TY - JOUR

T1 - Effects of kriging and inverse modeling on conditional simulation of the Avra Valley Aquifer in southern Arizona

AU - Clifton, Peter M.

AU - Neuman, Shlomo P.

PY - 1982/8

Y1 - 1982/8

N2 - The Avra Valley aquifer in southern Arizona is modeled stochastically at three levels of uncertainty. The highest level of uncertainty occurs when log transmissivity estimates are based on measured values of this parameter but without regard to the geographic location of each measurement point. The resulting steady state hydraulic heads in the aquifer, computed by unconditional simulation with the aid of a multivariate normal random number generator coupled with a finite element model, have a relatively large variance. This variance can be reduced by conditioning the log transmissivity estimates on the spatial arrangement of the data by means of kriging. When conditional simulation of the aquifer is performed at this intermediate level of uncertainty with the aid of the same technique as in the unconditional case, the variance of the predicted head values is reduced by a factor of 3.2. The lowest level of uncertainty is achieved when the log transmissivity estimates are further conditioned on data relating to the flow regime, such as flow rates and water levels in observation wells, by means of a statistical inverse procedure. Conditional simulation at this level of uncertainty is a novel concept. It results in a hydraulic head prediction variance that is 14.3 times lower than the corresponding variance based on kriged log transmissivities. The net effect of conditioning by means of kriging and inverse modeling is to reduce the prediction variance by a factor of 46.0. A similar study performed by Binsarti (1980) on the Cortaro aquifer in southern Arizona showed insignificant variance reduction due to kriging, but a factor of four reduction after inverse modeling. These results indicate that the conditioning effect of the inverse method may be much greater than that of kriging. The fact that conditioning can reduce the hydraulic head prediction variance by as much as a factor of 46 implies that one should be cautious when dealing with the results of stochastic aquifer models in which conditioning effects are disregarded.

AB - The Avra Valley aquifer in southern Arizona is modeled stochastically at three levels of uncertainty. The highest level of uncertainty occurs when log transmissivity estimates are based on measured values of this parameter but without regard to the geographic location of each measurement point. The resulting steady state hydraulic heads in the aquifer, computed by unconditional simulation with the aid of a multivariate normal random number generator coupled with a finite element model, have a relatively large variance. This variance can be reduced by conditioning the log transmissivity estimates on the spatial arrangement of the data by means of kriging. When conditional simulation of the aquifer is performed at this intermediate level of uncertainty with the aid of the same technique as in the unconditional case, the variance of the predicted head values is reduced by a factor of 3.2. The lowest level of uncertainty is achieved when the log transmissivity estimates are further conditioned on data relating to the flow regime, such as flow rates and water levels in observation wells, by means of a statistical inverse procedure. Conditional simulation at this level of uncertainty is a novel concept. It results in a hydraulic head prediction variance that is 14.3 times lower than the corresponding variance based on kriged log transmissivities. The net effect of conditioning by means of kriging and inverse modeling is to reduce the prediction variance by a factor of 46.0. A similar study performed by Binsarti (1980) on the Cortaro aquifer in southern Arizona showed insignificant variance reduction due to kriging, but a factor of four reduction after inverse modeling. These results indicate that the conditioning effect of the inverse method may be much greater than that of kriging. The fact that conditioning can reduce the hydraulic head prediction variance by as much as a factor of 46 implies that one should be cautious when dealing with the results of stochastic aquifer models in which conditioning effects are disregarded.

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U2 - 10.1029/WR018i004p01215

DO - 10.1029/WR018i004p01215

M3 - Article

AN - SCOPUS:0020332331

VL - 18

SP - 1215

EP - 1234

JO - Water Resources Research

JF - Water Resources Research

SN - 0043-1397

IS - 4

ER -