Estimating Cloud and Rain Parameters from Doppler Radar Data

Real-time mapping of the parameters of precipitating water clouds and rain making use of a vertically-directed Doppler radar is an important problem. In this paper, an algorithm based on an independent estimation of the droplet effective diameter and concentration is suggested. This approach differs...

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Datum:	2003
Hauptverfasser:	Bezvesilniy, O.O., Peters, G., Vavriv, D.M.
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Veröffentlicht:	Радіоастрономічний інститут НАН України 2003
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Zitieren:	Estimating Cloud and Rain Parameters from Doppler Radar Data / O.O. Bezvesilniy, G. Peters, D.M. Vavriv // Радиофизика и радиоастрономия. — 2003. — Т. 8, № 3. — С. 296-302. — Бібліогр.: 7 назв. — англ.

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spelling	irk-123456789-1224232017-07-04T03:03:14Z Estimating Cloud and Rain Parameters from Doppler Radar Data Bezvesilniy, O.O. Peters, G. Vavriv, D.M. Real-time mapping of the parameters of precipitating water clouds and rain making use of a vertically-directed Doppler radar is an important problem. In this paper, an algorithm based on an independent estimation of the droplet effective diameter and concentration is suggested. This approach differs from the Marshall-Palmer retrieval procedure that is based on a single estimated parameter, the radar reflectivity factor. It is shown that the Marshall-Palmer approach can provide good estimates of the averaged parameters, however is not suitable for producing the high resolution time-height maps of the parameters. The two-parameter retrieval algorithm under discussion was tested using the data obtained with the 36 GHz polarimetric Doppler cloud radar MIRA-36. The results of the measurements and their processing are presented. The algorithm suggested has appeared to be applicable for real-time measurements with the vertically-directed Doppler radars. Построение изображений параметров водяных облаков, дающих осадки, и дождя с помощью вертикально направленного доплеровского радиолокатора является важной задачей. В статье предложен алгоритм, основанный на независимой оценке эффективного диаметра и концентрации капель. Этот подход отличается от подхода Маршалла-Пальмера, основанного на оценке одного параметра – радиолокационной отражаемости. Показано, что подход Маршалла-Пальмера обеспечивает хорошую оценку усредненных параметров, но не годится для построения изображений параметров с высоким разрешением в координатах время – высота. Рассматриваемый подход с двумя параметрами был испытан на поляриметрическом доплеровском радиолокаторе MIRA-36. В статье приведены результаты измерений и их обработки. Предложенный алгоритм оказался приемлемым для работы в реальном времени на вертикально направленных доплеровских радиолокаторах. Побудова зображень параметрів водяних хмар, що дають опади, та дощу за допомогою вертикально орієнтованого доплерівського радіолокатора є важливою задачею. В статті запропоновано алгоритм, що базується на незалежній оцінці ефективного діаметра та концентрації крапель. Цей підхід відрізняється від підходу Маршала-Пальмера, що базується на оцінці одного параметра – коефіцієнта радіолокаційного відбиття. Показано, що підхід Маршала-Пальмера забезпечує добру оцінку усереднених параметрів, але не придатний для побудови зображень параметрів з високим розділенням в координатах час – висота. Розглянутий підхід з двома параметрами було випробувано на поляриметричному доплерівському радіолокаторі MIRA-36. В статті наведено результати вимірювань та їх обробки. Запропонований алгоритм виявився придатним для роботи у реальному часі на вертикально спрямованих доплерівських радіолокаторах. 2003 Article Estimating Cloud and Rain Parameters from Doppler Radar Data / O.O. Bezvesilniy, G. Peters, D.M. Vavriv // Радиофизика и радиоастрономия. — 2003. — Т. 8, № 3. — С. 296-302. — Бібліогр.: 7 назв. — англ. 1027-9636 http://dspace.nbuv.gov.ua/handle/123456789/122423 en Радиофизика и радиоастрономия Радіоастрономічний інститут НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
description	Real-time mapping of the parameters of precipitating water clouds and rain making use of a vertically-directed Doppler radar is an important problem. In this paper, an algorithm based on an independent estimation of the droplet effective diameter and concentration is suggested. This approach differs from the Marshall-Palmer retrieval procedure that is based on a single estimated parameter, the radar reflectivity factor. It is shown that the Marshall-Palmer approach can provide good estimates of the averaged parameters, however is not suitable for producing the high resolution time-height maps of the parameters. The two-parameter retrieval algorithm under discussion was tested using the data obtained with the 36 GHz polarimetric Doppler cloud radar MIRA-36. The results of the measurements and their processing are presented. The algorithm suggested has appeared to be applicable for real-time measurements with the vertically-directed Doppler radars.
format	Article
author	Bezvesilniy, O.O. Peters, G. Vavriv, D.M.
spellingShingle	Bezvesilniy, O.O. Peters, G. Vavriv, D.M. Estimating Cloud and Rain Parameters from Doppler Radar Data Радиофизика и радиоастрономия
author_facet	Bezvesilniy, O.O. Peters, G. Vavriv, D.M.
author_sort	Bezvesilniy, O.O.
title	Estimating Cloud and Rain Parameters from Doppler Radar Data
title_short	Estimating Cloud and Rain Parameters from Doppler Radar Data
title_full	Estimating Cloud and Rain Parameters from Doppler Radar Data
title_fullStr	Estimating Cloud and Rain Parameters from Doppler Radar Data
title_full_unstemmed	Estimating Cloud and Rain Parameters from Doppler Radar Data
title_sort	estimating cloud and rain parameters from doppler radar data
publisher	Радіоастрономічний інститут НАН України
publishDate	2003
url	http://dspace.nbuv.gov.ua/handle/123456789/122423
citation_txt	Estimating Cloud and Rain Parameters from Doppler Radar Data / O.O. Bezvesilniy, G. Peters, D.M. Vavriv // Радиофизика и радиоастрономия. — 2003. — Т. 8, № 3. — С. 296-302. — Бібліогр.: 7 назв. — англ.
series	Радиофизика и радиоастрономия
work_keys_str_mv	AT bezvesilniyoo estimatingcloudandrainparametersfromdopplerradardata AT petersg estimatingcloudandrainparametersfromdopplerradardata AT vavrivdm estimatingcloudandrainparametersfromdopplerradardata
first_indexed	2025-07-08T21:41:51Z
last_indexed	2025-07-08T21:41:51Z
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fulltext	Ðàäèîôèçèêà è ðàäèîàñòðîíîìèÿ, 2003, ò. 8, ¹3, ñòð. 296-302 © O. Bezvesilniy, G. Peters, and D. Vavriv, 2003 Estimating Cloud and Rain Parameters from Doppler Radar Data O. Bezvesilniy, G. Peters1, and D. Vavriv Institute of Radio Astronomy, Chervonopraporna St. 4, 61002, Kharkov, Ukraine, Email: obezv@rian.kharkov.ua Email: vavriv@rian.kharkov.ua 1Meteorological Institute, University Hamburg, Bundesstrasse 55, D 20146 Hamburg, Germany, E-mail: peters@miraculix.dkrz.de Received December 3, 2002 Real-time mapping of the parameters of precipitating water clouds and rain making use of a verti- cally-directed Doppler radar is an important problem. In this paper, an algorithm based on an indepen- dent estimation of the droplet effective diameter and concentration is suggested. This approach differs from the Marshall-Palmer retrieval procedure that is based on a single estimated parameter, the radar reflectivity factor. It is shown that the Marshall-Palmer approach can provide good estimates of the averaged param- eters, however is not suitable for producing the high resolution time-height maps of the parameters. The two-parameter retrieval algorithm under discussion was tested using the data obtained with the 36 GHz polarimetric Doppler cloud radar MIRA-36. The results of the measurements and their processing are presented. The algorithm suggested has appeared to be applicable for real-time measurements with the vertically-directed Doppler radars. 1. Introduction The paper is devoted to real-time retrieval of the water cloud and rain parameters with a verti- cally-directed Doppler radar. This problem has been considered by many researchers [1-5] be- cause of its importance for practical applications. One of the basic characteristics of water clouds and rain is the drop size distribution (DSD). The typical, often used form of the DSD is the Gam- ma-distribution [1-2], 00 0 0 1 ( ) . ( 1) D DN D N D e D D µ −  =  Γ µ +   (1) Here ( )Γ µ is the Gamma-function. This form of the DSD depends on three parameters, namely the droplet concentration, 0N 3[m ];− the droplet effective diameter, 0D [mm]; and the parameter µ, which is assumed to be known. Two particular cases are often considered [1-2], specifically 0,µ = which is used for rain drops, and 2,µ = which is for cloud droplets. The drop size distribution determines several integral parameters. For example, the liquid wa- ter content, LWC 3[g / m ], is proportional to the third moment of the distribution, 3 3 0 10 ( )d . 6 LWC D N D D ∞ − π= ∫ Substituting the DSD in the form (1), one can obtain the following expressions: 3 3 0 0 ( 1 3) 10 , 6 ( 1) LWC N D− π Γ µ + += Γ µ + Estimating Cloud and Rain Parameters from Doppler Radar Data 297Ðàäèîôèçèêà è ðàäèîàñòðîíîìèÿ, 2003, ò. 8, ¹3 or 3 3 0 010 ,LWC N D−= π (for 0).µ = (2) The radar reflectivity factor, Z 6 3[mm m ],−⋅ which describes the backscattered power is pro- portional to the sixth moment of the distribution, 6 0 ( )d ,Z D N D D ∞ = ∫ so that 6 0 0 ( 1 6) , ( 1) Z N D Γ µ + += Γ µ + or 6 0 0720 ,Z N D= ⋅ (for 0).µ = (3) Similarly to the effective diameter and the drop- let concentration, the droplet velocity, V [m/s], is an important microphysical parameter. It is a sum of the terminal fall velocity of droplet, ( ) 0,gV D > the mean air flow velocity, ,aV and the turbulent air flow velocity, tV [1-4], ( ) .a g tV V V D V= − + The turbulent velocity of droplets is a random quantity characterized by a zero-mean Gaussian distribution [1-3] with the variance .tσ The tur- bulent velocity is supposed to be independent of the droplet diameter. The terminal fall velocity depends on the droplet diameter. We have used the following approximation [2]: ( )0.670.67 0 0( ) 3.778 ( ) .g gV D D V D D D= ⋅ = The parameter as important as the rainfall rate, R [mm/h], depends both on the drop size distri- bution and the droplet vertical velocity, ( )3 3 0 3.6 10 ( ) ( )d . 6 g aR D V D V N D D ∞ − π= ⋅ −∫ 3 3 0 03.6 10 6 R N D− π= ⋅ × 0 ( 1 3 0.67) ( 1 3) ( ) , ( 1) ( 1)g aV D V  Γ µ + + + Γ µ + +× − Γ µ + Γ µ +  ( )3 3 0 0 03.6 10 2.46 ( ) ,g aR N D V D V−= ⋅ π − (4) (for 0).µ = Modern vertically-directed Doppler radars pro- vide the real-time images of the radar reflectivity factor, the mean Doppler velocity, and the Doppler spectrum width. These values can be used to re- trieve the cloud and rain parameters. In our research we used the Doppler cloud radar MIRA-36 [6] operating at the frequency of 36 GHz. The radar characteristics are listed in a Table. Table. Characteristics of the radar MIRA-36 Frequency 36 GHz Peak power 30 kW Pulse width 100÷400 ns Pulse repetition frequency 2.5, 5.0, or 7.5 kHz Antenna beam width 0.6° Range resolution 15÷60 m Time resolution 0.1 s Doppler analysis FFT FFT length 128, 256, 512 Maximum unambiguous velocity ± 15 m/s Doppler spectrum resolution 5 cm/s Polarization Transmitter Single polarization Receiver Dual polarization Remote control and observations TCP/IP (the Internet) O. Bezvesilniy, G. Peters, and D. Vavriv 298 Ðàäèîôèçèêà è ðàäèîàñòðîíîìèÿ, 2003, ò. 8, ¹3 The aim of this paper is to propose an algo- rithm for real-time retrieval of the high-resolu- tion images of the effective droplet diameter, the droplet concentration, the liquid water content, the vertical air flow velocity, and the rainfall rate. These additional images will improve the radar capacity for real-time observations of precipita- tion events and will provide important informa- tion on the cloud and rain structure. The paper is organized as follows. The intro- duction is followed by a brief review of the clas- sical retrieval approach based on the Marshall- Palmer expressions. Then a two-parameter retriev- al algorithm is considered. After that, results of the algorithm application are discussed. The pa- per ends with a brief conclusion. 2. Marshall-Palmer Approach Several retrieval algorithms have already been proposed. The classical approach is based on the Marshall-Palmer retrieval expressions [1-4]. Ac- cording to this approach, an empirical relation is assumed between the droplet effective diameter and the droplet concentration, 0 0 8000N D = 3m / mm.− (5) Moreover, the vertical air flow velocity is sup- posed to be small as compared to the terminal fall velocity, and an empirical relation for the rainfall rate is introduced, 0.21 01 4.1D R−= ⋅ . Thus, the Marshall-Palmer approach allows re- trieving the cloud and rain parameters from a sin- gle measured value, the radar reflectivity factor, 1.6200 ,Z R= ⋅ 0.880.072 .LWC R= ⋅ The scheme of the approach is given in Fig. 1. Proceeding from the reflectivity factor, the rain- fall rate is estimated, and then the effective diam- eter, the droplet concentration and the liquid water content are retrieved. However, it has been found out that the empir- ical relation between the effective diameter and the droplet concentration varies considerably. A number of similar empirical expressions with oth- er numerical coefficients have been proposed. The diversity of this relations, on the one hand, comes from the variety of the precipitation conditions, and, on the other hand, is a result of inhomogene- ity of the clouds and rain with time and height. Therefore, the Marshall-Palmer expressions are applicable for estimating the averaged cloud and rain parameters and not suitable for retrieving the high-resolution images of the parameters. 3. Two-Parameter Retrieval Approach We have not postulated the relation between the droplet effective diameter and concentration. Instead, we have used the retrieval algorithm based on an independent estimation of these two parameters. As will be shown below, the droplet effective diameter can be estimated from the Doppler spectrum width. The droplet concen- tration can be then retrieved from the reflecti- vity factor (3). In case of incoherent Rayleigh scattering, the radar backscattered signal (IQ-signal) is a zero- mean stationary random process with a well- known correlation function [1, 2, 5, 7], [ ]( ) exp 2s aR P ikVτ = − τ × [ ] ( )exp 2 ( ) exp 2 . ( ) g t D ikV D ikV D  σ τ × − τ σ (6) Fig. 1. Marshall-Palmer approach Estimating Cloud and Rain Parameters from Doppler Radar Data 299Ðàäèîôèçèêà è ðàäèîàñòðîíîìèÿ, 2003, ò. 8, ¹3 Here sP is the signal power, and 6( )D Dσ : is the Rayleigh backscattering cross section. Using (6), one can obtain the formula for the Doppler spec- trum moments, ( ) ( ) . ( ) n a g t n D V V D V V D  σ − +  = σ In particular, the mean Doppler velocity mea- sured by radar is a sum of the mean vertical air flow velocity, Va, and the mean terminal fall ve- locity of droplets, ,gV ,a gV V V= − (7) 0 ( ) ( ) ( 6 0.67 1) ( ) . ( ) ( 6 1) g g g D V D V V D D σ Γ µ + + += = σ Γ µ + + The Doppler spectrum width, σ, is a sum of the turbulent spread, σt, and the spread due to disper- sion of the terminal fall velocity of droplets, ,gσ 2 2 2,g tσ = σ + σ 2 2 2 ( ) ( ) ( ) g g g D V D V D σ σ = − = σ 2 2 0 ( 6 2 0.67 1) ( ) , ( 6 1)g gV D V Γ µ + + ⋅ += − Γ µ + + For the case of 0,µ = 03.6 ( ),g gV V D= ⋅ (8) 00.92 ( ).g gV Dσ = ⋅ (9) Thus, the main idea of the two-parameter ap- proach consists in the following. The spectrum spread due to dispersion of the terminal fall velo- city of droplets depends on the droplet effective diameter. Therefore, if the turbulent spread is small, the effective diameter can be estimated based on the Doppler spectrum width (9). The droplet con- centration can be then retrieved from the reflectiv- ity factor (3). Thus, within the framework of this algorithm, the effective diameter and the droplet concentration are estimated independently, in con- trast to the Marshall-Palmer approach. Calculating the mean terminal fall velocity of the droplets (8) and using the measured value of the mean Dop- pler velocity, the vertical air flow velocity can be extracted (7). Finally, the liquid water content (2) and the rainfall rate (4) can be retrieved. The scheme of the retrieval algorithm is shown in Fig. 2. In case of the fine-droplet clouds, the turbu- lent spread is comparable to the spread due to dispersion of the terminal fall velocity of drop- lets. The typical values of the spectrum width observed in these clouds are less than about 0.2 m/s. This value corresponds to the effective diameter of about 15 µm. This diameter has been considered as the minimum effective diameter that can be estimated within the framework of the approach discussed. Thus, our two-parame- ter approach is suitable for retrieving the pa- rameters of precipitating water clouds and weak or moderate rain. 4. Results and Discussion The retrieval approach suggested has appeared to be a convenient tool for the real-time estima- tion of the cloud and rain parameters. This has Fig. 2. Two-parameter approach O. Bezvesilniy, G. Peters, and D. Vavriv 300 Ðàäèîôèçèêà è ðàäèîàñòðîíîìèÿ, 2003, ò. 8, ¹3 been demonstrated with the K-band cloud Dop- pler radar MIRA-36. The images of the retrieved droplet effective diameter and the droplet con- centration for the case of weak rain and for the region below the melting layer are shown in Figs. 3 and 4. To examine the dependences between differ- ent cloud and rain parameters, the two-dimen- sional histograms have been built in the two- parameter planes. Let us consider the histogram of the measured values of the mean Doppler ve- locity and the Doppler spectrum width in the plane �velocity � spectrum width� shown in Fig. 5. The retrieval approach discussed is based Fig. 3. Image of the retrieved droplet effective diameter Fig. 4. Image of the retrieved droplet concentration on the assumption that the Doppler spectrum width is mainly determined by dispersion of the terminal fall velocity of droplets. Under this as- sumption, if there are no strong vertical air flows, the measured mean Doppler velocity should be on average linearly proportional to the Doppler spectrum width, (8), (9). This theoretical depen- dence is shown in Fig. 5 as a grey line. One can see that the theoretical relation is on average consistent with the observed distribution. Thus, we can conclude that in case of precipitating clouds and rain the spectrum width is principal- ly determined by the dispersion of the terminal fall velocity of droplets. Estimating Cloud and Rain Parameters from Doppler Radar Data 301Ðàäèîôèçèêà è ðàäèîàñòðîíîìèÿ, 2003, ò. 8, ¹3 In Fig. 6, the histogram in the plane of the re- trieved parameters �effective diameter � concentra- tion� is shown. According to this figure, on average the concentration decreases with the diameter. This is in contrast to the Marshall-Palmer relation (5) which is plotted in this figure as a light grey line and shows the reverse dependence. However, this line crosses the maximum of the distribution, implying that the Marshall-Palmer retrieval expressions allow to estimate the averaged values of the parameters. The observed distribution can be interpreted as follows. If the effective diameter and the con- centration are varying while the liquid water con- tent retains constant, then the concentration is a reciprocal of the third power of the effective di- ameter (2). This dependence is plotted as a dark grey line and on average demonstrates better agreement with the observed distribution. The images of the liquid water content, the verti- cal air flow velocity and the rainfall rate in the time- height plane have also been produced. The averaged values of the retrieved parameters are in agreement with the Marshall-Palmer retrieval expressions. 5. Conclusion The two-parameter retrieval algorithm suggest- ed has appeared to be suitable for the real-time observations with vertically-directed Doppler radars. The algorithm provides high-resolution images of the droplet effective diameter, the droplet concen- tration, the liquid water content, the vertical air flow velocity and the rainfall rate. These images provide important information on the cloud and rain struc- ture and thus improve the radar capacity for real- time observation of precipitation events. Acknowledgements This work has been done in the Institute of Radio Astronomy (Ukraine) in cooperation with the Meteorological Institute of Hamburg Uni- versity (Germany). References 1. H. Sauvageot. Radar Meteorology. Artech House, Boston, London, 1992. 2. R. J. Doviak and D. S. Zrnic. Doppler Radar and Weather Observations. Academic Press, 1984. 3. L. J. Battan. Radar Observations of the Atmosphere. The University of Chicago Press, Chicago, 1973. 4. D. Atlas. �Advances in Radar Meteorology�, in Advances in Geophysics. New York: Academic, pp.318-478, 1964. 5. A. G. Gorelik and A. G. Smirnov. Doklady Akad. Nauk SSSR. May 1961, 139, pp. 1098-1100. 6. V. Bormotov, G. Peters, K. Schünemann, D. Vavriv, V. Vinogradov, and V. Volkov. Proceedings of Fig. 5. The histogram of the measured values of the mean Doppler velocity and the Doppler spectrum width Fig. 6. The histogram on the plane of the retrieved effective diameter and the droplet concentration O. Bezvesilniy, G. Peters, and D. Vavriv 302 Ðàäèîôèçèêà è ðàäèîàñòðîíîìèÿ, 2003, ò. 8, ¹3 Millennium Conference on Antenna and Propagation. Davos, Switzerland, April 2000, pp. 319-320. 7. A. Ishimaru. Wave Propagation and Scattering in Random Media. Vol. 1, 2. Academic, New York, 1978. Îöåíêà ïàðàìåòðîâ îáëàêîâ è äîæäÿ ïî äàííûì äîïëåðîâñêîãî ðàäèîëîêàòîðà À. À. Áåçâåñèëüíûé, Ã. Ïèòåðñ, Ä. Ì. Âàâðèâ Ïîñòðîåíèå èçîáðàæåíèé ïàðàìåòðîâ âî- äÿíûõ îáëàêîâ, äàþùèõ îñàäêè, è äîæäÿ ñ ïîìîùüþ âåðòèêàëüíî íàïðàâëåííîãî äîïëå- ðîâñêîãî ðàäèîëîêàòîðà ÿâëÿåòñÿ âàæíîé çà- äà÷åé. Â ñòàòüå ïðåäëîæåí àëãîðèòì, îñíîâàí- íûé íà íåçàâèñèìîé îöåíêå ýôôåêòèâíîãî äèàìåòðà è êîíöåíòðàöèè êàïåëü. Ýòîò ïîä- õîä îòëè÷àåòñÿ îò ïîäõîäà Ìàðøàëëà-Ïàëüìå- ðà, îñíîâàííîãî íà îöåíêå îäíîãî ïàðàìåòðà � ðàäèîëîêàöèîííîé îòðàæàåìîñòè. Ïîêàçàíî, ÷òî ïîäõîä Ìàðøàëëà-Ïàëüìåðà îáåñïå÷èâàåò õîðîøóþ îöåíêó óñðåäíåííûõ ïàðàìåòðîâ, íî íå ãîäèòñÿ äëÿ ïîñòðîåíèÿ èçîá- ðàæåíèé ïàðàìåòðîâ ñ âûñîêèì ðàçðåøåíèåì â êîîðäèíàòàõ âðåìÿ � âûñîòà. Ðàññìàòðèâàå- ìûé ïîäõîä ñ äâóìÿ ïàðàìåòðàìè áûë èñïûòàí íà ïîëÿðèìåòðè÷åñêîì äîïëåðîâñêîì ðàäèîëî- êàòîðå MIRA-36. Â ñòàòüå ïðèâåäåíû ðåçóëüòà- òû èçìåðåíèé è èõ îáðàáîòêè. Ïðåäëîæåííûé àëãîðèòì îêàçàëñÿ ïðèåìëåìûì äëÿ ðàáîòû â ðåàëüíîì âðåìåíè íà âåðòèêàëüíî íàïðàâëåí- íûõ äîïëåðîâñêèõ ðàäèîëîêàòîðàõ. Îö³íêà ïàðàìåòð³â õìàð òà äîùó çà äàíèìè äîïëåð³âñüêîãî ðàä³îëîêàòîðà Î. Î. Áåçâåñ³ëüíèé, Ã. Ï³òåðñ, Ä. Ì. Âàâð³â Ïîáóäîâà çîáðàæåíü ïàðàìåòð³â âîäÿíèõ õìàð, ùî äàþòü îïàäè, òà äîùó çà äîïîìî- ãîþ âåðòèêàëüíî îð³ºíòîâàíîãî äîïëåð³âñü- êîãî ðàä³îëîêàòîðà º âàæëèâîþ çàäà÷åþ. Â ñòàòò³ çàïðîïîíîâàíî àëãîðèòì, ùî áà- çóºòüñÿ íà íåçàëåæí³é îö³íö³ åôåêòèâíîãî ä³àìåòðà òà êîíöåíòðàö³¿ êðàïåëü. Öåé ï³äõ³ä â³äð³çíÿºòüñÿ â³ä ï³äõîäó Ìàðøàëà-Ïàëüìå- ðà, ùî áàçóºòüñÿ íà îö³íö³ îäíîãî ïàðàìåò- ðà � êîåô³ö³ºíòà ðàä³îëîêàö³éíîãî â³äáèòòÿ. Ïîêàçàíî, ùî ï³äõ³ä Ìàðøàëà-Ïàëüìå- ðà çàáåçïå÷óº äîáðó îö³íêó óñåðåäíåíèõ ïà- ðàìåòð³â, àëå íå ïðèäàòíèé äëÿ ïîáóäîâè çîáðàæåíü ïàðàìåòð³â ç âèñîêèì ðîçä³ëåí- íÿì â êîîðäèíàòàõ ÷àñ � âèñîòà. Ðîçãëÿíó- òèé ï³äõ³ä ç äâîìà ïàðàìåòðàìè áóëî âèï- ðîáóâàíî íà ïîëÿðèìåòðè÷íîìó äîïëåð³âñü- êîìó ðàä³îëîêàòîð³ MIRA-36. Â ñòàòò³ íà- âåäåíî ðåçóëüòàòè âèì³ðþâàíü òà ¿õ îáðîá- êè. Çàïðîïîíîâàíèé àëãîðèòì âèÿâèâñÿ ïðèäàòíèì äëÿ ðîáîòè ó ðåàëüíîìó ÷àñ³ íà âåðòèêàëüíî ñïðÿìîâàíèõ äîïëåð³âñüêèõ ðàä³îëîêàòîðàõ.

Estimating Cloud and Rain Parameters from Doppler Radar Data

Institution

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