Relationship between rainfall and groundwater level using time-lagged regression

In Iran, the climatic conditions are such that even in the rainiest areas of the country, there is a need for groundwater resources, and this demand is increasing every year. Since, groundwater is one of the most valuable water resources in Iran, it is very necessary to predict its changes in order to use it optimally with the aim of sustainable development. One of the most complex hydrological processes in nature is the rainfall-groundwater level process, which is affected by various physical and hydrological parameters. Although, various models have been presented to predict the changes in the groundwater level using the rainfall patterns, but less attention has been paid to the transfer function model. Hence, the main objective of this research is to introduce and use the transfer function (TF) model to predict the monthly groundwater level using rainfall data and to compare its results with ANFIS and Artificial Neural Network (ANN) models.In the present study, 30-year data (1992-2021) of meteorological stations and observation wells in 3 watersheds of Galikesh, Ramian and Mohamadabad were used to model the rainfall and groundwater level. of the Gorganroud river basin.Then, considering that the years closer to the present time have more accurate information about the situation of this time, the years were considered as a forward process in artificial neural networks. The model fitting and prediction of the groundwater level values using rainfall data for the next 12 months was performed with applying three models: Artificial Neural Network (ANN), Adaptive neuro fuzzy inference system (ANFIS), and transfer function (TF). For this purpose, MINITAB SAS, SPSS, and R software were used. Next step, the validation of the values predicted by the models was evaluated using three indices Mean Absolute Distance (MAD), Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE).The results of the autocorrelation plots of the groundwater level of the wells revealed that all time series have a seasonal trend with a period of 12 months. Based on the cross-correlation plots, it was also found that rainfall has direct effect on the groundwater level in the two watersheds of Galikesh and Mohamadabad with lag time of three months and in the Ramian watershed with a delay of one month. The validation results of the models using three indexes MAD, RMSE and MAPE revealed that the artificial neural network model for predicting the groundwater level using monthly rainfall data in all three investigated watersheds had the most appropriate performance (RMSE=0.0778, 0.0243, 0.0532m) and the ANFIS model is ranked second (RMSE=0.1841, 0.0832, 0.1012m). Although the transfer function model was less accurate than the other two methods (RMSE=0.5711, 0.5023, 0.3234m), but this model has performed well in fitting the monthly groundwater level values. This model is very effective in identifying the delay in the impact between the input and output variables, as well as expressing the model based on which the impact of rainfall can be expressed as a model.The results of this research show that all three models of artificial neural network, ANFIS and transfer function can be used to predict the groundwater level using monthly rainfall values. Consecutive overestimation and underestimation, which increases the error and decreases the performance of the models, was not observed for the three used models. Also, all three models perform well in detecting trends and data changes. However, the artificial neural network model is more accurate than the other models. In addition, when forward process is used in artificial neural network modeling, compared to the case where the complete series of data is used, the efficiency of the model is significantly improved.