Field phenomena are ubiquitous in nature (e.g. temperature, wind speed, hydraulic head, ocean current velocity) and can be represented by physically based equations constrained by mathematical boundary conditions. Field data are usually stored in computer databases by gridding the solutions of these equations. This approach is inefficient with respect to computer memory and reduces the flexibility of the data with respect to spatial scale. The objective of this project is to create a new Geographic Information System (GIS) database paradigm in which fields are represented by storing three object data types that constitute a mathematical model of the field: (1) a physically-based system of equations; (2) boundary conditions for those equations; and (3) a solution engine for the equations. If the mathematical solution to the system of equations is unique, then solving for the field represented by the mathematical model is equivalent to storing the field itself.
The test application for this method is a GIS database for ground-water protection. Shallow ground-water flow is driven by hydraulic boundaries (lakes and streams) and guided by the Darcy Equation. A ground-water hydraulic potential field (head) can be represented by storing lake and stream features along with flow equations. The mathematically exact Analytic Element Method (AEM) is used to solve the flow equations, so that the potential field can be retrieved at high precision, at any resolution, over any area in the database domain. The result will be a suite of GIS tools coupled to a numerical ground-water flow model and an object-oriented GIS database.
This project will produce a new archetype for storing, manipulating, and conceptualizing spatially distributed earth science data. It encourages an object-oriented rather than grid-oriented approach to natural fields. To promote broader dissemination of this approach, a specialist meeting will be held and a graduate course will be offered to students in the existing NSF IGERT program at the University at Buffalo.
