Global Sensitivity Analysis Techniques for Probabilistic Ground Water Modeling

Global sensitivity analysis techniques are better suited for analyzing input-output relationships over the full range of parameter variations and model outcomes, as opposed to local sensitivity analysis carried out around a reference point. This article describes three such techniques: (1) stepwise rank regression analysis for building input-output models to identify key contributors to output variance, (2) mutual information (entropy) analysis for determining the strength of nonmonotonic patterns of input-output association, and (3) classification tree analysis for determining what variables or combinations are responsible for driving model output into extreme categories. These techniques are best applied in conjunction with Monte Carlo simulation-based probabilistic analyses. Two examples are presented to demonstrate the applicability of these methods. The usefulness of global sensitivity techniques is examined vis-a-vis local sensitivity analysis methods, and recommendations are provided for their applications in ground water modeling practice.     

Ecohydrologic Process Modeling of Mountain Block Groundwater Recharge

Regional mountain block recharge (MBR) is a key component of alluvial basin aquifer systems typical of the western United States. Yet neither water scientists nor resource managers have a commonly available and reasonably invoked quantitative method to constrain MBR rates. Recent advances in landscape-scale ecohydrologic process modeling offer the possibility that meteorological data and land surface physical and vegetative conditions can be used to generate estimates of MBR. A water balance was generated for a temperate 24,600-ha mountain watershed, elevation 1565 to 3207 m, using the ecosystem process model Biome-BGC (BioGeochemical Cycles) ( Running and Hunt 1993 ). Input data included remotely sensed landscape information and climate data generated with the Mountain Climate Simulator (MT-CLIM) ( Running et al. 1987 ). Estimated mean annual MBR flux into the crystalline bedrock terrain is 99,000 m³/d, or approximately 19% of annual precipitation for the 2003 water year. Controls on MBR predictions include evapotranspiration (radiation limited in wet years and moisture limited in dry years), soil properties, vegetative ecotones (significant at lower elevations), and snowmelt (dominant recharge process). The ecohydrologic model is also used to investigate how climatic and vegetative controls influence recharge dynamics within three elevation zones. The ecohydrologic model proves useful for investigating controls on recharge to mountain blocks as a function of climate and vegetation. Future efforts will need to investigate the uncertainty in the modeled water balance by incorporating an advanced understanding of mountain recharge processes, an ability to simulate those processes at varying scales, and independent approaches to calibrating MBR estimates.     

A Stable and Efficient Numerical Algorithm for Unconfined Aquifer Analysis

The nonlinearity of equations governing flow in unconfined aquifers poses challenges for numerical models, particularly in field-scale applications. Existing methods are often unstable, do not converge, or require extremely fine grids and small time steps. Standard modeling procedures such as automated model calibration and Monte Carlo uncertainty analysis typically require thousands of model runs. Stable and efficient model performance is essential to these analyses. We propose a new method that offers improvements in stability and efficiency and is relatively tolerant of coarse grids. It applies a strategy similar to that in the MODFLOW code to the solution of Richard's equation with a grid-dependent pressure/saturation relationship. The method imposes a contrast between horizontal and vertical permeability in gridblocks containing the water table, does not require "dry" cells to convert to inactive cells, and allows recharge to flow through relatively dry cells to the water table. We establish the accuracy of the method by comparison to an analytical solution for radial flow to a well in an unconfined aquifer with delayed yield. Using a suite of test problems, we demonstrate the efficiencies gained in speed and accuracy over two-phase simulations, and improved stability when compared to MODFLOW. The advantages for applications to transient unconfined aquifer analysis are clearly demonstrated by our examples. We also demonstrate applicability to mixed vadose zone/saturated zone applications, including transport, and find that the method shows great promise for these types of problem as well.     

Nonlinear Flow in Karst Formations

The variation of effective hydraulic conductivity as a function of specific discharge in several 0.2-m and 0.3-m cubes of Key Largo Limestone was investigated. The experimental results closely match the Forchheimer equation. Defining the pore-size length scale in terms of Forchheimer parameters, it is demonstrated that significant deviations from Darcian flow will occur when the Reynolds number exceeds 0.11. A particular threshold model previously proposed for use in karstic formations does not show strong agreement with the data near the onset of nonlinear flow.     

Investigation of Transport Processes inside Karst Aquifer by Means of STATIS

Environmental data sets are often multidimensional and consequently display complex structure. This article shows the limitations of principal component analysis (PCA) for the study of such three-dimensional (3D) data sets. These limitations can be resolved by the use of the statistical tool STATIS. The inlet (a swallow hole) and the outlet (a spring) of a karst system of the Western Paris basin were sampled during three rain events of various intensities. These 3D geochemical data sets (variables × sites × dates) for a karst system were analyzed by STATIS method to identify hydrological processes. STATIS proceeds in three steps (interstructure, compromise, and intrastructure), which allows us to focus the analysis of hydrologic systems at different temporal and spatial scales. Compromise plane shows that suspended matter and flood are not simultaneous and highlights a rapid flow, characterized by turbidity and phosphate, which represents a point source contamination, and a ground water flow contaminated by nitrate. Intrastructure plane allows us to compare hydrochemical variations between the swallow hole and the spring lead. By this way, hydrological processes such as direct transfer and resuspension of intrakarstic sediments before and after the flood were identified what cannot be realized by comparison of inlet and outlet breakthrough curves. Finally, results obtained from the same data set by STATIS and a coupled study using PCA and normalized hysteresis curves were compared. This comparison shows the efficiency of STATIS at the identification of transport processes and vulnerability of karst system and its potential for hydrological applications.