Documentation of a computer program to simulate stream-aquifer relations using a modular, finite-difference, ground-water flow model

Abstract

Computer models are widely used to simulate ground-water flow for evaluating and managing the ground-water resources of many aquifers, but few are designed to also account for surface flow in streams. A computer program was written for use in the U.S. Geological Survey modular finitedifference ground-water flow model to account for the amount of flow in streams and to simulate the interaction between surface streams and ground water. The new program is called the Streamflow-Routing Package.The Streamf low-Routing Package is not a true surface-water flow model but rather is an accounting program that tracks the flow in one or more streams which interact with ground water. The program limits the amount of ground-water recharge to the available streamflow. It permits two or more streams to merge into one with flow in the merged stream equal to the sum of the tributary flows. The program also permits diversions from streams.Streams are divided into segments and reaches. Each reach corresponds to individual cells in the finite-difference grid used to simulate groundwater flow. A segment consists of a group of reaches connected in downstream order. Leakage is calculated for each reach on the basis of the head difference between the stream and aquifer and a conductance term. It is subtracted or added to the amount of streamflow into the reach. The stage in each reach can be computed using the Manning formula under the assumption of a rectangular stream channel.The amount of leakage in each reach (either into or out of the aquifer) is incorporated into the ground-water flow model by adding terms to the finite-difference equations. Recharge to the aquifer in a reach ceases when all the streamflow in upstream reaches has leaked into the aquifer and the stream is dry. A stream is permitted to flow again in downstream reaches if the head in the aquifer is above the elevation of the streambed.Results from the program have been compared to results from two analytical solutions. One assumes time varying areal recharge to the aquifer and discharge only to a stream and the other assumes recharge to the aquifer from a change in stream stage. Results from the program reasonably duplicated the analytical solutions.

Simulation of ground-water flow and evaluation of water-management alternatives in the upper Charles River basin, eastern Massachusetts

“…This package simulates hydraulic interaction between the aquifer and adjoining streams and tracks the amount of water in each simulated stream. Simulated streams are divided into reaches, corresponding to individual model cells, and segments, which are groups of reaches that are connected in downstream order (Prudic, 1989). Water may flow in either direction at the boundary between the aquifer and streams.…”

“…Streams were simulated as head-dependent flow boundaries with a version of the Stream Routing Package (Prudic, 1989) that is compatible with MODFLOW-2000. This package simulates hydraulic interaction between the aquifer and adjoining streams and tracks the amount of water in each simulated stream.…”

Simulation of the recharge area for Frederick Springs, Dane County, Wisconsin

“…Therefore, stream-aquifer interactions and three-dimensional effects near the streams were simulated more accurately. A second refinement was the conversion of all streams in the TMR model domain from the MOD-FLOW River Package (McDonald and Harbaugh, 1988) to the more sophisticated Stream Routing Package (Prudic, 1989). The latter allows accounting of streamflow in the streams, and limits the amount of water a stream In addition to changes in model construction, model parameters were adjusted during the TMR model refinement.…”

Hydrogeology, simulated ground-water flow, and ground-water quality at two landfills in Bristol, Vermont

“…A stream-routing subroutine (Prudic, 1989) was used to simulate stream-aquifer interactions. This subroutine can account for streamflow volume in the simulated stream and allows a stream to dry up if the water level in the aquifer declines below the streambed.…”