Application of nonlinear-regression methods to a ground-water flow model of the Albuquerque Basin, New Mexico

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 de