Steven F. Carle

Transition probability-based indicator geostatistics

Traditionally, spatial continuity models for indicator variables are developed by empirical curvefitting to the sample indicator (cross-) variogram. However, geologic data may be too sparse to permit a purely empirical approach, particularly in application to the subsurface. Techniques for model synthesis that integrate hard data and conceptual models therefore are needed. Interpretability is crucial. Compared with the indicator (cross-) variogram or indicator (cross-) covariance, the transition probability is more interpretable. Information on proportion, mean length, and juxtapositioning directly relates to the transition probability: asymmetry can be considered. Furthermore, the transition probability elucidates order relation conditions and readily formulates the indicator (co)kriging equations.

Modeling Spatial Variability with One and Multidimensional Continuous-Lag Markov Chains

The continuous-lag Markov chain provides a conceptually simple, mathematically compact, and theoretically powerful model of spatial variability for categorical variables. Markov chains have a long-standing record of applicability to one-dimensional (1-D) geologic data, but 2- and 3-D applications are rare. Theoretically, a multidimensional Markov chain may assume that 1-D Markov chains characterize spatial variability in all directions. Given that a 1-D continuous Markov chain can be described concisely by a transition rate matrix, this paper develops 3-D continuous-lag Markov chain models by interpolating transition rate matrices established for three principal directions, say strike, dip, and vertical. The transition rate matrix for each principal direction can be developed directly from data or indirectly by conceptual approaches. Application of Sylvesters theorem facilitates establishment of the transition rate matrix, as well as calculation of transition probabilities. The resulting 3-D continuous-lag Markov chain models then can be applied to geo-statistical estimation and simulation techniques, such as indicator cokriging, disjunctive kriging, sequential indicator simulation, and simulated annealing.

Three‐dimensional hydrofacies modeling based on soil surveys and transition probability geostatistics

Typical hydrogeologic data sets consisting of information from boreholes provide excellent information on vertical variability of sedimentary deposits but very limited information on lateral distribution and variability. In cases where surface geomorphic features reflect processes similar to those responsible for past deposition, the soil survey offers a resource for assessing the lateral sediment variability. Facies mean length and transition probability measurements of C horizon textures from the soil maps on the Kings River alluvial fan, California, provide a basis for Markov chain models of spatial variability in the principal lateral directions and facies orientation information for the horizontal plane. Incorporation with a Markov chain model of vertical-direction transitions based on well data yields a three-dimensional Markov chain model of sediment variability which includes cross correlation between sediment types and representation of asymmetry (e.g., fining upward tendencies). Use of the model in geostatistical conditional simulation and simulated annealing produces a detailed, geologically plausible image of the subsurface hydrofacies distribution.

Analysis of groundwater migration from artificial recharge in a large urban aquifer: A simulation perspective

The increased use of reclaimed water for artificial groundwater recharge purposes has led to concerns about future groundwater quality, particularly as it relates to the introduction of new organic and inorganic contaminants into the subsurface. Here we review the development and initial application of a detailed numerical model of groundwater flow and migration in a region encompassing a large groundwater recharge operation in Orange County, California. The model is based upon a novel representation of geologic heterogeneity, which has long been known to influence local flow and transport behavior in the subsurface. The model and complementary series of isotopic analyses provide an improved scientific basis to understand flow paths, migration rates, and residence times of recharged groundwater, as well as to identify the source composition of water produced in wells near the recharge operation. From a management perspective these issues need to be confronted in order to respond to proposed regulatory constraints that would govern the operation of recharge facilities and nearby production wells. While model calibration is greatly aided by isotopic source and residence time analyses, the model also provides unique insights on the interpretation of isotopic data themselves. Isotopic estimates of groundwater age help discriminate between several equally acceptable simulations calibrated to head data only. However, the results also suggest that groundwater reaching a well spans a wide-ranging distribution of age, demonstrating the importance of geologic heterogeneity in affecting flow paths, mixing, and residence times in the vicinity of recharge basins and wells.

Implementation schemes for avoiding artifact discontinuities in simulated annealing

The simulated annealing algorithm has been applied successfully to conditional simulation of categorical variables (e.g., rock or facies units) with the objective of improving the match between measured and modeled spatial variability. In some implementation schemes, however, spurious features termed “artifact discontinuities” may occur near conditioning data, especially during the “zero- temperature” case referred to as simulated quenching. This paper shows that artifact discontinuities can be avoided by considering the anisotropy of the spatial variability model, reducing the number of lag vectors used in the objective function, and providing a rudimentary initial configuration. Results from several test cases suggest that the artifact discontinuities might be caused by overly precise fitting of measured to modeled spatial variability.

High-resolution simulation of basin-scale nitrate transport considering aquifer system heterogeneity

Nitrate contamination presents a growing threat to many groundwater basins relied upon for drinking water. This study combines geostatistical techniques, parallel computing of fl ow simulation, and particle tracking to develop realistic nitrate loading and transport scenarios. The simulation scenarios are patterned after the rapidly urbanizing Llagas groundwater subbasin in the south San Francisco Bay area of California. In the Llagas subbasin, groundwater is the sole municipal water supply. A key component of this study is the development of a highly resolved model of the heterogeneity in the aquifer system using a new geostatistical technique for simulating hydrofacies architecture that can incorporate uncertain or “soft” data, such as well driller logs. Numerical simulations of nitrate transport indicate the degree to which a heterogeneous conceptual model can account for dispersion relative to a conventional homogeneous model assuming typical dispersivity coeffi cients. The heterogeneous model transport results are found to be consistent with observed nitrate contamination patterns and depth distribution as well as groundwater-age trends with depth. The model provides a realistic test-bed for prediction of future nitrate concentrations, including the time frame for potential nitrate impacts to deep wells, given that geochemical data indicate that denitrifi cation is not likely to occur.

Simulation of Nitrate Biogeochemistry and Reactive Transport in a California Groundwater Basin

Nitrate is the number one drinking water contaminant in the United States. It is pervasive in surface and groundwater systems, and its principal anthropogenic sources have increased dramatically in the last 50 years. In California alone, one third of the public drinking-water wells has been lost since 1988 and nitrate contamination is the most common reason for abandonment. Effective nitrate management in groundwater is complicated by uncertainties related to multiple point and non-point sources, hydrogeologic complexity, geochemical reactivity, and quantification of denitrification processes. In this paper, we review an integrated experimental and simulation-based framework being developed to study the fate of nitrate in a 25 km-long groundwater subbasin south of San Jose, California, a historically agricultural area now undergoing rapid urbanization with increasing demands for groundwater. The modeling approach is driven by a need to integrate new and archival data that support the hypothesis that nitrate fate and transport at the basin scale is intricately related to hydrostratigraphic complexity, variability of flow paths and groundwater residence times, microbial activity, and multiple geochemical reaction mechanisms. This study synthesizes these disparate and multi-scale data into a three-dimensional and highly resolved reactive transport modeling framework.

Simulation of Radionuclide Migration in Groundwater Away from an Underground Nuclear Test

Reactive transport simulations are being used to evaluate the nature and extent of radionuclide contamination within alluvium surrounding an underground nuclear test at the Nevada Test Site (NTS). Simulations are focused on determining the abundance and chemical nature of radionuclides that are introduced into groundwater, as well as the rate and extent of radionuclide migration and reaction in groundwater surrounding the working point of the test. Transport simulations based upon a streamline-based numerical model are used to illustrate the nature of radionuclide elution out of the near-field environment and illustrate the conceptual modeling process. The numerical approach allowed for relatively complex flow and chemical reactions to be considered in a computationally efficient manner. The results are particularly sensitive to the rate of melt glass dissolution, distribution of reactive minerals in the alluvium, and overall groundwater flow configuration. They provide a rational basis from which defensible migration assessments can proceed.

Simulating Effects of Non-Isothermal Flow on Reactive Transport of Radionuclides Originating From an Underground Nuclear Test

Temperature can significantly affect radionuclide transport behavior. In simulation of radionuclide transport originating from an underground nuclear test, temperature effects from residual test heat include non-isothermal groundwater flow behavior (e.g. convection cells), increased dissolution rates of melt glass containing refractory radionuclides, changes in water chemistry, and, in turn, changes in radionuclide sorption behavior. The low-yield (0.75 kiloton) Cambric underground nuclear test situated in alluvium below the water table offers unique perspectives on radionuclide transport in groundwater. The Cambric test was followed by extensive post-test characterization of the radionuclide source term and a 16-year pumping-induced radionuclide migration experiment that captured more mobile radionuclides in groundwater. Discharge of pumped groundwater caused inadvertent recirculation of radionuclides through a 220-m thick vadose zone to the water table and below, including partial re-capture in the pumping well. Non-isothermal flow simulations indicate test-related heat persists at Cambric for about 10 years and induces limited thermal convection of groundwater. The test heat has relatively little impact on mobilizing radionuclides compared to subsequent pumping effects. However, our reactive transport models indicate test-related heat can raise melt glass dissolution rates up to 10{sup 4} faster than at ambient temperatures depending on pH and species activities. Non-isothermal flow simulations indicate that these elevated glass dissolution rates largely decrease within 1 year. Thermally-induced increases in fluid velocity may also significantly increase rates of melt glass dissolution by changing the fluid chemistry in contact with the dissolving glass.

A SERENDIPITOUS, LONG-TERM INFILTRATION EXPERIMENT: WATER AND RADIONUCLIDE CIRCULATION BENEATH THE CAMBRIC TRENCH AT THE NEVADA TEST SITE.

Underground atomic weapons testing at the Nevada Test Site introduced numerous radionuclides that may be used to characterize subsurface hydrologic transport processes in arid climates. Beginning in 1975, groundwater adjacent to the CAMBRIC test, conducted beneath Frenchman Flat in 1965, was pumped steadily for 16 years to elicit experimental information on the migration of residual radioactivity through the saturated zone. Radionuclides in the pumping well effluent, including tritium, {sup 36}Cl and {sup 85}Kr, were extensively monitored prior to their discharge into an unlined ditch flowing toward a dry lake bed over a kilometer away. We have applied a large (6km x 6km x 1km) and highly resolved (4 m) variably saturated flow model to investigate infiltration into the 220-m vadose zone underlying the ditch as well as subsequent groundwater recharge and well recirculation processes. A Lagrangian particle-tracking model has been used to compute flow pathways and estimate radionuclide travel and residence times in various parts of the system based upon the flow model. Results are consistent with rising tritium levels observed in a monitoring well since 1991. They suggest that recirculation of the ditch effluent through the vadose zone, into groundwater, and back to the test cavity and pumping well are responsible for diluted, tritium-based groundwater age dates observed in 2000 at these locations, as well as for increased tailing effects observed in the pumping well elution curves. Altogether, the models and experimental observations provide an improved basis to understand both historical and future movements of test-related radionuclides in groundwater near CAMBRIC.