ITR - (ASE+NHS) - (dmc): Fields as Objects in Geographic Information Systems, Applications to Ground Water

场现象在自然界中无处不在（例如温度、风速、水头、海流速度），并且可以由数学边界条件约束的基于物理的方程表示。现场数据通常通过对这些方程的解进行网格化来存储在计算机数据库中。 这种方法在计算机内存方面效率低下，并且降低了数据在空间尺度方面的灵活性。 该项目的目标是创建一个新的地理信息系统（GIS）数据库范例，其中字段通过存储构成字段数学模型的三种对象数据类型来表示：（1）基于物理的方程系统;（2）这些方程的边界条件;以及（3）方程的求解引擎。 如果方程组的数学解是唯一的，那么求解数学模型所表示的场就相当于存储场本身。 浅层地下水流由水力边界（湖泊和溪流）驱动，并由达西方程指导。 地下水水力势场（水头）可以通过将湖泊和河流特征沿着与水流方程一起存储来表示。 数学上精确的解析元法（AEM）被用来解决流动方程，使位场可以检索在高精度，在任何分辨率，在数据库域中的任何区域。 其结果将是一套地理信息系统工具与地下水流数值模型和面向对象的地理信息系统数据库相结合，这一项目将产生一个新的原型，用于存储、处理和概念化空间分布的地球科学数据。 它鼓励对自然领域采用面向对象而不是面向网格的方法。 为了促进这一方法的更广泛传播，将举行一次专家会议，并在布法罗大学为现有NSF IGERT项目的学生开设一门研究生课程。

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.