Analytical assessment and parameter estimation of a low-dimensional groundwater model

A class of transient groundwater models exists between the simple 0-dimensional storage–discharge functions and numerically-solved 2- and 3-dimensional spatially-distributed models. This class contains analytical solutions to linear partial differential equations subjected to time-varying stress, such as recharge or pumping. These solutions are limited to homogeneous 1-dimensional (1-D) representations of an aquifer. Their use in watershed models is rare to date, even though they are computationally efficient and overcome some of the major weaknesses of single-valued storage–discharge functions. Because these 1-D models have analytical solutions for hydraulic head and groundwater discharge, they allow both for a simpler initial assessment of model suitability and for initial estimation of model parameters using analytical methods. We evaluate two analytical, graphical parameter estimation methods whereby: (1) the second time derivative of a state (in this case, a volume) is plotted against the first derivative of the same state, and (2) the first time derivative of one state (volume) is plotted against another state (piezometric height). In both cases the identification of a data “envelope” is used to estimate model parameters, or groupings thereof. We use both methods to assess the suitability of a 1-D model to an alluvial plain system in New Zealand and examine the limitations of two graphical envelope techniques for estimating aquifer parameters at the catchment scale.