Non-Linear Time Series Analysis of Deep Groundwater Levels

Abstract

The objective of this study is to improve the simulation of deep groundwater levels by time se- ries models with pre-defined impulse response functions. This is attempted by adding a conceptual non-linear root zone model to simulate the recharge series to the model and by testing the use of a separate response function for the percolation zone. Three root zone models are developed based on two different recharge mechanisms: preferential flow, percolation, and a combination of the two. The performance of these models is compared to a linear model that is commonly used in time se- ries models to simulate the recharge. The approach is applied to groundwater level measurements in the Veluwe, a largely forested area in the Netherlands characterized by thick unsaturated zones. The effect of groundwater extractions and land reclamations is added to the model to further im- prove the simulation of the groundwater levels. The models are tested on three observations wells with increasing thickness of the unsaturated zone, varying from 7 m to 29 m to 49 m. The results show that model performance is improved by the implementation of a non-linear root zone model, particularly in simulating the peaks and lows in the groundwater levels. The recharge fluxes simulated by the non-linear models show different patterns that are physically more realistic than those simulated by the linear model. It is shown that different recharge series result in simulated groundwater levels that are very similar. This is a clear example of equifinality and it is recommended to introduce new sources of information to validate the modelled processes (e.g., water content measurements of the percolation zone or actual evaporation data). For the shallow well, the models with a single response function are selected as the best. The largest improvements for the deeper groundwater levels are obtained by the addition of a separate response for the percolation zone. For example, the average deviation from the observed ground- water levels decreased 0.18 m to 0.08 m for the deepest observation well by applying the separate response function. The models with an additional response function were better at simulating the estimated time to peak, the time it takes a recharge pulse to cause a peak in the groundwater levels. The time to peak is introduced in this research as a qualitative indicator to validate the modelled processes. The simulated responses indicate that the groundwater levels respond very quickly to water that leaves the root zone, even though the percolation zone is tens of metres thick. For each of the observations wells it is investigated if adding the effect of groundwater extrac- tions or land reclamations of Flevoland to the models improves the simulation of the groundwater levels. For the shallow well it is concluded that either the effect of land reclamations or groundwater extractions needs to be taken into account. Since these two stresses are correlated, it is concluded that only one of these should be taken into account when no further information is available to con- strain the models. For the medium deep well, the additional stresses did not significantly improve model performance and it is concluded that they do not have to be taken into account for this well. For the deep well, model performance is improved by both stresses. The largest improvements are observed when the effect of groundwater extractions is considered in the model. For implemen- tation of these stresses, the entire simulation period should be used for calibration, or constraints have to be implemented to obtain realistic results.