Use of RORA for Complex Ground-Water Flow Conditions

Abstract

The RORA computer program for estimating recharge is based on a condition in which ground water flows perpendicular to the nearest stream that receives ground-water discharge. The method, therefore, does not explicitly account for the groundwater-flow component that is parallel to the stream. Hypothetical finite-difference simulations are used to demonstrate effects of complex flow conditions that consist of two components: one that is perpendicular to the stream and one that is parallel to the stream. Results of the simulations indicate that the RORA program can be used if certain constraints are applied in the estimation of the recession index, an input variable to the program. These constraints apply to a mathematical formulation based on aquifer properties, recession of ground-water levels, and recession of streamflow. Introduction The RORA computer program estimates recharge to the water table on the basis of daily streamflow (Rutledge, 1998; 2000). The program is intended for analysis of a ground-water-flow system driven by diffuse areal recharge to the water table and by ground-water discharge to a gaining stream. When the program is used, regulation and diversion of streamflow should be negligible. The formulations that RORA uses are derived from a crosssectional-flow model that calculates ground-water discharge per unit of stream length on the basis of designated transmissivity, storage coefficient, distance from the stream to the hydrologic divide, and increase in head caused by recharge to the groundwater system (Rorabaugh, 1964, p. 433). The program is based on simple geometry, as illustrated in figure 1A, which represents a segment of a basin. The bold line on the left border represents the stream, and the right border represents the hydrologic divide. Because the stream extends along the length of the model, and because its altitude is uniform, the direction of ground-water flow is one-dimensional and perpendicular to the stream. A finite-difference-flow model, MODFLOW-96, then is used to generate the hydrographs of ground-water level and ground-water discharge to the stream (fig. 1B, details about this simulation are given in “Finite-Difference Simulation Design”). Before applying RORA, the user must designate the recession index (K). The input variable K is a measure of the time required for ground-water discharge to recede by one log cycle when the recession becomes linear (or nearly linear) on the semilog hydrograph. In the ideal model (fig. 1), K can be determined from the following equation, which is derived from Rorabaugh and Simons (1966, p. 12) as: (1) K 0.933a 2S T ---------------------= Use of RORA for Complex Ground-Water Flow Conditions U.S. Geological Survey Water Resources Investigation Report 03-4304 Figure 1. (A) Finite-difference-flow model (plan view) and (B) simulated flow to drains and simulated ground-water level. (Water levels are shown for the finite-difference cell in the middle of the model.) A B