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. © 2015 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd.     

Aeolian sediment fingerprinting using a Bayesian mixing model

Identifying sand provenance in depositional aeolian environments (e.g. dunefields) can elucidate sediment pathways and fluxes, and inform potential land management strategies where windblown sand and dust is a hazard to health and infrastructure. However, the complexity of these pathways typically makes this a challenging proposition, and uncertainties on the composition of mixed‐source sediments are often not reported. This study demonstrates that a quantitative fingerprinting method within the Bayesian Markov Chain Monte Carlo (MCMC) framework offers great potential for exploring the provenance and uncertainties associated with aeolian sands. Eight samples were taken from dunes of the small (~58 km²) Ashkzar erg, central Iran, and 49 from three distinct potential sediment sources in the surrounding area. These were analyzed for 61 tracers including 53 geochemical elements (trace, major and rare earth elements (REE)) and eight REE ratios. Kruskal–Wallis H‐tests and stepwise discriminant function analysis (DFA) allowed the identification of an optimum composite fingerprint based on six tracers (Rb, Sr, ⁸⁷Sr, (La/Yb)_n, Ga and δCe), and a Bayesian mixing model was applied to derive the source apportionment estimates within an uncertainty framework. There is substantial variation in the uncertainties in the fingerprinting results, with some samples yielding clear discrimination of components, and some with less clear fingerprints. Quaternary terraces and fans contribute the largest component to the dunes, but they are also the most extensive surrounding unit; clay flats and marls, however, contribute out of proportion to their small outcrop extent. The successful application of these methods to aeolian sediment deposits demonstrates their potential for providing quantitative estimates of aeolian sediment provenances in other mixed‐source arid settings, and may prove especially beneficial where sediment is derived from multiple sources, or where other methods of provenance (e.g. detrital zircon U–Pb dating) are not possible due to mineralogical constraints. Copyright © 2017 John Wiley & Sons, Ltd.     

Storm event sediment fingerprinting for temporal and spatial sediment source tracing

Sediment fingerprinting has been widely used to distinguish discrete sediment sources; however, application to intra-storm sediment source variability has received relatively little focus despite the benefit being long recognized. In this investigation, sediment fingerprinting was applied to a 53-hr storm event sampled hourly to determine sediment source dynamics throughout the event. Sediment sources were differentiated using 16 variables, and source contribution determined using Bayesian and Frequentist mixing models for comparison. Both models provided comparable source predictions for the dominant source estimates and the general temporal pattern. The Frequentist model appeared to exhibit some unreliable values coinciding with low GOF and attributed to inherent model structure. The Bayesian model showed higher uncertainty, likely due to the “process error” utilized associated with single sample mixtures. High variability in sediment source contribution was observed between hourly time steps; however, local smoothing reveals temporal trends during the event. A higher average proportion of mudstone is found in the falling limb (0.544) compared with the rising limb (0.464), and the reverse is observed for mountain range (0.218 vs. 0.283) and unconsolidated (0.073 vs. 0.055). In the initial hours of the storm, mudstone source contribution significantly drops, whereas mountain range and unconsolidated contributions peak. The SSC-Q clockwise hysteresis indicates proximal sediment sources, suggesting the mudstone sediment is stored channel sediment and easily entrained. This sediment flushes through, coinciding with a drop as the distal mountain range and unconsolidated sources arrive to peak contribution. The wider Manawatū discharge and sediment load then arrive, delivering increasing levels of mudstone throughout the remainder of the event while mountain range sediment diminishes. Spatial representation of the sediment source contribution was derived from distributing sediment source loads to the spatial extent of the source material according to sub-catchment sediment loads and was weighted according to slope. This provided an effective means to visualize the origin of the sediment and a better spatial interpretation of sediment fingerprinting results, which is typically limited by poor spatial resolution.     

Application of Bayesian model and discriminant function analysis to the estimation of sediment source contributions

Bayesian and discriminant function analysis (DFA) models have recently been used as tools to estimate sediment source contributions. Unlike existing multivariate mixing models, the accuracy of these two models remains unclear. In the current study, four well-distinguished source samples were used to create artificial mixtures to test the performance of Bayesian and DFA models. These models were tested against the Walling-Collins model, a credible model used in estimation of sediment source contributions estimation, as a reference. The artificial mixtures were divided into five groups, with each group consisting of five samples with known source percentages. The relative contributions of the sediment sources to the individual and grouped samples were calculated using each of the models. The mean absolute error (MAE) and standard error of (SE) MAE were used to test the accuracy of each model and the robustness of the optimized solutions. For the individual sediment samples, the calculated source contributions obtained with the Bayesian (MAE = 7.4%, SE = 0.6%) and Walling-Collins (MAE = 7.5%, SE = 0.7%) models produced results which were closest to the actual percentages of the source contributions to the sediment mixtures. The DFA model produced the worst estimates (MAE = 18.4%, SE = 1.4%). For the grouped sediment samples, the Walling-Collins model (MAE = 5.4%) was the best predictor, closely followed by the Bayesian model (MAE = 5.9%). The results obtained with the DFA model were similar to the values for the individual sediment samples, with the accuracy of the source contribution value being the poorest obtained with any of the models (MAE = 18.5%). An increase in sample size improved the accuracies of the Walling-Collins and Bayesian models, but the DFA model produced similarly inaccurate results for both the individual and grouped sediment samples. Generally, the accuracy of the Walling-Collins and Bayesian models was similar (p > 0.01), while there were significant differences (p < 0.01) between the DFA model and the other models. This study demonstrated that the Bayesian model could provide a credible estimation of sediment source contributions and has great practical potential, while the accuracy of the DFA model still requires considerable improvement.     

Sediment fingerprinting in fluvial systems： review of tracers,sediment sources and mixing models

Suspended sediments in fluvial systems originate from a myriad of diffuse and point sources, with the relative contribution from each source varying over time and space. The process of sediment fingerprinting focuses on developing methods that enable discrete sediment sources to be identified from a composite sample of suspended material. This review identifies existing methodological steps for sediment fingerprinting including fluvial and source sampling, and critically compares biogeochemical and physical tracers used in fingerprinting studies. Implications of applying different mixing models to the same source data are explored using data from 41 catchments across Europe, Africa, Australia, Asia, and North and South America. The application of seven commonly used mixing models to two case studies from the US （North Fork Broad River watershed） and France （Bldone watershed） with local and global （genetic algorithm） optimization methods identified all outputs remained in the acceptable range of error defined by the original authors. We propose future sediment fingerprinting studies use models that combine the best explanatory parameters provided by the modified Collins （using correction factors） and Hughes （relying on iterations involving all data, and not only their mean values） models with optimization using genetic algorithms to best predict the relative contribution of sediment sources to fluvial systems.     

The representation of sediment source group tracer distributions in Monte Carlo uncertainty routines for fingerprinting: An analysis of accuracy and precision using data for four contrasting catchments

Previous studies comparing sediment fingerprinting un-mixing models report large differences in their accuracy. The representation of tracer concentrations in source groups is perhaps the largest difference between published studies. However, the importance of decisions concerning the representation of tracer distributions has not been explored explicitly. Accordingly, potential sediment sources in four contrasting catchments were intensively sampled. Virtual sample mixtures were formed using between 10 and 100% of the retrieved samples to simulate sediment mobilization and delivery from subsections of each catchment. Source apportionment used models with a transformed multivariate normal distribution, normal distribution, 25th–75th percentile distribution and a distribution replicating the retrieved source samples. The accuracy and precision of model results were quantified and the reasons for differences were investigated. The 25th–75th percentile distribution produced the lowest mean inaccuracy (8.8%) and imprecision (8.5%), with the Sample Based distribution being next best (11.5%; 9.3%). The transformed multivariate (16.9%; 17.3%) and untransformed normal distributions (16.3%; 20.8%) performed poorly. When only a small proportion of the source samples formed the virtual mixtures, accuracy decreased with the 25th–75th percentile and Sample Based distributions so that when <20% of source samples were used, the actual mixture composition infrequently fell outside of the range of uncertainty shown in un-mixing model outputs. Poor performance was due to combined random Monte Carlo numbers generated for all tracers not being viable for the retrieved source samples. Trialling the use of a 25th–75th percentile distribution alongside alternatives may result in significant improvements in both accuracy and precision of fingerprinting estimates, evaluated using virtual mixtures. Caution should be exercised when using a normal type distribution, without exploration of alternatives, as un-mixing model performance may be unacceptably poor.     

Spatio-temporal suspended sediment fingerprinting under different land management practices

Understanding spatio-temporal suspended sediment dynamics is more important in large watersheds due to the decisive role of local source apportionment in sediment transport and yield. The Talar River with a large mountainous watershed in northern Iran, which plays a vital role in water supply for agriculture and drinking, recently has faced quality degradation. The current study explores the relative contribution of suspended sediment sources using geochemical tracers and fingerprinting techniqu...     

Temporal variations of reservoir sediment sources in a small mountainous catchment in Korea

An understanding of the temporal variation in reservoir sedimentation and identification of the main sources of sediment are necessary for the maintenance of sustainable reservoirs. For this purpose, field measurements, sampling, and fingerprinting of reservoir sediment were undertaken from July 2005 to November 2007. Source fingerprinting of reservoir sediment was conducted using cesium‐137 (¹³⁷Cs). The relative contributions of gully bank and forest road, and forest floor material to reservoir sediment were calculated using a mixing model. Bank and forest road material, estimated to make up about 96% of the reservoir sediment, was the dominant source. Enormous reservoir sedimentation, which amounted to about 60% of the total reservoir sedimentation during the observation period, occurred during a heavy rainstorm with an 80‐year recurrence time. To maintain the sustainability of the reservoir in this study, therefore, temporal and spatial preparation strategies for heavy rainstorms and bank and forest road erosion should be considered. However, spatial information on sediment sources from ¹³⁷Cs fingerprinting is limited. To better identify the sediment sources spatially and temporally, further studies applying soil erosion models and more detailed field studies are needed. Copyright © 2013 John Wiley & Sons, Ltd.     

An examination of geochemical modelling approaches to tracing sediment sources incorporating distribution mixing and elemental correlations

The identification of sediment sources is fundamental to the management of increasingly scarce water resources. Tracing the origin of sediment with elemental geochemistry is a well‐established approach to determining sediment provenance. Fundamental to the confident apportionment of sediment to their lithogenic sources is the modelling process. Recent approaches have incorporated distributions throughout the modelling process including source contribution terms for two end‐member sources. The shift from modelling source samples to modelling samples drawn from distributions has removed relationships, including potential correlations between elemental concentrations, from the modelling process. Here, we present a novel modelling approach that re‐incorporates correlations between elemental concentrations and models distributions for source contribution terms for multiple source end members. Artificial mixtures, based on catchment sources samples, were created to test the accuracy of this correlated distribution model and also examine modelling approaches used in the literature. The most accurate model incorporates correlations between elements, uses the absolute mixing model difference and does not use any weighting. This model was then applied to identify the sources of sediment in three South East Queensland catchments and demonstrated that Quaternary Alluvium is the most dominant source of sediment in these catchments (μ 44%, σ 12%). This study demonstrates that it is important to understand how different weightings may impact modelling results. Copyright © 2014 John Wiley & Sons, Ltd.     

Plant source water apportionment using stable isotopes: A comparison of simple linear,two‐compartment mixing model approaches

Plant source water identification using stable isotopes is now a common practice in ecohydrological process investigations. Notwithstanding, little critical evaluation of the approaches for source apportionment have been conducted. Here, we present a critical evaluation of the main methods used for source apportionment between vadose and saturated zone water: simple mass balance and Bayesian mixing models. We leverage new isotope stem water samples from a diverse set of tree species in a strikingly uniform terrain and soil conditions at the Christchurch Botanic Garden, New Zealand. Our results show that using δ²H alone in a simple, two‐source mass balance approach leads to erroneous results, particularly an apparent overestimation of groundwater contribution to xylem. Alternatively, using both δ²H and δ¹⁸O in a Bayesian inference framework improves the source water estimates and is more useful than the simple mass balance approach, particularly when soil and groundwater contributions are relatively disproportionate. We suggest that plant source water quantification methods should take into consideration the possible effects of ²H/¹H fractionation. The Bayesian inference approach used here may be less sensitive to ²H/¹H fractionation effects than simple mass balance methods.     

Semiparametric regression models for spatial prediction and uncertainty quantification of soil attributes

In many studies, the distribution of soil attributes depends on both spatial location and environmental factors, and prediction and process identification are performed using existing methods such as kriging. However, it is often too restrictive to model soil attributes as dependent on a known, parametric function of environmental factors, which kriging typically assumes. This paper investigates a semiparametric approach for identifying and modeling the nonlinear relationships of spatially dependent soil constituent levels with environmental variables and obtaining point and interval predictions over a spatial region. Frequentist and Bayesian versions of the proposed method are applied to measured soil nitrogen levels throughout Florida, USA and are compared to competing models, including frequentist and Bayesian kriging, based an array of point and interval measures of out-of-sample forecast quality. The semiparametric models outperformed competing models in all cases. Bayesian semiparametric models yielded the best predictive results and provided empirical coverage probability nearly equal to nominal.     

Application of a confluence‐based sediment‐fingerprinting approach to a dynamic sedimentary catchment,New Zealand

Fine sediment is a dynamic component of the fluvial system, contributing to the physical form, chemistry and ecological health of a river. It is important to understand rates and patterns of sediment delivery, transport and deposition. Sediment fingerprinting is a means of directly determining sediment sources via their geochemical properties, but it faces challenges in discriminating sources within larger catchments. In this research, sediment fingerprinting was applied to major river confluences in the Manawatu catchment as a broad‐scale application to characterizing sub‐catchment sediment contributions for a sedimentary catchment dominated by agriculture. Stepwise discriminant function analysis and principal component analysis of bulk geochemical concentrations and geochemical indicators were used to investigate sub‐catchment geochemical signatures. Each confluence displayed a unique array of geochemical variables suited for discrimination. Geochemical variation in upstream sediment samples was likely a result of the varying geological source compositions. The Tiraumea sub‐catchment provided the dominant signature at the major confluence with the Upper Manawatu and Mangatainoka sub‐catchments. Subsequent downstream confluences are dominated by the upstream geochemical signatures from the main stem of Manawatu River. Variability in the downstream geochemical signature is likely due to incomplete mixing caused in part by channel configuration. Results from this exploratory investigation indicate that numerous geochemical elements have the ability to differentiate fine sediment sources using a broad‐scale confluence‐based approach and suggest there is enough geochemical variation throughout a large sedimentary catchment for a full sediment fingerprint model. Combining powerful statistical procedures with other geochemical analyses is critical to understanding the processes or spatial patterns responsible for sediment signature variation within this type of catchment. Copyright © 2015 John Wiley & Sons, Ltd.     

A preliminary assessment of the spatial sources of contemporary suspended sediment in the Ohio River basin,United States,using water quality data from the NASQAN programme in a source tracing procedure

Reliable information on catchment scale suspended sediment sources is required to inform the design of management strategies for helping abate the numerous environmental issues associated with enhanced sediment mobilization and off‐site loadings. Since sediment fingerprinting techniques avoid many of the logistical constraints associated with using more traditional indirect measurement methods at catchment scale, such approaches have been increasingly reported in the international literature and typically use data sets collected specifically for sediment source apportionment purposes. There remains scope for investigating the potential for using geochemical data sets assembled by routine monitoring programmes to fingerprint sediment provenance. In the United States, routine water quality samples are collected as part of the US Geological Survey's revised National Stream Quality Accounting Network programme. Accordingly, the geochemistry data generated from these samples over a 10‐year period (1996–2006) were used as the basis for a fingerprinting exercise to assess the key tributary sub‐catchment spatial sources of contemporary suspended sediment transported by the Ohio River. Uncertainty associated with the spatial source estimates was quantified using a Monte Carlo approach in conjunction with mass balance modelling. Relative frequency weighted means were used as an alternative way of summarizing the spatial source contributions, thereby avoiding the need to use confidence limits. The results should be interpreted in the context of the routine, but infrequent nature, of the suspended sediment samples used to assemble geochemistry as a basis for the sourcing exercise. Nonetheless, the study demonstrates how routine monitoring samples can be used to provide some preliminary information on sediment provenance in large drainage basins. Copyright © 2011 John Wiley & Sons, Ltd.     

Disentangling human impact from natural controls of sediment dynamics in an Alpine catchment

Human activities have increasingly strong impacts on the sediment dynamics of watersheds, directly, for example through water abstraction and sediment extraction, but also indirectly through climate change. This study aims at disentangling these impacts on natural sediment fluxes for the Borgne River, located in the Alps of southwest Switzerland, using two approaches: First, an assessment of contemporary sediment sources and their relative contribution to the sediment delivered to the catchment outlet is undertaken by geochemical fingerprinting and a mixing model. Second, a spatially distributed conceptual model of suspended sediment production and transfer is used to quantify the contribution of different portions of the catchment to the total sediment yield. The model describes the influence of hydroclimatic variables (rainfall, snowmelt, and ice melt), water diversions and reservoir trapping on the sediment yield accounting for the erodibility of the different land covers present in the catchment. The analysis of different scenarios based on this conceptual model aids the interpretation of the fingerprinting results and the identification of the most important factors controlling sediment fluxes. Although the conceptual model overestimates the contribution of the downstream source area and underestimates the contribution of the upstream source area, the results allow us to qualitatively assess the impacts of different drivers influencing the sediment yield at the catchment scale. The results suggest: (1) high sediment yield from the uppermost part of the catchment due to sediment delivery by glacial ice melt; (2) delayed sediment transfer from areas impacted by water abstraction; and (3) reduced sediment contribution from areas upstream of a major hydropower reservoir that intercepts and traps sediment. Although process (1) and processes (2) and (3) serve to counter one another, our study emphasizes that the relative impacts of Anthropocene climate change and human impacts on sediment delivery may be disentangled through multi-proxy approaches. © 2019 John Wiley & Sons, Ltd. © 2019 John Wiley & Sons, Ltd.     

On the use of leaf water to determine plant water source: A proof of concept

Source water apportionment studies using the dual isotopes of oxygen and hydrogen have revolutionized our understanding of ecohydrology. But despite these developments—mostly over the past decade—many technical problems still exist in terms of linking xylem water to its soil water and groundwater sources. This is mainly due to sampling issues and possible fractionation of xylem water. Here we explore whether or not leaf water alone can be used to quantify the blend of rainfall event inputs from which the leaf water originates. Leaf water has historically been avoided in plant water uptake studies due to the extreme fractionation processes at the leaf surface. In our proof of concept work we embrace those processes and use the well-known Craig and Gordon model to map leaf water back to its individual precipitation event water sources. We also employ a Bayesian uncertainty estimation approach to quantify source apportionment uncertainties. We show this using a controlled, vegetated lysimeter experiment where we were able to use leaf water to correctly identify the mean seasonal rainfall that was taken up by the plant, with an uncertainty typically within ± 1‰ for δ¹⁸O. While not appropriate for all source water studies, this work shows that leaf water isotope composition may provide a new, relatively un-intrusive method for addressing questions about the plant water source.     

Sensitivity analysis and calibration of the Modified Universal Soil Loss Equation (MUSLE) for the upper Malewa Catchment, Kenya

Simulation models are widely used for studying physical processes such as surface runoff, sediment transport and sediment yield in catchments. Most models need case-specific empirical data for parameterization before being applied especially in regions other than the ones they have been developed. Sensitivity analysis is usually performed to determine the most influential factors of a model so that they can be prioritized for optimization. In this way uncertainties in model outputs can be reduced considerably. This study evaluates the commonly used modified universal soil loss equation (MUSLE) model used for sediment yield simulation for the case of the upper Malewa catchment in Kenya. The conceptual factors of the model are assessed relative to the hydrological factors in the model. Also, the sensitivity of the model to the choice of the objective function in calibration is tested. The Sobol' sensitivity analysis method was used for evaluating the degree of sensitivity of the conceptual and hydrological factors for sediment yield simulations using the MUSLE model. Nash-Sutcliffe Efficiency (NSE) and the modified Nash-Sutcliffe Efficiency (NSEm) are used to test the sensitivity of the model to the choice of the objective function and robustness of model performance with sediment data measured from upper Malewa catchment, Kenya. The results indicate that the conceptual factors are the most sensitive factors of the MUSLE model contributing about 66% of the variability in the output sediment yield. Increased variability of sediment yield output was also observed. This was attributed to interactions of input factors. For the upper Malewa catchment calibration of the MUSLE model indicates that the use of NSEm as an objective function provides stable results, which indicates that the model can satisfactorily be applied for sediment yield simulations.     

Isotope mixing models require individual isotopic tracer content for correct quantification of sediment source contributions

The use of isotopic tracers for sediment source apportionment is gaining interest with recent introduction of compound‐specific stable isotope tracers. The method relies on linear mixing of source isotopic tracers, and deconvolution of a sediment mixture initially quantifies the contribution of sources to the mixture's tracer signature. Therefore, a correction to obtain real sediment source proportions is subsequently required. As far as we are aware, all published studies to date have used total isotopic tracer content or a proxy (e.g., soil carbon content) for this post‐unmixing correction. However, as the relationship between the isotopic tracer mixture and the source mixture is different for each isotopic tracer, post‐unmixing corrections cannot be carried out with one single factor. This contribution presents an isotopic tracer model structure—the concentration‐dependent isotope mixing model (CD‐IMM)—to overcome this limitation. Herein, we aim to clarify why the “conventional” approach to converting isotopic tracer proportions to source proportions using a single factor is wrong. In an initial mathematical assessment, error incurred by not using CD‐IMM (NCD‐IMM) in unmixing two sources with two isotopic tracers showed a complex relation as a function of relative tracer contents. Next, three artificial mixtures with different proportions of three soil sources were prepared and deconvoluted using ¹³C of fatty acids using CD‐IMM and NCD‐IMM. Using NCD‐IMM affected both accuracy (mean average error increased up to a threefold compared with the CD‐IMM output) and precision (interquartile range was up to 2.5 times larger). Finally, as an illustrative example, the proportional source contribution reported in a published study was recalculated using CD‐IMM. This resulted in changes in estimated source proportions and associated uncertainties. Content of isotopic tracers is seldom reported in published work concerning use of isotopic tracers for sediment source partitioning. The magnitude of errors made by miscalculation in former studies is therefore difficult to assess. With this contribution, we hope the community will acknowledge the limitations of prior approaches and use a CD‐IMM in future studies.     

Sediment source apportionment in Laurel Hill Creek,PA, using Bayesian chemical mass balance and isotope fingerprinting

A Bayesian chemical mass balance (CMB) approach was used to assess the contribution of potential sources for fluvial samples from Laurel Hill Creek in southwest Pennsylvania. The Bayesian approach provides joint probability density functions of the sources' contributions considering the uncertainties due to source and fluvial sample heterogeneity and measurement error. Both elemental profiles of sources and fluvial samples and ¹³C and ¹⁵N isotopes were used for source apportionment. The sources considered include stream bank erosion, forest, roads and agriculture (pasture and cropland). Agriculture was found to have the largest contribution, followed by stream bank erosion. Also, road erosion was found to have a significant contribution in three of the samples collected during lower‐intensity rain events. The source apportionment was performed with and without isotopes. The results were largely consistent; however, the use of isotopes was found to slightly increase the uncertainty in most of the cases. The correlation analysis between the contributions of sources shows strong correlations between stream bank and agriculture, whereas roads and forest seem to be less correlated to other sources. Thus, the method was better able to estimate road and forest contributions independently. The hypothesis that the contributions of sources are not seasonally changing was tested by assuming that all ten fluvial samples had the same source contributions. This hypothesis was rejected, demonstrating a significant seasonal variation in the sources of sediments in the stream. Copyright © 2014 John Wiley & Sons, Ltd.     

Modeling discharge rating curves with Bayesian B-splines

River discharges are traditionally modeled by employing a standard power-law methodology. Recently, the Bayesian approached has successfully been applied to improve the estimates of the standard power-law. In this article, an extension to the standard power-law based on Bayesian B-splines is developed and tested on data sets from 61 different rivers. The extended model is evaluated against the standard power-law using two measures, the Deviance Information Criterion and Bayes factor. The extended model captures deviations in the data from the standard power-law but reduces to the standard power-law when that model is adequate. The standard power-law is inadequate for 26% of the rivers while the extended model provides an adequate fit in all of those cases and for the remaining 74% of the rivers the extended model and the power-law model both give adequate fit with almost identical estimates.     

Relative model score: a scoring rule for evaluating ensemble simulations with application to microbial soil respiration modeling

This paper defines a new scoring rule, namely relative model score (RMS), for evaluating ensemble simulations of environmental models. RMS implicitly incorporates the measures of ensemble mean accuracy, prediction interval precision, and prediction interval reliability for evaluating the overall model predictive performance. RMS is numerically evaluated from the probability density functions of ensemble simulations given by individual models or several models via model averaging. We demonstrate the advantages of using RMS through an example of soil respiration modeling. The example considers two alternative models with different fidelity, and for each model Bayesian inverse modeling is conducted using two different likelihood functions. This gives four single-model ensembles of model simulations. For each likelihood function, Bayesian model averaging is applied to the ensemble simulations of the two models, resulting in two multi-model prediction ensembles. Predictive performance for these ensembles is evaluated using various scoring rules. Results show that RMS outperforms the commonly used scoring rules of log-score, pseudo Bayes factor based on Bayesian model evidence (BME), and continuous ranked probability score (CRPS). RMS avoids the problem of rounding error specific to log-score. Being applicable to any likelihood functions, RMS has broader applicability than BME that is only applicable to the same likelihood function of multiple models. By directly considering the relative score of candidate models at each cross-validation datum, RMS results in more plausible model ranking than CRPS. Therefore, RMS is considered as a robust scoring rule for evaluating predictive performance of single-model and multi-model prediction ensembles.