An investigation into the effect of the integration time on the rainrate distribution

3 0 6 pp. 306-313

An investigation

John D. KANELLOPOULOS **

Panaviotis NIKAKIS **

George PAPPAS **

Christos PERELIS **

into the effect of the integration time on the rainrate distribution*

Abstract

An investigation into the effect of the integration time T on the rain rate distribution is presented using a rainfall rate data bank from an extensive network of raingauges around the Greek area (ccm-zones K and L). Comparison with results from other countries reveals again the significant climatic dependence of the conversion factors between the various T-min rainrate distributions.

Key words : Rainfall rate, Statistical study, Rain gauge, Climatology.

Contents

I. Introduction. II. Description of the data bank.

III. Analysis and numerical results. IV. Conclusions. References (11 ref.).

I. INTRODUCTION

I~TUDE DE L'INFLUENCE DU TEMPS D'INT~GRATION

SUR LA RI~PARTITION DE L'INTENSITI~ DE PRI~CIPITATION

R~sum~

L'effet du temps d'inMgration T sur la r#partition de l'intensiM de precipitation P(R) est s en utilisant une banque de donn~es obtenues gt raide d'un r#seau de pluviomdtres install# dans les zones K et L du ccm en Grdce. L' ~tude comparative avec les r~sultats obtenus dans d'autres pays montre r influence importante du cli- mat sur les facteurs de conversion entre les rdpartitions des taux de pluie en fonction du temps d'intdgration.

Mots cl~s : Intensit6 pr6cipitation, Etude statistique, Pluviom~tre, Climatologie.

It is widely accepted that attenuation of radio waves by atmospheric precipitation (mainly rain) represents a serious obstacle to microwave transmission at frequen- cies in excess of about 10 GHz. One of the serious problems in microwave communication planning is the prediction of the attenuation due to rain in a radio link by using reliable long-term rain rate statistics. It should be noted here that the prediction of the rain attenuation distribution usually requires quasi-instantaneous or at most 1-min point rainrate distributions. Recently, ccm has adopted the use of 1-min integration time as a conve- nient reference sampling time [1]. On the other hand, incomplete or short term rainfall data of such small integration time is usually available and this lack of in- formation has forced radio engineers to use sources of rain records such as those available in the meteorological services to estimate the rainrate distribution. Due to the limited resolution of the chart recordings the statis-

* The following text presents research results supported by the Hellenic PTT Consulting Organization S.A. (ESTTO) in the framework of the STAR program. The scientific responsibility is assumed by its authors. ** Division of Electroscience, Department of Electrical Engineering, National Technical University of Athens, Iroon Polytechniou 9, Zografou 15773, Athens, Greece

ANN. T~flCOMMUN., 47, n ~ 7-8, 1992 1/8

J.D. KANELLOPOULOS. - EFFECT OF THE INTEGRATION TIME ON THE RAINRATE DISTRIBUTION

tical distributions of rainrate derived by these accumu- lation rainfall amounts are referred to integration times T of not less than 5-min and this makes inevitable the development of conversion factors between the various T-min rainrate distributions. From the above, it is clear that the effect of the integration time on the rainrate distribution is of interest.

In the past years several attempts were made to relate instantaneous rainfall distributions, with those for large integration times. More particularly, Harden et al [2] tried to find the appropriate reduction factors by using rainfall distributions measured at Slough, United Kindgom. Further, Fedi [3], as a part of the EUROCOP- COST 25/4 project, examined the same effect for several European locations such as Rome, Italy and Darmstadt, Germany. Watson et al [4] also examined the 5- and 10-min rainfall conversion factors to 1-min for some other locations in Europe. Damosso et al [5] studied the characteristics of rainfall at Turin and Bari in Italy and presented power-law curves relating the various distributions with one another. A similar power-law fit was proposed by Flavin [6] and Ajayi and Ofoche [7] by examining the cumulative distributions for locations in Europe, North America, Australia and Nigeria. Most recently, Segal [8] has published conversion factors for Canada by analyzing a large data bank stressing the climatic zone dependence. Finally, Burguefio et al [9] investigated the effect of the integration time on the rainrate distribution by using a rainfall data bank of 49 years recorded at Barcelona, Spain. The dependence of the effect of the integration time upon the rainrate distribution on the climatic zone has also been observed there and the need for mapping the conversion factors from one locality to another has been made clear.

Following the above considerations, the same effect is examined here by using available rainfall rate data of various integration times for nine representative Greek localities belonging to two climatic zones (K and L). In this paper, we present the appropriate conversion factors between time-averaged distributions, and we compare them with those of other climatic zones. Some useful conclusions are deduced.

307

Italy, France, England, Germany, Sweden, Portugal etc, aimed at the collection and the appropriate elaboration of data concerning propagation of microwaves through rain medium. It should be noted here that Fedi [3] has already presented ratios of 5- and 10-min rainfall intensities to the equally probable 1-min rates for two European locations (Rome, Italy and Darmstadt, Germany) but without further analysis. The data for the Greek airspace is referred to the period 1974-75 and gives the appropriate experimental basis for the development of the present study.

The Special Meteorological Stations were equipped with two types of raingauges, rapid response (RRR) and standard rainganges (SSR). A description of the rapid response raingauge is given elsewhere [9], whereas the standard raingauges are the usual instruments employed by the meteorological services. Using the first type of raingauges (RRR), rainfall rate statistics were obtained referring to integration times 15 sec. This means that the rainrates are considered to be quasi-instantaneous. Further, the rainrate in a T-min interval was obtained by integrating the rainrate records within successive intervals of clock T min and dividing the result by T. In this way, 1 min, 5 min, 10 min, 30 and 60 min rainrate distributions have been derived. The above procedure, of integrating the rainrate records to derive a T-min rainrate RT is quite close to the value measured by a gauge which had an integration time of T min [9]. In our case, we have also verified the above argument by comparing the so obtained RT distributions (for T = 5, 10, 30, 60 min) with the corresponding ones taken from the standard raingange (SSR) measurements.

Finally, as perhaps expected, the PI(R) distributions are very close to the quasi-instantaneous distributions (15 s) for each locality over the whole range of rainrates. This has also been noticed by Burguefio et al [9] for the Jardi recordings from Barcelona and this could be due to the inevitable limited resolution of the chart recordings.

IlL ANALYSIS AND NUMERICAL RESULTS

II. DESCRIPTION OF THE DATA BANK

The nine Greek localities where Special Meteorologi- cal Stations have been installed are the following : Mikra (Salonica), Kefalinia, Kalamata, Milos, Hios, Aliartos, Kerkira, Heraklion, Yma (Athens). For each of the above localities the appropriate experimental results were taken from archives of rainfall rate data given by the Direction of Research of the Hellenic Telecommunication Organi- zation S.A. (OTE) and they constitute part of the final report of the research project COST 25/4. The above project in cooperation with other European countries such as

The conversion factors translating the quasi- instantaneous to equivalent r-min rainfall distributions may be carried out in different ways. In one, the conversion is expressed in terms of the ratio of equiprobable rainfall rates :

R I (P ) (1) P T ( P ) - R T ( P ) '

where R1 and RT are the rainfall rates exceeded with equal probability, P, for the two integration times. The value of 1 min as reference has been selected for convenience and to help in the comparison with other results. An alternative method of expressing the

2/8 ANN. TI~LI~COMMUN, 47, n ~ 7-8, 1992

308

conversion would be through the factor FT, which is defined as :

(2) r v ( n ) - P i ( R ) , P T ( R )

where/~ and PT are the average exceedancr probabilities for the rainfall rate R. From the theoretical point of view the two ratios are equally valid but, it was found that ratio FT varies over a greater range than p at any given location. This has also been pointed-out by Segal [8] for the precipitation records taken from 45 locations in Canada. As a result, only the behavior of PT is examined here.

The available data were merged into two regional groups. The first group has included the four localities (Milos, Kalamata, Yma (Athens) and Heraklion) corresponding to zone K, whereas the remaining five localities (Kefalinia, Mikra, Aliartos, Hios and Kerkira) belonging to zone L are contained in the second group. A map of Greece with both the separation between the K and L pluviometric zones and the locations of the stations is shown in Figure 1. Following the power-law

~ n

Zone K

FIG. 1. - - A map of Greece indicating the K and L pluviometric zones and the locations of the stations.

Carte de la Grdce pr~sentant les zones gdographiques K et L et les sites des stations.


Figures 2-9 exhibit the conversion factors PT =

R 1 / R T of the individual meteorological stations as well as the average distributions for each regional group and for T = 5, 10, 30 and 60 min from 10-4(%) to 3 . 1 0 - 2 ( % ) exceedance probabilities. The standard deviations about the mean curves are given in Table I, for various selected probability levels. As it is obvious, from the above data, the average ratios ~-~ increase as T increases, and decrease with increasing probability. Examining now the dispersion of the conversion factors concerning the individual meteorological stations inside each of the two regional groups, we can conclude that the differences between the two average distributions are approximately equal to the corresponding standard

l R~/RT

g

K-Zone (5 mm)

Mean . . . . . . MflOS - - ' - - Kalarnata

Yma (Athens) Herakhon

�9 ~ . . . "~ ~,~-- . .

L010-4 110-3 ~0-2 probablhty of occurrence (%)

FIG. 2. - - Ratio between rainfall rates R1 and RT with equal probability of being exceeded obtained during integration time T = 5 min for 4 Greek locations belonging to zone K, including the average

distribution.

Rapport entre les taux de precipitation R 1 et R T ayant la m~me probabilitd d'etre ddpassds obtenu pendant le temps d'intdgration T = 5 min pour les 4 sites grecs appartenant ~ la zone K, y compris

la distribution moyenne.

concept proposed by Flavin [6] and Ajayi and Ofoche [7], the data were treated logarithmically. The average and variance for each group of stations were calculated by means of the relations :

(3) log PT ---- EWz log PT,,

(4) ( N 1)O.2ogpT --_ ~wi( lOgpT, ) 2 _ (10----~T)2 '

where the wi are the individual weighting factors corresponding to the size of the data sample and N is the total number of stations included in this average. In our case all the wi can be considered to be equal. As far as the linear parameter p--~, we have :

(5) p----~- -- 10log PT

1 501 R)/RT K-Zone (10 mm) - - Mean

l MIles

- - �9 - - Kalamata . . . . Yma (Athens) . . . . . Herakhon

/ -" \ " ~

l 0 ' 10-2 i0-4 10 .3

probability of occurrence (%)

and

(6) apT(% ) ~- 50(10 al~ - 10--~176

ANN "I~JICOMMUN., 47, n ~ 7-8, 1992

FIG 3. - - Same as in Figure 2 but for r = 10 min.

Comme d la figure 2 mais pour r = 10 min.

3 / 8

J.D. K A N E L L O P O U L O S . - E F F E C T OF T H E I N T E G R A T I O N T I M E O N T H E R A I N R A T E D I S T R I B U T I O N 309

R~/RT 1 50 K Z o n e (30 mm) _ _ Mean

- - " " ~ . . . . . . Miles - - . - - Kalamata

"" ~ % . . . . Y m a (Athens) ~ , ~ _ ~ . . . . . Herakhon

_ _ _ - ,~ ~_>~>~. ~ . . �9 .~ ~.---~--.-___.

" - - . - - ' - ~ 2 ~ - . ~ ~

1.0 , , , , 10 -4 10 -3 10 2

probab=l~ty of occurrence (%)

FIG 4 . - - Same as in Figure 2 but for ~- = 30 m i n .

Comme ?t la figure 2 mats pour ~- = 30 m m

1 0

10-4

RI/RT K-Zone (60 mm) Mean

" ~ - " " ~ . ~ . . - - . . . . Miles ~... ' - - . - - Kalamata

. . . . Yma (Athens) ~ " ~ . . . . . Herakhon

"

lo 3 10-2

probabil i ty of occurrence (%)

FIG 5. - - Same as in Figure 2 but for ~- = 60 min.

Comme d la f igure 2 mais pour "r = 60 mm.

1 )1(/_ 4

R1/RT

L-Zone (10 m,n) - - Mean . . . . . Kefahnla - - ' - - Mtkra . . . . Ahartos . . . . . Hies . . . . . . Kerklra

�9 e . . o

. . . . .

�9 ~ " ~ - . - ~ " ~ "----2 ._~-<

i {3 3 110

probablhty of occurrence (%)

FIG 7 . - - Same as in Figure 6 but for "r = 1 0 m i n .

Comme ?t la f igure 6 mais pour ~- = 10 mm.

L-Zone (30 mm) R1/R T

_ _ Mean . . . . . Kefalmla . . . . Mtkra . . . . Ahartos . . . . . . Htos . . . . . . . Kerktra

~ ' - ~ o

~ . . ~ ~ - - - - ... ~ - \

- ~ - ~ . . ~

i[i -4 i~ 3 11o-2


FIG. 8 . - - Same as in Figure 6 but for 7- = 3 0 m i n .

Comme ?z la figure 6 mais pour 1 = 30 min.

A _ 1 20 i HI/RT L-Zone (5 mm) Mean

k Kefahma Mlkra 2 o-

�9 "* �9 Almrtos �9 --

_ ~ . ~ . . . H i e s

~ - ~ ~ Kerklra

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

�9 - - .

o ~

0


FIG 6. - - Ratio between rainfall rates R1 and R T with equal probability of being exceeded obtained during integration -r = 5 min for 5 Greek locations belonging to zone L, including the average

distribution. Rapport entre les taux de pr#cipitation R 1 et R T ayant la m~me pro- babilit# d'etre d#pass#s obtenu pendant le temps d'int#gration ~- = 5 min pour 5 sites grecs appartenant ?t la zone L, y comprts la

distributton moyenne.

1 0

10 -4

R1/RT L-Zone (60 mm) Mean

. . . . . . Kefal inla . . . . . Mtkra . . . . . . . Ahartos ......... HIOS

O ........... Kerklra o.. ~ ~

..'~

�9 ~ - ~ . " - ~ ...

. . . " < - . . ' - .

�9 " ~ . ~ . ~ . . . --. * .

\

, i

lO -3 lO-2

probabdtty of occurrence (%)

FIG 9 . - - Same as in Figure 6 but for "r = 6 0 m i n .

Comme ~ la figure 6 mais pour ~- = 60 mm.

4/8 ANN TI~L~COMMUN., 47, n ~ 7-8, 1992

310 J.D. KANELLOPOULOS. - EFFECT OF THE INTEGRATION TIME ON THE RAINRATE DISTRIBUTION

TABLE I. - - Standard deviations apt (%) about the average curves.

Probability levels (%)

K-zone (5 min)

L-zone (5 min)

K-zone (10 min)

L-zone (10 min)

K-zone (30 min)

10-4

4-2.37%

-4-2.032%

4-6.81%

4-2.649%

4-4.8785%

3.10 -4

4-1.91%

4-2.94%

4-2.66%

4-3.253%

4-5.902%

L-zone (30 min) 4-5.774% 4-4.7633%

K-zone (50 min) 4-9.032% -t-10.1074%

L-zone (50 min) 4-8.557% 4-10.10%

10-3 10-2

4-0.879% 4-0.849%

4-3.79% 4-2.836%

4-4.59% 4-1.93%

4-5.544% 4-4.603%

4-5.92% -t-5.236%

4-7.3081% 4-7.703%

-t-12.49% 4-10.99%

-t-9.715% 4-8.979%

3- 10 -2

4-1.09%

4-1.448%

4-2.447%

4-2.746%

-t-4.506%

4-6.574%

4-8.535%

4-8.65%

8

i 8

deviations. As a characteristic example, we have drawn (see Fig. 10) the mean curves for T = 60 min and the vertical bars indicating the standard deviations about the mean for one of the regional groups (particularly, L-zone). Bars have been omitted from the other curve (K-zone) for the sake of clarity. All the above remarks indicate that the division of the meteorological stations into the two regional groups conveys both physical reality and statistical significance.

As a next step, we can find the functional relationship between ~-f and the corresponding exceedance probability for the representative Greek regions. The mean regional results (see Fig. 2-9) can be approximated rea- sonably well by a power-law relation of the form :

(7) P-7(P) = c P d,

R1/RT

~60L.Zon e (60 mln) ~ mm)

1.0 10-4 10-3 11-2

probabd=ty of occurrence (%)

FIG. 10. - - Presentation of the average equiprobable 1-min to 50-min rainfall intensity ratios for the two regional groups in Greece. The vertical bars indicate the standard deviation about the mean for the

L-zone regional group.

Representation des rapports d'intensitds de prdcipitation ~quiprobables moyennes, de I min ~ 60 rain, pour les deux groupes r~gionaux en Grace. Les traits verticaux indiquent l' ~cart-type autour de la moyenne

pour le groupe de la zone L.

over a restricted range. This fact has also been proposed by Segal [8] for the Canadian locations. Table II gives the appropriate coefficients to the above approximation for T = 5, 10 min where the regressions were carried out over the probability range 1 �9 10 -5 < P < 3- 10 -4. Figures 11-12 show how the fitted curves for both the regional groups agree with experimental data. It is obvious that for the above probability range the agreement is very good.

Proceeding further, the fitting R1 = f ( R T ) between equiprobable rainrates is examined. As mentioned pre- viously, the same technique has also been tried by Ravin [6], Ajayi and Ofoche [7] and very recently by Burguefio

et a l [9] for the results taken from North America, Aus- tralia, Nigeria and Barcelona (Spain). For both regional groups of stations, it is shown that the above relationship should be of the form/~1 = a / ~ b with parameters a and b derived after an appropriate least squares regression

RIIRT I 20

- - experimental curve K-Zone . . . . . . fitted curve

5 rain

lO ' 110~4

probability of Occurrence (%)

1~o. 11. - - Presentation of the average equiprobable 1-min to 5-min and 10-min rainfall intensity ratios for the K-zone regional group,

along with the fitted curves.

Reprdsentation des rapports d' intensitd de precipitation ~quiprobables moyennes de 1 min d 5 min et t~ 10 rain, pour le groupe de la zone K,

ainsi que les courbes calcul~es.

ANN. T~LtCOMMUN.. 47, n ~ 7-8, 1992 5/8

311

d

- - 8.9266.10-3 -- 1.237.10 -2

- - 1.434.10 -2

-- 2.034.10 -2

8

RI/RT

lo ~' . . . . . . tFo r


30"

20.

15.

lO.

L-Zone

~ - ~ 5 rain expenm

..... fitted curve 200

150

100 .

FIG 12. - - Same as in Figure 11 but for the L-zone regional group.

Comme ~ la figure 11 mats pour le groupe r~gional L.

fitt ing. F igures 13 and 14 show the e q u i p r o b a b l e RT and R1 ra inra tes , and p o w e r fi t t ings for the ind ica ted

in tegra t ion t imes. Table III d i scussed b e l o w s u m m a r i s e s

the va lues o f a and b c o m p u t e d he re for r ep resen ta t ive

G r e e k local i t ies b e l o n g i n g to zones K and L, wi th cor-

r e s p o n d i n g va lues of the same pa rame te r s t aken f rom

B a r c e l o n a (Spain) [9] and I le-Ife (Niger ia ) [7].

TABLE III. - - a and b constants for the power fit R1 = aR~.

Location T (min) a b

Zone K (Average value of 5 1.00888 1.02170 stations Milos, 10 0.91474 1.06286 Kalamata, Yma, 30 0.96547 1.10416 Heraklion) 60 0.69160 1.25202

Zone L (Average value of 5 0.89388 1.04632 stations Kefalinia, 10 0.95440 1.05162 Mikra, Aliartos, 30 1.05134 1.05322 Hios, Kerkira) 60 0.86214 1.13746

Barcelona (Spain)

2 0.9334 1.0231 5 0.7945 1.0805

10 0.6823 1.1380 15 0.5914 1.2045 30 0.4040 1.3842 60 0.3153 1.5415

Ile-Ife (Nigeria)

2 0.872 1.055 5 0.991 1.098

10 1.797 1.016 20 4.311 0.853

In the las t pa rag raph , we shal l c o m p a r e the c o n v e r -

s ion fac tors c o r r e s p o n d i n g to var ious in teg ra t ion t imes

ob t a ined in d i f fe ren t geog raph ica l loca t ions . First , we

shal l use the ave rage ra t ios ~-~. F igures 15 and 16 show

the resul t s for the ind ica ted locat ions .

E x a m i n i n g the ava i l ab le da ta o f this k ind, we c an re-

m a r k the fo l l owing : resul t s for S lough , E n g l a n d ( Z o n e

R1 (mrn/h)

200

150 "

100"

Location T (min) c

Zone K (Average value of stations 5 0.9874 Milos, Kalamata, Yma, Heraklion) 10 1.012

Zone L (Average value of stations 5 0.93547 Kefalinia, Mikra, Aliartos, Hios, Kerkira) 10 0.93086

Rro R 3 o

. . . . . . l= R10 10 15 20 30 100 150 200 Rs

( rnm/h)

FIG 13. - - Equiprobable RT and R1 rainrates and power fittings for the indicated integration times (r = 5, 10, 30, 60 min), for locations

in zone K.

Taux de precipitation @quiprobables RT et R 1 et puissances corres- pondantes calculus pour les temps d'int@gration indiqu@s (T = 5, 10,

30, 60 min), pour les sites de la zone K.

R1 (mm/h )


TABLE I I . - Conversion factor PT (e) = c/x/.

30 Reo R3o Rio

2o ~ R5 15 20 30 100 150 200

(mm/h )

FIG. 14. - - Equiprobable RT and R 1 rainrates and power fittings for the indicated integration times (T ---- 5, 10, 30, 60 min), for locations

in zone L.

Comme ~ la figure 13 mats pour la zone L.

6/8 ANN. TI~LI~COMMUN, 47, n ~ 7-8, 1992

312 J.D. KANELLOPOULOS. - EFFECT OF THE INTEGRATION TIME ON THE RAINRATE DISTRIBUTION

c 8

I I I l i I ~ l J i

. . . . . . . . Darmstadt, FRG (Fed0

. . . . . . . . Slough, UK (Harden et al) - - - - _ _ Roma, Italy (Fed0 . . . . . . Italy (CCIR 1983 b) . . . . . Sweden (Wlckerts) . . . . . Greece (zone K) - - Greece (zone L)

~ ~ ~

~ 1 7 6 ~

�9

1.c 1 I 1 I t I l l l I 10-5 10 -4

probatofllty of occurrence (%)

FIG. 15. - - Presen ta t ion o f ra infal l intensi ty conve r s ion factors for 7- = 5 man.

Representation des facteurs de conversion de I'intensiM de precipitation pour 7- -- 5 min.

I 1 t 1 I I I l l I . . . . . . . . . Darmstadt, FRG (Fed0 . . . . . Slough, UK (Harden et al)

- - - - Roma, Italy (Fed=) ~ " . ~ . . . . . Italy (CCIR 1983 b)

~ . ~ ~ . - - Sweden (W=ckerts) . . . . . Greece (zone K)

Greece (zone L)

. . . . . . \ \ \ ) ' ' * !

x

\

T = t0 mm - ~ " ~ 1 "

/


FIG. 16. - - Presen ta t ion o f ra infal l intensi ty conve r s ion factors for 7- = 10 man.

Reprdsentation des facteurs de conversion de l'intensiM de precipitation pour -c = 10 min.

the conversion relations for T = 5, 10 min and concerning the two regional groups of stations, are presented in the above Figures.

It is worthwhile to notice that the conversion factors for the different regions in Canada [8] corresponding to 10 years of observations and merging into three groups (I comprising zones A, B, II made up of zones C, D, E and III consisting of zones F and K), are not presented in Figures 15 and 16. The reason is that the Canadian data are given in the form of fitted curves (see Equation (7)) and it is somewhat disturbing to have in the same figure mixture of fitted curves (nicely smooth) and experimental distributions (presenting a more irregular behaviour).

Agreement of the Greek results for both groups of stations seems to be very good with the multiyear set of data taken from Italy [11]. Examining now our Figures 15 and 16 with Figures 8 and 9 of Segal [8], some agreement is also obvious with the Canadian results especially for group I.

On the other hand, the rainfall - - intensity ratios for Rome and Darmstadt presented by Fedi [3] are signi- ficantly larger than those for other European locations such as for Sweden and England.

In addition, the constants of the R1 = aR b fitting taken from Greek, Barcelona (Zone L, 49-years of observations) and Ile-Ife, Nigeria (Zone N, 2-years) are shown in Table III. As we can see the constants taken from our results disagree with those of the Barcelona and Ile-Ife data. At this point we should notice the tropical nature of the Ile-Ife climate and that Barcelona has also storms of tropical nature.

From the above discussion, the climatic zone dependence of the conversion factors between the various ~-- min rainrate distributions becomes obvious. This is a quite significant result which has first been suggested by Segal [8], Burguefio et al [9] and is also confirmed here, although a longer time period of data basis would pro- bably be required. Moreover, the need for mapping the conversion factors from one locality to another, has led the CClR to recommend from various administrations to submit ratios R T / R 1 , as a function of exceedance probability P with indication of the CCIR climatic zone. This fact justifies the publication of the present work, contri- buting with the analysis and elaboration of data from an extensive network of raingauge, around the Greek area, to this direction.

E, 5-years of observations) have been reported by Har- den et al [2], whereas the Swedish data (Zone E, 3-years of observations), referring to 1-, 5- and 10-min distributions have been presented by Wickerts [10]. The 5- and 10-min rainfall intensity ratios for Rome (zone-K) and Darmstadt (zone E) have been presented by Fedi [3] and they are referred to 2-years of experiments. Additional data for Italy [Fucino near Rome and Gera-Lario, zone- K] is referred to set of multiyear observations (4-years) and is given by CCIR [11]. All of these data, as well as

IV. CONCLUSIONS

The dependence of the rainrate distribution upon the integration time of the raingauges is studied here by taking into account appropriate data from some representative Greek locations. Although, the time period of the available data is quite short (only 1 year), the comparison between our results and those referring to other

ANN ~ C O M M U N . , 47, n ~ 7-8, 1992 7/8

J.D. KANELLOPOULOS - EFFECT OF THE INTEGRATION TIME ON THE RAINRATE

a reas h a s r e v e a l e d a g a i n the s i g n i f i c a n t d e p e n d e n c e o f

t he c o n v e r s i o n f a c to r s f r o m the p a r t i c u l a r c l i m a t i c z o n e .

Fur the r , t he f ea s ib i l i t y o f u s i n g a p o w e r l aw to c o n v e r t

o n e - m i n u t e a v e r a g e d ra in fa l l r a t e s to o t h e r v a l u e s , sug -

g e s t e d b y s o m e a u t h o r s fo r I l e - I f e a n d B a r c e l o n a , has

a l so b e e n ve r i f i e d he re .

F ina l ly , as m e n t i o n e d b e f o r e , t he n e e d fo r m a p p i n g

the v a r i o u s c o n v e r s i o n f ac to r s b e c o m e s u rgen t . T h e

s a m e h a p p e n s w i t h t he d e v e l o p m e n t o f a m e t h o d o l o g y

s p e c i f y i n g t h e i m p a c t o f a l i m i t e d n u m b e r o f y e a r s u p o n

t h e r e l i ab i l i t y o f t he c o n v e r s i o n f ac to r s .

Manuscrit refu le 24 d(cembre 1991,

acceptO le 21 avril 1992.

DISTRIBUTION 313

[7] AJAYI (G. P.), OFOCrtE (E. B. C.). Some tropical rainfall rate characteristics at Ile-Ife for microwave and millimeter wave applications. J. Climate Appl. Meteor, USA, 23, pp. 562-567.

[8] SZGAL (B.). The influence of rain gauge integration time on measured rainfall intensity distribution functions. Journ. Atmos Oceamc Tech. (1986), 3, n ~ 4, pp. 662-671.

[9] BURGUE~O (A.), PUIGCERVER (M.), Vn~AR (E.). Influence of rain .gauge integration time on the rain rate statistics used in microwave communications. Ann. T(l(commun., (1988), 43, n ~ 9-10, pp. 522-527.

[10] WICKERTS (S.). Fine scale structures in time and space of ramfall rate. FAO Rep. C 20448-E2. National Defence Research Institute, Stockholm, Wicherk (1982), 79 p.

[11] CCIR Report, Influence of the integration time on rainfall m- tensity statistics. Document 5/105 (Italy). Int. Telecom. Union, Geneva (1983), 7 p.

BIOGRAPHY

REFERENCES

[1] *** CCIR Report 563-3, Dubrovmk, 1986, p. 131. [2] HARDEN (B. N.), NORBYRY (J. R.), WHITE (W. J. K.). Measu-

rements of rainfall for studies of millimetric radio attenuation. Microwave Opt. Acoust. (1977), GB, 1, pp. 197-202.

[3] FEDI (F.). Rainfall characteristics across Europe. Alta Freq. (1979), 48, pp. 52E-60E.

[4] WATSON (P. A.), SATHIASEELAN (V.), POTTER (B.). Development of a climatic map of rainfall attenuation for Europe. Rep. 300, Postgraduate School of Electrical and Electronic Engineermg, University of Bradford, U.K., 134 p.

[5] DAMOSSO (E.), DE RENZIS (E. G.), LINGUA (B.), OSSOLA (P.). Influence of the integration time and the height of raingange on rainfall rate statistics. Conf. Publ. 195, Pt. 2. Inst. Electr. Eng, London (1981), pp. 283-287.

[6] FLAV~ (R. K.). Rain attenuation consideration for satellite paths in Australia. Austr. T(l~commu. Res., Aus (1982), 16, pp. 11-24.

John D. KANELLOPOULOS was born in Athens, Greece on December 12, 1948. He received the diploma of mechanical and electrical engineering and the Dr. Eng. degree from the National Technical University of Athens (NTVA) in 1979, respectively. He has also received the DIC and Ph.D degree from Imperial College of Science and Technology, University of London, in 1979. He is now a Professor at the National Technical University of Athens.

Panaviotis NIKAKIS was born in Athens, Greece in 1943. He received the B.Sc in Physics from University of Athens in 1965. He is now a semor engineer working at the Hellenic Telecommunication Organization S.A., and also a scientific collaborator at the National Technical University of Athens.

George P~PAS was born in Athens, Greece. He received the diploma of Electrical Engineering from the University of Patras, Greece. He is now an engineer working at the Hellenic Telecommunication Organization, SA and also a scientific collaborator at the National Technical University of Athens.

Christos PEP, ELIS was born in Athens, Greece. He recewed the diploma of Electrical Engineering from the National Technical University of Athens. He is now an engineer working at the Hellenic Telecom- munication Organization, SA, and a scientific collaborator at the National Technical University of Athens.

8/8 ANN. TI~LI~COMMUN., 47, n ~ 7-8, 1992

Documents

An investigation into the effect of the integration time on the rainrate distribution