Parameter estimation in groundwater flow models with moments of the impulse response function

Groundwater is an important natural resource which is used all over the world. For a sustainable groundwater use it is important to know how groundwater systems are affected by human interventions. There are several modelling tools that can be used to analyse the influence of interventions on a groundwater system. Time series analysis is a tool that can be used to analyse the influence and contribution of external stresses on a measured time series (e.g. the effect of precipitation on groundwater heads). In the Pre-Defined Impulse Response Functions in Continuous Time (PIRFICT) method for time series analysis (von Asmuth et al. 2002), impulse response functions are used to characterize a groundwater system. Groundwater flow modelling is another approach that can be used to analyze, predict and quantify changes to a groundwater system. A groundwater flow model often contains parameters that represent physical properties of the subsurface such as the transmissivity and the storativity. It is difficult and expensive to measure these parameters, while it is much easier to measure, for example, the head. Therefore these parameters are often obtained with a parameter estimation method by adjusting the model to simulate measured heads. Parameter estimation for a transient groundwater flow model is an iterative method in which many runs of a transient groundwater flow model are used. This makes it impractical to estimate parameters of transient groundwater flow models when one transient run takes a significant amount of computation time. In this study two new parameter estimation methods for transient groundwater flow models are analyzed that do not use transient model runs. One method uses moments of the impulse response function as calibration targets, while the other uses observed groundwater heads. The methods are referred to as the moment matching and the head matching method, respectively. Both methods are based on the principles used in Bakker et al. (2008a and 2008b) and use the properties of an impulse response function to estimate parameter values for groundwater flow models. The performance of the new methods is tested with a synthetic model with varying configurations. All factors influencing the parameter values are known in the synthetic model. The results of the tests show that both new methods yield accurate parameter estimates for linear models. The performance of the parameters estimation methods for models with a spatially distributed recharge can be improved by using a spatially averaged recharge. The new methods are faster than methods using transient model runs, and their performance is independent of the time step size used in transient model runs. The performance of the moment matching method is tested in practice using a part of the existing Azure model; time constraints did not allow calibration with higher order moments. An elevated part of the Azure model (the Veluwe) is used because this system, which has a slow response to precipitation, is difficult to calibrate with current parameter estimation methods. The application of the new method to a part of the Azure model is complex. A linearized version of the Azure model is created to enable the use of the new method. This version is referred to as the “submodel”. Only the zeroth order moment is used for the parameter estimation of the submodel. ? The time series analysis is conducted using observed head and recharge time series. The results from time series analysis are reasonable but can be improved by using a more realistic recharge series and a longer observed head time series. The parameter estimates obtained with the moment matching method improved the match between the average observed heads and the average heads modelled with the modified Azure model. This is a promising result and a positive first step for further application of the new parameter estimation methods in practice.GeohydrologyWater ManagementCivil Engineering and Geoscience