Development of Mathematica Interactive Manipulations for Estimating Groundwater Recharge and Discharge Rates and Spatial Patterns

An Advanced Mathematica Summer School 2009 Project

Yu-Feng Forrest Lin, University of Illinois at Urbana-Champaign
Joshua Martell, Wolfram Research, Inc.

Abstract

The National Research Council (NRC) has characterized research on understanding groundwater recharge and discharge as a critical national research priority due to its complexity and importance in the hydrological cycle. Groundwater recharge and discharge rates and patterns are difficult to characterize, and currently no single method is capable of estimating recharge and discharge rates and patterns for all practical applications. Therefore, cross analyzing results from various estimation methods and related field information will likely be superior to using only a single estimation method.

We have developed a suit of Mathematica interactive manipulations that utilize advanced matrix computing and image-processing algorithms with several user interfaces to offer the flexibility to apply experts’ knowledge to extract spatial patterns. It also provides a generic pattern recognition approach that supports virtually any Spatial Decision Support System (SDSS) used to assist in management applications such as water resources, land use, and agricultural development. This groundwater recharge and discharge estimation for shallow aquifers requires only hydraulic conductivity, water table and bedrock elevation based on a finite difference mass balance approach in 2D, and steady state systems, which are widely accessible datasets. The result can be cross analyzed interactively with existing field information, such as land coverage, soil type, and topographic maps, in order to incorporate expert knowledge. The final recharge and discharge rates and patterns can be exported in various formats for use in different hydrology, climate, and groundwater modeling processes.