Indian Journal of Radio & Space Physics Vol. 37, October 2008, pp. 341-352

Estimation of parameters from spectral moments of L-band using Multi-Layer Perceptron Network model

Mahen Konwar 1, Diganta Kumar Sarma 1, Sanjay Sharma *, 1 , U. K. De 2, S. Pal 3 & Jyotirmoy Das 4 1Department of Physics, Kohima Science College, Jotsoma, Kohima, Nagaland 797 002, India 2Department of Environmental Science, Jadavpur University, Kolkata, India 3ECSU, Indian Statistical Institute, Kolkata 700 108, India 4Institute of Technology and Marine Engineering, Jhinga 743368, India Received 19 February 2007; revised 3 September 2007; accepted 11 July 2008

Two Multi-Layer Perceptron (MLP) models are developed to estimate the reflectivity factor (dBZ) and rain intensity (R) from the spectral moments of an L-band wind profiler. Out of the four spectral moment inputs of the MLP models, the backscattered power (P) and Doppler velocity (V D) were found to have better correlation with the rain parameters. The model results were validated with the Joss Waldvogel (JWD) observations. For the training and validation data sets of dBZ, the root mean square error (rmse) of estimated and observed data sets were found to be 5.05 and 5.32 dBZ with correlation coefficients of 0.90 and 0.86, respectively. Similarly, for the training and validation data sets of R, the rmse for estimated and observed values were found to be 4.27 and 7.74 mmh-1 respectively with correlation coefficients of 0.95 and 0.78. The developed models were validated with a rain event on 22 June 2000, that consisted of rain from both convective and stratiform regimes. The error between the estimated and observed rain accumulation was found to be ∼ 5%. The height profiles of estimated dBZ were able to identify the bright band during stratiform rain by virtue of high values of reflectivity gradient at around 4.0 km height. Though ambiguity in the estimation of R was observed at bright band level, overall estimated parameters were in good agreement with general characteristics of convective and stratiform rain.

Keywords: L-band wind profiler, Spectral moments, Joss Waldovogel Disdrometer, Radar reflectivity factor, Rain intensity, Multi-Layer Perceptron network PACS No.: 92.40.Ea; 92.40.eg; 92.60.gf

1 Introduction power is by utilizing the empirical Z-R relations, Measurement of rain parameters by remote sensing where Z is calculated by using the following radar technique is a fundamental objective in radar equation 2 meteorology. There are two types of sensors, i.e. 2 passive and active, for rain measurement by the C K Z P = … (1) remote sensing technique. The passive sensors, such r r 2 as microwave radiometer, measure radiance that is the end product of the integrated effects of the where Pr is backscattered power from the target, K the electromagnetic absorption-emission and scattering dielectric constant of the target, C the radar constant through the precipitating cloud along the sensor view and r the range of the target. Here, Z is a function of path 1. However, height assignment of cloud systems rain drop size distribution and is independent of radar by passive remote sensing is not very specific. On the frequency. other hand, active sensors provide specific height The wind profilers were originally developed to information of precipitating systems based on the time measure the height profiles of the three components delay of back scattered return power 1. Presently many of wind velocity. Subsequently however, many active sensor systems e.g. scanning reflectivity radar, researchers demonstrated its utility for the Doppler , polarimetric radar and identification/classification of precipitating systems 6-9 profiling micro rain radar 2-5 are being utilized for rain and in measuring the rain parameters, i.e. radar measurements by using back scattered power in terms reflectivity factor and rainfall intensity 10-14 . The of radar reflectivity factor ( Z). The common approach precipitating signatures obtained from the wind for measuring rainfall intensity from backscattered profiler are due to Rayleigh scattering from 342 INDIAN J RADIO & SPACE PHYS, OCTOBER 2008

hydrometeors 2. The Rayleigh scattering component In the past, non-parametric technique based Multi- observed by a vertically incident profiler results from Layer Perceptron 23 (MLP) networks have been convolution of normalized atmospheric turbulent utilized to solve many diverse problems in microwave probability density function with the hydrometeor remote sensing 24–26 . A similar approach is utilized for reflectivity 10 and it is expressed as the first time to estimate the rain parameters from follows Doppler spectra of L-band wind profiler. The motivating factor of the present study is to enhance S Rayleigh (v) = Sair (v − ω) × S hyd (v) the capability of the wind profiler as a rain profiling … (2) system during rainy situations, when clear air echoes = /1[ 2πσ ]exp[ −(v − ω) 2 2/ σ 2 ]× S (v) air air hyd are completely masked by echoes. The main objective of the present study is to develop MLP where v, is the fall velocity of hydrometeor; ϖ, the air network models to estimate the radar reflectivity velocity either in the upward or downward direction; factor (dBZ) and rainfall intensity ( R) from the and σair , the spectral broadening of clear air Doppler spectral moments of L-band wind profiler; and to spectrum. The hydrometeor spectrum in stationary air study the characteristics of the precipitating systems is represented by in terms of height profiles of the estimated

6 parameters. The multivariable MLP based non- S hyd (v) = N(D)D dD d/ v … (3) parametric techniques are important because of their ability in dealing with the above mentioned errors where N(D), D and d D/d v are number concentration common to wind profiler data. First of all, the of the hydrometeor distribution, the rain drop inclusion of the multivariable parameters reduce the diameter and the coordinate transformation from total dependency of dBZ and R measurements on terminal fall speed to diameter space, respectively. normalized back scattered power. In the present Extensive research has been carried out to estimate study, these parameters are estimated with the help of rain drop size distribution (RDSD) from the Doppler combined use of all the spectral moments of the spectra of either individual or combined use of Very Doppler spectra of L-band wind profiler and DSD High Frequency (VHF) and Ultra High Frequency 13-15 spectra from Joss Waldvogel Disdrometer (JWD). (UHF) wind profilers . For RDSD retrievals and Moreover, the training of the spectral moments with subsequently to estimate the rain parameters, the wind dBZ as measured from the independent system will profilers suffer from certain limitations, viz. overcome the limitation of the non-linear response of (i) Non-linear response of the receiver during rain - the receiver during rainy situations to a certain extent. During clear air measurements, clear air wind Further in the proposed methodology, it is not profiler receiver has a linear response. However, necessary to assume a specific model for the retrieval during rain, when backscattered signal is very of rain parameters, and to take into account the strong, profiler receiver has a non-linear natural variation of the rain parameters. response and an increase in the incident power produces only a small increase 16 in the measured 2 System descriptions and data preparation signal power ( S). At some point the receiver National Atmospheric Research Laboratory even becomes completely saturated and further (NARL), at Gadanki (13.5°N, 79.2°E), India, has the increase in incident power leads to no facility of collocated instruments. For the present measurable increase in S. In addition, the wind work, observations of L-band wind profiler and Joss profilers are not calibrated, which implies that Waldvogel Disdrometer (JWD) for the years 1998- radar reflectivity factor ( Z) can not be 2000 were utilized. The L-band wind profilers determined directly. operated at 1357 MHz is very sensitive to (ii) Another limitation is the assumptions made in precipitation particles 7 due to Rayleigh scattering, certain models 17-22 , both physical and empirical. where scattering cross-section is inversely Also, due to the natural variation of RDSD with proportional to the fourth power of wavelength. The respect to either Z or R, there is an inherent system description of the L-band wind profiler is limitation of the parametric approach to follow a shown in Table 1. particular model for the estimation of rain For the extraction of atmospheric parameters from parameters 11 . the back scattered signals of wind profiler it requires KONWAR et al. : RAIN PARAMETERS FROM WIND PROFILER USING MLP NETWORK MODEL 343

Table 1 ―System description of the L-band wind profiler onward only have been considered. The moment estimation of profiler spectra were carried out with Parameters Specification the help of Atmospheric Data Processor (ADP) 28 Frequency 1357.5 MHz software developed at NARL, Gadanki. Antenna Aperture 3.8m × 3.8m Phased Array The other system, i.e. JWD counts the number of Beam width 4° rain drops of different diameters with an integration Pulse width 1 µs time of one minute. For the present study, the dBZ Inter Pulse 80 µs and R obtained from JWD have been utilized. Number of FFT points 128 Number of coherent Integration 50 Although the JWD underestimates smaller raindrops Duty ratio 1.25% during heavy precipitation period due to dead error 29 time , still it is one of the most widely used tools to extensive signal processing. The signal processing of study rain characteristics. For the present data set, the these signals mainly consist of estimation of 0th, 1st dead error correction was applied to reduce the error and 2nd moments of Doppler spectrum 27 . These due to the underestimation of the smaller drops during moments correspond to total power ( P), mean heavy . The dBZ and R were estimated from 2 Doppler shift ( fD) and variance ( σ ) of the Doppler JWD observations, by using the following spectra and they are estimated by the following equations 30 : expressions 27 : dBZ = 10 log 10 ( )Z … (9) P = P … (4) ∑ i where

1 20 6 f D = ∑ Pi fi … (5) Z = /1( AT ) (N /V (D )) D ∆D … (10) P ∑ i i i i=1

2 1 2 20 σ = ∑ Pi ( f − f D ) … (6) 3 3 P I R = (π )(6/ 10/6.3 )( /1 AT )∑ N i Di ∆D … (11) i=1 Where Pi and fi are the power and Doppler frequency shift of the ith spectral line in Doppler spectrum, where A, is the collecting area of the sensor; T, the respectively. integration time of one minute; Ni, the number of Further, for the vertical incident beam of L-band drops in the ith channel; and Di, the mean drop wind profiler, fall velocity of the mean raindrop is diameter of the ith channel. given by To make the near simultaneous data points of L- band profiler and JWD, a time lag due to falling rain VD = f D (λ )2/ … (7) drops from a height of 0.75 km to the ground is incorporated. The time lag is calculated with the help where λ, is the wavelength of the L-band profiler. By of fall velocity parameter (V D) at 0.75 km. Averaging using this expression the Doppler frequency spectra of the DSD spectra was carried out from the start-to- can be converted to the corresponding velocity stop time observations of the vertical beam of the spectra. profiler to match the different integration time of the Along with these moments the noise level of the two systems. back scattered echoes were also estimated. From the returned power ( P) and noise level ( L), the signal-to- 3 Methodology noise ratio (SNR) was calculated by the following In this study, dBZ and R are estimated from expression spectral moments of L-band wind profiler with the

help of DSD observations from JWD by utilizing the SNR(dB) =10 log( P / L × NFFT ) … (8) 31 MLP network. No prior assumption of any model is where NFFT, is the number of FFT points. For L- made to the spectrum of the wind profiler. The MLP band profiler observations, though the measured networks consist of several layers of neurons, of parameters are available from 0.3 km onward, but due which first one is the input layer and the last one the to the presence of ground clutter, data from 0.75 km output layer and in-between layers are called hidden 344 INDIAN J RADIO & SPACE PHYS, OCTOBER 2008

layers. Every node, except the input layer nodes, where J, is the Jacobian matrix that contains first computes the weighted sum of its inputs and applies derivative of the network error with respect to weight an activation function, a sigmoid function to compute and bias; I, the unit matrix; Et, the error at output its output. This output is then transmitted to the nodes node and µ, the learning parameter. Depending upon of the next layer. The objective of the MLP learning is the magnitude of µ the method transit smoothly to set the connection weight in such a manner as to between the two extremes: Newton method ( µ – 0) minimize the error between the network output and and well known steepest decent method ( µ - ∞). For the target. The back propagation gradient decent L-M algorithm the performance index to be optimized method 32 of learning is utilized for this purpose. The is defined as architectural diagram of the present MLP is shown in 2 Fig. 1. The present MLP networks consist of three F(w) = ∑[∑(dkp − okp ) ] … (13) layers, viz. input layer with four nodes, hidden layer where dkp and okp are the target and output values of with 15 nodes and output layer with one node. It is to be mentioned here that the optimum number of the kth output and pth features. hidden nodes were found to be 15 in the present MLP After the supervised training to the prepared input network. The two MLP networks were trained data set with respect to target dBZ and R, the weight separately by using the four input vectors from the L- matrices for input- hidden layers and hidden-output layers in both the cases were estimated. These two band wind profiler, i.e. P, VD, σ, and SNR and output vectors as dBZ and R from the JWD. For the developed MLP network models were designated as MLP_dBZ and MLP_ R. Thereafter, with the help of present study the whole data set consists of ∼ 1000 developed MLP network models the dBZ and R were points. The data set is divided into two parts, i.e. 90% estimated for the given set of input spectral moments is utilized for training and remaining 10% for data. validation of the trained MLPs. The above network architecture is realized through the MATLAB toolbox 4 Results based on Levenberg-Marquardt (L-M) back Simultaneous observations of the L-band wind propagation algorithm. The advantage of using this profiler and JWD during convection-precipitation algorithm is that it converges quickly as compared to campaign at NARL, Gadanki were utilized for this most of the other algorithms. It can train any network work. A rain event on 22-23 June 2000 was selected as long as its weight, net input and transfer function to study the typical characteristics of different have derivative function. The L-M algorithm uses the moments of Doppler spectra during rainy situations. approximation to the Hessian matrix in the Newton This event consists of rain from both the convective method, where the weight vectors Xt is updated as and stratiform regimes. The height-time intensity T T X t+1 = X t −[J J + µI]− J Et … (12) (HTI) plots of P, VD, σ and SNR of Doppler spectrum are shown in Figs. 2(a), (b), (c) and (d), respectively. On this day, the convective rain started at around 2142 hrs LT and as evident from the profiler observations, it was characterized by high values of backscattered power up to the upper height of ~ 6 km [Fig. 2(a)]. In general, the convective rain is characterized by high intensity rain at ground. The stratiform type of rain is identified through the presence of bright band, which is indicated by a band of high value of back scattered powers at around 4.2 km. The bright band started to form at around 0131 hrs LT onwards on 23 June 2000. The stratiform rain at the ground is characterized by low intensity rain for longer duration of time. Figure 2(b) shows the mean

Doppler velocity of falling rain drops. It was observed Fig. 1 ―Architecture of three layers MLP network to estimate the that Doppler velocity of rain drops vary from 1 to 10 rain parameters from the spectral moments of L-band profiler m/s. The downward velocity is indicated by –ve sign. KONWAR et al. : RAIN PARAMETERS FROM WIND PROFILER USING MLP NETWORK MODEL 345

This parameter is a good indicator of rainy and non- rainy situations. Though its variation with rain intensity is not very significant, its value jumped from -10 dB to ≥ 10 dB from non-rainy to rainy situation. During this period, the temporal variation of dBZ and R at ground are shown in Figs. 2(e) and (f), respectively. During the convective spell the values of reflectivity factor were varying in the range ∼ 40-50 dBZ, whereas during the stratiform period its values were < 40 dBZ and minimum values observed up to 20 dBZ. Similarly, the temporal variation of R shows three spells of convective rain with intensity ranging from 25 to 78 mmh-1. These spells started at 2137 hrs LT (JWD data is available from 2143 hrs LT onwards) and ended at 0110 hrs LT followed by stratiform type of rain with low rain intensity < 5 mmh-1. The near simultaneous and collocated data points of the wind profiler and JWD are considered to study the characteristics of moments of the profiler with respect to dBZ and R. For this purpose, the scatter

plots for P-dBZ, VD-dBZ, σ-dBZ and SNR-dBZ are shown in Figs. 3(a), (b), (c) and (d), respectively. For the scatter plots, the dBZ values were considered from 10 dBZ onward. The power law is fitted to these data sets and their corresponding equations are provided in the respective panels. Maximum value of exponent (0.53) in the power law was observed for the P-dBZ relation and its values were found to be in descending

order for VD-dBZ, σ-dBZ and SNR-dBZ. The correlation coefficient (CC) for each scatter plot is also provided in the respective panels. Maximum correlation (0.70) was found for VD-dBZ and the CC were in decreasing order for P-dBZ, SW-dBZ and SNR-dBZ. Similarly, Figs 4 (a), (b), (c) and (d) show

the scatter plots for P-R, VD-R, σ-R and SNR-R, Fig. 2 ―HTI plots of (a) returned power, (b) Doppler velocity, (c) respectively. For these scatter plots the rain intensity Spectral width, (d) SNR of a Doppler spectrum of L-band wind values were considered from 0.1 mmh -1 onward. The profiler, (e) temporal variation of radar reflectivity factor and (f) temporal variation of rain intensity from JWD power law is fitted to these data sets and their corresponding equations are provided in the During convective regime the maximum Doppler respective panels. Maximum value of exponent velocity is found to be around 10 m/s at higher (0.107) in the power law relation was observed for P- altitudes. Figure 2(c) shows the HTI plot of spectral R plot and its values were in decreasing order for VD- width of Doppler spectra. Large values of SW present R, σ-R and SNR-R. The correlation coefficient for during convective rain indicate strong turbulence in each scatter plot is also provided in the respective the atmosphere. This parameter has positive panels. Maximum correlation (0.47) was found for correlation with rain as heavy rainfall in the ground the VD-R relation and in decreasing order for P-R, was preoccupied by strong turbulence in the SW-R and SNR-R. Interestingly, though the SNR-R atmosphere. Figure 2(d) shows the HTI plot of signal- relation has least values of exponent and correlation to-noise ratio during non-rainy and rainy situations. coefficient (CC) but it is a good indicator of rain. It 346 INDIAN J RADIO & SPACE PHYS, OCTOBER 2008

Fig. 3 ―Scatter plots for (a) returned power versus radar reflectivity factor, (b) Doppler velocity versus radar reflectivity factor, (c) spectral width versus radar reflectivity factor and (d) SNR versus radar reflectivity factor during the rainy situations

Fig. 4 ―Scatter plots for (a) returned power versus rain intensity, (b) Doppler velocity versus rain intensity, (c) spectral width versus rain intensity and (d) SNR versus rain intensity during the rainy situations KONWAR et al. : RAIN PARAMETERS FROM WIND PROFILER USING MLP NETWORK MODEL 347

was observed that as soon as rain started its SNR the estimated and observed dBZ for training and jumped from negative to positive values. validation data sets are shown in Figs 5(a) and (b), After developing the weight matrices of the MLP respectively. The root mean square error (rmse) value network model with the help of supervised training, as for training data set with respect to observed values discussed above, the dBZ and R were estimated by was found to be 5.05 dBZ, with a bias of -0.02 dBZ using the spectral moment as inputs from the training and correlation coefficient of 0.90 [Fig. 5(a)]. The and validation data sets. The estimated dBZ from the rmse value for validation data set was found to be training and validation data sets were further validated 5.32 dBZ with a bias of 0.93 dBZ and CC of 0.86 with the observed dBZ. Pixel-to-pixel comparison of [Fig. 5(b)]. Figures 6(a) and (b) show pixel-to-pixel

Fig. 5 ―Pixel-to-pixel comparison of estimated and observed radar reflectivity factor for (a) training data set and (b) validation data set

Fig. 6 ―Pixel-to-pixel comparison of estimated and observed rain intensity for (a) training data set and (b) validation data set 348 INDIAN J RADIO & SPACE PHYS, OCTOBER 2008

comparison of model estimated and observed R for the MLP_dBZ model were reasonably improved the training and validation data set. It was observed compared to that of regression model. Similarly, Fig. that most of the time the peaks of the estimated rain 7(a) shows the temporal variation of R as estimated intensity were following the observed intensity, from MLP_ R model and multivariable regression though in some cases there were some differences in model along with the observed values on this day. magnitudes. The rmse values for training and With respect to observed values, the rmse for the validation data set were found to be 5.32 mmh-1 and MLP _R estimated values was found to be 4.40 7.74 mmh-1, respectively. The correlation coefficients mmh-1, with a bias and CC of 0.17 mmh-1 and 0.91, for training and validation data set were found to be respectively. In case of regression model, the rmse 0.95 and 0.78, respectively. value of 8.77 mmh-1 was found with a bias and CC of -1 An independent validation of the model estimated 3.21 and 0.33 mmh , respectively. The observed and dBZ and R with the ground JWD observations was MLP_ R estimated total rain accumulation were found carried out for a rain event on 22 June 2000. Further, to be ∼ 21 mm and ∼19 mm, respectively with an the model estimated parameters were also compared error of ∼ 5.0 %. Here the rain accumulation from the with the results from the multivariable regression profiler measurement, i.e. MLP_ R was method 33 . This event consists of both convective and underestimated compared to rain accumulation from stratiform rain. The details of this rain event are JWD. Rajopadhya et al .34 , have reported an error, provided in Figs 2(a)-(d). The temporal variation of between estimated and observed rain rate, of around dBZ as estimated from MLP_ dBZ and multivariable 4% with a correlation coefficient of 0.76. In this regression method, along with the observed values are referred work the rain intensity was calculated from shown in Fig. 7(b). The rmse for the MLP_ dBZ the RDSD, which was estimated by fitting the Gamma estimated values with respect to the observed values function to the Doppler spectra of UHF profiler at the was found to be 5.10 dBZ with a bias of -1.08 dBZ height of 1.9 km, by taking into account the vertical and CC of 0.84. The rmse for the regression method clear air velocity. was found to be 5.44 dBZ and bias of 1.34 dBZ with a Further, on 22 June 2000, the height profiles CC of 0.69. It showed that the results obtained from of dBZ and R, as estimated by the proposed

Fig. 7 ―Temporal variation of estimated and observed (a) rain intensity (mmh -1) and (b) radar reflectivity factor (dBZ) [on 22 June 2000 obtained from regression and MLP method] KONWAR et al. : RAIN PARAMETERS FROM WIND PROFILER USING MLP NETWORK MODEL 349

Fig. 8 ―Height profiles of MLP estimated-Z during (a), (b) convective and (c), (d) stratiform; and height profiles of R during (e), (f) convective and (g), (h) stratiform, type of rain on 22 June 2000 methodology are shown in Figs. 8(a)-(d) and 8(e)-(h), respectively. During initial convective stage, the low respectively. The presented height profiles are at values of R of the order of 2-10 mm/h were observed, different stages of convective and stratiform rain. whereas during the mature stage, high values of R, of Figures 8(a) and (b) show the height profiles of dBZ the order of 50-90 mm/h were observed up to ∼ 5 km. during the initial and mature stage of the convective Figures 8(g) and (h) show height profiles of R during systems, respectively. During initial convective stage, different stages of stratiform rain. During stratiform the reflectivity factor of around 32 dBZ were situation, the overall values of estimated R were low, observed up to ∼ 2.0 km, whereas during mature i.e. of the order of 2-10 mmh-1. At the bright band stage the significant values of reflectivity factor of 40 level, there is an ambiguity of high values of R, which - 50 dBZ were observed up to ∼ 4.5 km. Figures 8(c) require a correction for the realistic measurements of and (d) show the height profiles of dBZ during these parameters at bright band level. During the different stages of stratiform rain. At the initial absence of strong bright band, this ambiguity is stage of the stratiform rain, at 0154 hrs LT, the reduced to certain extent [Fig. 8(h)]. Overall, the presence of bright band is quite obvious at a height values of the model estimated R at the lower heights of around ∼ 4.0 to 4.5 km by virtue of high value of is reasonably comparable with the JWD observations reflectivity gradient of ∼ 37 dBZ/km. At around 0216 at ground, which are provided in each panel. hrs LT, at the later stage of the stratiform rain, the On 18 May 1999, a case study was carried out to bright band was not very prominent as concluded by compare the height profiles of model estimated dBZ virtue of low value of reflectivity gradient of ∼ 12 and R with the Precipitation Radar (PR) observation dBZ/km at around same height [Fig. 8(d)]. [on board of Tropical Rainfall Measuring Mission Interestingly, the values of the estimated dBZ at the (TRMM) satellite]. On this day, the TRMM satellite lower heights are quite comparable with the JWD passed nearly over the radar site during precipitating observations at ground, which are provided at each time (TRMM orbit number 8463). For this panel. Similarly, for the same day Figs 8(e) and (f) comparison, the 2A25 data product of PR was show the model estimated height profiles of R during utilized. The nearly coincident footprints of TRMM- the initial and mature stage of the convective systems, PR and L-band profiler were selected for analysis. 350 INDIAN J RADIO & SPACE PHYS, OCTOBER 2008

The pixel resolution of PR is 16.0 km 2 with a height between these two parameters. The fall velocity of resolution of 250 km and a beam width of 1 °. The rain drops is most closely related with these profiler and PR estimated height profiles of dBZ and parameters in terms of high value of correlation R are shown in Figs 9(a) and (b), respectively. As coefficient. The SNR parameter of the profiler, these two systems have different height resolution, though poorly correlated with rain parameters, was a therefore, the MLP and PR estimated rain parameters good indicator to represent rain or no-rain situations. are plotted at 150 and 250 m resolutions, respectively. Overall good agreement between the estimated rain The important feature of this comparative study of parameters from the proposed methodology and the dBZ is the detection of a bright band at around JWD measured parameters were observed. It was also ~ 3.7 km, by virtue of reflectivity gradient of 11 found that the MLP model performed better compared dBZ/ km signifying the presence of weak bright to parametric regression models. The estimated rain band during stratiform precipitation [Fig. 9(a)]. parameters from the proposed methodology were also Though the height profile of R from MLP_ R is able to show the general characteristics of the comparable with PR measurements, it had slightly convective and stratiform rain by virtue of its high underestimated rain rate compared to PR. For the values of dBZ and R up to upper heights during height profile of R, at the bright band level, the convective rain and the presence of bright band ambiguity of rain rate estimation from MLP_ R is during stratiform rain. It was noticed that during the relatively less due to the presence of weak bright presence of strong bright band there is significant band [Fig. 9(b)]. Though this comparison may not be error in the rain rate estimation at that height. statistically very significant, overall good agreement The ambiguity of the rainfall estimation at the was found between the height profiles of model and bright band is expected because different PR estimated dBZ and R. microphysical processes dominate the precipitating mechanisms. The MLPs estimated dBZ and R were 5 Summary and discussions compared with the PR estimated height profiles over Artificial Neural Network (ANN) based two MLP Gadanki. Significantly the height profiles of dBZ models have been developed to estimate the dBZ and from both the systems have shown bright band R from the spectral moments of the L-band wind signature at around 3.7 km height. There are many profiler at NARL, Gadanki. The characteristics of the reasons to expect the discrepancy in the model spectral moments of the L-band wind profiler were estimated and the observed rain parameters 34 . There is studied with respect to rain parameters. It was a limitation of sample volumes in the estimation of observed that back scattered power P was most height profiles of the rain parameters. In the present closely related with these parameters by virtue of study, the spectral moments at the lower most reliable higher value of exponent in the power law relations range bin (0.75 km) were trained with the JWD

Fig. 9 ―Comparison of height profiles of (a) Z; and (b) R (from PR observed and MLP estimated) KONWAR et al. : RAIN PARAMETERS FROM WIND PROFILER USING MLP NETWORK MODEL 351

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Authors would Lett (USA) , 19 (1992) 1017. 14 Maguire W B & Avery S K, Retrieval of raindrop size like to thank Director, NARL, Gadanki and distributions using two Doppler wind profilers: Model Coordinator SVU-UGC Centre for MST Radar sensitivity testing, J Appl Meteorol (USA) , 33 (1994) 1623. Applications for providing the necessary support to 15 Sharma S, Sarma D K, Konwar M, Das J & Jain A R, conduct the experiment at radar site and subsequent Retrieval of raindrop size distributions from the L-band and VHF wind profilers during convective and stratiform rain, data analysis. The active support from the engineers at Indian J Radio & Space Phys, 37 (2008) 1850 . NMRF during the experiments is thankfully 16 Ralph F M, Neiman P J, Kamp van de D W & Law D C, acknowledged. Authors are thankful to NASA-GSFC Using spectral moment data from NOAA’s 404 MHz radar for providing the TRMM data. 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