IAES Inter national J our nal of Articial Intelligence (IJ-AI) V ol. 14, No. 1, February 2025, pp. 182 ∼ 192 ISSN: 2252-8938, DOI: 10.11591/ijai.v14.i1.pp182-192 ❒ 182 Le v enber g-Mar quardt-optimized neural netw ork f or rainfall f or ecasting Gujanatti Rudrappa 1,2 , Nataraj V ijapur 3 , Sateesh Hosamane 4 1 Department of Electronics and Communication Engineering, KLE T echnologi cal Uni v ersity Dr M. S. Sheshgiri Campus, Belag a vi, India 2 Research Centre, Department of Electronics and Communication, R V Institute of T echnology and Management, V isv esv araya T echnological Uni v ersity , Belag a vi, India 3 Department of Electronics and Communication Engineering, R V Institute of T echnology and Management, V isv esv araya T echnological Uni v ersity , Bang alore, India 4 Department of Chemical Engineering, KLE Dr . M. S. Sheshgiri Colle ge of Engineering and T echnology , KLE T echnological Uni v ersity , Belag a vi, India Article Inf o Article history: Recei v ed Jan 5, 2024 Re vised Jul 10, 2024 Accepted Jul 26, 2024 K eyw ords: Articial neural netw ork Le v enber g-Marquardt-optimized neural netw ork Principal component analysis Principal component re gression Rainf all forecasting ABSTRA CT Rainf all is a crucial meteorological indicator with applications in agriculture, a viation, and military . F oreca sting is essential due to unpredictable en vironmen- tal changes. Current methods use comple x statisti cal models, which are time- consuming. The present study is tar geted for forecasting rai nf all with the help of meteorological parameters, viz., temperature, humidity , wind speed, wind direction, and rain, using a specialized articial intelligence (AI) method and real-time data captured o v er the study area. The weather st ation installed at KLE Dr . M. S. Sheshgiri Colle ge of Engineering and T echnology in Karnataka, India, collects meteorological data. The models used were principal component re gres- sion (PCR) and Le v enber g-Marquardt -optimized neural netw ork (LMA ONN). The Le v enber g-Marquardt (LMA) backpropag ation (BP) algorithm performed better than other BP algorithms. The coef cient of determination ( R 2 ) ob- serv ed for the PCR and LMA ONN models were 0.57 and 0.87, respecti v ely . The LMA ONN model pro vided a better t for rainf all forecasting than the PCR model, with an inde x of agreement ( IoA ) of 0.96, indicating good forecasting. This is an open access article under the CC BY -SA license . Corresponding A uthor: Gujanatti Rudrappa Department of Electronics and Communication Engineering KLE T echnological Uni v ersity Dr M. S. Sheshgiri Campus Belag a vi, Karnataka 590008, India Email: rudraguj@gmail.com 1. INTR ODUCTION Rainf all is a natural phenomenon and af fects the meteorology and h ydrology domains. Rainf all af fects man y elds, such as w ater resource management [1], a viation industries [2], agriculture [3], and man y other ar - eas. Rainf all is af fected by man y f actors, such as minimum and maximum temperature, humidity , atmospheric pressure, altitude, and other meteorological parameters [4]. Predicting rainf all is crucial for agriculture, a viation, and other industries. F armers rely on r ainf all records and impro v ed forecasting skills to manage crops and boost the economy [5]–[7]. A viation is hea vily af fected by meteorological parameters, and rainf all can disrupt operations [2]. Flooding is another area af fected by rainf all, af fecting people’ s li v es and property [8], [9]. F orecasting rainf all helps pre v ent ooding, sa v es property , and manages w ater resources, hel ping o v ercome drought conditions. Numerous researchers ha v e J ournal homepage: http://ijai.iaescor e .com Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 ❒ 183 proposed w ays for rainf all forecasting, deli v ering accurate and timely forecasts to enhance human mobility acti vities and agricultural/industrial de v elopment. F orecasting the rain will be challenging for meteorologists due to the unpredictability of both the t ime and the amount of precipitation. F or a decade, statisticians ha v e used geographical coordinates (such as latitude and longitude) and other meteorological parameters (such as pressure, temperature, wind speed, and humidity) to e xamine the relationship between precipitation and rainf all forecasts [10]. Rainf all forecasting traditionally relies on numerical weather prediction (NWP) and statistical models [10], [11], which f ace challenges due to nonlinear changes in rainf all dynamics [12]. Linear re gression (LR) and its v ariations are used, b ut capturing the nonlinearit y of rain is chal lenging due to v arious m eteorological elements [13]. A rainf all forecasting model using multiple linear re gression (MLR) and multi-resolution analysis (MRA) w as presented for South Australia [14], sho wing more accurate monthly rainf all estimations compared to traditional re gression models. Principal component analysis (PCA) has been used to o v ercome collinearity problems and reduce the number of independent v ariables in LR, often call ed principal component re gression (PCR) [15]. Ho we v er , PCR has been found to result in heterogeneous errors due to multicoll inearity problems, leading to the incor - poration of Dummy v ariables generated by partial least squares re gression (PLSR). Meta-re gress or XGBoost re gressor w as emplo yed o v er the Karnataka re gion which outperformed the LR and random forest (RF) re gres- sion [16]. Articial neural netw orks (ANNs) are more popular for forecasting nonlinear characteristics lik e rainf all due to their capacity for pattern learning [17], [18]. ANNs outperform traditional statistical methods in terms of accurac y and prediction performance, making them a preferred method for rainf all prediction with high accurac y . ANNs can be trained using optimization algorithms such as backpropag ation (BP) and genetic algorithms, allo wing for ef cient tuning of model parameters and impro v ed prediction accurac y [19]. T raditional approaches to weather prediction are greatly hindered by the nonlinear characteristics of precipitation dynamics. Although LR and statistical models ha v e been emplo yed, the y frequently f ail to grasp the int ricate, nonlinear correlations present in weather data. W e need more precise and dependable forecasting methods since the timing and amount of precipitation are so unpredictable. Man y dif ferent types of b usinesses rely on accurate weather forecasts to help them prepare for a nd respond to unpredictable rains. There is a lack of kno wledge and forecasting methodologies for other areas because most of the a v ailable research only co v ers one or tw o nations. Because of its distinct climate and the signicance of precipitation for man y industries, the Indian state of Karnataka requires specialized methods for predicting when and ho w much rain will f all. The study describes the use of a h ybrid articial neural netw orks (HANN) called Le v enber g-Marquardt -optimized neural netw ork (LMA ONN) for rainf all forecasting in Belag a vi City , Karnataka, India. This h ybrid technique impro v es predicting accurac y by combining the strengths of ANNs with real-time meteorological data. The study not only describes the LMA ONN b ut also compares its performance to that of the PCR model. This comparison analysis sheds light on the ef cac y of the suggested LMA ONN in enhancing rainf all forecasts when compared to e xisting statistical approaches. By concentrating on the inef ciencies of present method- ologies, the study presents to help design a more ef cient and accurate rainf all forecasting model. This lls a subst antial v acuum in the literature and has the potential to benet a v ariety of sectors that rely on precise rainf all predictions. The rest of the paper is or g anized as mentioned – section 2 pro vides brief details of the study area and data acquisition and pre-processing. Section 3 gi v es details of PCR. Section 4 gi v es an insight into the LMO ANN model. Section 5 pro vides the details of the results and discussion and also gi v es the comparison with dif ferent models, and section 6 gi v es the conclusion for the proposed w ork. 2. METHOD This section pro vides the details of the study area and also details on the e xperimental setup used for data acquisition, data pre-processing and data transformation. 2.1. Study ar ea Belag a vi, formerly kno wn as Belg aum, is a district of the State Karnataka and Country India. At a mean altitude of 779 me ters, Belag a vi is located in the Northwestern parts of Karnataka and is situated at the foothills of the Sah yadri Mountains. I t lies close to the border of tw o states of India viz., Maharastra and Goa. The study area is located within Belag a vi at 15 ◦ 49’09.3”N 74 ◦ 29’54.4”E as sho wn in Figure 1. Belag a vi is kno wn for its mild climate throughout the year . W inter is the coldest season (the lo west temperature in Karnataka is typically recorded in Belg aum), and the monsoon rainf all is nearly continuous from June to Le venber g-Mar quar dt-optimized neur al network for r ainfall for ecasting (Gujanatti Rudr appa) Evaluation Warning : The document was created with Spire.PDF for Python.
184 ❒ ISSN: 2252-8938 September . April is sometimes mark ed by hailstorms in Belg aum. The minimum and maximum rain w as 0.25 to 109.50 mm during the study period. Figure 1. Satellite image of study area and weather monitoring station 2.2. Data acquisition Data used in the study is acquired from May 2022 to October 2022. The station collects m eteorological data e v ery 10 minutes and the data acquired is stored in the cloud storage [20]. In total, v e meteorological parameters are collected, which include temperature (T), humidity (H), wind speed (WS), wind direction (WD), and rainf all (R). The units for T , H, WS, WD, and R are de grees celsius ( o C), percentage (%), meters per second (m/s), de grees (de g), and millimetres (mm), respecti v ely . All the v e meteorological parameters are numerical v alues. Figure 2 sho ws the installed weather station at the location mentioned in the study area. Figure 2. W eather station installed at study area 2.3. Data pr e-pr ocessing The dataset consists of 15906 data points, b ut due to internet, de vice, or sensor issues, some data points were missing or had inconsistent v alues. T o address these issues, data cleaning w as performed, replacing missing or noisy v alues with pre vious points in time. Outliers were also remo v ed, resulting in a total of 7600 data points. The stati stical v alues for meteorological parameters are presented in T able 1, including minimum (Min), maximum (Max), mean ( µ ), and standard de viation (SD). T able 1. Basic statistical parameters of the meteorological parameters W eather parameter (Unit) Min Max µ SD T emperature ( o C) 19.00 30.00 22.26 1.47 Humidity (%) 50.90 89.60 78.67 5.52 W ind speed (m/s) 0.20 14.10 3.19 2.052 W ind direction (de g) 0.00 359.00 190.77 62.38 Rainf all (mm) 0.25 109.50 9.96 16.84 Int J Artif Intell, V ol. 14, No. 1, February 2025: 182–192 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 ❒ 185 2.4. Data transf ormation Data transformation is crucial in decision-making systems, impacting model performance and i n t er - pretability . PCA is used to transform 7600 data points, reducing the number of dimensions in lar ge datasets with n um erous dimensions/features per observ ation [21]. This process impro v es data interpretability while maintaining information and f acilitating multidimensional data display . PCA reduces the number of dimen- sions in a dataset, trans forming information into a ne w set of principle components (PCs) v alues. This reduces data v ariation, mitig ates o v ertting, and remo v es multicollinearity using PCs generated from input data [22]. The number of PCs is the same as the num ber of original features. In (1) is used to esti mate the standardized matrix’ s Eigen v alues. | Co v(X , Y) − λ I | = 0 (1) Where λ is Eigen v alue, and I is Indentiy matrix. No w , if v represents the Eigen v ector , then solving in (2) gi v es the Eigen v ectors corresponding to the λ Eigen v alues. Co v (X , Y ) ∗ v = λ ∗ v (2) From the correlation matrix, t he Eigen v ectors are calculated. The sum of the v ariances e xplained by each Eigen v ector is represented by its corresponding Eigen v alue. PCs with high orders contrib uting little to the o v erall v ariation are essentially noise. In (3) presents the i th v ariance of the i th PC. V ariance= λ i P n λ n (3) After obtaining all PCs, the original data set is turned into the orthogonal set by Eigen v ector multiplication. This accounts for the data transformation step in the data pre-processing. 3. PRINCIP AL COMPONENT REGRESSION A statistical technique called re gre ssion analysis nds the link between a dependent v ariable and a collection of independent (e xplanatory) f actors [23]. The re gression model can re v eal whether or not changes in the dependent v ariable are related to an y of the e xplanatory v ariables. The re gression model generates the response to determine the model’ s unkno wn coef cients. PCR is a re gression method that uses PCs as input parameters. The success of PCR is contingent on the selection of the es sential f actors emplo yed for re gression; PCR can accurately forecast the outcome based on model assumptions by using the decided number of PCs, which will e xplain about 60% of the v ariance. In (3) represents the PCR equation. Y = α 0 + α 1 ∗ PC 1 + . . . + α N ∗ PC N + e (4) Where, α 0 . . . α N are the coef cients of the re gression model estimated from the least-squares method, P C 1 . . . P C N are the N principal components, and e denotes the random error . 4. LEVENBERG-MARQ U ARDT - OPTIMIZED NEURAL NETW ORK MODEL Multilayer perceptron (MLP) ANN models are used to solv e nonlinear modelling problems by trans- forming input data to approximate output data. These models learn from monitored data e xamples and ha v e the ability to generalize. The LMA ONN model, which consists of three layers, is used in this w ork. The input is PCs obtained by applying PCA on input parameters, while the output layer outputs rainf all forecasting results. The hidden layer is enhanced through multiple trials using v arious architectures, resulting in lo w mean square error (MSE). The LMA ONN model’ s architecture is illustrated in Figure 3. Le venber g-Mar quar dt-optimized neur al network for r ainfall for ecasting (Gujanatti Rudr appa) Evaluation Warning : The document was created with Spire.PDF for Python.
186 ❒ ISSN: 2252-8938 Figure 3. The architecture of the LMA ONN model 5. RESUL TS AND DISCUSSIONS The correlation coef cient estimates the strength of the association between meteorological parame- ters [24]. The v alues are obtained by using (5). ρ XY = Co v (X , Y ) σ X σ Y (5) Where ρ X Y is the correlation coef cient, Co v ( X , Y ) is the co v ariance of v ariables X and Y , and σ X and σ Y are the standard de viations of v ariables X and Y , respecti v ely . Figure 4 sho ws the correlation of meteorological parameters for forecasting rainf all. It sho ws a ne g a- ti v e correlation between rainf all and temperature, while humidity , wind speed, and wind direction are positi v ely correlated to rainf all. High collinearity is observ ed between temperature and humidity , indicating the presence of collinearity between the independent v ariables. Measures such as the inde x of agreement (IoA), correlation coef cient (R), root mean square error (RMSE), normalised root mean square error (NRMSE), mean absolute error (MAE), R-squared (R 2 ), and mean square error (MSE) are emplo yed to assess the forecasting model’ s performance [25]. Figure 4. Correlation heatmap Int J Artif Intell, V ol. 14, No. 1, February 2025: 182–192 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 ❒ 187 The PCA analysis w as conducted using Minitab17 statistical softw are to e xtract critical informat ion (PCs) from data and rearrange the dataset description. PCA is adv antageous in minimizing the dimension of input v ectors, as it minimizes the redundanc y of the v ector components. T able 2 pro vides the PCA summary along with each PC’ s e xplained v ariance. The rst and second PCs e xplain 38% and 22% of the total v ariation of parameters, respecti v ely , making up 60% of the total v ariation used in forecasting models. T emperature and humidity e xplain 63% and 67% of rain v ariability , respecti v ely , from the rst PC, while wind speed and direction e xplain 75% and 57% of rain v ariability from the second PC. T able 2. PC v alues, Eigen v alues, and the v ariance of v arious parameters (PCA) V ariable PC1 PC2 PC3 PC4 PC5 T emperature -0.631 0.086 -0.021 0.408 0.654 Humidity 0.671 -0.101 0.071 -0.097 0.724 W ind speed -0.116 0.750 -0.217 -0.594 0.154 W ind direction 0.196 0.569 0.681 0.401 -0.114 Rainf all 0.315 0.310 -0.695 0.557 -0.106 Eigen v alue 1.918 1.129 0.917 0.821 0.211 Proportion of v ariance 0.384 0.226 0.184 0.164 0.042 Cumulati v e 0.384 0.610 0.793 0.958 1.000 LR model with the help of tw o PCs as input v ariables are used to forecast rain, which is the PCR model. The re gression equation used for rainf all forecasting using the PCR model is gi v en by (6). Rainfall= − 83 . 641 + 2 . 1324 ∗ vPC1 − 0 . 71003 ∗ vPC2 (6) The de gree of determination of the re gression lines with the PCR model w as 0.76 which is sho wn in Figure 5. Figure 5. V alidation for rainf all forecasting using PCR model 5.1. Le v enber g-Mar quardt - optimized neural netw ork model The three -layered LMA ONN with BP is utilized for forecasting rainf all. The rst tw o PCs, which account for 60% of the total parameter v ariation in PCA, are used for forecasting. The ANN’ s performance is enhanced by applying PC A to the input parameters [26]. The original data is di vided into three subsets: 70% training, 15% testing, and 15% v alidation. The netw ork’ s weights are initialized, and adjusted using the BP algorithm to obtain the lo wer MSE. The signicant component transformation matrix transforms future inputs. The de v elopment of BP netw orks has signicantly impro v ed the performance of the selected architecture. BP- type netw orks use a gradient approach to MSE, pro viding a gradient method with the gradient of MSE [27]. A three-layer netw ork w as created and trained considering 8 BP algorithms. T able 3 summarizes the MLP-BP designs that produced the best LMA ONN models. The top-performing LMA ONN models in v olv ed Le venber g-Mar quar dt-optimized neur al network for r ainfall for ecasting (Gujanatti Rudr appa) Evaluation Warning : The document was created with Spire.PDF for Python.
188 ❒ ISSN: 2252-8938 the usage of a logistic acti v ation function in the hidden layer . It w as found that the Le v enber g-Marquardt (LMA) BP algorithm is v ery ef cient for the present problem when compared to other BP algorithms as the rob ust BP algorithm and the conjug ate gradient algorithm. LMA w as pro v en to pro vide a lesser MSE of 40.39. The LMA w orks best for these situations, and the approximation w as precise. T able 3. Performance indices for the 8 BP algorithms Inde x BFG* CGB* CGF* CGP* GD* GDM* RP* LMA* MAE 11.09 4.46 4.21 4.29 11.09 7.73 3.93 3.04 MSE 438.34 46.08 44.19 44.50 438.34 232.48 42.06 40.39 RMSE 20.93 6.78 6.64 6.67 20.93 15.24 6.48 6.35 NRMSE 0.19 0.06 0.06 0.060 0.19 0.13 0.06 0.05 IoA 0.38 0.95 0.96 0.96 0.38 0.84 0.96 0.96 R - 0.92 0.92 0.92 - 0.75 0.93 0.93 R 2 0.39 0.85 0.85 0.85 0.39 0.26 0.86 0.87 * BFG - BFGS-Quasi-Ne wton Backpropag ation; CGB - Po well-Beale conjug ate gradi- ent Backpropag ation; CGF - Fletcher -Ree v es conjug ate gradient Backpropag ation; CGP - Polak-Ribiere conjug ate gradient Backpropag ation; GD - Batch Gradient Des cent; GDM - Batch Gradient Descent with Momentum; RP - Resilient Backpropag ation; LMA - Le v enber g-Marquardt Backpropag ation The study aimed to optimize a netw ork for rainf all forecasting by v arying the number of neurons in the hidden layer . The number of neurons and the MSE were optimized, with twelv e neurons making great predictions. The weight update with rotation pattern impro v ed the performance of most trained netw orks. The netw ork performed e xceptionally well with changing neurons at the hidden layers, with R 2 v alues of 0.87, 0.86, 0.88, and 0.86, respecti v ely for training, testing, and v alidation. The method by which rain is estimated most ef fecti v ely e xplains its superior performance. The logistic acti v ation function w as used in a single hidden layer of 12 neurons in LMA ONN models designed to forecast rainf all. The results sho wed that twelv e neurons pro vided a lo wer MSE of 40.39 for the LMA ONN model for each subset. Reducing the number of neurons belo w or abo v e twelv e increased the MSE v alues. Optimization of the number of neurons is cruci al for the ef cienc y of the de v eloped netw ork. Therefore, the number of neurons and the MSE were optimized. The netw ork optimization w as carried out by guessing neurons in each hidden layer . The MS E v alues for v arying numbers of neurons are presented in T able 4. T able 4. Performance indices for v arying numbers of neurons in the netw ork for selected BP algorithm Number of neurons Inde x 2 3 4 5 6 7 8 9 10 11 12 13 MAE 4.24 4.08 4.09 4.10 4.09 4.01 4.02 4.01 3.99 3.97 3.04 4.02 MSE 45.68 41.96 41.95 41.88 42.11 41.07 40.85 40.69 41.00 40.98 40.38 41.10 RMSE 6.75 6.47 6.47 6.47 6.48 6.40 6.39 6.37 6.40 6.40 6.35 6.41 NRMSE 0.061 0.059 0.059 0.059 0.059 0.058 0.058 0.058 0.058 0.058 0.057 0.058 R 0.92 0.93 0.93 0.93 0.93 0.93 0.93 0.93 0.932 0.93 0.94 0.93 R 2 0.85 0.86 0.86 0.86 0.86 0.86 0.87 0.87 0.86 0.87 0.88 0.86 IoA 0.96 0.96 0.96 0.96 0.96 0.96 0.96 0.96 0.96 0.96 0.97 0.96 In Figure 6, the log arithms of the e xpected rain are plott ed ag ainst the log arithms of the actual rain. The f act that the points tend to cluster along lines close to the 45-de gree tangent line sho ws that the model is good. The model has the lo west R 2 (0.26) with the GDM BP algorithm and has the highest R 2 v alue of 0.88 for LMA. The PC application benets the LMA ONN model because it helps e xplain the change in t he predictor . In this case, the h ybrid method chose the meteorological v ariables temperature and humidity as the most critical predictor v ariables based on the rst PC and wind speed and wind direction as the most vital predictor v ariables based on the second PC during model de v elopment. The coef cient of correlation (R) for the model w as 0.933, 0.931, 0.937, and 0.933, respecti v ely , for training, testing, v alidation, and o v erall data. This is represented in Figure 7. T ests were carried out for 1000 epochs for the LMA ONN model considering 12 neurons and the LMA algorithm. The best v alidation performance (MSE) of 39.96 w as obtained at 52 epochs. The v alidation performance for the LMA ONN model is sho wn in Figure 7. Int J Artif Intell, V ol. 14, No. 1, February 2025: 182–192 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 ❒ 189 Figure 6. T raining, testing, and v alidation for rainf all forecasting using the LMA ONN model Figure 7. T raining, testing, and v alidation MSE for rainf all forecasting using the LMA ONN model 5.2. Comparison between principal component r egr ession and LMA ONN models V arious statistical e v aluations were used for the PCR and LMA ONN models to measure the goodness of t. The performance metrics are obtained by comparing the actual and the forecasted rainf all estimates. T able 5 summarizes the statistical e v aluation indices. The LMA ONN model demonstrated a better t for the Le venber g-Mar quar dt-optimized neur al network for r ainfall for ecasting (Gujanatti Rudr appa) Evaluation Warning : The document was created with Spire.PDF for Python.
190 ❒ ISSN: 2252-8938 problem than the PCR model, with R 2 v alues of 0.57 and 0.87, respecti v ely . The fractional bias (FB) for both models w as 0.0002 and 0.0037, indicating the y grea tly predicted observ ed rainf all. The LMA ONN model’ s performance w as e vident in its MAE (3.04), MSE (40.38), RMSE (6.35), and R 2 (0.88), indicating its ability to accurately forecast rainf all in the Belag a vi re gion T able 5. Performance indices for comparing PCR and LMA ONN models Inde x PCR LMA ONN Inde x PCR LMA ONN Inde x PCR LMA ONN Inde x PCR LMA ONN MAE 8.9789 4.046 RMSE 11.614 6.355 R 0.756 0.934 IoA 0.8430 0.965 MSE 134.880 40.387 NRMSE 1.0470 0.0581 R 2 0.572 0.8719 FB 0.0002 0.0037 The results match those of other studies done by a comparable group of researchers. Rainf all in W estern Australia w as forecast using LR [28]. Peak R -v alues were between 0.47 and 0.53, and trough R- v alues were between 0.82 and 0.94. A reasonable range of R v alues (0.71-0.91), RMSE (10.68–23.08), MAE (9.00–20.90), and d (0.56-0.71) were produced by the use of non-linear re gression (NLR) modelling for forecasting rainf all in the Australian Capital T erritory [29]. F or rainf all forecast ing in the Indramayu dis- trict, PCR w as emplo yed, leading to an R -v alue of 0.75 and an RMSE of 28.84 [15]. A better performance w as obtained by applying meta-re gressor XGBoost (XGB) o v er the Karnataka re gion [16]; the performance measures in terms of MAE, RMSE, R, and R 2 were 94.53, 158.27, 0.92 and 0.84 respecti v ely . Rainf al l pre- diction w as obtained by t he application of rainf all forecasting for the Semarang re gion by applying ANN [18]; the model’ s performance in terms of RMSE and MAE w as 13.05 and 6.62 respecti v ely . The Indus Basin in P akistan used an ANN to predict when it will rain, and the results sho wed R 2 v alues between 0.19 and 0.91 and prediction accuracies between 0.85 and 0.82 [30]. Rainf all forecasting in the research location (Belag a vi) w as well handled by the suggested LMA ONN model, which utilized 12 neurons. The model’ s performance metrics is sho wn in T able 5. The comparison of LMA ONN model with other models is sho wn in T able 6. T able 6. Comparison of the v arious models discussed Performance measure LR [28] NLR [29] PCR [15] XGB [16] ANN [18] ANN [30] LMA ONN M A E 13.06-23.52 9.00–20.90 15.06 94.53 6.62 7.03-24.75 4.05 R M S E 21.21-36.45 10.68–23.08 28.84 158.27 13.05 16.46-26.01 6.36 R 0.47-0.92 0.71-0.91 0.75 0.92 0.89 0.44-0.89 0.93 R 2 0.22-0.85 0.51-0.82 0.57 0.84 0.79 0.19-0.79 0.87 6. CONCLUSION T w o predicti v e models, PCR and LMA ONN, were de v eloped for rain forecasting at Belag a vi, Kar - nataka and were compared with state-of-the-art models. The statistical analysis of meteorological data is e v al- uated for the signicance of the collected data. The data w as dimensionally reduced by applying PCA, and the PCs’ res ults were used for the PCR model. The PCR model performance w as relati v ely good, with an R 2 of 0.57. The PCR model performance w as impro v ed using a three-layered LMA ONN model with eight BP algorithms. Based on the optimization and model performance, the LMA BP algorithm performed well with twelv e neurons in hidden layers. The de v eloped PCR and LMA ONN performance is e v aluated with the coef - cient of determination (R 2 ) and w as found to be 0.57 and 0.87, respecti v ely . It w as observ ed that PCA helped in capturing the v ariability of rainf all. MSE, RMSE, and MAE for the PCR model were 134.88, 11.61, and 8.98, respecti v ely , whereas, for the LMA ONN model, the v alues were 40.39, 6.355, and 4.046, respecti v ely . The present study aims to enhance the precision of rainf all forecasting models by combining neural netw orks with other methodologies lik e fuzzy logic, e v olutionary algorithms, and ensemble methods. By broadening the scope of meteorological f actors and utilizing remote sensing technology lik e satellite imaging and radar data, the study aims to capture geographical and temporal uctuat ions in precipitation patterns, particularly in areas with limited data or during se v ere weather occurrences. This approach can be applied to v arious domains such as f arming, a viation, w ater resource management, and ood management. A CKNO WLEDGEMENTS The authors e xpress gratitude to V GST for funding their ”Establishment o f IoT and Articial Intel- ligence Lab for Problem-Based Learning” laboratory (under KFIST -L1, Grant number 958), which enabled successful project implementation and real-time data access, crucial for achie ving study objecti v es. Int J Artif Intell, V ol. 14, No. 1, February 2025: 182–192 Evaluation Warning : The document was created with Spire.PDF for Python.
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