On the formation of multiple local peaks in breakthrough curves

The analysis of breakthrough curves (BTCs) is of interest in hydrogeology as a way to parameterize and explain processes related to anomalous transport. Classical BTCs assume the presence of a single peak in the curve, where the location and size of the peak and the slope of the receding limb has been of particular interest. As more information is incorporated into BTCs (for example, with high-frequency data collection, supercomputing efforts), it is likely that classical definitions of BTC shapes will no longer be adequate descriptors for contaminant transport problems. We contend that individual BTCs may display multiple local peaks depending on the hydrogeologic conditions and the solute travel distance. In such cases, classical definitions should be reconsidered. In this work, the presence of local peaks in BTCs is quantified from high-resolution numerical simulations in synthetic fields with a particle tracking technique and a kernel density estimator to avoid either overly jagged or smoothed curves that could mask the results. Individual BTCs from three-dimensional heterogeneous hydraulic conductivity fields with varying combinations of statistical anisotropy, heterogeneity models, and local dispersivity are assessed as a function of travel distance. The number of local peaks, their corresponding slopes, and a transport connectivity index are shown to strongly depend on statistical anisotropy and travel distance. Results show that the choice of heterogeneity model also affects the frequency of local peaks, but the slope is less sensitive to model selection. We also discuss how solute shearing and rerouting can be determined from local peak quantification

Improving the accuracy of risk prediction from particle-based breakthrough curves reconstructed with kernel density estimators

While particle tracking techniques are often used in risk frameworks, the number of particles needed to properly derive risk metrics such as average concentration for a given exposure duration is often unknown. If too few particles are used, error may propagate into the risk estimate. In this work, we provide a less error‐prone methodology for the direct reconstruction of exposure duration averaged concentration versus time breakthrough curves from particle arrival times at a compliance surface. The approach is based on obtaining a suboptimal kernel density estimator that is applied to the sampled particle arrival times. The corresponding estimates of risk metrics obtained with this method largely outperform those by means of traditional methods (reconstruction of the breakthrough curve followed by the integration of concentration in time over the exposure duration). This is particularly true when the number of particles used in the numerical simulation is small ( 105), and for small exposure times. Percent error in the peak of averaged breakthrough curves is approximately zero for all scenarios and all methods tested when the number of particles is 105. Our results illustrate that obtaining a representative average exposure concentration is reliant on the information contained in each individual tracked particle, more so when the number of particles is small. They further illustrate the usefulness of defining problem‐specific kernel density estimators to properly reconstruct the observables of interest in a particle tracking framework without relying on the use of an extremely large number of particles

Investigating Mountain Watershed Headwater‐To‐Groundwater Connections, Water Sources, and Storage Selection Behavior With Dynamic‐Flux Particle Tracking

Climate change will impact mountain watershed streamflow both directly—with changing precipitation amounts and variability—and indirectly—through temperature shifts altering snowpack, melt, and evapotranspiration. To understand how these complex processes will affect ecosystem functioning and water resources, we need tools to distinguish connections between water sources (rain/snowmelt), groundwater storage, and exit fluxes (streamflow/evapotranspiration), and to determine how these connections change seasonally and as climate shifts. Here, we develop novel watershed-scale approaches to understand water source, storage, and exit flux connections using a dynamic-flux particle tracking model (EcoSLIM) applied in California's Cosumnes Watershed, which connects the Sierra Nevada and Central Valley. This work develops new visualizations and applications to provide mechanistic understanding that underpins the interpretation of isotopic field data at watershed scales to distinguish sources, flow paths, residence times, and storage selection. In our simulations, streamflow comes primarily from snow-derived water while evapotranspiration generally comes from rain. Most streamflow starts above 1,000 m while evapotranspiration is sourced relatively evenly across the watershed and is generally younger than streamflow. Modeled streamflow consists primarily of water sourced from precipitation in the previous 5 years but before the current water year, while ET consists primarily of water from precipitation in the current water year. ET, and to a lesser extent streamflow, are both younger than water in groundwater storage. However, snowmelt-derived streamflow preferentially discharges older water from snow-derived storage. Dynamic-flux particle tracking and new approaches presented here enable novel model-tracer comparisons in large-scale watersheds to better understand watershed behavior in a changing climate

Improving the accuracy of risk prediction from particle-based breakthrough curves reconstructed with kernel density estimators

An edited version of this paper was published by AGU. Copyright (2015) American Geophysical Union.While particle tracking techniques are often used in risk frameworks, the number of particles needed to properly derive risk metrics such as average concentration for a given exposure duration is often unknown. If too few particles are used, error may propagate into the risk estimate. In this work, we provide a less error-prone methodology for the direct reconstruction of exposure duration averaged concentration versus time breakthrough curves from particle arrival times at a compliance surface. The approach is based on obtaining a suboptimal kernel density estimator that is applied to the sampled particle arrival times. The corresponding estimates of risk metrics obtained with this method largely outperform those by means of traditional methods (reconstruction of the breakthrough curve followed by the integration of concentration in time over the exposure duration). This is particularly true when the number of particles used in the numerical simulation is small (<105), and for small exposure times. Percent error in the peak of averaged breakthrough curves is approximately zero for all scenarios and all methods tested when the number of particles is 10^5. Our results illustrate that obtaining a representative average exposure concentration is reliant on the information contained in each individual tracked particle, more so when the number of particles is small. They further illustrate the usefulness of defining problem-specific kernel density estimators to properly reconstruct the observables of interest in a particle tracking framework without relying on the use of an extremely large number of particles.Peer ReviewedPostprint (published version

On the similarity of hillslope hydrologic function: a clustering approach based on groundwater changes

Hillslope similarity is an active topic in hydrology because of its importance in improving our understanding of hydrologic processes and enabling comparisons and paired studies. In this study, we propose a holistic bottom-up hillslope clustering based on a region's integrative hydrodynamic response quantified by the seasonal changes in groundwater levels ΔP. The main advantage of the ΔP clustering is its ability to capture recharge and discharge processes. We test the performance of the ΔP clustering by comparing it to seven other common hillslope clustering approaches. These include clustering approaches based on the aridity index, topographic wetness index, elevation, land cover, and machine-learning that jointly integrate multiple data. We assess the ability of these clustering approaches to identify and categorize hillslopes with similar static characteristics, hydroclimate, land surface processes, and subsurface dynamics in a mountainous watershed – the East River – located in the headwaters of the Upper Colorado River Basin. The ΔP clustering performs very well in identifying hillslopes with six out of the nine characteristics studied. The variability among clusters as quantified by the coefficient of variation (0.2) is less in the ΔP and the machine learning approaches than in the others (&gt; 0.3 for TWI, elevation, and land cover). We further demonstrate the robustness of the ΔP clustering by testing its ability to predict hillslope responses to wet and dry hydrologic conditions, of which it performs well when based on average conditions.</p

Hysteresis Patterns of Watershed Nitrogen Retention and Loss Over the Past 50 years in United States Hydrological Basins

Patterns of watershed nitrogen (N) retention and loss are shaped by how watershed biogeochemical processes retain, biogeochemically transform, and lose incoming atmospheric deposition of N. Loss patterns represented by concentration, discharge, and their associated stream exports are important indicators of integrated watershed N retention behaviors. We examined continental United States (CONUS) scale N deposition (e.g., wet and dry atmospheric deposition), vegetation trends, and stream trends as potential indicators of watershed N-saturation and retention conditions, and how watershed N retention and losses vary over space and time. By synthesizing changes and modalities in watershed nitrogen loss patterns based on stream data from 2200 U.S. watersheds over a 50 years record, our work revealed two patterns of watershed N-retention and loss. One was a hysteresis pattern that reflects the integrated influence of hydrology, atmospheric inputs, land-use, stream temperature, elevation, and vegetation. The other pattern was a one-way transition to a new state. We found that regions with increasing atmospheric deposition and increasing vegetation health/biomass patterns have the highest N-retention capacity, become increasingly N-saturated over time, and are associated with the strongest declines in stream N exports—a pattern, that is, consistent across all land cover categories. We provide a conceptual model, validated at an unprecedented scale across the CONUS that links instream nitrogen signals to upstream mechanistic landscape processes. Our work can aid in the future interpretation of in-stream concentrations of DOC and DIN as indicators of watershed N-retention status and integrators of watershed hydrobiogeochemical processes

On the formation of multiple local peaks in breakthrough curves

The analysis of breakthrough curves (BTCs) is of interest in hydrogeology as a way to parameterize and explain processes related to anomalous transport. Classical BTCs assume the presence of a single peak in the curve, where the location and size of the peak and the slope of the receding limb has been of particular interest. As more information is incorporated into BTCs (for example, with high-frequency data collection, supercomputing efforts), it is likely that classical definitions of BTC shapes will no longer be adequate descriptors for contaminant transport problems. We contend that individual BTCs may display multiple local peaks depending on the hydrogeologic conditions and the solute travel distance. In such cases, classical definitions should be reconsidered. In this work, the presence of local peaks in BTCs is quantified from high-resolution numerical simulations in synthetic fields with a particle tracking technique and a kernel density estimator to avoid either overly jagged or smoothed curves that could mask the results. Individual BTCs from three-dimensional heterogeneous hydraulic conductivity fields with varying combinations of statistical anisotropy, heterogeneity models, and local dispersivity are assessed as a function of travel distance. The number of local peaks, their corresponding slopes, and a transport connectivity index are shown to strongly depend on statistical anisotropy and travel distance. Results show that the choice of heterogeneity model also affects the frequency of local peaks, but the slope is less sensitive to model selection. We also discuss how solute shearing and rerouting can be determined from local peak quantification.Peer ReviewedPostprint (published version

Integrated modeling of CO2 storage and leakage scenarios including transitions between super- and subcritical conditions, and phase change between liquid and gaseous CO2

Storage of CO{sub 2} in saline aquifers is intended to be at supercritical pressure and temperature conditions, but CO{sub 2} leaking from a geologic storage reservoir and migrating toward the land surface (through faults, fractures, or improperly abandoned wells) would reach subcritical conditions at depths shallower than 500-750 m. At these and shallower depths, subcritical CO{sub 2} can form two-phase mixtures of liquid and gaseous CO{sub 2}, with significant latent heat effects during boiling and condensation. Additional strongly non-isothermal effects can arise from decompression of gas-like subcritical CO{sub 2}, the so-called Joule-Thomson effect. Integrated modeling of CO{sub 2} storage and leakage requires the ability to model non-isothermal flows of brine and CO{sub 2} at conditions that range from supercritical to subcritical, including three-phase flow of aqueous phase, and both liquid and gaseous CO{sub 2}. In this paper, we describe and demonstrate comprehensive simulation capabilities that can cope with all possible phase conditions in brine-CO{sub 2} systems. Our model formulation includes: (1) an accurate description of thermophysical properties of aqueous and CO{sub 2}-rich phases as functions of temperature, pressure, salinity and CO{sub 2} content, including the mutual dissolution of CO{sub 2} and H{sub 2}O; (2) transitions between super- and subcritical conditions, including phase change between liquid and gaseous CO{sub 2}; (3) one-, two-, and three-phase flow of brine-CO{sub 2} mixtures, including heat flow; (4) non-isothermal effects associated with phase change, mutual dissolution of CO{sub 2} and water, and (de-) compression effects; and (5) the effects of dissolved NaCl, and the possibility of precipitating solid halite, with associated porosity and permeability change. Applications to specific leakage scenarios demonstrate that the peculiar thermophysical properties of CO{sub 2} provide a potential for positive as well as negative feedbacks on leakage rates, with a combination of self-enhancing and self-limiting effects. Lower viscosity and density of CO{sub 2} as compared to aqueous fluids provides a potential for self-enhancing effects during leakage, while strong cooling effects from liquid CO{sub 2} boiling into gas, and from expansion of gas rising towards the land surface, act to self-limit discharges. Strong interference between fluid phases under three-phase conditions (aqueous - liquid CO{sub 2} - gaseous CO{sub 2}) also tends to reduce CO{sub 2} fluxes. Feedback on different space and time scales can induce non-monotonic behavior of CO{sub 2} flow rates

The COACH risk engine: a multistate model for predicting survival and hospitalization in patients with heart failure

Aims: Several models for predicting the prognosis of heart failure (HF) patients have been developed, but all of them focus on a single outcome variable, such as all-cause mortality. The purpose of this study was to develop a multistate model for simultaneously predicting survival and HF-related hospitalization in patients discharged alive from hospital after recovery from acute HF. &lt;p/&gt;Methods and results: The model was derived in the COACH (Coordinating Study Evaluating Outcomes of Advising and Counseling in Heart Failure) cohort, a multicentre, randomized controlled trial in which 1023 patients were enrolled after hospitalization because of HF. External validation was attained with the FINN-AKVA (Finish Acute Heart Failure Study) cohort, a prospective, multicentre study with 620 patients hospitalized due to acute HF. The observed vs. predicted 18-month survival was 72.1% vs. 72.3% in the derivation cohort and 71.4% vs. 71.2% in the validation cohort. The corresponding values of the c statistic were 0.733 [95% confidence interval (CI) 0.705–0.761] and 0.702 (95% CI 0.663–0.744), respectively. The model's accuracy in predicting HF hospitalization was excellent, with predicted values that closely resembled the values observed in the derivation cohort. &lt;p/&gt;Conclusion: The COACH risk engine accurately predicted survival and various measures of recurrent hospitalization in (acute) HF patients. It may therefore become a valuable tool in improving and personalizing patient care and optimizing the use of scarce healthcare resources

Primary weathering rates, water transit times, and concentration-discharge relations:a theoretical analysis for the critical zone

The permeability architecture of the critical zone exerts a major influence on the hydrogeochemistry of the critical zone. Water flow path dynamics drive the spatiotemporal pattern of geochemical evolution and resulting streamflow concentration-discharge (C-Q) relation, but these flow paths are complex and difficult to map quantitatively. Here we couple a new integrated flow and particle tracking transport model with a general reversible Transition State Theory style dissolution rate law to explore theoretically how C-Q relations and concentration in the critical zone respond to decline in saturated hydraulic conductivity (K-s) with soil depth. We do this for a range of flow rates and mineral reaction kinetics. Our results show that for minerals with a high ratio of equilibrium concentration (C-eq) to intrinsic weathering rate (R-max), vertical heterogeneity in K-s enhances the gradient of weathering-derived solute concentration in the critical zone and strengthens the inverse stream C-Q relation. As C-eq/R-max decreases, the spatial distribution of concentration in the critical zone becomes more uniform for a wide range of flow rates, and stream C-Q relation approaches chemostatic behavior, regardless of the degree of vertical heterogeneity in K-s. These findings suggest that the transport-controlled mechanisms in the hillslope can lead to chemostatic C-Q relations in the stream while the hillslope surface reaction-controlled mechanisms are associated with an inverse stream C-Q relation. In addition, as C-eq/R-max decreases, the concentration in the critical zone and stream become less dependent on groundwater age (or transit time)