Predicting water table depths in space and time using a regionalised time series model

Abstract

A regionalised autoregressive exogenous variable (RARX) model is presented for the relationship between precipitation surplus and water table depth. The parameters of the RARX model are ‘guessed’ at unvisited locations using auxiliary information such as soil profile descriptions, topographic maps and digital elevation models (DEM). In the direct method, the guessed parameters are used to predict time series of water table depth at unvisited locations; observed water table depths are not used in the prediction procedure. In the indirect method, observed water table depths are used to correct the predictions resulting from the direct method for systematic prediction errors. The prediction performance is evaluated by cross-validation. The validation results show small random errors (standard deviation on average is 9.8 cm) but large systematic errors (absolute mean error on average is 18 cm). The root mean squared error of the predicted time series is, on average, 22 cm. Taking the uncertainty of both the future weather conditions and the RARX-model predictions into account, a map reflecting the risk that a critical depth will be exceeded at a critical day in a future year is constructed. Furthermore, maps showing the components of uncertainty in predicted water table depths are given.