Effect of grid size on digital simulation of ground-water flow in the southern High Plains of Texas and New Mexico

Three models of the aquifer in the southern High Plains were compared to determine the effect of grid size on simulated water levels. The first model, calibrated prior to this study, had 10-mile grid spacing. The mean difference between the simulated and measured predevelopment water levels in this model was +0.22 foot with a standard deviation of 41.6 feet. For 1980 water levels, the mean difference was +0.28 foot with a standard deviation of 25.8 feet. The second model, calibrated during this study independently of the first model, had 5-mile grid spacing. The mean difference between the simulated and measured predevelopment water levels was -0.01 foot with a standard deviation of 44.4 feet. For 1980 water levels, the mean difference was +8.22 feet with a standard deviation of 27.9 feet. The results from the first and second models were compared. The standard deviation of the differences in simulated water levels was 19.0 feet for the predevelopment period and 21.8 feet for 1980. There appeared to be no hydrologic significance to the pattern of the differences. A third model, constructed by aggregating the data from the second model, had 10-mile grid spacing. The mean difference in simulated predevelopment water levels between the second and third models was +0.86 foot with a standard deviation of 8.9 feet. For the 1980 water levels, the mean difference between the models was +0.39 foot with a standard deviation of 4.4-feet. The study found that the same hydrologic conclusions would have been reached had 5-mile grid spacing or 10-mile grid spacing been used. It was further concluded that the difference in simulated water levels between models with 5-mile grid spacing or 10-mile grid spacing was five to six times smaller than the differences between the simulated and measured water levels. INTRODUCTION The High Plains aquifer underlies about 174,000 mi 2 of the central Great Plains in parts of Colorado, Kansas, Nebraska, New Mexico, Oklahoma, South Dakota, Texas, and Wyoming. More than 20 percent of the irrigated land in the United States overlies the High Plains aquifer, and about 30 percent of the ground water pumped in the United States during 1980 was from the High Plains aquifer (Gutentag and others, 1984, p.7). From predevelopment (the 1930 f s) to 1980, over 400 million acre-feet of water have been pumped from the High Plains aquifer (U.S. Geological Survey, 1984, p. 40-41). This pumpage has caused water-level declines that exceeded 10 ft in over 50,000 mi 2 and exceeded 100 ft in about 3,000 mi2 (Luckey and others, 1981). The U.S. Geological Survey began a study of the High Plains regional aquifer in 1978 (Weeks, 1978). One of the major objectives of the study was to develop computer models to simulate the aquifer system. These models were used to calculate future water levels in response to continued ground-water use. For the purpose of computer simulation, the High Plains was divided into three parts (fig. 1). The southern High Plains included 29,000 mi 2 south of about 35° latitude, the central High Plains included 48,500 mi 2 between about 35° and 39° latitude, and the northern High Plains included 96,500 mi 2 north of about 39° latitude. Each of the three parts of the High Plains was simulated separately with a two-dimensional finite-difference model (Trescott and others, 1976) using a regular network of nodes that were spaced 10 mi apart in both the north-south and the east-west directions. There were 303 active nodes in the southern High Plains model, 513 active nodes in the central High Plains model, and 943 active nodes in the northern High Plains model. There was one common node between the southern and central High Plains models and five common nodes between the central and northern High Plains models. The models were calibrated before they were used to project future water levels. The calibration was done in two phases: (1) A predevelopment-period calibration that simulated the system prior to large-scale irrigation development, and (2) a development-period calibration that simulated the effects of irrigation development on the aquifer system. The calibration consisted of adjusting selected simulated hydrologic properties until the models adequately simulated the historical water levels, water-level changes, base flow to rivers, and cross-boundary flow. A complete discussion of the geohydrologic setting of the High Plains aquifer is given by Gutentag and others (1984). Detailed versions of the maps in that report provided the input data for the models. The details of model calibration are reported by Luckey and others (1986). A summary of the results of the calibration are repeated in this report in the sections on the coarse-grid model.