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#           Postaudit of head and transmissivity estimates and ground-water flow models of Avra Valley, Arizona      

      December 1, 1996    

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Ground water from regional alluvial-aquifer systems is the main source of water in the alluvial basins of Arizona, such as Avra Valley. Ground-water flow models are used to assess ground-water availability and the effects of development on the regional ground-water resources. A postaudit of regional-head and transmissivity estimates and the ground-water flow models of Avra Valley was used to evaluate potential errors in the distribution of aquifer properties and recharge that can cause predictive errors in ground-water models. Simulations of predevelopment conditions in 1940 and historical development conditions for 1960-79 provided the basis of comparison for assessing predictive errors of historical conditions for two regional ground-water flow models. Potential errors in the estimation of the regional-head and transmissivity and alternate conceptual models were compared with an existing calibrated two-layer flow model for predevelopment (1940) and developed conditions (1940-85).

Measured heads can be subdivided into a north-central region and a region south of the basin constriction. A more variable regional-head surface typical of developed aquifer systems was indicated by kriged developed heads (1985) with about 50 percent more uncertainty than predevelopment heads (1940). Incorporating heads from adjacent basins at the ground-water inflow and outflow regions reduced uncertainty in kriged heads for these boundary areas. Universal cokriging of heads with the strongly correlated land-surface altitudes may improve regional-head estimates and model comparisons where head data are sparse.

Local transmissivity estimates can be subdivided into northern and south-central regions that are distributed along the valley axis and the Santa Cruz River. Regional geostatistical estimates of transmissivity, which are based solely on local estimates, are low in the northern part of Avra Valley and are high in the south-central part when compared with the head-conditioned model-derived estimates. These differences may be related to a systematic bias between aquifer-test conditions and methods of aquifer-test analysis. Cokriging transmissivities with specific capacity and silt-and-clay content provided the least uncertainty of all kriged estimates.

Predictive errors for the Avra Valley model are the result of a different combination of factors that become significant in the simulation of ground-water flow for the periods representing predevelopment, historical development, and future development conditions. Predictive errors for simulation of predevelopment conditions are caused by potential systematic errors in estimates of local transmissivity, uncertainty in long-term mountain-front recharge, and uncertainty in predevelopment heads along the margins of the basin where recharge and transmissivity estimates are constrained by heads during model calibration. Analog-model historical predictions of future development indicate changes to 1985 were as much as 50 to 100 feet different from actual declines that were caused by errors in the spatial distribution and not the total amount of estimated future pumpage.

Predictive errors for simulation of historical development (1960-79) appear to be caused to a greater extent by combined errors in estimates of transmissivity and storage properties and to a lesser extent by estimates of net withdrawal and subsidence. Comparison of the two digital models resulted in differences in transmissivity of as much as 30,000 feet squared per day and differences in specific yield of as much as 0.1. In combination with some differences in net withdrawal, these model-parameter differences resulted in local differences in change in storage of as much as 4,000 acre-feet per square mile and are equivalent to historical predictive errors in water levels of as much as 40 feet. Areas with no differences in model parameters yield comparable simulated water-level declines that are similar to measured declines. The pattern of differences in transmissivity and storage parameters are similar to differences between model-derived estimates conditioned on heads and related geostatistical estimates derived from aquifer-test estimates.

A postaudit analysis of alternate conceptual models was explored on the basis of well-by-well comparisons of reductions in mean error and variance, and through the use of standardized calibration-error maps for predevelopment heads (1940) and developed heads (1985). Calibration-error maps provide a useful tool for exploring the spatial structure of model errors and the relative adequacy of model fit that is not available from traditional methods of model comparison. Calibration-error maps indicate estimated heads were too high in the southern part of Avra Valley, and estimated heads were too low in the northern part. Increased transmissivity in the southern part of the lower model layer; decreased hydraulic conductivity in the southwestern part of the upper layer; reduced ground-water inflow from Altar Valley; and increased recharge along the Tortolita Mountains, Tucson Mountains, and Brawley Wash yielded a significantly better model for predevelopment but not for developed conditions (1940-85). This may indicate that alternate conceptual models are different for different time periods or require analysis of time-varying model parameters for developed conditions, such as climatically variable recharge. Predictive errors for future simulations (1986-2025) also could potentially include errors of more than 40 ft from omission of subsidence from the simulation of regional ground-water flow in Avra Valley. Further refinement of the changing conceptual model of an aquifer system under continuing development and variable climate, such as Avra Valley, will require a variety of additional geophysical, geochemical, and hydraulic field data.

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