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Calibration of a mathematical model of the Antelope Valley ground-water basin, California
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...
Calibration of a mathematical model of the Antelope Valley ground-water basin, California
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...
Urban land use and water use in the Antelope Valley, California, have increased significantly since development of the valley began in the late 1800's.. Ground water has been a major source of water in this area because of limited local surface-water resources. Groundwater pumpage is reported to have increased from about 29,000 acre-feet in 1919 to about 400,000 acre-feet in the 1950's. Completion of the California Aqueduct to this area in the early 1970's conveyed water from the Sacramento-San Joaquin Delta, about 400 miles to the north. Declines in groundwater levels and increased costs of electrical power in the 1970's resulted in a reduction in the quantity of ground water that was pumped annually for irrigation uses. Total annual reported groundwater pumpage decreased to a low of about 53,200 acre-feet in 1983 and increased to about 91,700 acre-feet in 1991 as a result of rapid urban development and the 1987-92 drought. This increased urban development, in combination with several years of drought, renewed concern about a possible return to extensive depletion of groundwater storage and increased land subsidence. Increased water demands are expected to continue as a result of increased urban development. Water-demand forecasts in 1980 for the Antelope Valley indicated that total annual water demand by 2020 was expected to be about 250,000 acre-feet, with agricultural demand being about 65 percent of this total. In 1990, total water demand was projected to be about 175,000 acre-feet by 2010; however, agricultural water demand was expected to account for only 37 percent of the total demand. New and existing land-and water-use data were collected and compiled during 1992-93 to identify present and historical land and water uses. In 1993, preliminary forecasts for total water demand by 2010 ranged from about 127,500 to 329,000 acre-feet. These wide-ranging estimates indicate that forecasts can change with time as factors that affect water demand change and different forecasting methods are used. The forecasts using the MWD_MAIN (Metropolitan Water District of Southern California Municipal and Industrial Needs) water-demand forecasting system yielded the largest estimates of water demand. These forecasts were based on projections of population growth and other socioeconomic variables. Initial forecasts using the MWD_MAIN forecasting system commonly are considered "interim" or preliminary. Available historical and future socioeconomic data required for the forecasting system are limited for this area. Decisions on local water-resources demand management may be made by members of the Antelope Valley Water Group and other interested parties based on this report, other studies, their best judgement, and cumulative knowledge of local conditions. Potential water-resource management actions in the Antelope Valley include (1) increasing artificial groundwater recharge when excess local runoff (or imported water supplies) are available; (2) implementing water-conservation best-management practices; and (3) optimizing grou...
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