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Û THE CALIBRATION OF THE QUADRA WEATHER RADAR DURING GATE . ...

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The CalJbration of the Wéather Radar on the G.G.G.S. Ql.:JADRA . . During the GATE E xperiment ,

/ by

Robert Catalfamo

. ,

/

A the sis subplitted to the Faculty of Gradqate Studies and Research in partial fulfillment of the requirements for' ~he degree of Master of Science.

January, 1978 D epartment of Meteorology

il> MeGil! University . (

Montreal, Quebec

,

-------Cl Robert Catalfamo 1978" -,

)

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lI~e are in the oordinary ffosition. of scientists of having to be content

w ith piecemeal improvEiments: we c;:an make several things clearer.

but we cannot rnake anything c1ear. "

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Frank Plumpton Ramsey

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.. ABST RACT

The data obtained by the C anadian Coast Gua:rd ship QU'ADRA radar

during the GATE expe~im.ent is examined to assess its quality in order to

retrieve the maximum useful information from the data. The electrical , '

calil?ration of the radar system ie done in the usual way but the cros s -checking

/ with raingauge~ lB found more difficult in view oCtheir scarcityand contin-

li· . ual relative motion. , A method of interpolating radar data acrOS8 an area. .. .

in conjunction w~th matching PPlfs to obtam navigati~n information iB used

to augment the data. set. This being done, the l'adar-derived :rainfall estitnatea , ,

, 1

are linked directly to gauge rainfalls to propose a 2 -R relationship ,by a

method which differB from the conventional dis~rometer technique. It ie / ' .

shown that the 2 -R relation thus obtaine'ci (2 :::;253R 1. 27) agreee closely with . t, ~

those, previously proposed and provided that attenuation of th~ radar beam is \

kept in rnind. this Z -R relation and the radar calibration curve, pt"ovides . . \ '

th/link between 'the radar data and quantitative rainfaU estimates.

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,

RESUME

\ Les données recueillies durant l'experiénce ~T~ par le

radar du navire QUAD~ (garde-côte Canadien) ont êté ~xaminée

afin d'en évaluer la qualité et ainsi obtenire le ~ximum d'in­

formation sur l'ensembLe de ces données. Le calibrage' -électrique

du systeme de radarça été fait par la méthode conventiqnnelle

mais la comparaison avec les pluviométres était plus difficile • J

étant donné leur rareté et leu~ouvement relatif en continue. . ,

Pour augmenter la "qualité de l'échantillonage, ~~e métho'de

d'interpolation des données de radar au travers une surface a

été utilisé. Ceci étant fait, les quantités de pluie estimées

par le radar sont reliées directement à cel,les obtenues par les . .

pluviomètres afin de proposer une relation Z-R par une méthode

qui est differente de la technique conventionne"l.le du capteur

ae ~outtelettes. On démo~tre ~ue la relation Z-R obtenue ainsi

(Z =257Rl . 27 ) s'harmonise avec celles proposées antérieurement

et' tenant compte de l'atténuation du faisceau deoradar, cette

relation Z-R et la courbe de calibrage du radar permet le lien

entre les données de radar et Iles estimés quantit~tifs de pluie~

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ACKNOWLEDGEMENTS

The author would like ta thank his supervisor. 'Prof. Ge.off Austin. for

his-encouragement and hel'pfui d~scussions provided during the reseaJ;ch and

while w:t'Ïting the the sis. Many thanks a,:"e aiso due. to his wife. Lydia Austin.

for hâving p~vided the prototype computer program used in the t;esearch.

He is also grateful ta the staff of the McGill Radar Weather Observatory

for the help in computer processing; especially Ml'. A. Bellon, Dr. S.

Radhakant a!ld Mesdames A. Kilambi and P: Crawhall. 1

Thanks are due ta Dr. Mike Hudlow of NOAA who unstintingly provided

sorne of the na'Vigation data.

The splendid efforts pf the QUADRA officers and crew during the field

phase of GATE are gratefully acknowledged.

Since,re appreciation is extended ta Ms. Ursula Seidenfuss for the

photographie work and ta Mrs. Deborah Mathewson for typing the thesis:

Financial assistance was provided by a National Research Council \io

grant and a McGill Graduate Faculty/ fellowship.

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TABLE QF CONTENTS

Abstract

Résumé

Acknowledgements

List lof Figur es J

. List of Tables .1

1 Introduction 1. 1 Philosophy of GA TE ,and the role of radar 1. 2 Objectives and assotiated problems . 2 The QUADRA radar 2. 1 The meteorological radar equation 2.2 Measurements of raq.ar parameters 2.3 Radar dataov-erview 2.4 Summary

3 Derivation of a Z -R relationship for GATE 3. 1 Raison d'être ' 3. 2 The optimization technique 3.3 Summaty ,

4 Experimental work 4. 1 Navigation 4. 2 Data manipulation 4.3 Experimental results 4.4 Comparison of Z-R's with other proposaIs 4. 5 Sum'mar y "

5 Conclus~ons

Appendix 1 FORTRAN listing of optimization program

~PPEtf1dix II Julian date calendar

Biblio"'graphy

PAGE

ii

iii

iv

vi

ix

l 1 3

7 7 9

19 34,'

35 35 . 36 16

47 47 55 61 69 73-

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79

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s FIGURE

1.1 • 1.2

. 1. 3

2~ 1

2.2

2. 3

2.4

2.5

2.6

2.. 7 ,

2.8

2.9

vi

LIST OF, FlOURES

l

Ship array during Phase 1. ,

Ship array during Phase 2. ' . Ship array during Phase 3.

Transfer curv~ between tape number abd return 8 ignal powe r Pr.

Path traced out b/ radar beam in changing elevation angle.

PPl display for Julian Day 216 at 15:19 Z where aH intensity levels (tape numbers) we-re utilized. '

PPl display for Julian Day 216 at 15:19 Z where intensity levels l, 2. and 3 wer.e suppr,essed.

PPI display for Julian Day 216 at 15: 19 Z where intensity levels 1 tbrough 10 were suppressed·

. . .

PAGE

4

4

5

13

22/

24

25

26

Frequency of occurrence (%> of tape numbers taken 28 from random. scans, th;roughout the three GATE phases.' 'J C

Accumulated raiD per tape number for the frequency distribution of Fig. Z. 6.

~ean dBz "fielJor Phase 1-

Mean dBz field for Phase 2.. ' ~

29

31'

3l

2 .. 10 , Mean dBz field for Phasè 3. 33

3.1

3.2

3.3

3.4

'" 3.5

Straight line graph of the equa:tion Z=a.Rb

for different 31 "a\s".

Straight Une graph of the'equation Z=aRb showing 37 different log Z = constant.

, -Flow-chart of computer pro gram used to derive an 42 ,optimum Z -R relatioDship •

Variation of standard dèviation from the 1"atio G./R. 43 with exponent using different na's". 1 1

Error tioxes' on the line Z =300 1\ l. 3 that can be expected 44 from GATE data.

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vii

FIGURE PAGE 1

3.6

3.8

3.9

4,.1

4.2

4.,3

4.4

4.5

4.6

4.7

4.8

4.9

4.10

4.11'

4.12

4.13

..,. 4.14

/

Standard deviation from the mean ratio G ./R. ..... ("pe;-fect data "). 1 1

" % error of rad.ar.deri~ed accumUlau.ons41lperfect data")~ Standard devi."ation fr2~ the mean ratio VR. for the test dat., of Fig. 3. 5 • 1 1 ~ 'fi

% error or ~ad~r -derived accumu1ation1 for the test da.ta' of ~ig. 3. 5. . .' // ' _

1/ ~

Matching PPI's to aetermine position (rl,Q) of one ship relative to the other .' :

OCEANooRAPHÉR PPI display for Julian Day 194 at 08:0-1 Z.

QUADRA PPI display for J~lian D~y 194 at 08:00 Z with OC~O radar echoes superimposed thus showin'g (r 10) -COOl' :;inate s.

OCEANOG;RAP HER PPI display for Julian Day 245 al' 12:20 Z •

7)

QUADRA PPI display for Jul~n Day 245 at 12:20 Z with OCEO radar echoes superimposed.

Maximum differe'nc'e in range for each "~a.tchinlJ"' , 4 .. Ji

Maximum cro~s .;a.ng'e diff~~ence for e~ch' IImatfhingll.

Maxi~um total differe~ce for each "matChingll'ji " ri. B-scan display fo~. Julian'Day 245 at 17:28 Z.· ~i

f ~ 1

Partial PPI display fÇ)r Julian Day 248 at 13:10 Z showing isohyets "E" a~d tiF" along with the in ~rpolated'~ value in the blanked areas. ' j

Dist;ibution of deviations of i~terpOl:~ted valut!from actual v,alue. . ' :'j -, _ QUA DRA PPI dispiay for Julian Day 255 at 1:4!}55 Z showing path'from radar to gauge. r. '

""

45 • ,

45'

45

45 .

,50

51

52 .,.

52

54

54

54

56

59 '

.60

62. .

QU:ADRA PPl display for Julian Day 247 at 13:58 Z sh~wing 62 path from radar to gauge .

Section of a PPI dfsplay for. Juli~n Day 196 ~t 03:27 Z showing field about QUAD~. r' 64

1

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viii

"

FIGURE \. PAGE

4.15 Variation 0t standar,d deviation from G. IR. with exponent 66 (b) in Z =aR • ' l l • /

4.16 Variation of staniard error between gauge, and radar with 66 exp one nt in Z =aR. '

" 4.17 Frequ-~ncy of occurr~nce(O/O) of tape number (or dBz) for 71

storms which were analyzed. .

4.18 Accumulated raln per tape number (or dBz) for the GATE 71 Z -R relations. < •

.

4.19 Plot of 10 log Z (dBz)' ~s l'og R for the G:\TE and Marshall- 72 Palmer Z.-R relations 'ôf the f6rm Z = aR . , '

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ix

LIST OF TABLES

2.1 List of symbols (

Z. Z QUADRA radar and meteorological parameters

2. 3 Radar characteristics and specifications

,4.,1 1

'4.~

4.~ / ..

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Antenna elevàtion angles

Mean latitudês and longitudes and frequencies (in percent) of various de~iation~ from t~e meaI?-s

z -R 4elations from attenuation cases . .. Z -R relations .obtained from validate1i data

Rainfall rates from the var.ioU's Z-;.R relations ~

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(, Chapter 1

Introduction

1. 1 Philosophy of GA T E and the role of radar

/ !

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The (rAIIpl Atlantic Tropical E xperiment (GA TE) was cenducted 1

from 15 June to 30 September, 1974. The scientific plans for GATE are

summariz~ by Kuettner et al.( 1974) in which the GA T E Central Program's

primary objectives a.re-stated as follow.s:

1) to estimate the effects of smaller-scale tropical weather systems on the large-scale circulation 2) to advance the developinent of numerical modeling and prediction models.

With reference to the above: Kuettner states.

"It can immec;liately be seen that the first objective comprises studies of 'scale ~teractions' and Iparameterizationl. These have to be based on an aâequate description 6f the tropical phenomena existing on various scales (Iscale phenomenal) and of the basic state in which they are embedded. It is also obvious that the second general objective can be achieved by providing a good tropical data set and by an advaÎlce in the forementioned parameterization techniques. Il (

,; ,

The role of radar ~n helping to ach~eve these above mentioned objectives, e. - ,

is to study storm morphology and quântitative hydrology, of. which rainfall , , estimates are an important facet. With reference to the uses of rainfaU

estimates in GATE, Martinand Sgherer (1973)' state;

"Precipitation is important to GAT E -not so much for its own sake as for the elusive quantity which it represents - latent heat release. Bùt rainfall is not on1y a measure of the quantity of heat l'eleased in, the atmosphere; its areal distribution approximates the patterns of latent heat release, and also, in a gross 'sense, its intensity is a good m~sure of updraft

1. Global Atmospheric Research Program

"

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1 int~nsity. Thus. precipitation i8 a sensitive indicator of tbree variables cruci~l to conveçtive parameterization schemes':, the amount and distribution of latent heat release, the upward mass flux, and the spatialorgani­zation of conv~ction. In this role. it is an indispensable', element of heat and water budget studies of convective systems (cluster.s and individual cumulonimbi) and fixed volumes (thttB-scale array of GATE)."

The conv:entional way of measuX'ing, rainîall has been raingauges, but

on the open ocean, accuracy and reliability are very duficult to obtain because'

• of the spatial sampling' problem. In addition, such effects as the Bea spray

and the perturbation of the wind field produced by the buoys and ships are '

difficult probléms to solve. Radar, however, solves the sarnpling probl~m

becau8~ of its superior ability to ~urvey the ,atmosphere in space (both in

the horizontal and vertical dimensions) and in time. Hudlow (1975) derives

a mathematical relatio~ for tropical data (collected during BOMEX1) {rom /

which he concludes ~hat it "reflects the highly non1inear nature of convective

precipitation patterns and emphasizes the vital'>importance 'of using radar

estimates for deriving GATE rainfall estimates. 11

.J-

In recent years, much attention h~. b~en glven, to the u,se of satellite

rainfall estimation methods in which much of the "ground-truth" and calib­

ration datais supplied'by radar. (see Martin and S~er.er (1973}). The use \l\ _ !

pf radar in GATE lS, thus, advantageous for the above mentioned reasons

since radar can probably supply the most accurate and reliéjlble .precipitation

estimates over restricted areas of the ocean. ~

1. Barbados Oceanographie and Me teorological Experit:Q.ent

.\'i~1~ •

i.

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4

3

1.2. Objectives and associated problems

The- central objective in this work le to examine and validate the radar

data collected by the QUADRA1

"radar Q.uring .. GA;~ in order to obtain'Îa Z-R

relation(3hip. Âlthough a ~ -R relationship has been derived by Gillespie

(see Hud10w et al. 1976), the importance and unfqueness of the GATE d~ta

mer~.ts ·an independent e~aluation of the relation, . albeit by a different m~thod.

Si:nce the radar data are ncn-reproducible. it is of paramount importance that

,the- dàta be examined czlefully to ascertain :.vhether (and to what extent) they:

contain any idiosyncracies. Làstly, all of the rainfall information obtainable . .

from the.se data weighs heavily on the calibration of the radar and the , . . "

,establishment of "ground-truth 'l frOlTI .the ga.uges mOllnted on the GATE ships.

Thus, it is seen that although etudies of storm morpho10gy, quantitative • 4 1 ...... ~

\

hydrologyetc, are important in their own right, this pr~sent work supplies

the necessar,y inputs from which m.eaningful and quantitative results can

be had.

Obtaining "ground-truth" f:rôxn gauges ia the greatest problem faced

\ in this work. Firstly, there are onlya r;rmall number of gauges within

, . QUADRA radar range (fige. 1. l, 1. 2., and 1. 3) - at least one on the U. S.

'B-scale ships, i. e. , OCEANOGRAPHER, DALLAS and VANGUARD. How-

ever. precise navigati01 data fo;r: VANGUARD are not available and hence

" 'ca~ot_ b+ used for c~mparlng gaugo and radar Z v~Lues, Preciae navigation

data for ,~ALLAS -are available but the coarse tim~ resolution (6 hourly) _ , . • 1 •

prohibit:S ut~lization of the dat~ set white rnost of its fine reso1ution (3 minute) 1 .-,

. data -had to be deleted becau se of the gauge' s high failure rate. ~ Of the

1. The Canadian Coast Guard Ship "QUADRA" is the weather ship : contributed by Canada in the GATE effort.

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Ship array during Phase 3

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(Figures 1.1,"1. 2, Sr 1,<3 fr0I!l NOAA-technical" report EDS 18 )

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potentially available twenty daye of phase 3 data (days in which DAL;LAS is

'within 'QUADRA radar range). on1y 3 daye cOl)ld be sa1va~ed in which the.

1 \

DALLAS gauge was function,ing prope~ly. ,Hence only the OCEANOGRA-PHER , ,

g~uge and the QUADRA gauge (made available by a tech~ique described in

C1}.apter 4) provide the baSIC data set in this study. Although more gauge

information ia available. e.g. from: the ships METEOR. PLANET

(Federal Republic of Germany). HECLA (UnitefK~gdom). a!nd°pRq:F. VIZE { 1 " •

(USSR), either the time resolution i.s too coar.s'e or preci~e' ~~viga.ùon data

for the s)lips a,re not available during the time of this re search'work.

Two ~C?re problems are faced with the DA,LLAS. OCEANOGRAPHER

and QUA DRA gauges. The first is attenuation of the radar beam by inter-

vening precipitation between r,il.dar and gauges. This problem is discussed

more fully in Chaptel' 4. The second problem is that the storms which

could bè available for analysis are of short duration.· The optimization

technique described in Chapter 3 requires.at Least two pairs of gauge-radar

values which typically necessitate storm durations of at least one haur.

It can be seen from the above that while the data set i5 sparse. it is

the only one available. ·Although the gauges tllemselves might suffer /from

expos'ul'e pl'oblems. wind perturbation effeèts, etc. they supply the anly

GATE "ground-truth" data. As such, with the limited and unique set ,

available, it must be used to full advantage .

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C hapter Z

~ The QUADRA radar.

\

• 2. 1 The meteorologicalyradar equation

The reason that radar cah be used for quantitative precipitation measure-

mente is that there is a physical mechanism l'e)ating the size, shape and < ,

composition of precipitation pal"ticles with the echo which these reraQiate h'

when illuminated by microwave radiation. Furthe~more, radar meteorologists . have found "relations (called Z -R relations) between the intensity of precipi-

tation echoes and rainfall rate at the ground. A summary Qf th~se Z -R

relations and pertinent radar theory is discussed in a book by Battan (1973). \ '

Th~ basis which relates the observed re~utn power by radar and the parameters

of precipitation particles is the meteorological radar equation., The èquation'

derived by P robert-Jones (1962) is as follows , /

/

eq. 2.1 P r

3 = l'Ife

10,241n 2

11 The factors in the first bracket are radar system parameters white those in

the second ar~ parameters of the precipitation particles. Table 2. 1 defines , . the symbols in eq. Z.I.,

. "" .. " .. _. ,----.. --""""i,..-----------------: _I·-i.[_~_:·:....f ....;;..;. .... ' _ . .;....' '"",,,,,,' ~;.,:.,~, ......:..:-....:...:....;.:..:;" /:.:!..l_,_,' .., 1 d ~.. _ _

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TABLE. 2.\ List of Symbo\s

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propagation4tpeed of e\ectro~agnetic radiation

peak transmitted output power

avetage received power

pulse duration

antenna gain

antenna beamwidths to the -3dB level for one way transmission

radiation wavelength

refractive index of hydrometeors

equi~alent reflectivity factor (Z=I,d6 • where d= drop d~ameter)

r range

T,he practice in radar meteor010gy is to determine the equiva1ent , r '"

;-eflectivity facto~ t fl\om the average received power P r' S01ving fo~ Z

in eq. 1. 1 yields

, /

z = 10241n 2 3

11' ...co eq. 2.2.

l The quantity ,l m

2 -1 1 js assumed to be known and is usually rewritten As 2 . m +2 2

IKI . Investigators usually set IKl = O. ~3 when the precipitation particles

or scatterers are known to be camposed of. watèr. The quantity (P t'1:) is

thè pulse energy output of the transmitter and can be obtained by dividing the . -) . averag~ transmitter output power ...Ptav ' by the pulse repetition frequency F.

, /

Thus we have \ ->,., l,Y

1

, , -

'),;, {,.t./·~ij' .. ".( ~'1

1

1"

1 f ho.

, i.

!

l ' i

------------,_.~--..--...... -- ." ~ .... -~-------..-..........,. . -_. --- ~ .. -~ ~" ,..,..- -"" ~-.. ±-~"'--... -g: : œii:'i:;"î~ ~ ~ .n"1'"~=-:'.:i-~.=l7~n::. .... ~ __ :u~~.:==JZ -"-'r-

\

. . ! . J . ~ ,\ " ", ''''1'' ,,~" ", . '" " , J, l , .• ' ... ". ~""A' ~,t d' i Ir l ,.' hl' ~ ~I,~ , .... .tt»t

--,;.,.,.,-,-_____ ....... _____________ ~------------------____ l1li1l1li'·.

9

(:

Eq. Z. Z can then be written as

p r

or more conveniently, following Battàn (1973)

'or equivalently Pl' = l ,IKI Zz

e~. 2.3'

eq.2.4 Z

IKI z . c. \. ' . : In eq. 2.4, C is a constant completely determined Cy ~ radar characteristiçs

and th~ speed ~f ~lectromagnetic radiation: , It can ~~/een from the seco~d. equation in 2.4 that returned pow~lr is inversely proporti;nal to 1'2: Howev~r,

, " many/radars, including the QUADRA r4dar, have S. T. C. (sensitivity time

control) circuits which normalize the retur~ed power. The effect of S. T. C.

is that any precipitation giving rise to a particular Z will produc,e the same

Z, at any range (within the S. T. C. operating range). . With this in mind. and

having measured aU the radar pa!ameter's. eq. Z. '3 can be used to determine

Z from the returned power P. The Z in turn can be converted to a rainfall r

rate using an appropriate Z -R relationship. The measurement of the radar

parameters is di~cusBed in the next section.

Z. Z Measurement of 'radar parameters 1

l. la Radar calibration

'The need for proper radar-calibration in order to make adequate rain- \

, faU measu'rements has r~ceived considerable attention from radar meteorol­

ogists and has bee~ r,eviewed by Smith (1968). The measuremeqt of the radar

pal'ameters in eq. l. ~ of the previous section are rather, straig~tfo~ward

except for the antenna gain G. Althpugh the manufacturer of a radar system

---~_._--_. __ . - -----~--~--------.............

[

~ ,

1

f •

.... 6 .. ld , ~_;'k"~_" __ ~~~_

(

10

quotes measured or calculated values of G. there are losses in the antenna

and feed system, on s~te which cannat he determined fram first principles.

In the radar equation. the gain that should he used is the effective gain which

! incorporates these los ses .

( -, , "

. For the QUADRA radar. the effective gain was measured br ,~sing a

standard-gain antenna at a distance of 760 meters. This procedure is

e;xplained hy Smith (1968). Silver (1951) shows that the distance between the , -

stal'ld~rd gain a~enna and' the receiving antenna mllst be ,Buch that r> 2D Z, A

where r ie the separation between antennae, D lB the diameter of the receiving

a~tenna and" ie the radar wavelength. The QUADRA rad,ar operates at a

"wavelength À = 0.0536 meters with a dish diameter D-= 3.7 meters. Substi-

tution of these values in Silver's equation yields r = 510.8 meters: Thus

(,' ': ~_/ ,

the separation (760 rn~ters) was chosen to satis~y Si1v~r's equation. i. e ••

[

the standard gain ante~na was in the far field (radiation field) of the radar

antenna. In the measurement of G. car~ was also exercised to include such

los ses as space 108s etc. Table 2~2 gives the value of effective antenna ga;in

as well as other parameters.

TABLE 2.2 QUADRA radar and meteorological paramet e~s ';

G

)..

F

10 log P tav 8,~

r (s.t.c. )

IKI z

-J:lffecti ve antenna ga~~

wavelength

pulse repetition frequency

decibe1 average transmitter power "

beamwidths

range (sensitivity Ume control)

refracti ve index cons ta,nt

43.5 dB

0.0536 'meters .. , 320 Hz. . 53:! dBm.

10

15 - 150 km.

0.93 (dimensionless)

'. '

" .

r\-I , 1 , ,"

" " r 1

- 7 ~ -,-- - ~-~ ... r 7 -. ·.tr .... ___________ . ____ ~~~ ___ ·_,·_,~'·~ __ ~I_. __ +~'_ffl ______ __

(

t

11

1 Z.2b The QUADRA.rada,J' equation /-'

. .... 1

With calibration, the radar equation ~~n now be used to relate Z and p ... 1 r

, Recalling eq. Z.4, we have

\

\ 1

o ,Sincethe' r,ange depend~nce fa~tor (r 2) in the above is nor~alized by S. '1r'. c. thi.s facto~ is Jncorporated into ~ constant as' i~ IKI 2.

This equation can be written in terms of decibels as )

10 log Z = D log C + Kt log 'Fr

Hencè Z = Cp ... r eq. ,2.5

Substitution of the values from table 2.. 2 into equation Z. 2 yields (in the deci-

bel form of eq. 2.5)

10 log-Z = ~72.94 +D lel Ji r

The usual'practi,?è is to express Z in mm6 /m3,' w}lere

r: 3 [18- 6 3] r 6 3., 1:0 logL.m J = l~ log ~O mm lm _~ 180 Lmm Im,J.

rewri;ten a8

dBZ :: 180·-72.94 + 10 log P r

= 107.0'6 + 10 log P-, r

, eq. 2.6

Thué eq. 2. 6 is

It was found that the QUADRA radar beam had sl~ghtly narrower beamwidths

than quoted previous1y t11U8 giving a 2.7 dB improvement. Hence, for the

QUADRA radar. the equation l'elating average returned power and dBZ is

dBZ = 104.36+ 10 logPr eq. ~. 7

~~ ._~~~I""'l!. ___ ~",)101 s. ..... 7" ;~,.. . --...- ~-.. , ;

' .... ~t..;.~~""-'loJ~"'"-l.~

(

i ' "

(~

LZ /

• Z. 2e' The tral).sfer curve

Since the introduétion of radar as a remote' sensor of precipitati~n, it

-' has been obsetved that the signal re turned from precipitation fluctuates.

This fluctui!'-tion is due to the statistica1 rearrangement of the precipitation .. ,

particles observed by the radar., The statistical reairangement ls caused'

bX the different faU speeds of the hydhlmeters as well ~as the w~nd she~r. > ,

This subject has received, considerable attention from Marshall and

Hitehfeld (1953) Wallace (1953), Smith (1964), Rogers (1~71). a,'nd Marshall

-('1971). However. 'wit~ DVIP (digital video integratol,"" processar ) as

used on tJe QUAD RA. one need not concern himself with the many averaging

techniques to obtain P , the average received power. On the QUAD RA, the r

~VIP was i~terfaced to a minicomp~ter '0 that the differen~ return power

threshofds were stored as numbers on magnetic tape. These numbers,

which will be termed "tape numbers",o'r Uintensity levels" run from 1 to 256, , ,

where tape number 1 is above MDS (minimum detectable signal) and 256 , .. :.

correspond,s to the highist signal whieh the receiver can handle without , \ .' ..:..

seriously saturating. The procedure i~ to conv~rt ,P r to tape ~umber a:nd

then to dBZ. 'The step from P t~ tape number is carried out with ,the use ~f r

1

-1 1

1

a tran.sfer eurve which plots disèrete values of return power (fed int~ the ' i -.f '-

antenna w'it~ a signal generator) against tape numbers observed on magnetic tape "

tape. The transfer curve is shown in fig.' 2. 1. , ,

Examination of fig. 2. 1 shows that the log receiver behaves quite

linearly up to tape number ZOO where some ~eviaÙo~ i~ apparent. 'This

deviat~on is probably d~e to receiver saturation. '.t:his ,saturation p1\esent!l c " .

no difficulties, however, since na- tape numbers exceeding 130 have been . ' .

"

1

1

1 10

1 1 r i!

1:

,_ f

10

". '\

0, '------

0"

---~ . '.

•

~ .

"

..

"-•

'\.

240

220

200'1 • or

180 , J.c

CI 160 g .R 140

1_ ,ta

~ 1.20 E-t

100

80 60

40'

20

0

L .~-~

figure 2.t

.. 88

0

./

",'"

-78 -68 -58 ' -48 -38 728

cr :

--"", ... " ,,'

QI

/

f;~ (dBm)

~

r~

/

Transfer curve betwèen tape numbèr and retürn Signal power pr

" "

~

&.

".

o

----

.~

-'rzr~ , .

~ ~\~ ~

1. a l..t

('

~IiJ",

'"

"

l ,1 1 •

14

./

/

~ ~ , observed and even numbers as .high as 120 are quite rare. In retrospect.

this is.not surprisi:Qg-since aU radars an~uges during GATE showed

predominantly light ra}nf~ll rates.

For convenience. a least-squares Une Cit of the transfer curve is done .... fo~ the portion between tape numbers land 200. The relati?n between tape

number and received power can thus be expressèd (for tape n~rnber6 1 ~

N ~ 200) as

\'

dBrn ~ N T.44

88.23

where dBm = received power level N ;: tape number

The above equation can be combined with eq. 2.7 to ,give a relation between > v

N and dB Z. The resultant equation becomes

\ '\

July

dBZ = N 4.44

/ "

" ' .. . 'Ibere were three pha~s during GA TE. narnely Phase 1 (June 27 to

o t \ - '1

16), Phase 2 (July '2.8 to August 16), and Phase 3 (August 30 to , ,

At the end of Phase l, a noisy crystal was ehanged in the , ' ,

receiver hardwa~e giving a '4.5 dB improvement. The d:BZ - N relations

are then ~s follows -/

(J

/ •

"

dBZ = N + 16. 13 4.44

d}Z ::; -r-:Nrr-+ 11. 63 4.44

..

"

...

Phases 2 and 3

s'nUi' st

"""$ ..

(

2.2d

/ ~ .. -

-.. - ~ ... ~ ...... _-"_.-.... , -" .... , ....... ~=~ ... , ----------~-------15

~ The effect of electrical calibration errol

In section 2.2b, it was shown how the meteorolàgica1 radé\.:ç" equation

could relate the received power P to dBZ for the QUADRA radar. The r

"; role of the electrical calibration IS ta. evaluate various radar system. para-

meters such as antenna gain, beamwidths, transmitter pulse energy output

etc. producing an equation which la specifie to "the radar systerh being uaed.

For the QUADRA radar this equation ia

dBZ = 104.36 + 10 log P "r

eq. 2.7 ,

The constant (= 104. 36) in the above equation ia spetific to the QUADE,A

radar and is not trans(erable to other radar systems. Ideally, however,

. equations such as eq. 2.7 allow radar'systems ta produce the saIne dBZ .. " .. value for identical targets or in this case, rainshowers. This presumes.

of course, that there ia no error ln ~he electrical calibration of the system.

It will be seen in Chapter 4 that the electrical calibration of the QUADRA

radar system might have been in error by about 3 to 6 dB. In terms of

eq. -2. 7, this means that the QUADRA radar produced va1'ues which were )

approximately 3 ta 6 dBZ below those obtained by the ôther GATE radars. ,

This difference in dBZ. however, is a constant difference in that the dis- .

crepancy ia approxima teLy the same for aU return power P -values compared " r

to the other GATE radar s. With refC"'p-nce ta fig. 2. l, the calibration ~

error only moves the whole transfer curve vertically. ' Furthermore. sinc~

the QUA DRA receiver behaves quite linear1y. the constant discrepancy 1"

means that à fixed incremental change in tape t;lumber (linearly related to

dBZ) always c::orresponds to a fixed change ~n received power P r regardless

of which. portion of the transfer curve is used.

_1 ...... ~

(:

(

\

1 /

t r

'. 1

-~ .~;-_." ... - - '1'--"~ '. 1

16

/

The reaSOll for the above mentioned behaviour stems {rom the fact that

the ab501~te power levei ai the signal generator ~sed i'n the ealibration

procedure cannat be de1;.ermined very accurately with present day engineering

expertise. In essence, the measurement of the absolute power level is a 1

calorirnetry measurement and it is well known th~t suc~ a measurement can

emb~dy appreciable eri'ors. Furthe;rmore. any variation or deteriorat~on

in antenna gain. beamwidth etc. gives rise ta a constant discrepancy between

the obs~rved and ltac tl1al l1 value of return power. However, the difference

between different return power' levels can be very .:!.tcurately determined

since these are measured by attenuator steps which ~sually consist of a

high precision resistor volt~ge divider.

ln the above discussion it lS seen that, provided one has a receivel.'

that linearly relates dBZ and 10 log pr (=dBm), the el~ctricai calibration

allows a good determ.ination of the. slope of the tr-ansfer curve although the

intercept is less well known. However. since the observed dBZ values;

will be used ta determine a Z -R relationship, the effect of calibration error

on the Z -R relaHonship obtained is examined. It was shown in the previous

section that the tape numbers are related tà dBZ values by an equation of

the form.

dBZ = cN + d eq. 2.8

where N = tape number, c = constant linearly related to slope of transfer , ,

curve and d = constant linearly relat~d to intercept of transfer curve. If

one assumes a Z -R relation of the farm Z = aR b th en

dBZ = lOloga+ lOblogR eq. 2.9

where dBZ = 10 log Z. Thus the dBZ obtained from thè transfer curve

can be related ta the dBZ from the Z -R relation by combining equations ./

r t, <,' ". ~; ~)'I , j

.;... t • " ~

J :' • , l

f 'f; ~.

\ i

t t t 1:

~

1 i • r " , Î

'\

\ 1

1 ~ •. ---------_-!_ ....... ------

()

:-

.. ·C;

17

2:8 and' Z. 9. This gives

\" cN + d :; 10 log a + 10 b log R ,eq. 2.10

~~ the apove. the constant c ia weil determined aince it ia linearly related

ta t}{e slope of the transfer' curve. In the following chapter, the dU ,

values obtained by the radar are directly compared ta rainfall values ta

propose a Z-R relation .. ln terms of eq. 2.10, bath log Rand dBZ (=CN+d) .

are known and a relation between these valuès, is sought by varying both a ,

and b. However. only the value of b can be ,:\ccurately determined as. will

be shown prese,~t1y.

If one observes tape numbers Nl

and N Z for rainfall rates RI and RZ

~espectively. we have .from eq. 2. la

cN l + d = 10 log' a + 10 b log RI •

cNZ + d = la log a + 10 b log RZ

The above pair of eq uations yields

b ~ c(Nl - N Z}

10 log (RI -RZ)

\ \

Since C is well deter:mined from the slope of the transfer curve and the

difference (NI - NZ

) i8 invariant regardless of the intercept and because of

the linearity of the transfer curve. then b is well known. However. the

. pair of equ'ations above show that a depends on the value of d which i6 the

ill-determined intercept of the transfer c;urve. Becaus,e of this, there will

be less confidence in the value of the coefficiep,t.of the Z-R relatio~ derived ,

in Chapter 4.

.~. __ . ~---~- - -~--~~-"""""'=::..:::-..:..' -:::;,'..:,.' ... -----.... ·· .. -ii·-.. -iii:7Eiiii:.·-__ _

" 1 ., '" ' '.I~ i J ~ \ .. 1 ... d ''\'''Jl1

.Ir t.Jt_ ..... ,. ... :e ._ ... ", ___ • _. ____________ ~_~ .. ~ .. ,h • è • "' .. , t't''''~!' ,,!, , . l ." ~-' .. 'd',~" .

(

" . <-

c

18

"

Z. Ze Direct tape onumber to raingaug/e compar.ison

It is perhaps unfortunate that great stress is being placed on obtaining

" c ?rrect" dBZ values when working with radar. It must by borne in mind.

however. that radar is increasingly being used as an accurate remote sensor

of precipitation and as such ~s .called on to provide reliable rainfall estimates'

for hydrological studies. .In fact, (and this is m:ore particular to GATE). ,

the emphasis could well be placed on obtaining a direct relation between

rainfallias obse;rved by raingauges) él;nd any reproduceable. vâ,riable obtained

br radar. With the QUA DRA radar system. this would imply a relation

between the rainfall and the n~mbers st0red on magnetic tape without refer-

ence ta dBZ values. In this case, the "absolute" electrical calibration

could well be in error while still allowing a relation between tapé number

and rainfall. With the technique described in the next chapteJ;', a direct

comparison is sho.wn to be possible even though the lntermediate step of

translating tape numbers to dBZ v~lues is carried tllPugh. The rationale /

for converting to dBZ values is ta provide a parameter to check that aU

radars in GATE are 'consistent, sinee dBZ values are transferable variables

and are not peculiar to any radar system.

In Chapter 3 it will be seen that, without a clirect comparison technique,

. the only method ol relating rainfall to radar observab~es (averag~ ~eturn

power P ) is throU'gh the use of the reflectivity factor Z (or 10 log Z = d13Z). r .

This however, requires theoretical assumptions which will be explained

later. Since this work uses a direct comparison technique,. the "absolute"

measurement of dBZ values èQuld be of secondary importance for the

purpose of obtaining raU;fall estimates.

,1

<

(,

\ .

19

2. 3 Radar data overview

/

2. 3a QUADRA radar and antenna prograrn

Table Z. 3 pre sents the 'characteristic s of the radars aboard th~ Shi~B (

QUADRA, GILLIS, RESEARCHE R, and QGEANOGRAPHER. Of note i"JcJ' r that the QUADRA radar has the highest p~ak power a.nd pulse repetition

. l ,

frequency along with the smaUest beamwidths and pulse duration of the GATE .. snips. The QUADRA radar provides good space and intensity resolution of

precipitation echoe s.

The antenna pro gram of the pUADRA radar is a stepped helical scan \

which sam~les a three d~mensional volume _of space every five minutes.

Table Z. 4 gives the various elevation angle s of the antenna progt-am. The

antenna program ie such that the step in elevation a~ways occurs between due

north and nine degrees clockwise toward the eaet. During this period no

information is r~corded. The reasons for this blanking are twofold:, , '

1) the antenna electronics and processing hardware require a IIdead" Ume . ,

oti. purély logistics grounds and 2) the antenna oscillates about a mean

elevation angle during and shortIy after the step-up procedure thus giving

false elevation information. This oscillation ie quickly damped however.

,Fig. 2. 2 shows this damped oscillation. The antenna does however oscillate

very slightly about its rnean elevation angle. Yet, upon examination of ,

several hundred scans throughout the three phases, it is found that the mean

standard d1eviation about any particular ~elevation angle i8 about 0.011 degrees. !

This ~implies that at far range (200 km) there ie a vertical ~eam displacemetlt

of some 40 me~ers. This displacement is quite insignificant and points to

the stability of tlle a~tenna rotatioI;l about a mean elevation angle. \

...

_II/ila."""....,.".,., ..... .. __ -.a.......- 1. ci. • 'T:i;

"-20

.... ~

( TABLE Z',3 Radar CharacteristicB and Specifications

ÎI' .. QUADRA GILLIS RESt OCEO,2

wavelength (cm.) 5.36 5.3 5.3. 5.35'

peak transmitted power (kW.) 1000 250 225 215

,puIs e length (km.) 0.30 0.60 0.60 0.57'

pul.se repetitioIt frequency (hz.) 320 250 2501, 259 ,,'

po lariza tion vertical horiz. horiz. horiz.

1 antenna gain (dB.) C/ 43.5 39.0 35.0 39.9

antenna diameter (me ) .3.7 2.4 2.0 2.4

J antenna beamwidth (degrees)

j t ~ i

(- 3dB level, one way trans .) 1.0 1.5 2':0 1.5

1 anteIlfa rotation rate (r.p.m.) 3 3 3 3

~m. d"ectable signal (dBm) -88 :-100 -100 -104 ~ f eiver dynamic l'ange (dB.) 60 80 80 80

~ range normalization (km.) 15-150 yes 18- 2F 18- 232

1 elevation antenna pro gram

(. 1) #- of elevations /cycle 15 option option option 2) maximum angle (degrees) 30.4 Il " "

-t, 3)time/cycle '5 min. .. " " tape recording

mag. 3 -t l)iormat mag. mag. mag. E 2)#of levels 256 256 256 256 c ~ 3) range bins a)number 200 512 200 200 ~ b) Bize (km.) 1 variable 2 2 !

4) azimuth bin size (degrees) 1 1 2 2 l , j

J . radorne yes yes no yes

obstructions by ship's , ! 20·-30· • • supers truc,ture none none 20-}0 \.

'J ,

t 1 RES = RESEARCHER , 2 OCEO = OCEANOGRAPHER 3 mag. = magnet.4,c tape

.. /

, '1''''.1

21 o

..

},

( 1: t: ~ ~' 1. ff ~ . ~ -f t, ~ ~, , , , ,

)

• TABLE 2. 4 Antenna Elevation Angles

~

Angle Number Elevation Angle (degre'es~

l 0 ,/ 2 0.6

- 3 1.0 ,e...,

4 '" 1.6

~ 2.3

(~ 6 ~ 3.3

" 7 4.7

't 8 6.7

\ 9 9.3

LO 12.7

11 17.3

l 12 20.1

13 23.2 ,. 1

-' 14 26.6

f

,/

,15 30.4 , j

j

/

.UT "

f: " if, if, , l' (. 1; l,

r ,. ~;

l . •

d

1;

/'

( , J o

._----,.. ---',.,- -, --~--~-"

Fig. Z. Z

, ,.'.. ~'~ - l ,

'f!" ,.l~~ "':: , -, ~"

zz

/'

eleva;tion angle" m+!

~

elevation angle m

elevation angle m-l

. ,"

, Path traced out by radar beam in changing

elevation angle

, 1

..

,

1 '~

r i ~ ; Il r,

f

~

t ,

f li f

f l, l, {,

~ ~~

t·

f ~ ~

r ( }

f >

• , l

(

(1

(:

, '

, .. ,'"

23

The. 1086 of a 9 degree sector in the north is regrettable but fortunately / ~.

the QUADRA radar'does not have large sectors of shadow produced by its

ship BUPfilrstructure. Other GATE ship radars are not as fortunate, as for

example, the OCEANOGRAPHER radar which los es a 200 sector blocked .by

its ship superstructure. 'The effect of this blanking can be seen in the figures

supplied by Houze (1976) and Leary and Houze (1976).

, '

Z. 3b Radar background noise

/

The r~ceiver of the QUADRA radar was designed to distinguish between

256 levels of return power intensity. Given that the dynamic ,range of the

receiver is 60 dB (see Table 2.3), an incrernental.change of one rece~ver

level,corresponds to a difference of about O. 2 dB. Statistical fluctuations

in the signal, howe.ver,. suggest resolutions soinewhat better than 2 dB. The

literature, e. g. Smith (1964) and Wallace (1953), points to approximately

the sarne resolutlons. Th~s, the original 256 levels were grouped into 50

classes giving a 1 dB separati~n between classes. Although the resolution

is dos.er to 2 dB, a move to 1 dB was chosen to avoid decr'easing the aétual

resolution du~ to quantization effects. .

ln the initial stages. of the research effort. the raw digital radar data

.was examined to see whetber there were any idiosyncracies in the data.

Fig. 2'. 3 shows, a PPI representation of the precipitation pattern observed

on' Julian Day 216 (se~ Appendix II 10r Julian Day to calendar data conversion) ~

at lS:19Z. AU intensity levela, i. e., 1 throl"lgh 256, were utilized in

producing the PPI. lt can be seen that there are conspicuous radial sectors 'II

in the display which, however, are fictitious since precipitation patterns

have never been observed to have such a: geometry. lIn an effort to remove "

i 1 / fui ~ t ,. ~,

f {.

t t, Il

t , r

t r , >: ~ ~.

' • ..,.lIIll11hflllJfjJiIl!lllIll ..... • ... _"' .. _., _______ ~ f' ., ... _ .. ~ ... _. __ ~~ _____ i .... _-_1IIIIIIIiI __ llli'I/II.' .... __ ..... iJ._...:... __ .....;.,;....;.~._~' '~ . .;'.",,"".:,< _____ ~__ ;; "1"( 'r; I~" ~-

/

"

(',

(

24

1,,1 Of' tI.r.vATIO' '1 rolt D~r 21f A,. ",.. III.',"" 1

\

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:~ :; ~'. ~~·ii~~~~::::::::::::::::::::: :i~~!~:::::::: i: i~: :~: ::: ;;:: :A~: ::::::::: ii:;:::::: ::::: ::::::::::: ::::::::: ::::::: 41 •• :1 ... i~:;4.13 ...................................... ' ....... I ...... ~" ... w ............................................... . ", 1.11 ..... • ..................... 44 ......... 26 ......... IBC .. I •• ~lJ7lJ ............. , ..................................... . 4'1 'of "'f..~""1t7.:; •• t ...................... """8 •• 1.AU •• 4.2 ..... ,.r83TD ... 1 .............................................................. ,. ......... _ : .. '."74~~ '1 ~'3 3 ............ '111.llD97C11l •• 1.34 •• 1I ..... R:III.1 ... 1 .... 1 ....................................................... ,. ... . :"1 "r .. 3 .. :;."i'6.=l •• 4 .. ~ ............ 1 .•.. 3 ••• :sI ................................... ~ ............................................................ .

~~ ;:;~~~;3::: 7 •. ~~: :::: :::::::::::::::::::: :::: :::::::: :::::::: ::.::::: :::: ::::;:~::: :::::: :::::::: :~~::::: :~:. ::~::::::: :::: ";, i ...... '4 4!l ", ...................... 2 ..... 1.1 .................... ~ .................................................. 'O .:1 •••• 4 3 •• 1 .......... .

~; ::::~ ~1::~~: T:·::::::::::::::: :i:: ::: :~:::: :::::::: :::::: ::::::::::::: :::::::: ::t: :::::: ::::::::: :::::: :~: :~r;.:: ::~::.;::: !ilt .,., ... # .!J."' .......... ~ ........ 62 ..................................................................................... 4 ............. .

~: :: ~:::. ~~. :3:~::.:Î;~: :à: :s-r:~:: ::::: :::::::: :::::::: :::::::: ::::::::: ::: -: : .. :'::::::::::: ::::::::::: :::::~: :2:i.:~ii:~:::::: frJ ,. ~'.T.Ji' ... • .":J. ~6 .•• 6 .. .• ,1. ~ 47 ............................. ,. ....................................... 2':1 .......... 2 ..... :1 •• 6 ........ s ....... 4 ....... , ••• ,. ...... . ,.:t "~"I'''.'' .. .. 4 5:".6 .33:14 .................................. "' ............................. :!6 •• :a1'3~ ••• 6Ta'n •••••••.. ~ ....... 6' ............ . ',:, "",~'''''' ••• '':;3 4.4.~. tI ......... 3 .................................................... _ ." •• AIt94f07.IJ';':I: ............. U ............. a •••••• IIl. ,." " .... # ... ", ... ~'*"' ....... : .. n. .3:1.~ ............................................. 79.AJt91'11Aa .................... 1 ........................... . ", ., ... ,., •••• ' ..... 1 r .. a7 .... 3a:.19CllUtJ'.,.,UM~ ................... " ................... 3 •• M4llt3 .......................................... -.:. 1 •• " ., ... ", •• , .. ,1, ., ...... a .•..•• nr.El.J)l)~l" ............................................ sm .,'76$ ....................... 1' ................ . 1," #'1''''',. •• 111........... . ........... , .• rw" .......... 2 ....................................... 06.763 •••••••••••••• 4 ...... " .................... . (fi '~"'I •• ".~~,,, ... .. 1.4 ..................... :1 ..................... .o.o • .o ........................ 87 .......... s .............. ft ....... _ •••••• _ •••• "', ", .. ,1<"""."' .... ' .. ' .. 11 ................... .... ~ ....................... 'O .......... (1.(,76 ............ U7M ........... ~4 ................ _ ••••••••• " •••• -.. 7., , •• ".,,., •• :r .. Jtltr •••• ' •••• 1 •• , ....... 4~ ••• ' ......................... '1419973W-...... 09a ••••••••••••••••• ., .......................... . , •••• ','1' •••• " ••• ." ....... .................. .. «:1 ... ......... UT ... ~ ... 1n86 •• ŒA.~"'T ..... ~ .................... 1::1.44.4 ...... _ .................. .

~ :;::~::::::~;:;:::::=~;.:::::i:.:~:~~ •. :::...~~~~~::::~::::::::~::::.::~::::==::::::::l:::::::: 'i • • ". .. '..:'rr •••• " ..... _ ........... 4 •• 6. Hl1'.:t44MADC.\9A846 ••• » ......... ~'1'0 ................................ ~ •••• - ......... *. 7:; ..... #A: .. lI':" ....... «Jtf .................... 47 .466 .. .. RUBtl51.~ ....... • 4' ............ 48G9n1 ................. 44 ••• :l'.ne ............................ .. 7 •••• '.,II ..... ~ ................ ,.. ..... .a_ .. MGS4 .. 04S7'7 .......... , ••• -4 •• :l...... . .. Qi ••••••••••••• " a ..................... P' .............. _

Tt .. ,."#,, ................ ..r ....... p ... -. ... a7 ••• j ....... ~ ........ ~ ......... , •••••• iI ••• 3 ..... 4 •••• ~ ................. ~ ......... & ......... _

7. ,#,,,.JI. •• , ........... 4, ..... _ ................................ • 6 ............. :, ............ ~ ................. _ ........................... ... 1119 ..... 4L •• ,,_ ...... u .......... __ ... *»~ ___ •• , ................ 4. ,.4 •••••• t ........................................................... ... ~ .. #,. ....... * •• ~ ... ~ .............................................. ,.~ ............. 7 ..................... • ....... ..-. ................. .

'" • " ~... 0 - - -~- ....

J'i.gure 2.4 PPI c;I1sp1ay for Julian day 216 at 15: 19Z where

1ntensity level.s l. L2 Sc 3 wer .. suppressèd

dm

Il.· ....... _P''''.ft!_ ... _ .. __ ..... __ _ " nt

f

<

<

26

• ,

1'1 -,1 l.tJ."-:"f,. rnll DU :116 4T lit,.. III.''''''. o .~ ., :III t!J S. '\II .. .. le 1. H H Tt TI .. 8$ t. 915 1.. IN Il. III 1:10 1z:J

• """l'"'''''''''' ,. .. ".;,.0 .. " •• ..: ........................... ..-. ....................................................................... _.* ......... .. :1 W'" •• ,. .... ~ t •• '#r.~' ••• 1t •• * •• ".I:."" ••• ""'.** ........................................ ~ ..................................................... at ... "" ....... ~ .. :1 III"WO" ..... .0111"'". ... t ,. ... "" ............ IIt .......... .1 •••• ~ ........ 10 ..................................... " .............................. _ ....................... .

: :~::::~::::::::::::::::::::::::::~~:::: :':::::::::::::::::::::::::::: :::::::::::::: :::: ::~=:::::::~::::::::::::~::::::: ..... , ........ l1li: ........... #* .......................................................................................................... __ ........ .. 1 rA ... ,. ••• ,. .......... ~, ............................................................................ Ct. •••••• Ct. ........................................... ".

Il ."."' •• :11 ... .,. •• ,." •• 111 ........ * ........................................................................................................................... ____ ~ '1 ., .. ".,.'". ... 111#" ....... , ........................................................... <1 ............................ " .............................. 111 ••••••• 1 •• " ........... IIl .. lC ..... 111 .. 4; .................... O' .......... O' ......................... _ ...................................... ,. ....................... .

II .111' ... " ......... " ......................................................................................................................................... IIf3& ••••••••• JI ft1.'4111"." •••• "._ ............................................................................................................... ~ ........................... . 13 .... ,. .. -r- ...... II ~ •• ,............... ...... • .... .... ..... .. ............. •• .... ................................ ............... .... • •••• .. ............ ................ &.1 14 1 ..... "-r'.I~.J-.6." ...................... ................................................................................................ * .... * ••••••• ." •• :: :::;::;;::::~::::::::::::::::::: :::::: ::::::::::::::::: ::: ::::::::::: ::::::::::::~: ::: ::;J.::::'~~::.~:: ;~:::::: :~~::::::::::::. ::. :;:=:;:;::~:.::::::::::::::::::::::: ::::::::: :::::::::::::: :::::::::: ::::::::::: :': :::::::::: ::: ::::::::l; :::::: :::::::::::::: .. 1: ~5~~~;~~~~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~: ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~ ~ ~ ~~~ ~ ~ ~ ~ ~~ ~ ~ ~ ~ ~ ~ ~ ~~ ~~ ~ ~ ~ ~ ~~ ~~ ~ ~ ~ ~ ~~~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~ ~ ~ ~ ~~ ~~~~ ~ ~ ~ ~ ~ ~~ ~ ~ ~ ~~ ~~ ~i~ ~ ~~~ggg ,

, 'l'Ir .......................... ~n ................................. ...................................................... 0 ................. . .. .. ,. ........................... ~ ......................................... ~ ................................................. , ....... . ! ~~~~~ ~ ~ ~ ~ ~~ ~ ~ ~ ~ ~ ~ ~ ~~ ~~ ~ ~ ~ ~: ~~~ 4.~ ~ ~ ~~ ~ ~ ~ ~ ~ ~ ~~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~ ~~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~ ~ ~ ~ ~ ~ ~ ~~ ~ ~'~ ~~ ~~i~ ~~~~ ~ ~i~~~ ~ ~ ~ ~~~ ~ ~ ~~ ~~ ~ ~~ ~ ~~~g ~ .. ;=:::::::::::::::::: :::::::::::::: :::: :::::::::::::::: ::::: :::::::: ~~:~k :Taé6"~~::~~~~~~::::::: :::::::: :::::::: :::: :11 ....................................................................... 1.6862 •••••• 1 ............................. jI •• 7f ••••• -!J~ ., .......................................................... 1 ... 1 ••••••••••• 1 ...................... ,.... ................................ 4 •

• :):s ........................................ , ................................. &0 .. 4 .................... 40 ................................................ 7 ..... . a ..................................................................................................................... 1' ..... .

~~ ~: ~ jj ~! j ~ jjjjj j j j ~jjjjj jj; j ~ j j jj [j jjjjjj j j j j jjjj j [~~4Ijij j jjjjjjjjjj~jj j~~j j~!~jj~ljjlliEllij~j~jjjjrtttm~t;f '4" ......................... :...... ............ 0 .................................. a ............................ ,O' ....... I ..... I ......... \. ......................... . 41 ..................................... ~ ................ '.4:a ••. .-..................................................................... . .. :r •• ~ ....................................... :a ....... AJ' .. I ..................................................................... .. l' ..... ........................... C4~RII6AIW:!nl ...................................... , .............................. ,

:,: ': .. :::.:::::: ::.:::::::::::::::: :~:~:::::::::: :~~: :~::: ::Î-i :1':: ~~: :~::~:: ;:::::::: :::::::::::::: :::::: :::::: ::: :::: .. 7 ................................................................. :~6A .................................................. . <Cit Ir .................................................... 6 ••••• ' ..... 1BC: ...... ~;6' ........................................................ &

~~ :.:::::: ::::::::::::::::::: :?9::-m:::: :~::~~:: ;-:.~~:::!:: ::: ::::::::::: :::::: ::?:::::::::::: ::: ::::: :::::::: :::::::: .QI ........................... ~ ..... 7 ........... 1 ........................................................ -; ..................................... .

;~ ::;::::: :::: :::::::::::::::::::::::::::::::: :::::::::::::: ::::::::::: :::~:: ::::: :::::::::::::: :::::::::: :::::::: ::::::::: :~:: .... ., .......................................... O' ........ ~ .............................. , .......... 4 ........................................ -! ••••••• ti::; , .. _ ................................................................................................................................................. .. .!;I, .II.W .......... * ................ " .................................................................................................................... "'.

:'7 :t~,,4I ................................... I~ ••••••••••• I .................................................................................. ,.. :'11 " .. , .......................... ' ................................................................................................................ ~ .. .

!: ;;:;::.:: .. :::::::::: ::4::::::: ::: :::: ::::: :::::~:::: ::::: ::::::::: ::: ::::::::::: ::~::::::::: :::::::;: ::: :::::::: :::: ::~:::::: ~~ :::~::::a:r'::::::':"'" (.::::: :::::::::::::::::::::: :~:: :':: ::::::::: ~ :::::: ::~:: :â: ::::::: :i: :à:i:: ::: ::::: :::!::::: ::;:::::::: " ...... , .• ~ ................. D ....................................... 1\ ................................ 9930:1$.73 ....................... fi ................... ~ , •••

' ... , ... ~ ............ ~ •••• ,. ............. :13 ................................................... 1\ ....... 7A.OJtM ........................................ t::.,. ,,~ ., ..... ." •• ,...... • ....... , ............. 9aooDFA.3AB:JS ............... ~ ............................................. 7831AJ11t6 .................................. __ ...... 1111" .... .

~; ;:~:;::;:::~:. •.. :::::::::::: :~~~:~~:::::::::::::::: :::: :::::::::::::: :~2::::~::::: :::::::::::: :::::::.~::::::::~::: (,St ............ It.r ... t.:a ...................................................................... i. ..................... 76.7'1 ................................... ~_" ••••• :II'.".* • .... .......... , ........ yTa_ •••••••• • ~ ..................................................... 7, ••••••••• fi ..... " .............................. _ •••• a •••••• , ••• 7" , ....... #'.I.r' ........ ## ................................................... Gft.B7 .......... G.7-.............................................. . '71 ~ ••• w ........... _ ............... O' ................ • 1 •••• :171 .... 1C978877 ."86 .......................................... --................. ..... 7:1 ", .. r~.iIf' ••• ". ___ .""" ............................ 41\CA4AA.AII ..... 3'fA777 ... 43 ................ fI ........ 11 ......... ~ ..... * .... * ... ... 1" 1'~'.'i';.jl6 ... ~ ................. ...•••••••. 47B'1\CDCBA7 ............. ~~ .. :a ................................... -..-................ ,. .... . ;~ ::=;:::::::::::::::::::::-.-::::::::::: : .. :=;~~::::::::::::::::: ::iT.::::::::::::::::::: ::: .. -=:::::::::::::::::::: '4 .. , .......... 11 ...... # .... " .... _ ....... :s8 ....... a ..... "' .......................... Di ........... fI .......... _.... .................. ** ....... .. 77 , •• 1. •• "' ••••• 11: •••••••••• '**._ ...................... 4 .............................................................................. - ............. * ...... . '$ ....... •• .... ···, ..... • .......... I1 ........... P ......................................................... *-" ••••• _ ...... _ ................. . 79 ................ -= ••••• & ............. _ ........................................................ __.. ............. aca. ................. .. M ••••• .,. ............ 4 .......... ~ •• iI:.*~ ..................... ~ , ...... r'" .... ___ ** __ ........ __ .. • ... **---v,..ult ...

Figure 2.5 PPI' display for Julian day 216 at 15:19Z where

intensity levels 1 through 10' were .suppressed ..

/ ..

~,,~:jw,,_.t,l.',r,~ _ __ .. __ .. _~._ ... _!t_"_ ....... __ ..... _"._~~.. ..._ .... _-_._,..,..._-_ .. _ ....... --

(,

(

(

v ~__ _ _~ .. _ -" ---

27

or Hlter ;these sectors, intensity levels l, 2, and 3 were suppressed. TJle

result of t~s:."s~ppression is portra~d n the PPI representation of fig. 2.4:­

It can be seeJ t~at although the radial sector~ are no longer present, the

PPI is quite spotty. Again, precipitation patterns' have never been observed

to be as spotty as shown in fig. 2.4. Upon examinati<;m of many PPI' s

randomly distributed t?roughout aU three phases ot GATE, it was decided to

Hlter out aU intensity'le~els Iess than 11 in 6rder to preserve the meteoro­

Iogically significant phenomena while suppressing what appeared to be simply

no~se. The result o~ filtering out levels l through 10 is shown in fig. 2.5 \

which is a PPI representation for the same time as figs. 2.3 and 2.4. The

PPI of fig. 2.5 does not appear to contain noise and all features are probably J

meteorologicél-l. Elimination of levels l through 10 does not significantly

obliterate any meteorological information as can be se en by comparing the

correspond~ng .areas labelled A, B. C, and D in figs. 2.3,2.4 and 2.5.

A computer prograrp was developed by Aldo Bellon of the McGiU Stormy .,

. Weather Research Group to count the occurrence of each intensity level.

The results of one such addition is shawn in"fig. 2.6 which 'plots percentage '

occurrence "'(ersus intensity level or tape numbe~. The raw' data was

chosen a~. random throughout aU the three GATE phases. It can be seen .'

that there seems to be an abnormally high occurrence of intensities below

, level 11.·· B Y converting the, intensi~y Ievela ta rainfall aInou~ts t~rough a

Z -R relatlo~ship one can also examine the pcc~rrence of thè ace umulated

rainfall correspondiDg to each intensity levei.. The graph of fig. Z.7 was

obtained {rom the data in fig. 2.6 by using Z := 300 R 1.3 Again, one notes

ÏIl fig. 2.7 the abnormally high contribution of rain due ta intensities 1 through 10.

) •

" P •

......... 'Mb'J.!!!/"*+'f.td I h,,'&htc st 'i V t • 3 ~ t ào' M -( t Kt $ 'M 2 j 'f • ' t

Q

B t r rb ( Frf' *

•

28 o >

/ , /

,----/ ~

•

"--... ..

f" - -

I~

1 J

i,

-:;:

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/ r-~

~ -l' #. & -10' ~ U .

" s= /

10 lof

('), lof 0 \

- ., U

/

U 0

~·1 .... ' . 0 >. 'II

U r:: ' , , II) 0 ct 10 , , k

" rz. ê.

.0 .,.

--~~ ...

'-

1

1_001 0 20 40 60' 80 100 120 tape l\UIlber

1

r Fig. 2.6 ·Frequency of occurrence (%) of tape numbers taken

from randorn .cane throughout the three GATE phases. '-

1

-Cl ./

~ 'II

/

"

lIEtt - Z2Z3JCZbZM .... 1_ .. :mI&&lA

• '1 'II • ~ '," ,,', f ,,'-" ' ---""'. ____ 1 _, .... ...:...:.:..... ..... __ """""'-' _'- .. __ ......... : ....... -l.-..t_, __ .:. • ..:...-_:...~-_./..i) "ow'\oIiIIioiU",;'_oiI'III'IiIiI'''''' ... ' ...... ,&.f.;';iMI;rflllilftÎlilè#lIiIIIt' .. r.-... ?,".6 .. ' !iIoi' ______ ........ __ ·, ..... ,

. " , ~,

/

c

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-s:I ., J4

ra1 .... '0 .... ~ 0

~ -0

s:I /

., J4.

~ '"

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j 0 0 cC

•

Ci

29

o.

.0 0 '20

tisure Z.7

/

f"

,

1 /

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40 60

" 80 1Z0 - ~ '1'ape

muaber

AccUllulated rain per tape Iluaber for the frequenc7 ~8t~but1oD of F1gure Z.6 •

•

l, t'

\,

(

,(

, ~_ .... _-~ ____ , ___ . _ .... , _1 _________ .. _ .... l_.....:: _____ n alll.1III1."

1 30

"

On the basis of figs. Z.3 thraugh 2.7. it ~as d'écided that intensities {!J

l through 10 were prabably in the noise. regime and in aH subseq",ent data

analysis these intensity levels were disrega..rded.

Another computer program was developed which averaged the dBZ

field of the radar data for e~ch of the three GA TE phases. The data

utilized were 4 km x 4 km bins and these were narmalized with an arbitrary

output scale usee} in producing the PPI representation of the dBZ field.

The field thus obtained i's shawn in figs. 2.8, Z.9 and 2.10 f<Tr phases l, 2

and 3 respectively. One conspicuous feature which can be seen in each of

these 'figures is the blank sector stretching northward from the radar at th~ .. " '

centre of the displaY. The réason for this blanking has been explained in

section 2. 3a but its effect 18 cleaxly visible in these disphl.Y:s, Another

incongruity that can be aeen at far range 'i8 an apparent decrease in the out-

put scale values (proportional td dBZ) along the periphery of the displays.

Several effects might account for the far range decrease. The most

ir::nportant la beam HUing. Whereas at 20 km range the QUADRA radar has

-2 3 200 . a pulse volume of the order of lO km, the pulse volume at km lS about

1 km3 _ a factor of 100. Ones sees, then; that at longer ,ranges it becomes

increasingly difficult to intercept the be:am completely thus lowe:t:ing the

ohserved dBZ va,lues. FurtherOlore, at increasing range there are fewer

and !ew,er individual polar data sites available from which to integrate the

dBZ values making up the 4 km x 4 km bins. Finally. the return power is

inversely proportional ta th~ aquareof the range. Although the QUA DRA

radar' 8 data were range normalized by S. T. C .. circ uitry, the operating

S. T.C. range only extended to 150 km. Thus a:t far range, Le. greater

that 150 km; the dBZ values were down by up to 2.5 dB at 200 km although

,,------_..-... -... ~~ ttt 'ne ,r' .*,. "alIté te

ts dt t tt.tw t hi 'di.!

-... (

, ,

31

" h

11 le' 11 :M :IIJ If __...- ... le •• ..' " 'N .,. 1 ..... *.* ••••••••• ~................... . ...... 111 •••• 6 ••••

1 ._ ••••• _ •• - •• ~ •••••• ~ ••• * •• * ............................... . m ••••••••••• A •••••••• ~.......... • ••• ~ •••••••••• II •••••••••.•• • •.... " ..•. 11..................... . ............. ". 111 •• "" .... " .1' 1 ..... " ••••••• 1f •••• 'f ........... ~... .. ............. , ............... 11 ............ 111 ... ~ •• 1 ••

• \ .................... ~ .......................... "." ••• " .. "" •• 1 .......... " w. •• 11." •• 1.1 •• ., ............................................ "J ••..• J •••• ~ ••• IJ .......... .

\ ......... - .................................. , ••••••••• 1 •••• 11 •••••• 1 ••• 1111 •••• 1 ••• " •• .-................. . ....................... 1 ......... 1. 4 ..... 11111.1111111111

• e •••• .! ...................................................... , III tllll.111111 Il ........ - ......................................... , ...... 11111I1l1I1II111

112 ••••••• - ................................ 1 ............... 11,.1.,1 •• 11'111 ,13 ........................................................... 11111111111111111 ,1 ......... -_ .............................. 1 ....... 11 ...... 11111111111 1111 ,15 .............. "' ....................... 1.1 ... 1 ... 11111 ..... 111111111111 1111 116 .................................... 1111 ...... 1I11I.t .. 1111111111 111' ...... -- ...................... IUIJI.I .. ~IIIII .... IIIUIIIII

~I. .......... .. .................... 11111111 •• 111111 .... 11I1I1~1;;~n~~~ 19 •••••• - ...................... 11111111 •• 1111111 ••• 1111111

~ ::::1· .. • :::: ::::::: ::::: :::::::: ::::: :it:;;; mk: ~: m:1 _... • ............................ 11111111111111 .. 1111 Il • lI' ............................... 111111.11 li .••• 111111 :/. _U. . .................................... 1111111 •• 111111 1111

21". • ................ 1 .................... 1I1111l •• 11I11I1I1I1 2. • • ......... : ..................... I .. llIllllIlIl.11I1l1l1l11i 27 ..................................... Il.'. Il 11111111. 111l111l1l1 Il lu." .................................. IHIlIIIlIIIl.t1l1l1l1l1l1l

1

29 - .................................... 111.1111111.1111111111111 .. .... .............................. ..... • 11111111111 1.1111111111'111 Il'' .............. ; .................... 1 1l1l1l111l1l.1212111t1l1l1ll 82 ..................................... 111111111111.1 "'11111111111 SI" ................................... 1.11111111111.. 1111111111111 U ........... t ............. I ........ III1I1IlIIt·U. 1111 sa .......................... IJlIIl ... Il1llllllllllll. .. • •• .................. .... • 11111111 .. IIUlllllllt 11' ........................... IIIUllllllllllllUI SIl .......................... 1.11111111111111111 •• ............................ 1111 11111111'11111 .. ............. 1 ............. 111111111111 .1 .111 •• 11 •••• 1111 ••• 11 •• 1111111111111 Il 42 .1111111111 ......... 1111111111111111 Il

411 .111 U.llllIlIlIllI.III1I1IlIlIIlUI:::~~;~;~ .. 11111 JI •• 111111111111111 111111" 111 4$ 1IiIIJltllllll ... llttUllIllIllllIl '" 11I1I1I1l1I1 ..... 1I1l11I1I1I1I111I1 • 7 Il.1I111111U ...... 11111110111

1

48 11111111111111 .... 1111111111111 •• 1111111111111111111111111 $ •• 1111111 J1111 1I11111l11l1

I:~ ::mm::all::m::mlli~~~~i 113 1111111111 11111 .. IIIIUIII

'611 111111111 l .. 111111111 ,57 \1 11111 1 M 1:111111 .. " , ,II '))

F:LS. 2.8 Mean dBz f:Leld for Phase l

/

.---- ..... .­• • • • • • ~ • • •• Il .. .. •• •• 1 • . ., •• •• .. al .. .. .. .. .. !If .. .. .. a • .. ... _ ...... - ..

IJIIPI~· .. .. .. ... .. .. .. •• .. :: ... .. ." .. .. .. 81 .. .. .. .. .. 11'

:1 :,. .1 .. .. .. .. .. . ., .. .. ft ~. ft ft ft

iï#a-... I: n ft

" • al • • ..

. ~ '.

(

l' r t ~

l, i

j

f , ~

, _______ ~ _______ ~.~ __ ~ __ ~ ______ _w __ ........................ t~: ............................ ____ ~ ______ ........ ..

32

• 1. 15 ft ft .. .. 4e'" le as " 611 T. - -YI .. es 1 ................ _ ....................................... . • ............... .." .. »................. . .................... " .. *. · ".............................. """ ... ~ ......... " .. """"""""."".,, • .~ ••• e ........................................................ ~ï:llr 15 •••• ,." ••••• _ ••••• *........ """""""""""."""".""""""""""".,. .... ",,,,,,, ~! !! 1 6 .......... * ••••••• ** ............................................... Il !!!! 7 ....... "'f'R*& ................ •••••••••••••••••••••••• 1 •••• " •••••••••• 1. J'J"'. • .... ,. ............ _.... • •••••••••••••••••••••••• 1 ••••• ' •••••• 1111 •• 111111 III • ~ •• _* ....... _.~ ................................. 1 ••••••••••• 1. 111111111111111

Ile ...................... • ............................ 1 ........ 1.lIlIl.111I11I1I1I1 1 . Il ......................................................... 11.111111 1 1IIIIJJlIIJ~~:

, .a .......... "....... . J ...... ............. a .................. 111111 J IJ J J IIl1a"IJI !! ! IS ...... "*, ........ _ ................... 1 ............... 1 ....... 11111111111111 11111111 ~ ~ : lot ....................................... 11111 ... 1 .. 11 ...... 111111111 1 1 11111111111 ~!.l.!J.!: Il ......... n ............. 11 ....... II .... 11111 .. 11 .. 11 ..... 111111111 1 1 Il ~ II 1,

'1 •••• - ................ 11 1 ...... 11 .... 11 •• 1.1111. 111 ..... 1 III Il\lt r 17 ..... _u ............... III ..... Il.1 Il Il J 111.1 "llltll.I ... 1 1121111

':: !:::::::: .. 1 ~ :i:li i: :11 i:::: li:::::::: m: Il 11~11Jl: 1:: i :~lm::Hl '2e ....... ·A •• 11111111 1 1111 ••• lIll

i N!il 1111111111 Il ~!. Iii, 1 .. !~~i i ii

1~21 .......... 1IIIJlIIIIIII~~11I11I1I1 1I1111111~:~: ... ::ffif"lJ'!l: •••• l'irllllllllllll 1I11l11l1l"t~ [Ill!'

.1" ...... UllllJ1l1lllll1 ~J!III1II:lt:~l1i~ ::l •• _..... 1111111111111 JI I.'!'l' Il:

I ~I. ua_.' .. 11 1 1I11111!!1 ~!; PH ::11 ...... .." li .. "'... .. 1I1111:U ,1" ~~.I ji 27 ....... IIIHIII..... . rii ~ :::. iiiill::1JI j~ï:''''>''-''''~[In !! a. 1\1111 Il Ir' 1.1111 .a .s 1111/11 'li ::;JI ImW =~~ lia • 1111111' /1 a ... 11111 lia

'83'1 11I1 U· 1., .. III illl; la. orj 1111 ' .. ~IJII 1*':'1. ,:: 147 ,...A

Il:: ~:}I s. !II .a 'n 1 ...

1

:: 17 la

,1" ... !~~ ~

•• • 1 .. .T .. .. ..... : T •••• \: 71 T2 T3 T .. 71 7. n TU .,. 1:: a:&

li : 1

:;.;,

C W ...

~I .i! , ............ .

art NI

"" lM ,.". ....

, ... ~

,c,

4 ...

.it .. ,

.~

Il

..... I~ •

• • • • • " • 9 1. Il ,. 1. 1. 1. 1. l?

.• a •• -:u a

!!t~= 28

!~! .. !H\5S !~:e ::

"HU !!:i::: H~: / W":

41 .. 48 44 .. .. 41' ... ft .. i

=;; .à .. .. .. .. .1' .. •• .,. TI ft Ta Toi Ta 1'6 7J' .,. n -81 a es .. es .. 1ft .. et •• •• .. .11 ~

[

iL •• .,:1 ... , ..... , , •• ')ou ...... , .• !.,.,.,. • • ................... .. ........................... !! . .,. ." ......... . :: ::::::::::::~::: .... ............. 1

~~~~ •• *.*~* •• ~ ••••• ~ •• * ....... * ••. !!

Fig. 2.9 Hean dBz field for Phase Z " ..

• -------------------.-. -----' ...... 9'.", """,,--,u;:t:'''''''"'''':: •. ;-, ..... <o::iU!\"'Ç'il"'7t,.'7 .. tl·:~"i.!».":';1!.~:;:.!'i"' .• 1::''.l'd'!':!.-..... __ .. '"''

(

III '2 '1 '4 \1 ••

1

·7 III .t =­lU 22 Ils 24 21 116 11' 211 2. lM 1. 12 III H III .. U .. S' .. 4 •

. 42 , 4t

lE 47 te

149 ,H

\:~ ,R ':;4; lB

" ST III

1 1. Il

:: ... t..I..<I. 6. :-..

1" l':; 1:: f ~1

,': ;; 1 ;: •

r4

l, ru

Tt ,:;

/

183, ........ ~ r'~~ 1: .M.o~

I§ I ~ t"J , ta 1 t. 1:: ln j ta : ... il ..

"".

Fig. 2.10

-------~.

33

of ... • ••

.... ~ ".

::~: ., II:U ::.

1i~L • ...... "lI

~.~! ' ... ~.,,..,

:: .

'ilt: " ~:~ .. Il ••

"';

~I~. ~ !.

i , 1

..

1 t

'. 7. TI .. .. .1 ...

1 • • 4 1 1 7 1 • •• n Il •• '4 Il '1 Il' '1 '1 .. •• .. .. If Il .. 11' .. .. .. ., .. .. M .. .. .. .. .. : ta fi .. fi .. 41' fi ft .. •• •• U M SI .. 17 .. ft .. • t ..

_~~':':.::== .. ::_~ir:::::~:~: ~:!~I;~ .; .. .. 41' .. .. 'te 1'1 ft ,. .,.

..... , ,.",,,,,-,., .,. ,........ . ... , r' ..... .

71 .-_7. n .,. 1'9 .. 1. BI • et • .. lit .. .. .. 9' ta .. ft te .. .r .i!

Mean dBz field for Phase 3

.. ,

'.e i~

! ; " • t.';' l) • li ,~

~' ~­.. " ,

i l'

,(C r •

f

,

th

34

..

.. this decrease 18 not overwhelming. Having noted these non-meteorological

feature'S. a review oi fig. s 2. 8. 2.9 and 2. 10 shows that these do not reveal ,

any radial sectors or concentric annuli about the radar - - effects which are /' ,

indicative of biased radar operations or faulty data processing. One 'concludes

that the QUADRA radar does not suIfer apprec~a,bly from any serious range , -

dependent errora in receiving echo information from arbitrary directions

and ranges.

These figures aiso show a dBZ "swath" slightly south of the radar

oriented SW to NE , which lies farther north in phases 2 and 3 relative ta

phase 1. lt must be remembered ~hat although ,QUADRA's position was

slightly farther south during phase 3, this moyement is a reflection of the ,l,

northward movement of the Atlantic Intertropical Convergence Zone during "-

"" the sumI'l\er mo,nths (see Hudlow, 1977).

2.4 sum~ /

\ " Pert,inent ràd:~r theor\ as applie,d to the QUADRA radar was' reviewed

in this chapter. 'A rE!lation \as derived which ,relates the intensities re-" \

corded on the QUADRA'Î'l1,agnet~ tapes and the Z ~alues obtained from the \

meteorological radar equaÙon. A review of the QUADRA radar hardwit-e

was presented along with th~ limitations of the radar data set. Finally,

an_analysis of the -average daZ field about QUADRA showed that the radar

data do not suffer fro,m serious range effects and that thé northward move- "" 1

ment of the dBZ .flswath" might be a reflection of the movement of the

Intertropical Co~ver genee Zone.

"'~""fi __ ._",,_"" " ___ ~V ____ ",r-"-_""

~ ~ .. >

t /,

f 1

1

l 1 t I!,

f 1 ~ f

.1

~ t ~"

j-

1".",. ft lb 4_ '. M ....

(

'", r· i,' ( ,

"

()

11 ._ ~f

C hapter 3

Derivation of a Z -R relationship fOf GAT E

3. 1 R aison d'~tre ,

"

• T 0 date, one method used in GA T E to derive a Z -R r,elationship

has been to link the ;rainfall rate R and the reflectivity factor Z through drop

sÏ2:e disfributions. This has been done by Gillespie (see Hud10w, 1975) 1

for GA T E using aireraft data and a shipboard disdrometer. H ow ever,

the use of a disdrometer on ship presents problems w hich are not encount-

ered on land. The two most important problems are ship vibration and

turbulent flow patterns due to, the ship superstructure. Both of the se effects

tend to cancel the smaU drop contribution to the total aecumulated raine .'

F urthermore, the disdrometer infers the drop diaméters from their momenta

w:here the drops are assumed to be falling at terminal velocity. This

assumption is questionable due ta the .spurious flow patterns caused by the

ship. Finally, the drop size distribution must be related ta the reflectivity

factor Z through the relation? = I:D6

, where D is the drop diameter.

Although the disdrometer has been used suceessfully in the past, an alternate \ . method (similar t~ Smith et al (1975) and Hodge and Austin (1977» is

\

presented for ~èriving a Z -R relation which, although admittedly empirical,

is more direct and rriakes few assumptioI\s in going !rom the reflectivity

b factor Z to the rainfaU rate' R except that thes'7 ar~ related by Z :l: aR

where a and b are emplt-ically determined constq.nts. The method involves

a direct comparison of the QUAD R A radalj observations (Z valuês) and

, rainfall observations from shipboard gauges. The method has been used

/'

------ -- .-.. _~_._--,.-, ..... )...~--- - -- ...... -.---_.- ~~. --_ ... -~~ ...... -.... _--~-------

i ·l 1 l

1

p

1

, r ! f ~~._""~_w==~_. ____________ ~ _____________ ~ __ ~ ___________________ '_,~~ __________ ~ ________ ~ __ "fI.""

(

.- --' ... -

36 / ,

.successfully by Smith et al (1915) although their work was done oh dry l~nd.

Although a rain gauge on ship does suffer from exposure problems. the s~ip

, vib~ation does ,not appreciably influence gauge (not iipping-bucket) perfor­

mance as it would a disdrometer. However,' since the' wiIld speeds dUl'ing

GATE were rather light. the exposure problem for the gauges is'. reduced.,

Wilson (1910) shows that radar provides areal rainfall estimate s ,

w~ich are comparable to a close network of g~uge8 and as such. obtaini~g

a Z -R relationship for the GA,TE' area is meaningful. The same paper

concludes that even ~ one gàuge compar~son fo, the radar reduces the R . .M.S.

error of the radar by about 40%.

3. 2 The opt-imization technique

3. Za Theory ,

The technique assumes that a Z-R relàtionship'in the form Z=aRb

exist& Smith et al. (1975) have used a 8irnilar technique although theirs is

a convergence optimization procedure due to Hooke and Jeeves (1961). The

present technique uses a multiple regression approach; rA computer

program. first used by Hodge and Austin (1977). but extensively reformulated

for this particular application. tries different ~alues of "b" while at the .

same Ume varying lia" to obtain the best agreement between the gauge

observed rainfalls and fu~' radar derived rainfalls. The quantity optirnized

- in t'he program for the best Z -R relation will be discussed later.

If one takes logat:,ithms of both sides 'of the equation Z = a Rb ,one obtains

log Z = log a t b log R.

The straight line form of this equation is shown graphically in fig. 3. l for

- -*_ ... - ~ .. _ ... ~~ -! 1 A -~->II"'--- ~ .. ..- ...... "-"'- ~ ."'-.. .. ~-; :--.~-j P'C\~ ~, ::1 ... ::;;:;;iL.- ..... "2,.û>::::t, ..... ..P .... _,::t:::3Z·

!'!"f' ~

\

~ ~

-III .... ... I=l ::s >. ,.. 1\1 ,.. .... ....

..0 ,.. 1\1 -N ~ 0 -log al

" log a

2

l''t ,\

RZ -- --- - - - - - log Zz J

10 2

log R ( arbitrary units )

Fig.3.1 Straight line graph of the equation

Z=aRb for diIferent "a's"

.... - .... ~,,;;:e tS (Bi(........,.!t:ttJ>'*('~ ............ 'r~ '" ~ ... ~«:<7"'WE4-..,.--~\'" ,.-..... ~ ~ ,.. ~"', ·-..'iO:'~M'r .... :~Çi4m

III .... . ... ,::: ::s >-,.. ni ... .... ... .a ... ni -N ~ 0 -log a1

t'""\.

o

1 ___ ' ____ '7R.!/-Ij~loB Zl

_____________ 10g Z3

log R ( arbitrary units )

~ -J

ti

Fig. 3. Z Straight line graph of- the equation

Z=aRb showing different

log Z = cons tant

"

! i ~

1 !

1 • ,

-\

• i c; •. 'i

(

f "

" ,;. f.' i r

t ~~

{ f \\~

• f

< <

i ~

(,'/ 1" ~ !

i ~, 1

l • , , t ~ r

,,~ ~ ~

f t , f

t

[ ,

1 ,

t ~

1 '(

, .' 1 _ ........ ___ ~_ ....... ''-______ ~ • .'1/! ,~ _______ -1 . ---J 'r 1 •

38

different ~ntercepts (log a) "but the same slope (b). One assumes that the

optimum' Z -R relation is represented by the line containing points RI and

R3 in fig. 3. 1. Also, one assur:nes that the program ,attempts a Z-R

relation represented by the line containing the points R land R, 4. Given .

that the Hnes ha:ve identical slopes but different intercèpts, one seeks. for

a given log Z = con~tant. 'a relation between the rainfall rates - points RI

and RZ and also R3 and R4' Examination o{ fig. 3. 1 yields the following

equations

-log Zz = log al + blog RI:; logaz + bIogR Z

log Zl = log al + blogR3 :;: logaz + blogR4

Thus, log RI :; (log Zz - 10ga1)/b

log RZ = (log Z Z ,- log a Z) lb

log R3 :; (log Zl - log al )Jb

log R4 :; (log ZI :- 10gaZ}/b.

From the above equations one obtains

10gR2 - 10gR l = 10g Z Z '- log a Z - log Zz + log al = (log al -log àZ}/b

b

- -log R4 - log R'3 :; log Z 1 - ~og al - log Z 1 + log al == (log al .. log aZ)/b

b

Hence, log R 2 - log RI = log R4 - log R3 = Kl

o~ lOg(:lzt IOg(~: r KI Thua, RZ

RI

KI = R4= e' :; KZ ( a constant).

R3

( a constant)

l, It can be shown that uaing any arbitrary log Z yields -

R Z = R4 = .•• = Rm :; Ka -- --RI R3

.,

IR n

"-'"1, '<~"'V'M~F~!st{';~'w-1'tjWl tj@fJJ!!?, ~l'RJW.t .... )J _ ... t ~~ti ~!./ ~ t~ ~'"' .).~'\ti';i ,/it~ "':;~~~<.1):~~ .. ~".,,~:' .~~.~ .-!":.à,ÜÜI!BM ....

MI FA""''''1l:

1 ., f

~:' L,'

" , li<

,;;, <

" ~

CI ',.~

1 ~ ~, ;!

t . '1,

1 <-~ • ~(

~

i

(-

. '

_ ... ~ ~~ -~ .. -~ .......-....... - ... -.....-.----------_ .... __ .... _---'-----_ .......... ' 39

1

1

The above result shows that for any two Z-R relations of the forro Z = aRb

which have the same iexponent lib", the ratio of their respective rainfall

rates for any given Z is a constant. It can also be shown, rather trivially •

that if one of the rela,tions vylelds the rainfall ratee RI' R l' ... RN' while

the.o~hér relation yields RI" Rl' •... RN

'. then

N I:R.'

. l 1 ,,= fil

/ I:R. = R '= R 1 = .i".l l 1 l

RI Rl

see·(fig. 3.l).

=K l eq. 3.1

The above hol~8 true onLy if the Z -R rc::lations differ in coefficient

only. Use will be made' of eq. 3.1 in the following development .

One assumes that the optimum Z -R relation (as shown in fig. 3.1)' , '

passes through pc;>int Rl' It is also assumed that the computer program is

testing 'the Z!R relation passing through point RI where it has been e stab­

lished (in the program) that the xatio of the rainfall rates (fol' Log Z=constant)

from each Z -R relation is a constant (= K l ). This is equivalent' to saying

that the slopes of the two relations are identical although their intercepts ,

are different. Knowing that'Rz = ~2Rl one seeks a,. relation between the

_ intercepts,a'l and al (see fig. 3.1).

From fig. 3. l, one p.as

RI' = exp log Z 2 •. log al

b

RZ = exp log Zz - log a Z b

/'

Combining the above two e~uation8 and recalling that R Z =, KZ RI one obtains

""P ( log Z \- log a9 = ~;,,,p ( log Zr log a2 )

~ ? ~

, ~,

t " t

1< j . " ~~,

J,

f 1

{ ~ t r

.J t - - ,~j .. 'r~ ... _ ... __ -r-_______ ~_+------------""'t..;. ..... - ... --..... _ .... _.;;..,.ioI. __ ....: ___ ' ... _., r~l" "P

(

- /

Cr 1

40

Mathematical manipulation of the above yields

-b a 2 = a1KZ .

.,

The followin~ conclusions result from the foregoing analysis. ,

• .{3

(1) If two'Z-R relations differ in coefficient oruy. tb.en the ratio , of the ~espective rainfall rates for a~y arbitrary Z is a constant.

(2)

(3)

Thé' ratio of their re8p~ctive r~infall rates for any Z ie identical to the ratio of their integxated rainfall rates for aJl Z 1 S.

If two Z-R relations differ in coefficient oruy. the relation be­tween their coefficients .is aZ = al K -b W1ere KZ iè the ratio of the rainfall rates and b is the eXPQn~nt in ,the Z -R ~elations.

3. lb Tlte computer program

o The program's input parameters are gauge accumulations and Z

values fo'r the same period as the gauge accumulations. The Z values are ,

not averaged but are dirèctly convert~d to a. r"àinfall rate through an, ass.um.ed , /

Z -R relation. The program uses an ar~ittary but fixed value for "ail in

the relaDn,Z = aR b. It then sequentially utilizes different values of "b"

until a termination criterion - which will be disc~ssed shortly - is satisfied. ,

Ole assumes t~at there are N gauge accumulations and N intègrated o

Z values. Using a fixed lia" and "b" the program. éomputes the radar

derived rainfall for each Z value. The N individual gauge accum,ulations

are denoted as G. and the N individual radar derived raiilfal1s are denoted . 1

., \ ~

as R.. The pro gram. com.putes the ratio G./a.. for aU N values. It then / 1 1 l , .

changes "b" and computeJs the same ratio. The ite~ation continu.es until /

the ratio of each Gi /R_i is t~e same ~onstant. At this point it is known that,

the program's proposed Z':R relationship has a'slope identical to.the optimfm,

Z-R relation. This was sho-wn ~ conclusio~ (1) in.the previous sec::tion~ j':' - As well it is now kno~ that the o_ptimum Z-R IS intercept is related to

i 1

',. j ---------.~. _=l''~'i!~-''''''''''~~,,,,S''' ____ _

r

• t

~~ ~ f, i'

\'

\'

, ,0

• l'IM J' t "~ .. ------------.. --... -._' ------______________ ~ __ ~'~[ 1 .~~----~----~~--------.........

(\

(:

41 , \

.-,...,., , -b '

"";h~ p,rogram l s Z -R by the rel~tion a Z = al KZ where KZ i8~ the ratio of the /

''total N gauge accumulations and the total N radar .derived accumulations. l '

This was shqwn in c,onclusion,s (2) and (3) of section 2. Zao Hence the "\ 1 J

optimum Z -R relation is unique1y determined. A flow the program

is shown-in fig. 3.3. (See Appendix 1 for FORTRAN (~---- .

3. Zc Numerical test of the program

One crucial test performed was to evalua'te the insensitivity of the

program to the selecti~n of the coefficient "~II in Z ::; a Rb referred to in the

prev:ious section.' Fig. c3.4 shows the results of this tesf with a = 100. 200.

300. 400 and 500. It can be' seen that the program gives identical' results

regardless of the choice of the initial coefficient lia".

As stated previou~ly. the QUADRA radar has the capabili~y of

attaining resolutions of approximately 2dB Z. The conventional gauges

used during GATE could measure rain to a resolution of about 0.25 mm.

With this uncertainty in radar signal and limited gauge resolution the ... ,. Il

expected ~sut'ement error can be evalua~ed and is shown 'in fig. 3.5

whi~h plots error boxes on the 1ine Z = 300R}' 3 The yertica1lines show

the radar uncertainty; ZdBZ ,.above and below the nominal value while the , - . 1

horizontalline,s ,show the expected resolùtiUon error due to the gauges. The ...

above uncertainties as sum.e, however, that (l) there i8 no beam attenuation.

(Z) the beam radar volume i8 completely filled and (3) the gauges have

proper exposure. It can be seen in fig. 3.5 that at high rainfall rates the

limited resolution of. ~e gauges becomes insignificant while the radar ,

uncertainty is constant. One notes then that even with the above three

assumptions anQ aS6uming that the sample population has no statistical

Mt 7 ,

, ......

. ~.

Π~ , ~~

'e t fi

t

." __ ~ __ -L-. .

C' INPUT

/'

o

1

/ (J

( .

•

{

~ l'

co.put. rat10

1 IJ

F1aure 3.3

1 t

42

"

N ,aug. valuee

)

YES

\

If Z values

assulle b

/

..... _-;;--...... ~

1e a CODstant 1

coa»ute the 1ntercept stat. the alop.

f

Flow-chart" or coa»utar pro&ra. u.ad to dari.. an opt1aua ,-. relatloD8b1p

(~" j

c-.~~· /

/

.Mo - , ........ ,.":P" .•

•

,1 1

liibi'i ;:u ;;:;;;; :1:i;~:·'I:l;;:::: l:t::.~~,~=:.: : ".u,.d._Îto1illJdse: StUI'......,.'._ Pi $4. 1q:I4!14 ..... ~""'<p,i!~".~ ... l>4~4M'!~ql_iiQ"t'!i;::;~

~

" ."

-JO-

.j

i \ j ...

CG

. ~

\

\

~

'" \

.0

o

tOI' a • 100 200

.300 ltQ() SOO

~

~

.00 1 Y 1.6 1.8 2.0 _%pbaet

0-

I,~ ~ /,

'--

1.0 1.2 1.4

n.aur. 3.4 . Variation 'ot atandard ·deviatioJl rro. thé rat1o~ 011Bt W1tho .... ÇOftU\

ua1.Da titterent "a'.a" /

~.

.,

.. VI

.' '';.

, .

f 'f ~ -" ;/.O'~"', f"~ ," ~ ,,~J • " ,\,\. ~.~ !.~: .... ,. ,r -: ~ ..... ~" .. 1) •• ' •

1 ~ .. r:tir··r' 'If rtf'~r r~' 's "',~ ...

44 40 ,

J , , :,-

, () -:( al . Je,

..., " :" \ 03 ,

Il ~ fal· 'f • ~ .. -.'" " ~ ~ '\ a.:,..:J

. s " p; 2 -..

tIC 0 'Cf

W • ..., , , u .,. •

~ 4)

0 • 4)

\ oC\! .Cl

\ \ ~ ,. \ \ / 0

\ \ ..., \ \ ,.' Id

A \ \ \0 ..., , • '\ \ ri .....

\ \ • 1 ~ ,

-\ \ ~". " Il 1

~ ,C\I N

• ri 4)

A .. f"'f

4)

~ CO " • 0

CD •• "

j '.8

Je ..:t' 2 • ~

\t\ . rt\

• 0 •

~.

i'! ~

--: .:t' ~ , ni 00 ~ ~ \0 ~ '" .;t ..... ni

(2S(P) 2: ~Ol ot

(." ., /,

~ ) '.' : ". t ,;

, ' ~ "'" 'li "l î:&, 1SK"i\l!lWj~3@JJt.Mli'JffiM ' " 4S 1,. ~ t. • ,.. > ~ lt.1J:H .<;'

...... ----------------,---~--------------------~.~' .... ----------------

(

45

/

s= 1.6 0 ... ....

'" .~ l.Z 41 Cl -t:I 0.8 k ni 'è

~ 0.4 fi)

0-.0 1.0

exponent

Fig.3.6 . Standard Deviation/from the mean .,

c:: 0 .... ~ ... '> Cl Q

'tf J.t' ~ 'tf c:: S (Il

ratio G./R. ("perfect data") l l

Z.O

O.

O.

O.~--~~~--~----r-~

1.0 1.Z 1.4 1.6 l.8 Z.O exponent

" Fig. 3.8 Standard Deviation hom the

mean tatlo G:/R. for the test· 1 1

, 50

.. 0 .. ..

Cal tJ!.

J.t

e

L

40

30

ZO

19

0 l.0 Z.O

exponent

Fig. 3. 7 % error of radar­

deri,ved accumulations

("perfect ~ta")

50

40

.. 30 fzl JI!.

20

10

o 1.0 l.2 1.4 l.6 1.8 Z.O

expo.nent

Fig. 3.9 ,. error of radar -

derived· accumulations for the

data of Fig. 3,5 , .

, test data of Flg. 3.5

, ;

----_IO!'I' ... '-. -----_ . ......,.,..,~

, , '.

....

(

•

i l }

t r t r ~

~,

( , ~

f J > r } ~

t ~ J

f, k l,

t ~

1 .~ . i ~ ( ~ 1

i , j

~~~''''',..:-

/

46

variability. the best e~timates are limted ta those enrrors shown in fig. 3.5 .

Figs. 3.6 and 3.7 plot the program outputs for "perfect" data as de-

fined above while figs. 3.8 and 3.9 give outputs {or test data with the

unce rtalnt y ,shawn in fig. 3.5,

One sees that for figs. 3.6 throu'gh 3.9' the minima in the curves give

the exponents for the optimum Z-R relations. The coefficient is calculated 1

separately by the program for the exponent which gives a m,inimum in the

èurves. The variation of the coefficient'with exponent carries na meaning

bul once the coeff~cient is, found, one can see the effect of varyj,ng' the

exponent on the radar derived estimates as shown in figs. 3,7 and '3",9. '-

3.3 Summary

An a1ternate method (similar to Smith et al (1976» of deriving Z-R

relationships which compares Z and R directiy has been discussed, The

theory and the testing of the computer program has been demonstrated.

Aaide/from the Cact that fuis program was utilized primarily to derive a

Z -R relation for the GA TE area, use of the program could be very beneficial

in operational applications to lDcorporate d,ay-to-day or storm-to-storm

variations (perhaps .with ~auge telemetry) in, a. Z -R relation. The

distinguishing feat,ure of the program lies in its simplicify and its

incorporation of few theoretical assumptions.

..

~ -... -.~.-._.-~ "---:--, &7"":"~.'r""'!-::~~~,~:"'l''''.!.-j~'''':' .. /-':':'''-.-~ .. ~~.~_~~\ ::::.~ ___ u _,,"""i_ - "'~. "'" .... 1 ,~ ____ _

- ...... -fi Il "'~~--~;':..er...';!:"d·)" ...

1 " ..

) 4 ;ag t

t

t

\ .'

'. ,

t # ç

•

~

1

& f

t

\.~~"~tttw~"'·I'~.'________________________ -______________ ~ __ ............ ____ .. _________ ~~ ______ JI . ~ - ~. . ... _-

(

(

( .)

,....,.~ ... _' .. "n

47

Chapter 4 ,

') ,E xperimental w ork

4. 1 f'l avigation

4. la Precipitation aloft versus precipitation at the ground

In order to Unk radar Z values w.i,th .sauge values it is necessary to ,

observe echo returns above the gauge and h~othesize that the precipitation

observed aloft by the radar is the same as w i11 ultimately be observed in the \

gauge. Two difficulties are encountered in this re6pect. The first is that

the sarnpling volumes of radar and raingauge are very different w ith the

radar's sampling volume being typica~ly larger by at 1ea'f. a factor of 1000

as presented in Roesli and Waldwogel (1972). H owever this does not reprel-

sent a major problem and meaningful results have been obtained by previou 8

investigators in spite of th~ disparity between sampling volumes. The second

problem is the effect of horizontal motion of the prec,ipitation due to wind which

might cause the precipitation aloft to be displaced horizontally by the time it

reaches the ground. The problem can be solved however either by trans-

lating the precipitation pattern with the wind speed and the faH velocity of the

preèipitation or by extrapolating the radar information from different heig~ts

down to the ground. ' Both of these methods have been investigated .by Austin

and Ahn (1913) and Srivastava (1974). , The correction {or the effect of horizontal motion lS not introduced in

this work sinee. rather light wind speeds of about 5 m se.c -1 were observed

throughout the days used for intercompariaon. The effect of a wind of

~

;,

r ,

'.

~, ~ . J:

-? r

t

f

r 1

l

<'

(

, __________________________ . __________ ~ __ ~! ____ '.u~, .. ~*~t ______ ~ ______________ ... ,..' 48

-1 . 5 m sec could displace a precipitation pattern by approximately 2 km from'

the re,gion wh~re the pattern is observed to the area C?n the earth's surface

where it falls, assuming ~ drop faU ~peed of 10 m sec -1 F urthermore,

P estaina-Haynes and Austin (1916) report that precipitation patterns, speci-o

fically precipitation Unes c6rrelated w ith the 1000mb w ind were observed to

-1 move rather slowly at a mean speed of >3 m sec during GATE. The effect , ,

of horizontal motion is thus quite negligible in, the present study.

4.1 b Mean ship positions

)

T he GATE ships kept tbeir assigned positions by a ffsteam-and-drift" \

mode. A lthough o?,e can define mean confidence drcles within which a ship

is expected to remain, the deviations from the ,mean are tao large for a com­

parison between Z values observed, above a ship and tJ:1e gauge (0,1' gauges)

mounted on the Bame ship. Table 4. l, supplied by the "National Oceanic

and Atmospheric Administration" using navigation data obtained from the .

"National Climatic Center, U. S.A. " gives mean ship latitudes and longitudes f •

for OCEANOGRAPHER and QUADRA and also gives frequencies (as percentage)

of various deviations from the meane. ,It can be seen that even w hilé' accepting !

a 90% confidence limit, the relative positions of the ships are known only to , . about 12 km. This is unsatisfactory and navigation by mean ship positions

was abandoned. 1

l f' 'i' "

~---•....

{

---~--~- --.. ,~ .. _--_ .. -.... - ........ ~---,_--,... __ "'"-___ ~ _____ ....... t .,.

49

TABLE 4.1 Mean latitudes ancd longitudes and frequencies (in percent)

I\Phase of various deviations from the means.

Ship Mean Position

1 OCE02 OS030'N 23

029'W

2 OCEO OS030'N 23°30. S'W

3 OCEO 07°45'N 220

13'W

1 QUADRA 090

17'N ZZo09'W

2 QUADRA 090 l8'N 220

09'W

3 QUADRA 09°0Z'N 2Z035'W

1 \ ~ Nmi -= nautical mile = 1. 852 ktn

OCEO =' OCEANOGRAPHER

\ \

\ ". le ! Matching PPI's

,

\

percent of hourly times within 3 Nmi ff 5 Nmi of lONmi of mean mean mean

90% 95% 98%

95'0 99.5% 100%

95~ 99.5% 100%

92'){. 97% 100%

95% 99.5% 100%

80% 90% 97%

puring aU three phases of GATE the ships QUADRA a.nd

O~EA~OGRAPHER were within radar range of each other. This offered the

pOSBibility of determining the relative positions of the ships by matching

precipitation patterns from the PPI displays of each ship's radax-. Fig. 4. 1

shows schematically how the relative positions were obtained. . When the

corresponding precipitation features are matched. the range and !lzimuth of

one ship relative to the other are determined .

. 4.2 shows an actual PPI di~play from the OCEANOGRAPHER

radar 0 Julian Day 194 at 0800 Z, white fig. 4.3 shows the sarne for the

-

(

(r '

.. '

,",J 1 r

" "1 ~ f i' 1.'

50

OCElNOGRAPHER PPI QUADRA' PPI

Match1ns PPI's to 4etera1ne' poait10D(r,B) of ODe ab1p relat1ye to ~e other '

.. ,

, "

....

.,

, " r'

~,

l ~, 1-~ l 1

i' ! ~ J f. ~ ~

V. r~ r·

... ... " __ I ........ !HiiA\O~~I:;;;9i''''!I\lIfi\'k@l$d *"'1.,."i!'!~~~r~~"'" '"";"~"-9' , :wou:! ::W;N'''_ ; j$2: Li: iiJJIII kil!i '&4l.l1:4$tIlsllUg IItJ.4i1iS=: '~~"". \-" " 1:' ~ 1 1 j r ~ \ --1 1

!

, j

Fig. ".2 OCEANOGRAPHER PP! diBplay

for Julian Day 194 ai 08:01 Z

-

~-

~

..

• 1"'· ... '\. R""

tt'

\

~ ,. , ~ .,

Fig. 4.3 QUADRA PP! display for Julian

Day 194 a.t 08:00 Z with OCE,O ra.dar echoes

luperimposed thus showing (r,.) coordinates

(QUADRA a.nd OCEO PPI's not to sa.me Bcale)

"x

Vt -l f •

1 , 1 , •

1

1 '. ----- • - R , 8' ; S J

~

"'.ia SI.;; lj Mi.' Ag Ai lm", tii;llll!il$llWil!'_..M1!(i A {(\Ulllk 'l~iiM"Mlf!" diiAH\';;i!iii!!i.4X"'M 4 ,,%"i~~< ......

l, Il !, l' 0

d' L

\ .. o· -

, /

1"'.

'~,

1

Fig. 4.4 OCEANOGRA~HER PPI dbp1ay

for Julian Day 245 at 12:20 Z

;:,

-~-

• "'\

..: """";-~~~

1 _ -1 .au :kt =: -- ..... _, ___ ~ __ :r;::",1( , Hfrt .. ~~r.!6

Fig. 4.5 QUADRA PPI di,play for Julian ,

Day 245 at 12:20 Z with,QCEOradar echoes<·

.uperirnpo.ed

( QUADRA a~d OCEO PPI'. not to sarne seate)

<;'<

.. - ~ ,

.ut N

,

~ t

f f

; ~ :

, , '-r $ t j t !

; -

~~f"··~_'llô...w-.,. ....... _ •• _ .. .--. __ d'.W" 1III.2i"II~""''''~;''''41( .... 4 ;a .... d ..... II!I! ...... ___ ...J,.. ______ ~ ___ :..... __ ..r...._~-.:.î .,..:.. ______ '7.°. if

(

('.

(

53

QUADRA radar. Superimpo~ed on fig. 4. 3 a~e the radar echoes observed by

the OCEANOGRAPHER radar. lt can be seen that the echoes can be matched

quite objectively because of the Many "point" echoes observed by bath radars.

This. can be contrasted with the situation shown in figs. 4. 4 and 4. 5 taken

from Phase III of GATE. Although the echoes càn be matched there is room

for subjectivity.

In orde r ta evaluélte the variability in determining the relative ship

positions. a number of "matchings" were redone several times to-,deter~ine . .

the difference in range and cross-range for each '''matching''. Fig. 4.6 plots

the maximum differetlce in range for each of the "matchings" while fig. 4.7,

plots the maximum difference in cross-range. From these figures one

concludes that the av~rage maxi mum range difference for aU of the matchings l

is 2.7 km, while the average maxi mum cross -range difference is 3. 1 km.

Combining the maxi mum range and cross-range differencee yields the maxi-

mum total distance difference. This ie shown in fig. 4. 8. T~e average

maxi"mum total distance difference is 4. 6 km. As in the case of navigating

by Mean ship positions this average differen~e i. ~oo large. In fig. 4. 8 one

Sees that the 8mallest difference is 1.6 km and the largest is 10.9 km. Thua .. - ,

for the present application. the method of matching echoes was abandoned as

being tao imprecise. With the availability of the best navigation information

(described in the next section) it was, foupd that the average range error

between the PPl matching tectnicpe and navigation information was approxi­

mate1y 5 km- while the average cross-range error W&S about 6 km. It can be

Been that the naviga~ion information obtained by echo matching gives resulte

to within about 8 km and the method is quite workable (for other studie8)

though time con8uming~ , ,

...

(

. ' 0

. -(; '~

'.

(.

54

10 . -/ •

E ..!t 8 -4) U I:l 6 e 4)

'<-4 -\t.4 4 ... 'tS

~ 2 111, e/ 0

10 · e .!II: 8 -G)

u ~ 6 1)--k t)

:::: 4 ... 'tS

· )( 2 lit S

0

12

-· 10 e .!II:

G) 8 u J: G)

6 k G)

\t.4 \t.4 .... 't1 4 ,

~ \

E 2

0

f ' '- ........ """ fi -

1 , . '1 - 1 . 1 1 f 1 average max. difference = / /2.7 km. . ..

/ " ,

, , < .

. -1

- , - / r /1'

-. f

1 2 3 w 4 5. 6 7 8 9 ~ 11 -trial

~ig. 4. 6 ~a~imum differe~ce in range for ea/h "matching"

/

- / 1

a~erage max. difference = - 1

/ . ~

- . /

- / • , "

. - -

~ - r J ,

- 1 f r 1 trial 1 2 4 5 6 7 8 9 10 11

Fig. 4. 7 Maximum' cross -rang~ difterence for each "matching"

- -- dilfere}lce 4. average tnax. == 6 km.

~ -1

- . - '.

. -, .

> -, trial

l 3 4 5 6 7 8 9 10 n

Fig. 4.8 Maximum, total difference for each "matching'U 1

~ 'i )

(

1

JI' ,

I~ ..

• , 11 $" .' " 55

4.1 d Navigation methods: Satellite, celestial,' radar, dead reckoning , , \

It vias apparent that only the best navigation information could be used

to ,Unk radar Z values and gauge values. F or thi~ purpose, navigation data. , were ob,tained hom the navigation 10gs kept by the ships QUADRA 1 DAJ!.LAS

and OCEANOGRAPHER during GATE. The ship positions were determined

by satellite, celestial, and radar fixes in addition t<? dead reckoning. AU "

data ,obtained were' vaUdated by the Canadian and Arnerican national processing

cent?'s and then stored on magnetic tape. The QUADRA navigati~:m data gave

ship latitude a.nd longitude at approximate hal! .,.hour intervals to the neare st ,

thousandth' of a minute, while the OCEANOGRAPHER and DALLAS data could

be acce~sëdl as frequently as every tenth of a second. The OCEANOGRAPHÈR

and DALLAS data were fitted by the U .-S. National Processing Center with a

second-order polynomial in order to interpolate data to achieve O. 1 second

time r,esolution. These data gave ship latitude and longitude to the nearest

"hundredth of a'minute. 'Although the data are quite accurate, the coarse time

resolution of the QUADRA data, coupled with observations of the half hourly

(r, Q) coordinat~6 of one ship relative to the other, limited ship position deter-. -..,

mination to the nearest kilometer. The ~rogram used to obtain the (r, Q) ,

cooJ;'dinates was a great circle navigation routine.

4. Z Data manipulation

1

4. Za Raw data

One data ,set for obtaining r~dar Z

intensities'" referred to in section 2. 2e.

'" q ,. \

values was the B-sc~ of "tape number 1 ï

An example is showp in fig. 4.9 for

Julian Day Z4S at 17:28 z. ·TlJ.e azimuth runs from 165 to 185 d~rees while the ,

range rons from 45 to 65 km. The enc'irc1ed~ape numbers (producing a

J \, -,,' 1

iilihb l44 bUlL $ 1 li ft" .JQI"SIIII _,_ .. / ,\'. " > _. • ... ,_ de : !!!'I,e 44 *Il IiIIM 4 AI! tJ4iS Ibn ,._ • ,_-.~ __ ~.J J " ' . ~ 4li4 .. " 4 ____ .~ __ --<> < ,- -~ --' -',:-.<. $ ta:ctJIIIH

! i,

,!Tl

1 J

1

l ~ f l . ...

1 .. l .

!

j

•

'"

f":'.. '-" "-

,.,.

.. -

4l ,'-

" ...

"'.

"

" 10 f •

~ f------_______

, 24&' 1728 Ranse JWlcZ LIHITB-45-ro--6'S--- -~;...-- ----------------, 165 36-47414833 33 57 54.576265 6G 676163 67 64 64-61 61 67 166 48' 37 42 4e 59 56 33 44 14 ~9 64 64 71 61 61 64 66 64 68 89 63 167 49 S8 8448 SS 57 6'·47 49 GI(IS 63 68 6. 71 63 S8 62 63 64 7. 168 37 33 37 48 48 46 49 46 49 15 55 55 61 68 66 62 64 '8 61 61 19-169 28324146 n8 43 44 49 48625468626819 186368 68 67 64' 17e 29 31 42 33 31 49 48 42 14,82 ~7 62 6817 13 38 89 54 61 66 61. ;171 25 31 39 46 :U 53 G2 49 14 5S S7 14 63 S4 68 S3 156 12 68 63 56' 172 20 22 37 42 43 41 S3 49 35 63 11 59 S1 64 S7 69 S9 S3 S4 S5 S.

~ 1 A 173 16 17 29 48 47 38 48 49. S6 40 S3 016 35 se 62 6S c 63 62 S4 46 51' ~ '174 8 21 47 41 42 41 50 eu 38 48 S' S7 S7 6S 68 64 S86. 62 ::s '175 Il 35 89 51 42 41 4S 36 48 sa 51 S7 S2 64 S9 61 68 S8 ' .!1116 11 .. 1 41 11 .... 49 S'o 38 G2 as a. H 52 51 DT S9 cn sa' ~ 177 31 S3 47 45.43 47 47 ..... 41 S6 38 3. 47 SI S9 S8 64 a2 sa 89, -. 178 28 35 43 48,41 41 46 47 49 4,7 .. 1 ... 83 sa 41 sa se 58 62 sa 4a.

179 38 41 48 48 37 33 44 47 39 36 5S 38 32 2$ 31 39 41 sa tU S3 47 UJQ 34 44 39 38 41 36 38 34 35 32 32 se 31 rr 55 43 4S Ge 4& 86 44 '181 31 36 38 .. 1 39 41 33 37 31 ~U ~ 42 34 29 31 44 SI 46 47 49 S6 182 25 25 31 44 43 44 ~ 31 43 38 48 31 28 24 28,34 'as 48 47 56 54 183 28 26 33 41 48 41 38 3S 25 27,26 19 19 2$ 54 44 tri 56 65 58 58 '184 19 15 ~ 3fi 38 55 86 28 24 S"'~2 29 28 29 .37 48 5. G'1 56 G~ 47

01. \

"

Figure· 4.9.. B-acb c11ap1ay ,for J~i:.ah cllq Z4S at 17lasZ

~

...

(QUADRA pOa1t~on ~nd1cate4 b7 laner box ~ocate4 at asiauth 11'· and rance bin nuaber 57)

~ ... \.. '<C.,

-fi

.. ,.. .\ -~. .. " ~

'"

Ut 0'

,-.

~

f t f , i

--+-r

" ~

i. t ~ ~ ;, r ci

"

.. _ .......... J1I""'. ___ ~_".. ...... _ ......... _____ -..:. _________ ... , _. __ ..;...._ ...... ___ ••• Id ... ___________ ... _.

(

'"

/

C·

(

51

3 bin x 3 bin area) wer'e averaged and then convert~d to a Z value from the.

~ransfer curve of section, Z. Ze. ;

Beeauae of the uncertainty in shi; position

it was decided not to use s~lely the nominal value at the centr~.of the 3 binx 3 bin

area. ExperimentaUy it wa. observed that using,only the nominal value

resulted in situations where the raingauge reported precipitation while the

eorresponding Z value was either below the receiver noise level or was dis-. .

proportionately amall for the rain obeerved thU8 indicating that the ,navigation

was in error. Using a larger area than the 3 bin x 3 bin are~ was of dubious

value ~eeau8e of the averaging error introduced· by the "rain int~ns~y variabi­... lit y in space. Again .. experirnentally it'was 'e~n that averaging over !i large

area resulted Ùl Z values which wet'.e much too small. Of course, if the

precipitation were uniform as in stratifdl'm rain. space ave~aging would have

litUe effect. D uring GATE • J;1owev~r. much of the precipitation"was ,

observed to be of the convective (high intensity cores) type. Fig. 4.9 shows

this variability {or a typical rain situation.

The Z 'values'were obtained every 5 minutes du ring the length of the

storm and th~se\ were compared to 'the corresponding raingauge values in 1

order to obtain a Z-R relationBh~p.

4. 2 b PPI" data (into

erpolation of precipitation echoes âcrOBB ,QUADRA)

.. In some cases wh en both radar,and gauge information were ,available at

the gauge site, there also existed moderate or high precipitation between radar ,

and gauge. It has been known for a long time - see Battan (1973) - that at

a 5 cm wavelength. the attenuation experienced can be appreciable. ThuB the

Z values obtained in such a case wouldt be in error. <il

l

/

•

"

1

j, :

(

\

(

1 J

dt •• • b b

58

In order to avoid beam atteJ\uation problems and also to increase the

data set, an alternate procedure for obtaining simultaneou8 radâ'r and gauge

". . information was to use the QUADRA gauge and interpolate the QUADRA

radar ech~e8 over the ship. The need for interpolation stems from the fact

that the QUADRA radar scan mode was a stepped helical scan and this left a

,"cone of silence" above the radar' for which there was no echo information.

'ln ~ddition, observations of ocean clutter in early tests suggested a minumum

.,radar range of approximately 10 km. Hence the interpolation required was

one which operated over an area of at least 10 km x 10 km.

In fig. 4. 10 one sees tV10 blank areas of identical dimensions to that area

blanked out over the QUADRA represented by stars in the centre of the PPI

display. !ts dimensions are 10.5 km in ,the north-south direction and 16.8 km

in the east-west direction. It can be seen that isohyets (lines of equal rainfall)

can be traced quite objectively. Admittedly, the PPI field is quite uniform

around the blank areas, but onLy fields of the, sarne uniformity were used in

interpolating over the QUADRA region ..

In order to evaluate how well the interpolate'd value using isohyets

...

compared to the actual value, a test wa~ done by blanking out nurnerous regions

'~.on several PPI' s, ~nterpolating across the areas and later comparing these

values with the actual values. On fig. 4. Il is plotted the deviations of .the'

interpolated value from the actual value. On the abscissa a value of zero

implies no error while positive (negative) values show by how many classes

the interpolated vaLue overestimated (un'derestirnated) th~ actual value. From

• the same figure it can be se en tl).at 690/0 of the interpolated values are within

" II' one class of the -actual values. In terms of dBZ this corresponds to an

uncertainty (precluding radar calibration error) of 1. 5 to 2 dBZ depending

-------_ .. _-~~-------_._------~~-----'~~----~--~.--.. -~~~~~~~~~~ •

~. 59 1

1 .. .. ~.

( - 1 <-

~: fil

il "- .. ir ~ * -, • \ 111111111~~~:~:.~;lllll· njiU .. .. . . . . . . . ,. .... 1 1

~1:~W >-...... "il; .. ·· · .cl · . : : : : : : :t : : : : : ~ r' :: :: : : :: : : .. : "ut .. 0

t · . . . . . . . . . . . . .. . . . . . • .. . . .. . . . .. .. . , ... ,. ..... . .... .... · ................ ., . :~ : ::::::.::' 'II!::::;: 1:10 t· •• , • • ,. •••• C · .. . . . .. ....

'M i' .••.. . .. ~ · . ,. ...

~ • •• J •• • l · ..... j \ · .. fil .. . · . Il · • ... N fil

'"tI C'fl .. 0 .... C't'I d

"" fil / .... ... A l' •••• ft! " ....

J " QI) ~ .. ~

.. N d

" · 1 e >- .... fil Il

'B 'd :s C

.... .-cf > ... .... ~ ::s

(t ..., 11

/ · . ... fil 0

.... · .... ., . 8-. , ..... · . · . .... · ...... · ...... · . ~

... · ...... · ...... . .. Il · ....... ... · ...... .... .... · ..... ~ C · ....... · .. · ...... . .. • . ... · ...... ... , · · .. 'd .-.

~: : : : · . · .. ~ .. : = ! il: /

· ...... · . ... ~ · ..... .. . . . . ~ .... · .... . ... .... ~ fil · , ... \ .... tII · ..... .. d

/ ... · ...... CIII 0 · ..... .... · ..... ~, fil t •••••. · .. , .. r .. · .. · ....... · ..... · .... · .... ,.. ...... 0 "" ...... F. ••••• ... .. : : : : : • iiJtl T; HW .... Ile , ............ II·· .. ·· .. · . . ... Il''i'' ... Jz. " •• Il r.l!:

1~~III."II;II:;aaI'*;"~*1~tt';~=II.=I!I;I~ ,

,

, ... (, .- )

/

f .t .... 1 --- t.

lEi; ri' ~: : :a": ;'>: :::. ~ ': ':~:: : :: : :: :<.;: ~ ::::. :-:- 1:: :'t~-J~':/i ~-', Jlll III U~J 'li WMHM" l, bd, Z ",a<u _4.' ___ ---... '& d $

~ .. -

".

c

. "

l'

ii t

1·

., a ". -...,

0 ~ • g. • ~

~

,ff' 'b

o \

.f'\ .-

, ,

"-

401 "

30 -. • • ,"00 GaMa ..

20

10

~

0' Iii 1 E j i 1 i 1 i 1 i 1 i 1 i 1 / l ,Ii t;ç:t -6 -4

Figure 4.11

-2 0 +2 +4 ~6 cla .. d.1ftu-ence , Distribution of> 4e'f1au'oJUI of '1DterpolatH value fro. actual .&lue

• \

/

!"\

"" ç

"" 0

'\

. d

cl'" F'"

\

( on 'the rainlall rate corresponding to the classes. T he test was carried out , l

oN ith 100, different intêrpolations taken randomly at different timel! and at '

different locations. 0 n the basis of t\i: findings rev~aled in fig. ,4.11 it was

concluded that interpolation was a valid technique for the area blanked out

aroul)d the radar uaing the particular P PI representation of fig. 4. 10.

4. 3 E xperirnental results

~ \ ~ ,

r 4. 3a Intercomparison methods and limitations

i.

1 T hree different sets of data were used in the intercomparison. The 1

" r • first set compared the QUADRA radar echoes (as raw data (8ee sec. 3. Za))

above the OCEAN OGRAPHER with, the precipita'tion falling in a gauge

t f

mounted on the OOEANOGRAPHER . The second used the rainfall observed

i ,: ( " ,~

"

~

in the DALLAS gauge. ,Finally, the third set used both the QUADRA inter- ~

polated Z values (,J~e sec. _4. 2b) and the QUADRA gal2ge. r l f

Of aU 35 intercomparison events (or storms) available (defined such

, that both radar and gauge data were available) only eight atorma were found l

- ~t , usable. In many cases there wa.s much intervening precipitation, posaibly f

f t

, causing attenuatiàn, between the QUADRA radar and the gauge. This situation

1

1 ie shown in fig. 4.1 Z as contrasted to that in fig. 4. 13. The Z -R relation-

1 1 ships obtained from the attenuation case~ were extremely different from aU

the Z -R relations (see table 7. l Battan (1973) obtained to date by various

workers. -Table 4. Z lists some Z -R relations obtained from the attenuation

cases. In other cases when using PPI data, the field about the QUADRA was

both non·uniform and restricted in spatial extent. This prohibited the use

ôf the interpolation technique discussed in the precious section.'; An example

,0J this case is shown fin fig. 4. 14. In phase III, the DALLAS was within

j'

1 !

l'

1 !

, . . .

.'

~

\ ,

, \

il

<>

/

/ /

\

.. f. ..

., ..

Fig. 4.12

--'---"

- .. --~

ri"., f 1

t ".

\

\ 1 \ ,

.. \ 1

)

QUADRA PPI display for Julian Day ~,55

'. at 14:55 Z showing path from radar to gauge

"

'""~~.""""" ... 1~~ ___ ~ T,':,

,~

;\ ~

of.

, .. , • . '

, .~

Fig. 4.13

• -(

,~" "\ Lil A'

QUADRA PPI di .. play for Julian Day Z47

at 13·:58 Z .bowing path !rom radar to gauge

~ ...

t:/' N

~

. "

\ '

/'

'"

. "

, TABLE 4.i Z-R relations {rom attenuation cases

Julian Day Time (G.M. T.) Z -R relation

183 08:30 - 11:30 Z = 260 RO. 4

189 . 16 :30 - 18:00 Z \~ 143-R 0.4

C, 195 00:30 - 02:30 Z=172RO. 7

196 01:30 - '04:30 Z:l115RO. 5

196 07:00 - 08:30 Z = 266 R~·4 248 18:00 - 19:30 Z = 290 RO. 6

249 05:30 - 07:30 Z=293RO. 9

255 14:00 - 16:00 Z = 861 Ro. a "..

1 •

! .....

/

/ ./ .,

"

(j

\ . ..

. -_ .. -."' ........ - . , ----_ .... ~

ft biiWl

1 _ , ;

~ -1

\

il,ridë .. 5 il ; &;; ; 3 " Z % JI 1i(!lllliJ4i!Ot:e t: iii &1J!li\ &iilCaM $2 U .( ; u rn;;:;::;;." Cil (ttllU •. nP5iiIlU§!Qtllitn,4JS t 1Jii4 ,_.mh~·_- .-' -_ N> -, h ~" ~ ........ -"."

~ e ~

" .,. " ..

.' l'rt Of F.lJo:VATIOK

3 10 r FOlt DAY 196 AT

llJ 20 :m 3U n:27

33 ftlnnCTa ro

40 4U Be 55 68 6n 7. on 88 BIS 91 t:s 100 1.,:1 110 11:1 ID 12$ :JO 31

• !J!: n3 :1 .. :1;:; 3(, 31 38

. :I? 40 41 42 43 44 45 46 41 48

'49 18

................. f' ......... , •• f •• -' .7 ... 267 ..................................................................................................................................... * ..

.......................... 79 ••• ::us. 1. 9A!J7 ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 39"1",6 •• 6'1.7988 ••• ~ ................................. .-;9.11067 ..... 7 ................. 11. .............................. 1).666 •• 3379 \n.\667991W997B1_ ............................. 7:1 •••••••• 177 A9. 4 •• 97 ••••••••..••.••••••••••• 1. ••••••••••••• t .4676. MfJRl1I):!99 \q63~")c)II'IOq6693 ••••• • •••••••••••••••••••••••••••••••••••• 7776SDJ)(;n • .,1>, .............. T ••••• 1793 •• 664n?4." ••• 14. 44UI)099 \1199 \99c)i\d3r.'JII799640?1} \9 •••• • ••••••••••••••• , ••••••••• , ••••••••••••••• 3ACI\OO. 23 ••• 21 •••••••• 1 • G3G9.\DEDCCMDnn.\I"' ••••• 6C)TnlJ8lJnA9 AA9869 • :1 •• !ST •• a:s. 6M90 •••• • •••••••••••••• , ••••••••••••••••••••••••••• 7lJCEDAM6 •• 14 •••••• ,"lIfiGBO~:!1lC77M9CEI)J).·J)61 ••• lUI)!i •• ,\llnA.\lJIWJ07:f73 •• 6 •• 91'67.696 ••• ............................................................................. 4ABUUt1("Jl8.'796 .. 1. 1 ..... 77q7 .... G4 ........ AB61769 \9 ....... 7 ................. 61 .......... AD .2 .... 6933 .......... .. :J ........................................................................................ 67ADCCD99B7nA6. 9D3A9GB2 ........ G. ..... Il ....... 2770 ..................................... 06 ... 3.33. an. 766 ....... .. ......................................................... 89 ............................... "IOM ..... 17'32 • ., .... 6ts ......... 29396 ...... 1 ......... 00944 ............................. B\M ...... ?!l ....... u ....... 1 t" ......... 1 ............................................ 98~ .................................. 6 ................... 1!l190090·\4I)8 ............. 1. DCU .............. 4Tt6+6?9 \2 ....... 76 •• 677 ............ .. ........................ ~ ........ f ................ 4 ..... 78 ........................................... 796 J .. *****79 t\C9906173 ................. 7AABB\9B7 ....... :l8\AADA ....... 816 ... 99l .......... .. • •••••••••••• 3 ••••••••••••••••••• 97 ••••••••••••••••••••• 9CCBAD9 J671:S7G. J 1 ••••• 1 J2. 471191\9 \JlC8l\A ••••• 3AB43 ••••• :J073:l.' .3 ••••••• • •••••••••••• 3)3Oli •••••••••••• 2 •• 6991 •••••••••••••••••••• 19CDCCB5M7 •• 7 •••••••• 269AA9MDCCCCR9Bl •• 3781 ••• 3:l •• G36 •••••••••••••• " ............ " ••••• Il ......... ,. 1869BBD96876 •••• 2 •• 5 •• 4. 3A2. 8DEDt.&B06761UU5 ••••••••• 8DA'A99ADCCDDCB ••• 1 •••• t ............ " •• A •••••• • ........................ iloilo ........ iloilo ..... 6ABCIJJ\O .... 99BCBDOCDA6AABACDCl139Gl ........... 1 8969ADDA9.\9AAB7 iloilo •• '" •••••• '" iloilo ••••••• 1 ••••••••• • •••••••••••••••••••••••••• " •••••••• 7BDEDAlJ9DCDJH:DDDDVD8761J7 AC87 •••••••• 63 ..... 17669:\DA79716 .................................. . • •••••••••••• '" ............................ 1. ACCDDCDEf)CCDDAA.BCA42 •• 984 ••• 42 •••••••••••• G909U.I ••••••••••••••••••• Il •••••••••••••• iloilo •

•• • • • • • • • .. • • • • .. • • '" ••••• '" ft ........ ft ...... 84 .. IDDABB8l\.ABIlOO919 J\81868 1 1 ........ 1 ••••• ' ••••• IM36 ........................................ . a •• " ••••••••••••• " ••••••• " .......... 7 ••• 19A98D8D9ADA.A99S • • 641:& ••••• " ••••••• ,J ••• " ••• • 86 •• " ••••••••••••••• " •••••••••••••••••••• ~ .......................... " " •• " ........... 685.798464973996" .... 9 ••••••• " •••••••• " •••••••• " ........................................ ~ ••• ~

Fipre 4.14 -Sect10n of a PPI d.1sp~ay for Jul.:1an ~~ ~96 at 03:27Z

showing ti'eld about QUADRA (QUADRA position 1D.d1catec:t b1 •t· ... ~ ••••• - ...... )

~

-.~ - ~~

(/'­....

~ t ~ m.

. , , ,

1

... MT~ •• ~~~-' _____ ._M_. __ ._. ______ ... r __ I ______________ .... MU •• ,F __________________________________________ __

(_ 1

c

'1.

.... ,.u ___ - ........ -

65.

aUADR!\ radar range but it. siphon gauge was not functioning correctly and

qnly t?Jo atorme could be analyzed with' the siphon gauges operational.

4. 3b Validated data

The vaUdated data from eight atorma were treated with the computer

program (Bee AppendixI) described in Chapter 3. An example of one run with

the data for JuU'an Day ZZZ is shawn in fig. 4. 15 which plots th~ standard - J

deviation (defined in Chapter 3. sec.' 3. 2c) agamst the exponent in the relation

Z = aRb

. A minimum is seen for b=1.4. The value of "a" at this point is

"a = 125 as output by the prograrn. It was sh.pwn in Chapter 3 that the variation

of "a" witli exponent has no meaning., However, if the value of "ait is taken

from the point where the standard deviation is minimal as shown in fi8,t 4. 15

then it is possible to observe the variation of the percent standard error of , estimate

1 betwe~n ~auge and radar with exponent. This is shawn in fig. 4. 16

wherè the minimum percent standard error of estirnate (17.8%) occurs at

b = 1. 4. Thus the optimum Z -R relationshlp for the storm which occjlrred , 1.,

.!ln Julian pay fZZ is Z = 125R 1.4 with a percent -standard error of estimate

of 17.8'0. This means that even when the optimum Z -R relation is found in

this case there "'is still an R. M. S. error of about 20'0 between the gauge

rainfall and the radar derived rainfall.

1. If R is the difference between gauge and radar derived rain!all, then the square of the standard error of estimate is

Z 0' = 1 ~

n Rc

where R is the radar derived value and n is the number of cases. c

\

"",-

•

M • • 111_ 1 ~ . . ~ 1"'- 66 .,. !

i~ ï i 0.20 >-~ ~I ,

~ 0.19 '" (. " ::

0.18

0.17

0.16 , ~

'0 1

:t O'~15 .. ~ • 0.14 ~

f '1j

J

~ ,,0.1,3 '1j

~ 0.12 +1 ca

0.11 , 0.10 . ,

1.0 1.2 1.4 1.6 -1.8 2.0 { Exponent

Figure 4.15 Variation ot standard deviation trom G1/R1 - b

C with exponent(b) in Z=aR

80

70

60 ", 0 k 50 ", r.1 a

'V 40 ~ ~

'" ~. 30, +t • fi)

-' 20 ' .

• 10 ,

.i '. .,.

'0 -""

1.0 1.2 1.4 1.6 1.8 Exponent

( Figure 4.16 Variation or standard error between g-,ge

and radar wi th b ..,.. .

exponent in Z=aR

(

c

c.

.. '" .. !ota ._ F '" • • JI •

67

TABLE 4.3 Z - R relations obtained from vaUdated data

Julian Day Time(G. M. T.)

183 12:00-13:30

222 00:30-02:00

\ 247

259

1 194

248

245

246

13:00-17:00

10:00-12:30

13:00-17:00

15:00-17:00

17:00-18:3'0

18:00-20:00

Source

raw data, QUADRA radar OCEO gauge *

as above

as above

as above

PPI data, QUADRA radar QUADRA gauge

as above

raw data, QUADRA radar DALLAS gauge ..

as above

*OCEO = OCEANOGRAPHER ?

Z -R relation

Z =298R1•1

Z=125R1•4 , .

Z=298R 1.4

Table 4.3 shows the Z -R relations obtained by the program for the eight

stopns with vaHdafed data. The average standard ,error of estimate for -

these Z -R relations was calculated as being 26%. This means that using a

point-by-point comparison between radar and gauge yields a 26% R.M.S. errOr

between thé two fo~ the storms analyzed. '

The standard deviation in ua" was calculated to be a = 75, while for IIb" -

the standard deviation was O. 13. Thus the Z-R relationship derived from

these eight storms is Z = 257 {! 75)Rl. 27 (t," 13) • .~

(

t T lut t.'---~~~ _________ ' _______ "'''.fiIII .... __ ...... t. __ ~ ______ .. _ ........... __ _

lr 1 ." \

i

68

,

4.3c Discussion

Examination of table 4. 3 shows the v~iability in thé Z -R relationships

obtained. It i~ unclear whether the variability ia due ,~o radar error or day­

to-day variation caused by atmospheric conditions. as f.or exam{>le. la~ge

dew.point depression which would càuse high evaporation. Thus th~ precipi­

tation drops obseived by the r~dar might be reduced in Bize by the time they , -

reach the earth's surface. T~e problem with the "GATE" data ~owever was

the establishment of "ground truth".· ln this study it was implicitly ~ssumed

>that the gauges did indeed l1ecord the "true" rainfall but there was no way of . ,

verüying that assurnption since no other gauges were available except those

mounted on the S'hips. ,The best way of testing the hypothesis wtls to'have o ~

several radars within approxirnately 15 km of eadi other with a standard

gauge between the ships. This was attempted during the intercomparison

periods betwe'fn the ~hree GA TE phases but unfortunately no precipitation

occurred within radar range of the ships during these tirnes. During post-o

field analysis with overlapping radar data it was -observed, however. that the,

QUADRA radar calibration needed sorne modification sinee it showed a 3 ~o • \

6 dB differenee from the U. S. ship radars. The modification amounted to a

change in the transfer curve intercept described in section Z. Ze i. e.

,

dB Z = N + 16. 13 4.44

. dBZ = N + Il. 63

4":'44

phase l

phase Z + 3

The intercepts 16.13 and 11. 63 were moved up to Zl. 13 and 17. 63 respectively.

The effect of this modification on the Z ~R relations as obtained by the pl'ogram

des cribed in Chapter 3 was to increase the "a" in Z = aRb.. without affecting

i t 1 "

~ ~(

1 w-~~ !..

!' i t ~,

~

1 !

1 , f . ~

, \

f' ,

(

(

(

:'~- -

•• 1 ,. J' If ... 69

, the, exponent lib Il • T hus the Z -R relations shown in Table 4.3 were

1 .'

modified in view of keeping the "GA TE ff radars consistent. H ow ever.

since there is some question as to the electrical calibration of either the , ,

QUADRA radar or perhaps the OCEANOGRAPHER radar. the determination ~

of the coefficient in these Z -R relations i8 Iess certain than for the exponent. ,

A lthough the Z -R relationships shown in Table 4. 3 refer epecifically

" to the storms in question it is highly de.sirable to obtain a n'lean Z -R relation

for GA TE, by averaging those in Table 4.3.' The result of the averaging

Yl'eld& Z --25,7 R 1. 27 h' h . h 1 h . 1 d l t' . W lC 1& rat er c ose to t e prevlous y propose re a lons

bf other investigaqons (see H udlow et al (1976)).

4. 4'-G.,omparison ofZ -R 'a with other propoaals

Some of the Z -R relations proposed since the completion of the ,field

phase of ~ATE are Z = 300 R 1. 3. Z = Z30 R 1. 25. and finally the one proposed

in this WQrk Z = Z57 R 1. Z7. It ie not sufficient to examine either the "a' s"

or the "b' Sil in these relations in order to evaluate whether the Z -R 's are 'f

similar or note Rather. one must examine the resultant rainfall rate that .. each of these relations produce for a given value o,f Z. Clearly. any two of

these relations interttect at a particular point where both of these relations

ghre 'ldentical rainfall r.ates. Moving away from this point produces a

di sparity, in ter~s of rainfall rate for a given Z. bet~een the two relations.

However. special 'att~ntion must be given to the range over which rainfall is

obse'rved to occur m"st frequently in the field. It 18 in th~s rang~ that the

Z -R 1 s should be evaluated. It iB clear that these thrte relatit:ms will give

differènt results for a value of saYl55 dB Z " but Buch a high dBZ value does

not contribute v~ry ,much. for example, to the total accumulated rain of one

- ... ~ r-- .... ........L---

ifiM2:z,!,etI.::,..~~\~"r':~;'· "r.~-:-4ç:,,;;;;'1;;,iL,,~,~~1!1~~

YI~!i iXttb_C

.l; 1 , 1:

(

• •

('

; ~ ,

( ,

.104 ; 1N44Ziit4""" .. i $ "" --_________ ._~--______ .... i 1 70

day's duration.

Fig. 4. 17 shows the cumulative frequency of occurrence in percentage

of tape numbers with corresponding dBZ values durj,ng the 'storme which l ,

t • were analyzed. It should be note in the same figure that. tape numbers below

10 are not included for ,reasons explained in section 2. 3b. The dBZ values

(occurrences ftom fig. 4. 17) ~an be transformed to percentage raiIifa~l '

occurrence through a Z -R relationship: Fig. 4. 18 gives the corresponding

accu~ulated rain generated with Z = 300, R 1. 3" 2 = 257 R 1. 27 and 2 =230 R 1. 25.

It can be seen that the curves peak at 38. 2 dBZ which corresponds to a rain­

fall rate of approximately 1 2mm h -1 for the three 2 -R relations.' AlsO'",

inspection of the figure shows.that approximately ·80% of the rain occurs

between 28.8 dBZ and 44.6 dBZ. Thus the Z -R relations should be compa'red

within that range. \

Fig. 4. 19 is a plot of the three 2-R relations discu8sed in this section

and ~lso the Marshall:-Pa1mer (1948) relation. 1t can be seert thatl the three

relations are very c1os~ to each other and that the relation proposed by the

author (2 =257R 1. 2!) is. intermediate to tpe two previous1y proposed for GATE. . ' It clin aiso be noted that between the dB 2 values 30 and 45, which are the

limits between which there is a 80% contribution of r,ain, the Z -R relations

are especially compatable. The MarB~all-Palmer relation (2 =120R 1. 6)

is contrasted to the three prev~ously mentioned although the M-P relation

holds good for continental stratiform rain rather than for tropical convective.

1

\

At

(

~

•

"

Cl

r

/

lit -

-• +t

il ~

~ ... .., -rf

i -~

~ ... 'd .,

.~~

j u

'u <oC

! '" '

71

1 '

/'

1

.01!'~~-?--~--~~~~ __ ~~~-'~-r~T-~~-10 Z4.}

30 28.8

c

)

l'1.gure 4. 17 Frequency of' occurence (,,) of tape Auber (or Dbz) ,or 8to~ .h~ch •• re aaaly .. d

14

12

10

2.

o

1 _

. . .

A .... .. - *. " " " " .* .. B· •. . . : . . .

• • • *. ~" : " .. .. ~

.! •• * C *. ~ .* •• * ••

" 0 . . . .... ..:. .. ... . . . .. . . .. . ,

:". ..,: . : .' . ..... ':.~ .. " .*. •. . .. . .. . .-.• *. ..*.*.. ~ :,~ . ........ ~ ~ ~ a •••• _ •• _ •• * .. ~:

10

•• •••••• •• '! :: . . . .. ... .... ~ \~ ~ ,~

r ". ;

•

70

• 1. • l'

~ :~ ~ ~ · .~ • 1-· " • 00 · ' .. * ••• .. ~

*. \~ .. ' .. ' . .' .. " .. ' • 0" *:.*. e::

110

A Za~r·2S B Z=257re27 c z::}OOr-30

Tape Humber

Figure 4.18 Accumulatedrain per .a,Pe number (or Dbz) tfr the GATE Z-R relations

u

, , . , / .

... - ~~~~ ...... - .... :---.... ~-" .• !;...~.f1III _ ..... __ •• - - ..... ~9_."',">t t,...,.~ ...... -J __ .. ~1'!' .......... ~_~_._.': __ ....... _.....,..,,~ __ .......... ____ ....

\

l "

: ,

i Il "

;

t i , t ~ ! ~

t l:-"

~------------------~----"""""""~'~).;~')~",".,~, •. ~.:.~:.~.',·',~·~·,,?',"·"·>·f"~ ~ __ .::... __ "'______ 1/1 • ' .ru A ..

"-)

,(

-

.

()

-M

~ ~

eq

fIG 0 .... o' ....

60

, 55

50

45

40

35

! •

.A

B

C

D "

72

> ,

""

1 Z=220R1 •6 (Maraball-Palller) Z=300Rl~3 ' z=25'l~. 2.1 ~ z=z3Qr·25'

• "

, .

----------

. \

HeSion 0 t :lntereat

• -_ ........ ------•

o. .8 o •

1.2 , \.' > ,-,

1.'6 z.o 2.4 2.8 (P] Z:1IUIl-hr-l

", log R

Figure 4.19 Plot ot 10L0,Z ~dBz) va. 10gB for the GATE and Marshall-Palmer Z-B relationa of the

, torm Z:aRb

" . ' \

,.

(

.\

v

73

Table 4. 4 shows the rainCaU rates calcu1ated from the various Z-R

relations for different values of dBZ. . .

TABLE 4.4 RainCall rates trom the variOU8 Z-R relations

. dBz z= i30Rl. 25 z= 257Rl. 27 z= 300al. 3

25 L 29· 1. 18 1. 04 c

30 3.-24 2.91 2.52 35 8. 14 7.22 6.12 40 20.45 17.87 14.84 45 51. 36 44. 23 35.98. 50 1 19. 61 109. 50 87.23 55 324.05 ~ ? 271. 10 ll1. 49

r

* (R] = -1 "\ mm-hr

It can be seen that the -di8crepancy between the Z -R relations increasea

ytith larger dBZ values but that the discrepancy at 45 dBZ (near upper limit

observed during GATE) ia approximately 28,.. But it muat be borne in mind -......... that thfs discrepancy ia of the same ordel-~een gauge a~d radar

derived rainfalls. Thus i~ can be said that aU the Z -R~"y.elations supply

essentially compatable rain eatimates.

4. 5 S\JtTlmarr

The problems associated with deriving a Z -R relation frotTl ship mounted ,

l radar and raingauge have been demonatrated. It was also shown that naviga-\

tion information can be derived from. matching precipitation patterns obtained

from ship radars although the resulting accuracy ia of the order of 8 km. ,

Interpolation of precipitation patterns by using isohyets has been demonstrated. <J :l '

Finally. a Z -R relation for the GATE area has been derived by linking '-

, simultaneous "gause and radar observations.

--,--,,---.. ,--......... - .-..... --.------~-~" ~ -- .. --~ .. ~~ .• - ..... -. - --_-.. - - . ---_' .. ~ ... "'r _~ ", .. ~~ "'!"" __ .. ==, • ,~ .............. := ..............

f ,

!I~"""""";A~~I8i!Jt!llll.""M11L\)iMI"''''''''_ .. .:.,.:._._._ .. ______ ............ ' ... ,' ....... ~4>::J.1MIIWjn.JrJ •••• ab • .. J t 16d'. '-.

(

"

(

:, ( ,. i

1 ) i JI· r

1

- .,..~.-----

~~r.t.t t'là.. r

74

" J Chapter 5

l Conclusions

,

•

With the limited data set available, it has been show n that a Z -R

relation could be obtained in orqer to producp. meaningCul rainCall estimates

from the radar data. T lite Z -R relation deri~ed here (Z,=257R 1. 21) is

similar to those previously proposed which is fi,rst1y satisfying but at the , "'1

same tirne lends more credibility to the pz"bposed Z -R relations since thes'e ,

were obtained by diCferent methods. Furthermore, the gauge-radar data

w ere ,obtained at different distances approximately 20 km (QUADRA

radar data interpolation), 50 km (DALLAS gauge data) and 150 km

(OCEANOGRAPHER gauge, data). The fact that the tuge-radar data sets

obtained at dilferent dista;nces 'gave plausible Z -R relations sugg~sts that

the methods used for each sèt were appropriate. ~

Several conclusions can be drawn from these di,fferent methods.

F irstly, it has b~en shown that interpolation of radar-patterns by using

isohyets over an area of approximately 11 km by 17 km can be perfol'med .. . and that the "inteq~olated" pattern is rather close to the "true" pattern. It

has also been demonstrated that direct radar echo' ~nd gauge cornparisons , t'

can be carried out even at a' distance of approximately 150 km provided i -

that there was no fntervening precipitation between radar and gauge.

Att~nuation has proven to have large effectsj in fact it has been shown

that a 5 cm wave1ength beam can be attenuated to such. a degree that no

meaningful relation can, be derived between Z and R even at moderate

, ,",

/< ' ,

~,. l~ •• ~IM' l'!W ... ~ .... ~",> ~ ___ ..... t_~M""."'.tt"'fd"'_._'''''';I_'''_ ........ , _________ • __ , .... t"", ..... "';"' ___ 1 _n ____ .... l......i~Io.... ____ .. _.m

(

75

distances of the order of 50 km. Although the above mentioned methods

required precise nav,ation information. it has been demonstrated that

navigation by mat ching PPI ~isplays from different ships is feasible and is

acc urate to about 8 km.

With r<eference to the electrical calibration of the QUADRA radar, it

• was se'en that~lthough the logarithmic receiver behaved quite linearly. some,

problems Wlt.h the data were experienced at very low return power levels. , .

Examination Q1 both PP'l's and frequency of occurrence of dBZ' values showed

that the lower end of the transfer curve appeared to be in the noise regime

of the receiver. Yet, no significant data were lost by truncating the lower

, portion. The conèlusion to be drawn here was that the minimum detectabLe

signal-(M.D.S. ) did not affect the behaviour of the receiver alth'ough very 'II

light rainfall rates could not be detected if the M.D.S. were tO? high. It

was aiso concluded that even though the pre-experiment elecfrical calibration

was performed as well as the state of the art allowed, comparison with the

r other C-band radars showed that the "absoIute" calibration of the QUADRA

radarmight have been in error by ,-pproximately 3 to 6 da. Viewed in

terme of the tranefer curve this constant error only moved the curve,

vertically. Thus the error in the "absolute" kalibration was ooly an addi-,

tive constant rather than a multiplicative con'!tant. In terms of -the Z -R

relations obtained via thus transfer curve, t~e coefficient "ail i~ Z=aR b

was not as weIl determined as "b". One concludes, t~el'ef~J:e, that the ".

"absolute" calibration of the radar must be well determined if the Z-R

relation obtained is ta be reliable. Fortunately. comparison with the ot,her

C-band radars showed that the QUADRA r'adar might have had a biased .

calibration and these other rada~8 p,rovided the inform<,l.tion to correct the

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'"""" -----.-OpADRA calibration. However. regardless of tlle actu1l1 Z -R relationship

. dE!hved, the relation between "tape numbers" ana direct raingauge obser­

vati4ns was sufficiently well e~tablished to yield good rainfall estimates for ,

hydrological studies ..

With the "absofute" calibration of the QU~DRA having been performed .

and the optimum Z -R relation deter,tnined it was possible to translate to

rainfall rate the 'requency o(occurrence of oDserved dBZ values from many

r.andom scans throughout the three GATE phases. Using Z=Z51R 1. 27,

calculations sh~wed that the most frequent rainfall rate observed by the

QUADRA radar was of the order of 1 mm h -1. and le88, while the hi8~est ./

rainfall rate observed, albeit very seldom, was approximately,90 mmh -1.

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ACCL"ULATE FACA~ F_t"'fALL

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,END

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79

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APPENDIX" n

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JULIAN DATE CALENDAR

0., .Ion f.ta Mot ,., Moy J_ JuIy Aue Sep Oct Nov o.c Oey

• 001 on 060 091 121 "2 112 21.1 J44 27' )OS :tU 1 J 002 033 061 092 IH 153 113 ,.. 2U 275 .. m 2

3 003 034 1162 093 12:1 154 1'" ,.5 246 276 :107 3:11 , • 004 035 063 094 124 155 lU 216 247 277 - ua • , 005 036 ON on 125 156 '" 217 2. m 309 Ut 5 .- 006 037 065 O'M 126 157 117 JII 2 ... 279 :110 uo • 7 007 031 066 097 i27 ISI 1" 219 2$Q HG 311 34' 7

• 001 039 .7 09t lU 159 'If 220 251 211 :112 . :141 J , 009 0.0 .,.. 099 129 1'" 190 221 252 212 313 S4 •• 10 010 041 069 100 130 .61 '" m 253 m '14 ,.. 10 .. 011 0;2 om Jt1l 131 .62 192 m ,,. ,.. 31S us Il

Il 012 043 MI 102' 132 163 ln H4 us 215 316 346 12 Il 013 o.w on 103 lU '64 1" m 2$6 216 317 347 l' 1. 014 GoIS 073 104 134 '6S 195 m 257 217 3 •• ,..

l' Il OIS 046 07. 105 135 ", '" 227 251 ,. 31. ". 15 ,. 016 047 075 106 '36 167 197 228 259 219 320 uo ,. 17 017 CNe 076 107 137 ,. lt1 nt 2tO -~ 321 UI 17 .. 011 019 077 101 138 .. , 199 230 261 2fl m :au t' If 019 oso 071 1. Ilt 170 200 nI 262 2ft ln :au .9 .. oao OSt 079 110 140 171 201 J32 263 m ".- U4 20 Il 021 0S2 010 III 'CI ln 20Y 2U 264 ". us us 21

12 OH GA 011 112 141- 173 203 234 2., m nt U6 22

13 ou 054 Olt 112 1'3 174 .. ns 166 aM 317 U1 2:J

2. 024 0S5 013 Il. 'u .75 205 JM 267 297 3. 3. 2'

2S 025 056 OIA ilS 1" 176 206 J37 ,.. 291 329 Ut' 2S

26 026 -"F Cl5 116 1 .. 177 207 231 269 291 330 .. » 27 027 05. 016 117 147 171 201 U. 210 300 ~I 361 27

21 02' 10.., 017 III 1 ... • 17' 209 240 271 301 m 361 ft

29 029 : 01' If'- '" 110 JIO J.' 21' 30J Ut 363 29

30 030 019 120 ISO III 211 2'2 ~n -334 364 30 ,

31 031 090 151 212 20 * . lM :111

/,J 0 1

('from GATE DATA CATALOGUE, aupplemfllnt N- Z

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, BIBLIOGRAPHY

Austin, G. L. and Y. D. Ahn 1913: records of showers.

Vertical motion patterns in radar J . .Appl. Meteor. g. 354-358.

Battan, L. J. 1973: Radar Observation of the AtmosEbere. U p.iversity of Cbic~go press, 3Z4 pp.

Bellon. A. and G. L.' Austin 1977: The real time test and evaluation of "SHARP". A short term precipitation forecasting procedure. McGill University. Stormy Weather Group Rep. MW~9,1. 55pp.

Hodge, D. and G. L. Austin 1" 1911: The calibration of meteorological rada_rs for attenuation studies. Radio Science (in press) .

• - Hooke, R. and T.A. Jeeves 1961:

statistical problems. Direct search solution of numerical and

J. Assoc.Comp.Macb . .!.Z, 212-229.

Hauze. R .. A. 1976:- GATE radar observations of a tropical aquallline. P roc. 17tb Radar Met. Conf., AMS. Seattle, Wash .• 382-389.

~ .

Hudlow, M.n. 1975: Collection and handling of GATE sbipboaTd radar data. l'roc. 16th Radar Met. Conf., AMS. Houston. Texas, 186-193.

Hudlow, M.n., P. J'. Pytlowany and F.D. Marks 1976: Objective analyais of ~E collaeted radar and rain'gauge data. Proc. 17th Radar Met. Conf., AMS, Seattle. Wa.h., 414-421-

Hudlow, ) " .. '

M.D'. 1977: Precipitation elimatology for the three phases of GATE. Second Conf. on Hydromet., AMS. Bod(,n Mass. , 290-297. /

0",

Kuettner, J. P .• D. E. Parker. D. R. Rodenhaus. H. Hoeber. H. Kraus and G. Philander, 1974: GATE final international acientific plans. Bull.Amer. Meteor. Soc., 55, 711-744.

Leary. C.A., and R .A. Houze 1916: ' Analyaia o(OATE radar data for a tropical cloud eluster in an easterly wave.· Proe. 11tb Radar Met. Conf., AMS, Seattle, Wasb. -, 376-383. .... . ,

Marshall, J.S. and W.Mc.K. Palmer 1948: Rain intensities.by radar. J. Meteor., 5, 165-166;

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Marshall, J. S. and W. Hitschfeld 1953: Interpretation of the fluctuating echo from randomlY. distributed scatte:rers. Cano J. Phys. ,. 31, 96Z-994.

Marshall, J. S,. 1971: Peak reading and thresholding of radàr signals. J.App!. Meteor., !!. lZI3-1Z~3.

Martin. D. W. and W.D. Scherer 1973: Reviewnf satellite rainfall estimation methods. Bull. Amer. Meteor. Soc., ~ 661-674.

Pestaina-Haynes', M. and G. L Austin 1976: Comparison between maritime tropical (GATE and Barbados) and continental midl.atitude (Montreal) precipitation lines. J. Appt. Meteor. !.!, 10. 1077 -108Z.

Probert-Jones. J.R. 196Z: The radar equation in metéorology.,' Quart.J. a. Met. Soc.. 88, 485-495.

-

~oesli.·H~P. and A. Waldvogel' 191Z: The lower bound of accurâcy of a radar raingauge. Proc. 15th Radar Met. Conf .• ANs. Champaign-Urbana, Ill., 181-184.

R oger~. R. R. 1971: The effect -of variable target relectivity on wea~r radar measurements. Quart. J. R. Met. Soc .• 97, 154-167.

, !

Silver. S. 1951: Micrdwave Antenna. Theory and Desiln. McGN.w Hill Book 0). 1 New York .

Smith. P. L. 1964:. Interpretation of the fiuctuating echo from randomly distributed 'scatterers. McGill University. Stormy Weather Group Rep. MW.-39. 7Opp.

Smith, P. L .• Jr ..... 1968:. Calibration of weathe .. radArs .. Proc. Il'th Bada~ Met. Conf •• AMS. Montrèal, P. Q., 60-65.

Smith. P. L. , Jr., D. E. Cain and A. S. Dennis 1975: Derivation of an R -2 relatronship by compute .. optimization and its ute in maa.8urilla daily areal raiufall. Proc. 16th :RadAr C ouf., ANS. Houaton Texas, 461-466.

Strivastava, S. N. 1974: c Quantitative aspects of weather radar operation8~ Ph. D. tbesia. McGP.l University. 120 pp. r-'

J

Wallace. P. R.· 1953: Interpretation of the fluctuating echo from randomly distr~but~d 8catterers. Can. J. Phys. '31. 995-1009.

Wilson. J. W. 197 0: Integration of radar and raingaugo data from improved '. rainfall measurement. J.Apfl. Meteor . .1.. 489-,497.

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