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

Water authorities in the Netherlands are not only responsible for managing surface water, but also for managing the groundwater reserves. Particularly the water table depth is an important variable, determining agricultural production and the potential for nature development. Knowledge of the spatio-temporal variation of the water table depth is therefore vitally important for regional scale water management. This raises the following question: At what spatial density and which temporal frequency must the water table depth be observed to obtain a complete spatio-temporal picture at a required accuracy and at minimal costs. In this paper this problem is tackled by using a statistical space-time model of the water table depth in combination with a space-time Kalman filter. The statistical model is built as follows. A simple time series model (called ARX model) is used to describe water table depth as a function of precipitation surplus (precipitation minus potential evapotranspiration). The ARX model is calibrated first at locations where time series of water table depth are available (Bierkens et al., 1999). ARX parameters at non-visited locations are estimated through geostatistical interpolation using auxiliary information, such as surface elevation from a digital elevation model (DEM). The result is a so called regionalized ARX model or RARX model (Knotters and Bierkens, 2001). The parameters of the geostatistical model (i.e. the semivariogram) are estimated by embedding the RARX model in a space-time Kalman filter and minimisation of a maximum likelihood criterion built from the filter innovations. The resulting state-space model can be used for optimal space-time prediction of water table depth, space-time conditional simulation and network optimisation (Bierkens, 2001). The parameters of the RARX model can interpreted physically, such that the predicted water table depth can used to predict specific drainage discharge. Hence, it is possible to predict the total discharge from a catchment with predominantly groundwater flow. This way, it is also possible to assimilate discharge measurements to improve predictions of water table depth. A case study is presented where the RARX model and the Kalman filter are used for optimisation of an existing network of 233 piezometers in the water authority Reest and Wieden, the Netherlands. Water table depths are recorded two times a month for all locations. Observation and maintenance costs of this network are high. The accuracy of the existing network is analysed using the RARX model and the Kalman filter. The accuracy is both "modelled" (assuming an additive noise process that is discrete and white in time and continuous, coloured and multiGaussian in space) and estimated with cross-validation. Several options for decreasing observation efforts are analysed. A particularly promising option is observing a limited number of well placed locations with high frequency (i.e. using divers) and the remaining locations only occasionally.