The eigenstructure representation of groundwater dynamics, as a precursor for aquifer management

Abstract

Increasing abstraction of groundwater for irrigated agriculture on the Central Canterbury Plains of New Zealand has environmental effects on surface waters connected to the aquifers. There is a requirement by the regulatory authorities for design of robust rules, acceptable to the agricultural industry, for management of the groundwater resource. The aquifers constitute a 2300 km2 distributed system of stored water that responds dynamically to climatically-driven recharge and pumped abstraction. This system can be mathematically described by the eigenvalues and eigenfunctions of the groundwater flow equation. The equivalent continuous-time, discrete-space numerical groundwater models can also be represented in modal (eigenstructure) state-space format. This format forms the basis for design of system control. A simplification for practical control design is achieved by application of analytical solutions for the eigenstructure of groundwater dynamics for simple aquifers. These solutions enable spreadsheet-based computation and presentation of control options for public debate.