Calibration of a mathematical model of the Antelope Valley ground-water basin, California

Abstract

_______________________________________________ 1 Introduction __________________________________ _ _________!__________ _ ____ _ 1 Well-numbering system ____________________________________ 2 Description of the study area ________________________________-_--__--____ 3Location and general features ________________________________ 3 Ground-water geology __________________________________________________ 3 Ground-water movement ____________________________________________ 6 The mathematical model ______________________________________________ 7 Steady-state model _______________________________________________ 9Natural recharge ______________________________________________ 10 Natural discharge ___________________________________________ 3.048x 10-1 ft/mi (feet per mile)1.894x10-1 ft/yr (feet per year) 3.048x10-1 ft2 (square feet) 9.290x10-2 ft2/d (feet squared per day) 9.290x10-2 in. (inches) 2.540x10 in./yr (inches per year) 2.540x10 mi (miles) T. 10 N.T. 9 N.T. 8 N.T CALIBRATION OF A MATHEMATICAL MODEL OF THE ANTELOPE VALLEY GROUND-WATER BASIN, CALIFORNIABy TIMOTHY J. DURBIN ABSTRACT Antelope Valley is a closed topographic basin in the western part of the Mojave Desert in southern California. A ground-water basin with a surface area of 900 square miles (2,300 square kilometers) and a thickness of as much as 5,000 feet (1,500 meters) underlies the valley floor. The ground-water system consists of two alluvial aquifers separated by fine-grained lacustrine deposits. During the last 50 years, pumpage of ground water in excess of natural recharge has resulted in the steady decline of the ground-water level in the basin. The change in water level has been as much as 200 feet (61 meters). By 1972 the cumulative overdraft was about 9 million acre-feet (11,000 cubic hectometers). To help evaluate the possible impact of various water management alternatives, a mathematical model of the ground-water basin was constructed.Construction of the ground-water model was the first part of a two-part study. The second part of the study will consist of the use of the model to evaluate the impact on the ground-water basin of various water-resource management alternatives. This report describes the mathematical model.The model was calibrated by comparing the computed hydraulic heads to the corresponding prototype water levels for both steady-state and transient-state conditions. For the steady-state model the area-weighted median deviation of the computed hydraulic heads from the prototype water levels was 12 feet (3.7 meters). For the transient-state model the median deviation was 25 feet (7.6 meters).The mathematical model is based on the governing equations of ground-water flow. The solution to the equations was approximated numerically by the Galerkin-finite element method.