Conference paper presented at the MODSIM03, International Congress on Modelling and Simulation, held July 2003, Jupiters Hotel and Casino, Townsville, Queensland.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 km² alluvial aquifer in Canterbury,
New Zealand
