Forecasting pressure drop and maximum sustained wind speed associated with cyclonic systems over Bay of Bengal with neuro-computing

The current research anticipates developing a model based on adaptive neuro-computation to foresee the minimum pressure drop (PD) at the centre as well as the maximum sustained wind speed (MSWS) accompanying with cyclonic systems over Bay of Bengal (BOB). The cyclonic systems taken in this work contain systems of different ranges starting from deep depression to extreme severe cyclones. For predicting PD and MSWS, suitable predictors have been sorted using factor analysis and it is observed that low-level vorticity (LLV), mid-tropospheric relative humidity (MRH) and vertical wind velocity at 850, 500 and 200 hPa pressure levels are appropriate parameters to create input matrix of neural network (NN). The adaptive NN representations are skilled with the data from 1990 to 2015 to estimate the PD as well as MSWS over BOB for 47 cyclonic systems. The outcome divulges that the multi-layer perceptron (MLP) NN model delivers decent precision at 6- and 30-h lead time in foretelling the PD. But the lowest error has been found at 6-h lead time in forecasting the central PD during mature stage of cyclonic systems. The result also illustrates that the MLP model is the utmost capable in forecasting the MSWS during mature stage of cyclonic structures with the lowest prediction error at 60-h lead time. The model results were validated and compared with the operational forecast by IMD for the 10 cyclonic systems from 2016 to 2019.


Introduction
Tropical cyclones (TCs) characterise the standard term for severe low-pressure cyclonic systems that mature over tropical warm water bodies. The TCs are branded by highspeed winds and spirally inward ordered thunderstorms in warm oceans that yield heavy rain. Historical archives claim that 8 out of 10 cyclonic cases over North Indian Ocean (NIO) have instigated rigorous mutilation in terms of life loss (Secretariat of the World Meteorological Organization 2010). From studies (Singh and Singh 2007;Balaguru et al. 2014;Kotal et al. 2019;Wahiduzzaman and Yeasmin 2019), it is obvious that NIO experiences 7% (about four in the Bay of Bengal and one in the Arabian Sea per year) frequency of the world's tropical cyclones. In India, most of the TCs strike at the east coast causing huge damages (Mohanty et al. 2020). Timely mitigation thus requires early prediction of the systems. Prediction of TC has been provided mostly in terms of intensity and track. Both these forecasting components depend on pressure drop and wind speed of TCs. During the development of a cyclonic system, the genesis process is controlled by a sequence of events that lead to the development of a self-sustaining warm-cored vortex, which can continue to intensify exclusively due to its own interactions with the warm underlying sea surface and tropical cyclogenesis occurs when the tropical storm can continue to intensify without the help from its ambient environment (Alpert et al. 1996;Montgomery et al. 2006;Tory et al. 2006) once formed. The cyclonic systems become extremely nonlinear in their developing or weakening stages and the predictions of the systems are often associated with huge error (Osuri et al. 2012(Osuri et al. , 2013. Since the last two decades, several operational and research communities are associated with improvements in the forecast proficiency using various statistical as well as dynamical modelling approaches. Osuri et al. (2012Osuri et al. ( , 2013 used the Weather Research and Forecasting (WRF) model for TC track and intensity forecasts in near real-time over the NIO basin and found that the mean initial position and initial intensity errors are about 57 km and 8-10 m/s respectively. The forecast errors during the simulation of the severe cyclone JAL and the very severe cyclone THANE have been appreciably reduced due to the improved observations and assimilation methods which are efficiently integrated in Advanced Research WRF (ARW) mesoscale model (Yesubabu et al. 2014). The study by Osuri et al. (2017) showed an improvement to predict the speedy intensification of TC PHAILIN using an advanced HWRF model. The India Meteorological Department (IMD) has used various statistical and dynamical models, implemented from different national and international collaborations (Mohapatra et al. 2013a; Mohapatra and Sharma 2019). A single model ensemble prediction system (EPS) from various global models and multi-model ensembles (MME) was also introduced at IMD to provide the best possible forecast of TC over NIO (Kotal and Roy Bhowmik 2011;Mohapatra et al. 2013b). As per the report of IMD, a recent prediction of very severe cyclone "Bulbul" was quite good but it poses error (RMSE) of about 9.2, 9.2 and 11.3 knots for forecasting hours of 24, 48 and 72 respectively.
Several studies over NIO (Mohanty et al. 2015;Osuri et al. 2017;Bhalachandran et al. 2019;Kotal et al. 2019;Nadimpalli et al. 2019) have used dynamical models to foretell the cyclonic activity well in advance. Unlike dynamical models, statistical models mostly have used the statistical record of current and previous TC position for training and thereafter predict next position and analyse the TC behaviour. A number of models have been developed for probabilistic TC forecasting, including the HURRAN hurricane, multiple regression model-CLIPER (Climatology-Persistence) which is based on a set of polynomial regression using a number of predictors on predictands (Vickery et al. 2000) and Markov Chain Monte Carlo simulation (Emanuel et al. 2006). Even though many statistical models are available for predicting the intensity of cyclonic systems over the Atlantic, eastern north Pacific and western north Pacific basins Kaplan 1994, 1999;Law and Hobgood 2007), however, the studies over the Indian Ocean are limited.
The development of cutting-edge techniques like artificial intelligence and related adaptive artificial neural network (ANN) models and machine learning has emerged as new alternatives for the oceanic and atmospheric studies (Chaudhuri et al. 2013;Chen et al. 2020;Na et al. 2021;Sharoni et al. 2021;Wang et al. 2022;Zhang et al. 2022). ANN technique was effective in several remote sensing application areas, such as cloud detection, cloud motion detection, road network detection (Brad and Letia 2002;Barsi and Heipke 2003;Jang et al. 2006) and in different applications in meteorology including short-term temperature forecasting (Lanza and Cosme 2002), long-range flood forecasting (Jin et al. 1999) and typhoon track prediction (Yang and Wang 2005). Wang et al. (2022) proposed a hybrid optimization model, combining the 3D convolutional neural network, gated recurrent unit and smoothing algorithm that provides dependable TC track prediction in the Western North Pacific. The utility and potential of MLP-based approach in TC intensity forecast over the Atlantic basin was studied by Xu et al. (2021). Na et al. (2021) used a repeated neural network model to a best track dataset obtained from the US Joint Typhoon Warning Center to forecast the intensities of TCs up to 24 h in the north-western Pacific Ocean basin. The mean absolute error (MAE) of wind speed was obtained as 11.38 knots for 24-h forecasts. Baik and Paek (2000) found that models based on the neural network technique performed better than the multiple linear regression techniques to predict tropical cyclone intensity changes in the western North Pacific up to 72 h. Lee (2009) predicted typhoon storm surge in Taiwan using the back propagation neural network (BPNN) model. Artificial intelligence technique has been successfully used in cyclogenesis prediction over the NIO (Chaudhuri et al. 2014), maximum wind speed prediction of TCs over NIO (Chaudhuri et al. 2017), forecasting severe thunderstorm over Kolkata (Chaudhuri 2010) and so many.
The present study is aimed at predicting the maximum intensity of cyclonic systems in terms of PD and MSWS over the BOB of NIO. This will aid in predicting the category of TC with adequate lead time. It is evident that both intensity and track are very essential components for forecasting cyclogenesis; however, the present study is concerned on the category prediction of a cyclonic system, considering maximum intensity as target output. Most of the cited studies have predicted maximum wind speed to predict intensity. However, the present study has considered both PD and MSWS to predict maximum intensity attained by the cyclonic system; though, both are interrelated. Fifty-seven cyclonic systems that occurred between 1990 and 2019 over the BOB have been considered in this study. The study has utilised different neural network models, considering essential parameters and their association with PD and MSWS. Details of the data used in this study have been discussed in Section 2 along with the methodology adopted and implementation procedure. In Section 3, results of the study have been discussed in detail followed by conclusion in Section 4.

Data
The dataset considered in this study includes the records of cyclonic systems reported over the BOB and collected from IMD Best Track during the period from 1990 to 2019 (http:// www. rsmcn ewdel hi. imd. gov. in). The best track data is available in the Annual Cyclone Review reports and Annual Regional Specialized Meteorological Centre (RSMC) reports published by IMD. The selection is based on best data available and provided by IMD. The study analyses total 57 TCs data over BOB. The parameters selected in this study are sea surface temperature (SST), mid-tropospheric relative humidity (MRH), surface to middle troposphere equivalent potential temperature difference (EPTD), inverse of wind shear (IWS), low-level vorticity (LLV) at 10 m above sea level and the vertical wind velocity (omega) at 850, 500 and 200 hPa pressure levels. The parameters SST, MRH, EPTD, IWS and LLV are referred to as the primary genesis parameters for cyclogenesis (Gray 1975). The SST data has been collected from the National Oceanic and Atmospheric Administration (NOAA) (Reynolds et al. 2007) Optimum Interpolation ST V2 High Resolution Dataset at spatial grid resolution of 0.25° × 0.25° and 1-day temporal resolution. The data of vertical wind velocity at different pressure levels and other meteorological parameters (temperature, specific humidity, relative humidity and wind) have been used from the National Centres for Environmental Prediction-National Centre for Atmospheric Research (NCEP-NCAR) reanalysis (Kalnay et al. 1996) at 2.5° × 2.5° resolutions. As the study concerns the intensification of cyclonic systems, vertical velocity has been taken as a proxy of synoptic-scale precursors to TC rapid intensification (Grimes and Mercer 2015). The MRH is computed as the average of the relative humidity data between 500 and 600-hPa pressure levels. The EPTD has been computed using the temperature and specific humidity data between surface and 500-hPa levels. The IWS is computed from wind shear between 850 and 200-hPa pressure level wind data. The LLV at 10 m has been computed from the Cross-Calibrated Multi-Platform (CCMP) Ocean Surface Wind Vector (Atlas et al. 2011). CCMP provides a consistent, gap-free long-term time-series of ocean surface wind vector analysis fields from 10 July 1987 to 30 May 2016. The CCMP V2 data is available at 0.25° × 0.25° spatial resolutions and 6-h temporal resolutions. Low-level relative vorticity is one of the prime factors for formation of tropical cyclones as it indicates pre-existing disturbances (Singh et al. 2016). The values of all meteorological parameters at the centre of the storm have been calculated by averaging four nearest grid data of original lat/long of TCs. Latitude and longitude have been taken from IMD best track data. The values of PD and MSWS at the successive stages of the cyclonic system are also collected from IMD best track data. The dataset used in this study has been separated into two parts: (a) the data from 1990 to 2015 have been used to train the NN models and (b) the data from 2016 to 2019 has been utilised to validate the NN model to assess the model skill. For validation, LLV at 10 m has been computed from the SCATSAT-1 Level 4 (operational version 1.0) gridded wind vector data obtained at 10 m above sea level at 25-km spatial resolution. SCATSAT-1 data are available through the SAC-ISRO website (www. mosdac. gov. in). Cyclone Kyant, Nada and Maarutha; severe cyclone Mora and Phethai; very severe cyclone Vardah, Titli, Gaja and Bulbul; and extreme severe cyclone Fani have been considered for validation. In this present study, no super cyclone has been considered due to limitation of sample.

Methodology
The statistical method and the artificial intelligence technique have been implemented in this study as the methodologies. Statistical method has been adopted to analyse the data and artificial intelligence has been used to develop the forecast models. The conventional statistical method of box-whisker plots (Chaudhuri and Middey 2011) is used to find the variability in the parameters associated with the cyclonic systems. The box-whisker plot organizes the data class according to the category of the system. The five main values low, first quartile, median, third quartile and high are represented in the plots, which have been evaluated using the data set.
Factor analysis has been implemented to pre-filter the data field in order to train the neural network models. Factor analysis can represent as a set of multivariate statistical technique, mostly used for data reduction and to recognise the measured variables by determining the number and nature of common factors needed to account for the patterns of observed correlations (Fabrigar et al. 1999). In general, factor analysis should retain factors until additional factors account for trivial variance; however, different methods of specifying the number of factors to retain often lead to different solutions. One of the most used methods is the Kaiser criteria, which retains factors with eigenvalues greater than 1 (Kaiser 1960). Factor analysis can be observed as further preferment of principal component analysis (PCA), but the factor analysis can contain more original info than PCA (Ding et al. 2021). For factor analysis, 8 variables have been analysed for 57 vortical systems; hence, subject to variable (n/p) ratio is 7.1 which is quite large than threshold value (3). Details of the cases have been discussed in Section 2.3. By means of factor analysis, study has organised a matrix of input for neural network.
In the present study, artificial neural network (ANN) model in the form of multi-layer perceptron (MLP), radial basis function networks (RBFN) and generalised regression neural network (GRNN) is attempted with the selected parameters as the inputs to identify the best network to forecast the exact category of the cyclonic system over BOB by estimating the respective PD and MSWS at maximum intensity. The multi-layer perceptron (MLP) is perhaps the most popular neural network architecture in use. Studies (Chaudhuri 2010;Chaudhuri et al. 2014;Sarkar et al. 2021;Lawrence et al. 2022) show that MLP ANN shows least error in forecasting wind speed for tropical cyclones as well as for routine forecast. It is a feed-forward network of interconnected neurons, typically trained using the error back propagation (BP) algorithm. In an MLP network, the basic blocks are input layer, hidden layer and output layers. The input signals are reproduced by the linking weights and first totalled in hidden layer and then directed to a transmission function to get the output. A skilled ANN can be functional to foresee the outcome of the new self-governing input data set. The neural associates/weights require to adjust throughout the generation of a neuron through training algorithms. In ANN, several training algorithms like backpropagation (BP), Levenberg-Marquardt (LM) and conjugate-gradient (CG) are mostly used to resolve nonlinear problems (Guhathakurta et al. 1999;Chaudhuri et al. 2016;Singh 2018). Present study has utilised back-propagation (BP) method as training algorithm of MLP ANN. The BP algorithm works by iteratively changing the interconnecting weights of the network to reduce the model error. Mathematically, this can be expressed as: where, w is the vector of weights, x denotes the vector of inputs, b is the bias and is the activation function. The performance of the neural network mostly depends on the number of layers defined; the number of nodes used in each layer and the amount of connectivity among the nodes (Wilson et al. 2002). The number of nodes in the hidden layer should be fewer than the input parameters (Singh 2018). Hence, the number of input and output units is defined by the problem. A basic structure of MLP ANN is given in Fig. 1a.
The radial basis function network (RBFN) is a special type of neural network containing three layers: the input layer, a hidden layer and the output layer shown in Fig. 1b. Since the functions used in radial basis function (RBF) network are nonlinear, it is not required to have more than one hidden layer. The elements shifted to each node of the hidden layer as a linear grouping of scalar weights. In the hidden layers, a RBF (activation function) has been applied to get output, which is a linear grouping of the outputs from the hidden nodes to produce the final output. The final output can be obtained as (Sun et al. 2009;Yang et al. 2022):  Super cyclonic storm ≥ 80.0 ≥ 120 T 6.5-8.0   5:5-5-1:1 (0.14) 5:5-1-1-1:1 (0.17) 5:5-2-2-1:1 (0.14) 5:5-5-4-1:1 (0.09) where y is the output, i(x) is the radial basis function of the ith hidden node and k is number of hidden nodes. A generalised regression neural network (GRNN) is a single-pass ANNs and is very popular for function approximation. It also consists of input layer, hidden layer and output layer but there is no iterative learning process between the input and output. GRNN performed with a set of input vectors and training targets using two steps. The first step is to calculate the weights associated with the training patterns of input vectors, which are premeditated using the following equation: where, n is the number of training pattern, x is the input pattern, x i is an element of input pattern and σ is the smoothing factor that controls the weights. Next, the training targets ŷ are averaged as per their weights to obtain the output: where, k is the number of hidden nodes. The basic structure of GRNN is almost like RBFN. The only difference is the computation at each node of hidden layer. The success of the GRNN method depends mainly on the spread factors; the larger the spread, the smoother is the function approximation (Al-Mahasneh et al. 2018;Martínez et al. 2022).
The present study has used these three ANNs for every forecasting hour. Since it includes different types of variables, it can generate noise from different ranges of variables. So, before using as input in ANN, each variable must be normalised so that the spread values remain between 0 and 1. This gives minimum mean-square error for the testing period. Before the training of NN models, each input parameters as well as the target output is standardized using following equation (Comrie 1997): where, O i , O max and O min are the original, the maximum and the minimum values, respectively.

Implementation procedure
In developing an intelligent model based on adaptive neurocomputation to forecast the exact category of cyclonic systems, the data and record of total 57 cyclonic systems over BOB have been analysed during the period from 1990 to 2019. The fifty-seven cyclonic systems over BOB include seven deep depression (DD), eighteen cyclonic storm (CS), nine severe cyclonic storm (SCS), twelve very severe cyclonic storm (VSCS) and eleven extreme severe cyclonic   (Table 1). In this study, "0" hour for each cyclone has been considered when it was first declared by IMD as "DD" for DD system, "CS" for CS system, "SCS" for SCS system, "VSCS" for VSCS system and "ESCS" for ESCS system (from Best Track data). For example, consider a "SCS" system which has gone through stages DD, CS and SCS while intensifying and while decaying, the sequence stages are SCS, CS and DD. Hence, "0" hour of this system is the time whenever it attains SCS strength while intensifying. For each system, a single time has been designated as "0" hour. Hence, for 57 cyclonic systems, there exists 57 "0" hour in target for analysis. Among these 57 cyclonic systems, 47 cyclonic systems have been used to train the ANN model and remaining 10 have been used for validation. The values of the input parameters have been computed from 90 to 6 h before reaching the highest intensity ("0" hour) with 6-h interval for each cyclonic system. The PD and MSWS at "0" h of each cyclonic system have been considered as the target output. Factor analysis is implemented on "0" hour data that comprises eight parameters to find out the significant input parameters for ANN model. The variability in each input parameter at different stages of cyclonic systems has been assessed through the box-whisker plots. One important input parameter is MRH that indicates the existence of relatively moist mid layers and is more favourable for deep cumulus convection, which acts as the primary mechanism for cyclonic circulation. Vertical wind velocity (omega) depicts updraft and downdraft capacity of the cyclonic systems. Negative value of omega depicts updraft and positive signifies downdraft. Higher value of omega increases the updraft capacity of the TCs. The predictors selected for the study might not be able to predict the intensity of TCs individually but are useful while perform in combination. Before using selected parameters in ANN, all parameters must be standardised using Eq. (5). Then, under given condition of input (5), the number of hidden layer (1-5) and output (1) and best ten ANN models (three GRNN, three RBF and four MLP) have been used based on low select error for each lead hour forecast. Low select error provides a list of balance models that are neither overestimate nor underestimate the output. Configuration of all models used in PD and MSWS forecasting is summarized in Table 2 and Table 3 respectively. At every lead forecast hour, the ANN model with the lowest train error has been considered as the best ANN model. The forecast verification is carried out using best ANN models with different architecture and is validated with observation. To assess the precision in the prediction, the mean absolute error (MAE), root mean square error (RMSE) and the prediction error (PE) have been computed using the following formulae: where, < > implies the average over the whole test set. n denotes the number of events. The model predicted and actual values of the parameters are denoted by Y dP and Y da , respectively.
The skill of MLP model has been compared with the IMD operational forecast (Table 4). IMD operational cyclone intensity forecasts are issued by analysing the output from various numerical weather prediction (NWP) models including IMD Global Forecast System (GFS), European Centre

Results
Data dimension reduction has been performed using factor analysis, which extracts significant factors having eigenvalue greater than 1. Hence, two factors (F1 and F2) have been kept for further analysis. Variance analysis shows that F1 and F2 can explain almost more than 50% variance (Fig. 2a). To understand the loading of each variable towards these two factors, factor loading has been assessed (Fig. 2b). Factor loading greater than 0.7 depicts significant contribution of variables towards F1 and F2. Figure 2b depicts that MRH, w850, w500 and w200 are substantial for F1, while LLV is noteworthy for F2. The LLV, MRH and vertical velocities at 850 hPa, 500 hPa and 200 hPa therefore come out as suitable input parameters to form the ANN model.  The variability in different input and output parameters is estimated through box-whisker plots for different categories of TCs (Figs. 3, 4, 5, 6, 7 and 8). The variability of "0" hour PD during different category of TCs shows that the variability increases as the severity of the system increases. Maximum variability in PD is observed for the ESCS category of the cyclonic system (Fig. 3a). The variability of "0" hour MSWS during different cyclonic systems depicts the spread of data for each cyclonic category (Fig. 3b). It shows that median of MSWS for DD has value of 30 knots and variability is minimum as attributed from box height. In case of CS, median lies at 40 knots with data varying within 35 to 45 knots; for SCS stage, median lies at 55 knots having maximum variability between 55 and 60 knots at "0" hour. Likewise, MSWS for VSCS category mostly varies between 65 and 75 knots with median at 70 knots. In ESCS category, "0" hour MSWS is found to vary between 90 and 105 knots with median at 101 knots (Fig. 3b). The variability in different input parameters has been estimated during different lead time (6-90 h) for each category of TCs. Figure 4 shows the variability in MRH during different lead time hours for each category of TC. The minimum variability in MRH is observed at 18, 24, 60, 30 and 42-h lead times for DD, CS, SCS, VSCS and ESCS categories of TCs respectively  (Fig. 4a-e). The results further show that the variability in MRH increases with lead time for CS, VSCS and ESCS categories of TCs. However, the variability in MRH fluctuates with lead time for DD and SCS categories. The variability in LLV during different lead time from 6 to 90 h for each category of TCs has been estimated (Fig. 5). LLV has minimum variability at 78 h before "0" hour for DD and SCS while for CS and VSCS, least variability has been observed at 90 h before "0" hour. For ESCS, the minimum variability of LLV has been observed at 54 h before "0" hour ( Fig. 5a-e). The results show that the value of LLV is less during minimum variability for all the categories of TCs. The results further show that the variability in LLV decreases with increase in lead time for the DD, CS and SCS categories of TCs. The variability in LLV fluctuates with lead time for the VSCS category. However, the variability in LLV first decreases and then increases with lead time for the ESCS stage.
The variability in vertical wind velocity at low level (850 hPa) has been evaluated during different categories of TCs (Fig. 6). The minimum variability in omega (850 hPa) is observed at 78, 90, 60, 6 and 36-h lead times for DD, CS SCS, VSCS and ESCS categories of TCs respectively (Fig. 6a-e). The results show that the value of omega is positive/negative during minimum variability for DD, CS, SCS/VSCS and ESCS categories of TCs. The results further show that the variability in omega (850 hPa) increases with lead time for VSCS category, whereas the variability in omega (850 hPa) fluctuates with lead time hour for DD, CS, SCS and ESCS categories of TCs. The variability in vertical velocity at mid-level (500 hPa) has been estimated for different stages of TCs (Fig. 7). Omega (500 hPa) has minimum variability at 66 h before "0" hour for DD, while for CS and SCS, least variability has been observed at 84 h before "0" hour. For VSCS, minimum variability has been observed at 18 h before "0" hour and for ESCS, minimum variability of Omega (500 hPa) has been observed at 90 h before "0" hour ( Fig. 7a-e). The results show that the value of vertical velocity at mid-level (500 hPa) is positive/negative during minimum variability for DD/CS, SCS, VSCS and ESCS categories of TCs. The results further show that the variability in vertical velocity at mid-level (500 hPa) increases with lead time for the VSCS category, whereas the variability decreases with lead time for the DD, CS and SCS categories of TCs. However, the variability in the vertical velocity at 500 hPa fluctuates with lead time for ESCS category. The variability in vertical velocity at 200 hPa level has been estimated for different stages of TCs (Fig. 8). The minimum variability in vertical velocity at 200 hPa is observed at 72, 90, 60, 84 and 90-h lead times for DD, CS, SCS, VSCS and ESCS categories of TCs respectively (Fig. 8a-e). The results show that the value of vertical velocity at 200 hPa is positive/ negative during minimum variability for SCS/DD, CS, VSCS and ESCS categories. The results further show that and generalised regression neural network (GRNN) models are made for the purpose. Ten different neural nets with maximum 3 hidden layers and up to 5 nodes at each hidden layer have been trained with a back-propagation training algorithm with 90-h lead time to identify the best for forecasting PD and MSWS of TCs over BOB at "0" hour. The result shows that the minimum train error is obtained from the MLP model at each forecast hour for PD and MSWS forecast. Figure 9a shows the train error of ten neural network models obtained at each forecast hour in forecasting found at 6-h lead time (Fig. 9c). Likewise, the train error of 10 different neural network models has been computed to find out the skill of the models in forecasting MSWS of TCs at "0" hour over BOB (Fig. 10a). The evaluation of the error during MSWS forecast also depicts that the minimum train error is obtained through the MLP models at each forecast hour. The minimum prediction error in forecasting the MSWS of TCs at "0" hour is observed with the MLP model at 60-h lead time. Evaluation of MAE and RMSE also reveals that error is minimum with MLP model at 60-h lead time (Fig. 10b). During validation of the model product, the minimum error has been observed at 60-h lead time (Fig. 10c). It is observed that MLP-ANN with two hidden layers containing four hidden nodes at each layer (5:5-4-4-1:1) performed good for PD prediction while MLP-ANN with one hidden layer containing five hidden nodes (5:5-5-1:1) has been proved to be better for MSWS prediction. The details of the model architecture are shown in Fig. 11.
To check the robustness of the result, the best ANN models obtained in PD and MSWS forecast have been compared with a lesser number of samples. Figure 12 demonstrates the estimated forecast errors for different numbers of samples in forecasting PD and MSWS. Result depicts that the error decreases with increase in the number of training samples except when the model is trained with a minimum number (17) of data-sample. It is also observed that the model that predicts PD performs best with 47 data-samples (Fig. 12a). In case of MSWS, the minimum error is obtained, when the model is trained with 47 data samples (Fig. 12b). Hence, 47 data samples are enough to use for model training in present study.
A comparative analysis between prediction from ANN method and corresponding IMD observation has been carried   (Fig. 13). Figure 13a shows the predicted PD values in comparison with IMD observation. The result shows that, in some cases, the present model overestimates the PD while the increasing pattern of PD with severity has been well captured by the model (Fig. 13a). Figure 13b shows predicted MSWS values in comparison with IMD observation. Here, it is found that the predicted MSWS with 60-h lead time is well comparable with the IMD observation (Fig. 13b). Validation also shows similar behaviour as the analysis (Fig. 14). The model predicted central PD with 6-h lead time is found to be closer to the IMD observed PD for most of the cases during validation (Fig. 14a). It is also observed that the values of MSWS obtained from the MLP model at 60-h lead time are well comparable with the actual values during validation (Fig. 14b). Figure 15 shows the sensitivity analysis on the input variables to identify which input parameter is more sensitive to the neural network used for forecasting the PD and MSWS of tropical cyclones. Sensitivity analysis rates the variables according to the deterioration in modelling performance that occurs if that variable is no longer available to the model. So, it is the ratio of the error

Skill comparison of the present model with the existing conventional models
The skill of the present model is estimated by comparing its performance with IMD operational forecast model (Table 4). As per the "IMD Preliminary Report 2019" of IMD, a recent prediction of extremely severe cyclone "FANI" poses error (RMSE) of about 13.5 knots in intensity (wind) forecast for 60-h lead period. The present study attempted to forecast the category of a cyclonic system in terms of the central PD and MSWS at the stage of the highest intensity over the BOB with the MLP model. The skill of intensity forecast in terms of maximum sustained surface wind is verified by computing the RMSE. The forecast error obtained for cyclone FANI is 9 knots with 60-h lead time (Table 4).

Limitation
This research is useful to forecasting the TC category over the BOB Sea. However, it is important to be aware of the predictive limitations of the study. It is observed that the study has predicted MSWS quiet well than PD due to the improper simulation of PD variability. From gradient wind balance, it is observed that the central pressure deficit in a tropical cyclone depends principally on two velocity scales: the maximum azimuthal-mean azimuthal wind speed and half the product of the Coriolis parameter and a measure of outer storm size (Chavas et al. 2017). Hence, to make better prediction for PD, other factors are needed to consider. The primary limitation lies on the fact that MLP ANN only considers the pattern and nonlinear interaction among input and output. Hence, accuracy of ANN is pertaining to selection of variables. Also, the accuracy of ANNs has been evaluated using RMSE, MAE and PE to get the best lead hour for forecasting PD and MSWS at the highest intensity of cyclone. However, further development as well improvement of ANN model can be done by reducing bias either by adding more associated parameters or by changing weightage factor.

Discussion and conclusion
The endeavour of the present research is to develop a neuro-computing-based model to observe the forecast efficiency in predicting the PD and MSWS associated with different categories of TCs over the BOB at the stage of the highest intensity with adequate lead time and precision. From the literature, it is evident that ANN has been widely used in predicting track and intensity while there is very little study on prediction of intensification using ANN. Since TC involves with the large-scale interaction, it can be controlled by several ambient condition. The state of ambient environment has been depicted by several variables. Present study considers eight parameters, and those parameters are analysed for 6-to 90-h lead time from the target "0" hour. The present study considers 8 variables among which 5 variables comes out as significant through factor analysis. These are LLV, MRH and vertical wind velocity at 850, 500 and 200 hPa pressure level. These 5 variables are used to prepare input matrix for ANN. Here, two sets of experiments with different types of ANN models have been set up for two target output (PD and MSWS). Before implementing ANN, a meticulous variability analysis is carried out. It depicts that the variability of PD and MSWS has been increased with increasing severity of cyclone, but in the case of MSWS, variability for CS and VSCS appears to be same while variability is slightly less for SCS. However, maximum variability has been observed for ESCS. Three types of ANN models namely, MLP, RBFN and GRNN have been tested to identify the best model for forecasting PD and MSWS associated with different categories of cyclonic systems over BOB at the stage of the highest intensity. MLP model is found as the most efficient for forecasting PD (model 1) and MSWS (model 2). The architecture of model 1 is 5:5-4-4-1:1 specifying five inputs with two hidden layers having four hidden nodes in each layer and one output. The model has the competence to forecast PD of cyclones at their highest intensity with 91% accuracy (6-h lead time). The MLP model (model 2) with configuration 5:5-5-1:1 (five input layers, one hidden layer with five nodes and one output layer) was observed to perform best (minimum forecast error) for forecasting maximum wind speed with 60-h lead time. During validation, a similar result has been observed except PETHAI and TITLI. It is important to note that prediction error usually increases with increasing lead hour whereas present study observes that prediction error does not change much throughout the forecast hours. This represents that error growth in the model is less. Use of factor analysis for identification of significant as well as sensitive parameters to create input matrices for ANN may explain the reduced growth of error in ANN model. It is observed that MSWS has been predicted well than PD. The five inputs for MSWS prediction show almost same sensitivity towards output. There is no sharp change in sensitivity whereas in case of PD prediction, sensitivity of input variables towards output changes randomly.
Author contribution All authors contributed to the study conception and design. Jayanti Pal and Ishita Sarkar performed the analyses and wrote the paper. All authors read and approved the final manuscript.

Data availability
The datasets analysed during the current study are available in IMD website (http:// www. rsmcn ewdel hi. imd. gov. in).
Code availability Not applicable.

Declarations
Ethics approval Not applicable.

Conflict of interest
The authors declare no competing interests.