every month to calculate this annual average was
estimated as well. The value of N used in a given month to estimate its missing daily
record(s), for a year that had more than half of its records missing, was assumed to be the
annual average (estimated previously) minus the percentage contributed by this month
(when their records were complete).
Na, Nb, Nc: Annual accumulated precipitation of the three closest stations to the one where
the record is missing. For every case, the three stations chosen had no missing data in that
year.
As it can be seen in Figure 6, because of the small numbers of stations with available records
after the year 2000 (4 stations in 2001 and 2002, 3 in 2003, 2 in 2004 and 1 in 2005), it was
decided to only fill the missing records for every station from 1985 till 2000.
TABLE 4
*1: For eve
in each
4. Percentage
record and
ry station with m
h row represent t
e difference
d the annual
missing precipitat
he 3 stations use
e between th
precipitatio
ion data (these a
d for each case t
27
he annual p
on of the thre
are shown in the
to estimate the m
precipitation
ee closest st
second column f
missing precipitati
of the stati
tations with
for every year), t
ion data.
ion with the
available da
the values highlig
e missing
ata *1
ghted in bold
3.1.3. D
After fil
consiste
average
individu
precipit
Change
instrum
A straig
station
double
for ever
conditio
then the
Figure 8
a
DOUBLE M
lling the m
ency of the
e precipitat
ual station b
tation of on
s can be
ment, metho
ght line was
against the
mass plot o
ry station, i
ons. If a stra
e changes i
. Double ma
and the othe
MASS ANA
issing preci
e rainfall da
ion of certa
because the
ne station i
understood
od of observ
s obtained
e annual a
of the Tocum
t can be sa
aight line w
n slope sho
ass plot betw
er 6 stations
ALYSIS
pitation rec
ata. This m
ain number
eir errors co
is sensitive
d as a cha
vation.
when plott
ccumulated
men station
id that the
was not obta
uld have be
ween precipit
s with availab
28
cords, doub
method is b
r of station
ompensate
to the cha
ange in th
ting the ann
d average
n shown in F
records of
ained in the
een adjuste
tation recor
ble records.
ble mass an
based on th
ns is not se
each other
anges that
e location
nual accum
precipitatio
Figure 8). Si
each statio
e double ma
d.
ds of the To
nalysis was
he fact tha
nsitive to t
r; meanwhi
occur to th
of the in
mulated prec
on of the o
ince the pre
on were obt
ass plot of a
cumen mete
used to ch
at the accu
the changes
le the accu
his (Cedeño
nstrument,
cipitation f
other statio
evious was
tained by t
any of the s
eorological s
heck the
mulated
s of one
mulated
o, 1997).
type of
or every
ons (e.g.
the case
he same
stations,
station
29
3.1.4. PRECIPITATION AS INPUT DATA
The precipitation input data for the models have to be introduced as an areal mean
precipitation. Errors in areal mean precipitation are due to the high spatial and temporal
variability of precipitation (Xu, 2010a). This spatial variability can be explained in part due to
the orographic effect of the topographic characteristics of any catchment, since at higher
elevations rainfall intensity tends to be higher than at lower elevations (Hoyos, 2011;
Goovaerts, 1999).
In small catchments, one rain gage may produce sufficient information for long term water
balance forecasting (Hoyos, 2011; Xu, 2010a). A very dense network of rain gauges is
necessary for an accurate estimation of the spatial and temporal distribution of rainfall in a
catchment, as well as for accurate runoff estimations (Goovaerts, 1999). Records from a
network of rain gauges are useful for estimating flood peaks or for determining the spatial
variability of runoff production from individual events (Xu, 2010a).
For this study, only one station was used for estimating the areal mean precipitation of the
Juan Diaz River basin. The Tocumen meteorological station was chosen because it is an
active station, being the closest to the basin, and because its available records matched with
the observed discharge records of the hydrological station (from 1985 till 2005). Since this
station is located at an elevation of 14 m above sea level and at higher elevations rainfall
intensities are expected to be higher, the precipitation records of the Tocumen station had
to be adjusted with an elevation factor to get an estimation of the long term rainfall at the
average elevation of the basin at the discharge station.
The average elevation of the Juan Diaz River basin upstream the discharge station is 171
meters above sea level. This elevation was calculated with equation (13) (Monsalve Sáenz,
1999).
∑ ∗
∑ ............................(13)
where
n: corresponds to the total numbers of cells that integrates the basin in the Digital Elevation
Model. Every cell dimension of the Digital Elevation Model available was 90 m x 90 m.
"Area i": corresponds to the area of each cell that integrates the basin, for this case every
cell had an area of 0.0081 km2.
As it can be seen in Figure 9, the Juan Diaz River basin has two large contributories, one that
comes from the north and one that comes from the west.
Figure 9
o
a
To obta
register
located
seen in
precipit
the curv
. Elevation r
on top; 3D v
are in meter
ain the elev
red on all t
was plotte
n Figure 10
tation and e
ve with the
ranges of the
view is show
rs. Map Sour
vation facto
he stations
ed (the prev
0, a curve
elevation. F
data.
e Juan Diaz R
wn below). D
rce: USGS (20
or a graph
(from 198
vious data
was then f
For this plot
30
River basin a
Dimensions
011).
showing t
5 till 2000)
of each sta
fitted to th
t, Las Cumb
at the discha
in the color
he long te
versus the
ation are sh
he data to
bres station
arge station
bar and in t
rm accumu
e elevation
hown in Tab
find a rel
n was omitt
(plant view
the axes "x"
ulated prec
in which th
ble 5). As it
ationship b
ted for bett
is shown
" and "y"
ipitation
hese are
t can be
between
ter fit of
TABLE
met
Name
Hato
Tocum
Cerro
Las C
Utive
Loma
Altos
Figure
met
From Fi
long ter
basin. T
at the a
precipit
5. The lon
teorological
e of Station
Pintado
men
o Azul
umbres
e
a Bonita
s de Pacora
10. The lo
teorological
gure 10 (or
rm precipit
The elevatio
average ele
tation at the
ng term ac
stations wit
Acc
ong term a
stations wit
r by using th
tation was
on factor res
evation of
e Tocumen
ccumulated
th available
cumulated P1985−2000
31
28
47
35
40
42
57
accumulated
th available
he equation
calculated
sults from t
the upper
station. For
31
precipitatio
records and
Precipitation0 (mm)
1,955
8,435
7,738
5,253
0,798
2,307
7,146
d precipitat
records vers
n derived fro
at the ave
the division
part of the
r this study,
on register
the elevatio
ion register
sus the eleva
om the fitte
rage elevat
n of the long
e basin and
, the elevat
red (from
on in which t
Eleva(m above
6
2
8
red (from
ation in whic
ed curve), a
tion of the
g term estim
d the long
ion factor w
1985 till 2
these are loc
vation e sea level)
45
14
660
200
80
100
850
1985 till 2
ch these are
an estimatio
upper par
mated prec
term accu
was 1.54.
2000) at
cated.
2000) at
located.
on of the
rt of the
ipitation
mulated
32
3.2. POTENTIAL EVAPOTRANSPIRATION
The pan evaporation records of the Tocumen meteorological station were used as the
potential evapotranspiration data with a correction factor. But first, the missing data in the
pan evaporation records had to be filled.
3.2.1. ESTIMATION OF MISSING PAN EVAPORATION DATA
The pan evaporation records of the Tocumen station had at least one missing daily datum in
every year of the series. Most of the missing gaps (91% of the missing data) were 1 to 4 days
long. There were only 3 gaps longer than 5 days. One was a 6−day gap (from 22−Dec−89 to
27−Dec−89), another was a 15−day gap (from 28−Sep−02 to 12−Oct−02), and the last one
was a 28−day gap (from 21−Sep−93 to 18−Oct−93).
For all these gaps, the pan evaporation missing records were estimated by doing linear
interpolation between the value before and after each gap. After all the missing data were
filled, the average pan evaporation was calculated for the months where the longest missing
gaps were filled, and then compared to the long term monthly average pan evaporation in
which those long gaps happened. For example, the 28−day gap occurred between
September and October, after filling that gap, then the average pan evaporation of those
two months in particular (with estimated values) were compared with the long term average
pan evaporation of September and October. The monthly average pan evaporation of the
two longest gaps was similar to the long term monthly average pan evaporation in which
these gaps occurred.
3.2.2. QUALITY CONTROL OF POTENTIAL EVAPOTRANSPIRATION DATA
The correction factor used for this study was set to 1 in order to satisfy the long term water
balance condition (EP + Q >> P).
As a comparison, the annual average of the estimated potential evapotranspiration was
compared to the annual average potential evapotranspiration map of Panama created by
ETESA (UNESCO, 2008). See the previous map in ANNEX B.
The annual average of the estimated potential evapotranspiration in this study was 1,589
mm (from 1985 to 2005) and the annual average from the potential evapotranspiration map
was 1,388 mm (from 1971 to 2002). Although these two differed approximately 15%, the
correction factor was considered to be good enough for modeling since the long term water
balance condition was satisfied with the value chosen.
33
3.3. TEMPERATURE
The temperature records of the Tocumen meteorological station were used as a reference of
the temperature of the Juan Diaz River basin. No modification was made to the available
temperature records. These records also had missing data which had to be filled.
3.3.1. ESTIMATION OF MISSING TEMPERATURE DATA
There were 4 gaps of missing data longer than 6 days: a 61−day gap (from 01−May−94 to
30−June−94), a 59−day gap (from 01−Jan−94 to 28−Feb−94), a 14−day gap (from 29−Sep−02
to 12−Oct−02), and an 8−day gap (from 23−Nov−03 to 30−Nov−03). These 4 gaps
represented 80% of the missing data.
All the missing data from 1994 till 1999, including the two longest gaps were filled using the
atmospheric data‐base of the International Research Institute for Climate and Society (IRI,
2011). The following two longer gaps (the one with 14− and the one with 8−day gap) were
filled using the Wunderground data‐base (Wunderground, 2011). Both data‐bases have
Tocumen as a reference.
For all the other gaps, the missing temperature records were estimated by doing linear
interpolation between the value before and after each gap.
3.4. RELATIVE HUMIDITY
The relative humidity records of the Tocumen meteorological station were used as a
reference of the relative humidity of the Juan Diaz River basin. No modification was made to
the available relative humidity records. These records also had missing data which had to be
filled.
3.4.1. ESTIMATION OF MISSING RELATIVE HUMIDITY DATA
There were 5 gaps of missing data longer than 5 days: a 30−day gap (from 01−April−88 to
30−April−88), two 27−day gaps (from 05−Jan−92 to 31−Jan−92, and from 01−Mar−93 to
27−Mar−93), a 14−day gap (from 29−Sep−02 to 12−Oct−02), and an 8−day gap (from
23−Nov−03 to 30−Nov−03). These 5 gaps represented 54% of the missing data.
For the three longest gaps in the relative humidity records (the one of 30 and the two of 27
days), there were no data‐base found to fill their missing values. All the missing data from
1996 till 2005 were filled using the Wunderground data‐base, including the following two
longer gaps (the one of 14 and the one of 8 days).
Besides the three longest gaps, which could not be filled, most of the missing data before
1996 were 1− to 3−day gaps. These last were estimated by doing linear interpolation
between the value before and after each gap.
34
3.5. OBSERVED DISCHARGE
There is high uncertainty in every observed discharge record, since these are based on water
level measurements taken in river cross sections that change in time due to erosion and
sedimentation processes (Westerberg, 2008).
The available observed discharge records also had missing data, but for this study those
values were not filled. Since it is not known how uncertain the available data is, applying
methods such as linear interpolation will make the records more uncertain. Even though the
missing data was not filled, some quality control was made of the available discharge
records.
The original unit of the observed daily discharge records was volume per time (m3/s). This
was transformed to runoff (mm) by using the area of the Juan Diaz River basin upstream of
the discharge station (102 km2).
3.5.1. QUALITY CONTROL OF OBSERVED DISCHARGE DATA
Quality control of the discharge records in this study started with a visual data inspection.
Observed monthly discharge records were plotted to identify seasonality (Figure 11). From
this plot, the observed monthly discharge records from August−2005 ll December−2005
were flagged and checked on the daily time scale because these discharge records were high
compared to previous years. As it can be seen in Figure 12, the daily data from August−2005
till December−2005 besides being high values, no pattern could be found. This uncommon
behavior during this period was expected to cause difficulties in the simulations.
The precipitation values shown in Figures 11 to 17 and in Figure 25 correspond to the
adjusted precipitation values obtained in Section 3.1.4. The observed discharge values
shown in Figures 11 to 25 correspond to the transformed runoff records in Section 3.5.
35
Figure 11. O
bserved M
onthly Discharge
‐Juan
Diaz (dark blue line) an
d M
onthly Precipitation‐Tocumen (red bars) 1985−2005.
Figure 1
(red
figu
men
Frequen
runoff v
purple d
Figure 1
(red
max
eve
12. Observed
d bars) Aug−
ure were fix
ntion.
ntly occurri
value 11.16
dashed circ
13. Observed
d bars) April
ximum prec
en though th
d Daily Disc
−Dec 2005. T
xed to 100
ing values w
6 mm was
le in Figure
d Daily Disc
−Dec 1991. T
cipitation an
ere were hig
charge‐Juan
The maximu
mm, even
were found
repeated c
13).
charge‐Juan
The purple d
nd observed
gher values t
36
Diaz (dark
um precipita
though the
d and flagg
consecutive
Diaz (dark
dashed circle
discharge v
than the pre
blue line) a
a on and ob
ere were hi
ged on the
ely from 01
blue line) a
e represents
values in thi
evious menti
nd Daily Pre
bserved disc
igher values
daily scale
1−Oct−91
nd Daily Pre
s a frequent
s figure wer
ion.
ecipitation‐T
charge value
s than the
e. For exam
ll 23−Dec−
ecipitation‐T
occurring va
re fixed to
Tocumen
es in this
previous
mple, the
−91 (see
Tocumen
alue. The
100 mm,
Zero va
consecu
zero val
Figure 1
(red
max
eve
Quality
compar
During t
records
versa w
found in
irregula
difficult
are goo
inspecti
alues were
utive zero v
lues were v
14. Observed
d bars) Jun−
ximum prec
en though th
control o
ring the dail
the rainfall
compared
were found a
n which the
ar cases we
ties in the s
od or not,
ion.
also found
alues from
ery unlikely
d Daily Disc
−Dec 1986.
cipitation an
ere were hig
f the obse
ly runoff res
‐runoff com
to rainfall
as it can be
e discharge
re flagged
imulations.
it will be
d and remo
27−Jul−86
y because m
charge‐Juan
The orange
nd observed
gher values t
erved disch
sponses to t
mparison so
events an
seen in Fig
was decrea
but not rem
This decisi
subjective
37
oved from
ll 12−Aug−
most of them
Diaz (dark
e circle rep
discharge v
than the pre
harge data
the daily ra
ome inconsi
d no discha
gures 15 and
asing even
moved from
ion was tak
e to discre
the series.
−86 (see ora
m occurred
blue line) a
presents a lo
values in thi
evious menti
a was follo
infall pulses
istencies su
arge respon
d 16. In add
thought the
m the data,
ken because
dit the rec
For examp
ange circle i
during the
nd Daily Pre
ong series o
s figure wer
ion.
owed by a
s.
uch as low o
nses to rain
dition to the
ere was a r
even thou
e it is not kn
cords by a
ple, there w
in Figure 14
rainy seaso
ecipitation‐T
of zero val
re fixed to
a visual ins
observed d
nfall pulses
e latter, cas
rainfall puls
gh they ma
nown if the
applying jus
were 17
4). These
on.
Tocumen
ues. The
100 mm,
spection
ischarge
s or vice
ses were
e. These
ay cause
e records
st visual
Figure 1
(red
A co
May
pre
the
A
B
C
15. Observed
d bars). The
orresponds
y−Dec 1998
cipitation an
re were high
d Daily Disch
green circle
to the perio
8. C corres
nd observed
her values th
harge‐Juan
s represent
od between
ponds to t
d discharge v
han the prev
38
Diaz (dark b
inconsistenc
May−Dec 1
the period
values in thi
vious mentio
blue lines) a
cies found in
1995. B corr
between M
s figure wer
on.
and Daily Pre
n the rainfal
esponds to
May−Dec 19
e fixed to 10
ecipitation‐T
l‐runoff com
the period
999. The m
00 mm, eve
Tocumen
mparison.
between
maximum
n though
Figure 1
(red
run
wer
After th
coefficie
precipit
evapotr
0.66, ca
for the
by doin
year, all
Even th
modelin
hydrolo
TABLE 6
YEAR
1985
1986
1987
1988
1989
1990
16. Observed
d bars) May
off compari
re fixed to 10
he previou
ent results
tation (Q/P
ranspiration
alculated as
21 years of
g the sum
l the years o
hough stran
ng from 19
ogically repr
. Long term
RunoffCoefficie
0.52
0.69
0.78
0.64
0.73
0.70
d Daily Disc
y−Dec 2003.
ison. The ma
00 mm, even
s cases we
from the d
P). This coe
n losses. As
s the sum o
f available r
of all the d
obtained a
nge rainfall
985 till 200
resented by
runoff coeff
f ent
YEAR
1991
1992
1993
1994
1995
1996
charge‐Juan
The green
aximum pre
n though the
ere flagged
division bet
efficient is
is shown in
f all the day
records. Wh
ays in whic
runoff coeff
and runoff
05 to deter
y records of
ficient.
Runo
Coeffic
0.8
0.6
0.7
0.6
0.5
0.6
39
Diaz (dark
circles repr
ecipitation a
ere were hig
d, the runo
tween long‐
expected
n Table 6, t
ys in which
hen calculat
ch there wa
fficient belo
f behaviors
rmine how
the availab
off cient
YEA
87 199
63 199
2 199
62 200
4 200
64 200
blue line) a
esent incon
nd observed
gher values t
off coefficie
‐term obse
to be belo
the runoff c
there was
ting the run
as an obser
ow to 1, exc
s were foun
well the J
ble instrume
AR Run
Coeffi
97 0.5
98 0.5
99 0.5
00 0.6
01 0.4
02 0.6
nd Daily Pre
sistencies fo
d discharge
than the prev
ent was ch
rved discha
ow 1 due
coefficient f
an observe
noff coeffic
ved dischar
ept for the
nd, these d
Juan Diaz R
entation.
off cient
YEA
51 200
58 200
59 200
68 ALLTHEDAT
47
68
ecipitation‐T
ound in the
values in th
vious menti
hecked. The
arge and lo
to the lon
for all the d
ed discharg
ient for eve
rge record
year 2005.
data were u
River basin
AR Ru
Coeff
03 0
04 0
05 1
L E ATA
0.
Tocumen
e rainfall‐
his figure
on.
e runoff
ong term
ng term
data was
e record
ery year,
for each
used for
can be
noff ficient
.51
.47
.41
.66
3.6. FL
The ava
shown
known t
3.6.1.
First, th
observe
register
Accordi
precipit
register
values (
precipit
unlikely
Figure 1
dot
reco
high
LOOD DAT
ailable histo
in Section
to what ext
QUALITY
he observed
ed discharg
red, there w
ng to the f
tation regis
red (see gre
(below 20
tation value
y as well.
17. Observed
s). Green cir
orded. Purp
h precipitati
TES REGIST
orical flood
2.3.3. From
tend these r
CONTROL
d discharge
ge data are
was no obse
flood dates,
stered, as w
een circle
mm) were
es registere
d discharge
rcle represen
le square re
on recorded
TERED
records of
m 1985 till
records are
L OF THE F
e and rainfa
daily aver
rved discha
, there wer
well as in
in Figure 1
found regi
ed above 4
and rainfall
nts flood eve
epresents flo
d.
40
the Juan D
2005 there
correct.
FLOOD RE
all recorde
rages and n
arge record
re flood eve
days when
17), which i
stered duri
45 mm (see
recorded d
ents register
ood events r
iaz Townsh
e are 31 fl
ECORDS
d on the fl
not daily m
ed, perhaps
ents in day
n there wa
is unlikely.
ing the floo
e purple sq
during flood
red with low
registered w
ip are not c
oods regist
lood dates
maxima. In
s due to its
ys when the
as a low o
Also low o
od dates in
quare in Fi
dates from
w precipitatio
with low disc
complete, a
tered, but
were plott
four of th
magnitude
ere was litt
observed d
observed d
n which the
igure 17), w
1985 till 20
on and low d
charge recor
as it was
it is not
ted. The
e floods
.
tle or no
ischarge
ischarge
ere were
which is
005 (blue
discharge
rded and
41
4. MODEL QUALITY
Two performance measures (the Nash‐Sutcliffe model efficiency coefficient and the
coefficient of determination) were used to assess the quality of the hydrological and
statistical simulations.
4.1. WASMOD CALIBRATION AND QUALITY OF THE SIMULATIONS
To assess the quality of any hydrological model, first its parameters have to be calibrated.
Calibration consists of the search for the "best" parameter set, which is the set that gives the
best fit between the observed and calculated runoff (Xu, 2010a).
The WASMOD calibration was performed manually and subjectively by changing the
parameter sets until most of the peak flows in the observed hydrograph were matched. How
much we can trust from a simulation depends on how well it reproduces the observations.
The calibration period, as well as the simulation period, was from 1985 till 2005.
Two objective functions were used to determine the quality of the simulations. One of the
objective functions was the Nash‐Sutcliffe model efficiency coefficient. This coefficient is
"one of the most widely used performance measures in hydrology" (Westerberg, 2010). The
Nash‐Sutcliffe coefficient is defined by equation (14):
1 ∑
∑ …………………………………………………………………................................(14)
where
R2: Nash‐Sutcliffe coefficient
qt: observed discharge for a day (or month) t.
dt: calculated runoff for a day (or month) t.
: mean observed discharge
The Nash‐Sutcliffe coefficient compares the residual variance (described by the numerator)
to the initial variance (described by the denominator). This coefficient can range from ‐∞ to
1. An efficiency of 1 indicates a perfect fit between the observed and the calculated runoff.
An efficiency of 0 indicates that the calculated runoff is as accurate as the mean observed
discharge. Efficiency values below 0 indicate that the mean observed discharge is a better
predictor than the calculated runoff (Nash and Sutcliffe, 1970).
The other objective function used to determine the quality of the simulations was the
coefficient of determination, R2. This coefficient ranges from 0 to 1. When this is expressed
as a percentage, it represents the ratio that can be predicted by the regression line (Xu,
2010b). The coefficient of determination, R2, is defined by equation (15):
∑
∑
where
: are t
: is the
: are t
For eve
left afte
were 36
Table 7
daily an
b1 was t
the bes
tried wi
model r
upper p
*1: For an e
In an at
were es
runoff.
∑
∑……
the observa
e mean of t
the predicte
ery WASMO
er the warm
65 days and
shows the
nd monthly
tried for 0,
st results w
ith 1 and 2,
results were
part of the b
TABL
energy limited sys
tempt to im
stimated ag
…………………
ations of the
he depende
ed values of
OD simulatio
m up period
d 36 months
best mode
simulations
0.5, 1 and
ere obtaine
and the be
e obtained
basin is a fo
E 7. Best mo
stem, a4 is const
mprove the
gain, using t
………………..
e dependen
ent variable
f the depen
on, both ob
d. The warm
s respective
el paramete
s.
2. Since th
ed when b1
est results w
when a6 wa
rest area (s
odel paramet
rained by 0 <= a4
model qua
the average
42
..................
nt variable
e
dent variab
bjective fun
m up perio
ely.
er set obtai
he Juan Dia
1 was fixed
were obtain
as closed to
ee Section
ter set obtai
4 <= 1.
lity in the d
es of 3, 5, 10
..................
ble
nctions wer
ds for the d
ined from t
z River bas
to 0 or 0.5
ned when b2
o zero, this
2.2.1.6).
ined from m
daily simulat
0 and 30 da
..................
re calculate
daily and m
the manual
in is located
5 (see Secti
2 was fixed
could be re
manual calibr
tions, both
ays of obser
..................
ed with all t
monthly sim
l calibration
d in an arid
ion 2.2.1.5)
to 1. Also,
easonable s
ration.
objective f
rved and ca
.......(15)
the data
mulations
n for the
d region,
. b2 was
the best
since the
unctions
alculated
5. RESU
5.1. W
No goo
monthly
On the
observe
discharg
runoff r
above 5
every y
most of
season
in the fi
18.
Figure 18
/
A
B
A
B
ULTS
WASMOD S
od represen
y resolution
daily scale,
ed daily dis
ge records f
ranged in t
50 mm repr
ear, at som
f the years
was April. W
irst 5 years
8. Observed
/ WASMOD
A correspon
B correspon
SIMULATIO
ntation of t
n. In both th
, all the ob
charge reco
from 1985 t
he same pe
resented le
me point du
s, when ref
When refer
of simulatio
d (red line) ve
‐ Juan Diaz.
ds to the pe
ds to the pe
ONS
the observ
here were u
served pea
ords below
till 2005 ran
eriod from
ss than 0.3
uring the d
ferring to re
ring to resid
ons, especia
ersus Calcula
riod betwee
riod betwee
43
ved dischar
underestima
aks above 3
w 32 mm w
nged from
0 to 49 m
5% of the a
ry season t
esiduals, th
duals, the b
ally in the m
ated (dark b
en May−Dec
en May−Dec
ge records
ation and ov
32 mm were
were undere
almost 0 to
m. The obs
available re
the calculat
he month b
best simulat
month of De
blue line) Dai
1989.
1990.
was found
verestimati
e underesti
estimated. T
o 214 mm. T
served daily
cords of th
ted daily ru
best simula
tions of the
ecember, as
ily Runoff
d in the d
on of peaks
imated. 50%
The observ
The calculat
y discharge
he rainy sea
unoff was z
ted during
e rainy seas
s is shown i
aily and
s.
% of the
ved daily
ted daily
records
son. For
zero. For
the dry
on were
in Figure
After th
the beg
In gene
From 19
was mo
after 19
the obs
most of
As is sh
produce
simulati
all the o
of its irr
Figure 19
/
A
B
A
B
he first five y
ginning or at
ral, for mos
986 till 199
ostly under
995, the ob
served daily
f the years t
hown in Fi
ed a poor
ions from A
observed di
regular beh
9. Observed
/ WASMOD
A correspon
B correspon
years of sim
t the middle
st of the yea
95, during t
estimated
bserved dai
y runoff wa
the observe
igures 18 a
fit since th
August−200
ischarge da
avior (see S
d (red line) ve
‐ Juan Diaz.
ds to the pe
ds to the pe
mulation, th
e of it.
ars the dry
he first mo
until July. D
ly runoff w
as mostly u
ed runoff wa
and 19, th
he biggest
5 ll Decem
ta registere
Section 3.5.1
ersus Calcula
riod betwee
riod betwee
44
e best fits o
season was
onths of the
During the
was overest
underestima
as overestim
e general
peaks wer
mber−2005
ed during th
1).
ated (dark b
en May−Dec
en May−Dec
of the rainy
s underestim
e rainy seas
previous m
timated. Fro
ated. Durin
mated.
perception
re not well
shown in F
hat period w
blue line) Dai
1999.
2005.
season occ
mated from
son, the ob
months, for
om Septem
g Decembe
is that th
simulated
Figure 19.B
were under
ily Runoff
curred rando
m February
bserved dail
most of th
mber till No
er and Janu
he daily sim
. As expec
were poor
restimated
omly at
till April.
ly runoff
he years
vember,
uary, for
mulation
ted, the
. Almost
because
45
Figure 20. O
bserved (red line) versus Calculated (dark blue line) Monthly Runoff / W
ASM
OD ‐ Juan
Diaz (1988−2005).
46
On the monthly scale, there were also overestimations and underestimations. The observed
monthly discharge records from 1985 till 2005 ranged from 15 mm to 764 mm. In these
records, 5 months were above 500 mm, all underestimated. Of those 5, 4 were found in
2005 (from August till November). The calculated monthly runoff by WASMOD ranged from
0 to 499 mm in the same period. Most of the calculated monthly runoff data above 400 mm
were overestimations, except one. During the dry and rainy season, the months best
simulated for most of the years, when referring to residuals, were April and December,
respectively. As it can be seen in Figure 20, WASMOD had difficulties to simulate most of the
peak values in every rainy season, less in 1988, 1989, 1992 and 1996.
TABLE 8. Values of objective functions applied to the calculated runoff by WASMOD from 1985−2005.
Input Data
Calibration Data
Time Scale
Objective Function
1 dayaverage
3−day average
5−day average
10−day average
30−day average
Tocumen (pt, ept)
Juan_Diaz (Observed Discharge)
Daily
Nash‐Sutcliffe
0.296 0.402 0.442 0.486 0.551
R2 0.302 0.410 0.451 0.498 0.564
Monthly
Nash‐Sutcliffe
0.554 ‐ ‐ ‐ ‐
R2 0.560 ‐ ‐ ‐ ‐
The values of the objective functions in Table 8 indicate that the WASMOD simulations
poorly represented the Juan Diaz River basin with the records of the available
instrumentation. Both objective functions were low on the daily scale. On the monthly scale,
the basin was better represented, but still poor. These results confirm what was shown
graphically; no perfect fit was achieved.
Both objective functions estimated for the 3, 5, 10 and 30 days averages of the observed and
calculated runoff (referring to the ones shown in Table 8) are the best results obtained for
every case, but each case was not estimated by averaging the "best" single daily simulation
(referring to the one calculated with the parameters shown in Table 7). In other words, more
single daily simulations were performed with different parameter sets; from these single
daily simulations, many series of n−days average were obtained, and for each series the
objective functions were calculated. From all the single daily simulations, the best objective
functions for every case were not obtained by averaging the "best" single daily simulation.
When comparing the values of the objective functions resulting from the 30−day averages of
the observed and calculated runoff to the ones obtained in the monthly simulation, similar
results were obtained.
5.2. LIN
Many
evapotr
variable
observe
overest
The set
consiste
Since so
the pred
rainfall
On the
observe
linear m
discharg
rainy se
best mo
of it (e.
months
Novemb
observa
NEAR MU
combinatio
ranspiration
e, the total
ed daily an
imations of
of indepen
ed of precip
ome of the
dictions too
pulses.
Figure 21
daily scale,
ed discharge
multiple reg
ge records
eason. Whe
onth simula
.g. Figures
s of the rai
ber, most
ations were
ULTIPLE RE
ons of i
n, humidity
runoff. No
nd monthly
f the peaks.
ndent varia
pitation, po
independen
ok a cardiog
1. Observed
Linea
, all the ob
e records be
gression, ran
above 37 m
en referring
ted during
22.A and 2
ny season
of the o
half overes
EGRESSION
ndependen
y and tem
one of thes
y runoff. I
bles that ga
tential evap
nt variables
gram behav
(red line) ve
ar Multiple R
served pea
elow 24 mm
nged from
mm repres
g to residua
the rainy se
22.B). For m
(until Augu
observation
stimated an
47
N
nt variable
mperature,
se combinat
In both ca
ave the bes
potranspira
s used in th
vior as show
ersus Estimat
Regression ‐
aks above 2
m were ove
0 to 37 mm
ented less
als, there w
eason, this w
most of the
ust) were o
s were u
nd half unde
es, such
were used
tions gave
ases there
st fit using
ation, temp
is approach
wn in Figure
ted (dark blu
Juan Diaz (1
24 mm were
restimated
m from 198
than 1% o
was not a cl
was random
e years, all
overestimat
nderestima
erestimated
as precip
d to predi
a good rep
were und
the linear m
erature and
h did not dir
21, even w
ue line) Daily
1999).
e underesti
. The estima
5 to 2005.
f the availa
ear pattern
mly at the m
the dry se
ed. Then fr
ted. Durin
d.
pitation, p
ict the de
presentatio
derestimatio
multiple re
d relative h
rectly affec
when there
y Runoff /
imated. 65%
ated daily r
The observ
able record
n of which
middle or at
eason and
rom Septem
ng Decemb
potential
pendent
n of the
ons and
gression
umidity.
t runoff,
were no
% of the
unoff by
ved daily
ds of the
was the
the end
the first
mber till
ber, the
Figure 2
Similar t
Decemb
behavio
As is sh
linear m
peaks o
B
A
C
2. Observed
/ Linear M
A correspo
B correspo
C correspo
to the WAS
ber−2005 (s
or of the ob
hown in Fig
multiple reg
of the observ
d (red line) ve
ultiple Regre
onds to the p
onds to the p
nds to the p
SMOD simul
shown in F
servations d
ures 21 an
gression is t
ved dischar
ersus Estima
ession ‐ Juan
period betwe
period betwe
period betwe
lation, the m
Figure 22.C)
during that
d 22, the g
that it was
rge in the w
48
ated (dark bl
n Diaz
een May−De
een May−De
een May−De
multiple reg
) did not g
period.
general per
poor since
whole series
lue line) Dai
ec 1986.
ec 1995.
ec 2005.
gression est
ive good re
ception of
e it could n
.
ly Runoff
timation fro
esults beca
the estima
ot well rep
om August−
ause of the
ated daily ru
present the
−2005 ll
strange
unoff by
e highest
49
On the monthly scale, there were also overestimations and underestimations. Similar to the
WASMOD simulation, from the 5 months above 500 mm in the observed discharge series, all
were underestimated. The estimated monthly runoff using linear multiple regression ranged
from 0 to 397 mm from 1985 to 2005. All estimated monthly runoff data above 330 mm
were overestimations of the observed discharge. As it can be seen in Figure 23, the best fits,
when referring to residuals, occurred at the end of the rainy season and at the beginning of
the dry season. Still, during the dry and rainy season from year to year; there was not a
single month, in which it could be said that it was the best estimated; the month best
estimated in both seasons varied randomly. For every rainy season, almost every peak value
was poorly estimated, less in 1992 and 1997.
TABLE 9. Values of objective functions applied to the estimated runoff by linear multiple regression
from 1985 to 2005.
Input Data
Calibration Data
Time Scale
Objective Function
1 dayaverage
3−day average
5−day average
10−day average
30−day average
Tocumen (pt, ept, Temp, Rel. Hum.)
Juan_Diaz (Observed Discharge)
Daily
Nash‐Sutcliffe
0.228 0.307 0.327 0.341 0.353
R2 0.228 0.314 0.340 0.365 0.379
Monthly
Nash‐Sutcliffe
0.526 ‐ ‐ ‐ ‐
R2 0.519 ‐ ‐ ‐ ‐
The results of the objective functions in Table 9, indicate that the linear multiple regression
estimations also poorly represented the Juan Diaz River basin with the records of the
available instrumentation. The estimated runoff by linear multiple regression did not fit the
observations well. The values of the objective functions obtained in the linear multiple
regression estimations were lower than those obtained in the WASMOD simulations.
The monthly estimation was better than the daily estimation, but its representation of the
upper part of the basin was still not good. Using 30−day averages of observed and es mated
runoff, did not give the same results or even approximately to the one using monthly data.
50
ib
d(
dli
)i
d(d
kbl
li)
hl
ff/
ilil
ii
()
Figure 23. O
bserved (red line) versus Estimated (dark blue line) Monthly Runoff / Linear M
ultiple Regression ‐ Juan
Diaz (1985−2005).
51
To study the runoff responses to accumulated rainfall events, a new independent variable,
namely rainfall that occurred 3, 5, 10 and 30 days before the day t, was included to take soil
moisture into consideration. A resume of the values of the objective functions obtained in
every case is shown in Table 10.
TABLE 10. Values of objective functions applied to the estimated runoff by linear multiple
regression when an approximation of soil moisture was added as independent variable.
Estimation performed on a daily scale from 1985−2005.
Input Data Calibration
Data Time Scale
Objective Function
Sm: 3 days
acc.
Sm: 5 days
acc.
Sm: 10 days
acc.
Sm: 30 days
acc.
Tocumen ("Soil Moisture", pt, ept, Temp, Rel. Hum.)
Juan Diaz (Observed Discharge)
Daily
Nash Sutcliffe
0.247 0.252 0.262 0.275
R2 0.247 0.251 0.261 0.275
When adding as independent variable an approximation of soil moisture, the quality of the
daily estimations barely increased from when this was not used (compare daily values of the
objective functions obtained for 1 day average runoff in Table 9 to those shown in Table 10).
The quality of the estimations increased when more days were summed in the
approximation of soil moisture, but the results of the objective functions indicated that the
estimation was poor.
In this approach, the best estimations were obtained when the total rainfall from the 30
previous days was used as soil moisture proxy. For this case, all the observed daily peaks
above 24 mm were underestimated. 61% of the observed daily discharge records below 24
mm were overestimated. The estimated daily runoff using this approach ranged from 0 to 34
mm from 1985 to 2005. The observed daily discharge records above 34 mm represented less
than 2% of the available records of the rainy season. When referring to residuals, there was
not a clear pattern of which month was the best estimated during the rainy season, this was
randomly at the middle or at the end of it (e.g. Figure 24).
In general, for most of the years the dry season was underestimated during February and
March. Then, during April and the first months of the rainy season (until August), the
estimated runoff seemed to exceed the observations. From September till November, most
of the observed runoff data were underestimated. During December and January, most of
the estimated runoff exceeded the observations.
The general perception of this approach was that the estimations were poor, since it was not
able to predict the high peaks.
Figurre 24. ObservRegressioA correspB correspC corresp
ved (red lineon ‐ Soil Moiponds to theponds to theponds to the
e) versus Estisture Proxy e period betw period betwperiod betw
52
imated (dar(total rainfaween May−Dween May−Dween May−D
k blue line) Dall of the 30 Dec 1986. Dec 1989. Dec 1998.
Daily Runoffprevious day
f / Linear Muys) ‐ Juan Di
ultiple az.
5.3. LO
To esta
against
shown i
Every ye
on the
most of
were th
availabl
2005).
The obj
result o
than th
around
expecte
the obs
regressi
ONG TERM
blish a lon
rainfall dat
in Figure 25
early datum
days in wh
f the years
he ones whi
e data, on
jective func
obtained wi
ose obtaine
the regre
ed values in
served yea
ion curve, s
Fig
M RAINFAL
g term rain
a was plott
5, the 95% c
m shown in
ich there w
have missi
ich had mo
ly 3 did no
ction used
ith this fun
ed in the d
ession curv
the regress
arly values
ome observ
gure 25. Obse
The bla
The red
LL‐RUNOF
nfall‐runoff
ed in the ye
confidence l
Figure 25
was an obse
ng discharg
re than 70%
ot satisfy th
in this sec
ction with
daily and m
e. The sta
sion curve w
fell within
vations mis
erved Yearly
ack curve rep
d curves rep
53
FF RELATIO
f relationsh
early scale a
limits on th
represents
erved daily
ge data, the
% of their d
he previous
ction was th
the yearly
onthly reso
andard dev
was 213 mm
n the range
sed the reg
y Runoff vers
presents the
resent 95%
ONSHIP
ip, a graph
and a curve
e regressio
the accum
discharge r
e years take
daily dischar
s condition
he coefficie
available d
olution, but
viation betw
m. It has to
e of the 9
gression cur
sus Yearly R
e regression
confidence l
h showing o
e was fitted
n curve wer
ulated daily
registered fo
en into acc
rge data. Fr
(these we
ent of dete
ata was 0.7
t still the d
ween the
be noticed
95% confide
ve by 350 m
ainfall Data
curve.
imits of the
observed d
to the prev
re also calcu
y rainfall re
for each yea
ount for th
rom the 21
re 2001, 2
ermination,
70, which i
ata were s
observed
that even w
ence limits
mm or more
(blue dots).
regression c
ischarge
vious. As
ulated.
egistered
ar. Since
his graph
years of
004 and
R2. The
s higher
cattered
and the
when all
s of the
e.
curve.
54
6. DISCUSSION
The main objective of this thesis was to establish how well the Juan Diaz River basin could be
hydrologically represented by records of the available instrumentation, using a hydrological
model and a statistical method. In both approaches, the same input data were used,
however more variables were considered in the statistical method.
Precipitation is the largest quantity and perhaps the most important in the hydrological
cycle. Between 5 and 10 stations for every 250 km2 is recommended to capture the rainfall
variability in a catchment (Cedeño, 1997). This is not the case in the Juan Diaz River basin.
Precipitation data in the basin are scarce. Nowadays, there are no active meteorological
stations within the basin. Precipitation records from some active and inactive meteorological
stations located in the proximity of the Juan Diaz River basin were available.
Several methods, such as Thiessen polygon and the isohyetal method can be used for
estimating the areal mean precipitation of any catchment. The Thiessen polygon was not
used in this study because it would have given biased estimations since the studied site is
close to the sea and mountains. The isohyetal method was not used either because it
requires an extensive gage network to draw accurate isohyets (Goovaerts, 1999; Cedeño,
1997). Precipitation records from an active meteorological station, which was the closest to
the basin from the ones with available records, were used in this study to estimate the areal
mean precipitation of the basin. Accurate estimation of the spatial and temporal distribution
of rainfall in a mountainous catchment with only one station is a difficult task. The lack of
precipitation data to accurately calculate the areal mean precipitation of the basin makes
the application of any hydrological model unreliable.
In addition, many inconsistencies were found in the precipitation input data and the
observed discharge data. Inconsistencies such as no runoff responses with rainfall pulses or
vice versa, frequently occurring values or low observed discharge records compared to the
rainfall events, made it difficult to establish an acceptable relationship between rainfall and
runoff both in the daily and monthly resolution and in the long term.
For this thesis the calibration of the hydrological model was performed manually, based on
visual comparison of plots and by using two objective functions to measure the quality of the
simulations. The calibration and simulation of the hydrological model was complicated
because of the inconsistencies found. Unknown uncertainties in the precipitation input data
and on the observed discharge data for calibration make any hydrological representation
questionable.
For comparison, these two objective functions were also calculated in the statistical method.
According to the objective functions, WASMOD simulated the observed discharge better.
Even though some peaks were well simulated, most of them were underestimated by the
two methods. The values of the objective functions indicated that the estimations by both
methods were poor.
55
When an approximation of soil moisture, based on an accumulated value of previous rainfall
events, was added as an additional independent variable, the quality of the daily simulation
barely increased. The quality of the estimations increased when more days were summed in
the approximation of soil moisture, but the values of the objective functions indicated that
the simulations with this approach also performed poorly.
Additional linear multiple regressions using only the data of the flood dates were planned to
be performed, but at the end this approach was disregarded because of the inconsistencies
found in the flood dates registered.
The simulations of any model are not reliable when it is not known how large the error in the
input and output data is. It can be stated that the Juan Diaz River basin cannot be
represented accurately in the daily and monthly resolution with the available
instrumentation within (and close to) it at this point. In the long term, the available
instrumentation gave a better relationship between the rainfall and discharge data but care
has to be taken if this approach is used since the limited quantity of data in this scale were
scattered around the regression curve and some of the values varied more than one and a
half times the standard deviation.
Resources have to be put in the Juan Diaz River basin to address the issue of limited data
quantity. By increasing the precipitation network data in any catchment, modeling
uncertainties will be reduced and reliable simulations can be obtained for better planning of
the available water resources. A network of at least five rain gauges would be reasonable to
have within the Juan Diaz River basin in order to cope with the spatial and temporal
variability of precipitation. One should be placed at the west of the basin, close to previous
location of the inactive Las Cumbres station. Three more should be placed at the north east
to account for the rainfall pattern in the higher elevations of the basin. The last one should
be placed at the central part of the basin to account for the rainfall pattern in the lower
parts of it.
To reduce uncertainty in the observed discharge records, two more hydrological stations
could be desirable within the basin. Both could be placed at the central part of the basin, just
upstream from where the two largest contributories from the north and west connect (one
for each contributory).
For rainfall and observed discharge compatibility, both should be measured at the same time
and with the same time spans (30 to 60 min) in order to make effective modeling possible.
McKay (2004) points out the necessity of creating a national network for hydro‐
meteorological monitoring and to adopt a plan for integral management of the hydrographic
basins in Panama, but that is an objective that has not been achieved yet. Hopefully the
results obtained in this thesis will encourage decision makers to increase the available
instrumentation in the Juan Diaz River basin and others.
56
7. CONCLUSIONS
Accurate estimation of the spatial and temporal distribution of rainfall in a
mountainous catchment like the Juan Diaz River basin with only one station is not
feasible.
Inconsistencies in the input and output data were found. These inconsistencies made
it difficult to establish an acceptable relationship between rainfall and runoff in the
daily and monthly scale. In the long term a better relationship was found than in the
two previous scales, but care has to be taken if this approach is used since the limited
quantity of data in this scale were scattered around the predictions.
Unknown uncertainties in the precipitation input data and in the observed discharge
data for calibration make any hydrological representation questionable.
Neither the hydrological model, WASMOD, nor the statistical method, linear multiple
regression, could well represent the Juan Diaz River basin with the records of the
available instrumentation.
The meteorological station chosen for this study could not well represent the Juan
Diaz River basin.
The available instrumentation of the basin is not sufficient for modeling or
forecasting at this point. This emphasizes the importance of having an adequate and
active precipitation network within the basin of study in order to capture its rainfall
variability and to make it possible for simulation or forecasting that will support
better water resources management.
Inconsistencies in the flood dates registered were found. Flood records must be
improved in order to find a relationship between floods and hydro‐meteorological
events.
57
ACKNOWLEDGEMENTS
I would like to thank Sven Halldin, Lars‐Christer Lundin and Chong‐Yu Xu, my supervisors, for
their guidance, advice and patience during this study project. I wouldn't have made this far
in this project without their support. Thanks also to Jose Luis Guerrero for his help and tips
with the WASMOD programming.
I would like to also thank the Swedish International Development Cooperation Agency (Sida)
for giving me the opportunity to study in Sweden and being part of the project "Research
Capacity Building in Nature‐Induced Disaster Mitigation in Central America 2008−2010".
Many thanks to ISP for taking care of me and my wife during our time in Sweden.
Thanks also to Juan Antonio Gomez of the Panama University (Universidad de Panama) for
linking me with Sida and for his guidance to earn this fellowship.
Thanks to the Department of Hydro‐Meteorology of ETESA (Gerencia de Hidrometeorología
de ETESA), who provided me the data used in this project and also for giving me permission
to reprint some figures of past documents prepared by them (Figure 1 and figure shown in
ANNEX B in this study).
Thanks also to Murugesu Sivapalan for letting me reprint a figure from one of his lecture
notes (Figure 3 in this project).
Special thanks to Nilsa, my wife, who has always believed in me and has never stopped
encouraging me to aspire for better things.
Thanks to my mom for her unconditional support and for all the sacrifices she made to make
me the person I am now. To my sister, that even with the distance has always been there for
me.
Finally, but not least, thanks to my friends in Panama and to the new ones I met in Sweden
for always being there and for their support during my studies in Sweden.
58
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60
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61
ANNEX A. List of Equations used in this thesis for the WASMOD system (snow free
catchment).
Hydrological Process Equation
Actual Evapotranspiration (for an energy limited systems)
min 1 , ,
where is available water
Slow Flow Component
Fast Flow Component
where 1 , is active rainfall
Routing Routine of the Fast Flow Component
where is the routing storage
Total Runoff
Water Balance Equation
max , 0
ANNEX
(UNESC
B. Annua
CO, 2008). R
al Potentia
Reprinted w
al Evapotra
with permiss
62
anspiration
sion from ET
n Map cre
TESA.
eated by EETESA, 19771−2002
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