Temporal-spatial modeling of precipitation using an approach based on MLR, ANN, HBA-ANN hybrid algorithm

Introduction

Life on earth is influenced by precipitation. Precipitation is one of the most significant factors that affects the hydrological cycle. Therefore, estimating the amount of this important atmospheric factor in each month or year for each region and watershed is of particular importance in the management and optimal planning of water resources. In recent decades, many new algorithms have been presented in engineering and computer science. These algorithms have significantly reduced errors and increased accuracy, but considering that hydrological systems rely on random events, none of the methods can be completely and accurately selected as a superior model for modeling and estimating. The honey badger algorithm is an innovative algorithm that requires a small number of iterations to achieve an optimal solution, and this increases its quality. In current study investigated the performance of three models, including multiple linear regression, artificial neural network and hybrid artificial neural network with honey badger optimization algorithm for modeling the temporal-spatial precipitation in East Azerbaijan province, the best developed model was selected evaluation criteria such as R, RMSE, NRMSE, MBE and NSE, the best model is selected



Materials and Methods

The multiple linear regression (MLR) model is one of the methods methods to analyze and investigate several variables. For this purpose, this method requires a large number of accurate and high accuracy data. In this method, the model has one dependent variable and several independent variables. So that a linear equation is generated between the independent variables called X1, X2, ..., Xn and the dependent variable Y.

Artificial neural network (ANN) is a model based on the performance of parallel processes of human biological nervous systems and communicates between the input and output data of a process without knowing its physics. One of the most used methods is the BP method, which includes of two stages. The first stage, which is entiled feed-forward (FF), the error value is calculated, after comparing output and objective values. In the second stage, which is labeled the back-propagation (BP), the error value calculated in previous step is corrected. The mentioned two stages continue until the output of the model approaches the desired output.

The honey badger algorithm (HBA) is a new meta-heuristic algorithm that simulates the honey-seeking behavior of a creature called the honey badger. The HBA includes two phases of discovery and exploitation. In the first phase, the locations of this creature are calculated, and in the second phase, the exact distance between the HBA and the prey (d_j) is calculated based on the honey intensity (S) and the honey smell intensity (I_j), as well as its new and optimal location to the prey X_new. In the HBA-ANN model, the HBA algorithm is used to determine the most optimal output value in the neural network and increase performance in modeling. Therefore, the developed hybrid model can have the characteristics of both ANN and HBA methods.



Results and Discussion

In this study, in the first stage, the temporal modeling and in the second stage, the spatial modeling of the monthly precipitation of 18 stations in East Azerbaijan province during the period of 1996-2022 using multiple linear regression (MLP), artificial neural network (ANN) and hybrid ANN with honey-eating badger algorithm (HBA-ANN) models has been paid. In order to model precipitation time, one and two month precipitation delay steps of the stations were used as input parameters. The first 70% of the dataset were selected for the training phase and the last 30% of the dataset were selected for the test phase. Based on the results obtained from R, RMSE , R,MBE, NSE evaluation criteria and graphic diagrams such as Taylor diagram, Violini plot and relative error diagram, it can be concluded that the HBA-ANN model indicated significant accuracy compared to other models in precipitation time modeling. Also, by comparing the results of the stations in the HBA-ANN model, the Herris station with the R equal to 0.94, RMSE equal to 2.25, NSE equal to 0.79, NRMSE equal to 0.04 and MBE equal to 1.06 in the test stage performed better compared with other stations. In order to model precipitation spatially, the geo-graphic coordinates of the stations, which include longitude, latitude, and altitude, are used as input parameters, and average monthly precipitation is used as output parameter. From eighteen stations, 70% of the stations (thirteen stations) were selected for the training phase and 30% of the stations (Charoymag, Bonab, Marand, Bostanabad and Ahar) were selected for the test phase. The approach to select the stations in the test phase is to cover the whole study area. Based on the results obtained from R equal to 0.95, RMSE equal to 1.03, NSE equal to 0.92,NRMSE equal to 0.03 and MBE equal to -0.81 and graphical diagrams such as Taylor diagram, Violini plot and relative error percent (RE%) plot, it can be concluded that the HBA-ANN model revealed significant accuracy compared to other models in spatial modeling of precipitation.



Conclusion

Precipitation is one of the most important factors that significantly change the hydrological cycle. Therefore, modeling and estimating this parameter is vital. In this study, the performance of multiple linear regression (MLR), artificial neural network (ANN) and hybrid ANN using honey badger algorithm (HBA-ANN) models were used for the spatial and temporal modeling of precipitation in East Azarbaijan province. In order to spatial modeling, the time delay steps of one and two months of stations precipitation were selected as input parameters. Also, in order to temporal modeling, the longitude, latitude and altitude parameters were used. The mentioned models were evaluated by R, RMSE, NSE, NRMSE and MBE assessment criteria. According to the results of temporal modeling, the HBA-ANN model for all stations especially Heris station with R=0.94, RMSE=2.25, NSE=0.79, NRMSE=0.04 and MBE=1.06 selected as superior model. Also based on the results obtained from spatial modeling the HBA-ANN model with R=0.95, RMSE=1.03, NSE=0.92, NRMSE=0.03 and MBE=-0.81 selected as best model. MLR and ANN models, respectively presented a relatively poor performance compared to the developed hybrid model.