Accuracy of spatio-temporal RARX model predictions of water table depths

Time series of water table depths (H t ) are predicted in space using a regionalised autoregressive exogenous variable (RARX) model with precipitation surplus (#E5 /E5# t ) as input variable. Because of their physical basis, RARX model parameters can be guessed from auxiliary information such as a digital elevation model (DEM), digital topographic maps and digitally stored soil profile descriptions. Three different approaches to regionalising RARX parameters are used. In the `direct' method (DM) #E5 /E5# t is transformed into H t using the guessed RARX parameters. In the `indirect' method (IM) the predictions from DM are corrected for observed systematic errors. In the Kalman filter approach the parameters of regionalisation functions for the RARX model parameters are optimised using observations on H t . These regionalisation functions describe the dependence on spatial co-ordinates of the RARX parameters. External drift kriging and simple kriging with varying means are applied as regionalisation functions, using guessed RARX model parameters or DEM data as secondary variables. Predictions of H t at given days, as well as estimates of expected water table depths are made for a study area of 1375 ha. The performance of the three approaches is tested by cross-validation using observed values of H t in 27 wells which are positioned following a stratified random sampling design. IM performs significantly better with respect to systematic errors than the alternative methods in estimating expected water table depths. The Kalman filter methods perform better than both DM and IM in predicting the temporal variation of H t , as is indicated by lower random errors. Particularly the Kalman filter method that uses DEM data as an external drift outperforms the alternative methods with respect to the prediction of the temporal variation of the water table depth.