A Deep and Wide Neural Network-based Model for Rajasthan Summer Monsoon Rainfall (RSMR) Prediction

In past researchers have applied numericalDucrocq et al. (2002) and statistical modelsLi and Shao (2010); Montanari and Grossi (2008) for rainfall prediction. But with gaining popularity of artificial intelligence and increasing machine computation power, training abundant data using machine learning and deep learning models are becoming the center of attraction for researchers Zhang et al. (1998). One of the major reasons of scientists switching from traditional numerical approaches to artificial intelligence based approaches is that the statistical and numerical models fail to capture the dynamic nature of rainfall Singh et al. (2012a) whereas neural networks are quiet smart in capturing the hidden trends and seasonality existing in time series rainfall data. The numerical and statistical models were used majorly for two to three decades but these methods lacked forecasting accuracy Gadgil et al. (2005) resulting into failure in predicting major rainfall variations Kalsi et al. (2004); Sikka (2003). There are evidences from the past where these numerical methods failed Gadgil et al. (2002); Preethi et al. (2011) to predict the monsoon rainfall and severe droughts were observed.

Pritpal Singh (2018a) has made an attempt to predict the ISMR using monthly monsoon rainfall values and applied fuzzy sets and artificial neural network (ANN). When the parameters on which the rainfall depends are very high then in order to predict ISMR, Saha et al. (2016) used auto encoder Ng et al. (2011) for reducing the number of parameter and then predicted the ISMR. Saha et al. (2021) studied the climatic variables responsible for ISMR and used deep learning feature for monsoon rainfall prediction.This study also shows the monsoon deviation from long period average (LPA) rainfall. Johny et al used an adaptive Ensemble Model of ANN which was capable of capturing very low and very high rainfall in the Indian state of Kerala Johny et al. (2020). Dubey et. al Dubey (2015) used three artificial neural network based algorithms ( feed-forward back propagation algorithm, layer recurrent algorithm and feed-forward distributed time delay algorithm) for rainfall prediction over the region of Pondicherry, India. Some amount of monsoon rainfall prediction is done by applying feed forward neural network Chakraverty and Gupta (2008); Sahai et al. (2000); Singh and Borah (2013).

Fluctuations in the summer monsoon rainfalls can’t be captured efficiently by traditional linear statistical models Singh (2018b); Dash et al. (2018). This motivated us to use Deep Learning based model which are efficient in capturing this non-linearity and dynamic nature of ISMR. As per IMD weather forecasting manual ³³3https://imdpune.gov.in/Weather/Forecasting_Mannuals/IMD_IV-13.pdf, Indian rainfall is very well known for its variability in space and time. There is hardly any seasonal distribution of rainfall over entire India. At two different station locations which are a few miles apart, if we consider one day rainfall, we may observe that one station experiencing heavy rainfall whereas the other station may go completely dry. This kind of variation is not only found in monsoon rainfall period(June to September) but also during post monsoon period (October to December) as well.

A good amount amount of work has been done in the field of ISMR as presented above but at present to the best of our knowledge, no work is done in the field of RSMR prediction, which attracted the authors of this paper to explore this untouched area. An attempt to predict the agricultural drought index in Rajasthan is done by Dutta et al Dutta et al. (2013) using standardized precipitation index. In this proposed work, an extensive study is done in predicting RSMR for the first time. The good thing about Rajasthan is the strong Rain Gauge network from IMD, Water Resource Department, Rajasthan and the Revenue Department which has resulted into the abundant supply of rainfall data for analysis and prediction.

Research work done in the field of Rainfall Prediction and Estimation for the state of Rajasthan is very less. Vikas et al Bajpai et al. (2020) used the historical time-series data for daily rainfall prediction. However worked in analyzing the trends of rainfall in the state of RajasthanPingale et al. (2014); Yadav et al. (2018). Bryson and Swain (1981) made an effort to present the holocene variations of monsoon rainfall in Rajasthan. Meena et al. (2019) made an attempt to explore the spatial and temporal differences to identify trends in monthly, seasonal and annual rainfall over the Rajasthan region. They observed the prevailing homogeneity of rainfall at various stations in the state. In another work Singh et al. (2012b) authors tried to estimate the one day maximum rainfall in Jhalrapatan, a city in the state of Rajasthan. Authors have done the probability analysis for this purpose. Lal Meena et al. (2020) studied the rainfall pattern in Chaksu, Rajasthan.

Our objective is to predict the RSMR which starts in the month of June and ends in the month of September. In this work we propose a time series based prediction model which depends on the fundamental of present and future time series data dependency on past time series data Singh (2016). We adapt and improvise wide and deep learning model originally proposed by Cheng et al Cheng et al. (2016b) for recommendations. Many authors h ave used this concept in different domains like regression analysis Kim et al. (2020), quality prediction Ren et al. (2020), rainfall prediction Bajpai et al. (2020) etc. Wide networks are used for memorization and deep networks are used for generalization. In this work we propose a Deep and Wide Monsoon Rainfall Prediction Model (hereafter DWMRPM) to predict monsoon rainfall prediction in the Indian state of Rajasthan.

The rest of the paper is organized as follows. Section 2 explains the proposed model for summer monsoon rainfall in Rajasthan. Details of experimental evaluations, model training, results of rainfall prediction and comparison with other deep learning approaches is given in section 3. Finally we conclude the paper in Section 4 and provide avenues for future work.

1. 1.

   In this work, we propose a novel architecture based on deep and wide neural network for the purpose of summer monsoon rainfall using historical time-series data. The model efficiently captures the dynamic nature of monsoon rainfall and works well in its prediction. To the best of our knowledge, we are the first who have tried to solve this challenging problem.

2. 2.

   We compare our work with various advanced deep learning algorithms for sequence prediction on two different types of datasets and have obtained very promising results.

3. 3.

   The algorithms we designed has the generalization ability and can be used to predict summer monsoon rainfall for atmospherically different regions of Rajasthan.

In this work we address the problem of summer monsoon rainfall in Rajasthan, which is the largest state of India and is located in the North-Western part of the country. Rajasthan has very distinct physiographic characteristics. On one side it has India’s biggest desert area, called The Thar Dessert and on the other side this state has Eastern Plains and the ranges of Aravalli Hills Enzel et al. (1999). These ranges are in the direction of South-west monsoon, which is responsible for rainfall in the region Roy and Jakhar (2002). Atmospherically Rajasthan is divided into four zones: North West Desert Region, Central Aravalli Hill Region, Eastern Plains and South Eastern Plateau Region Upadhyaya (2014). Details of the districts, which come under the respective zones are given below:

• North-West Desert Region: Jaisalmer, Jodhpur, Hanumangarh, Shriganganagar, Barmer, Churu, Nagaur, Pali, Sikar, Bikaner and Jhunjhunu

• Central Aravalli Hill Region: Udaipur, Dungarpur, Sirohi, Jalore, Pali, Banswara, Bhilwara, Chittorgarh, Rajsamand and Ajmer

• Eastern Plains: Alwar, Bharatpur, Tonk, Sawai Madhopur, Karauli, Jaipur, Dausa and Dhoulpur

• South-Eastern Plateau Region: Kota, Bundi, Jhalawar and Baran

All these zones have different atmospheric and climatic conditions. The problem of predicting summer monsoon rainfall in Rajasthan is different from the prediction of Indian summer monsoon rainfall (ISMR, hereafter). Most of the time-series-based methods for predicting ISMR consider average monthly rainfall values by taking weighted average of the 306 well distributed rain-gauge stations in the non-hilly areas of Indian sub-continent Dash et al. (2018); Singh (2018b); Singh and Borah (2013); Sahai et al. (2000). Rajasthan being a dry state lies in arid and semi-arid zones and characterized by low and uneven rainfall Kulshreshtha et al. (2013), therefore, a dedicated system is required which can predict monsoon rainfall for different geographical regions separately. We use historical monthly rainfall data from two different sources to train and analyze the performance of our model in prediction of Rajasthan Summer Monsoon Rainfall. Details on the datasets are given in Section 2.2

For ISMR researchers used monthly rainfall values of June to September across all the years Dash et al. (2018) or just have captured the dependency of months of a single year Singh (2018a) In order to avoid loss of any information, we are using rainfall values of all the months of previous years for the prediction of rainfall for the months of June, July, August and September. For example in order to predict rainfall for the month of June 2019, we use rainfall values of all the months from May 2000 to May 2019.

In this work, we propose a deep and wide monsoon rainfall prediction model (DWMRPM) for the prediction of the total monthly rainfall intensity for the summer monsoons months of Rajasthan. The wide network is used to extract low-dimensional features. Here, instead of using a sequence of monthly rainfall values directly, we are using features obtained after applying a convolutional layer, as it is very effective in learning spatial dependencies in and between the series of data Van et al. (2020). High-dimensional features, on the other hand, are derived using Multi-layer perceptron (MLP) Pal and Mitra (1992) in which a sequence of rainfall intensity values are passed on to a deep network. In order to incorporate a geographical generalization ability in the model, so that a single model can be used to make rainfall predictions in different geographical conditions, information of geographical parameters (latitude and longitude) is included at the time of training. The operational steps involved in the development of our proposed DWMRPM for the prediction of rainfall are shown in Figure 1.

To evaluate the performance of the proposed method, we use two standard statistical metrics, namely mean absolute error (MAE) and root mean square error (RMSE). We compare our results with the advance deep learning models like MLP and one dimensional convolutional neural networks (1-DCNN) which are very popular for sequence based predictions.

In this work we have used Water Resources Department dataset and Indian Meteorological Department (IMD) gridded rainfall data with a high spatial resolution of $0.25^{\circ}\times 0.25^{\circ}$ Pai et al. (2014). From IMD data set, we selected the rainfall data of the Rajasthan meteorological sub-division ranging from $23^{\circ}3.5^{\prime}$N to $30^{\circ}14^{\prime}$N latitude and $69^{\circ}27^{\prime}$E to $78^{\circ}19^{\prime}$E longitude, for the period of 118 years from the year 1901 to 2018. It gave the rainfall data for 1008 rain-gauge stations. We have also collected the rainfall data from Rajasthan’s water resources department, for more than 500 rain-gauge stations, over a period of 61 years (from the year 1957 to 2017). The datasets were noisy in terms of negative and missing values. After initial level data pre-processing and cleansing steps, we selected 484 co-ordinates from IMD dataset of High Spatial Resolution of (0.25X0.25 degree) and 158 stations from Rajasthan’s water resources data for our analysis. The distribution of the selected stations from water resources data, over 33 districts are depicted on the map of Rajasthan in Figure 2

In this paper, authors have made use of both the Station data (data collected from various Rain Gauge Stations in Rajasthan) and the Gridded data Pai et al. (2014). The idea behind using both the data sets is that when only the station data is used, for experimentation, one uses the data for single point of scale whereas when the gridded data is used the application of different meteorological data for a region is applied depending upon the resolution. In large catchment areas where less number of Rain Gauges are installed, modeling may not be that much accurate, on the other hand gridded data is more continuous and may prove better than single point estimates. Gridded data contains the data from stations or satellites (in our case, it’s rain gauge station data) which undergoes interpolation over a grid. This interpolation needs careful analysis for biases and outliers Rajeevan et al. (2005); Pai et al. (2014). Station data on the other hand is unbiased single point data. For our study, we have used quality controlled data sets from both the categories. If someone has enough single point station in the region under study, then the station data can be easily utilized but since the rain gauge distribution is not uniform ( as shown in Raj_WRD), specially in the dessert areas where the rain gauge station installation density is very low, combination of both the data set seems to be optimal. Another advantage of using gridded data is that it acts as a source of replacement to the data missing from the records of rain gauge stationsMeher and Das (2019). Any area or zone where the observed station data (point data) is comparatively less, interpolated gridded data can work as a potential alternative means Bandyopadhyay et al. (2018).

These datasets contained daily rainfall values from which we calculated monthly rainfall values for January to December. In order to provide rainfall pattern in Rajasthan, mean rainfall values for each month and the monsoon season (combined rainfall of June, July, August and September) from the year 1901-2018 for a randomly picked rain-gauge station is shown in Table 1. We also provide the minimum and maximum rainfall for each month and monsoon season, over the duration of 118 years. It can be observed that the significant amount of annual rainfall occurs in the monsoon months and the in the remaining months, the aggregate rainfall is very less.

We have considered time-series values of monthly rainfall and geographical parameters like latitude and longitude for the prediction of rainfall during the monsoon months in different regions of Rajasthan. The rainfall intensity values ranges from 0 mm to more than 800 mm while coordinate values of latitude and longitude lies between $23^{\circ}3.5^{\prime}$N to $30^{\circ}14^{\prime}$N and $69^{\circ}27^{\prime}$ to $78^{\circ}19^{\prime}$E, respectively. Since the data is of different dimensions and dimensional units, therefore we normalize the data to make it dimensionally uniform. When the magnitude of different parameters in a dataset is different, the parameters with higher values suppresses the role of the parameters with lower values in model training. To handle this issue, we use the min-max normalization method to convert all rainfall intensity values to number between 0 and 100 (latitude and longitude values are already in this range). The mathematical representation of the min-max normalization method is as follows:

where, $I^{*}$ is the normalized value of the monthly rainfall intensity value, $I$ represents a value in the original dataset, $I_{max}$ and $I_{min}$ are the maximum and minimum intensity values, respectively. Normalization can also help in improving the learning capability of the model and in reducing the computational complexity Shanker et al. (1996).

We use deep and wide neural network-based architecture Bajpai et al. (2020) for the purpose of summer monsoon rainfall prediction in the Indian state of Rajasthan. The following paragraphs explains the major components of the model.

All the experimental programs are coded using Keras Chollet et al. (2015) API of TensorFlow framework Abadi et al. (2016); Gulli and Pal (2017). The hardware setup includes computer processor from Intel with i7-8750H configuration supported by 32GB RAM. The upcoming sections and subsections describe the designing and implementation setup of proposed approach and baseline approaches followed by results obtained.

For prediction of monthly rainfall of monsoon season, we consider different training windows of lengths ranging from 2 years to 10 years. We found that 9 years training window gives most accurate prediction results for the monsoon months of June, July August and September.

In the following subsections, we present the results of experimental analysis and comparison of the proposed method with the baseline approaches described in Section 3.1.4.