Geology topics

Christopher T. Green

Publications and source records attributed to Christopher T. Green.

At least 19 recordsLinked to original sources

USGS2024

Prioritizing US Geological Survey science on salinization and salinity in candidate and selected priority river basins

The US Geological Survey (USGS) is selecting and prioritizing basins, known as Integrated Water Science basins, for monitoring and intensive study. Previous efforts to aid in this selection process include a scientifically defensible and quantitative assessment of basins facing human-caused water resource challenges (Van Metre et al. in Environmental Monitoring and Assessment , 192(7), 458 2020). In the present work, we explore this ranking process based on water quality considerations, specifically salinity and salinization. We selected top candidate basins to study salinity and salinization issues in 18 hydrologic regions that include 163 candidate basins. Our prioritization is based on quantitative assessment of sources of salinity, drivers of change, and receptors that must respond to those sources and drivers. Source terms represented in the prioritization include geology, depth to brackish groundwater, stream conductivity, chloride in precipitation, urban and agricultural land use, application of road salt as a deicer, and irrigation. Drivers represented in prioritization include changes in chemical weathering as a result of changes in rainwater chemistry. Receptors include measures of water stress, measurements of stream ecological health, and socioeconomic factors. In addition, we present research activities for the USGS on salinity and salinization that can be pursued in these basins including assessment of sources, pathways, and loadings; predicting and understanding changes in sources, peaks, and trends; understanding the components of salinity and mobilization of contaminants; understanding the relationship between salinization and changing ecosystems; and developing knowledge on the causes and distribution of groundwater salinity, brackish water resources, and challenges related to desalination.

Enviornmental Monitoring and Assessment↗

USGS2018

Comparison of time nonlocal transport models for characterizing non-Fickian transport: From mathematical interpretation to laboratory application

Non-Fickian diffusion has been increasingly documented in hydrology and modeled by promising time nonlocal transport models. While previous studies showed that most of the time nonlocal models are identical with correlated parameters, fundamental challenges remain in real-world applications regarding model selection and parameter definition. This study compared three popular time nonlocal transport models, including the multi-rate mass transfer (MRMT) model, the continuous time random walk (CTRW) framework, and the tempered time fractional advection–dispersion equation (tt-fADE), by focusing on their physical interpretation and feasibility in capturing non-Fickian transport. Mathematical comparison showed that these models have both related parameters defining the memory function and other basic-transport parameters (i.e., velocity v and dispersion coefficient D ) with different hydrogeologic interpretations. Laboratory column transport experiments and field tracer tests were then conducted, providing data for model applicability evaluation. Laboratory and field experiments exhibited breakthrough curves with non-Fickian characteristics, which were better represented by the tt-fADE and CTRW models than the traditional advection–dispersion equation. The best-fit velocity and dispersion coefficient, however, differ significantly between the tt-fADE and CTRW. Fitting exercises further revealed that the observed late-time breakthrough curves were heavier than the MRMT solutions with no more than two mass-exchange rates and lighter than the MRMT solutions with power-law distributed mass-exchange rates. Therefore, the time nonlocal models, where some parameters are correlated and exchangeable and the others have different values, differ mainly in their quantification of pre-asymptotic transport dynamics. In all models tested above, the tt-fADE model is attractive, considering its small fitting error and the reasonable velocity close to the measured flow rate.

Water↗

USGS2018

Regional variability of nitrate fluxes in the unsaturated zone and groundwater, Wisconsin, USA

Process-based modeling of regional NO3− fluxes to groundwater is critical for understanding and managing water quality, but the complexity of NO3− reactive transport processes make implementation a challenge. This study introduces a regional vertical flux method (VFM) for efficient estimation of reactive transport of NO3− in the vadose zone and groundwater. The regional VFM was applied to 443 well samples in central-eastern Wisconsin. Chemical measurements included O2, NO3−, N2 from denitrification, and atmospheric tracers of groundwater age including carbon-14, chlorofluorocarbons, tritium, and tritiogenic helium. VFM results were consistent with observed chemistry, and calibrated parameters were in-line with estimates from previous studies. Results indicated that (1) unsaturated zone travel times were a substantial portion of the transit time to wells and streams (2) since 1945 fractions of applied N leached to groundwater have increased for manure-N, possibly due to increased injection of liquid manure, and decreased for fertilizer-N, and (3) under current practices and conditions, approximately 60% of the shallow aquifer will eventually be affected by downward migration of NO3−, with denitrification protecting the remaining 40%. Recharge variability strongly affected the unsaturated zone lag times and the eventual depth of the NO3− front. Principal components regression demonstrated that VFM parameters and predictions were significantly correlated with hydrogeochemical landscape features. The diverse and sometimes conflicting aspects of N management (e.g. limiting N volatilization versus limiting N losses to groundwater) warrant continued development of large-scale holistic strategies to manage water quality and quantity.

Wisconsin↗

USGS2018

Metamodeling and mapping of nitrate flux in the unsaturated zone and groundwater, Wisconsin, USA

Nitrate contamination of groundwater in agricultural areas poses a major challenge to the sustainability of water resources. Aquifer vulnerability models are useful tools that can help resource managers identify areas of concern, but quantifying nitrogen (N) inputs in such models is challenging, especially at large spatial scales. We sought to improve regional nitrate (NO 3 − ) input functions by characterizing unsaturated zone NO 3 − transport to groundwater through use of surrogate, machine-learning metamodels of a process-based N flux model. The metamodels used boosted regression trees (BRTs) to relate mappable landscape variables to parameters and outputs of a previous “vertical flux method” (VFM) applied at sampled wells in the Fox, Wolf, and Peshtigo (FWP) river basins in northeastern Wisconsin. In this context, the metamodels upscaled the VFM results throughout the region, and the VFM parameters and outputs are the metamodel response variables. The study area encompassed the domain of a detailed numerical model that provided additional predictor variables, including groundwater recharge, to the metamodels. We used a statistical learning framework to test a range of model complexities to identify suitable hyperparameters of the six BRT metamodels corresponding to each response variable of interest: NO 3 − source concentration factor (which determines the local NO 3 − input concentration); unsaturated zone travel time; NO 3 − concentration at the water table in 1980, 2000, and 2020 (three separate metamodels); and NO 3 − “extinction depth”, the eventual steady state depth of the NO 3 − front. The final metamodels were trained to 129 wells within the active numerical flow model area, and considered 58 mappable predictor variables compiled in a geographic information system (GIS). These metamodels had training and cross-validation testing R 2 values of 0.52 – 0.86 and 0.22 – 0.38, respectively, and predictions were compiled as maps of the above response variables. Testing performance was reasonable, considering that we limited the metamodel predictor variables to mappable factors as opposed to using all available VFM input variables. Relationships between metamodel predictor variables and mapped outputs were generally consistent with expectations, e.g. with greater source concentrations and NO 3 − at the groundwater table in areas of intensive crop use and well drained soils. Shorter unsaturated zone travel times in poorly drained areas likely indicated preferential flow through clay soils, and a tendency for fine grained deposits to collocate with areas of shallower water table. Numerical estimates of groundwater recharge were important in the metamodels and may have been a proxy for N input and redox conditions in the northern FWP, which had shallow predicted NO 3 − extinction depth. The metamodel results provide proof-of-concept for regional characterization of unsaturated zone NO 3 − transport processes in a statistical framework based on readily mappable GIS input variables.

Wisconsin↗

USGS2016

Bounded fractional diffusion in geological media: Definition and Lagrangian approximation

Spatiotemporal Fractional-Derivative Models (FDMs) have been increasingly used to simulate non-Fickian diffusion, but methods have not been available to define boundary conditions for FDMs in bounded domains. This study defines boundary conditions and then develops a Lagrangian solver to approximate bounded, one-dimensional fractional diffusion. Both the zero-value and non-zero-value Dirichlet, Neumann, and mixed Robin boundary conditions are defined, where the sign of Riemann-Liouville fractional derivative (capturing non-zero-value spatial-nonlocal boundary conditions with directional super-diffusion) remains consistent with the sign of the fractional-diffusive flux term in the FDMs. New Lagrangian schemes are then proposed to track solute particles moving in bounded domains, where the solutions are checked against analytical or Eularian solutions available for simplified FDMs. Numerical experiments show that the particle-tracking algorithm for non-Fickian diffusion differs from Fickian diffusion in relocating the particle position around the reflective boundary, likely due to the non-local and non-symmetric fractional diffusion. For a non-zero-value Neumann or Robin boundary, a source cell with a reflective face can be applied to define the release rate of random-walking particles at the specified flux boundary. Mathematical definitions of physically meaningful nonlocal boundaries combined with bounded Lagrangian solvers in this study may provide the only viable techniques at present to quantify the impact of boundaries on anomalous diffusion, expanding the applicability of FDMs from infinite do mains to those with any size and boundary conditions.

Water Resources Research↗

USGS2016

Regional oxygen reduction and denitrification rates in groundwater from multi-model residence time distributions, San Joaquin Valley, USA

Rates of oxygen and nitrate reduction are key factors in determining the chemical evolution of groundwater. Little is known about how these rates vary and covary in regional groundwater settings, as few studies have focused on regional datasets with multiple tracers and methods of analysis that account for effects of mixed residence times on apparent reaction rates. This study provides insight into the characteristics of residence times and rates of O 2 reduction and denitrification (NO 3 − reduction) by comparing reaction rates using multi-model analytical residence time distributions (RTDs) applied to a data set of atmospheric tracers of groundwater age and geochemical data from 141 well samples in the Central Eastern San Joaquin Valley, CA. The RTD approach accounts for mixtures of residence times in a single sample to provide estimates of in-situ rates. Tracers included SF 6 , CFCs, 3 H, He from 3 H (tritiogenic He), 14 C, and terrigenic He. Parameter estimation and multi-model averaging were used to establish RTDs with lower error variances than those produced by individual RTD models. The set of multi-model RTDs was used in combination with NO 3 − and dissolved gas data to estimate zero order and first order rates of O 2 reduction and denitrification. Results indicated that O 2 reduction and denitrification rates followed approximately log-normal distributions. Rates of O 2 and NO 3 − reduction were correlated and, on an electron milliequivalent basis, denitrification rates tended to exceed O 2 reduction rates. Estimated historical NO 3 − trends were similar to historical measurements. Results show that the multi-model approach can improve estimation of age distributions, and that relatively easily measured O 2 rates can provide information about trends in denitrification rates, which are more difficult to estimate.

California↗

USGS2015

Inverse modeling with RZWQM2 to predict water quality

This chapter presents guidelines for autocalibration of the Root Zone Water Quality Model (RZWQM2) by inverse modeling using PEST parameter estimation software ( Doherty, 2010 ). Two sites with diverse climate and management were considered for simulation of N losses by leaching and in drain flow: an almond [ Prunus dulcis (Mill.) D.A. Webb] orchard in the San Joaquin Valley, California and the Walnut Creek watershed in central Iowa, which is predominantly in corn ( Zea mays L.)–soybean [ Glycine max (L.) Merr.] rotation. Inverse modeling provides an objective statistical basis for calibration that involves simultaneous adjustment of model parameters and yields parameter confidence intervals and sensitivities. We describe operation of PEST in both parameter estimation and predictive analysis modes. The goal of parameter estimation is to identify a unique set of parameters that minimize a weighted least squares objective function, and the goal of predictive analysis is to construct a nonlinear confidence interval for a prediction of interest by finding a set of parameters that maximizes or minimizes the prediction while maintaining the model in a calibrated state. We also describe PEST utilities (PAR2PAR, TSPROC) for maintaining ordered relations among model parameters (e.g., soil root growth factor) and for post-processing of RZWQM2 outputs representing different cropping practices at the Iowa site. Inverse modeling provided reasonable fits to observed water and N fluxes and directly benefitted the modeling through: (i) simultaneous adjustment of multiple parameters versus one-at-a-time adjustment in manual approaches; (ii) clear indication by convergence criteria of when calibration is complete; (iii) straightforward detection of nonunique and insensitive parameters, which can affect the stability of PEST and RZWQM2; and (iv) generation of confidence intervals for uncertainty analysis of parameters and model predictions. Composite scaled sensitivities, which reflect the total information provided by the observations for a parameter, indicated that most of the RZWQM2 parameters at the California study site (CA) and Iowa study site (IA) could be reliably estimated by regression. Correlations obtained in the CA case indicated that all model parameters could be uniquely estimated by inverse modeling. Although water content at field capacity was highly correlated with bulk density (−0.94), the correlation is less than the threshold for nonuniqueness (0.95, absolute value basis). Additionally, we used truncated singular value decomposition (SVD) at CA to mitigate potential problems with highly correlated and insensitive parameters. Singular value decomposition estimates linear combinations (eigenvectors) of the original process-model parameters. Parameter confidence intervals (CIs) at CA indicated that parameters were reliably estimated with the possible exception of an organic pool transfer coefficient (R45), which had a comparatively wide CI. However, the 95% confidence interval for R45 (0.03–0.35) is mostly within the range of values reported for this parameter. Predictive analysis at CA generated confidence intervals that were compared with independently measured annual water flux (groundwater recharge) and median nitrate concentration in a collocated monitoring well as part of model evaluation. Both the observed recharge (42.3 cm yr −1 ) and nitrate concentration (24.3 mg L −1 ) were within their respective 90% confidence intervals, indicating that overall model error was within acceptable limits.

Book chapter↗

USGS2015

Multimodel analysis of anisotropic diffusive tracer-gas transport in a deep arid unsaturated zone

Gas transport in the unsaturated zone affects contaminant flux and remediation, interpretation of groundwater travel times from atmospheric tracers, and mass budgets of environmentally important gases. Although unsaturated zone transport of gases is commonly treated as dominated by diffusion, the characteristics of transport in deep layered sediments remain uncertain. In this study, we use a multimodel approach to analyze results of a gas-tracer (SF 6 ) test to clarify characteristics of gas transport in deep unsaturated alluvium. Thirty-five separate models with distinct diffusivity structures were calibrated to the tracer-test data and were compared on the basis of Akaike Information Criteria estimates of posterior model probability. Models included analytical and numerical solutions. Analytical models provided estimates of bulk-scale apparent diffusivities at the scale of tens of meters. Numerical models provided information on local-scale diffusivities and feasible lithological features producing the observed tracer breakthrough curves. The combined approaches indicate significant anisotropy of bulk-scale diffusivity, likely associated with high-diffusivity layers. Both approaches indicated that diffusivities in some intervals were greater than expected from standard models relating porosity to diffusivity. High apparent diffusivities and anisotropic diffusivity structures were consistent with previous observations at the study site of rapid lateral transport and limited vertical spreading of gas-phase contaminants. Additional processes such as advective oscillations may be involved. These results indicate that gases in deep, layered unsaturated zone sediments can spread laterally more quickly, and produce higher peak concentrations, than predicted by homogeneous, isotropic diffusion models.

California, Nevada↗

USGS2015

The effects of numerical-model complexity and observation type on estimated porosity values

The relative merits of model complexity and types of observations employed in model calibration are compared. An existing groundwater flow model coupled with an advective transport simulation of the Salt Lake Valley, Utah (USA), is adapted for advective transport, and effective porosity is adjusted until simulated tritium concentrations match concentrations in samples from wells. Two calibration approaches are used: a “complex” highly parameterized porosity field and a “simple” parsimonious model of porosity distribution. The use of an atmospheric tracer (tritium in this case) and apparent ages (from tritium/helium) in model calibration also are discussed. Of the models tested, the complex model (with tritium concentrations and tritium/helium apparent ages) performs best. Although tritium breakthrough curves simulated by complex and simple models are very generally similar, and there is value in the simple model, the complex model is supported by a more realistic porosity distribution and a greater number of estimable parameters. Culling the best quality data did not lead to better calibration, possibly because of processes and aquifer characteristics that are not simulated. Despite many factors that contribute to shortcomings of both the models and the data, useful information is obtained from all the models evaluated. Although any particular prediction of tritium breakthrough may have large errors, overall, the models mimic observed trends.

Utah↗

USGS2015

Rapid removal of nitrobenzene in a three-phase ozone loaded system with gas-liquid-liquid

This study explores the removal rate of nitrobenzene (NB) using a new gas-liquid-liquid (G-L-L) three-phase ozone loaded system consisting of a gaseous ozone, an aqueous solvent phase, and a fluorinated solvent phase (perfluorodecalin, or FDC). The removal rate of NB was quantified in relation to six factors including 1) initial pH, 2) initial NB dosage, 3) gaseous ozone dosage, 4) free radical scavenger, 5) FDC pre-aerated gaseous ozone, and 6) reuse of FDC. The NB removal rate is positively affected by the first three factors. Compared with the conventional gas-liquid (water) (G-L) two-phase ozonation system, the free radical scavenger (tertiary butyl alcohol) has much less influence on the removal rate of NB in the G-L-L system. The FDC loaded ozone acts as an ozone reservoir and serves as the main reactive phase in the G-L-L three-phase system. The reuse of FDC has little influence on the removal rate of NB. These experimental results suggest that the oxidation efficiency of ozonation in the G-L-L three-phase system is better than that in the conventional G-L two-phase system.

Chemical Engineering Communications↗

USGS2015

Peclet number as affected by molecular diffusion controls transient anomalous transport in alluvial aquifer-aquitard complexes

This study evaluates the role of the Peclet number as affected by molecular diffusion in transient anomalous transport, which is one of the major knowledge gaps in anomalous transport, by combining Monte Carlo simulations and stochastic model analysis. Two alluvial settings containing either short- or long-connected hydrofacies are generated and used as media for flow and transport modeling. Numerical experiments show that 1) the Peclet number affects both the duration of the power-law segment of tracer breakthrough curves (BTCs) and the transition rate from anomalous to Fickian transport by determining the solute residence time for a given low-permeability layer, 2) mechanical dispersion has a limited contribution to the anomalous characteristics of late-time transport as compared to molecular diffusion due to an almost negligible velocity in floodplain deposits, and 3) the initial source dimensions only enhance the power-law tail of the BTCs at short travel distances. A tempered stable stochastic (TSS) model is then applied to analyze the modeled transport. Applications show that the time-nonlocal parameters in the TSS model relate to the Peclet number, P e . In particular, the truncation parameter in the TSS model increases nonlinearly with a decrease in P e due to the decrease of the mean residence time, and the capacity coefficient increases with an increase in molecular diffusion which is probably due to the increase in the number of immobile particles. The above numerical experiments and stochastic analysis therefore reveal that the Peclet number as affected by molecular diffusion controls transient anomalous transport in alluvial aquifer–aquitard complexes.

Journal of Contaminant Hydrology↗

USGS2014

Field-scale sulfur hexafluoride tracer experiment to understand long distance gas transport in the deep unsaturated zone

A gas-tracer test in a deep arid unsaturated zone demonstrates that standard estimates of effective diffusivity from sediment properties allow a reasonable first-cut assessment of gas contaminant transport. Apparent anomalies in historic transport behavior at this and other waste disposal sites may result from factors other than nonreactive gas transport properties. A natural gradient SF 6 tracer experiment provided an unprecedented evaluation of long distance gas transport in the deep unsaturated zone (UZ) under controlled (known) conditions. The field-scale gas tracer test in the 110-m-thick UZ was conducted at the U.S. Geological Survey’s Amargosa Desert Research Site (ADRS) in southwestern Nevada. A history of anomalous (theoretically unexpected) contaminant gas transport observed at the ADRS, next to the first commercial low-level radioactive waste disposal facility in the United States, provided motivation for the SF 6 tracer study. Tracer was injected into a deep UZ borehole at depths of 15 and 48 m, and plume migration was observed in a monitoring borehole 9 m away at various depths (0.5–109 m) over the course of 1 yr. Tracer results yielded useful information about gas transport as applicable to the spatial scales of interest for off-site contaminant transport in arid unsaturated zones. Modeling gas diffusion with standard empirical expressions reasonably explained SF 6 plume migration, but tended to underpredict peak concentrations for the field-scale experiment given previously determined porosity information. Despite some discrepancies between observations and model results, rapid SF 6 gas transport commensurate with previous contaminant migration was not observed. The results provide ancillary support for the concept that apparent anomalies in historic transport behavior at the ADRS are the result of factors other than nonreactive gas transport properties or processes currently in effect in the undisturbed UZ.

California, Nevada↗

USGS2014

Accuracy of travel time distribution (TTD) models as affected by TTD complexity, observation errors, and model and tracer selection

Analytical models of the travel time distribution (TTD) from a source area to a sample location are often used to estimate groundwater ages and solute concentration trends. The accuracies of these models are not well known for geologically complex aquifers. In this study, synthetic datasets were used to quantify the accuracy of four analytical TTD models as affected by TTD complexity, observation errors, model selection, and tracer selection. Synthetic TTDs and tracer data were generated from existing numerical models with complex hydrofacies distributions for one public-supply well and 14 monitoring wells in the Central Valley, California. Analytical TTD models were calibrated to synthetic tracer data, and prediction errors were determined for estimates of TTDs and conservative tracer (NO 3 −) concentrations. Analytical models included a new, scale-dependent dispersivity model (SDM) for two-dimensional transport from the watertable to a well, and three other established analytical models. The relative influence of the error sources (TTD complexity, observation error, model selection, and tracer selection) depended on the type of prediction. Geological complexity gave rise to complex TTDs in monitoring wells that strongly affected errors of the estimated TTDs. However, prediction errors for NO3− and median age depended more on tracer concentration errors. The SDM tended to give the most accurate estimates of the vertical velocity and other predictions, although TTD model selection had minor effects overall. Adding tracers improved predictions if the new tracers had different input histories. Studies using TTD models should focus on the factors that most strongly affect the desired predictions.

California↗

USGS2014

Simulating water-quality trends in public-supply wells in transient flow systems

Models need not be complex to be useful. An existing groundwater-flow model of Salt Lake Valley, Utah, was adapted for use with convolution-based advective particle tracking to explain broad spatial trends in dissolved solids. This model supports the hypothesis that water produced from wells is increasingly younger with higher proportions of surface sources as pumping changes in the basin over time. At individual wells, however, predicting specific water-quality changes remains challenging. The influence of pumping-induced transient groundwater flow on changes in mean age and source areas is significant. Mean age and source areas were mapped across the model domain to extend the results from observation wells to the entire aquifer to see where changes in concentrations of dissolved solids are expected to occur. The timing of these changes depends on accurate estimates of groundwater velocity. Calibration to tritium concentrations was used to estimate effective porosity and improve correlation between source area changes, age changes, and measured dissolved solids trends. Uncertainty in the model is due in part to spatial and temporal variations in tracer inputs, estimated tracer transport parameters, and in pumping stresses at sampling points. For tracers such as tritium, the presence of two-limbed input curves can be problematic because a single concentration can be associated with multiple disparate travel times. These shortcomings can be ameliorated by adding hydrologic and geologic detail to the model and by adding additional calibration data. However, the Salt Lake Valley model is useful even without such small-scale detail.

Utah↗

USGS2014

Decadal surface water quality trends under variable climate, land use, and hydrogeochemical setting in Iowa, USA

Understanding how nitrogen fluxes respond to changes in agriculture and climate is important for improving water quality. In the midwestern United States, expansion of corn cropping for ethanol production led to increasing N application rates in the 2000s during a period of extreme variability of annual precipitation. To examine the effects of these changes, surface water quality was analyzed in 10 major Iowa Rivers. Several decades of concentration and flow data were analyzed with a statistical method that provides internally consistent estimates of the concentration history and reveals flow-normalized trends that are independent of year-to-year streamflow variations. Flow-normalized concentrations of nitrate+nitrite-N decreased from 2000 to 2012 in all basins. To evaluate effects of annual discharge and N loading on these trends, multiple conceptual models were developed and calibrated to flow-weighted annual concentrations. The recent declining concentration trends can be attributed to both very high and very low discharge in the 2000s and to the long (e.g., 8 year) subsurface residence times in some basins. Dilution of N and depletion of stored N occurs in years with high discharge. Reduced N transport and increased N storage occurs in low-discharge years. Central Iowa basins showed the greatest reduction in flow-normalized concentrations, likely because of smaller storage volumes and shorter residence times. Effects of land-use changes on the water quality of major Iowa Rivers may not be noticeable for years or decades in peripheral basins of Iowa, and may be obscured in the central basins where extreme flows strongly affect annual concentration trends.

Iowa↗

USGS2014

Linking aquifer spatial properties and non-Fickian transport in mobile-immobile like alluvial settings

Time-nonlocal transport models can describe non-Fickian diffusion observed in geological media, but the physical meaning of parameters can be ambiguous, and most applications are limited to curve-fitting. This study explores methods for predicting the parameters of a temporally tempered Lévy motion (TTLM) model for transient sub-diffusion in mobile–immobile like alluvial settings represented by high-resolution hydrofacies models. The TTLM model is a concise multi-rate mass transfer (MRMT) model that describes a linear mass transfer process where the transfer kinetics and late-time transport behavior are controlled by properties of the host medium, especially the immobile domain. The intrinsic connection between the MRMT and TTLM models helps to estimate the main time-nonlocal parameters in the TTLM model (which are the time scale index, the capacity coefficient, and the truncation parameter) either semi-analytically or empirically from the measurable aquifer properties. Further applications show that the TTLM model captures the observed solute snapshots, the breakthrough curves, and the spatial moments of plumes up to the fourth order. Most importantly, the a priori estimation of the time-nonlocal parameters outside of any breakthrough fitting procedure provides a reliable “blind” prediction of the late-time dynamics of subdiffusion observed in a spectrum of alluvial settings. Predictability of the time-nonlocal parameters may be due to the fact that the late-time subdiffusion is not affected by the exact location of each immobile zone, but rather is controlled by the time spent in immobile blocks surrounding the pathway of solute particles. Results also show that the effective dispersion coefficient has to be fitted due to the scale effect of transport, and the mean velocity can differ from local measurements or volume averages. The link between medium heterogeneity and time-nonlocal parameters will help to improve model predictability for non-Fickian transport in alluvial settings.

Journal of Hydrology↗

USGS2013

Effect of correlated observation error on parameters, predictions, and uncertainty

Correlations among observation errors are typically omitted when calculating observation weights for model calibration by inverse methods. We explore the effects of omitting these correlations on estimates of parameters, predictions, and uncertainties. First, we develop a new analytical expression for the difference in parameter variance estimated with and without error correlations for a simple one-parameter two-observation inverse model. Results indicate that omitting error correlations from both the weight matrix and the variance calculation can either increase or decrease the parameter variance, depending on the values of error correlation (ρ) and the ratio of dimensionless scaled sensitivities (r dss ). For small ρ, the difference in variance is always small, but for large ρ, the difference varies widely depending on the sign and magnitude of r dss . Next, we consider a groundwater reactive transport model of denitrification with four parameters and correlated geochemical observation errors that are computed by an error-propagation approach that is new for hydrogeologic studies. We compare parameter estimates, predictions, and uncertainties obtained with and without the error correlations. Omitting the correlations modestly to substantially changes parameter estimates, and causes both increases and decreases of parameter variances, consistent with the analytical expression. Differences in predictions for the models calibrated with and without error correlations can be greater than parameter differences when both are considered relative to their respective confidence intervals. These results indicate that including observation error correlations in weighting for nonlinear regression can have important effects on parameter estimates, predictions, and their respective uncertainties.

Water Resources Research↗

USGS2013

The impact of medium architecture of alluvial settings on non-Fickian transport

The influence of heterogeneous architecture of alluvial aquifers on non-Fickian transport is explored using the Monte Carlo approach. More than two thousand high-resolution hydrofacies models representing seven groups of alluvial settings are built to test the effects of varying facies proportions, mean length and its anisotropy ratio, juxtapositional tendencies, and sub-facies heterogeneity. Results show that the volumetric fraction (P(Z)) of floodplain layers classified by their thicknesses Z controls the non-Fickian tailing of tracer transport at late times. A simple quantitative relationship S BTC ≈S P(Z) /2-1 is built based on a multi-rate mass transfer analysis, where S BTC is the slope of the power-law portion of tracer breakthrough curve, and S P(Z) denotes the slope of the power-law portion of the distribution of P(Z) which can be measured, e.g., in core logs. At early times, the mean length of hydrofacies affects the non-Fickian tailing by controlling the channeling of flow in high-permeability non-floodplain materials and the sequestration in surrounding low-permeability floodplain layers. The competition between channeling and sequestration generates complex pre-asymptotic features, including sublinear growth of plume mean displacement, superlinear growth of plume variance, and skewed mass distribution. Those observations of the influence of medium heterogeneity on tracer transport at early and late times may lead to development of nonlocal transport models that can be parameterized using measurable aquifer characteristics.

Advances in Water Resources↗