Uncertainty and relative importance of hydraulic properties: A stochastic framework to prioritize site characterization and modeling needs

This dissertation develops a stochastic framework that accounts for the uncertainty, relative importance and relative contribution of uncertain and spatially variable parameters and the influence of model assumptions. We have applied this methodology to the physical problem of one-dimensional infiltration into variably saturated heterogeneous multi-layered formations under constant infiltration rate. Evaluation of which parameters dominate the uncertainty of a final solution (e.g. pressure head, flux, or concentration) will allow us to understand the limitations of our predictive capabilities as well as to allocate resources for better characterization of the critical parameters. We have used and analyzed field data from the U.S. Department of Energy project at Yucca Mountain, Nevada and have quantified the relative importance of the saturated hydraulic conductivity (K_s) and the van Genuchten α (air-entry scaling) and β (pore size distribution index) parameters using a Monte Carlo numerical technique. These parameters were considered as random variables and assumed to follow the same distribution model. Two cross correlation cases between the parameters were considered: uncorrelated and perfectly correlated parameters. The analysis showed that the assumption of a specific distribution for the data is critical, and significant information on the detailed shape of the probability distribution is required in order to produce meaningful predictions of pressure head (<h_p>) and saturation (<S>) profiles. The variance of the <h_p> increases with decreasing <h_p> and the variance of <S> appears to increase in coarse textured soils. Our results indicate that the cross correlation between the parameters significantly influences the prediction of <h_p> and <S>-profiles especially if the parameters are exponentially or lognormaly distributed (i.e. for perfectly correlated parameters larger <h_p> and <S>-profiles, in absolute value, were produced). Overall for the prediction of <h_p> it appears that for all layers and models the K _s and the β parameters need to be treated as stochastic variables with the exact statistical model clearly defined for each layer in order to establish the correct hydraulic behavior. Our results indicate that for all distribution types the variation in <h_p> and <S> values grew as the infiltration rate decreased.