Simulation of Daily Rainfall from Concurrent Meteorological ParametersoverCoreMonsoonRegionof India : ANovelApproach

In the present work, daily rainfall is simulated over the coremonsoon region of India by using a feedforwardmultilayer perceptron (MLP) model. Daily rainfall is found to be optimally dependent on four concurrent meteorological parameters, namely, geopotential height, specific humidity, zonal, andmeridional wind at 1000mb, 925mb, 850mb, and 700mb pressure levels during 00, 06, 12, and 18 Greenwich Mean Time (GMT). +e architecture of the optimized feedforward MLP model consists of 64 nodes in the input layer, 10 nodes in the hidden layer, and 1 node in the output layer. +e results from the model are compared with the 3B42 (version 7) rainfall product. In terms of root mean square error (rmse) and correlation coefficient (cc), the model is performing better compared to the satellite-derived 3B42 rainfall product, whereas in terms of bias, the performance of the 3B42 product is better compared to the model.+e weight matrices of the feedforwardMLPmodel are estimated at a particular location (22.5°N, 82.5°E). +ese weight matrices are able to simulate daily rainfall at neighbourhood locations also with reasonably good accuracy with cc in the range of 0.41 to 0.55. +e performance of the model improves in case of an aerial average of daily rainfall with significantly enhanced cc (0.72). +e model is able to capture monthly and intraseasonal variation of rainfall with reasonably good accuracy, with cc of 0.88 and 0.68, respectively. +e simulation model has a limitation that it is not able to simulate extreme high rainfall events (>60mm/day). Overall, the developed model is performing reasonably well. +is approach has a potential to be used as a rain parameterization scheme in the dynamical atmospheric and coupled models to simulate daily rainfall. Nevertheless, the present approach can also be used for multistep prediction of rainfall.


Introduction
Rainfall is a core component of the hydrological cycle.e knowledge of rainfall at different time scales is of paramount importance for many scientific and operational applications.Over continental regions, operational measurement of rainfall in general, is carried out by ground-based rain gauges.Over the ocean, relatively few rain gauges are available at buoy platforms.Due to its nature of point observation and limited access, rainfall measurement from rain gauges is supplemented by radars [1], satellites [2], rain parameterization schemes of physical models [3], and empirical statistical models [4].Although the merged rainfall product is a new trend where precipitation estimation is based on the combined use of satellite, rain gauge, and the numerical weather prediction (NWP) model rain output, the fundamental issue of accuracy of rain product of each component is still a topic of active research.It is further pointed out that at finer scales, merged rainfall product performs better compared to model output, whereas model rainfall products are better at larger spatial (>10 6 km 2 ) and temporal (monthly and longer) averaged scales [5].
e nature of height profiles of temperature and humidity are important parameters for the development of moist convective systems in the atmosphere, which culminate in rainfall [6].Many researchers have tried to find a possible association of different meteorological parameters with rainfall, such as temperature [7]; geopotential height at 850 mb [8]; relative humidity at 700 mb; specific humidity; perceptible water, zonal, and vertical components of wind velocity [9]; meridional wind [10]; 850 mb zonal wind gradient anomaly [11]; wet day frequency; minimum and maximum temperature; and cloud cover [12].
In recent years, artificial neural networks (ANNs), under nonparametric category, have found their ways to solve many problems related to rainfall such as rainfall forecasting [13][14][15][16][17][18][19][20], rainfall-runoff model [21][22][23], rainfall estimation by radars [1,24,25] and satellites [26][27][28][29][30][31], and temporal and spatial rainfall disaggregation [32,33].e advantage of an ANN approach is that it can be used to develop a functional relationship, including a nonlinear relationship, amongst the various parameters of the process under study even in the absence of full understanding of its mathematical model [34].e ANN techniques such as feedforward, feedback, and competitive neural networks are extensively used for rainfall forecasting at different time scales such as, yearly [35][36][37], monthly/seasonal [13,14,[38][39][40][41][42][43][44], and weekly/daily basis [45][46][47].By using the soft computing techniques, the rainfall forecasting can be categorized in two groups: either by using historical time series rainfall data [48] or by using historical time series data of meteorological variables [45].Over the Indian region, ANN techniques have been utilized extensively for forecasting of long range Indian summer monsoon rainfall with time lagged climatic indices-rainfall relationship approach [49] or from the stochastic time series data of rainfall [35,41].e simulation of daily rainfall by using height profiles of concurrent meteorological parameters is still to be seen over the Indian monsoon region in particular and over the globe in general. is aspect needs an attention, and the present work is an effort in this direction.
e main objective of the study is to identify suitable concurrent meteorological parameters with respect to pressure depth in the atmosphere and to simulate daily rainfall by using these identified meteorological parameters.For this purpose, a feedforward multilayer perceptron (MLP) model is considered.e simulation is carried out over the core monsoon region of India.
e manuscript consists of five sections.e description of the study region and the characteristics of meteorological parameters over the study region are provided in Section 2. In Section 3, the methodology of the proposed work is outlined.e results are provided in Section 4. Section 5 consists of summary, discussion, and conclusion.

Study Region.
e study has been carried out within the Indian core monsoon region as shown in Figure 1. e simulation study is carried out on a grid point 22.5 °N, 82.5 °E, and results are tested at four neighbourhood locations (22.5 °N, 77.5 °E; 22.5 °N, 80.0 °E; 22.5 °N, 85.0 °E; 22.5 °N, 87.5 °E).e study region consists of the central India plateau region coupled with the Chota Nagpur plateau and the plain of the West Bengal.Over the study region, terrain elevation is varying from mean sea level to around 2 km of height.

Characteristics of Rainfall over the Region.
In order to have a preliminary information about the number of rainy days during the study period   During 1953-1994, the climatology of monthly mean rainfall is shown in Figure 2. e annual mean rainfall is 1490 mm. e location receives maximum rainfall during the southwest monsoon season (June-Sep) with maximum mean rainfall in the month of July (450 mm) followed by August (415 mm).In the months of June and September, the mean rainfall is around 200 mm.
ere is a significant standard deviation in the rainfall during the monsoon season, varying in the range 70-190 mm with the maximum value in the month of June (190 mm).e significant standard deviation is attributed to the various climatic indices, namely, El Nino Southern Oscillation (ENSO), Indian Ocean Dipole (IOD), and so on, which affects the onset of monsoon and received rainfall.
Further, the interannual variation of the southwest monsoon rainfall during 1953-1994 is shown in Figure 3 e equation of the trend line is provided in the respective figure panel.It is observed that characteristic of interannual trend is different for these categories.In the range of 0 < R ≤ 20 mm/day, it has an increasing trend (slope: +0.30).Whereas for the category 20 < R ≤ 40 mm/day and R > 60 mm/day, it has a decreasing trend, and for the range 40 < R ≤ 60 mm/day, apparently there is no trend.It is interesting to mention that in the year 1961, the year of maximum rainfall of 2600 mm (Figure 3), the rainfall in the range of 40 < R ≤ 60 mm/day and R > 60 mm/day had significant contribution in the overall rain accumulation.Overall, the result suggests that over the grid point, the number of rainy days with 0 < R ≤ 20 mm/day are increasing, whereas the number of days with R > 20 mm/day are decreasing.Further, during the training and testing  and validation (1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)  Further, it is to be mentioned that the temporal and spatial inhomogenity in the meteorological data may be present due to various factors such as due to the method of data collection, change in topography, and change in global or regional climatic indices.erefore, it is important to test the homogeneity of the data set.e homogeneity test can be done in two ways: absolute method and relative method [51].For absolute method, the test is applied for each station separately, and in relative method, neighbouring stations are also taken into account.Both the methods have limitations and advantages.As the utilized daily rainfall data is at a single location, the absolute method is considered for the homogeneity test.We tested the homogeneity of daily rainfall data for different months using three tests namely, Pettitt's test [52], standard normal homogeneity test (SNHT) [53], and the Buishand test [54] at 95% (alpha � 0.05) confidence level.e results are presented in Table 2.If the p value is more than 0.05, the data is considered as homogeneous, otherwise inhomogeneous.From the table, it is observed that out of three tests, two tests show the inhomogeneous result for the months of April, June, and July; one test shows the inhomogeneous result for the months of January, February, March, May, September, and October.On the other hand, daily rainfall data for the months of August, November, and December show homogeneous results for the entire three

Characteristics of Meteorological Parameters over the
Location.Similar to rainfall, the characteristics of meteorological parameters are also studied at the same location.e meteorological parameters are considered from the NCEP/NCAR reanalyzed data set [55].It is a gridded data set with a grid size of 2.5 °× 2.5 °. e data set consists of observational as well as NWP output meteorological parameters.e meteorological parameters at each grid point are categorized as "A", "B", "C", and "D" [55].e class "A" indicates that the gridded meteorological parameters are primarily the observed values; therefore, the parameters under this class are the most consistent.
e parameters under class "B" are basically derived with the help of observed and model values.e parameters under "C" are fully derived from the model, whereas those under the class "D" are climatological data.
At the outset, four meteorological parameters of level "A" (atmospheric temperature, geopotential height, u-wind, and v-wind) and two parameters of level B (specific humidity and pressure vertical velocity (PVV) (ω)) are considered at eight pressure levels (1000, 925, 850, 700, 600, 500, 400, and 300 mb) during the four times a day (00, 06, 12, and 18 GMT).e climatology of mean monthly variation of the six meteorological parameters, namely, atmospheric temperature, geopotential height, specific humidity, u-wind (zonal wind), v-wind (meridional wind), and PVV (ω) at eight pressure levels are shown in Figures 5(a)-5(f ), respectively.For atmospheric temperature, the maximum value is in the month of May (premonsoon) at 1000-700 mb pressure levels and at 600-300 mb pressure levels, its maximum value is in the month of July and August (monsoon).e higher value of temperature at higher pressure levels during the southwest monsoon is attributed to the release of latent heat by virtue of phase conversion of water in the convective clouds present during the southwest monsoon season.e characteristics of the monthly variation of geopotential height (Figure 5(b)) show that over 1000 to 600 mb, the minimum geopotential height is during the monsoon season.On the other hand, at 400 and 300 mb, this feature is reversed; that is, the minimum height is observed during the winter (Jan).In case of specific humidity, it is always maximum during the monsoon months (July and August), with overall lesser values towards the lower pressure levels (or upper heights) (Figure 5(c)).
e velocity vectors are characterized in terms of magnitude and direction.As far as sign convention of u-wind vector (zonal wind) is concerned, +ve sign indicates westerly wind, that is, wind flow from west to east and −ve sign indicates easterly flow, that is, wind flow from east to west.For u-wind (Figure 5(d)), it is observed that from the premonsoon to monsoon seasons, its values at lower pressure levels of 600, 500, 400, and 300 mb changes from westerly to easterly and again becomes westerly during postmonsoon season (Nov-Dec).During the premonsoon season, the maximum value of westerly at 300 mb (around 30 m/sec) is attributed to the presence of the jet stream.Its value at higher pressure levels (1000, 925, and 850 mb) is though predominantly westerly, but it has a lesser magnitude varying in the range of 0-5 m/sec.For v-wind (meridional wind), vector +ve sign indicates southerly flow, that is, flow from south to north and −ve sign indicates northerly flow, that is, wind flow from north to south.Its seasonal variation at various pressure levels has different characteristics (Figure 5(e)).At 300 mb, wind vector is always southerly with varying magnitude, having a minimum value during the monsoon and the maximum value during the postmonsoon.It is further observed that, except at 300 mb, v-wind vector at all pressure levels is predominantly northerly and has minimum magnitude during the monsoon season.It has significant value during the premonsoon followed by a postmonsoon season.Similarly, sign convention of PVV vector (ω) is such that +ve sign denotes downward motion and −ve sign denotes upward motion.For ω also, at each pressure level, there is seasonal variation in its characteristic.At 600, 500, 400, and 300 mb pressure levels, ω value has downward air motion during the premonsoon and postmonsoon seasons, whereas it becomes upwards during the monsoon season (Figure 5(f)).On the other hand, at 700, 850, 925, and 1000 mb, the air flow is in the upward direction during the premonsoon which changes to downwards direction in the monsoon and the postmonsoon seasons.Overall, systematic variation is observed in the monthly variation of these meteorological parameters at various pressure levels as well as of ground rainfall.
e results suggest that these meteorological parameters at the location may be utilized to simulate rainfall.

Methodology
e relative role of the considered meteorological parameters for the formation of precipitating system and subsequent rainfall is uncertain.On the other hand, an MLP network has capability to map nonlinear relation between input and output parameters.It is assumed that, if rainfall characteristics with respect to meteorological parameters at a place for a certain period are known, then the architecture of an MLP model can be designed and trained to generate corresponding weight matrices, and thereafter, rainfall can be simulated from the concurrent meteorological parameters by using the generated weight matrices.It is to be mentioned that in the present work, we have not tried a forecasting (of rainfall) approach, where generally a time series data of either rainfall or meteorological parameters are used as inputs and time-lagged rainfall data as an output for the training of a selected neural network architecture.When a time series or temporal sequence data are used in that case, a feedback neural network is a better option.For the present study, the approach is different in the sense that there is a simulation of rainfall with the help of concurrent meteorological parameters, where daily rainfall is a cumulative effect of the favorable properties of height profiles of the meteorological parameters at four times in a day.In this article, nature of the proposed objective falls under the pattern recognition of a static input and output data.For the   Advances in Meteorology objectives of this nature, feedforward networks are reasonably suitable.erefore, in the present study, a feedforward MLP network is considered to simulate daily rainfall.is model consists of an input and output layers and in between one or more hidden layer(s).e nodes between the two adjacent layers are interconnected, the value of the parameters in the subsequent layers are a weighted sum of the input values.

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e hidden layer helps to capture the nonlinear relation between the input and output parameters.A model of a neuron and an architecture of an MLP network are shown in Figures 6(a e learning of an MLP is carried out primarily in the four steps, namely, (i) normalization of input and output vectors, (ii) estimation of activation function for hidden and output layers, (iii) estimation of error for output and hidden layers, and (iv) adjustment of weights by many iterations, till the prescribed limit is achieved [56].
e training of the feedforward MLP is carried out on MATLAB platform.To simulate daily rainfall by using a feedforward MLP model, working methodology is planned into four steps, namely, (i) data preparation, (ii) identication of optimum depth of pressure level to be considered for the model, (iii) selection of a suitable number of input concurrent meteorological parameters for the model, and (iv) development of optimum weight matrices of an MLP model at 22.5 °N, 82.5 °E location.ereafter, by using the developed weight matrices, daily rainfall is also simulated at neighboring locations.e detail is provided in the following subsections.Advances in Meteorology ). e data set (both input and output) for the period 1953-1994 are randomized and then normalized within 0 and 1.All the input and output data sets are normalized between 0 and 1, by using the following formula: where X max and X min are the maximum and minimum value of each input and output parameter, respectively, X i is the specific value of each parameter for which we want to get the normalized value, and X N is the normalized value that corresponds to X i value.erefore, in the data file, there is always a positive value between 0 and 1.Since actual minimum rainfall is not negative, model output of the rainfall is not negative.e data sets for the period 1953-1994 are further divided into two parts: one part consists of 80% data points which are to be utilized for training purpose and the remaining 20% are to be utilized for testing purpose.e data set for the period 1995-2004 (validation data set) is also normalized between 0 and 1 without randomization.

Sensitivity Analysis of the Optimum Depth of Pressure
Level.For this purpose, at the outset, six meteorological parameters at eight pressure levels, and at four times a day, are considered (Table 3).In order to find the optimum depth of the pressure level, a detailed sensitivity analysis is carried out for different slabs of the pressure level.ese slabs are (1) at 1000 mb, (2) from 1000 to 925 mb, (3) from 1000 to 850 mb, (4) from 1000 to 700 mb, (5) from 1000 to 600 mb, (6) from 1000 to 500 mb, (7) from 1000 to 400 mb, and (8) from 1000 to 300 mb.For slabs 1, 2, 3, 4, 5, 6, 7, and 8, the total number of meteorological parameters are 24, 48, 72, 96, 120, 144, 168, and 192, respectively (Table 4).A feedforward MLP model is trained and tested for the period 1953-1994 at 22.5 °N, 82.5 °E.For training purpose, the number of hidden layers is considered in the ratio of 10:1 with respect to total number of nodes in the input layer.e model is validated for the period 1995-2004 for each considered pressure depth.
e simulated daily rainfall is compared with the observed daily rainfall (gridded rainfall data) in terms of root mean square error (rmse), bias, and correlation coefficient (cc) using the following relations: where S i is the model simulated rainfall, O i is the observed rainfall, S and O are their arithmetic mean, and n is the number of data points.e results are provided in Table 4.It is observed that for the slab with pressure levels from 1000 to 700 mb, the rmse is minimum and cc is maximum for both testing and validation data sets (testing: rmse: 11.82 mm/day and cc: 0.51.validation: rmse: 9.78 mm/day and cc: 0.48).erefore, an atmospheric slab from 1000 to 700 mb (four levels) is considered as an optimum depth of pressure level to simulate the daily rainfall.erefore, at this stage, the six meteorological parameters at four pressure levels and at four times a day constitute total 96 inputs to an MLP model.

Sensitivity Analysis for an Optimum Number of the Input Meteorological Parameters.
Once the optimum depth of pressure level (1000-700 mb) is identified, the next step is to identify suitable meteorological parameters for the MLP model.A detailed sensitivity analysis is carried out in different combinations of meteorological parameters.For this purpose, twelve different combinations are tried as shown in e error statistics between the simulated daily rainfall and observed daily rainfall is calculated for each case during the validation period, and it is presented in Table 5.From the error statistics, it is found that amongst all the cases, the minimum rmse and maximum cc (rmse: 9.63 mm/day, bias: −0.9 mm/day, cc: 0.49) are observed when, out of the six parameters, atmospheric temperature and PVV (ω) are excluded.Further, it is also observed that as an individual parameter, u-wind is the most crucial parameter, that is, without it, the rmse is maximized.Eventually, optimum number of input meteorological parameters at each pressure level is found to be four.ese four parameters (geopotential height, specific humidity, u-wind, and v-wind) at four pressure levels (1000, 925, 850, and 700 mb) at four times a day (00, 06, 12, and 18 GMT) constitute total 64 inputs (Table 6) to a feedforward MLP network to develop its optimized weight matrices.Further, an analysis has also been carried out to check the consistency of the selected meteorological parameters.
e selected meteorological parameters from the NCEP/NCAR reanalyzed data set are compared with NOAA 20th century reanalysis data set [57] in terms of cc, and the results are presented in Table 7.It is observed that the calculated cc for individual meteorological parameters between these two data sets are pressure level-dependent.Overall, the maximum cc is observed for geopotental height, which is varying in the range 0.94-0.99 with the maximum cc at lower heights (1000, 925, and 850 mb level).It is followed by specific humidity which has a cc in the range 0.94-0.87 with higher cc at lower heights (1000 and 925 mb).For the wind parameters, v-wind (meridional wind) has the highest correlation (0.71-0.76) at lower heights (1000-850 mb), whereas in contrast, u-wind (zonal wind) has a maximum correlation (0.83) at a higher height (700 mb).Overall, it is observed that for the selected meteorological parameters, cc between these two data sets is significantly higher, which suggests that the considered parameters from NCEP/NCAR reanalyzed data set are consistent.

Estimation of Optimum Weight Matrices for the MLP
Model.After identification of the optimum depth of pressure level and suitable meteorological parameters with the  Advances in Meteorology number of nodes in the hidden layer with a ratio of 10 : 1 with respect to number of input nodes, further experiments are conducted to find the optimum number of nodes in the hidden layer by trial and error method.e error statistics is provided in Table 8.It is observed that rmse and bias is least with 10 nodes in the hidden layer.erefore, the optimized MLP network is a three-layer network, consisting of 64 nodes in the input layer, 10 nodes in the hidden layer, and one node in the output layer (64 : 10 : 1).e positive bias and negative bias imply that the simulated daily rainfall is over-and underestimated, respectively, compared to observed daily rainfall.In order to have a better visualization of the characteristics of the input meteorological parameters on a rainy day, a case study is provided for the simulation of rainfall on 17th August, 1995.e values of the input meteorological parameters are provided in Table 9.Here, the geopotential height and specific humidity are relatively higher in the evening hours, whereas the wind vectors are relatively less in the evening hours.On this particular day, the simulated rainfall and observed rainfall are found to be 10.82 mm/day and 9.6 mm/day.e simulated rainfall is closely matching the observed rainfall.

Results
e result section consists of the following three subsections: (i) simulation of daily rainfall and its year-wise comparison with observed and satellite derived daily rainfall at the training location during the validation period (1998-2004), (ii) simulation of daily rainfall at each neighborhood location and their aerial average within the core monsoon region during the validation period (1998-2004) and its year-wise comparison with observed and satellite derived rainfall, (iii) assessment of the simulated rainfall with respect to observed rainfall in terms of interannual variation of monthly rainfall and intraseasonal variation of the monsoon rainfall.

Simulation of Daily Rainfall and Its Year-Wise Comparison with the Observed and Satellite-Derived Daily
Rainfall.
e temporal variation of the simulated and observed daily rainfall during 1998-2004 is provided in Figure 7(a).It consists of total 2557 number of days.e daily rainfall is plotted against the Julian days.e overall error statistics of the simulated rainfall with respect to observed value is provided in the figure panel.It is observed that the simulated daily rainfall is able to capture the overall features of the monsoon rainfall as well as dry season reasonably well.
e overall rmse, bias, and cc during this period are found to be 9.44 mm/day, 0.90 mm/day, and 0.52, respectively.e temporal variation shows that the MLP model could simulate the maximum rainfall up to 60 mm/day, which further suggests that the developed model is not able to capture the extreme rainfall events (>60 mm/day).To assess the relative performance of the simulation model, Tropical Rainfall Measuring Mission (TRMM) Multisatellites Precipitation Analysis (TMPA) data product 3B42 (version 7) [58] is considered.It is a multisatellite rainfall product.It uses an optimal combination 2B-31 (TRMM product) 2A-12 (TRMM product) along with the Special Sensor Microwave Imager (SSMI), Advanced Microwave Scanning Radiometer (AMSR), and Advance Microwave Sounding Unit (AMSU) rainfall data products to adjust infrared rainfall estimates from a geostationary satellite.is data product utilized TRMM Microwave Imager and TRMM-precipitation Radar as a calibration source to the Infrared (IR) estimated rainfall from a geostationary satellite [58].For each day, it provides 3 hours of average rainfall during 0000 to 2100 UTC. e pixel resolution of the data product is 25 km.e temporal variation of the 3B42 and observed daily rainfall during 1998 to 2004 is provided in Figure 7(b).e daily rainfall is plotted against the Julian days.e overall error statistics is provided in the gure panel.It is observed that 3B42 rainfall is also able to capture the overall features of the monsoon rainfall and dry season reasonably well.It is observed that rmse (cc) of simulated daily rainfall is lesser (more) compared to 3B42 rainfall product, whereas the bias for simulated daily rainfall is more compared to the 3B42 rainfall product.It thereby suggests that in terms of rmse and cc, the performance of the rainfall simulation model is relatively better compared to the 3B42 rainfall product.
Further, year-wise (during 1998-2004) error statistics for simulated versus observed daily rainfall at training location is provided in Table 10.ere is interannual variation in the error statistics.e maximum rmse is observed in the year 1998, followed by 2004 with −ve bias. is result is consistent with Figure 7(a), which shows that in both the years, extreme rainfall events are more, particularly in the year 1998 compared to other years.In 1998 and 2004, the observed daily rainfall is found up to around 225 and 125 mm/day, respectively (Figure 7(a)).It is attributed to the fact that the MLP model is not able to capture the extreme rainfall events.e model captured up to 50 mm/day in the year 2000.In terms of rmse (6.59 mm/day), the optimum simulation is observed in the year 1999, which is attributed to the absence of extremely high and low daily rainfall events.Overall, the cc is varying in the range of 0.50-0.62.Further, a comparative study has also been carried out between the 3B42 versus observed daily rainfall.e result is provided in Table 10.

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Similar to simulated versus observed rainfall statistics, the maximum rmse is observed in the year 1998, followed by 2004.Unlike the simulated rainfall, in terms of rmse (8.72 mm/day), the optimal estimation is observed in the year 2002.Overall result suggests that in terms of rmse and cc, the MLP model is performing better compared to 3B42 daily rainfall product, whereas in terms of bias 3B42 product is relatively better.

Simulation of Daily Rainfall at Other Locations within the
Core Monsoon Region and eir Aerial Average.In order to assess the robustness of the estimated weight matrices of the MLP network, the same weight matrices are utilized to simulate daily rainfall at other neighbourhood locations also.e selected locations are 22.5 °N-77.5 °E; 22.5 °N-80 °E; 22.5 °N-85 °E; and 22.5 °N-87.5 °E. e error statistics of the simulated rainfall versus observed daily rainfall at different locations is provided in Table 11.For the simulated rainfall, the error statistics is reasonably consistent with the training location, where rmse, bias, and cc are varying in the range of 6.87 to 11.08 mm/day, −1.13 to 1.36 mm/day, and 0.41 to 0.55, respectively.For the 3B42 versus observed daily rainfall also, the error statistics is reasonably consistent, where rmse, bias, and cc are varying in the range of 11.59 to 15.40 mm/day, 0.03 to 0.75 mm/day, and 0.14 to 0.39, respectively.Overall, it is observed that at each location, the rmse (cc) for the simulated rainfall is less (more) compared to the 3B42 rainfall.
ereafter, an areal average of the simulated and 3B42 rainfall within the core monsoon region is calculated and compared with the observed daily rainfall.e comparison of the temporal variation of an aerial average of simulated and 3B42 daily rainfall with the observed rainfall from 1998 to 2004 is shown in Figures 8(a) and 8(b), respectively.e daily rainfall is plotted against the Julian days.e error statistics is provided in the respective figure panels.It is observed that the simulated rainfall is able to capture the average features of the monsoon rainfall as well as dry season reasonably well.It is observed that compared to point observations, performance of the MLP model improves significantly by virtue of enhanced cc.It is also observed that the performance of the MLP model is reasonably better compared to 3B42 rainfall product.Similar to the analysis at the training location, the year wise error statistics (during 1998-2004) of the aerial average of simulated and 3B42 daily rainfall with respect to the observed rainfall are provided in Table 12.In both the cases, there is interannual variation in the error statistics.For simulated versus observed daily rainfall, rmse, bias and cc are varying in the range of 3.49 to 6.8 mm/day, −0.10).e maximum value of rmse (6.82 mm/day) and bias (−0.53 mm/day) of simulated rainfall in 1998 are attributed to the occurrence of extremely high rainfall events in that particular year, which recorded 1698 mm of rainfall, an amount, well above the average rainfall.
e higher rmse and −ve bias in the simulated rainfall in the year 1998 further suggests that though the model could simulate normal rainfall with reasonably good accuracy, a simulation of extreme high rainfall events is still an issue.It is observed that with reference to the observed aerial average daily rainfall, the simulated rainfall has smaller rmse and higher cc compared to 3B42 daily rainfall.Overall Advances in Meteorology result suggests that in terms of rmse and cc, the model is performing consistently better compared to 3B42 daily rainfall.It is to be mentioned that the mechanism for simulation of the rainfall by the model and the estimation of daily rainfall by the satellite sensors is completely different.e simulation method is based primarily on the outcome of the underlying physics of the convective systems, whereas the 3B42 rainfall is based on the interaction of infrared and microwave radiation with the hydrometeors.

Assessment of the Developed Model in Terms of Interannual Variation of Rainfall at Different Time Scales.
To further assess the performance of the developed rainfall simulation model, rainfall accumulation at larger time scale, namely, monthly and intraseasonal (during active and break periods of the monsoon) is analysed and compared with the observed rainfall.e rainfall at larger time scale is calculated by applying the bias correction.

Interannual Variation of Monthly Rainfall.
Interannual variation of monthly simulated rainfall and observed rainfall for 10 years during 1995-2004 is shown in Figure 9.
e error statistics of the monthly simulated rainfall with respect to observed rainfall is provided in the figure panel.It is observed that the simulated rainfall is closely following the observed rainfall during the premonsoon, monsoon, and postmonsoon seasons with significant cc (0.88).Overall, the simulated rainfall is matching reasonably well during the years 1995, 2001, 2002, 2003, and 2004 (particularly in the month of August).Whereas, during the years 1997, 1999, and 2000, the simulated rainfall is overestimated compared to the observed rainfall and in the years 1996, 1998, and 2004 (particularly in the month of June and July), it is underestimated.In order to understand the interannual variability of the error statistics of the monthly simulated rainfall with respect to the observed rainfall, the number of rainy days over seven different rainfall categories at the increment of 10 mm/day along with the total number of rainy days, annual rainfall, and monsoon rainfall during 1995-2004 are provided in Table 13.It is observed that there is significant overestimation in the year 2000.During this year, the observed rainfall was significantly low (712 mm) compared to other years.It is attributed to the limitation of the positive bias for the simulated rainfall during the presence of nonrainy days.e underestimation of rainfall during the years 1996, 1998, and 2004 (particularly in the month of June and July) is attributed to significant occurrence of higher daily rainfall events.During these three years, the number of rainfall days with >60 mm/days were 5, 6, and 5, respectively, whereas in the remaining years, it is varying in the range 0-4.Overall, the result suggests that the overestimation took place during the years when there was a shortfall of observed rainfall and underestimation took place during the years when the extreme high rainfall events (rainfall ≥ 60 mm/day) were prevalent.It is attributed to the limitation of the rainfall simulation model with respect to its positive bias, particularly in case of no rainfall situation and also its inability to simulate the extreme Advances in Meteorology rainfall events.In terms of spatiotemporal averaging of the simulated rainfall, the performance of the MLP model improves considerably.e results also suggest that the error statistics is predominantly a ected by the characteristics of rainfall.

Intraseasonal Variation of Rainfall (Active-Break Days).
e Indian summer monsoon is characterized by a strong intraseasonal variation of rainfall, indexed as an active and break periods [59].During the active and break periods, the normalized anomaly of rainfall over the core  14 Advances in Meteorology monsoon region (18 °-28 °N; 65 °-88 °E) exceeds +1 or is less than −1, respectively [60].e active and break days are de ned during the peak monsoon months of July and August.It is also to be mentioned that this criterion has to be satis ed at least for three consecutive days.During 1998 to 2004, total active and break days are considered from previous works [59,60].To further assess the performance of the model, the intraseasonal variation of the simulated rainfall is studied in terms of active and break periods.e performance of the model is compared with observed rainfall during these periods.During this period, the simulated rainfall and observed rainfall for each active and break events are shown in Figure 10.e cc (0.68) is quite signi cant.It suggests that the model is able to simulate the active and break periods with reasonably good accuracy.

Summary, Discussion, and Conclusion
In the present work, an attempt is made to explore a viable alternate approach to supplement existing rain parameterization schemes in the NWP and rainfall simulation models.e idea of the present work is inspired by the concept of hybrid environmental model, where a deterministic numerical model can be combined with an ANN-based parameterization scheme which takes into account the underlying physical processes [61].In the present work, daily rainfall is simulated by using four concurrent meteorological parameters, namely, geopotential height, speci c humidity, zonal wind, and meridonial wind, during 00, 06, 12, and 18 GMT at di erent pressure levels, that is, 1000, 925, 850, and 700 mb pressure levels by using the feedforward network.e architecture of the feedforward MLP model consists of 64 nodes, 10 nodes, and 1 node in the input, hidden, and output layers, respectively.It is a one-step simulation approach.In terms of rmse and cc, the model is performing better compared to 3B42, whereas in terms of bias, the performance of 3B42 is better compared to the model.In this regard, it is to be mentioned that 3B42 rainfall is a global rainfall product, whereas the developed model is region speci c. e model is able to simulate daily rainfall at neighbourhood locations with reasonably good accuracy.
e model simulation improves signi cantly for areal average over the core monsoon region.e model is able to capture monthly, its interannual and intraseasonal variation with reasonably good accuracy.
e applicability of the model outside the core monsoon region is yet to be seen.Nevertheless, the model is not without its limitations.Two major limitations of this MLP model are (i) its inability to capture extreme high rainfall events and (ii) simulation of marginal rainfall, even during the no rain situation.Error statistics of simulated rainfall is signi cantly a ected by rainfall characteristics.When there are more extreme rainfall events, there is an underestimation of rainfall, and during the predominantly low rainfall events, there is overestimation of rainfall.Some error may also arise due to the uncertainties in the input parameters.Underestimation of rainfall in case of more extreme rainfall events is due to the fact that the model  Advances in Meteorology fails to capture the heavy rain events.During the training period, there are very less number of heavy rain situations and hence, it is not able to capture heavy rain.By repetition of heavy rain episodes in the training period, this limitation may be overcome.Overestimation of rainfall during the predominantly low rainfall events is due to the cumulative effect of simulation of marginal rainfall in no rain situation.By putting a threshold, the simulated marginal rainfall in no rain situation may be removed, and it may improve overestimation of rainfall during periods of scanty rainfall.e present work is different from the majority of the work reported on the forecasting of rainfall at different time scale, where the time series data of either rainfall or meteorological parameters are utilized to forecast the timelagged rainfall.In the present scenario of rainfall forecasting, researchers have utilized various sets of surface meteorological variables such as minimum and maximum temperature [35,39,41,[43][44][45][46].Some other researchers have utilized extended meteorological parameters in addition to temperature variables such as relative humidity and previous day rainfall [62].In some cases, rainfall forecasting is carried out by taking into account historical time series of rainfall only [48].Majority of these works have utilized various form of feedback ANN, such as time delay network, recurrent network, and wavelet network to take into account temporal variation of the input variables.
e present effort is a novel approach in the sense that the simulation of daily rainfall is a hybrid approach, which blends the statistical and physical model by taking into account the underlying physical processes.For example, it takes into account the convection process, by virtue of the height profiles of the considered meteorological parameters, unlike the extensively used historical time series rainfall or surface-based meteorological data to simulate rainfall.Our nature of objective falls under the pattern mapping of a static input and output data.For the present objective, the feedforward networks are reasonably suitable.
Overall, the developed model is performing reasonably well. is approach has a potential to be used as a rain parameterization scheme in the dynamical atmospheric and coupled models to simulate daily rainfall.Nevertheless, the present approach can also be used for multistep prediction of rainfall.
. Rainfall is varying in the range of 600 mm (in the year 1979) to 2600 mm (in the year 1961).A trend line is fitted.e equation of the best fit line is provided in the figure panel.e negative slope (−8.60) of the best fit line suggests an overall decreasing trend of the annual rainfall.In order to further explore the trend of the annual rainfall pattern, the interannual variation of the number of rainy days in different rainfall categories, namely, 0 < rainfall (R) ≤ 20 mm/day, 20 < R ≤ 40 mm/day, 40 < R ≤ 60 mm/day, and R > 60 mm/day are shown in Figures 4(a)-4(d), respectively.

Figure 6 :
Figure 6: Schematic diagram of (a) an elementary neuron model with multiple inputs and (b) an architecture of multilayer perceptron model.

Figure 8 :
Figure 8: Variation of aerial average of (a) simulated and observed daily rainfall and (b) 3B42 and observed daily rainfall over the monsoon region during 1998-2004.

Figure 10 :
Figure 10: Interannual variation of simulated and observed rainfall during the active and break periods of southwest monsoon during 1998-2004.

Table 1 :
Characteristics of rainy days during the model training, testing, and validation periods.

Table 3
[50]r the same geolocation, daily rainfall data are considered from daily gridded rainfall data set[50].Meteorological parameters are considered as input and daily rainfall is considered as output.edata set is separated into two groups, namely, (i) training and testing data set (1953 to 1994) and (ii) validation data set(1995 to 2004

Table 3 :
Total number of vectors for the input layer of feedforward MLP.

Table 5 .
For each combination, the total number of input meteorological parameters to an MLP model is shown in the same table.An optimized MLP model is trained and tested for the period 1953-1994 at 22.5 °N, 82.5 °E and the MLP model is validated for the period 1995-2004 for each considered combinations.

Table 4 :
Sensitivity analysis of MLP model with respect to input meteorological parameters at different pressure levels between 1000 and 300 mb.

Table 5 :
Sensitivity analysis of ANN model for different combination of input meteorological parameters between the pressure levels 1000 and 700 mb.

Table 6 :
Finally selected meteorological parameters as an input to the MLP model.

Table 7 :
Comparison of the selected input parameter (NCEP/N-CAR reanalysis data set) with the NOAA 20th century reanalysis data set.

Table 8 :
Selection of number of neuron of hidden layer for threelayer MLP model having 64 input nodes and 1 node in the output layer.
10H is in meter; SH is in g/kg; u and v are in meter/sec.10Advances in Meteorology 53 to 0.89 mm/day and 0.62 to 0.77, respectively, with a minimum value of rmse and bias in 2000 and 2002-2003, respectively, and maximum value of cc in 2001.Further, for 3B42 versus observed daily rainfall rmse, bias, and cc are varying in the range of 5.05 to 8.26 mm/day, −0.05 to0.79 mm/day, and 0.42 to 0.60, respectively, with a minimum value of rmse and bias in 2000 and 2002, respectively, and the maximum value of cc in 2004.e results are similar in nature with the error statistics of training location (Table

Table 10 :
Error statistics of model simulated and 3B42 daily rainfall with respect to observed daily rainfall at the training location (22.5 °N, 82.5 °E) during the validation period.