Space-time modeling of water table depth using a regionalized time series model and the Kalman filter

The spatiotemporal variation of shallow water table depth is modeled with a regionalized version of an autoregressive exogenous (ARX) time series model. The ARX model relates the temporal variation of the water table depth at a single location to a time series of precipitation surplus. The ARX model is calibrated first at locations where time series of water table depth are available. ARX parameters at nonvisited locations are estimated through geostatistical interpolation using auxiliary information, resulting in a regionalized ARX model or RARX model. The parameters of the geostatistical model are estimated by embedding the RARX model in a space-time Kalman filter and minimization of a maximum likelihood criterion built from the filter innovations. The resulting state estimator can be used for optimal space-time prediction of water table depth, network optimization, and space-time conditional simulation.