Premium
Using Semivariogram Parameter Uncertainty in Hydrogeological Applications
Author(s) -
PardoIgúzquiza Eulogio,
ChicaOlmo Mario,
GarciaSoldado Maria Jose,
LuqueEspinar Juan A.
Publication year - 2009
Publication title -
groundwater
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.84
H-Index - 94
eISSN - 1745-6584
pISSN - 0017-467X
DOI - 10.1111/j.1745-6584.2008.00494.x
Subject(s) - variogram , kriging , geostatistics , hydrogeology , interpolation (computer graphics) , range (aeronautics) , covariance , monte carlo method , uncertainty quantification , computer science , aquifer properties , statistics , environmental science , spatial variability , mathematics , aquifer , groundwater , geology , engineering , geotechnical engineering , artificial intelligence , motion (physics) , groundwater recharge , aerospace engineering
Geostatistical estimation (kriging) and geostatistical simulation are routinely used in ground water hydrology for optimal spatial interpolation and Monte Carlo risk assessment, respectively. Both techniques are based on a model of spatial variability (semivariogram or covariance) that generally is not known but must be inferred from the experimental data. Where the number of experimental data is small (say, several tens), as is not unusual in ground water hydrology, the model fitted to the empirical semivariogram entails considerable uncertainty. If all the practical results are based on this unique fitted model, the final results will be biased. We propose that, instead of using a unique semivariogram model, the full range of models that are inside a given confidence region should be used, and the weight that each semivariogram model has on the final result should depend on its plausibility. The first task, then, is to evaluate the uncertainty of the model, which can be efficiently done by using maximum likelihood inference. The second task is to use the range of plausible models in applications and to show the effect observed on the final results. This procedure is put forth here with kriging and simulation applications, where the uncertainty in semivariogram parameters is propagated into the final results (e.g., the prediction of ground water head). A case study using log‐transmissivity data from the Vega de Granada aquifer, in southern Spain, is given to illustrate the methodology.