State-space modeling of water table fluctuations in switching regimes

Abstract

A nonlinear state-space model is developed for describing water table fluctuations in groundwater systems that are influenced by drains. As drains are only active if the water table is above drainage level, the regime of the system switches at the drainage level. The water table depth is related to observations on precipitation and evapotranspiration, regional groundwater flow, and drainage flux. The drainage flux is a nonlinear function of water table depth in the sense that it switches from a constant (zero) flux if the water table is below drainage level, to a flux that is linearly related to the water table depth if the water table is above drainage level. The system noise is also nonlinearly related to the water table depth. The model is calibrated on a time series of water table depths using a maximum likelihood criterion. For this purpose, the model is processed through a truncated first-order filter. To increase filter performance, the strong nonlinear relation between water table depth and drainage flux is smoothed. The state-space model is tested at two locations. It is shown that the model performs well. Moreover, it is superior to commonly applied linear transfer function-noise models. The applications illustrate the applicability of the state-space model for estimation of the effect of interventions, characterization of the groundwater system, simulation, and prediction.