Report Abstract

Application of Nonlinear-Regression Methods to a Ground-Water Flow Model of the Albuquerque Basin, New Mexico

By Claire R. Tiedeman, John Michael Kernodle, and Douglas P. McAda

This report documents the application of nonlinear-regression methods to a numerical model of ground-water flow in the Albuquerque Basin, New Mexico. In the Albuquerque Basin, ground water is the primary source for most water uses. Ground-water withdrawal has steadily increased since the 1940's, resulting in large declines in water levels in the Albuquerque area. A ground-water flow model was developed in 1994 and revised and updated in 1995 for the purpose of managing basin ground- water resources. In the work presented here, nonlinear-regression methods were applied to a modified version of the previous flow model. Goals of this work were to use regression methods to calibrate the model with each of six different configurations of the basin subsurface and to assess and compare optimal parameter estimates, model fit, and model error among the resulting calibrations.

The Albuquerque Basin is one in a series of north trending structural basins within the Rio Grande Rift, a region of Cenozoic crustal extension. Mountains, uplifts, and fault zones bound the basin, and rock units within the basin include pre-Santa Fe Group deposits, Tertiary Santa Fe Group basin fill, and post-Santa Fe Group volcanics and sediments. The Santa Fe Group is greater than 14,000 feet (ft) thick in the central part of the basin. During deposition of the Santa Fe Group, crustal extension resulted in development of north trending normal faults with vertical displacements of as much as 30,000 ft.

Ground-water flow in the Albuquerque Basin occurs primarily in the Santa Fe Group and post-Santa Fe Group deposits. Water flows between the ground-water system and surface-water bodies in the inner valley of the basin, where the Rio Grande, a network of interconnected canals and drains, and Cochiti Reservoir are located. Recharge to the ground-water flow system occurs as infiltration of precipitation along mountain fronts and infiltration of stream water along tributaries to the Rio Grande; subsurface flow from adjacent regions; irrigation and septic field seepage; and leakage through the Rio Grande, canal, and Cochiti Reservoir beds. Ground water is discharged from the basin by withdrawal; evapotranspiration; subsurface flow; and flow to the Rio Grande, canals, and drains.

The transient, three-dimensional numerical model of ground-water flow to which nonlinear-regression methods were applied simulates flow in the Albuquerque Basin from 1900 to March 1995. Six different basin subsurface configurations are considered in the model. These configurations are designed to test the effects of (1) varying the simulated basin thickness, (2) including a hypothesized hydrogeologic unit with large hydraulic conductivity in the western part of the basin (the west basin high-K zone), and (3) substantially lowering the simulated hydraulic conductivity of a fault in the western part of the basin (the low-K fault zone). The model with each of the subsurface configurations was calibrated using a nonlinear least- squares regression technique. The calibration data set includes 802 hydraulic-head measurements that provide broad spatial and temporal coverage of basin conditions, and one measurement of net flow from the Rio Grande and drains to the ground-water system in the Albuquerque area. Data are weighted on the basis of estimates of the standard deviations of measurement errors. The 10 to 12 parameters to which the calibration data as a whole are generally most sensitive were estimated by nonlinear regression, whereas the remaining model parameter values were specified.

Results of model calibration indicate that the optimal parameter estimates as a whole are most reasonable in calibrations of the model with with configurations 3 (which contains 1,600-ft-thick basin deposits and the west basin high-K zone), 4 (which contains 5,000-ft-thick basin deposits and the west basin high-K zone), and 6 (which contains 5,000-ft-thick basin deposits and the low-K fault zone). The presence in the model of either the west basin high-K zone or the low-K fault zone results in lower simulated hydraulic heads in the western part of the basin, which improves the model fit at some head-observation locations. Without either of these features in the model, the regression tended to lower heads in the western part of the basin by increasing the estimates of some hydraulic-conductivity parameters such that they are outside the ranges of values expected on the basis of prior information. In calibrations 3, 4, and 6, the estimate of the hydraulic conductivity of the undivided upper part of the Santa Fe Group remains outside the expected range of values, although the estimate is much closer to this range than in the other calibrations. This result indicates that the model is not yet completely satisfactory and strongly suggests that further modifications need to be made to the conceptual model of the basin hydrology and geology that is implemented in the numerical flow model.

Although the model is not yet completely satisfactory, evaluation of weighted residuals and of simulated hydraulic heads and ground-water budgets for calibrations with the most reasonable parameter estimates is useful for identifying model error and for assessing the differences between the calibrations. Evaluation of calibrations 4 and 6 shows that the spatial distribution and magnitudes of the weighted hydraulic-head residuals do not differ significantly between these two calibrations. Detailed analyses of the weighted residuals indicate that model fit is generally good at shallow wells in the central and southern parts of the basin but is fair to poor at basin margins and in the north. At deep wells in the Albuquerque area, model fit is generally good for simulations of conditions during the 1950's but worsens for conditions in the 1990's, suggesting that model error related to the representation of pumpage could increase with simulation time. Evaluation of patterns in the spatial distribution of weighted residuals indicates likely error in the representation of hydrogeologic units in the southern and northern parts of the basin. Assessment of model fit to observed vertical hydraulic gradients at piezometer nests suggests that vertical anisotropy is not uniform throughout the basin and that underflow at depth may be a larger source of inflow to the northwestern part of the basin than is simulated in the model.

In some parts of the basin, there are major differences between simulations 4 and 6. West of the low-K fault zone in subsurface configuration 6, hydraulic heads in simulation 6 are as much as 160 ft higher than those in simulation 4. Net recharge from precipitation and stream water is about 12,000 acre-feet/year larger in simulation 4 than in simulation 6, mostly because of a larger optimal estimate of recharge along the Jemez River in calibration 4. This difference results in greater discharge from the ground-water system to the inner-valley surface-water bodies in the southern part of the basin.

Abstract from Water-Resources Investigations Report 98-4172



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