Performance of nonlinear time series models to simulate synthetic groundwater table time series from an unsaturated zone model

Abstract

Transfer function noise (TFN) modelling is a form of time series analysis which regularly uses the recharge as a stress to explain the groundwater table fluctuations. Often the recharge flux is estimated as a linear combination of the precipitation and the (potential) evaporation. However, this is a simplification of the actual hydrological processes in the unsaturated zone. This is tried to be overcome by implementing a nonlinear recharge model in TFN time series models. Additionally, TFN models can use different impulse response functions, where some of them account for dispersion and retardation due to the unsaturated zone. In this report the performance of a linear and nonlinear recharge model, inside the TFN model, are tested against synthetic time series of the groundwater table. These time series for the groundwater table are created with the unsaturated/saturated zone model HYDRUS-1D. With HYDRUS-1D, thirty-five synthetic time series are created for five different soil types and seven different unsaturated zone thicknesses (up to 5 m). The three most commonly used response functions, exponential, gamma and four-parameters are also tested for these thirty-five time series. The results show that TFN models using the nonlinear recharge model are almost always better in estimating the groundwater table time series than the linear recharge model. This is confirmed in both the calibration and validation period. The common disadvantage of the linear recharge model, undershooting the groundwater table in (dry) summers, is not observed for the nonlinear recharge model. This can improve the forecasting abilities of TFN models during droughts. Additionally, the nonlinear recharge model gives a more realistic representation of the fluxes in the root zone. This is confirmed goodness-of-fit parameters when comparing of the recharge flux and evaporation reduction calculated by HYDRUS-1D and the nonlinear recharge model. Especially when using the exponential response function, the recharge flux can be estimated quite well by the nonlinear recharge model. However, the nonlinear recharge model is currently not able to estimate groundwater uptake (upwards recharge) while it is observed in the HYDRUS-1D simulations. The linear model does perform decently for shallow groundwater tables down to a depth of 150 cm since that is where large groundwater fluctuations and more days with groundwater uptake (upward recharge) are observed. The use of the gamma and four-parameter response functions significantly improves the performance of the linear recharge model. This can be explained by the compensation of these response functions for dispersion and retardation in the root zone. Nevertheless, when performing groundwater table time series analysis on synthetic time series created with HYDRUS-1D, the nonlinear recharge model is preferred to simulate the groundwater table.