Choosing between linear and nonlinear models and avoiding overfitting for short and long term groundwater level forecasting in a linear system

Groundwater level forecasting is a useful tool for a more efficient and sustainable groundwater resource management. Developing models that can accurately reproduce groundwater level response to meteorological conditions can lead to a better understanding of the groundwater resource availability. Here an autoregressive neural network (NNARx) approach is proposed and compared with autoregressive linear models with exogenous input (ARx) in order to forecast groundwater level in an aquifer system where a linear groundwater level response to recharge by rainfall is observed. A well known problem regarding neural networks consists in the high risk of overfitting. Here, three NNARx model were trained using different methods to avoid overfitting: Early stopping, Bayesian regularization and a combination of both. The results show that on the short term forecasting (up to 15 days) the performance of NNARx and ARx are comparable but the ARx model generalizes better, while the NNARx trained with Bayesian regularization outperforms the linear models and the other NNARx models on longer scenarios on the test set. As linear models are less time demanding and do not require high computational power, they can be considered as suitable tools for short term groundwater level forecasting in linear systems while when longer scenarios are needed neural networks can be considered more reliable, and training them with Bayesian regularization allows to minimize the risk of overfitting.