Bayesian evaluation of groundwater age distribution using radioactive tracers and anthropogenic chemicals

pre-printThe development of a Bayesian modeling approach for estimation of the age distribution of groundwater using radioactive isotopes and anthropogenic chemicals is described. The model considers the uncertainties associated with the measured tracer concentrations as well as the parameters affecting the concentration of tracers in the groundwater, and it provides the posterior probability densities of the parameters defining the groundwater age distribution using a Markov chain Monte Carlo method. The model also incorporates the effect of dissolution of aquifer minerals on diluting the 14C signature and the uncertainties associated with this process on the inferred age distribution parameters. Two demonstration modeling cases have been performed. First, the method was applied to simulated tracer concentrations at a discharge point of a hypothetical 2-D vertical aquifer with two recharge zones, leading to a mixed groundwater age distribution under different presumed uncertainties. When the error variance of the observed tracer concentrations is considered unknown, the method can estimate the parameters of the fitted exponential-lognormal distribution with a relatively narrow credible interval when five hypothetical samples are assumed to be collected at the discharge point. However, when a single sample is assumed, the credible intervals become wider, and credible estimations of the parameters are not obtained. Second, the method was applied to the data collected at La Selva Biological Station in Costa Rica. In this demonstration application, nine different forms of presumed groundwater age distributions have been considered, including four single forms and five mixed forms, assuming the groundwater consists of distinct young and old fractions. For the medium geometrical standard deviation dc,i = 1.41, the model estimates a young groundwater age of between 0 and 350 years, with the largest odds being given to a mean age of approximately 100 years, and a fraction of young groundwater of between 15% to roughly 60%, with the largest odds for 30%. However, the method cannot definitively rule out larger fractions of young groundwater. The model provides a much more uncertain estimation of the age of old groundwater, with a credible interval of between 20,000 to 200,000 years

Residence time distributions for hydrologic systems: Mechanistic foundations and steady-state analytical solutions

International audienceThis review presents the physical mechanisms generating residence time distributions (RTDs) in hydrologic systems with a focus on steady-state analytical solutions. Steady-state approximations of the RTD in hydrologic systems have seen widespread use over the last half-century because they provide a convenient, simplified modeling framework for a wide range of problems. The concept of an RTD is useful anytime that characterization of the timescales of flow and transport in hydrologic systems is important, which includes topics like water quality, water resource management, contaminant transport, and ecosystem preservation. Analytical solutions are often adopted as a model of the RTD and a broad spectrum of models from many disciplines has been applied. Although these solutions are typically reduced in dimensionality and limited in complexity, their ease of use makes them preferred tools, specifically for the interpretation of tracer data. Our review begins with the mechanistic basis for the governing equations, highlighting the physics for generating a RTD, and a catalog of analytical solutions follows. This catalog explains the geometry, boundary conditions and physical aspects of the hydrologic systems, as well as the sampling conditions, that altogether give rise to specific RTDs. The similarities between models are noted, as are the appropriate conditions for their applicability. The presentation of simple solutions is followed by a presentation of more complicated analytical models for RTDs, including serial and parallel combinations, lagged systems, and non-Fickian models. The conditions for the appropriate use of analytical solutions are discussed, and we close with some thoughts on potential applications, alternative approaches, and future directions for modeling hydrologic residence time

A Stochastic Simulation Procedure for Selecting Herbicides with Minimum Environmental Impact

A mathematical environmental transport model of roadside applied herbicides at the site scale (∼100 m) was stochastically applied using a Monte-Carlo technique to simulate the concentrations of 33 herbicides in stormwater runoff. Field surveys, laboratory sorption data, and literature data were used to generate probability distribution functions for model input parameters to allow extrapolation of the model to the regional scale. Predicted concentrations were compared to EPA acute toxicity end points for aquatic organisms to determine the frequency of potentially toxic outcomes. Results are presented for three geographical regions in California and two highway geometries. For a given herbicide, frequencies of potential toxicity (FPTs) varied by as much as 36% between region and highway type. Of 33 herbicides modeled, 16 exhibit average FPTs greater than 50% at the maximum herbicide application rate, while 20 exhibit average FPTs less than 50% at the minimum herbicide application rate. Based on these FPTs and current usage statistics, selected herbicides were determined to be more environmentally acceptable than others in terms of acute toxicity and other documented environmental effects. This analysis creates a decision support system that can be used to evaluate the relative water quality impacts of varied herbicide application practices

Stochastic And Deterministic Parameter Estimation Of Coupled Bacteria-Sediment Fate And Transport In Streams

E. Coli is widely used as an indicator organism to assess the risk of pathogenic bacteria in water bodies. Due to their strong association with suspended and bed sediments, the fate and transport of micro-organisms in water bodies is strongly controlled by sediment dynamics. It has been shown that bed sediments can contain orders of magnitude larger pathogen concentration than the water column and these sediment-associated bacteria can be released into the water column as a result of high flow velocities that cause sediment resuspension. In this presentation parameter estimation of a mechanistic model of bacteria-sediment interaction using a deterministic method through a hybrid genetic algorithm and also stochastically through Makov-Chain Monte Carlo (MCMC) approach will be presented. The physically-based model considers the advective-dispersive transport of sediments as well as both free-floating and sediment-associated bacteria in the water column and also the fate and transport of bacteria in the bed sediments. The bed sediments are treated as a distributed system which allows modeling the evolution of the vertical distribution of bacteria as a result of sedimentation, resuspension, diffusion, and bioturbation in the sediments. The model is applied to sediment and E. coli concentration data collected during a high flow event in a small stream historically receiving agricultural runoff. The genetic algorithm and MCMC method are used to estimate the likeliest values as well as the joint probability density functions of model parameters including sediment deposition and erosion rates, critical shear stress for deposition and erosion, attachment and detachment rate constants of E. coli to/from sediments and also the effective diffusion coefficients of E. coli in the bed sediments. The uncertainties associated with the estimated parameters are quantified via the MCMC approach and the correlation between the posterior distribution of parameters have been used to assess the model adequacy and parsimony

Evaluating Management Decisions to Reduce Environmental Risk of Roadside-Applied Herbicides

Management decisions concerning the spraying of herbicides on highway roadsides are evaluated on the basis of their impact on resulting environmental risk. A mathematical transport model was previously applied to the State of California with a Monte Carlo technique, and in this study the results are manipulated to evaluate the risk reduction that results from restricting herbicide application on the basis of site characteristics or changing other application practices. Results show that eliminating herbicide applications where the slope of the grass adjacent to the highway is greater than 30° has little or no effect on risk. Eliminating application where the width of the grass adjacent to the highway is less than 2 m or where soil organic carbon content is less than 0.5% can lead to significant reductions in environmental risk for certain herbicides. Additionally, limiting the width of the spray zone and applying the minimum manufacturer-suggested application rate reduce the risk to aquatic ecosystems. Applying at the minimum rate has the greatest potential to decrease risk. Results of this study show that management decisions can have a significant effect on limiting herbicide runoff risks to aquatic ecosystems. Decision makers would have to weigh costs of alternatives to herbicide spraying for controlling roadside vegetation against the environmental risk reductions

High-temporal resolution fluvial sediment source fingerprinting with uncertainty: a Bayesian approach

This contribution addresses two developing areas of sediment fingerprinting research. Specifically, how to improve the temporal resolution of source apportionment estimates whilst minimizing analytical costs and, secondly, how to consistently quantify all perceived uncertainties associated with the sediment mixing model procedure. This first matter is tackled by using direct X-ray fluorescence spectroscopy (XRFS) and diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) analyses of suspended particulate matter (SPM) covered filter papers in conjunction with automatic water samplers. This method enables SPM geochemistry to be quickly, accurately, inexpensively and non-destructively monitored at high-temporal resolution throughout the progression of numerous precipitation events. We then employed a Bayesian mixing model procedure to provide full characterization of spatial geochemical variability, instrument precision and residual error to yield a realistic and coherent assessment of the uncertainties associated with source apportionment estimates. Applying these methods to SPM data from the River Wensum catchment, UK, we have been able to apportion, with uncertainty, sediment contributions from eroding arable topsoils, damaged road verges and combined subsurface channel bank and agricultural field drain sources at 60- and 120-minute resolution for the duration of five precipitation events. The results presented here demonstrate how combining Bayesian mixing models with the direct spectroscopic analysis of SPM-covered filter papers can produce high-temporal resolution source apportionment estimates that can assist with the appropriate targeting of sediment pollution mitigation measures at a catchment level

Sensitivity of fluvial sediment source apportionment to mixing model assumptions: A Bayesian model comparison

Mixing models have become increasingly common tools for apportioning fluvial sediment load to various sediment sources across catchments using a wide variety of Bayesian and frequentist modeling approaches. In this study, we demonstrate how different model setups can impact upon resulting source apportionment estimates in a Bayesian framework via a one-factor-at-a-time (OFAT) sensitivity analysis. We formulate 13 versions of a mixing model, each with different error assumptions and model structural choices, and apply them to sediment geochemistry data from the River Blackwater, Norfolk, UK, to apportion suspended particulate matter (SPM) contributions from three sources (arable topsoils, road verges, and subsurface material) under base flow conditions between August 2012 and August 2013. Whilst all 13 models estimate subsurface sources to be the largest contributor of SPM (median ∼76%), comparison of apportionment estimates reveal varying degrees of sensitivity to changing priors, inclusion of covariance terms, incorporation of time-variant distributions, and methods of proportion characterization. We also demonstrate differences in apportionment results between a full and an empirical Bayesian setup, and between a Bayesian and a frequentist optimization approach. This OFAT sensitivity analysis reveals that mixing model structural choices and error assumptions can significantly impact upon sediment source apportionment results, with estimated median contributions in this study varying by up to 21% between model versions. Users of mixing models are therefore strongly advised to carefully consider and justify their choice of model structure prior to conducting sediment source apportionment investigations

An extended Bayesian sediment fingerprinting mixing model for the full Bayes treatment of geochemical uncertainties

Recent advances in sediment fingerprinting research have seen Bayesian mixing models being increasingly employed as an effective method to coherently translate component uncertainties into source apportionment results. Here, we advance earlier work by presenting an extended Bayesian mixing model capable of providing a full Bayes treatment of geochemical uncertainties. The performance of the extended full Bayes model was assessed against the equivalent empirical Bayes model and traditional frequentist optimisation. The performance of models coded in different Bayesian software (‘JAGS’ and ‘Stan’) was also evaluated, alongside an assessment of model sensitivity to reduced source representativeness and non-conservative fingerprint behaviour. Results revealed comparable accuracy and precision for the full and empirical Bayes models across both synthetic and real sediment geochemistry datasets, demonstrating that the empirical treatment of source data here represents a close approximation of the full Bayes treatment. Contrasts in the performance of models coded in JAGS and Stan revealed that the choice of software employed can impact significantly upon source apportionment results. Bayesian models coded in Stan were the least sensitive to both reduced source representativeness and non-conservative fingerprint behaviour, indicating Stan as the preferred software for future Bayesian sediment fingerprinting studies. Whilst the frequentist optimisation generally yielded comparable accuracy to the Bayesian models, uncertainties around apportionment estimates were substantially greater and the frequentist model was less effective at dealing with non-conservative behaviour. Overall, the effective performance of the extended full Bayes mixing model coded in Stan represents a notable advancement in source apportionment modelling relative to previous approaches. Both the mixing model and the software comparisons presented here should provide useful guidelines for future sediment fingerprinting studies

Continuum-based models and concepts for the transport of nanoparticles in saturated porous media: A state-of-the-science review

Environmental applications of nanoparticles (NP) increasingly result in widespread NP distribution within porous media where they are subject to various concurrent transport mechanisms including irreversible deposition, attachment/detachment (equilibrium or kinetic), agglomeration, physical straining, site-blocking, ripening, and size exclusion. Fundamental research in NP transport is typically conducted at small scale, and theoretical mechanistic modeling of particle transport in porous media faces challenges when considering the simultaneous effects of transport mechanisms. Continuum modeling approaches, in contrast, are scalable across various scales ranging from column experiments to aquifer. They have also been able to successfully describe the simultaneous occurrence of various transport mechanisms of NP in porous media such as blocking/straining or agglomeration/deposition/detachment. However, the diversity of model equations developed by different authors and the lack of effective approaches for their validation present obstacles to the successful robust application of these models for describing or predicting NP transport phenomena. This review aims to describe consistently all the important NP transport mechanisms along with their representative mathematical continuum models as found in the current scientific literature. Detailed characterizations of each transport phenomenon in regards to their manifestation in the column experiment outcomes, i.e., breakthrough curve (BTC) and residual concentration profile (RCP), are presented to facilitate future interpretations of BTCs and RCPs. The review highlights two NP transport mechanisms, agglomeration and size exclusion, which are potentially of great importance in controlling the fate and transport of NP in the subsurface media yet have been widely neglected in many existing modeling studies. A critical limitation of the continuum modeling approach is the number of parameters used upon application to larger scales and when a series of transport mechanisms are involved. We investigate the use of simplifying assumptions, such as the equilibrium assumption, in modeling the attachment/detachment mechanisms within a continuum modelling framework. While acknowledging criticisms about the use of this assumption for NP deposition on a mechanistic (process) basis, we found that its use as a description of dynamic deposition behavior in a continuum model yields broadly similar results to those arising from a kinetic model. Furthermore, we show that in two dimensional (2-D) continuum models the modeling efficiency based on the Akaike information criterion (AIC) is enhanced for equilibrium vs kinetic with no significant reduction in model performance. This is because fewer parameters are needed for the equilibrium model compared to the kinetic model. Two major transport regimes are identified in the transport of NP within porous media. The first regime is characterized by higher particle-surface attachment affinity than particle-particle attachment affinity, and operative transport mechanisms of physicochemical filtration, blocking, and physical retention. The second regime is characterized by the domination of particle-particle attachment tendency over particle-surface affinity. In this regime although physicochemical filtration as well as straining may still be operative, ripening is predominant together with agglomeration and further subsequent retention. In both regimes careful assessment of NP fate and transport is necessary since certain combinations of concurrent transport phenomena leading to large migration distances are possible in either case