Estimating fluctuation quantities from time series of water-table depths using models with a stochastic component

Abstract

A method is developed to estimate fluctuation quantities of water-table depths independently of the precipitation excess during the monitoring period, whose length is generally limited to 4–10 years. For this purpose, one-dimensional models are calibrated with the precipitation excess as an input variable. These models include the SWATRE soil moisture accounting model, supplemented with a stochastic model for the noise series, and transfer function-noise (TFN) models. The models are used to simulate realizations of time series of water-table depths with lengths of 30 years, from which the mean highest and mean lowest water-tables ( MHW and MLW, respectively) are calculated. These estimates can be used in water management for making strategic decisions, because they reflect the conditions of the prevailing climate (i.e. average weather conditions over, say, 30 years) and not just the meteorological conditions during the groundwater monitoring period, which is usually of limited length. The results show that MHWs and MLWs which are estimated from an 8-year series may deviate more than 20 cm from those estimated from 30-year series. The results of the SWATRE models and the TFN models differ only slightly, despite having clearly different theoretical starting-points. The minimum length of series needed for calibration is of practical value; stationary series of 4 years were generally found to be sufficiently long to model the dynamic systems in this study adequately. Both SWATRE models and TFN models could be improved in order to obtain a constant residual variance: in SWATRE models hysteresis of the soil water characteristics could be incorporated, whereas in TFN models a non-constant variance of water-table depths could be taken into account.