Ground water systems can be categorized with respect to quantity into two groups: (1) those that will ultimately reach a new equilibrium state where pumping can be continued indefinitely and (2) those in which the stress is so large that a new equilibrium is impossible; hence, the system has a finite life. Large ground water systems, where a new equilibrium can be reached and in which the pumping is a long distance from boundaries where capture can occur, take long times to reach a new equilibrium. Some systems are so large that the new equilibrium will take a millennium or more to reach a new steady-state condition. These large systems pose a challenge to the water manager, especially when the water manager is committed to attempting to reach a new equilibrium state in which water levels will stabilize and the system can be maintained indefinitely.

Introduction __________________________________ _ _________!__________ _ ____ _ 1 Well-numbering system ____________________________________ 2 Description of the study area ________________________________-_-__-____ 3 Location and general features ________________________________ 3 Groundwater geology __________________________________________________ 3 Groundwater movement ____________________________________________ The mathematical model ______________________________________________ 7 Steady-state model _______________________________________________ Natural recharge ______________________________________________ Natural discharge ___________________________________________ 13 Calibration of the steady-state model ____________________________________ Transient-state model __________________________________________________ Pumpage __________________________________________________________ Irrigation return ________________________________________________ Selection of net pumpage for model calibration ________________________ Reduction of natural discharge ________________________________________ Calibration of the transient-state model ________________________ Description of modeling errors _.________________________________ Sources of error ____________________________________________________ Errors of prediction _____________________________________________ Numerical solution of the groundwater equations ________________________ The Galerkin-finite element concept __________________________________ Galerkin approximation __________________________________________ Trial functions ______________________________________________ 41 Integration of the approximating equation ______________________________ Finite-difference approximation of the time derivative __________________ Assembly of the two-aquifer solution __________________________________ Recurrence algorithm ______________________________________________ Summary __________________________________________________________________ References cited ________________________________________________________ ILLUSTRATIONS [Plates are in pocket] PLATE 1. Map of Antelope Valley, California, showing geographic setting, generalized geology, boundaries used in the mathematical model, and geologic sections through the groundwater basin. 2. Potentiometric map for 1915, Antelope Valley, California. 3. Potentiometric map for 1961, Antelope Valley, California. 4. Map of Antelope Valley, California, showing finite-element configuration used in the mathematical model of the principal aquifer. in IV CONTENTS PLATE 5. Map of Antelope" Valley, California, showing finite-element configuration used in the mathematical model of the deep aquifer. 6. Map of Antelope Valley, California, showing geographic distribution of natural groundwater recharge and discharge. 7. Map of Antelope Valley, California, showing transmissivity used in the mathematical model of the principal aquifer. 8. Map of Antelope Valley, California, showing transmissivity used in the mathematical model of the de...

AESTRACT An evaluation of the Maxey‐Eakin method for calculating recharge to ground‐water basins in Nevada was performed. The evaluation consisted of comparing Maxey‐Eakin estimates with independent estimates of recharge, and analyzing the nature of the differences between the groups of estimates. In the comparison with the Maxey‐Eakin estimates, two different groups of independent estimates were used: (1) 40 recharge estimates that were identified from water budgets contained in reports by the Nevada Department of Conservation and Natural Resources and (2) 27 recharge estimates that were identified from previous studies that used models. The results of the comparisons indicate generally good agreement between the Maxey‐Eakin estimates and both groups of independent estimates. To quantify this agreement, an analysis was conducted to estimate the uncertainty in the Maxey‐Eakin method. The analysis produced an upper bound on the standard deviation of the Maxey‐Eakin estimate for a given basin. For the group of 40 water‐budget estimates, the upper bound on the standard deviation for an individual basin is 4,800 acre‐ft/yr, and the corresponding coefficient of variation of the Maxey‐Eakin estimate is no greater than 44 percent. For the group of 27 model estimates, the upper bound on the standard deviation is 4,100 acre‐ft/yr, and the corresponding coefficient of variation is no greater than 24 percent.

This document describes a computer program that simulates three-dimensional groundwater systems using the finite-element method. The program was developed to simulate regional groundwater systems, but it can be applied to small-scale problems as well. This program can be used to simulate both confined and water-table aquifers. The program simulates a linearized three-dimensional free-surface groundwater system with a fixed grid. FEMFLOW3D is applicable to the simulation of various free-surface groundwater systems for which the change in aquifer thickness is small relative to the overall aquifer thickness. The finite-element method provides flexibility in the design of a geometric grid that represents the physical dimensions of an aquifer system. For example, features that can be well represented with a finite-element grid include irregular, random geographic and geologic features; irregular boundaries; and increased detail within localized areas of particular interest within the study area. The structure of the computer program consists of a main program, which serves as a simple driver, and a set of subroutines in which the calculations are performed. The background, mathematical basis, structure, and inputs for each of the subroutines are described in the document where applicable. Each subroutine generally handles (1) a part of the mathematical calculations related to the finite-element method, (2) a specific feature of the hydrologic system, or (3) special features related to the management input or output data. Hydrologic features that can be represented with the program include stream-aquifer interactions, phreatophytic evapotranspiration, highly permeable fault zones, land subsidence, and land-aquifer interactions associated with land-use activities. The program can also represent the primary features associated with complex irrigation systems, such as irrigated agriculture, and can calculate the groundwater recharge that results from these activities. Three boundary conditions, including specified-head boundaries, specified-flux boundaries, and variable-flux boundaries, can be represented with the program. The program also provides a method for identifying aquifer and riverbed parameters that can be used in the calibration of models.

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