Gradual Variation Analysis for Groundwater Flow

TL;DR

This paper introduces a novel mathematical model based on gradually varied functions for reconstructing groundwater flow data, offering flexibility over traditional methods like MODFLOW by not requiring strict boundary conditions.

Contribution

The study develops a new model using gradually varied functions that can handle arbitrarily shaped aquifers without strict boundary conditions, unlike existing methods.

Findings

Successfully modeled groundwater flow with arbitrary aquifer shapes.

Implemented two models for real data processing: individual and sequential flow data.

Established a supporting MySQL database for research data management.

Abstract

Groundwater flow in Washington DC greatly influences the surface water quality in urban areas. The current methods of flow estimation, based on Darcy's Law and the groundwater flow equation, can be described by the diffusion equation (the transient flow) and the Laplace equation (the steady-state flow). The Laplace equation is a simplification of the diffusion equation under the condition that the aquifer has a recharging boundary. The practical way of calculation is to use numerical methods to solve these equations. The most popular system is called MODFLOW, which was developed by USGS. MODFLOW is based on the finite-difference method in rectangular Cartesian coordinates. MODFLOW can be viewed as a "quasi 3D" simulation since it only deals with the vertical average (no z-direction derivative). Flow calculations between the 2D horizontal layers use the concept of leakage. In this project, we have established a mathematical model based on gradually varied functions for groundwater data volume reconstruction. These functions do not rely on the rectangular Cartesian coordinate system. A gradually varied function can be defined in a general graph or network. Gradually varied functions are suitable for arbitrarily shaped aquifers. Two types of models are designed and implemented for real data processing: (1) the gradually varied model for individual (time) groundwater flow data, (2) the gradually varied model for sequential (time) groundwater flow data. In application, we also established a MySQL database to support the related research. The advantage of the gradually varied fitting and its related method does not need the strictly defined boundary condition as it is required in MODFLOW.