A time-series analysis framework for the flood-wave method to estimate groundwater model parameters

Hydrogeol J DOI 10.1007/s10040-016-1436-5 PAPER A time-series analysis framework for the flood-wave method to estimate groundwater model parameters Christophe Obergfell 1 & Mark Bakker 1 & Kees Maas 2 Received: 12 November 2015 / Accepted: 31 May 2016 # The Author(s) 2016. This article is published with open access at Springerlink.com Abstract The flood-wave method is implemented within the framework of time-series analysis to estimate aquifer parameters for use in a groundwater model. The resulting extended flood-wave method is applicable to situations where groundwater fluctuations are affected significantly by time-varying precipitation and evaporation. Response functions for timeseries analysis are generated with an analytic groundwater model describing stream–aquifer interaction. Analytical response functions play the same role as the well function in a pumping test, which is to translate observed head variations into groundwater model parameters by means of a parsimonious model equation. An important difference as compared to the traditional flood-wave method and pumping tests is that aquifer parameters are inferred from the combined effects of precipitation, evaporation, and stream stage fluctuations. Naturally occurring fluctuations are separated in contributions from different stresses. The proposed method is illustrated with data collected near a lowland river in the Netherlands. Special emphasis is put on the interpretation of the streambed resistance. The resistance of the streambed is the result of stream-line contraction instead of a semi-pervious streambed, Electronic supplementary material The online version of this article (doi:10.1007/s10040-016-1436-5) contains supplementary material, which is available to authorized users. * Christophe Obergfell 1 Water Resources Section, Delft University of Technology, Delft, The Netherlands 2 KWR Watercycle Research Institute, Nieuwegein, The Netherlands which is concluded through comparison with the head loss calculated with an analytical two-dimensional cross-section model. Keywords The Netherlands . Time series analysis . Groundwater/surface-water relations . Analytical solutions . Numerical modeling Introduction The development of methods to estimate aquifer parameters from stream–aquifer interaction dates back to the 1960s and the early application of computers in hydrology (Cooper and Rorabaugh 1963; Pinder et al. 1969; Venetis 1970). The approach proposed at that time, referred to as the flood-wave method, is similar to a pumping test, as the groundwater head in an aquifer is perturbed by a single stress, in this case a flood wave in a stream adjacent to the aquifer. The aquifer diffusivity is obtained by fitting a simple equation for stream–aquifer interaction to the observed heads. This equation fulfills the same function as the well functions of pumping tests. Hall and Moench (1972) refined the method by using convolution integrals to relate stream stage fluctuations and head fluctuations. Later, Moench and Barlow (2000) extended the method by adding equations for a set of different stream–aquifer configurations. Alternatively, groundwater head response to a time series of stream stage fluctuations can be obtained analytically by replacing the time series of observed stream stage by a series of basis splines (Knight and Rassam 2007; Rassam et al. 2008). A limitation of the flood-wave method is that it is applicable only to situations where head fluctuations can be clearly related to river stage fluctuations (Ha et al. 2007). Hydrogeol J In many cases, however, this is not possible as fluctuations due to other stresses, like recharge and evaporation, interfere with fluctuations due to stream stages variations. To solve this issue, the influence of each stress needs to be identified separately. This is where time series analysis can improve the flood-wave method. The objective of this paper is to embed the flood-wave method into a time-series-analysis framework in order to derive aquifer parameters for use in distributed groundwater models. The framework is the method of predefined response functions (Von Asmuth et al. 2008), in which a specific response function (also referred to as a transfer function) is chosen for each stress. Each function is able to simulate the head response due to an impulse of a specific stress. Convolution of each response function with the corresponding stress time series results in the separate fluctuations caused by each stress, where it is assumed that the system’s response is linear. The method of predefined response functions has recently been extended to simulate nonlinear reactions of the phreatic water table in Australia (Peterson and Western 2014; Shapoori et al. 2015a, b, c). An evaluation of the method using synthetic data was presented by Shapoori et al. (2015a, b, c). Another extension of the method concerns the estimation of aquifer parameters from time series analysis in the vicinity of well fields (Obergfell et al. 2013; Shapoori et al. 2015a, b, c). Typically, the selected response functions do not depend on physical parameters. For example, a scaled gamma distribution function is commonly used as the impulse response function for groundwater recharge. The novelty of this paper is two-fold—first, an analytical groundwater model is used as the predefined response function similar to the functions used in the flood-wave method; second, the flood-wave method is placed in the framework of time series analysis. The resulting approach is an extension of the flood-wave method in the sense that it is applicable to situations in which other time-varying stresses than stream stage variations have a significant effect on head fluctuations. This paper is organized as follows. First, the method of time series analysis by predefined response functions is reviewed and it is explained how the flood-wave method can be placed in a time series framework. Next, a description of the hydrogeological situation of the field site is given for which response functions are developed. The time series model is fitted to data collected near the Dutch lowland river ‘Aa’, and aquifer parameters are estimated. These parameters are then entered into a numerical distributed groundwater model to evaluate their adequacy as parameters estimates. The physical significance of the parameter values is discussed, with a special emphasis on the interpretation of the resistance of the streambed. Review of time-series analysis with predefined response functions Response functions In this paper, the flood-wave method is placed in a time-seriesanalysis framework. Time series analysis is performed with the method of predefined response functions (Von Asmuth et al. 2002). Transfer functions, a term widely used in system theory and time series analysis, can be considered as synonymous to response functions. Similar to linear systems theory (Hespanha 2009), output signals are obtained by convolut (...truncated)