Shape of the rain drop size distributions and classification of rain type at Gadanki

Transcription

1 Indian Journal of Radio & Space Physics Vol. 35, October 2006, pp Shape of the rain drop size distributions and classification of rain type at Gadanki Mahen Konwar, Diganta Kuar Sara, Jyotiroy Das 1 & Sanjay Shara Kohia Science College, Jotsoa, Kohia, Nagaland , India 1 Electronics and Counication Sciences Unit, Indian Statistical Institute, Kolkata , India [e-ail: sanjay_shara11@hotail.co] Received 26 August 2005; revised 22 May 2006; accepted 3 July 2006 Three different rain drop size distribution (RDSD) odels naely exponential, lognoral and gaa distribution are fitted to RDSD as spectra observed fro Joss-Waldvodgel Disdroeter (JWD) at Gadanki (13.8ºN, 79.18ºE). Gaa distribution shows overall good agreeent with observed RDSD for all ranges of rainfall rate. Rainfall rate calculated fro gaa drop size distribution is found to have iniu root ean square error and biasing copared to exponential or lognoral distribution. The intrinsic shape of RDSD is found out fro noralized RDSD which follows an S shape for both low rain 10 h -1 and high rain > 10 h -1. The convective and stratifor rains are separated for an event. The equations of separation for convective and stratifor rains have been derived assuing power law for log 10 (R) - D, log 10 (N * 0 ) - log 10 (R) and log 10 (N * 0 ) - D. The coefficients and exponent for these equations are α DR = 0.145, α RN = 10, α DN = , and β DR = 4.70, β RN = 0.15, β DN = 0.94, respectively. Keywords: Rain drop size distribution (RDSD), Exponential DSD, Lognoral DSD, Gaa DSD, Convective rain, Stratifor rain PACS No: Jq IPC Code: G01S13/95; G06T1/40 1 Introduction Rain drop size distribution (RDSD) is one of the ost widely used paraeters for better understanding and coplete description of rain phenoenon. Different RDSD odels naely exponential 1, lognoral 2, gaa 3 and Weibull 4 are being used to study rain characteristics. Marshall and Paler 1 paraeterized the RDSD and found that it follows an exponential distribution of the following for N( D) = N exp( Λ D)... (1) 0 where, N(D) ( -3-1 ) is the concentration of raindrops per diaeter interval D (), D () the rain drop diaeter, N 0 the intercept paraeter with a fixed value of , Λ ( -1 ) the slope paraeter with a power law relation Λ = 4.1 R , and R the rainfall intensity in h -1. It is found that exponential distribution under predicts (over predicts) the upper tail of the distribution in very light (heavy) rainfall 5. Due to the departure of RDSD s fro exponentiality, any authors have preferred threeparaeter odels to describe rain characteristics 2. Feingold and Levin 2 fitted three-paraeter lognoral odel to frontal convective clouds and found deviation fro an exponential distribution in ost cases. They concluded that the lognoral representation is suitable for a broad range of applications and can facilitate interpretation of the physical processes which control the shape of the distribution. Its paraeters have a siple geoetrical interpretation. The lognoral distribution has the following expression 2 Nt 2 2 N( D) = exp[ Ln ( D/ D ) / 2 ] 0.5 g Ln σ (2 π) ( Lnσ) D (2) where N t ( -3 ) is the total nuber of drops, D g () the geoetric ean of the drop diaeter (or edian size diaeter), and σ the standard geoetrical deviation of D. Ulbrich and Atlas 6 has shown that accuracy in deducing rainfall rates fro RDSD can be iproved if it is assued to be a gaa distribution. The gaa distribution is a three-paraeter distribution. The following relation gives the odified gaa drop size distribution N( D) = N D exp( Λ D) (3) 0 μ

2 KONWAR et al.: RAIN DROP SIZE DISTRIBUTION & CLASSIFICATION 361 where, N 0 ( -1-μ -3 ) is the intercept paraeter, μ the shape paraeter and Λ ( -1 ) the slope paraeter of the distribution. 3, 7 Method of oents approach can be used to calculate the paraeters 8 N 0, μ and Λ. Different representations of RDSDs such as exponential, lognoral and gaa have their own liitations. For exaple the intercept paraeter of gaa distribution is not well defined and not considered as a physical quantity 9. Hence noralization of N(D) is considered as one of the options in studying the shape of RDSD. Sekhon and Srivastava 10, 11 and Willis 7 suggested a noralization of the rain drop diaeters and of the drop size distribution in order to deal directly with the whole set of the spectra on a unique plot, where the paraeters of the RDSD were fitted ore robustly and independently of R. Noralization of N(D) gives rise to the intrinsic shape of RDSD that copares the shape of the two spectra, not having sae liquid water content (LWC) and/or edian volue drop diaeter (D ). Testud et al. 9 developed a atheatical technique to noralize rain spectra and found it to follow an S shape. For any rain event the classification of convective and stratifor rain is very iportant due to its different nature of contribution of latent heat released to cliate. Tokay and Short 8 observed a significant change of gaa paraeter, i.e. interceptor N 0, during the transition fro convective to stratifor rain. Interceptor N 0 of exponential distribution also deonstrates a siilar nature during the transition period 5. Atlas et al. 12 classified rain events as convective, transition and stratifor type rather than convective and stratifor type. They identified rain event as initially convective, if rain rises sharply to peak in excess, about h -1 while D 0 (ass weighted ean diaeter) does not vary greatly. When D 0 and R decrease siultaneously following convective period, the rain is classified as transition. The stratifor rain is characterized by approxiately steady rain having R 10 h -1 and usually with higher values of D 0 (). In recent ties any works have been carried out to find suitable relationships between the gaa paraeters and rainfall type. Ulbrich 3 reported that the gaa RDSD paraeters such as N 0, μ and Λ display a systeatic dependence on one another between different rainfall types, as well fro oent-to-oent within a given rainfall type. Tokay and Short 8 found that it is possible to classify convective and stratifor types of rain fro N 0 -R and Λ-R relations. Maki et al. 13 studied the shape of odified gaa RDSD during convective and stratifor regions. They found distinct characteristic RDSDs for both occasions. Testud et al. 9 also separated stratifor and convective rain types by noralizing the spectra. They presented scatter plots of log 10 (R) versus D, log 10 (R) versus log 10 (N * 0 ), and log 10 (N * 0 ) versus D and found separate clusters of convective and stratifor types of rain. In India nuerous researchers are studying different RDSD odels to fit the to rain phenoenon. For Indian cliate Jassal et al. 14, Vera and Jha 15 studied lognoral drop size distribution and proposed lognoral RDSD odel over Dehradun. Suresh and Bhatnagar (personal counication) found lognoral distribution to fit well with observed DSD in rain spectra at Cuddalore (11.46ºN, 79.46ºE) during north-east onsoon. However they observed soe deviation in the rain rate, h -1 during pre-onsoon and south-west onsoon season. A siilar study was ade by Reddy and Kozu 16, who exained the seasonal variation of gaa paraeters at Gadanki. Over Gadanki, Rao et al. 17 separated precipitating systes using Doppler spectra of VHF/UHF wind profilers and established their associated Z-R relationships. They also discussed the respective RDSDs during convective, transition and stratifor periods. In this paper an effort is ade to present a study of the characteristics of the RDSD and different types of rain with the help of Joss-Waldvodgel Disdroeter (JWD) 18 observations. The study has been carried out with the following objectives: (i) To exaine the fitting of the three RDSD odels, i.e. exponential, lognoral and gaa, to the observed RDSD spectra for different rainfall intensity (ii) To exaine the intrinsic shape of RDSD rain spectra (iii) To separate convective and stratifor rain types fro RDSD characteristics This paper is organized in the following anner. Section 1 presents introduction. Section 2 describes the observational syste and data analysis ethodology. Sections 3 and 4 describe the observations. Results and conclusions are presented in Section 5. 2 Syste description and data analysis The JWD is one of the ost widely used

3 362 INDIAN J RADIO & SPACE PHYS, OCTOBER 2006 instruents around the globe for analyzing the rain RDSD and rain characteristics. The data used in this study are collected fro the JWD, located at National Laboratory for Atospheric Research (NLAR) at Gadanki (13.8ºN, 79.18ºE), India. The JWD estiates the diaeter of the drops by sensing the voltage induced fro the downward displaceent of a 50 c 2 styrofoa cone, once it is hit by rain drops. The output voltage relates to the diaeter of the raindrop falling at terinal velocity. The standard output of the JWD is utilized in this study, which is the nuber of drops that are sorted into 20 size intervals ranging fro 0.3 to about for a one-inute integration tie. However, one disadvantage of JWD is its inability to detect the lower drops during heavy precipitation. For reducing this error, dead error correction ethod has been applied 19. Various rain paraeters such as rainfall rate, liquid water content, radar reflectivity factor, kinetic energy of the falling drops can be easured with the help of JWD. The third oent of the RDSD gives the rain fall rate R in h -1, expressed by the following relation R = (π/6) (3.6/10 6 ) (1/AT) (n i D 3 ) (4) where A is the collecting area of the disdroeter, T the integration tie, n i and D the nuber of drops and drop diaeter of the i th channel of JWD, respectively. The intrinsic shape of the RDSD is obtained by noralizing the nuber density N(D) by a ter N 0 *, thus eliinating the effect of rain rate R on the shape of the distributions. The noralized theoretical or observed raindrop spectra are obtained by the following expressions 9 * 0 N( D) = N F( D/ D ) (5) The scaling paraeter for concentration N * 0 is calculated by the relation N 4 * w D LWC = (6) πρ The ass weighted ean diaeter D, which is equal to the ratio of fourth oent to the third oent of RDSD spectra, given by D M 4 = (7) M 3 where M 3, M 4 are the 3 rd and 4 th oent of RDSD spectra. There is a relationship between Λ and μ of gaa distribution given by the following expression 3 μ + 4 Λ= (8) D where the shape paraeter μ is obtained fro 11G 8 + [ G( G+ 8)] μ= 2(1 G) 3 1/2 (9) M 4 with G = (10) M 2 M 3 6 where M 6 is the 6 th oent of RDSD spectra. For the present study, analysis is carried out with RDSD spectra collected during the period fro 1998 to 2001 at Gadanki. RDSD spectru of rainfall intensity greater than 0.1 h -1 is considered as a rainy event. 3 Observations and results The average RDSDs for rainfall intensity of 5, 25, 50 and 75 h -1 are shown in Figs 1(a), (b), (c) and (d), respectively. The averaged RDSDs are obtained by considering the various RDSD spectra of nearly equal R. In case of 5 h -1, the average spectru is obtained by averaging 1170 spectra. For 25 h -1, 87 spectra in the range fro 24 to 26 h -1 are considered. In case of 50 h -1, 11 spectra are averaged and lastly for 75 h -1, 6 spectra are considered. The exponential, lognoral and gaa RDSD odel paraeters are calculated fro oents ethod 2,5,8. The odel paraeters corresponding to each RDSD odel for the four rain intensity regies are given in Table 1. It is seen that for rain rate of 5 h -1, the three odels are showing good fit to the observed RDSD [Fig. 1(a)]. At rain rate of 25 h -1 and 50 h -1, the exponential RDSD overestiates the observed RDSD at the saller drop diaeter and along the iddle and higher diaeter ranges it is showing good agreeent with the observed RDSD. At rain rate of 50 h -1, the gaa and lognoral RDSD shows good agreeent with the observed RDSD. At 75 h -1 the lognoral RDSD underestiates at the saller diaeter ranges [Fig. 1(d)]. On the other hand the exponential RDSD overestiates at the lower and higher drop diaeter and underestiates at the iddle drop diaeter ranges. The gaa RDSD shows a

4 KONWAR et al.: RAIN DROP SIZE DISTRIBUTION & CLASSIFICATION 363 fairly good agreeent between the odel RDSD and observed RDSD at very heavy rain in all drop diaeter ranges. Value of R ( h -1 ) calculated fro exponential, lognoral and gaa RDSD are copared with those observed fro the JWD, and root ean square errors are found out. Figures 2(a), (b) and (c) show the frequency distribution of the root ean square error at various ranges in increent of 1.25 for exponential, lognoral and gaa RDSD odel, respectively. The corresponding axiu range of error is found to be 15.0, 12.5 and 10.0 for these three odels. The biasing factor in case of exponential RDSD is while the root ean square error (RMSE) For lognoral RDSD, the biasing factor and the RMSE are found to be and , respectively. In case of gaa RDSD, the biasing factor coes out to be and RMSE Rainfall rate calculated fro exponential RDSD underestiates while lognoral RDSD overestiates towards higher rain rate copared to observed values. Gaa RDSD exhibits a good agreeent between calculated and observed rainfall intensity, where the RMSE and biasing factor are found to be iniu copared to the other two RDSD odels. Hence fro this coparative study it is revealed that the Gaa RDSD is perforing better copared to the other two RDSD odels. Figures 3(a), (b), (c), (d) and (e), present the frequency distribution of R, D, µ, Λ and log 10 (N * 0 ) for rainfall intensity 10 h -1. Frequency distribution of R is shown in Fig. 3(a), where ean rainfall intensity is 1.56 h -1 with standard deviation (SD) of 1.96 h -1. The ean value of D is found to be 1.21 and SD of As shown in Fig. 3(c), the ean value of gaa shape paraeter µ is found to be and SD of In case of Λ, the ean value is found to be while the SD of The ean value of scaling paraeter log 10 (N * 0 ) is 3.42 and SD Rain events having R greater than 10 h -1 are referred here as high rain and belong ostly to convective regie. High rains consist of nearly 10.0% of total rainfall observations. Frequency distributions of the various paraeters for high rain are presented in Figs 3(f), (g), (h), (i) and (j). Mean rainfall intensity is h -1 with a SD of h -1 [Fig. 3(f)]. Fig. 1 Averaged nuber density spectra (solid line), exponential RDSD (dash line), lognoral RDSD (long short dash line) and gaa RDSD (dot line) for (a) 5 h -1, (b) 25 h -1, (c) 50 h -1 and (d) 75 h -1 rainfall intensities Table 1 Model paraeters for various RDSD odels Fig. 2 Bar diagra of errors obtained fro the observed rain rate and estiated rainfall intensity fro (a) exponential, (b) lognoral and (c) gaa RDSD Rainrate Rain Drop size distribution Exponential Lognoral Gaa R N 0 Λ N t σ D g N 0 µ Λ h μ

5 364 INDIAN J RADIO & SPACE PHYS, OCTOBER 2006 Figure 3(g) shows the frequency diagra of D, with the ean D found to be 2.09 with a SD of The ean of μ is 9.47 and SD value of 6.22 [Fig. 3(h)]. The ean Λ is found to be with SD of [Fig. 4(i)]. Frequency distribution of log 10 (N * 0 ) is shown in Fig. 3(j). Its ean and SD values are 3.70 and 0.49, respectively. It is observed that though there is a large variability of R for both low (stratifor) and high (convective) rainfall intensity categories, there is nearly sae ean value of μ and log 10 (N 0 * ) for both types of rain. The intrinsic shape for low rain 10 h -1 is shown in Fig. 4(a). It is obtained by plotting N(D)/N 0 * versus D/D. This shape is different fro any of Fig. 3 Frequency distribution of (a) R, (b) D, (c) μ, (d) Λ, (e) log 10 (N 0 * ) for R 10 h -1 and frequency distribution of (f) R, (g) D, (h) μ, (i) Λ, (j) log 10 (N 0 * ) for R >10 h -1 Fig. 4 Intrinsic shape for (a) R 10 h -1 and (b) R > 10 h -1

6 KONWAR et al.: RAIN DROP SIZE DISTRIBUTION & CLASSIFICATION 365 RDSD odels naely exponential, lognoral or gaa distribution and it follows an S type shape. The intrinsic shape for high rainfall rate, i.e. greater than 10 h -1, also follows a siilar S shape to that of low rain intensity [Fig. 4(b)]. It suggests that irrespective of rainfall rate, liquid water content, type of rain, edian volue drop diaeter and gaa RDSD paraeters, the intrinsic shape of RDSD follows a universal S shape. This result is siilar to the intrinsic shape as shown by Testud et al. 9 It is encouraging to note that the intrinsic shape of noralized RDSD follows the sae shape, i.e. S shape, irrespective of different geographical locations. It is to be noted that in general rain events having R > 10 h -1 ostly occurs during convective rain and low intensity rain having R 10 h -1 during stratifor rain period. Though different types of icrophysical echaniss are doinant during convective and stratifor rain, siilar types of S shape are observed in both types of rain. 4 Classification of rain type In order to separate convective and stratifor type of rain fro R, D and N 0 * paraeters, a rain event on May 1999 is selected. The teporal variation of R, N 0, log 10 (N * 0 ) and D are presented in Figs 5(a), (b), (c) and (d) respectively, fro 2123 to 0332 hrs LT. Maxiu rainfall intensity of 87 h -1 is observed fro JWD observations, considered to belong to convective type of rain. The sudden jup down of N 0 paraeter is considered as the starting of stratifor rain 5. As shown in Fig. 5(b), at the tie of starting of stratifor rain, the gaa intercept paraeter N 0 jups down fro to μ -3 at around 2344 hrs LT. As the transition period is conventionally classified as a part of the decaying stage of convective rain (Atlas et al.) 12, for siplicity we considered the data of transition phase as part of convective regie. In Fig. 5 this is arked by a solid line to specify the boundary line for both types of rain. The noralization paraeter N * 0 is found to follow the rainfall intensity [Fig. 5(c)]. During stratifor rain, considerably large and nearly constant values of D is observed; although sall rainfall with low rainfall intensity < 10 h -1 is observed for a long duration of tie fro 2344 to 0332 hrs LT [Fig. 5(d)]. Scatter plots of log 10 (R) - D, log 10 (N * 0 ) log 10 (R) and log 10 (N * 0 ) - D are shown Fig. 5 Teporal variation of (a) R, (b) N 0, (c) log 10 (N 0 * ) and (d) D of the event on May, 1999 fro 2123 LT to 0333 LT

7 366 INDIAN J RADIO & SPACE PHYS, OCTOBER R= 0.145D (11) * N0 = 10 R (12) * N0 = D (13) Siilar observations are also reported by Testud et al 9. However their equations of separation are different fro present analysis. They studied the JWD data collected fro Tropical Ocean and Global Atosphere Coupled Ocean-Atosphere Response Experient (TOGA COARE). They found the following as the equations of separations for 4.25 stratifor and convective type of rain R= 1.64D, * N0 = 10 R and N * = D. Both the convective and stratifor type of rain are having well separated clusters exhibiting distinct behaviour of both types of rain. Fig. 6 Scatter plot of (a) log 10 (R)- D, (b) log 10 (N 0 * )- log 10 (R) and (c) log 10 (N 0 * )-D [The convective rain is indicated by circle while stratifor by star arks.] in Figs 6(a), (b) and (c), respectively. Two separate clusters of stratifor and convective type of rain are observed in all the plots. Power law equations are assued between the DR of the for R DRD β RN =α, N 0 =α RN R β and N 0 =α. The estiated equations that separate these two clusters are given as follows DN DN D β 5 Conclusions The gaa distribution is found to be a good representative of RDSD, showing an overall agreeent with observed RDSD. The RMSE of estiated rain fro gaa distribution is found to be iniu, which is better than both exponential and lognoral distributions. The ean values of μ and log 10 (N * 0 ) show ore or less constant values for both types of low and high rainfall intensity rain categories, though they have large variability in R. The intrinsic shape of RDSD has been exained by the procedure followed by Testud et al. 9 It is found that the S shape structure is proinent in convective as well as in stratifor rain. Invariability in universal S shape is observed despite having widely varying ranges of rainfall intensity, ass weighted drop diaeter and gaa RDSD paraeters. The robustness of the universal shape of RDSD also evokes that any presuption of the shape of RDSD is not required as it departs fro exponential, gaa and lognoral RDSD. Rain type such as convective and stratifor are separated by scatter plots of log 10 (R) - D, log 10 (N * 0 ) - log 10 (R) and log 10 (N * 0 ) - D. Separate clusters of stratifor and convective rain are obtained in each scatter plot and corresponding equations for separation are derived. Acknowledgeent Authors fro Kohia Science College, Nagaland acknowledge gratefully the financial support fro the

8 KONWAR et al.: RAIN DROP SIZE DISTRIBUTION & CLASSIFICATION 367 Indian Space Research Organization (ISRO), Bangalore to carry out this work under RESPOND progra (10/4/362). Authors thank the Director, NMRF for providing the Disdroeter data. Active support fro the Engineers of NMRF is thankfully acknowledged. The kind support fro coordinator of UGC-SVU center of MST Radar application is gratefully acknowledged. Authors are indebted to the authorities of Kohia Science College for providing necessary facilities to carry out the research work. References 1 Marshall J S & Paler W M, The distribution of raindrops with size, J Meteorol (USA), 5 (1948) Feingold G & Levin Zev, The lognoral fit to raindrop size spectra fro frontal convective clouds in Israel, J Cli & Appl Meteorol (USA), 25 (1986) Ulbrich C W, Natural variations in the analytical for of the raindrop size distribution, J Cli & Appl Meteorol (USA), 22 (1983) Jiang H, Sano M & Sekine M, Weibull raindrop-size distribution and its application to rain attenuation, IEE Proc Microwave Antennas Propag (UK), 144 (1997) Waldvogel A, The N 0 jup of raindrop spectra, J Atos Sci (USA), 31 (1974) Ulbrich C W & Atlas D, Assessent of the contribution of differential polarization to iproved rainfall easureents, Radio Sci (USA), 19 (1984) Willis P T, Functional fits to soe observed drop size distributions and paraeterization of rain, J Appl Meteorol (USA), 41 (1984) Tokay A & Short D A, Evidence fro tropical raindrop spectra of the origin of rain fro stratifor versus convective clouds, J Appl Meteorol (USA), 35 (1996) Testud J, Oury S, Blake R A, Aayene P & Dou X, The concept of Noralized distribution to describe raindrop spectra: A tool for cloud physics and cloud reote sensing, J Appl Meteorol (USA), 40 (2001) Sekhon R S & Srivastava R C, Snow size spectra and radar reflectivity, J Atos Sci (USA), 27 (1970) Sekhon R S & Srivastava R C, Doppler radar observations of drop-size distributions in a thunderstor, J Atos Sci (USA), 28 (1971) Atlas D, Ulbrich C W, Marks Jr F D, Aitai E & Willias C R, Systeatic variation of drop size and radar-rainfall relations, J Geophys Res (USA), 104 (1999) Maki Masayuki, Keenan T D, Sasaki Y & Nakaura K, Characteristics of the raindrop distribution in tropical continental squall lines observed in Darwin, Australia, J Appl Meteorol (USA), 40 (2001) Jassal B S, Vera A K & Singh L, Rain drop-size distribution and attenuation for Indian cliate, Indian J Radio Space Phys, 23 (1994) Vera A K & Jha K K, Raindrop size distribution odel for Indian cliate, Indian J Radio Space Phys, 25 (1996) Reddy K K & Kozu T, Measureents of raindrop size distribution over Gadanki during south-west and north-east onsoon, Indian J Radio Space Phys, 32 (2003) Rao T N, Rao D N, Mohan K & Raghavan S, Classification of tropical precipitating systes and associated Z-R relationships, J Geophys Res (USA), 106 (2001) Joss J & Waldvogel A, Ein Spektrograph für Niedersclagstropfen it autoatischer Auswertung, Pure Appl Geophys (USA), 68 (1967) Sauvageot H & Laucaux J P, The shape of averages drop size distributions, J Atos Sci (USA), 52 (1995) 1070.