Weather Forecasting Using Radial Basis Function Neural Network in Warangal, India

Abstract

Weather forecasting is an essential task in any region of the world for proper planning of various sectors that are affected by climate change. In Warangal, most sectors, such as agriculture and electricity, are mainly influenced by climate conditions. In this study, weather (WX) in the Warangal region was forecast in terms of temperature and humidity. A radial basis function neural network was used in this study to forecast humidity and temperature. Humidity and temperature data were collected for the period of January 2021 to December 2021. Based on the simulation results, it is observed that the radial basis function neural network model performs better than other machine learning models when forecasting temperature and humidity.

1. Introduction

The daily atmospheric fluctuation is called weather (WX). WX forecasting, as a vital and necessary function in people’s everyday lives, analyzes changes in the existing state of the atmosphere. It is a critical activity that impacts many areas such as agriculture [1,2,3], irrigation [4], and the marine trade [5], and it has the potential to save many lives from unanticipated mishaps [6]. It is described as the examination of atmospheric factors such as temperature [7,8], irradiation [9,10,11,12,13,14], airflow, wind speed [15,16], wind direction, humidity [17], precipitation [18], and rainfall [19]. Forecast precision can be affected by a variety of circumstances. Season, geographical location, input data accuracy, WX classifications, lead time, and validity time are some of these effective elements [20,21].

Warangal is the ancient capital of the Kakatiyas Dynasty and currently one of the major cities in Telangana State, India. The Warangal district map is shown in Figure 1. It is spread over 1766 square kilometers. According to the 2011 census (https://warangal.telangana.gov.in/ (accessed on 12 March 2023)) Warangal has a population of 890,651 people. Agriculture is the most important economic sector, with irrigation mostly dependent on monsoon and seasonal rainfalls. Paddy, cotton, mango, and wheat are the most important crops. In addition to rainfall, crops also grow with groundwater using pumps that require electricity. WX forecasting is very important in this region as it affects agricultural yield and the load on the electric substations.

2. Literature Review

WX forecast provide essential information about future WX conditions [22]. WX forecasting employs various methodologies, ranging from basic sky observations to complex computerized mathematical models. Presently, WX forecasts are primarily based on physical computer models that utilize discrete numerical grids to solve governing equations. Overall, this approach has been highly successful. However, many important applications still face limitations with current numerical WX prediction (NWP) models [23,24,25]. Initially, linear techniques and machine learning approaches were used for WX forecasting over NWP [26]. For instance, solar irradiation was forecast using a multiple linear regression model [27], while support vector machines were employed for predicting solar power generation [28]. Neural networks were utilized for precipitation forecasting [29], and their performance was compared to linear regression models.

In Beijing, surface temperature, humidity, wind speed, and wind direction at 24 automatic WX stations were forecast using an ensemble of a spatial–temporal attention network and multi-layer perceptron [30]. In Göztepe, İstanbul, a neuro-fuzzy network and ARIME model-based approach were used for WX forecasting [31]. Temporal convolutional neural networks were implemented for WX forecasting [32], while photovoltaic power generation was predicted using a sequential model, namely long short-term memory [33]. All these works have made valuable contributions to WX forecasting using machine learning models such as artificial neural networks, convolutional neural networks, linear regression, and support vector machines.

This study focused on forecasting two WX parameters: temperature and humidity. The values of temperature and humidity from one hour and one day prior, as well as the season, were used as input features for temperature (Temp(T)) and humidity (Humd(T)) prediction. Therefore, the input features for forecasting temperature and humidity include Temp(T-1), Temp(T-24), Humd(T-1), Humd(T-24), and Season. A radial basis function neural network (RBFNN) [34] was employed to forecast the WX in terms of temperature and humidity. The optimal RBFNN model was identified by tuning hyperparameters such as the number of centroids and the width parameter. The best model was determined based on the lowest mean square error on the validation data.

The remaining sections of the paper are organized as follows: Section 2 explains the data analytics, RBFNN architecture, and its training algorithm. Section 3 presents the simulation results, and Section 4 discusses the conclusions of this work, and Appendix A describes sample radial basis function neural network (RBFNN) architecture, and Appendix A.1 presents unsupervised learning between input and hidden layers of RBFNN, and Appendix A.2 presents supervised learning between output and hidden layer of RBFNN, and Appendix B explains prediction using trained RBFNN.

3. Materials and Methods

This section provides a detailed explanation of the analytics conducted on the temperature and humidity data collected in the Warangal region from January 2021 to December 2021. It also describes the architecture of the radial basis function neural network (RBFNN) and the training procedure.

3.1. Temperature Dataset

The temperature dataset consists of a total of 5 input features: Temp(T-1), Temp(T-24), Humd(T-1), Humd(T-24), and season. The dataset also includes one output label, Temp(T). The data for this dataset were obtained and arranged from the source available at https://data.mendeley.com/datasets/tj54nv46hj (accessed on 28 August 2022). A few sample entries from the temperature dataset are presented in

Table 1. Five samples from temperature dataset.

Temp(T-1)	Temp(T-24)	Humd(T-1)	Humd(T-24)	Season	Temp(T)
62	65	89	90	1	65
65	78	90	49	1	78
78	83	48	34	1	83
83	81	32	42	1	80
71	67	73	87	1	67

. Statistical information such as the mean, standard deviation, minimum, and maximum values of the temperature dataset can be found in

Table 2. Statistical information from temperature dataset.

Parameter	Temp(T-1)	Temp(T-24)	Humd(T-1)	Humd(T-24)	Season	Temp(T)
count	8736	8736	8736	8736	8736	8736
mean	81	81	68	68	1	81
std	9	9	21	21	1	9
min	50	50	14	14	0	50
25%	77	77	52	52	0	77
50%	81	81	72	72	1	81
75%	86	86	87	87	2	86
max	108	108	102	102	2	108

.

3.2. Humidity Dataset

The humidity dataset also comprises 5 input features: Temp(T-1), Temp(T-24), Humd(T-1), Humd(T-24), and season, which are the same as the temperature dataset. However, the output label for the humidity dataset is different, namely Humd(T). A selection of sample entries from the humidity dataset is presented in

Table 3. Five samples from humidity dataset.

Temp(T-1)	Temp(T-24)	Humd(T-1)	Humd(T-24)	Season	Humd(T)
62	65	89	90	1	90
65	78	90	49	1	48
88	78	73	90	2	73
81	82	84	70	0	70
78	84	91	77	0	91

. Statistical information, including the mean, standard deviation, minimum, and maximum values of the humidity dataset, can be found in

Table 4. Statistical information from humidity dataset.

Parameter	Temp(T-1)	Temp(T-24)	Humd(T-1)	Humd(T-24)	Season	Humd(T)
count	8736	8736	8736	8736	8736	8736
mean	81	81	68	68	1	68
std	9	9	21	21	1	21
min	50	50	14	14	0	14
25%	77	77	52	52	0	52
50%	81	81	72	72	1	72
75%	86	86	87	87	2	87
max	108	108	102	102	2	102

.

3.3. Data Pre-Processing

The temperature and humidity data underwent several data pre-processing techniques, including missing value treatment, outlier data treatment, normalization, and data splitting. The missing value information for each column in the dataset is presented in

Table 5. Missing value information.

Column	No. of Missing Values
Temp(T-1)	0
Temp(T-24)	0
Humd(T-1)	0
Humd(T-24)	0
Season	0
T	0
Humd(H)	0

. It can be observed from Table 5 that there are no missing values in the data.

The box plot for each feature in the temperature dataset is depicted in Figure 2. This box plot helps visualize any outliers present in the data. It can be observed from the box plot that there are a few outlier samples; however, these outliers are not considered actual outliers. The samples fall outside the box due to the significant variation in the data from the winter season to the summer season in Warangal, as illustrated in Figure 3.

Similarly, the box plot for each feature in the humidity dataset is presented in Figure 4. This box plot is used to identify any outliers in the data.

Data normalization was implemented on the data using Equation (1) in order to reduce data redundancy in a table and improve data integrity.

$$Dat{a}_{norm}=\frac{Data-Dat{a}_{min}}{Dat{a}_{max}-Dat{a}_{min}}$$

(1)

Finally, the data were randomly divided into training and testing sets to train and validate the radial basis function neural network (RBFNN). As part of the data split, 5853 samples were used for training, and 2883 samples were used for testing.

3.4. Radial Basis Function Neural Network (RBFNN)

The RBFNN consists of one input layer, one hidden layer, and one output layer [35,36,37]. The input layer comprises five neurons since temperature and humidity are forecast using five input features. The output layer consists of one neuron, as only either temperature or humidity is forecast by this model. The number of neurons in the hidden layer, also known as centroids, is a hyperparameter that will be tuned to obtain the best model. Unlike an ANN [38,39], the training of the RBFNN includes both supervised and unsupervised learning. The training between the input layer and hidden layer is based on unsupervised learning [40], while the training between the output layer and hidden layer is based on supervised learning. The hidden layer uses the Gaussian activation function [41], which is mathematically represented by Equation (2). The standard deviation $\sigma$ [42] is calculated based on the width parameter “p” as shown in Equation (3). The RBFNN architecture for temperature forecasting is illustrated in Figure 5, and for humidity forecasting, it is depicted in Figure 6. The complete algorithm to train the RBFNN model using the stochastic gradient descent optimizer [43] is presented in Algorithm 1. The performance of the RBFNN is evaluated in terms of mean square error [44,45,46,47,48], as shown in Equation (4).

$$g(x,\mu ,\sigma )=e^{-\frac{{(x-\mu )}^2}{2{\sigma }^2}}$$

(2)

$$\sigma (p,{\mu }_i)=\sqrt{\frac{1}{p}\sum {({\mu }_i-{\mu }_j)}^2}$$

(3)

$$MSE=\frac{1}{n_{sample}}\sum _{i=1}^{n_{sample}}{(Actual load-Predicted load)}^2$$

(4)

Algorithm 1 RBFNN training algorithm.

Step 1: Read input and output features of temperature dataset ▹ X = {Temp(T-1), Temp(T-24), Humd(T-1), Humd(T-24), season} and Tempt(T), In case of humidity forecasting output is Humd(T) instead of Temp(T)

Step 2: Initialize number of centriods (neurons) in hidden layer, weights $W_{hk}$, bias parameter $b_k$, learning rate $\eta$ and tol = 1

Step 3: Randomly pick few samples from training dataset and assign as mean vector ($\mu$) for each neuron/centriod.

while tol ≥ 0.001 do   ▹ Unsupervised learning between input and hidden layer of RBFNN

Step 4: Calculate the euclidean distance (ED) between each sample and mean vector using Equation (5) $$ED=\sqrt{{(X-\mu )}^2}$$ (5)

Step 5: Assign the sample which has minimum ED to that particular centroid and update mean value ($\mu$) as an average of all assigned samples to that particular centroid.

Step 6: Calculate tolerance (tol) as the maximum difference between old and new mean values among all centriods.

end while

Step 7: Calculate the standard deviation ($\sigma$) using Equation (6) $$\sigma =\sqrt{\frac{1}{P}(\sum _{jϵP\_neighbour}{(C_i-C_j)}^2)}$$ (6)

Step 8: Calculate the output of each hidden neuron (h) using Equation (7) $$O_h=\exp \frac{-{(X-{\mu }_h)}^2}{2{\sigma }_h^2}$$ (7)

while $de{l}_W\ge 0.001$ do   ▹ Supervised learning between output and hidden layer of RBFNN

Step 9: Calculate output of the RBFNN output layer using Equation (8) $$O_k=W_{hk}^T{O}_h+b_0$$ (8)

Step 10: Update $W_{hk}$ using Equation (9) and $b_k$ using (10) $$W_{hk}=W_{hk}+\eta (Temp(T)-O_k)O_h$$ (9) $$b_o=b_o+\eta (Temp(T)-O_k)$$ (10)

Step 11: Find $de{l}_W$ as maximum change among $W_{hk}$ and $b_k$

end while

Step 12: Store model in terms of model parameters $W_{hk}$, $\mu$, $\sigma$ and $b_k$, and architecture

4. Results

The proposed RBFNN model was trained and tested using the temperature and humidity data collected from January 2021 to December 2021, comprising a total of 8736 samples. The model training and testing were implemented using Python programming in the Visual Studio environment, leveraging the specified dataset.

Optimal RBFNN Model to Forecast the Temperature

The RBFNN architecture with the minimum validation loss is considered the optimal model. Several RBFNN architectures are developed by tuning the number of centroids/neurons and the width parameter (P) in the hidden layer. The training and validation losses for different RBFNN architectures used for temperature forecasting are presented in

Table 6. RBFNN training loss for temperature forecast.

Width Factor
Centroids	2	3	4	5	6	7	8	9	10	11	12
4	0.0085	0.0074	0.0064	-	-	-	-	-	-	-	-
6	0.0067	0.0057	0.0052	0.0046	0.0038	-	-	-	-	-	-
8	0.0072	0.0065	0.0049	0.0041	0.0038	0.0040	0.0032	-	-	-	-
10	0.0079	0.0058	0.0055	0.0047	0.0037	0.0042	0.0038	0.0036	0.0032	-	-
12	0.0078	0.0059	0.0050	0.0042	0.0040	0.0038	0.0039	0.0037	0.0044	0.0037	0.0039

and

Table 7. RBFNN validation loss for temperature forecast.

Centroids	2	3	4	5	6	7	8	9	10	11	12
4	0.0082	0.0105	0.0057	-	-	-	-	-	-	-	-
6	0.0066	0.0053	0.0044	0.0034	0.0032	-	-	-	-	-	-
8	0.0081	0.0077	0.0065	0.0033	0.0034	0.0043	0.0109	-	-	-	-
10	0.0081	0.0049	0.0079	0.0079	0.0046	0.0079	0.0064	0.0032	0.0026	-	-
12	0.0075	0.0043	0.0034	0.0037	0.0039	0.0037	0.0024	0.0031	0.0024	0.0022	0.0028

, respectively. Among these architectures, the RBFNN model with 12 centroids and a width parameter of 11 was selected as the optimal model due to its lower validation loss of 0.0022, while the corresponding training loss is 0.0037.

The optimal RBFNN architecture for temperature forecasting, consisting of 12 centroids and a width parameter of 11, was trained using different batch sizes: 8, 16, 32, and 64. The convergence characteristics of the RBFNN architecture for these batch sizes are illustrated in Figure 7. It can be observed from the figure that the RBFNN model trained with a batch size of 32 achieves the minimum validation loss of 0.0022. Furthermore, the small difference between the training and validation losses indicates that the model is well trained without encountering underfitting or overfitting issues.

The training and validation losses for different RBFNN architectures used for humidity forecasting are presented in

Table 8. RBFNN training loss for humidity forecast.

	Width Factor
Centroids	2	3	4	5	6	7	8	9	10
4	0.01685	0.01376	0.0112	-	-	-	-	-	-
6	0.01272	0.0119	0.0109	0.01158	0.0101	-	-	-	-
8	0.0137	0.0118	0.0102	0.01121	0.01	0.0110	0.01	-	-
10	0.0137	0.012	0.012	0.011	0.0112	0.0106	0.0108	0.0116	0.01
12	0.01381	0.01061	0.0110	0.01051	0.0099	0.0118	0.01	0.01	0.011

and

Table 9. RBFNN validation loss for humidity forecast.

	Width Factor
Centroids	2	3	4	5	6	7	8	9	10
4	0.0165	0.0122	0.0105	-	-	-	-	-	-
6	0.0122	0.0139	0.0100	0.0112	0.0083	-	-	-	-
8	0.0134	0.0100	0.0098	0.0088	0.0112	0.0095	0.0082	-	-
10	0.0188	0.0099	0.0098	0.0086	0.0086	0.0164	0.0087	0.0083	0.0083
12	0.0136	0.0135	0.0111	0.0090	0.0123	0.0095	0.0096	0.0084	0.0078

, respectively. Among these architectures, the RBFNN model with 12 centroids and a width parameter of 10 is considered the optimal model due to its lower validation loss of 0.0078. The corresponding training loss for this architecture is 0.011.

The optimal RBFNN architecture for humidity forecasting, consisting of 12 centroids and a width parameter of 10, was trained using different batch sizes: 16, 32, 64, and 128. The convergence characteristics of the RBFNN architecture for these batch sizes are illustrated in Figure 8. It can be observed from the figure that the RBFNN model trained with a batch size of 128 achieves the minimum validation loss of 0.0075. Additionally, the small difference between the training and validation losses indicates that the model is well trained without encountering underfitting or overfitting issues.

The performance of the RBFNN model for temperature forecasting was validated by comparing it with the decision tree model [49], support vector regression [50], and elastic net regression [51] in terms of training and validation losses, as shown in Figure 9. From Figure 9, it is observed that the RBFNN model has lower validation losses, while the decision tree model exhibits signs of overfitting. Similarly, the performance of the RBFNN model for humidity forecasting was validated by comparing it with the decision tree model in terms of training and validation losses, as shown in Figure 10. From Figure 10, it is observed that the RBFNN model achieves lower validation losses compared to the decision tree model. Additionally, the decision tree model shows signs of overfitting. These comparisons demonstrate the superior performance of the RBFNN model over the decision tree model in terms of validation losses for both temperature and humidity forecasting tasks.

A web application was developed to enable temperature and humidity forecasting in the Warangal region. The application utilizes the RBFNN model in the backend. Figure 11 depicts the user interface of the web application. It can be accessed through the web link: https://sru-stlf-temp-humidity-rbf.streamlit.app/ (accessed on 12 March 2023).

Temperature and humidity forecast obtained from different machine learning models, including the RBFNN, decision tree model [49], support vector regression [50], and elastic net regression [51], were compared with the corresponding actual values. As depicted in Figure 12 for temperature comparison and Figure 13 for humidity comparison, it can be observed that the forecast from the RBFNN model are closer to the actual values compared to the forecast from the other models.

Model explainability, which demonstrates the impact of each feature on temperature forecasting and humidity forecasting, is presented in

Table 10. RBFNN model explainability for temperature forecast.

	Weightage of Feature
Feature	Temperature Forecasting	Humidity Forecasting
Temp(T-24)	0.6090 +/− 0.0361	0.0319 +/− 0.0034
Temp(T-1)	0.3438 +/− 0.0358	0.0344 +/− 0.0048
Humd(T-24)	0.0239 +/− 0.0027	0.1512 +/− 0.0610
Humd(T-1)	0.0200 +/− 0.0021	0.7757 +/− 0.0598
Season	0.0033 +/− 0.0018	0.0068 +/− 0.0025

. From the table, it is observed that temperature data from one hour and one day before have a greater impact on temperature forecasting. Similarly, humidity data from one hour and one day before have a greater impact on humidity forecasting. The impact of various input features such as Temp(T-1), Temp(T-24), Humd(T-1), Humd(T-24), and season on temperature forecasting is shown in Figure 14. Similarly, the impact of various input features on humidity forecasting is shown in Figure 15.

5. Conclusions

In this study, an RBFNN model was developed to forecast weather (WX) conditions, specifically temperature and humidity, in Warangal, Telangana State, India. The objective of this research is to provide accurate forecasts for proper planning in the agriculture and electric sectors. The RBFNN model was trained and optimized by tuning the hyperparameters, including the number of centroids, width factor, and batch size.

After tuning, an optimal RBFNN model was identified for temperature forecasting, with 12 centroids, a width factor of 11, and a batch size of 32. This model achieves a validation loss of 0.0022. Similarly, for humidity forecasting, the optimal RBFNN model has 12 centroids, a width factor of 10, and a batch size of 128, with a validation loss of 0.0075.

To make the forecasting models accessible and user-friendly, a web application was developed. This application utilizes the optimized RBFNN models in the backend to forecast both temperature and humidity. The input features considered for the forecasts include temperature and humidity values from one hour and one day before, as well as the season.

Furthermore, this work can be extended by incorporating additional parameters such as air density, precipitation, and barometric pressure to enhance the forecasting accuracy and provide more comprehensive WX forecasts.