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Joseph A. Hevesi
,
Jonathan D. Istok
, and
Alan L. Flint

Abstract

Values of average annual precipitation (AAP) are desired for hydrologic studies within a watershed containing Yucca Mountain, Nevada, a potential site for a high-level nuclear-waste repository. Reliable values of AAP are not yet available for most areas within this watershed because of a sparsity of precipitation measurements and the need to obtain measurements over a sufficient length of time. To estimate AAP over the entire watershed, historical precipitation data and station elevations were obtained from a network of 62 stations in southern Nevada and southeastern California. Multivariate geostatistics (cokriging) was selected as an estimation method because of a significant (p = 0.05) correlation of r = .75 between the natural log of AAP and station elevation. A sample direct variogram for the transformed variable, TAAP = ln [(AAP) 1000], was fitted with an isotropic, spherical model defined by a small nugget value of 5000, a range of 190 000 ft, and a sill value equal to the sample variance of 163 151. Elevations for 1531 additional locations were obtained from topographic maps to improve the accuracy of cokriged estimates. A sample direct variogram for elevation was fitted with an isotropic model consisting of a nugget value of 5500 and three nested transition structures: a Gaussian structure with a range of 61 000 ft, a spherical structure with a range of 70 000 ft, and a quasi-stationary, linear structure. The use of an isotropic, stationary model for elevation was considered valid within a sliding-neighborhood radius of 120 000 ft. The problem of fitting a positive-definite, nonlinear model of coregionalization to an inconsistent sample cross variogram for TAAP and elevation was solved by a modified use of the Cauchy-Schwarz inequality. A selected cross-variogram model consisted of two nested structures: a Gaussian structure with a range of 61 000 ft and a spherical structure with a range of 190 000 ft. Cross validation was used for model selection and for comparing the geostatistical model with six alternate estimation methods. Multivariate geostatistics provided the best cross-validation results.

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Joseph A. Hevesi
,
Alan L. Flint
, and
Jonathan D. Istok

Abstract

Values of average annual precipitation (AAP) may be important for hydrologic characterization of a potential high-level nuclear-waste repository site at Yucca Mountain, Nevada. Reliable measurements of AAP are sparse in the vicinity of Yucca Mountain, and estimates of AAP were needed for an isohyetal mapping over a 2600-square-mile watershed containing Yucca Mountain. Estimates were obtained with a multivariate geostatistical model developed using AAP and elevation data from a network of 42 precipitation stations in southern Nevada and southeastern California. An additional 1531 elevations were obtained to improve estimation accuracy. Isohyets representing estimates obtained using univariate geostatistics (kriging) defined a smooth and continuous surface. Isohyets representing estimates obtained using multivariate geostatistics (cokriging) defined an irregular surface that more accurately represented expected local orographic influences on AAP. Cokriging results included a maximum estimate within the study area of 335 mm at an elevation of 7400 ft, an average estimate of 157 mm for the study area, and an average estimate of 172 mm at eight locations in the vicinity of the potential repository site. Kriging estimates tended to be lower in comparison because the increased AAP expected for remote mountainous topography was not adequately represented by the available sample. Regression results between cokriging estimates and elevation were similar to regression results between measured AAP and elevation. The position of the cokriging 250-mm isohyet relative to the boundaries of pinyon pine and juniper woodlands provided indirect evidence of improved estimation accuracy because the cokriging result agreed well with investigations by others concerning the relationship between elevation, vegetation, and climate in the Great Basin. Calculated estimation variances were also mapped and compared to evaluate improvements in estimation accuracy. Cokriging estimation variances were reduced by an average of 54% relative to kriging variances within the study area. Cokriging reduced estimation variances at the potential repository site by 55% relative to kriging. The usefulness of an existing network of stations for measuring AAP within the study area was evaluated using cokriging variances, and twenty additional stations were located for the purpose of improving the accuracy of future isohyetal mappings. Using the expanded network of stations, the maximum cokriging estimation variance within the study area was reduced by 78% relative to the existing network, and the average estimation variance was reduced by 52%.

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