Granger Causality-Based Forecasting Model for Rainfall at Ratnapura Area, Sri Lanka: A Deep Learning Approach

Abstract

Rainfall forecasting, especially extreme rainfall forecasting, is one of crucial tasks in weather forecasting since it has direct impact on accompanying devastating events such as flash floods and fast-moving landslides. However, obtaining rainfall forecasts with high accuracy, especially for extreme rainfall occurrences, is a challenging task. This study focuses on developing a forecasting model which is capable of forecasting rainfall, including extreme rainfall values. The rainfall forecasting was achieved through sequence learning capability of the Long Short-Term Memory (LSTM) method. The identification of the optimal set of features for the LSTM model was conducted using Random Forest and Granger Causality tests. Then, that best set of features was fed into Stacked LSTM, Bidirectional LSTM, and Encoder-Decoder LSTM models to obtain three days-ahead forecasts of rainfall with the input of the past fourteen days-values of selected features. Out of the three models, the best model was taken through post hoc residual analysis and extra validation approaches. This entire approach was illustrated utilizing rainfall and weather-related measurements obtained from the gauging station located in the city of Ratnapura, Sri Lanka. Originally, twenty-three features were collected including relative humidity, ssunshine hours, and mean sea level pressure. The performances of the three models were compared using $\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}$. The Bidirectional LSTM model outperformed the other methods (RMSE < 5 mm and MAE < 3 mm) and this model has the capability to forecast extreme rainfall values with high accuracy.

1. Introduction

Background

Weather is important in many aspects of human life. It influences decisions in agriculture, food production, hydropower generation, traveling, and transport. Adversely, it brings forth sudden life-threatening disaster situations such as droughts, floods, extreme rainfall, and pandemics [1,2,3,4]. Occasionally, some of these weather-driven events appear as a chain of events. For example, long-term warm weather increases the level of evapotranspiration which often leads to heavy or extreme rainfall. The chain can end up triggering a flash-flood event [5,6,7,8,9,10]. Proactive reactions to this unbreakable natural chain can be executed by making accurate forecasts of these weather patterns.

Among weather prediction studies, rainfall forecasting is critical and challenging due to its intervention in sequential disastrous events, and difficulty in producing more accurate forecasts with adequate lead time [11]. Due to inherent uncertainty in rainfall fluctuations, a substantial research gap has been created in capturing its extremely rare events, called extreme rainfall events [2,12,13,14,15].

Moreover, rainfall is interconnected with many weather and meteorological variables like relative humidity, mean sea level pressure, sunshine hours, cloud cover, wind speed, and temperature patterns [1,4,16]. The complex relationships among these variables make the selection of the best set of predictor variables for a rainfall forecasting model more critical [13].

Past studies reveal that rainfall forecasting is conducted by predicting rainfall occurrence at a certain location, e.g., [2,4,9,17] or obtaining forecasts for future rainfall for a particular timestep, e.g., [1,3,6,7,8,10,18,19]. For both types of studies, researchers have used various and different structures of predictor variables. In addition to the conventional numerical approach, some studies have been supported by weather-related radar and image data, e.g., [2,9,17].

Building a model for accurately forecasting rainfall, most importantly extreme events, is catalyzed by an effective selection of input features, e.g., [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28]. Selecting an appropriate set of features leads to a parsimonious model and prevents over-fitting data [29,30]. This can be conconducted using many approaches such as Random Forest Feature Section, Lasso, Principal Component Analysis, Correlation Coefficient, Information Gain, Sequential Forward and Backward Selection, and Genetic Algorithm [30]. These approaches are categorized under filters, wrappers, and embedded algorithms methods [29,30,31]. Past studies further point out that embedded algorithms like Random Forest are an intermediate solution between filter and wrapper methods [30]. Many studies which describe applications in different areas such as global warming, genetic population assignment, network security, and cancer diagnosis (e.g., [32,33,34,35,36]) have used Random Forest to identify the best set of features for their models and gained better performances than standalone approaches. Though the Pearson Correlation Coefficient is widely used (e.g., [37,38,39,40,41,42]) as a feature selection method, it is limited to the selection of predictor variables which are linearly related with the response variable without making any adjustment of other exogeneous variables.

As a causality dependence approach, recently, the Granger Causality test has gained much attention among researchers to identify the best set of input features to models. The review in [43,44,45,46,47,48] emphasizes the applications of the Granger Causality technique in addressing specific causality problems in the climate system. Due to its strength in identifying the predictor variables which show a significant impact on the response variables, we applied the Granger Causality test to identify predictor variables to the rainfall forecasting model. However, only the non-categorical predictor variables can be chosen from this technique. Therefore, the Random Forest technique was adopted aiming to identify suitable categorical predictor variables.

As mentioned in the recent study [9], many researchers have attained better forecasts of rainfall by employing machine learning or deep learning methods, including K-Nearest Neighbor (KNN), Random Forest, Artificial Neural Network (ANN), and Convolutional Neural Network (CNN). Nowadays, deep learning models are being vastly applied to develop forecasting models, including rainfall forecasting models (e.g., [49,50,51,52,53,54,55,56]). Hybrid models such as CNN-LSTM are also becoming popular in weather forecasting. For example [14], used hybrid models to combine ground-level weather variables and satellite images, and obtained an accuracy of 75% in short-term rainfall forecasting. The literature (e.g., [18,57,58,59,60,61] reveals that LSTM is the most popular model that is used for rainfall forecasting. Different versions of LSTM, such as Bidirectional LSTM and LSTM Autoencoder-based models [49,57,62] were applied by past studies. In accordance with past studies, we also adopted three types of LSTM versions: Stacked LSTM, Bidirectional LSTM, and Encoder-Decoder LSTM. These models facilitate sequential modeling of inputs and outputs of time series.

Obtaining accurate forecasts for extreme events is another key concern as sequential input-output modeling of the time series. Extreme rainfall events are complex, hazardous, and costly, and their frequency and intensity are reported to be increasing [7,13,27]. Thus, there is a crucial need to identify such events as early as possible, probably, at least one day in advance to warn relevant vulnerable groups of individuals [8,11]. The study in [11] identified the nonlinear relationship between global Sea Surface Temperature (SST) and extreme precipitation through the Distance Correlation-Pearson Correlation method to extract key inputs from SST to feed into the Random Forest model for forecasting monthly extreme precipitation. The resultant model had an R² value of 0.81 and relatively small $\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}$ and $\mathrm{M}\mathrm{A}\mathrm{E}$ values.

Different configurations of LSTM were applied to model extreme rainfall with 12 isobaric pressure levels and surface data from meteorological stations in Brazil’s southeastern region. The study incorporated a mechanism for dealing with imbalanced data found in rainfall data. With the input of the past 24 h to obtain 6 h ahead forecasts, the model came up with better results: an $\mathrm{M}\mathrm{A}\mathrm{E}$ of 6.9 mm and $\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}$ of 6.94 mm [13]. Another application of deep learning to forecast extreme rainfall occurrence was found in study [28]. Initially, the Stacked Auto-Encoder (SAE) model was conducted for feature extraction, and then the reduced features were used for classification with Cost-sensitive Support Vector Machine (SVM). The proposed model was capable of predicting extreme rainfall events 6 to 48 h before their occurrence, even though it resulted in several false positives. The study further highlights the difficulty in predicting such events 1 to 2 days earlier, and the importance of accurate early predictions in avoiding vast damages. The study in [63] used six extreme rainfall indices including the 90th percentile of rain day amounts (mm/day) and greatest 5-day total rainfall (mm) as factors in the Back Propagation Neural network model with stepwise regression to forecast the average extreme rainfall in the coming year. Nonetheless, the study claims that the model’s accuracy is not satisfactory and needs to be further improved. Another drawback of this model is that it does not provide the exact day or time when extreme rainfall happens, i.e., annual average extreme rainfall will not be sufficient to mitigate harmful consequences. These past studies stress the essential need of finding more sophisticated methods for accurate modeling of extreme rainfall. Our study also emphasizes obtaining accurate forecasts of extreme rainfall, as the identification of extreme rainfall in advance will help to plan disaster mitigation actions. Unlike past studies, our study attempts to forecast extreme rainfall events in a considerably longer period ahead, probably 3 days-ahead. Such a longer forecast horizon is essential to implement necessary disaster mitigation actions.

Ratnapura in Sri Lanka is severely affected by floods almost every year. It is situated in the wet zone of the country and receives heavy rain during south-west monsoon periods. Due to its geographical location and the nature of the Kalu River which passes through the area, Ratnapura experiences floods almost every year and sometimes more than once a year. Further, most of the existing global weather forecasting systems (e.g., Google Weather Forecasting System and MSN Weather Forecast) only provide the chance of having precipitation in the said area. Nonetheless, the intensity of the rainfall is necessary to decide the continuation of the day-to-day tasks, as well as to predict future devastating events like floods. Therefore, building a rainfall forecasting model that is capable of identifying accurate extreme rainfall in Ratnapura, at least a few days ahead, is vital.

Among the limited number of published studies that aimed at forecasting rainfall in different locations of Sri Lanka, only a few studies are related to the Ratnapura area (e.g., [2,64,65]). The study described in [2] forecasted the occurrence of rain in selected weather stations including Ratnapura station with the help of Markov models. The study conducted in [64] forecasted rainfall of the Wet and Dry zones of Sri Lanka based on regression techniques and the authors of the study included the rainfall of Ratnapura Station when modeling rainfall of the Wet Zone. Annual rainfall of Ratnapura was forecasted based on mathematical models in [65]. None of the aforementioned studies applied deep learning models for building forecasting models nor paid special attention to forecast extreme rainfall with high accuracy. Though [64] reduced the dimension of the input variables through Principal Component Analysis, an attempt was not taken to identify an optimal set of input variables. None of the other studies also paid attention to selecting a suitable set of predictor variables. Our study attempts to fill this gap by applying suitable techniques to identify an optimal set of predictor variables.

Considering the importance of obtaining accurate rainfall predictions including extreme events through effective feature selection, and the research gap found in the application of such a model to vulnerable areas like the city of Ratnapura in Sri Lanka [2,9,66,67], this study presents a two-way feature selection method to identify the best set of variables for rainfall modeling with deep learning. More importantly, this study incorporates spatial dependencies into the forecasting model by including a predictor variable representing the rainfall of neighboring stations. The model developed in this study forecasts rainfall with higher accuracy, notably extreme rainfall. This is very important for developing countries like Sri Lanka where agriculture has become one of the major sources of income for the citizens, and often seeks ways and means to reduce the significant allocation of budget for disaster management activities [68,69].

The rest of the paper is organized as follows. The next section explains the feature selection methods and deep learning approach used in modeling rainfall. The Results and Discussion section summarize the key findings and limitations. The last section provides the conclusion and proposes future research directions.

2. Materials and Methods

2.1. Data and Data Pre-Processing

The target or dependent variable of the study is the daily precipitation data collected for the Ratnapura rainfall gauging station located in Sri Lanka with longitude, latitude coordinates of (80.40, 6.680). The potential predictor variables include relative humidity (day/night), temperature (maximum/minimum), mean sea level pressure (morning/evening), wind speed (morning/evening), wind direction (morning/evening), cloud amount (morning/evening), dew point (morning/evening), evaporation, sunshine hours, Nino index, and southern oscillation index (SOI). To capture the spatial impact, rainfall of six neighboring gauging stations, namely, Balangoda (St1_Bal), Detanagalla (St2_Det), Elston (St3_Els), llumbuluwa (St4_Ill), Keragala (St5_Ker), and Moralioya (St6_Mor) were also considered for the study. Spatial interpolation was computed by applying the spatiotemporal kriging method [9] on daily rainfall gathered from these six stations, and rainfall estimates taken from satellite image modeling were also included as potential predictor variables. Additionally, three new variables generated using existing precipitation data from the target station, accumulated rainfall, consecutive dry days, and consecutive wet days, were also added to the list of potential input variables. Altogether, there were 23 potential predictors. The study covered the data from the period of 1 January 2015–31 December 2019.

2.2. Feature Selection and Model Building

Selection of input features to the forecasting model is vital as the accuracy of forecasted value heavily depends on the input features. The study applied two feature selection methods. First, the Random Forest model was developed using all potential predictor variables and obtained feature importance. Starting from the least important feature, the backward elimination approach was conducted to rebuild Random Forest models with reduced features. The features of the model which produced the best performance were extracted. Secondly, the Granger Causality test was applied to all pairs of time series variables consisting of the dependent variable and each potential non-categorical predictor variable. By this process, the non-categorical input features which show a significant impact on the dependent variable were identified as suitable input features to the forecasting model. Through this dual feature selection approach, it was expected to select the lagged values of the non-categorical predictor variables identified by the Granger Causality tests together with the lagged observations’ categorical predictors obtained by the Random Forest model as the optimal feature set to feed into the final rainfall model. However, none of the categorical variables were selected by the Random Forest model. Therefore, only the sets of features suggested by Granger Causality tests were fed into the three LSTM models, Stacked LSTM, Bidirectional LSTM, and Encoder-Decoder LSTM. Based on the performances of the three models, the best method was selected for forecasting rainfall values at Ratnapura.

2.2.1. Random Forest Regression

Random Forest is known as a supervised ensemble learning method which can be applied for both classification and regression [70]. In the regression problem, it constructs a multiple of independent regression trees with controlled variation, and each tree in the ensemble is trained on a different subset of the training data. The selection of the subset is performed with replacement, and this method is as popular as bagging or bootstrap aggregating [9,71]. Then, it makes its own independent prediction. The final prediction is obtained based on the average or weighted average of all the individual predictions of regression trees.

Another important aspect of Random Forest is the two measures it generates as end results, the importance of the features, and the internal structure of the data (the proximity of different data points to one another). When estimating the importance of a feature, Random Forest determines how much prediction error increases when data for that feature is dropped while all other features are kept unchanged [72].

2.2.2. Granger Causality Test

The bivariate Granger Causality was first defined by C. W. J. Granger [73], by building a causal model between two jointly covariance stationary time series, $X_t$ and $Y_t$. The simple idea behind the causality test is that the time series $X_t$ is causal for the other time series $Y_t$ if knowledge of the past history of $X_t$ is useful for explaining the future state of $Y_t$ over and above knowledge of the past history of $Y_t$ itself. If the prediction accuracy of $Y_t$ is significantly improved by including lag variables of $X_t$ as predictors in the model, then $X_t$ Granger causes $Y_t$ [46,47].

The simple causal model of $x\left(t\right)$ and $y\left(t\right)$ can be defined as:

$$y_t=\sum _{i=1}^{p_{max}}{\alpha }_i y_{t-i}+\sum _{i=1}^{p_{max}}{\beta }_i x_{t-i}+{\epsilon }_t$$

(1)

where $\alpha$ and $\beta$ are regression coefficients that can be determined from the data by using ordinary least squares method,${\epsilon }_t$ is the error term at time $t$, and $p$ is the lag length varies from 1 to a maximum value $p_{max}$ which is finite and less than the size of the given time series.

To test whether $X_t$ causes $Y_t$, a restricted form of Equation (1) is estimated eliminating $X_t.$ This is conducted by setting $\beta$ in Equation (1) to zero.

$$y_t=\sum _{i=1}^{p_{max}}{\alpha }_i^{\prime } y_{t-i}+{\epsilon }_i^{\prime }$$

(2)

Then, to test whether the restricted form in Equation (2) is significantly different from the unrestricted form in Equation (1), the F ratio is calculated as follows:

$$F_{X_t~Y_t}={\displaystyle \frac{({SSE}_r-{SSE}_{ur})/H}{{SSE}_{ur} /(n-K)}} ~ F_{H, n-K}$$

(3)

where ${SSE}_r$ and ${SSE}_{ur}$ are sum of squared errors with respect to the models given by Equations (2) and (1), respectively, $H$ is the number of coefficients set to zero in the restricted form, $K$ is the number of predictors in the unrestricted form, and $n$ is the number of observations.

If $F_{X_t~Y_t}>F_{\alpha \%, H, n-K}$, then, the null hypothesis of the predictor variable, $X_t$ does not Granger cause the variable, and $Y_t$ is rejected. It indicates that $X_t$ Granger causes $Y_t$.

2.2.3. Long Short-Term Memory (LSTM)

Recurrent Neural Network (RNN) is a supervised deep learning model which contains a recurring connection in each unit of the hidden layer that is interconnected in every different time [3]. LSTM, which is an extension of the RNN, overcomes the vanishing gradient problem often faced by RNN. It is also effective in capturing long-term dependencies. It has four layers interacting in a very special way. The memory cell consists of a forget gate, input gate, and output gate [9,74].

As illustrated in Figure 1, the output of the last moment and current input value are fed into the forget gate to obtain the output, $f_t$ at the forget gate:

$$f_t=\varnothing \left(w_f .\left[h_{t-1}, x_t\right]+b_f\right)$$

(4)

where $f_t\in \left(0, 1\right)$, $w_f$ is the weight at forget gate, $b_f$ is the bias at forget gate, $x_t$ is the current input value, and $h_{t-1}$ is the output at previous moment. Then, the same previous output and current input value are inputted to the input gate to find the output value. The candidate cell state at the input gate is as follows:

$$i_t=\varnothing \left(w_i .\left[h_{t-1}, x_t\right]+b_i\right)$$

(5)

$${\tilde{C}}_t=tanh\left(w_c .\left[h_{t-1}, x_t\right]+b_c\right)$$

(6)

where $i_t\in \left(0, 1\right)$, $w_i$ is the weight at input gate, $b_i$ is the bias at input gate, $w_c$ is the weight at candidate input gate, and $b_c$ is the bias at candidate input gate. Then, the current cell state is updated as depicted in Equation (7).

$$C_t=f_t\ast C_{t-1}+i_t\ast {\tilde{C}}_t$$

(7)

In order to obtain the output $O_t$ at the output gate, $h_{t-1}$ and $x_t$ are fed into output gate at time $t$ (Equation (8)).

$$O_t=\varnothing \left(w_o .\left[h_{t-1}, x_t\right]+b_o\right)$$

(8)

where $w_o$ is the weight at output gate and $b_o$ is the bias at input gate. Finally, the output of the LSTM is computed with the current cell state and output at the output gate as below:

$$h_t=O_t\ast tanh\left(C_t\right)$$

(9)

The Stacked LSTM, Bidirectional LSTM, and Encoder-Decoder LSTM are extensions of Vanilla LSTM (with a single hidden layer of LSTM units). The Stacked LSTM has multiple hidden LSTM layers where each layer contains multiple memory cells. This makes a more ideal representation of sequence data, and therefore works more effectively [75,76]. The Bidirectional LSTM learns the input sequence for both forward and backward directions and concatenates both interpretations. The Encoder-Decoder LSTM is especially designed to address the sequence-to-sequence or seq2seq problem [77].

2.2.4. Model Evaluation

The evaluation of Random Forest Regression and LSTM models were conducted using the performance metrics of Root Mean Squared Error ($\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}$) and Mean Absolute Error ($\mathrm{M}\mathrm{A}\mathrm{E}$).

The computation of $\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}$ and $\mathrm{M}\mathrm{A}\mathrm{E}$ was conducted as shown below [78].

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{{\displaystyle \frac{1}{n}} \sum _{i=1}^n{\left(y_{ai}-{\widehat{y}}_{pi}\right)}^2}$$

(10)

$$\mathrm{M}\mathrm{A}\mathrm{E}={\displaystyle \frac{1}{n}} \sum _{i=1}^n\left|y_{ai}-{\widehat{y}}_{pi}\right|$$

(11)

where ${\widehat{y}}_{pi}$ is the predicted value and $y_{ai}$ is the actual value at the time point $i$. The smaller the values of $\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}$ and $\mathrm{M}\mathrm{A}\mathrm{E}$ the better the accuracy of forecasted values is. All the models were fitted using Python 3.10 and run in Google Colab.

3. Results and Discussion

3.1. Feature Selection

The importance of all the aforementioned 23 potential input variables were tested through a two-way feature selection process to get rid of the curse of dimensionality in LSTM modeling. With the reduced feature modeling, it is expected to obtain an efficient model in forecasting rainfall at Ratnapura.

3.1.1. Modeling with Random Forest Regression

Initially, the past three days’ values of the potential predictor variables were modeled with the current day rainfall amount at Ratnapura with Random Forest Regression. The training set includes 80% of the data while the test set consists of the last 20% of the data.

For the full model with all potential predictor variables, the feature importance was obtained, and based on the importance score, feature ranking was established (see

Table A1. Random Forest Regression—feature importance.

X	Score	Rank	X	Score	Rank	X	Score	Rank
arain-1	0.064382	1	Tmax-2	0.014435	25	WsM-2	0.008733	49
krig-1	0.055808	2	RhN-1	0.013962	26	ClM-2	0.00819	50
MslpM-3	0.042258	3	WdM-1	0.013813	27	SOI-3	0.007514	51
DwE-2	0.033979	4	DwE-3	0.013768	28	SOI-2	0.007351	52
krig-3	0.033791	5	MslpE-2	0.013196	29	WdM-2	0.007021	53
Evp-3	0.03149	6	arain-2	0.013001	30	ClM-1	0.006932	54
DwM-1	0.030326	7	Evp-2	0.012845	31	Con_rainD-1	0.006644	55
SunS-3	0.026023	8	Tmax-1	0.012527	32	SOI-1	0.006516	56
Evp-1	0.024442	9	Tmin-1	0.012433	33	Con_rainD-3	0.0062	57
MslpE-1	0.023756	10	RhN-2	0.012348	34	ClE-2	0.005406	58
RhD-1	0.022631	11	WsE-1	0.011952	35	ClE-3	0.005384	59
Tmin-3	0.021286	12	arain-3	0.011473	36	Con_rainD-2	0.004991	60
MslpE-3	0.021097	13	RhD-2	0.011363	37	ClE-1	0.004071	61
krig-2	0.019664	14	WdE-2	0.011105	38	satellite-3	0.003898	62
SunS-1	0.019503	15	DwM-2	0.010978	39	Con_dryD-2	0.003573	63
DwM-3	0.018093	16	WsM-1	0.01076	40	Con_dryD-3	0.00233	64
MslpM-1	0.017396	17	rain-1	0.01069	41	nino-2	0.001527	65
WsE-2	0.016956	18	WsE-3	0.010488	42	satellite-1	0.001499	66
DwE-1	0.016285	19	WdE-3	0.010026	43	nino-1	0.001373	67
Tmax-3	0.016263	20	RhN-3	0.010019	44	nino-3	0.001285	68
SunS-2	0.015948	21	WdE-1	0.009944	45	satellite-2	0.001259	69
RhD-3	0.015594	22	WdM-3	0.009841	46	Con_dryD-1	0.001116	70
WsM-3	0.014633	23	Tmin-2	0.009725	47	rain-3	0.000839	71
MslpM-2	0.014511	24	ClM-3	0.008754	48	rain-2	0.000787	72

in Appendix A). Then, the backward elimination approach was used to re-model the Random Forest Regression Tree with the reduced feature. The feature or the potential predictor variable with the lowest rank, i.e., the least important feature, was eliminated first in building the second regression tree. This process continued until the model consisted of one predictor variable which was the most important. The tunned model parameters are listed in

Table 1. Optimal parameter settings in Random Forest Regression model.

Parameters	Value
n_estimator	100
n_samples	60%
max_features	n_features
k (in k-fold cross-validation)	5

, and the performances of the built models are tabularized in

Table A2. Random Forest Regression models obtained through backward elimination.

Training				Testing
Number of Features	R2	RMSE	MAE	R2	RMSE	MAE
1	−0.1795	21.1003	11.7105	−0.1219	16.0250	10.24466
2	−0.03761	19.8320	11.1934	−0.07725	15.7029	10.3040
3	0.021505	19.3014	11.3090	−0.02741	15.3353	10.4247
4	0.005957	19.5047	11.3620	0.032873	14.8786	10.2054
5	−0.00268	19.4815	11.3543	0.080018	14.5114	10.0594
6	0.013278	19.3550	11.2862	0.042413	14.8051	10.4354
7	0.009207	19.3524	11.2642	0.02596	14.9317	10.3643
8	0.001962	19.3912	11.3569	0.051679	14.7332	10.2129
9	−0.0084	19.4972	11.4726	0.0247	14.9411	10.4089
10	−0.0073	19.4222	11.4170	0.0129	15.0312	10.4358
11	0.0158	19.3157	11.3796	0.0056	15.0867	10.4711
12	0.0101	19.3121	11.4324	−0.0040	15.1594	10.4680
13	0.0092	19.3161	11.4465	−0.0136	15.2319	10.5142
14	0.0049	19.3632	11.4963	−0.0046	15.1638	10.5279
15	0.0120	19.3231	11.4601	−0.0291	15.3481	10.5831
16	−0.0002	19.3797	11.4916	−0.0321	15.3705	10.5693
17	−0.0049	19.4316	11.5121	−0.0406	15.4334	10.6077
18	−0.0079	19.4679	11.5468	−0.0436	15.4558	10.6201
19	−0.0105	19.4733	11.5540	−0.0383	15.4161	10.6424
20	−0.0123	19.5170	11.6042	−0.0317	15.3672	10.6127
21	−0.0084	19.5156	11.5922	−0.0280	15.3400	10.6164
22	−0.0056	19.4805	11.5965	−0.0335	15.3809	10.6181
23	0.0001	19.4661	11.5491	−0.0298	15.3535	10.5880
24	−0.0105	19.4853	11.5909	−0.0263	15.3267	10.5838
25	−0.0126	19.4970	11.5897	−0.0176	15.2617	10.5336
26	−0.0102	19.4973	11.5775	−0.0156	15.2472	10.5101
27	−0.0049	19.4477	11.5785	−0.0229	15.3015	10.5633
28	−0.0069	19.4922	11.5962	−0.0200	15.2802	10.5384
29	−0.0087	19.4707	11.6265	−0.0268	15.3308	10.5958
30	−0.0055	19.4675	11.6042	−0.0089	15.1965	10.5306
31	−0.0079	19.4874	11.6298	−0.0223	15.2970	10.5888
32	−0.0094	19.4916	11.6369	−0.0247	15.3153	10.5707
33	−0.0115	19.5196	11.6441	−0.0358	15.3975	10.6290
34	−0.0125	19.5078	11.6534	−0.0306	15.3589	10.6261
35	−0.0123	19.5417	11.6789	−0.0375	15.4106	10.67682
36	−0.0163	19.5666	11.6731	−0.0350	15.3919	10.6520
37	−0.0150	19.5494	11.6880	−0.0348	15.3907	10.6676
38	−0.0165	19.5748	11.7174	−0.0394	15.4244	10.7113
39	−0.0165	19.5883	11.7245	−0.0358	15.3976	10.7152
40	−0.0227	19.5843	11.7440	−0.0275	15.3356	10.6883
41	−0.0201	19.6020	11.7252	−0.0336	15.3814	10.6883
42	−0.0241	19.6019	11.7253	−0.0329	15.3761	10.6903
43	−0.0187	19.6067	11.7185	−0.0333	15.3794	10.7274
44	−0.0175	19.5922	11.7277	−0.0361	15.3998	10.7273
45	−0.0205	19.5951	11.7326	−0.0356	15.3967	10.7319
46	−0.0210	19.6070	11.7214	−0.0316	15.3668	10.7050
47	−0.0209	19.5930	11.7347	−0.0356	15.3964	10.7023
48	0.0187	19.5874	11.7058	−0.0304	15.3580	10.6828
49	−0.0195	19.5836	11.7230	−0.0282	15.3411	10.6673
50	−0.0206	19.5985	11.7161	−0.0266	15.3294	10.6545
51	−0.0238	19.5840	11.7407	−0.0400	15.4293	10.7135
52	−0.0237	19.6094	11.7457	−0.0375	15.4107	10.7151
53	−0.0213	19.6192	11.7448	−0.0214	15.2903	10.6330
54	−0.0231	19.6211	11.7492	−0.0286	15.3443	10.6539
55	−0.0190	19.6044	11.7468	−0.0284	15.3427	10.6515
56	−0.0169	19.6136	11.7476	−0.0270	15.3326	10.6323
57	−0.0235	19.6045	11.7517	−0.0323	15.3715	10.6643
58	−0.0236	19.6022	11.7543	−0.0271	15.3329	10.6479
59	−0.0228	19.6005	11.7327	−0.0306	15.3595	10.6586
60	−0.0226	19.5983	11.7545	−0.0301	15.3557	10.6597
61	−0.0219	19.5983	11.7519	−0.0230	15.3022	10.6315
62	−0.0218	19.6041	11.7305	−0.0298	15.3530	10.6674
63	−0.0189	19.5895	11.7310	−0.0281	15.3408	10.6527
64	−0.0243	19.6274	11.7374	−0.0239	15.3089	10.6453
65	−0.0218	19.6204	11.7403	−0.0258	15.3234	10.6613
66	−0.0220	19.6035	11.7437	−0.0285	15.3431	10.6806
67	−0.0204	19.5975	11.7346	−0.0262	15.3261	10.6556
68	−0.0234	19.6060	11.7363	−0.0260	15.3246	10.6438
69	−0.0233	19.6104	11.7214	−0.0263	15.3274	10.6439
70	−0.0206	19.6176	11.7527	−0.0273	15.3342	10.6593
71	−0.0227	19.6305	11.7416	−0.0275	15.3362	10.6570
72	−0.0219	19.6040	11.7263	−0.0290	15.3474	10.6818

.

Since the performances of the models with varying numbers of predictor variables fluctuated with slight differences, the model with the best set of features was difficult to identify. Thus, the most important 15 predictor variables were considered to proceed with the study. However, none of the categorical variables are included in this subset of input variables.

3.1.2. Granger Causality Test Results

As a thorough verification of potential input features, bivariate causality was checked between the time series of rainfall at Ratnapura and each potential input variable except the categorical predictors including wind direction (morning/evening).

The results from the Granger Causality test indicated that mean sea level pressure (morning/evening), southern oscillation index, and wind speed (morning/evening) did not show any causal effect on the rainfall at Ratnapura during the study period. The predictors that showed a significant causal effect on the rainfall at the target station and number of significant lags are summarized in

Table 2. Causal predictor variables and significant lags.

Predictor Variable	Significant Past Lag Range (at 5% Significance Level)	Minimum of p Values Within 14 Lags
accumulated rain	1–2	0.0007
kriging interpolation	1–9	0.0009
dew point (evening)	more than 14	<1 × 10−12
evaporation	more than 14	0.0001
dew point (morning)	more than 14	<1 × 10−12
sunshine hours	more than 14	<1 × 10−12
relative humidity (day)	more than 14	<1 × 10−12
temperature (minimum)	1–5	0.0001
relative humidity (night)	more than 14	<1 × 10−12
temperature (maximum)	1–2	0.0055
cloud amount (morning)	1	0.0127
cloud amount (evening)	more than 14	<1 × 10−12
continuous dry days	1–12	<1 × 10−12
continuous wet days	1–2	0.0014

.

As depicted in Table 2, the significant past lag range was different for each causal feature. When incorporating past lags of the selected features to final rainfall modeling, selecting the farthest lags may not add a significant amount of information to the model, especially when conducting the short-term rainfall forecasting [79,80]. It will also increase the complexity of the model, thereby reducing computational efficiency. It is worth noting that our study concerns the short-term rainfall forecasting at Ratnapura. The Granger Causality test results show less than 14 significant lags for some predictor variables and more than 14 lags for other predictors. Therefore, considering these matters, a two-week period of data (i.e., 14 past lags) was taken as a moderate length of historical values from all the predictive features to be input as final sequential inputs to the LSTM rainfall models. As LSTM itself chooses optimal weights for inputs, feeding 14 past lags of predictive features to LSTM will not degrade the performance of the forecasting model. Further, the rainfall forecasts from this network model are intended to be used as input values for our following study on flood forecasting. This model is also a concern of short-term forecasting. The preliminary study on flood occurrence at Ratnapura confirmed that the rainfall of the recent previous days (mostly the past 03 days) greatly impacts flood occurrence in the next day. Therefore, 3 days-ahead outputs or rainfall forecasts were obtained in our study.

3.2. Rainfall Modeling with LSTM Models

Three different LSTM models, Stacked LSTM, Bidirectional LSTM, and Encoder-Decoder LSTM were employed to identify the better model in producing 1 to 3 days-ahead rainfall forecasts at Ratnapura with the inputs of the past 14 days-values of extracted 14 optimal predictive features. Therefore, the set of inputs to the model and obtaining predictions for the next three days’ rainfall values as outputs from the model were the same for all the three utilized models. The training was conducted with moving windows with the selected data which resulted in a size of a $14\times 14$ matrix (14 variables $\times$ 14 lags). The data from 1 January 2015 to 31 December 2018 were taken for the training and daily data of the year 2019 were used for the testing purpose. The data from the said period was considered to exclude the periods with sequential missing values of rainfall series.

The comparison of the performance of the three models is summarized in

Table 3. Performance of Stacked LSTM, Bidirectional LSTM and Encoder-Decoder LSTM.

Model		Stacked LSTM			Bidirectional LSTM			Encoder-Decoder LSTM
Forecasted Day-Ahead		1	2	3	1	2	3	1	2	3
January	RMSE	4.34	4.81	4.94	3.59	4.06	4.40	4.02	4.57	5.49
	MAE	3.43	3.69	2.97	2.18	2.77	2.71	2.99	3.26	3.57
May	RMSE	11.10	10.10	9.99	4.83	5.40	5.97	8.07	7.13	7.47
	MAE	8.14	7.70	8.12	2.85	3.76	4.09	6.68	5.66	5.92
August	RMSE	26.80	20.60	42.00	9.50	10.60	11.20	30.70	28.90	38.10
	MAE	16.70	14.50	23.70	6.38	7.60	7.85	18.00	16.50	19.10
November	RMSE	16.20	15.90	18.50	7.28	9.86	9.24	15.70	16.10	16.70
	MAE	11.90	11.60	14.00	5.19	7.06	7.69	12.60	11.50	12.10

The lowest $\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}\mathrm{s}$ and $\mathrm{M}\mathrm{A}\mathrm{E}\mathrm{s}$ values are depicted in bold.

and

Table 4. Comparison of the rainfall class-wise prediction capability of Stacked LSTM, Bidirectional LSTM, and Encoder-Decoder LSTM models for selected months in 2019.

	Rainfall Event/Class	Number of Days Forecasted Ahead
		1		2		3
Stacked LSTM		Actual Count	Accurately Forecasted Count	Actual Count	Accurately Forecasted Count	Actual Count	Accurately Forecasted Count
	No/Mild Rain	30	30 (100)	29	29 (100)	28	28 (100)
January	Moderate Rain	1	0 (0)	1	0 (0)	1	0 (0)
	Extreme Rain	0	0	0	0	0	0
	No/Mild Rain	29	22 (76)	28	24 (86)	27	23 (85)
May	Moderate Rain	2	0 (0)	2	0 (0)	2	0 (0)
	Extreme Rain	0	0	0	0	0	0
	No/Mild Rain	22	12 (55)	21	10 (48)	20	9 (45)
August	Moderate Rain	7	4 (57)	7	4 (57)	7	4 (57)
	Extreme Rain	2	1 (50)	2	1 (50)	2	0 (0)
	No/Mild Rain	20	10 (50)	19	9 (47)	19	10 (53)
November	Moderate Rain	10	8 (80)	10	8 (80)	9	4 (44)
	Extreme Rain	0	0	0	0	0	0
Bidirectional LSTM
	No/Mild Rain	30	30 (100)	29	29 (100)	28	27 (96)
January	Moderate Rain	1	0 (0)	1	0 (0)	1	0 (0)
	Extreme Rain	0	0	0	0	0	0
	No/Mild Rain	29	27 (93)	28	25 (89)	27	26 (96)
May	Moderate Rain	2	1 (50)	2	1 (50)	2	1 (50)
	Extreme Rain	0	0	0	0	0	0
	No/Mild Rain	22	17 (77)	21	12 (57)	20	16 (80)
August	Moderate Rain	7	7 (100)	7	5 (71)	7	6 (86)
	Extreme Rain	2	2 (100)	2	2 (100)	2	2 (100)
	No/Mild Rain	20	18 (90)	19	14 (74)	19	15 (79)
November	Moderate Rain	10	9 (90)	10	8 (80)	9	8 (89)
	Extreme Rain	0	0	0	0	0	0
Encoder-decoder LSTM
	No/Mild Rain	30	30 (100)	29	28 (97)	28	27 (96)
January	Moderate Rain	1	0 (0)	1	0 (0)	1	0 (0)
	Extreme Rain	0	0	0	0	0	0
	No/Mild Rain	29	24 (83)	28	26 (93)	27	25 (93)
May	Moderate Rain	2	0 (0)	2	1 (50)	2	0 (0)
	Extreme Rain	0	0	0	0	0	0
	No/Mild Rain	22	10 (45)	21	10 (48)	20	10 (50)
August	Moderate Rain	7	3 (43)	7	3 (43)	7	3 (43)
	Extreme Rain	2	1 (50)	2	1 (50)	2	0 (0)
	No/Mild Rain	20	8 (40)	19	13 (68)	19	9 (47)
November	Moderate Rain	10	6 (60)	10	8 (80)	9	6 (67)
	Extreme Rain	0	0	0	0	0	0

, and the common parameter settings of those models are presented in

Table 5. Common parameter setting in LSTM models.

Parameters	Value
Activation function	ReLU
Epochs	100
Number of hidden layers	1
Number of neurons in hidden layer	100
Batch size	72
Learning rate	0.01
Optimizer	Adam
Loss function	MAE
n_steps_in/historical window	14
n_step_out/forecast step	3

.

When selecting the best model, 1st to 3rd days-ahead forecasts only for the periods 1–31 January, 1–31 May, 1–31 August, and 1–30 November 2019 (which represent dry, moderate and extreme rainfall seasons) obtained from the three models, were compared. When obtaining the forecasted values, for instance, firstly the forecasted rainfall of 1–3 January 2019 was obtained by feeding the input values corresponding to the immediate past 14 days to the trained models. Secondly, the forecasted rainfall of 2–4 January 2019, was obtained using the input values corresponding to the past 14 days from 1st January backward as illustrated in Figure 2. This procedure was repeated until the forecasted rainfall of the last 3 days of the testing period was obtained. With respect to $\mathrm{RMSE}$ and $\mathrm{MAE}$ values, the best fit was selected to obtain forecasts for the rest of the days in 2019.

Table 3 presents the $\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}$ and $\mathrm{M}\mathrm{A}\mathrm{E}$ values obtained when applying the three selected LSTM models on the four testing periods selected. The results evidence that the Bidirectional LSTM model has outperformed the other models in each step and each month of the forecast. Further illustrating, it can be explained that the aforementioned model holds the lowest $\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}$ and $\mathrm{M}\mathrm{A}\mathrm{E}$ values in forecasting each upcoming day’s rainfall value when compared to the other two models.

Furthermore, a summary of forecasting actual rainfall events as No or Mild Rain (≤12.5 mm), Moderate Rain (>12.5 mm and <100 mm), and Extreme Rain (≥100 mm) were obtained and are depicted in Table 4. Both the correctly forecasted counts and percentages (within parentheses) are given. In setting the above cut-off values, the definition of light rain and heavy rainfall by the Meteorology Department of Sri Lanka was taken into consideration.

Moreover, the training loss and validation loss of the Bidirectional LSTM Model for January, May, August, and November in 2019 were separately plotted to diagnose the behavior of the model (see Figure A1 in Appendix B). The figure showed that the model has not under- or over-fit the data.

The above results confirm the capability of the Bidirectional LSTM model in rainfall forecasting at Ratnapura, especially the extreme rainfall events. Therefore, the model was further used to forecast the rainfall at Ratnapura for the rest of the period (1 February 2019–24 December 2019).

The sequential model was run in GPU of Google Colab. Since the model was trained with moving windows, training was not computationally efficient. Therefore, the prediction has to be conducted monthly-wise in Colab to avoid the kernel becoming interrupted in the middle of the training. Moreover, the aim was to build a less complex model.

Even though the model was simple and needless to use a High-Performance Computer (HPC), the fitted model could produce better performance in forecasting rainfall values of the target station, especially the extreme values. Figure 3 depicts the fitness of the Bidirectional LSTM model as the rainfall forecasts are closer to the actual rainfall values of the target station for the months of February and August of 2019. The predictions obtained for the rest of the months are illustrated in Figure A2. The two months, February and August, were picked to represent a period from relatively dry and relatively wet seasons of the Ratnapura area. These figures underline that the results obtained from the selected model can be generalized irrespective of the dry or wet season. The major concern of the study is to obtain accurate forecasts for extreme rainfall events. However, the performance of the model in forecasting No or Mild Rainfall, Moderate Rainfall, and Extreme Rainfall events were illustrated for the overall period of the whole year, 2019.

The Meteorology Department of Sri Lanka defined the heavy rainfall cut-off value as 100 mm for Ratnapura. The month of February shows all the rainfall events below 100 mm (no heavy rainfall shows up). The maximum rainfall of that month is recorded as 99.9 mm on 9 February 2019. Figure 3 underscores that the Bidirectional LSTM could closely capture these moderate rainfall patterns in Ratnapura.

On the other hand, the month of August depicts heavy rainfall events on 13 August 2019 (184 mm) and 29 August 2019 (137.4 mm). Figure 3 evidences that these extreme events are accurately forecasted by the model giving 1st day-ahead forecasts of 206.4 mm and 127 mm, respectively. The strong matches between the actual and forecasted rainfall values are the same for the 2nd and 3rd day-ahead forecasting.

Table 6. The rainfall class-wise prediction capability of Bidirectional LSTM model for 2019.

Rainfall Event/Class	Number of Days Forecasted Ahead
	1		2		3
	Actual Count	Accurately Forecasted Count	Actual Count	Accurately Forecasted Count	Actual Count	Accurately Forecasted Count
No/Mild Rain	266	244 (91.73)	266	224 (84.21)	266	238 (89.47)
Moderate Rain	87	76 (87.36)	87	73 (83.91)	87	67 (77.01)
Extreme Rain	03	02 (66.67)	03	02 (66.67)	03	03 (100)

summarizes the ability of forecasting actual rainfall events, No or Mild Rain (≤12.5 mm), Moderate Rain (>12.5 mm and <100 mm), and Extreme Rain (≥100 mm) by the Bidirectional LSTM model for the testing period 1 January 2019–24 December 2019. The accurately forecasted percentages of each category are also shown in parentheses.

As per Table 6, the accuracy rate of the 1st day-ahead forecast for the first two categories is higher than the 2nd and 3rd day-ahead forecasts. However, the 3rd day-ahead forecasts have well captured the extreme rainfall events. It seems that the 3rd day-ahead forecasts are better than their counterparts in forecasting extreme rainfall. It also seems that the trained Bidirectional LSTM model has the ability identify extreme rainfall even 3 days in advance. However, further experiments are needed to arrive at a conclusion.

By closely examining the plots of actual and predicted rainfall of all 12 months, it was noted that all the No/Mild rainfall cases have predicted correctly or as Moderate rainfall events. Additionally, none of the No/Mild rainfall events are predicted as Extreme rainfall events. During the aforesaid period, only two Mild rainfall events which are closer to 100 mm are predicted as Extreme rainfall events, nevertheless with amounts closer to 100 mm.

These results primarily verified the outperformance of the Bidirectional LSTM model in forecasting rainfall at Ratnapura. The application of the Granger Causality test after Random Forest feature selection was validated by the results obtained through modeling the selected best set of predictors by Random Forest with rainfall at Ratnapura using LSTM methods. The predictions taken for January 2019 depicted the lowest $\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}$ and $\mathrm{M}\mathrm{A}\mathrm{E}$ values with Autoencoder LSTM. $\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}\mathrm{s}$ are 4.61 (Day + 1), 4.02 (Day + 2), and 4.15 (Day + 3), and $\mathrm{M}\mathrm{A}\mathrm{E}\mathrm{s}$ are 3.28 (Day + 1), 3.08 (Day + 2), and 3.32 (Day + 3) which are higher than results obtained with Bidirectional LSTM after applying Granger Causality ($\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}\mathrm{s}$ are 3.59 (Day + 1), 4.06 (Day + 2), and 4.40 (Day + 3), and $\mathrm{M}\mathrm{A}\mathrm{E}\mathrm{s}$ are 2.18 (Day + 1), 2.77 (Day + 2), and 2.71 (Day + 3)).

3.3. Residual Analysis

The study was further continued to examine the adequacy of the fitted Bidirectional LSTM model. In doing so, the randomness of residual series (=Actual rainfall amount − Predicted rainfall amount) was analyzed [81,82] using LJung Box test, Autocorrelation, and Partial-autocorrelation [83,84,85,86,87].

The Ljung Box test verified that the residuals are uncorrelated and follows a White Noise process by not rejecting the Null Hypothesis ($p>0.05$), i.e., no significant autocorrelations are found in the residual series. The test results are depicted in Figure A3.

Figure 4 and Figure 5 show the Autocorrelation and Partial-autocorrelation plots of the residual series corresponding to the test period. This plot also evidences that there are no significant autocorrelations among the observations indicating that the residual series is random.

Results of the residual analysis confirm that the fitted Bidirectional LSTM model is adequate for short-term forecasting of the rainfall at Ratnapura station, and it is not required to add any other input variables.

3.4. Verification of Capacity of the Bidirectional LSTM Model in Forecasting Extreme Rainfall Events

The results shown in Section 3.2 confirm that the overall accuracy of the developed forecasting model is inspiring. However, the number of extreme rainfall events included in the testing period is 03 (see Table 5). Even though the forecasting accuracy of the extreme events was considerably high, further studies are needed to verify whether those notable results of the model were given by chance or not. Therefore, a separate period (1 March 2014–31 December 2016) was extracted for training of the same Bidirectional LSTM model with the same optimal features, and it was tested in the period of 1 January 2017–31 December 2017. The selection of the time period was based on the continuous availability of data in the collected data set.

Figure 6 below demonstrates the capability of the Bidirectional LSTM model in forecasting daily rainfall for May and September 2017, which include four extreme events.

The month of May consists of heavy rainfall events on 24 May 2017 (104.1 mm) and 25 May 2017 (348.5 mm). The 1st day-ahead rainfall forecasts for these days are 94.5 mm and 433.4 mm, respectively. The 2nd and 3rd day-ahead forecasts are also close to the actual values. As depicted in Figure 6, the heavy rainfall events in September on 6 September 2017 (135.6 mm) and 07.09.2017 (121.8 mm) were intently captured by the model in all 3 days-ahead forecasting.

Further,

Table 7. Ability of forecasting extreme rainfall by Bidirectional LSTM model in 2017.

Rainfall Event/Class	Number of Days Forecasted Ahead
	1		2		3
	Actual Count	Accurately Forecasted Count	Actual Count	Accurately Forecasted Count	Actual Count	Accurately Forecasted Count
Extreme Rain	4	3 (75.00)	4	4 (100)	4	3 (75.00)

highlights the number of correctly forecasted extreme rainfall by the Bidirectional LSTM model for the testing period of 1 January 2017–29 December 2017.

Table 7 indicates that the 2nd day-ahead forecasting has correctly captured the four actual extreme events.

Results of Table 5 and Table 6 show that the fitted Bidirectional LSTM model has a high ability (more than 85%) to identify extreme rainfall events 3 days in advance. The selection of appropriate predictor variables may also enhance this ability of forecasting extreme rainfall events.

4. Conclusions

Accurate rainfall modeling is crucial for mitigating future disastrous hazards like flash-flood events. Such a rainfall forecasting model becomes more reliable and applicable if it can capture extremely rare events, called extreme rainfall events, and make accurate forecasts in advance, for example, 3 days-ahead. Moreover, the model should be computationally effective by grabbing the most important predictive features and incorporating their hidden patterns into the model.

Therefore, this study proposes an approach in producing accurate rainfall forecasts using both feature selection methods and deep learning. The optimal set of predictive features were extracted using Random Forest Regression and the Granger Causality test. The selected fourteen features were fed into the Bidirectional LSTM model that was selected as the best through a model comparison. The model training was conducted with the historical moving windows approach and the forecasting horizon was set to 3 days-ahead. The developed model produced very low $\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}$ (<5 mm) and $\mathrm{M}\mathrm{A}\mathrm{E}$ (<3 mm) values for the test sample comparatively better than the performances depicted in studies, ref. [3] (MAPE > 50%), ref. [7] ($\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}$ > 10 mm), ref. [19] ($\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}$ > 8 mm and $\mathrm{M}\mathrm{A}\mathrm{E}$ > 4 mm), and [64] ($\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}$ > 8 mm).

The study used rainfall and weather data collected from the rainfall gauging station located at Ratnapura in Sri Lanka. The performance of the Bidirectional LSTM, post hoc analysis conducted upon residual series produced by the model, and dual validation of the selected model thoroughly confirmed the suitability of the selected modeling approach in obtaining accurate forecasts, including extreme events for 3 days-ahead rainfall at Ratnapura. This modeling approach may be effectively used to forecast rainfall in other locations around the globe, especially extreme rainfall.

The study is further bridging the research gap existing in the aforesaid climatologically vulnerable area in Sri Lanka. The best forecasting model identified by this study has the ability to forecast the rainfall at Ratnapura with high accuracy.

When conducting the study, the high rate of missing data within a long period of time (30 years of data) was the main problem. Therefore, the time period has to be reduced to 05 years to get a complete and consistent data set for final modeling.

The future study will be directed toward modeling the flood events in the same vulnerable area feeding the rainfall forecasts determined by the identified model.