Forecasting groundwater levels using nonlinear autoregressive networks with exogenous input (NARX)

While the application of neural networks for groundwater level forecasting in general has been investigated by many authors, the use of nonlinear autoregressive networks with exogenous inputs (NARX) is relatively new. For this work NARX were applied to obtain groundwater level forecasts for several wells in southwest Germany. Wells in porous, fractured and karst aquifers were investigated and forecasts of lead times up to half a year were conducted for both influenced (e.g. nearby pumping) and uninfluenced wells. Precipitation and temperature were chosen as predictors, which makes the selected approach easily transferable, since both parameters are widely available and simple to measure. Input and feedback delays were determined by applying STL time series decomposition on the data and using auto- and cross-correlation functions on the remainders to determine significant time lags. Coefficient of determination, (relative) root mean squared error and Nash-Sutcliffe efficiency were used to evaluate forecasts, the model selection was based on an out-of-sample validation on rolling basis. The results are promising and indicate an outstanding suitability of NARX for groundwater level predictions with such a small set of inputs in all three aquifer types.