Improving parameter estimation in transient groundwater models through temporal differencing

Abstract

In the majority of transient groundwater modelling studies, parameters are estimated by matching calculated heads to timeseries of observed heads. In regional groundwater systems, the variation in head between bores can be 10s or 100s of meters, while variation of head over time seldomly is larger than a few meters. Reducing the mismatch between observed and calculated heads, especially with automated calibration procedures, will often lead to a good approximation of the average water level in the bore, while the temporal dynamics are less well reproduced. The temporal dynamics however are often of the utmost importance to understand and predict the aquifer system under study. This study explores the potential of using the sign of the difference of two subsequent head measurements as an additional calibration target to improve parameter estimation. The sign of the difference between two measurements isolates the temporal signal in the data, while it reduces the amount of redundant information in the calibration dataset, compared to adding the difference between two observations. The relative parameter error reduction, introduced by Doherty and Hunt (2009), is used to assess the added value of temporal differencing for parameter estimation. This measure is based on linear error propagation through singular value decomposition of the sensitivity matrix of the model. This implies that it can be calculated even before actually calibrating a model, as long as an estimate of the error for the potential new observations is provided. The methodology is tested on a regional-scale, calibrated transient groundwater model of the Upper Namoi valley in New SouthWales (McNeilage, 2006). The results show that the introduction of temporal differencing as additional calibration data reduces the error variance of the estimated parameters. The results however also highlight that choices in the conceptualisation of the model, especially the implementation of boundary conditions, can dominate the amount of information that can be extracted from a calibration dataset and negatively affect the succes of parameter estimation through inverse modelling.