PREDICTION AND ANALYSIS OF WEATHER DATA BY USING DOPPLER WEATHER RADAR FOR AIRCRAFT NAVIGATION

8/20/2019 PREDICTION AND ANALYSIS OF WEATHER DATA BY USING DOPPLER WEATHER RADAR FOR AIRCRAFT NAVIGATION

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PREDICTION AND ANALYSIS OF WEATHER DATA BY

USING DOPPLER WEATHER RADAR FOR AIRCRAFT

NAVIGATION

BACHELOR OF SCIENCE IN AERONAUTICAL ENGINEERING

SUBMITTED BY

Abdullah Al Faysal Student No: 201122017

Khondoker Onosultana Student No: 201122030

Afroza Rokhsana Student No: 201122040

Abdullah Al Amin Student No: 201122046

SUPERVISED BY

Dr. Pran Kanai Saha

Professor , Department of Electrical and Electronic Engineering

BUET, Dhaka-1000, Bangladesh.

DEPARTMENT OF AERONAUTICAL ENGINEERING

MILITARY INSTITUTE OF SCIENCE & TECHNOLOGY

DHAKA, BANGLADESH

DECEMBER 2014


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PREDICTION AND ANALYSIS OF WEATHER DATA BY

USING DOPPLER WEATHER RADAR FOR AIRCRAFT

NAVIGATION

A thesis submitted to the Department of Aeronautical Engineering, Military

Institute of Science and Technology as a part of the requirements in order to

complete the BSc degree in Aeronautical Engineering.

SUBMITTED BY





SUPERVISED BY

Dr. Pran Kanai Saha

Professor, Department of Electrical and Electronic EngineeringBUET, Dhaka-1000, Bangladesh.

DEPARTMENT OF AERONAUTICAL ENGINEERING

MILITARY INSTITUTE OF SCIENCE & TECHNOLOGY

DHAKA, BANGLADESH


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CERTIFICATION

This thesis entitled as “PREDICTION AND ANALYSIS OF WEATHER DATA BY USING

DOPPLER WEATHER RADAR FOR AIRCRAFT NAVIGATION” submitted by the group asmentioned below has been accepted as satisfactory as a part of the requirements in order to

complete the BSc degree at the Department of Aeronautical Engineering, Military Institute of

Science and Technology, Bangladesh. This paper embodies the original work done under mysupervision. Undersigned is on deputation from department of Electrical and Electronic

Engineering at BUET and had been the thesis supervisor for the group up to December, 2014.

GROUP MEMBERS





SUPERVISOR

-------------------------------------------

Dr. Pran Kanai Saha

Professor , Department of Electrical and Electronic Engineering

BUET, Dhaka-1000,

Bangladesh.


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DECLARATION

We the authors hereby declare that, thesis entitled as “PREDICTION AND ANALYSIS OF

WEATHER DATA BY USING DOPPLER WEATHER RADAR FOR AIRCRAFT NAVIGATION” is submitted to the Department of Aeronautical Engineering, Military Institute

of Science and Technology as a part of the requirements in order to complete the BSc degree in

Aeronautical Engineering (Course Number 400). This is our original work and was not submitted

elsewhere for the award of any other degree or any other publication.

AUTHORS

-------------------------- -----------------------

Abdullah Al Faysal Afroza Rokhsana

Student No: 201122017 Student No: 201122040

----------------------------- -------------------------

Khondoker Onosultana Abdullah Al Amin

Student No: 201122030 Student No: 201122046


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ACKNOWLWDGEMENT

All praises to the most gracious and most merciful, the Almighty Allah who bestowed upon us

the will for the successful completion of our thesis work within the scheduled time.

We would like to express our heartfelt gratitude and indebtedness to the thesis supervisor Dr.

Pran Kanai Saha, Professor , Department of Electrical and Electronic Engineering, BUET,Dhaka-1000, Bangladesh, whose encouragement, continuous guidance, valuable suggestions,

cooperation and cordial support from the initial to the final level to enable us complete the thesis

successfully. His advice, initiative, moral support and patience are very gratefully acknowledged.

We are thankful to Bangladesh Meteorological Department for providing us the required

information. And also we are thankful to our department and our respected faculty members for

their support and co-operation.


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ABSTRACT

Weather prediction plays a vital role in day to day life. Prediction is done through analyzing the

nature of reflected signals from meteorological targets with respect to the transmitted signal.

In this thesis, radar reflectivity has been found out from drop diameter by using Marshal

Palmer’s Drop Size Distribution (DSD) formula. Then the relationship between radar reflectivity

and rain fall rate for a particular period of time in Bangladesh has been analyzed for proving the

validation of previously established formula (Z=aR b

). Since the values of constants a and b

depends on geographical locations and seasonal changes, hence from the rainfall rate and

reflectivity data these values have been found out for a particular season. A correlation between

reflectivity, temperature and ice water contact for a particular place at a given period of time has

been found out. Effect of humidity on reflectivity has also been discussed from the acquired data.

Rainfall probably the key observable in any weather forecast. In this thesis, mostly the

discussions has been made about rain fall rate and reflectivity, factors for their dependence,

detection procedure and problems in rainfall estimation.


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TABLE OF CONTENTS

CERTIFICATION .......................................................................................................................... ii

DECLARATION ........................................................................................................................... iii

ACKNOWLWDGEMENT ............................................................................................................ iv

ABSTRACT .................................................................................................................................... v

TABLE OF CONTENTS ............................................................................................................... vi

LIST OF FIGURES ..................................................................................................................... viii

LIST OF TABLES ......................................................................................................................... ix

NOMENCLATURE ...................................................................................................................... xi

CHAPTER 1 ................................................................................................................................... 1

INTRODUCTION .......................................................................................................................... 1

1.1 BACKGROUND OF WORK ............................................................................................... 1

1.2 LITERATURE REVIEW ...................................................................................................... 2

1.3 WEATHER RADAR OBSERVATION OF THE ATMOSPHERE .................................... 3

1.4 WEATHER FORECASTING ............................................................................................... 3

1.5 WEATHER FORECASTING FOR AIR TRAFFIC ............................................................. 4

1.6 WEATHER RELATED DECISION MAKING IN AVIATION ......................................... 41.7 WEATHER RADAR AND WEATHER RELATED DECISIONS ..................................... 5

1.8 BENEFITS OF USING WEATHER RADAR ..................................................................... 5

1.9 DISSERTATION OBJECTIVE ............................................................................................ 6

CHAPTER 2 ................................................................................................................................... 7

SCIENCE OF WEATHER RADAR .............................................................................................. 7

2.1 FUNDAMENTALS OF RADAR .................................................................................... 7

2.1.1 Definition ........................................................................................................................ 7

2.1.2 Components of Radar ..................................................................................................... 7

2.1.3 Radar Classification ........................................................................................................ 8

2.2 WEATHER RADAR .......................................................................................................... 11

2.2.1 Weather Radar Principle .................................................................................................. 11

2.2.2 Weather Radar Equation ............................................................................................... 12


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TABLE OF FIGURES

CHAPTER 2

1. Figure 2.1: Basic Radar Block Diagram ……………………………………………...8

2. Figure 2.2: Basic Radar Classification ……………………………………………......9

3. Figure 2.3: Secondary Radar Block Diagram ………………………………………....9

4. Figure 2.4: Frequency VS Time Curve ……………………………………………....11

5. Figure 2.5: Signal Transmission Principle …………………………………………...12

6. Figure 2.6: Weather Radar Signal Observation ……………………………………...17

7. Figure 2.7: Radar network Example in X-band: (a) Channel Allotment.

(b) Radar System Structure………………………………………………………… ...18

8. Figure 2.8: Signal Processing Flow Diagram ………………………………………..19

9. Figure 2.9: Snow Detection …………………………………………………………..21

10. Figure 2.10: Representation of Different Detections ……………………………...…22

CHAPTER 3

1. Figure 3.1: Frequency Changes due to Movement of O bject ……………………..…23

2. Figure 3.2: PDF of Marshal-Palmer DSD with Diameter Interval 0.1 mm and 0.2mm

……………………………………………………………………………….... ..........27

3. Figure 3.3: PDF of Marshall-Palmer DSDs with Three Different Rain Rates……….29

4. Figure 3.4: Co- relation between Rainfall Velocity VS Raindrop Diameter………....30

5. Figure 3.5: Normalized Gamma Distribution, with μ Variations.…………….……...31

6. Figure 3.6: Reflectivity VS Rainfall Rate Graph………………………….………...34

7. Figure 3.7: Rainfall Data for Consecutive Three Months in Dhaka, Bangladesh……358. Figure 3.8: Recorder Average Rainfall Rate of March 2011 in Dhaka,

Bangladesh……………………………………….......................................................36

9. Figure 3.9: Graph for Comparing Different Z-R Relations………………………......38

10. Figure 3.10: Comparison between Different Z-R Relation with Specific Z-R

Relation……………………………………………………………………………….43

11. Figure 3.11: Recorded Rainfall Rate of April 2011 in Dhaka, Bangladesh………….44

12. Figure 3.12: Z-R Relation Comparison from Z=200R 1.6

...............45

13. Figure 3.13: Comparison between Base Reflectivity VS Rainfall Rate…………..…46

14. Figure 3.14: Graphical Representation of Z=142R 1.7………………………………..48

15. Figure 3.15: Graphical Representation of Rainfall VS Reception Power……………51

16. Figure 3.16: Graphical Representation between ICW (Ice Water Content) and

Reflectivity………………………………………………………………………....…53


Reflectivity…………………………………………………………………………… 54


Reflectivity…………………………………………………………………………… 55


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19. Figure 3.19: Ice Water Content VS Reflectivity Factor for a Rayleigh Scattering

Radar ……………………………………………………………………………...…...56

20. Figure 3.20: Specific Humidity VS Atmospheric Attenuation Curve…………...…....58

21. Figure 3.21: Reflectivity Measurement from PPI Plot………………………………..59

22. Figure 3.22: Schematic of the Procedure Used to Calculate the Total Wind From Radial

Velocities……………………………………………………………………………....6123. Figure 3.23: Schematic Describing the Calculation of the Total Wind ……...……….62

24. Figure 3.24: Co-relation between Wind Speed VS Height…………………………....63


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LIST OF TABLES

Table 3.1: Weather Data of Dhaka, Bangladesh for April, 2014……………………………….32

Table 3.2: Reflectivity VS Rainfall rate ………………………………………………………..34

Table 3.3: Rainfall rate per day ………………………………………………………………..35

Table 3.4: Rainfall rate data of March 2011 in Dhaka, Bangladesh…………………………...36

Table 3.5: Rainfall and Reflectivity Data of March 2011 in Dhaka, Bangladesh ……………..38



Table 3.8: Rainfall and Reflectivity Data of March 2011 in Dhaka, Bangladesh...……………40

Table 3.9: Rainfall and Reflectivity Data of March 2011 in Dhaka, Bangladesh...……………40

Table 3.10: Rainfall and Reflectivity Data of March 2011 in Dhaka, Bangladesh…………….41

Table 3.11: Rainfall and Reflectivity Data of March 2011 in Dhaka, Bangladesh…………….41

Table 3.12: Recorded Rainfall Rate of April 2011 in Dhaka, Bangladesh…………………….44

Table 3.13: Rainfall Rate VS Reflectivity of April 2011 in Dhaka, Bangladesh………………45

Table 3.14: Rainfall Rate VS Reflectivity of March 2011 in Dhaka, Bangladesh……………..49

Table 3.15: Rainfall Rate VS Reception Power Chart…………………………………………50

Table 3.16: Temperature, Reflectivity and corresponding ICW data.........................................52

Table 3.17: Temperature, Reflectivity and corresponding ICW data………………………….53

Table 3.18: Temperature, Reflectivity and corresponding ICW data………………………….54

Table 3.19: Specific humidity and gaseous attenuation data…………………………………..58

Table 3.20: Co-relation between θ, VTOTAL & VREDIAL………………………………………...62


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NOMENCLATURE

CHAPTER 1

Z Radar reflectivity.

R Rainfall Rate.

a Coefficient of Z − R relationship; Z = aR b

.

b Exponent of Z − R relationship; Z = aR b

.

CHAPTER 2

PRF Pulse repetition frequency.

n Number of pulses.

f 0 Radar operating frequency.

C Velocity of light in space.

R Target range.

Pr Received power.

Pt Transmitted power.

G Antenna gain.

Ae Effective aperture.

σi Radar cross section .

V Volume.

dB Used to demonstrate something used in decibels.

|K w|2

Coefficient related to the dielectric constant of water.

σ Radar reflectivity in units of m2 3

.

D Diameter over a unit volume.


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λ Wavelength.

Ze Effective radar reflectivity factor.

Z 0l Minimum detectable reflectivity of pulse compression radar.

L Reference length.

SNR Signal to noise ratio.

|K|2

Dielectric factor.

H0 Reference height.

C Radar constant.

F N Noise figure.

T0 Noise reference temperature.

B Beam width.

Φ Beam width (vertical).

Θ Beam width (horizontal).

τ Lag time.

CHAPTER 3

Vr Radial velocity.

N0 Drop concentration for drops of zero size.

^ Marshall and Palmer (1948) rain parameter, a function only of R.

D Drop diameter.

R Rainfall rate.

N ( D) Raindrop size distribution (DSD).

f(μ) Normalizing function in normalized gamma distribution relates to the shape parameter.

Nw The drop concentration (normalized for constant liquid

water content. [close to R]).


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ZDR Differential Reflectivity.

μ Shape parameter.

V N Nyquist velocity.

SH Specific humidity.

Ag Gaseous Attenuation.

Z Reflectivity.

ICW Ice water content.

T Temperature.

V Volume.

α Visible extinction coefficient.

mi Mass of particle j.

ρi Density of solid ice.

|Ki|2

Dielectric factor of solid ice.

i Ratio of the actual backscattering cross section to that

predicted by Rayleigh theory.

n(D) Number concentration of particles with diameter

between D and D+Dd.

FZ(μ) A function of the shape parameter resulting from

integration for reflectivity.

a Coefficient of Z − R relationships; Z = aR b

.

b Exponent of Z − R relationships; Z = aR b

.


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CHAPTER 4

ZDR Differential Reflectivity.

Z Radar reflectivity.

R Rainfall rate.

a Coefficient of Z − R relationships; Z = aR b

.

b Exponent of Z − R relationships; Z = aR b

.

Nw Drop concentration (normalized for constant liquid

water content. [close to R]).


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CHAPTER 1

INTRODUCTION

1.1 BACKGROUND OF WORKThe development of radar systems is accompanied by the development of radio

technology, where the word „radar‟ actually comes from the expression „Radio Detection

And Ranging‟. Radar is a type of passive remote sensing device which uses microwave

frequencies for transmission and reception of signals [36].

Radar developed quickly after its invention by Watson-Watt in 1936 (although whether

this was the true invention is debated) [36].By the end of World War II radar had beenwell developed and was very successful, especially for the Allied forces. During the war,weather returns were generally considered a nuisance, but before the end of the war,the Meteorological Office had 10 cm radar. Since, radar has evolved, withimprovements in all the technologies used in radar. Probably the greatest advances inradar were the invention of the transistor and the computer. The computer wasespecially important for radar meteorology, so that the large quantities of datagenerated can be utilized and archived. The first work in the UK done on the accuracyof precipitation from radar was in the late 1940s [37]. Meanwhile in Canada, Marshall etal. (1947) derived an early Z-R relation. However, it was not until 1967 that the use ofradar to provide quantitative rainfall measurement in the UK was studied [37]. Thisexperiment used 10 cm radar but suffered from a number of problems including a largebeam width. Hence the radar was converted to 5.6 cm in 1973, reducing the beam to 1.In the early 70s the Dee Weather Radar Project based in north Wales pioneeredresearch into the use of radar for rainfall rates, much of the work remains valid, thoughperhaps too confident, this project lead us to have the operational network we now havein the UK [37]. This is now the operational radar band in the UK. This wavelengthchange means that the radar suffers more from attenuation of the radar beam in veryheavy rain, but means that smaller radar antennas are required for the same beamwidth. In the UK and Europe, the very heavy, attenuating rains are less frequent than inthe USA which is a major reason for the difference in radar wavelengths in theserespective regions. The advent of polarization radar occurred in the early 1950s [37].Initially polarization was exploited with circular polarization, where promise was foundfor suppressing clutter. Drop shapes were found to depolarize the returns to the radar,leading to the development of the linear depolarization ratio. Seliga and Bringi (1976)used the shapes, sizes and orientation of rain drops to show differential reflectivity gavea measure of drop size, and when used in combination with Z has the potential to derivemore accurate rainfall rate estimates. To measure differential reflectivity Seliga andBringi (1976) suggested a radar design which utilized horizontally and verticallypolarized pulses, measuring the returns at both polarizations [37]. The CAMR radar in


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Chilbolton was the first to implement this technique with alternate horizontally andvertically polarized beams, then as now this radar operated at S-band.(note theoperational radar network in Britain uses C-band). Sachid (1987) suggested the use ofdifferential phase shift to improve rainfall estimation [37]. Meanwhile, operational radarnetworks grew throughout the world at various frequencies, mostly operating at S-band

in America, but at C-band in Europe and Japan. Recent years have seen thedevelopment and installation of the first polarization radars in the operationalenvironment.

1.2 LITERATURE REVIEWUsing radio as a way of communication, the radar technology went through evolutionaryprogresses during World War II. Soon after the war, many realized the potential of usingradar for civilian purposes. As one of the most popular radar applications in our modernday life, radar is able to detect the location and track down the movement of weathersystems.

The principle behind weather radar are the same as the air traffic radar, receiving backscattered energy from a target. In this case, the targets are water drops, some energy isscattered by drops while some continuous on to be scattered by other drops. If wavelength is too long, excessive energy passes through the cloud and it will not be visible. Ifwave length is too short, all energy back scatters from the outer edge of the cloud andno information arrives from its interior. Most weather radar operates at a frequency of9375 MHz in the X band [34]. It suffers all the problems associated with primary radar,particularly the received signal power. Again the same solution may be applied, such ashigh radiated power and high gain antenna.

In our thesis we use Doppler weather radar. The term „Doppler‟ is in honor of the

Austrian physicist, Christian Johann Doppler, who first explained the principle of the„Doppler effect‟ in 1842 [35]. The Doppler Effect is the increase or decrease in the pitchor frequency of sound waves when a source of waves is moving toward or away fromthe listener. This is quite evident to an observer who is listening to the blare of anautomobile horn as it passes by. The observer hears first a relatively high frequencywave and then a marked drop in frequency.

Unlike sound waves, which have vibrations in the direction of propagation,electromagnetic waves have vibrations in a plane transverse to the direction ofpropagation. Through careful design of the radar, the direction of the electric field in theplane of oscillation can be controlled thereby creating a particular polarization [35]. The

polarization of the electromagnetic waves has a profound effect on their interaction withatmospheric scatters.

Radars are now used to help navigate ships in fog and airplanes in bad weather. Radar

can detect a speeding car and track a satellite. Most importantly for meteorologists,

radars can detect all sorts of atmospheric phenomena.


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1.3 WEATHER RADAR OBSERVATION OF THE ATMOSPHERE

Radar is an active sensor that emits electromagnetic pulses into the surroundings. Thebackscattered energy that is reflected from the objects in its path is received by theradar. A typical radar system consists of at least the following four components: a

transmitter that generates high frequency signals, an antenna that sends the signal outand receives the echoes returned, a receiver that processes the returned signals so thatthey are ready to be used, and a data display system (Rinehart 1997). The radar partthat is visible to the general public is usually the antenna covered with a dome shield, arandom, and installed on top of an observation tower.

Weather radar is a ground based continuous remote sensing instrument. Bothtransmission and reception of the signals are carried out by the same antenna. In orderto scan the entire atmosphere around the radar, the antenna first rotates horizontallyand then moves to another pointing angle. After scanning of a number of angles, thewhole volume scan of the atmosphere is completed.

The electromagnetic radiation in the nature has a very large range of frequencies,where only the band from 100 MHz to 100 GHz is normally used by the radarmeteorologists. It was found convenient to designate letters to certain radar types basedon frequency bands.

Lower frequency and higher wavelength indicates that the radar has stronger signalpower and less attenuation, therefore larger antenna dimension is required.

1.4 WEATHER FORECASTINGWeather forecasting is the application of science and technology to predict the state of

the atmosphere for a given location. Human beings have attempted to predict the

weather informally for millennia, and formally since the nineteenth century. Weather

forecasts are made by collecting quantitative data about the current state of the

atmosphere on a given place and using scientific understanding of atmospheric

processes to project how the atmosphere will change.

Rainfall is probably the most important weather observable to the public: will it rain? Ifso, how much? Rain is possibly the most important part of any weather forecast.Rainfall information also affects many industries, notably agriculture, where rainfall

predictions can influence sowing and harvesting times. Unfortunately, rainfall remainsone of the most difficult features of the weather to forecast. Until very recentlyoperational numerical weather prediction models operated with grid scales far too largeto resolve rainfall so cloud and rain must be parameterized within the models. However,new high resolutions models are being developed and introduced that reduce theresolution to 1-4 km, scales at which the rainfall is being much more accuratelyrepresented.


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Weather Service forecasters use radar to help determine:• The movement and trend of thunderstorms • Variability and concentration of precipitation There are two important aspects of radar that we‟re concerned with :• Amount of energy scattered back from a target to the radar estimate the intensity of

storms and the amount of precipitation• Velocity of a target relative to the radar estimate air motions and circulations withinclouds.

1.5 WEATHER FORECASTING FOR AIR TRAFFIC

Because the aviation industry is especially sensitive to the weather, accurate weatherforecasting is essential. Fog or exceptionally low ceilings can prevent many aircraft fromlanding and taking off. Turbulence and icing are also significant in-flight hazards.Thunderstorms are a problem for all aircraft because of severe turbulence due to their

updrafts and outflow boundaries, icing due to the heavy precipitation, as well as largehail, strong winds, and lightning, all of which can cause severe damage to an aircraft inflight. Volcanic ash is also a significant problem for aviation, as aircraft can lose enginepower within ash clouds. On a day-to-day basis airliners are routed to take advantage ofthe jet stream tailwind to improve fuel efficiency. Aircrews are briefed prior to takeoff onthe conditions to expect en route and at their destination. Additionally, airports oftenchange which runway is being used to take advantage of a headwind. This reduces thedistance required for takeoff, and eliminates potential crosswinds.

1.6 WEATHER RELATED DECISION MAKING IN AVIATION

Despite significant advances in the technology related to the prediction and reporting ofweather conditions, the safety and efficiency of a flight remains dependent upon thepilot making an accurate and expeditious decision concerning the impact of theconditions reported. These so called „weather -related decisions‟ remain the province ofthe operator and, therefore, are subject to the vagaries of human performance.

Errors in relation to weather-related decision-making are difficult to establish for anumber of reasons, not least of which is the fact that a significant proportion of theseaccidents, especially in general aviation, result in fatalities. For example, in the 1999calendar year, the National Transportation Safety Bureau (NTSB 2003) recorded that, ofthe 106 general aircraft accidents involving Instrument Meteorological Conditions,54.7% resulted in fatalities [38].

The rate of weather-related decision errors is also difficult to establish due to theprocess of summarizing aircraft accident and incident statistics amongst investigativeauthorities. In many cases, it is not clear whether aircraft accidents or incidents thatoccurred in poor weather were due to poor decision-making on the part of the pilot ordue to some other factor, such as mechanical failure. The result is a possibleunderestimation of the significance of weather-related decision errors in aircraft accidentand incident causation


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1.7 WEATHER RADAR AND WEATHER RELATED DECISIONS

In addition to weather reports and forecasts, the pilots of advanced technology aircraftnow have available, weather radar systems that display a vast array of weather-relatedinformation in real-time. It is assumed that the provision of this information has thepotential to improve weather-related decision-making by enabling pilots to recognizechanges in the weather conditions at a relatively early stage of the flight and therebytake appropriate action. However, it is not clear precisely how or when these types ofdecisions should take place to safeguard the integrity of the aviation system.

The experience of pilots in commercial environments is one of safeguarding thepassengers and aircraft while, simultaneously, ensuring the expeditious arrival of theaircraft at the destination. This balance between safety and efficiency is particularlyevident in relation to decisions about weather. The difficulty associated with weatherconditions is that, despite an increase in the amount of information available to pilots,notions of severity and the extent of the impact of a particular weather pattern, remainboth uncertain and dynamic.

Reference to the interpretation and use of weather radar systems remainsconspicuously absent from the vast majority of aircraft accident and incident reportsinvolving weather. Arguably, this is due to the fact that the use of the weather radardisplay was not implicated in the accident or incidence sequence, and/or that theweather radar was simply not identified as a significant factor in the occurrence. Theissue becomes slightly more complex when issues pertaining to design and training areconsidered in relation to weather radar displays.

.

1.8 BENEFITS OF USING WEATHER RADAR

Weather radar provides detailed, instantaneous and integrated rainfall rates, a Realrainfall estimates over a wide area and information in near – real time. It givesinformation in remote land areas and over adjacent seas, location of frontal andconvective precipitation. Monitoring movement and development of precipitation areasare also made by weather radar. Data can be assimilated into numerical weatherprediction models. So, in a nutshell Doppler weather radar can be used for

Wind velocity measurement

Estimated prediction of rainfall rate

Detection of front location

Finding out clear air features

Forecasting of thunderstorm initiation

Severe storm detection like tornadoes, macro bursts, hails.

Detection of aviation weather like microbursts warnings, wind shift forecasts,weather impacted airspeed.


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1.9 DISSERTATION OBJECTIVEWeather Radar detects the presence of precipitation in atmosphere from the powerreceived of the echo signal and the reflectivity. From the nature of these detectedsignals wind velocity, wind turbulence, probability of rain, rain fall rate, thunderstorm,snowfall etc. can be predicted.

The objective of our research work is summarized as follows:

a. To find out the reflectivity from drop diameter by using Marshal Palmer‟s DSDformula.

b. To analyze the relation between radar reflectivity and rain fall rate for a particularperiod of time in Bangladesh.

c. To proof the validation of the formula (Z=a*Rb) between rainfall rate and

reflectivity by establishing the values of the constant factors (a and b).d. To find out the effect of different atmospheric losses, attenuations and their

impact on reflectivity.e. To find out the correlation between reflectivity, temperature and ice water contact

of a particular place.f. To find out the relation between reflectivity and humidity.g. To find out the velocity profile of precipitation.


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CHAPTER 2

SCIENCE OF WEATHER RADAR

2.1 FUNDAMENTALS OF RADAR

2.1.1 Definition

RADAR stands for Radio Detecting And Ranging and as indicated by the name, it isbased on the use of radio waves. Radars send out electromagnetic waves similar towireless computer networks and mobile phones. The signals are sent out as shortpulses which may be reflected by objects in their path, in part reflecting back to theradar. When these pulses intercept precipitation, part of the energy is scattered back tothe radar. This concept is similar to hearing an echo. For example, when you shout intoa well, the sound waves of your shout reflect off the water and back up to you. In thatsame way, the pulse reflects off precipitation and sends a signal back to the radar. Fromthis information the radar is able to tell where the precipitation is occurring and howmuch precipitation exists.

2.1.2 Components of Radar

Radars in their basic form have four main components:

1. A transmitter, which creates the energy pulse.2. A transmit/receive switch that tells the antenna when to transmit and when to

receive the pulses.

3. An antenna to send these pulses out into the atmosphere and to receive thereflected pulse back.

4. A receiver, which detects, amplifies and transforms the received signals intovideo format. The received signals are displayed on a display system. [29]

Radar output generally comes in two forms: reflectivity and velocity. Reflectivity is ameasure of how much precipitation exists in a particular area. Velocity is a measure ofthe speed and direction of the precipitation toward or away from the radar. Most radarscan measure reflectivity but you need a Doppler radar to measure velocity.


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Figure 2.1: Basic Radar Block Diagram

2.1.3 Radar Classification

When we start reading about radar, we come across various terms which are explaineddifferently. There are various kinds of Radar classified in different ways. Following arethe various classification of radar types in a lucid manner.

Classification based on the primary function of radar is shown in the following figure.

Figure 2.2: Basic Radar Classification


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Primary Radar

A Primary Radar transmits high-frequency signals toward the targets. The transmittedpulses are reflected by the target and then received by the same radar. The reflectedenergy or the echoes are further processed to extract target information.

Secondary Radar

Secondary radar units work with active answer signals. In addition to primary radar, thistype of radar uses a transponder on the airborne target/object.

A simple block diagram of secondary radar is shown below

Figure 2.3: Secondary Radar Block Diagram

The ground unit, called interrogator, transmits coded pulses (after modulation) towardsthe target. The transponder on the airborne object receives the pulse, decodes it,induces the coder to prepare the suitable answer, and then transmits the interrogatedinformation back to the ground unit. The interrogator/ground unit demodulates theanswer. The information is displayed on the display of the primary radar.The secondary radar unit transmits and also receives high-frequency impulses, the socalled interrogation. This isn't simply reflected, but received by the target by means of atransponder which receives and processes. After this the target answers at anotherfrequency.Various kinds of information like, the identity of aircraft, position of aircraft, etc. areinterrogated using the secondary radar. The type of information required defines theMODE of the secondary radar.

Pulsed RadarPulsed radar transmits high power, high-frequency pulses toward the target. Then itwaits for the echo of the transmitted signal for sometimes before it transmits a new


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pulse. Choice of pulse repetition frequency decides the range and resolution of theradar.Target Range and bearings can be determined from the measured antenna position andtime-of-arrival of the reflected signal.Pulse radars can be used to measure target velocities. Two broad categories of pulsed

radar employing Doppler shifts are

• MTI (Moving Target Indicator) Radar The MTI radar uses low pulse repetition frequency (PRF) to avoid range ambiguities,but these radars can have Doppler ambiguities.

• Pulse Doppler Radar Contrary to MTI radar, pulse Doppler radar uses high PRF to avoid Doppler ambiguities,but it can have numerous range ambiguities.

Doppler Radars make it possible to distinguish moving target in the presence of echoes

from the stationary objects. These radars compare the received echoes with thosereceived in previous sweep. The echoes from stationary objects will have same phaseand hence will be cancelled, while moving targets will have some phase change.If the Doppler shifted echo coincides with any of the frequency components in thefrequency domain of the received signal, the radar will not be able to measure targetvelocity. Such velocities are called blind speeds.

……………………(2.1)

Where, f 0 = radar operating frequency.

Continuous Wave RadarCW radars continuously transmit a high-frequency signal and the reflected energy isalso received and processed continuously. These radars have to ensure that thetransmitted energy doesn‟t leak into the receiver (feedback connection). CW radars maybe bistatic or monostatic; measures radial velocity of the target using Doppler Effect.

CW Radars are of Two Types:

a. Un-modulated An example of un-modulated CW radar is speed gauges used by the police. Thetransmitted signal of this equipment‟s is constant in amplitude and frequency. CW radartransmitting un-modulated power can measure the speed only by using the Doppler-effect. It cannot measure a range and it cannot differ between two reflecting objects.


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b. ModulatedUn-modulated CW radars have the disadvantage that they cannot measure range,because run time measurements is not possible (and necessary) in un-modulated CW-radars. This is achieved in modulated CW radars using the frequency shifting method.In this method, a signal that constantly changes in frequency around a fixed reference is

used to detect stationary objects. Frequency is swept repeatedly between f 1 and f 2 .On examining the received reflected frequencies (and with the knowledge of thetransmitted frequency), range calculation can be done.

……………………(2.2)

Figure 2.4: Frequency VS Time Curve

If the target is moving, there is additional Doppler frequency shift which can be used tofind if target is approaching or receding.Frequency-Modulated Continuous Wave radars (FMCWs) are used in Radar Altimeters.

2.2 WEATHER RADAR

2.2.1 Weather Radar Principle The weather radar seen on local TV news program, The Weather Channel, or othernews channel is Doppler radar. Doppler radar emits beams (pulses) of microwaveenergy from a transmitter into the atmosphere. When these beams collide with objectsin the atmosphere such as raindrops, hail stones, snowflakes, cloud droplets, birds,insects, dust particles, trees, and even the ground, some of the energy bounces backtowards the radar. A receiver on the radar then collects the reflected energy and

displays it in different ways.


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Figure 2.5: Signal Transmission Principle [25]

2.2.2 Weather Radar Equation

A simple form of radar equation for a “point target” is used to relate the dependence of

the received echo power (Pr) on the radar parameters; transmit power (Pt), antennagain (G) and effective aperture (Ae), and the target range (R) and the target radar crosssection (σi)

P r = ………………………………………..(2.3) [36]

The effective area of the receiving antenna can be related to antenna gain then equation (2.3) becomes:

P r =

………………………………….(2.4)

However, for the meteorological target, such as rainfall the target is not a singlescattered; rather, the radar beam illuminates a volume containing a large group ofraindrops. Thus, the range gate defines the measurement volume V in terms of theantenna beam widths (in orthogonal planes) and the transmit pulse length, σradar,

V=π( )(

)( ), m

3…………………….…………….(2.5)

Within this volume, each raindrop backscatters some energy, and if we assumeraindrops are randomly distributed and do not interact (no multiple scattering), the totalbackscattering cross section is the sum of the individual cross section of rain drops.


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Thus, the backscattering cross section per unit volume is defined. It is also called radar

reflectivity, σ m2m .

Since Rayleigh scattering applies, is related to the summation of the sixth power ofthe diameters over a unit volume,

=10-10 || ∑ ………………(2.6) Where |Kw|

2is a coefficient related to the dielectric constant of water

K w = ………………………..…………………………. (2.7)

Where n is the complex index of refraction of the droplet relative to the air background;

Taken n=8.87-j 0.628 at 3GHz from [10], |Kw|2 0.93 for liquid water. ∑ in equation

[4] is the summation of the sixth power of all drop diameters per unit volume. It definesthe radar reflectivity factor Z, in unit of mm6m . We can rewrite radar reflectivity as,

=10-10

|| m2 /m3 ………………………….(2.8)

If reflectivity is approximately uniform over the backscattering volume V, thebackscattered cross section of scattering volume can be defined as:

σ = ɳ V , m2

Now we can replace the σ i in equation (1) with σ toback scattering from volume-distributed scattered as radar equation:

P r = C|K w|2 ……………………………………….(2.9)

where C is the radar constant depending on the characteristics of the radar. The use ofradar reflectivity factor Z is only valid for Rayleigh scattering and spherical raindrops,but this is not always the case. Hence, it is common to replace Z with the effective radarreflectivity factor Ze [7]. It is more appropriate to express the actual observed Pr as:

P r = C|K w|2 ……………………………………(2.10)

Ze has the same unit as Z (mm6m

-3 ), but practical radar reflectivity may span several

orders of magnitude so, a logarithmic scale of Ze is introduced [3] and is expressed inunit of dBZ.


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dBZ=10 log 10 ( )…………………….(2.11)

2.2.3 Modes of Operation

a. Clear Air Mode

In this mode, the radar is in its most sensitive operation. This mode has the slowestantenna rotation rate which permits the radar to sample a given volume of theatmosphere longer. This increased sampling increases the radar's sensitivity and abilityto detect smaller objects in the atmosphere than in precipitation mode. A lot of what youwill see in clear air mode will be airborne dust and particulate matter. Also, snow doesnot reflect energy sent from the radar very well. Therefore, clear air mode will

occasionally be used for the detection of light snow. In clear air mode, the radarproducts update every 10 minutes.

b. Precipitation Mode

When rain is occurring, the radar does not need to be as sensitive as in clear air modeas rain provides plenty of returning signals. In Precipitation Mode, the radar productsupdate every 6 minutes.

2.2.4 Key Terms Associated With Weather Radar

a. Reflectivity "Reflectivity" is the amount of transmitted power returned to the radar receiver. dBZstands for decibels relative to Z. It is a logarithmic dimensionless technical unit used inweather radar, to compare the equivalent reflectivity (Z) of a radar signal reflected off aremote object to the return a droplet of rain with a diameter of 1 mm. It is proportional tothe number of drops per unit volume and the sixth power of drops diameter and is thusused to estimate the rain or snow intensity. With other variables analyzed from the radarreturns, it will help to determine the type of precipitation, too.

b. Attenuation Attenuation is the weakening of a radar beam as it moves downstream due to some ofthe energy being lost to scattering and absorption. The further a radar beam movesdownstream the more dust, hydrometeors, etc. the radar beam will have to passthrough. Because of attenuation, storms close to the radar are better sampled thanstorms far from the radar site. Beam spreading and attenuation both combine toproduce a much poorer sampling of storms far from the radar. Attenuation is higherwhen the radar beam has the flow through a large number of hydrometeors. Storms andprecipitation close to the radar degrade the radar energy before it reaches storms


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further from the radar. Smaller wavelength radar beams attenuate more rapidly thanlong wavelength radar.

c. The Radiated Beam WidthGenerally, we consider the radar beam as being cone shaped.

To maximize the signal return from a weather target, it should be observed through thecenter of the beam where the highest level of energy is located (or at least within theadvertised beam width for that antenna). That beam width for the 30-inch antenna is 3.0degrees, for the 24-inch antenna is 4.5 degrees and for 12-inch it is 8.0 degrees.

d. Anomalous PropagationWhen some special atmospheric conditions occur, such as sudden change in the airdensity, the radar beam is likely to bend downwards and hit the ground. Therefore theobserved echoes are not real precipitation and are called radar clutters. It should benoticed that not only anomalous propagation can cause clutters; they also appear whenside lobes hit ground objects at short range or stationary obstacles presence close to

the radar. For radar QPE, it is extremely important to remove spurious echoes, becausethey can greatly damage the data quality.

e. ClutterOne type of interference that detracts from the performance of airborne weather radar isground clutter. Ground clutter of airborne weather radar is divided into the main lobeclutter, side lobe clutter and altitude clutter .the main lobe clutter is the clutter thatgenerates when the main lobe of the radar antenna illuminate the ground. The side lobeclutter is the clutter that generated when side lobe beam irradiate to the ground. Thealtitude clutter is the clutter that generated when the side beams irradiation to theground along vertical direction.

There are several methods to eliminating ground clutter. The first is to improve antennadesigns to reduce side lobe in the ground direction. Asymmetrical reflector antennas areoften used, but the phased array antenna is inherently superior in side lobe reduction.

Another technique in the reduction of ground clutter is analysis of the Doppler shift ofthe return signal. Knowing the aircraft altitude, ALG, and ground speed, the expectedDoppler shift of returns from the ground at specific ranges may be calculated.Therefore, returns with Doppler shifts in this range may be eliminated as ground clutter.

f. Tilt

One of the least understood aspects of airborne weather radar is the subject of antennatilt. The display on the panel has a control that allows the pilot to tilt the antenna up ordown. This can be the most critical adjustment of all. The radar antenna platform up inthe nose is stabilized in the roll mode. The antenna platform is tied into the horizontalgyro circuit so that the platform remains level in reference to the Earth's horizon as theaircraft turns. Proper antenna tilt, when taking a read on a thunderstorm, makes thedifference between valuable information, and no information.


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2.2.5 Weather Radar Network

A small-clustered radar network, rather than one with single large coverage radar, hasadvantages in terms of information quality and measurement reliability. By coveringsimilar area with multiple radars, additional capabilities such as dual-Doppler estimation

of horizontal wind vectors or pinpoint tracking of storms are provided. Also, the effectivedesign of such network radar systems can provide reduced power and less antennasize. Much research exists regarding the use of meteorological radar networks forsensing weather phenomenon. Such work has focused on the node and networkstructures, data link and transmission, adaptive scanning and radar control as well asthe advantages of small radar networks. Especially, CASA IP1 has implemented realenhanced network using four relatively low-powered X-band magnetron-based radars,the merits of each being clearly discernible. Conversely, additional considerationregarding radar networks is required. In particular, the use of numerous narrow-pulsenetwork radars is not efficient with regards to frequency resources and interference.

Although a peak power, of tens of kilowatts, is relatively smaller than current large-scale

operating radars, such radars still aspect long distance areas and interfere with otherradars or radio systems with common frequency bands. For example, although a rangeof 9:3 » 9:5 GHz is allotted for radar application in X-band including the meteorologicalremote sensing | many military-purposed and marine radars have already usedconsiderable available resources in such frequency band. In regards to frequencyresource, pulse compression radar systems can provide advantages in weathernetworks. For given resolution requirement, transmitting peak power is greatly reducedby employing relatively long pulses. Since radar detection ability depends on averagerather other than peak power, peak power decreases with the use of high duty factorradar. Thus, the effects from neighboring transmitting power become less in pulsecompression radar systems and this means frequency reuse planning, similar in cellular

communication, is more applicable for small clustered radar networks. especiallyregarding maximum dual-Doppler overlapping, hexagonal cell arrangement, i.e., joiningthree neighboring radar forms at a 60 degree angle, is most effective [15]. Fig. 1 depictsfour channel usage (frequency bands) for such a configuration. Frequency reusepatterns are extendable with more numbers of channels translating into longerdistances for identical channel sites. Additionally, assuming scanning information foradjacent radar sites is available, radar possibly acquires bi- or multi-static data asshown in Fig. 2. Hence, dual or multi-Doppler estimation at a single site is possible.When original velocity vectors of the targets are similar to the direction of tangentialbeam injection, bi-static data is more effective in obtaining Doppler information.

Although such results increase the data quality, mono- and bi-static signals should be

processed simultaneously. Hence, we introduced identical baseband waveform foradjacent radars [3].


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(a) (b)

Figure 2.6: Weather Radar Signal Observation: (a) A Hexagonal Weather Radar

Network Using 4 Different Channels, (b) Simultaneous Observation of Mono and Bi-

static Signals [3].

Figure 2.7(a) illustrates one example of X-band frequency allotment. If 15MHz ofbandwidth are used for very fine range resolution of 10 m, then nearly 12 channels willbe available at X-band. By combining four channels into one band, then three bandsbecome available. Such a band concept especially applies to frequency availability in aparticular region. Radar system structures can be constructed as shown in Fig. 2.7(b).By the combination of LO1 frequencies (local oscillator 1) for band selection and LO2

(local oscillator 2) for channel selection, the desired channel signals are transmitted. Inthe receiver, the band is already selected by sharing LO1 with the transmitter and thechannel is selected in the digital domain with IF under-sampling techniques. Infact, not only mono- but bi-static information from adjacent channel signals can simplybe extracted by adequately changing frequency values during down-converting signalprocessing. Such a concept has been experimentally verified with signal generation,acquisition and channel selection in signal processing easily.


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(b)

Figure 2.7: Radar Network Example in X-band: (a) Channel Allotment. (b) RadarSystem Structure [2].

2.2.6 Data Processing

Digitized data were processed on the PC. Processing was divided into signalprocessing by extracting IQ data via pulse compression and data processing in order to

extract the parameters, i.e., received power and velocity from IQ data. As shown in Fig.6, the first stage of the processing involved the digital down converter block, translated100MHz digitized samples into complex data consisting of in-phase (I) and quadrature(Q) components. During radar network consideration, multi-static data from the adjacentsites were acquired by changing only channel selection frequency during downconverting. If the signal processing block had been built parallel, the radar would haveobtained bi- and mono-static data simultaneously. Low-pass anti-aliasing filter andoutput data-reducing decimator were deployed [4]. In our case, the decimation number


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stood at eight, determined by the ratio of the chirp bandwidth and the sampling rate. Forpulse compression, correlation processing was performed using FFT (Fast FourierTransform) in the frequency domain. Complex conjugate values of the reference data,

Figure 2.8: Signal Processing Flow Diagram [4]

Sampled from transmitted pulse and converted in the frequency domain were multipliedwith receiving data. And this value was again converted to the time domain value usingIFFT (inverse FFT). Before IFFT, weighting functions (windows) were used on thecompressed pulse spectrum in order to reduce side lobe levels. However, this alsobroadened main lobe width and degraded range resolution slightly. Various windowfunctions such as Hamming, Hanning, Blackman and Blackman-Harris, were applicable.For LFM (linear frequency modulation) waveform, the combination of Hamming andBlackman- Harris were applied. For the NLFM (nonlinear frequency modulation),waveform itself demonstrated window function characteristics with our proposedmethod, thus being more effective than LFM in point of power conservation.Data processing was initiated by arraying complex discrete signals resulting duringsignal processing of pulse compression within the observation range. Fig. 2.7 revealsthe block diagram of the present data processing scheme. By arraying N = 64 pulserepetition interval samples and applying FFT, the discrete power spectrum of the signalwas thus acquired. Afterwards, the S/N (signal to noise ratio) as well as Doppler velocityand spectrum width were estimated. Although more than 70 dB of cross couplingexisted between transmitter and receiver due to antenna separation, a considerableamount of power nevertheless owed directly into the receiver chain. For rejections ofnon-moving clutters as well as such cross coupling effects, a fixed-width clutter filtermethod was employed, removing zero-Doppler spectrum components and interpolatingacross the gap. To obtain the S/N from received signals, noise power was estimated bythe mean power of reference noise heights where, as it is assumed, no meteorologicaltargets existed. By establishing experimentally-determined threshold values related tonoise variation, the scattered signal spectrum was thus obtained [4]. One form in thereceived power point is as follows:


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P r =

() …………………………………………………..(2.12)

Minimum detectable reflectivity of pulse compression radar Z 0l is:

Z 0l =Z 0

……………………………………………………………. (2.13)

The meteorological radar reflectivity factor was measured in dBZ, as follows:

Z (dBZ) =10log [Z (mm6 /m3 )] = 10 log [10 -18 .Z (m6 /m3 )] ………………… (2.14)

For convenience, the reference height H0 was also introduced, as follows:

10log (SNR)= 10log[

||

]

+ 10log(

) +SNR(dB) ……………………………………(2.15)

Introducing radar constant C (dB), We had the following :

C (dB)= 10log[

||

] ...........(2.16)

Z (dBZ) = C (dB) + 20 log (

) + SNR (dB) ………………………..…… (2.17)

Using weather radar we may detect snow here a Photo of the designed radar withseparated Tx and Rx Antennas & Doppler spectrum measured.


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(a) (b)

Figure 2.9: Snow Detection [6]

Compared with other forms of precipitation, snow has the characteristics of relativelylow refractive index and it demonstrates low reflection. Short wavelength radar is moreadvantageous in detecting snow. Despite being weak, we confirmed that radar was ableto detect snow signals from as far away as 1 km. Because of the distance betweenantennas, low altitude observation area was smaller than observation with singleantenna system. Based on frequency analysis, velocity components of snow weredistributed at nearly zero. A middle rain event occurred weather radar may observe it byfollowing procedure [8]:

a) Detection of clouds by LFM. b) Detection of cloud & rain by NLFM.


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c) Detection of Rain by NLFM. d) Doppler Spectrum Measured.

Figure 2.10: Representation of Different Detections [8]


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CHAPTER 3

DETECTION OF WEATHER CONDITIONS

3.1 DETECTION OF AIR VELOCITY

In addition to measurement of returned signal power from the targets, weather radar isalso capable of measuring the wind velocity by analyzing the Doppler frequency shiftwhich is introduced by the motion of air particles or the precipitation particles.

• The amount of “shift” can be determined by comparing the frequency of the transmit

pulse with the frequency of the reflected pulse

• Particles moving toward the radar are shifted to higher frequency

• Particles moving away from the radar are shifted to lower frequency

Figure 3.1: Frequency Changes due to Movement of Object [25]


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3.1.1 Frequency Shift Produced Due to Wind Velocity

The phase shifting φ of an electromagnetic wave from the radar antenna to the aim andback results from the ratio of the covered distance and the wavelength of thetransmitted energy multiplied with the scale of the full circle (2·π):

……………………………………………..(3.1) φ = phase-difference between the transmitted and the received signal2r = the distance: the way and the way back2π = 360°: the period of an oscillation λ = wavelength of the transmitted energy

If the aim has the radial speed,

…………………………………….(3.2)

Then the value of the phase changes to

…………………………………………………. .(3.3)

This is equivalent to the Doppler- frequency f D according to:

………………………………….(3.4)

|| ……………………………………………… .(3.5)

f tx = is the transmitters frequencyc0 = is the speed of the lightvr = is the radial speed of the aim


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This means, in practice the Doppler- frequency occurs twice at radar. Once on the wayfrom the radar to the aim, and then for the reflected (and already afflicted by a Doppler-shift) energy on the way back.

In the radar signal processing the Doppler frequency will be divided by the actual

transmitted frequency to eliminate the influence of different transmitter‟s frequencies.Now the Doppler frequency is a measure of the radial speed only and is called“normalized”.

Weather radar utilizes the Doppler capability of the NEXRAD radars to detect

storm circulations (e.g., tornados and hurricane spiral bands) as well as to

identify air flow boundaries created by storms (e.g., outflows and microbursts)

In cases when only one radar is available, the air motion that is detected is

relative to the location of the radar: radar meteorologists call this radial velocity.

flow toward the radar is called “inbound” and flow away from the radar is called

“outbound”.

By convention, velocities toward the radar (inbound) are negative and velocities

away from the radar (outbound) are positive.

3.2 ANALYZING THE REFLECTIVITY & RAINFALL

3.2.1 Rain

Rain is formed by a very complex process, which involves the condensation of water

vapor and the coalescence of tiny droplets from clouds. Raindrops are typically two

orders of magnitude larger in diameter than cloud droplets. During their fall from clouds

to earth‟s surface, small droplets may coalesce with each other forming bigger drops.

Sometimes droplets are surrounded by warm and dry air, and they may evaporate

before reaching ground. In general, rain consists of a distribution of drop sizes in the

range of 0.5 mm to 8 mm.

3.2.2 Types of Rain

There are different types of rain with different spatial scales that range from a fewkilometer in diameter to a few tens of kilometers. Among these types, two major onesare convective and strati form rain. Their characteristics primarily differ in spatial extent,rain drop sizes and in vertical air motion that is instrumental in the rain formationprocess. Convective rainfall is usually formed from convective clouds (precipitationcells) in the tropics that are associated with strong up-drafts that carry moisture quickly


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to high altitudes well above the freezing level. Rain drops form rapidly through collisionand accretion with other droplets. Because these rain cells contain frozen precipitation(above the freezing level where the air temperature is < 0 C), they are usuallyassociated with strong electrical activity and lightning; therefore they are commonlycalled thunder storms, which are characterized by high spatial and temporal intensity

gradients. As opposed to the vertical development of convective rain, strati form rain isformed from stably stratified clouds. Strati form clouds are horizontally widespread incharacter, and its rain has extensive horizontal development. In strati form clouds,precipitation grows in a widespread forced updraft of low magnitude. Raindrops form instrati form clouds primarily by condensation. Because of a lack of a strong updraft tokeep droplets aloft, strati form rain falls out of the cloud with lower rain rate. Strati formrain is more uniform in intensity and consists of relatively small raindrops. Althoughmost rain consists of a combination of the two, identifying the characteristics of rain helpthe study of rain intensity and raindrop size distribution. Convective rain is generallyheavy due to large drop size and high rain intensity. Strati form rain is a gentle, longlasting rain with no lightning. High reflectivity and reflectivity gradient separate the

convective rain from the strati form rain.

3.2.3 Raindrop Size Distribution (DSD)

Rain comprises drops of many different diameters, which are characterized by a

particular raindrop size distribution (DSD) that provides information on the number and

size of raindrops in a sample. Because the DSD is a unity area distribution, calculated

at different resolutions gives different distribution curves, which can be seen in Figure

3.2. Choosing the same rain rate, different scale of drop size interval defines a different

probability density function (pdf) of DSD within a unit volume. Thus DSD, usually

denoted by N (D) with units of m

-4

, is a fundamental quantity used to describe thecharacteristic of rain.


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Figure 3.2: PDF of Marshal-Palmer DSDs with Diameter Interval 0.1 mm and 0.2mm

The raindrop size distribution has been studied by many investigators and generallymodeled as an exponential distribution. The most widely used DSD in scientific

literature is Marshall and Palmer [1], which is a special case of the exponential

distribution with two fitting parameters N0 and ˄ . Marshall-Palmer DSD is defined as:

N(D)=N 0 e- ΛD ,m-4 ……………………………………………..(3.6)

Where N0 = 8.10 m-4, D is the drop diameter in unit of meters and is the slope

parameter. It is related to rain rate R (mm/h) as:

Λ=4100R -0.21 m-1 ……………………………………………….(3.7)


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3.2.4 Rainfall Rate, R

Rain rate R is a measure of the intensity of rain by calculating the volume of rain that falls to ground in a given interval of time. The rain rate is expressed in units of length(depth) per unit time (mm/h), which is the depth of rain captured in a collection vessel

per unit time. Figure 3.3 shows a graphical representation of the PDF of Marshall-Palmer DSD with three different rain rates. As rain intensity increase, the drop sizeincreases. Under strati form rainfall conditions, the vertical air motion is weak and isusually neglected because its value is generally not known. The error introduced isbelieved to be small compared to the terminal velocity of most rain drops. Rainfall rate Ris related to N (D).

R= ∫

………………………………..(3.8)

Where v(D) represents the relationship between the raindrop terminal fall velocities in

stillair and the equivalent spherical raindrop diameter D (mm). An exponential expression offall speed to diameter relationship is derived:

v(D)=[(α 1-α 2 ) exp(-α 3D)](ρ0 /ρ)0.4 ,m/s ………………………………(3.9)

Where a1 = 9.65 m/s , a2 = 10.3 m/s, and a3 = 0.6 m/s. is a density ratio factor adjustingterminal fall speed due to air density change with altitude. Equation 3.4 can be used toestimate the diameter of the raindrops from weather Doppler motion (when vertical airmotion is not present). As drop size increases, the fall velocity increases rapidly and

following an exponential curve as shown in Figure 3.3.I have taken the raindropsdiameter sizes from 0 to 7mm with 0.1mm size interval as input to calculate the terminalfall velocity. Due to aerodynamic forces, at larger drop diameters surface tension isinsufficient to overcome drag forces. As a result, raindrops larger than 7mm tend toflatten out and break apart into smaller droplets; therefore these diameters do not existin the DSD.

:


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Figure 3.3: PDF of Marshall-Palmer DSDs with Three Different Rain Rates


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1 2 3 4 5 6 7 8 9 10

Raindrop diameter (mm)

Figure 3.4: Correlation between Rainfall Velocity VS Raindrop Diameter

3.3 ESTIMATING Z − R RELATIONS If the observed values of Z and ZDR over a small region are used to characterize the rain

drop spectra over that region, better rainfall rate estimates will be a reality. Recall thenormalized gamma distribution of raindrops.

N(D)=N w f(μ)(D/D0 ) μ exp(-

) …………………………………(3.10)

f(μ)=

………………………………………………(3.11 )


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In this equation there are three variables:

Shape parameter μ. High values of μ imply a more truncated spectrum. DropConcentration Nw, normalized so that, despite changes in μ, liquid water content remains constant.

Figure 3.5: Normalized Gamma Distribution, with μ Variations. For This Plot D0 is 1 mand Nw is 8000m

-3mm-1.

This drop spectrum only changes with rainfall rate, which would make convertingreflectivity to rainfall a trivial task (which leads to Z = 200R1.6). Unfortunately theMarshall-Palmer drop spectrum does not represent the wide variation in drop spectrafound in nature, which lead to the introduction variation of drop concentration. A gammafunction for raindrops were suggested by Ulbrich (1983). However, variation in theshapeparameter caused changes to the drop concentration required for the same rainproperties ,so a normalization was added.

By following the work of Bringi and Chandrasekar (2001), this leads to Z − R

relationships of the form:

Z = aR 1.5 …………………………………………………..(3.12)

with a dependent on N w and μ . Integration of the suitably weighted normalized gammafunction produces the expression:

Z = F z (μ)N w ……………………………………………(3.13 )


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Making the assumption that the terminal velocity is proportional to D.67 ,

R=F R (μ) N w D0 4.67

………..……………………………………(3.14)

& by removing DO this becomes:

= H(μ) (

)1.5 ............................................(3.15)

Where H(μ) =f z (μ)f r (μ)1.5

,Hence

Z=H(μ)N w -.5 R 1.5 =

√ ……………………………….(3.16)

From Equation (1) we may said that,

a=√ ………………………………………………………..(3.17)

So over the chosen region of data, if the drop spectrum can be characterized toestimate N w , it will be possible to derive the values of a in equation (3.12) (assuming avalue of μ ). Next consider the physical drop spectrum cause of variations in b. Initiallyconsider the case where N w remains constant. Increased rainfall rate is caused simplyby an increase drop size D0 .Equation (3.13) shows Z varies as D0

7 and (3.14)

demonstrates R varies as D0 4.67 So, substituting into equation (3.12) gives b = 7/4.67 =

1.5 . However, it is possible that N w is a function of D0 , and this possibility will result indifferent values of b. Consider the case where N w rises as D0

2 so as rainfall rates

increase

there are both more and larger raindrops. This implies, via equations (3.13)and (3.14) that Z and R vary as D0 9 and D0

6.67 , leading to a b of 1.35 . Now consider thecase where N w

varies as 1/Do, a case where as the drops get larger, their numbers

decrease, suggesting Z and R vary as D0

6 and D0

3.67 so b = 1.63. Now consider a more

extreme example. If, rather than N w being constant, Do remains constant and as rainfallrate increases it is a result of more drops of the same size, Z and R scale together withN w , so b = 1, Now consider the case with high aggregation of snowflakes leading to N w scaling with 1/D0

2 Now Z and R vary as D0 5 and D0

2.67 resulting in a, b of 1.87 .Varying a & b with the change of drop diameter D0 , from equation (3.12)

Table 3.1: Weather Data of Dhaka, Bangladesh for April, 2014

No of equation Dropdiameter(D0)

Varying a & b Z –R Relation

1 9-6.67 a=190,b=1.62 Z=190R .

2 7-4.67 a=289,b=1.5 Z=289R.

3 6-3.63 a=244,b=1.35 Z=244R1.35


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From the above equation, we can determine the value of reflectivity on different value ofrainfall rate, R:

Date: 11-04-2014 R=25mm/hZ1=34947.52

Date: 23-4-2014 R=14mm/hZ2=8603

Date: 28-04-2014 R=11mm/hZ3=10543

Approximate reflectivity which was measured by Bangladesh metrological center on thatparticular date:

Z1=35261

Z2=8234Z3 =11401

Percentage of Error:

Zerror1 = 0.89%Zerror2 = 4.48%Zerror3 = 7.52%

From that result we may say that Although the expected behavior can be seen from asingle day of heavy rain the best test would involve a longer record for statistics. Notexact but appropriate value come out from our formula.so validity of our formula exists.

3.4 RAINFALL RATE, REFLECTIVITY, Z-R RELATIONSHIP

CONSTANT A AND B, RECEPTION POWER

3.4.1 Value of Coefficient a and b from Comparing Different Z-R

Relationship for a Specific Radar in Specific Region

Reflectivity VS rainfall rate equation can be given by the equation, Z = a R b

Where, Z = reflectivity, R = rainfall rate and a, b = constant

The changes in the coefficients of the Z-R relations for different rain events are different.

The coefficient a of the Z-R relation is higher for the convective stage followed by the

strati form and transition stages. The coefficient b values are higher for the transition


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stage followed by the strati form and convective stages. So, depending on rain event or

rain type it is different in different region and season.

So, we see if we can measure the value of rainfall rate of a specific region for a season

and get the reflectivity from the radar which measured the rainfall rate then we will be

able to find the Z-R relationship ,in other word we will be able to find the value of a andb for that specific region.

Consider a Doppler weather radar which has the below rainfall rate VS reflectivity chart,

Table 3.2: Reflectivity VS Rainfall Rate.

Reflectivity , Z (dBZ) Rainfall rate ,R

10 0.25

15 0.5

20 1

25 2.530 4

35 7

40 13

45 25

50 48

55 92

If we plot it in graph, then we will get the graph given below:

Figure 3.6: Rainfall Rate Graph Reflectivity VS Rainfall Rate Chart.


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If this radar is used in Bangladesh then what will be the value of coefficient a and b can

be found easily if we collect the rainfall rate chart of a specific month of specific season.

We, know a whole year can be divided into four season (pre-monsoon, monsoon, post-

monsoon and winter) which countries are lies under monsoon climate region. So,

Bangladesh can be divided into four seasons. In this thesis, we will take the data ofrainfall rate of pre-monsoon season of Bangladesh of 2011.

The data of rainfall rate is given below for pre monsoon period:

Figure 3.7: Recorded Daily Country Average Rainfall of Pre-monsoon Season ofBangladesh in 2011 [32]

From the above data taking the value of the month of get the value of rainfall rate of

month of March 2011 Dhaka, Bangladesh.


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Figure 3.8: Recorded Daily Average Rainfall Rate of March 2011 in Dhaka,

Bangladesh.

From this chart we get the daily rainfall rate data as follows:

Table 3.4: Rainfall Rate Data of March 2011 in Dhaka, Bangladesh.

Day Rainfall rate Day Rainfall rate Day RainfallRate

1 0 11 0 21 0.25

2 0 12 3 22 0

3 0 13 0 23 0

4 0 14 0.25 24 0

5 0 15 1 25 4

6 0 16 0.75 26 2.5

7 0 17 0.25 27 4

8 0.25 18 0.25 28 59 0 19 0 29 11

10 0 20 0.25 30 3

In month of March rainfall rate differs from 0 to 16 and the values are 0 , 0.25 ,0.5 , 0.75

, 1 , 2.5 ,3 , 4 , 5 , 16 from low to high .


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There are total 7 types of Z-R relation is practiced all over the world and they are,

1) Z = 75 R2

2) Z = 300 R

1.4

3) Z = 250 R1.2

4) Z =316 R1.6

5) Z=250 R1.5

6) Z= 32 R1.65

7) Z= 200 R1.

Now, for different Z-R relation we will find reflectivity for rainfall rate of March 2011 and

compare it with actual relation of Z-R that is given for specific radar. Which relation will

be identical or close to the actual relation, that should be practiced in Bangladesh for

that specific radar.

(a) Z- R Relationship in Summer


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(b) Z-R and Z-S Relationship in Winter

Figure 3.9: Z-R relations that are practiced all over world in different season [33].

Now, we will find the values of reflectivity for specific Z-R relation,

1) Z=75 R^2

Table 3.5: Rainfall and Reflectivity Data of March 2011 in Dhaka, Bangladesh.

Rain fall rate Reflectivity Base reflectivity (dBZ)

0 0 0

0.25 4.68 6.7

0.5 18.75 12.73

0.75 42.18 16.26

1 75 18.75

2.5 468.75 26.703 675 28.29

4 1200 30.79

5 1875 32.73

16 19200 42.83


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2) Z= 300 R^1.4


Rainfall rate reflectivity Base reflectivity (dBZ)

0 0 0

0.25 43.07 16.34

0.5 113.67 20.56

0.75 200.54 23.02

1 300 24.77

2.5 1082.02 30.34

3 1396.7 31.45

4 2089.3 33.20

5 2855.5 34.55

16 14550.9 41.62

3) Z= 250 R^1.2


Rainfall rate reflectivity Base reflectivity(dBZ)

0 0 0

0.25 47.4 16.76

0.5 108.82 20.37

0.75 177.02 22.48

1 250 23.98

2.5 750.7 28.75

3 924.3 29.704

4 1319.5 31.204

5 1724.7 32.367

16 6964.4 38.43


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4) Z= 316 R^1.6


Rainfall rate reflectivity Base reflectivity(dBZ)

0 0 0

0.25 34.4 15.36

0.5 104.24 20.18

0.75 199.4 22.9

1 316 24.996

2.5 1368.93 31.363

3 1832.66 32.63

4 2903.9 34.63

5 4149.91 36.1816 26685.7 44.26

5) Z= 250 R^1.5


Rainfall rate reflectivity Base reflectivity (dBZ)0 0 0

0.25 31.25 14.95

0.5 88.38 19.46

0.75 162.4 22.11

1 250 23.98

2.5 988.2 29.95

3 1299.04 31.136

4 2000 33.01

5 2795.04 34.46

16 16000 42.04


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6) Z= 32 R^1.65


Rainfall rate reflectivity Base reflectivity (dBZ)0 0 0

0.25 3.249 5.117

0.5 10.196 10.08

0.75 19.9 12.99

1 32 15.051

2.5 145.128 21.617

3 196.06 22.92

4 315.17 24.986

5 455.46 26.586

16 3104.19 34.919

7) Z= 200 R^1.6


Rainfall rate Reflectivity Base reflectivity

(dBZ)0 0 0

0.25 21.76 13.37

0.5 65.98 18.19

0.75 126.21 21.09

1 200 23.01

2.5 866.44 29.38

3 1160 30.64

4 1838 32.64

5 2626.53 34.193

16 16889.7 42.28


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From these values we can draw reflectivity VS rainfall rate graph and comparing with

these curves with given Z-R value curve we can assume the relation of Z-R

PREDICTION AND ANALYSIS OF WEATHER DATA BY USING DOPPLER WEATHER RADAR FOR AIRCRAFT NAVIGATION

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