Stochastic capture zone delineation within the generalized likelihood uncertainty estimation methodology: Conditioning on head observations

Abstract

Abstract. A stochastic methodology to evaluate the predictive uncertainty in well capture zones in heterogeneous aquifers with uncertain parameters is presented. The approach is based on the generalized likelihood uncertainty estimation methodology. The hydraulic conductivity is modeled as a random space function allowing for the uncertainty that stems from the imperfect knowledge of the parameters of the correlation structure. Parameters are sampled from prior distributions and are used for the generation of a large number of hydraulic conductivity fields, which are subsequently used to solve the groundwater flow equation. A likelihood is calculated for every simulation, based on some goodness-of-fit measure between simulated heads and available observations. Using inverse particle tracking, a capture zone is determined which is assigned the likelihood calculated for that particular simulation. Statistical analysis of the ensemble of all simulations enables the predictive uncertainty of the well capture zones to be defined. Results are presented for a hypothetical test case and different likelihood definitions used in the conditioning process. The results show that the delineated capture zones are most sensitive to the mean hydraulic conductivity and the variance, whereas the integral scale of the variogram is the parameter with the smallest influence. For all likelihood measures the prior uncertainty is reduced considerably by introducing the observation heads, but the reduction is most effective for the very selective likelihood definition. The method presented can be used in real applications to quantify the uncertainty in the location and extent of well capture zones when little or no information is available about the hydraulic properties, through the conditioning on head observations.

A manifesto for the equifinality thesis

“…In distributed groundwater modelling, this type of model evaluation suggests that equifinality is endemic to the problem (see Feyen et al, 2001;Binley and Beven, 2003). Similarly, in rainfall-runoff modelling, the use of distributed observational information (disappointingly) does not appear to help much in eliminating the equifinality problem (see Lamb et al, 1998;Blazkova et al, 2002;Blazkova and Beven, 2003;Christiaens and Feyen, 2002).…”

“…In part, the origins of this concept lie in purely empirical studies that have found many models giving good fits to data (e.g. Figure 1; for other recent examples in different areas of environmental modelling see Zak et al, 1999;Brazier at al., 2000;Beven and Freer, 2001a,b;Feyen et al, 2001;Mwakalila et al, 2001;Blazkova et al, 2002;Blazkova and Beven, 2002;Christiaens and Feyen, 2002;Freer et al, 2002;Martinez-Vilalta et al, 2002;Schulz and Beven, 2003). …”

Assessment of conceptual model uncertainty for the regional aquifer Pampa del Tamarugal – North Chile

“…Rojas et al, 2008Rojas et al, , 2009c, subjectively chosen threshold limits (e.g. Feyen et al, 2001) or set as a minimum level of performance (e.g. Binley and Beven, 2003).…”

Bridging the gap between GLUE and formal statistical approaches: approximate Bayesian computation

“…An informal likelihood measure is used to avoid over conditioning and exclude parts of the model (parameter) space that might provide acceptable fits to the data and be useful in prediction. Since its introduction in 1992, GLUE has found widespread application for uncertainty assessment in many fields of study, including modeling of the rainfallrunoff transformation (Beven and Binley, 1992;Freer et al, 1996;Lamb et al, 1998), soil erosion (Brazier et al, 2001), tracer dispersion in a river reach (Hankin et al, 2001), groundwater and well capture zone delineation (Feyen et al, 2001;Jensen, 2003), unsaturated zone (Mertens et al, 2004), flood inundation (Romanowicz et al, 1996;Aronica et al, 2002), land-surface-atmosphere interactions (Franks et al, 1997), soil freezing and thawing (Hanson and Lundin, 2006), crop yields and soil organic carbon (Wang et al, 2005), and ground radar-rainfall estimation (Tadesse and Anagnostou, 2005). Applications of GLUE are also found in distributed hydrologic modeling (McMichael et al, 2006;Muleta and Nicklow, 2005).…”