Realistic forecasting of groundwater level, based on the eigenstructure of aquifer dynamics

Short-term management of groundwater resources, especially during droughts, can be assisted by forecasts of groundwater levels. Such forecasts need to account for the natural dynamic behaviour of the aquifer, likely recharge scenarios, and recent but unknown abstractions. These requirements mean that forecasts, at say monthly intervals, need to be updated with current observations on a real-time basis. One established procedure for this kind of problem is to fit autoregressive, moving-average, exogenous-variable (ARMAX) time-series models to the history of groundwater levels in response to estimates of land surface recharge. The ARMAX difference equations are then converted into forecast equations that allow real-time updating to include recent forecast errors as an additional source of information. Some disadvantages of this pure time-series analysis approach are the apparent lack of physical concepts in the model formulation and statistical aspects of model identification and calibration that are related to the inherent structure of ARMAX equations. This paper addresses these issues by describing a method for formulating ARMAX forecast equations from a linear system description based on the eigenvalues and eigenvectors (eigenstructure) of the dynamic behaviour of an aquifer. For the piezometric response of a heterogeneous aquifer to a fixed spatial distribution of land surface recharge, with time-varying magnitude, only a few eigenvalues are significant for describing the dynamics. The resulting model has a simple robust parameter structure, and is easily calibrated and implemented in spreadsheet form. The eigenstructure approach enables transfer of some parameter information from locations with good data records to those with sparse data. This modelling approach is demonstrated with monthly values of land surface recharge, estimated from a daily water balance model, and groundwater level data from an observation well in a 2000 km alluvial aquifer in Canterbury, New Zealand.