Study region: Hindon River Basin, North India. Study focus: Accurate estimation of water balance components is crucial for water management applications yet challenging due to errors in monthly gridded water balance data products. Error and uncertainty quantification is especially important in the absence of extensive in-situ data. This paper presents a prior uncertainty analysis for such situations consisting of two components: (i) quantification of prior uncertainties using metrics that quantify errors in individual products and variability and consistency between products, and (ii) reduction of prior uncertainties by eliminating unrealistic water balance estimates. New hydrological insights for the region: Grid-scale inter-product uncertainty or variability, computed as the coefficient of variation (CV, %) at various temporal scales, reveals discrepancies between water balance products due to a combination of factors, including methodological differences, inherent spatial variability, data sources, and resolution disparities. At the mean annual scale, P fluxes display a lower grid-scale inter-product uncertainty (5–9 %) than ET (20–55 %), while the ∆TWS from GRACE solutions show a moderate mean annual grid-scale inter-product uncertainty (15–19 %). Grid-scale inter-product uncertainties of ∆SMS for July – representing the onset of the monsoon season – are high (CV = 54–122 %), indicating that the uncertainty in estimates of this component may have a large impact on water balance analyses. P fluxes exhibited fewer spatio-temporal uncertainties (R² above 0.8) than ET fluxes (R² less than 0.75). The exclusion of the unreliable data sets resulted in (a) reducing uncertainties in input water balance components with triple collocation range shifting from 15–38 to 17–23 mm/month for ET and from 16–52 to 11–23 mm/month for P, (b) obtaining updated prior estimates of seasonal water balance. The updated priors of water balance variables per season suggest a net basin outflow (from −318 to −57 mm/season) during the monsoon (rainy) season and net basin inflow (from −38 to 330 mm/season) during the non-monsoon (dry) season, the latter related to surface-water imports from outside the basin. All GRACE data sets exhibit a regional long-term decreasing trend in total water storage (ranging from −31 to −61 mm/year), qualitatively confirming previously documented unsustainable groundwater depletion in the basin. Prior ranges and uncertainties for all water balance variables reported here can be used as input into a posterior analysis that uses in-situ data for locally calibrating (bias-correcting, noise-filtering) and further updating the prior estimates.

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Climatic variability can considerably affect catchment-scale root zone storage capacity (S _umax), which is a critical factor regulating latent heat fluxes and thus the moisture exchange between land and atmosphere as well as the hydrological response and biogeochemical processes in terrestrial hydrological systems. However, direct quantification of changes in S _umax over long time periods and the mechanistic drivers thereof at the catchment scale are missing so far. As a consequence, it remains unclear how climatic variability, such as precipitation regime or canopy water demand, affects S _umax and how fluctuations in S _umax may influence the partitioning of water fluxes and therefore also affect the hydrological response at the catchment scale. Based on long-term daily hydrological records (1953-2022) in the upper Neckar River basin in Germany, we found that variability in hydro-climatic conditions, with an aridity index I _A (i.e. E _P/P) ranging between ∼ 0.9 and 1.1 over multiple consecutive 20-year periods, was accompanied by deviations ΔI _E between -0.02 and 0.01 from the expected I _E inferred from the long-term parametric Budyko curve. Similarly, fluctuations in S _umax, ranging between ∼ 95 and 115 mm or ∼ 20 %, were observed over the same time period. While uncorrelated with long-term mean precipitation and potential evaporation, it was shown that the magnitude of S _umax is controlled by the ratio of winter precipitation to summer precipitation (p < 0.05). In other words, S _umax in the study region does not depend on the overall wetness condition as for example expressed by I _A, but rather on how water supply by precipitation is distributed over the year. However, fluctuations in S _umax were found to be uncorrelated with observed changes in ΔIE. Consequently, replacing a long-term average, time-invariant estimate of S _umax with a time-variable, dynamically changing formulation of that parameter in a hydrological model did not result in an improved representation of the long-term partitioning of water fluxes, as expressed by I _E (and fluctuations ΔIE thereof), or in an improved representation of the shorter-term response dynamics. Overall, this study provides quantitative mechanistic evidence that S _umax changes significantly over multiple decades, reflecting vegetation adaptation to climatic variability. However, this temporal evolution of S _umax cannot explain long-term fluctuations in the partitioning of water (and thus latent heat) fluxes as expressed by deviations ΔIE from the parametric Budyko curve over multiple time periods with different climatic conditions. Similarly, it does not have any significant effects on shorter-term hydrological response characteristics of the upper Neckar catchment. This further suggests that accounting for the temporal evolution of S _umax with a time-variable formulation of that parameter in a hydrological model does not improve its ability to reproduce the hydrological response and may therefore be of minor importance for predicting the effects of a changing climate on the hydrological response in the study region over the next decades to come.

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High-quality citizen science data can be instrumental in advancing science toward new discoveries and a deeper understanding of under-observed phenomena. However, the error structure of citizen scientist (CS) data must be well-defined. Within a citizen science program, the errors in submitted observations vary, and their occurrence may depend on CS-specific characteristics. This study develops a graphical Bayesian inference model of error types in CS data. The model assumes that (1) each CS observation is subject to a specific error type, each with its own bias and noise, and (2) an observation's error type depends on the static error community of the CS, which in turn relates to characteristics of the CS submitting the observation. Given a set of CS observations and corresponding ground-truth values, the model can be calibrated for a specific application, yielding (i) number of error types and error communities, (ii) bias and noise for each error type, (iii) error distribution of each error community, and (iv) the single error community to which each CS belongs. The model, applied to Nepal CS rainfall observations, identifies five error types and sorts CSs into four static, model-inferred communities. In the case study, 73 % of CSs submitted data with errors in fewer than 5 % of their observations. The remaining CSs submitted data with unit, meniscus, unknown, and outlier errors. A CS's assigned community, coupled with model-inferred error probabilities, can identify observations that require verification and provides an opportunity for targeted re-training of CSs based on mistake tendencies.@en

Stable isotopes (I18O) and tritium (3H) are frequently used as tracers in environmental sciences to estimate age distributions of water. However, it has previously been argued that seasonally variable tracers, such as I18O, generally and systematically fail to detect the tails of water age distributions and therefore substantially underestimate water ages as compared to radioactive tracers such as 3H. In this study for the Neckar River basin in central Europe and based on a >20-year record of hydrological, I18O and 3H data, we systematically scrutinized the above postulate together with the potential role of spatial aggregation effects in exacerbating the underestimation of water ages. This was done by comparing water age distributions inferred from I18O and 3H with a total of 21 different model implementations, including time-invariant, lumped-parameter sine-wave (SW) and convolution integral (CO) models as well as StorAge Selection (SAS)-function models (P-SAS) and integrated hydrological models in combination with SAS functions (IM-SAS). We found that, indeed, water ages inferred from I18O with commonly used SW and CO models are with mean transit times (MTTs) of g1/4g1-2 years substantially lower than those obtained from 3H with the same models, reaching MTTs of g1/410 years. In contrast, several implementations of P-SAS and IM-SAS models not only allowed simultaneous representations of storage variations and streamflow as well as I18O and 3H stream signals, but water ages inferred from I18O with these models were, with MTTs of g1/4g11-17 years, also much higher and similar to those inferred from 3H, which suggested MTTs of g1/4g11-13 years. Characterized by similar parameter posterior distributions, in particular for parameters that control water age, P-SAS and IM-SAS model implementations individually constrained with I18O or 3H observations exhibited only limited differences in the magnitudes of water ages in different parts of the models and in the temporal variability of transit time distributions (TTDs) in response to changing wetness conditions. This suggests that both tracers lead to comparable descriptions of how water is routed through the system. These findings provide evidence that allowed us to reject the hypothesis that I18O as a tracer generally and systematically "cannot see water older than about 4 years"and that it truncates the corresponding tails in water age distributions, leading to underestimations of water ages. Instead, our results provide evidence for a broad equivalence of I18O and 3H as age tracers for systems characterized by MTTs of at least 15-20 years. The question to which degree aggregation of spatial heterogeneity can further adversely affect estimates of water ages remains unresolved as the lumped and distributed implementations of the IM-SAS model provided inconclusive results. Overall, this study demonstrates that previously reported underestimations of water ages are most likely not a result of the use of I18O or other seasonally variable tracers per se. Rather, these underestimations can largely be attributed to choices of model approaches and complexity not considering transient hydrological conditions next to tracer aspects. Given the additional vulnerability of time-invariant, lumped SW and CO model approaches in combination with I18O to substantially underestimate water ages due to spatial aggregation and potentially other still unknown effects, we therefore advocate avoiding the use of this model type in combination with seasonally variable tracers if possible and instead adopting SAS-based models or time-variant formulations of CO models.

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This paper is concerned with the formulation of an adequate likelihood function in the application of Bayesian epistemology to uncertainty quantification of hydrologic models. We focus our attention on a special class of likelihood functions (hereinafter referred to as distribution-adaptive likelihood functions), which do not require prior assumptions about the expected distribution of the residuals, rather inference takes place over the hypotheses (model parameters) and space of distribution functions. Our goals are threefold. First, we present theory of a revised implementation of the generalized likelihood (GL) function of Schoups and Vrugt (2010) wherein residual standardization precedes the treatment of serial correlation. This so-called GL⁺ function, enjoys a solid statistical underpinning and guarantees a more robust joint inference of the autoregressive coefficients and residual properties. Then, as secondary goal, we present a further generalization of the GL⁺ function, coined the universal likelihood (UL) function, which extends applicability to highly asymmetrical lepto- and platy-kurtic residual distributions. The UL function builds on the 5-parameter skewed generalized Student's t distribution of Theodossiou (2015) which makes up a large family of continuous probability distributions including (but not limited to) symmetric and skewed forms of the generalized normal, generalized t, Laplace, normal, Student's t, and Cauchy-Lorentz distributions. As our third and last goal, we present the use of strictly proper scoring rules to evaluate, compare and rank likelihood functions. These scoring rules condense the accuracy of a distribution forecast to a single value while retaining attractive statistical properties. The GL⁺ and UL functions are illustrated using data of a simple autoregressive scheme and benchmarked against the GL function, Student t likelihood (SL) of Scharnagl et al. (2015) and normal likelihood (NL) for a conceptual hydrologic model using measured streamflow data. Our results show that, (i) the GL⁺ function is superior to the GL function, (ii) the active set of nuisance variables exerts a large control on the performance of the GL⁺, SL and UL functions, (iii) the treatment of autocorrelation deteriorates the scoring rules and performance metrics of the forecast distribution, (iv) a leptokurtic distribution is favored for discharge residuals, (v) scoring rules are indispensable in our search for the true forecast distribution, and (vi) the use of multiple strictly proper scoring rules turns the selection of an adequate likelihood function into a multi-criteria problem.

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The low density of conventional rain gauge networks is often a limiting factor for radar rainfall bias correction. Citizen rain gauges offer a promising opportunity to collect rainfall data at a higher spatial density. In this paper, hourly radar rainfall bias adjustment was applied using two different rain gauge networks: tipping buckets, measured by Thai Meteorological Department (TMD), and daily citizen rain gauges. The radar rainfall bias correction factor was sequentially updated based on TMD and citizen rain gauge data using a two-step Kalman filter to incorporate the two gauge datasets of contrasting quality. Radar reflectivity data from the Sattahip radar station, gauge rainfall data from the TMD, and data from citizen rain gauges located in the Tubma Basin, Thailand, were used in the analysis. Daily data from the citizen rain gauge network were downscaled to an hourly resolution based on temporal distribution patterns obtained from radar rainfall time series and the TMD gauge network. Results show that an improvement in radar rainfall estimates was achieved by including the downscaled citizen observations compared with bias correction based on the conventional rain gauge network alone. These outcomes emphasize the value of citizen rainfall observations for radar bias correction, in particular in regions where conventional rain gauge networks are sparse.@en

Study region: This study develops the first daily runoff forecast system for Bukan reservoir in Urmia Lake basin (ULB), Iran, a region suffering from water shortages and competing water demands. Study focus: A weather forecast downscaling model is developed for downscaling large-scale raw weather forecasts of ECMWF and NCEP to small-scale spatial resolutions. Various downscaling methods are compared, including deterministic Artificial Intelligence (AI) techniques and a Bayesian Belief Network (BBN). Downscaled precipitation and temperature forecasts are then fed into a rainfall-runoff model that accounts for daily snow and soil moisture dynamics in the sub-basins upstream of Bukan reservoir. The multi-objective Particle Swarm Optimization (MOPSO) method is used to estimate hydrological model parameters by maximizing the simulation accuracy of observed river flow (NSE_Q) and the logarithm of river flow (NSE_LogQ) in each sub-basin. New hydrological insights for the region: Results of the weather forecast downscaling model show that the accuracy of the BBN is greater than the various deterministic AI methods tested. Calibration results of the rainfall-runoff model indicate no significant trade-off between fitting daily high and low flows, with an average NSE_Q and NSE_LogQ of 0.43 and 0.63 for the calibration period, and 0.54 and 0.57 for the validation period. The entire forecasting system was evaluated using inflow observations for years 2020 and 2021, resulting in an NSE of 0.66 for forecasting daily inflow into Bukan reservoir. The inflow forecasts can be used by policymakers and operators of the reservoir to optimize water allocation between agricultural and environmental demands in the ULB.

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Holocene climate reconstructions are useful for understanding the diverse features and spatial heterogeneity of past and future climate change. Here we present a database of western North American Holocene paleoclimate records. The database gathers paleoclimate time series from 184 terrestrial and marine sites, including 381 individual proxy records. The records span at least 4000 of the last 12 000 years (median duration of 10 725 years) and have been screened for resolution, chronologic control, and climate sensitivity. Records were included that reflect temperature, hydroclimate, or circulation features. The database is shared in the machine readable Linked Paleo Data (LiPD) format and includes geochronologic data for generating site-level time-uncertain ensembles. This publicly accessible and curated collection of proxy paleoclimate records will have wide research applications, including, for example, investigations of the primary features of ocean-atmospheric circulation along the eastern margin of the North Pacific and the latitudinal response of climate to orbital changes. The database is available for download at https://doi.org/10.6084/m9.figshare.12863843.v1 (Routson and McKay, 2020).

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To fully benefit from remotely sensed observations of the terrestrial water cycle, bias and random errors in these data sets need to be quantified. This paper presents a Bayesian hierarchical model that fuses monthly water balance data and estimates the corresponding data errors and error-corrected water balance components (precipitation, evaporation, river discharge, and water storage). The model combines monthly basin-scale water balance constraints with probabilistic data error models for each water balance variable. Each data error model includes parameters that are in turn treated as unknown random variables to reflect uncertainty in the errors. Errors in precipitation and evaporation data are parameterized as a function of multiple data sources, while errors in GRACE storage observations are described by a noisy sine wave model with parameters controlling the phase, amplitude, and randomness of the sine wave. Error parameters and water balance variables are estimated using a combination of Markov Chain Monte Carlo sampling and iterative smoothing. Application to semiarid river basins in Iran yields (a) significant reductions in evaporation uncertainty during water-stressed summers, (b) basin-specific timing and amplitude corrections of the GRACE water storage dynamics, and (c) posterior water balance estimates with average standard errors of 4–12 mm/month for water storage, 3.5–7 mm/month for precipitation, 2–6 mm/month for evaporation, and 0–2 mm/month for river discharge. The approach is readily extended to other data sets and other (gauged) basins around the world, possibly using customized data error models. The resulting error-filtered and bias-corrected water balance estimates can be used to evaluate hydrological models.

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Hydrological regimes of alpine catchments are expected to be strongly affected by climate change, mostly due to their dependence on snow and ice dynamics. While seasonal changes have been studied extensively, studies on changes in the timing and magnitude of annual extremes remain rare. This study investigates the effects of climate change on runoff patterns in six contrasting Alpine catchments in Austria using a process-based, semi-distributed hydrological model and projections from 14 regional and global climate model combinations for two representative concentration pathways, namely RCP4.5 and RCP8.5. The study catchments represent a spectrum of different hydrological regimes, from pluvial-nival to nivo-glacial, as well as distinct topographies and land forms, characterizing different elevation zones across the eastern Alps to provide a comprehensive picture of future runoff changes. The climate projections are used to model river runoff in 2071-2100, which are then compared to the 1981-2010 reference period for all study catchments. Changes in the timing and magnitude of annual maximum and minimum flows, as well as in monthly runoff and snowmelt, are quantified and analyzed. Our results indicate a substantial shift to earlier occurrences in annual maximum flows by 9 to 31gd and an extension of the potential flood season by 1 to 3 months for high-elevation catchments. For low-elevation catchments, changes in the timing of annual maximum flows are less pronounced. Magnitudes of annual maximum flows are likely to increase by 2g%-18g% under RCP4.5, while no clear changes are projected for four catchments under RCP8.5. The latter is caused by a pronounced increase in evaporation and decrease in snowmelt contributions, which offset increases in precipitation. In the future, minimum annual runoff will occur 13-31gd earlier in the winter months for high-elevation catchments, whereas for low-elevation catchments a shift from winter to autumn by about 15-100gd is projected, with generally larger changes for RCP8.5. While all catchments show an increase in mean magnitude of minimum flows by 7-30% under RCP4.5, this is only the case for four catchments under RCP8.5. Our results suggest a relationship between the elevation of catchments and changes in the timing of annual maximum and minimum flows. For the magnitude of the extreme flows, a relationship is found between catchment elevation and annual minimum flows, whereas this relationship is lacking between elevation and annual maximum flow.

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Improving precipitation accuracy over a watershed is one of the highest priorities in water resources studies and management. Several global precipitation datasets are available for estimating precipitation over any region in the world. However, local or regional application of these datasets should account for and correct potential errors in the original products. This article presents a novel spatiotemporal calibration framework to improve the accuracy (bias and correlation) of global precipitation datasets in regional applications. The proposed methodology consists of two steps. First, gridded global precipitation datasets are regressed pointwise against rain gauge data. This yields downscaled and bias-corrected precipitation values at the point scale. Second, the resulting point-scale regression parameters are used to build a geostatistical model that predicts the regression parameters across the region of interest, allowing for bias-correcting the precipitation datasets at the regional scale. The framework is applied to the Urmia Lake Watershed in northwestern Iran. Eight global high-resolution monthly precipitation datasets (CHIRPS, ERA-5, IMERG, PERSIANN, PERSIANN-CCS, PERSIANN-CDR, TRMM and Terra) are evaluated and three downscaling approaches including linear, Q-Q and Linear Scaling (LS) regression methods are used to calibrate the precipitation datasets based on a regional network of rain gauge observations. Ordinary kriging is subsequently used to predict the regression parameters at ungauged locations. Out of all combinations (i.e., eight datasets and three methods), downscaled IMERG using linear and Q-Q regression methods showed the best performance in estimating the spatiotemporal variations of monthly precipitation across the watershed of interest. The original IMERG dataset overestimated the monthly precipitation by approximately 20% compared to the precipitation from rain gauges. After applying the proposed methodology in this article, the IMERG bias was reduced by 93%, with an additional 26% decrease in the RMSE.

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Conceptual rainfall-runoff models account for the spatial dynamics of hydrological processes in a basin using simple spatially lumped storage-flow relations. Such rough approximations introduce model errors that are often difficult to characterize. Here, we develop and apply a methodology that recursively estimates and accounts for model errors in real-time streamflow prediction settings by adding time-dependent random noise to the internal states (storages) of the hydrological model. Magnitude of the added noise depends on a precision (inverse variance) parameter that is estimated from rainfall-runoff data. A recursive Bayesian technique is used for estimation: posteriors of hydrological parameters and states are updated through time with an ensemble Kalman filter, whereas the posterior of the precision parameter is updated recursively using a novel gamma density approximation technique. Applying this algorithm to different model error scenarios allows identification of the main source of model errors. The methodology is applied to short-term streamflow prediction with the Hymod rainfall-runoff model in a semi-cold, semi-humid basin in Iran. Results show that (i) streamflow prediction in this snow-dominated basin is more affected by model errors in the slow flow than the quick flow component of the model, (ii) accounting for model errors in the slow flow component improves both low and high flow predictions, and (iii) predictive performance further improves by accounting for Hymod parameter uncertainty in addition to model errors. Overall, accounting for model errors increased Nash-Sutcliffe efficiency (by 1–5%), reduced mean absolute error (by 2–43%), and improved probabilistic predictive performance (by 50–80%).

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Accurate estimation of the spatial distribution of precipitation is crucial for hydrologic modeling. To achieve the realistic estimation of precipitation, developing a ground-based observatory system is a costly and time-consuming strategy compared with other solutions such as using a combination of satellite- and ground-based observations. In this paper, to improve the estimation accuracy of spatial precipitation variation, various linear regression methods were used that combine digital elevation model (DEM) data, rain gauge observations, and Tropical Rainfall Measuring Mission (TRMM) products. Specifically, fuzzy cluster-based linear regression (FCLR), local multiple linear regression using historical similarity (LMLR-HS), model tree (MT), and moving least squares (MLS) were used in the proposed methodology based on local data behavior. The results were compared with those obtained from multiple linear regression (MLR) methods including simple multiple linear regression (SMLR), robust multiple linear regression (RMLR), and generalized linear model (GLM) for monthly precipitation estimation. The study area was Namak Lake watershed, one of the largest watersheds in Iran. The results, estimated for wet and dry years (years 1999 and 2003, respectively), show superiority of local linear regression methods over the other linear methods. Based on the statistical metrics used for assessing the quality the results, FCLR and MLS outperformed other tested methods.

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Competition for water between agriculture and the environment is a growing problem in irrigated regions across the globe, especially in endorheic basins with downstream freshwater lakes impacted by upstream irrigation withdrawals. This study presents and applies a novel simulation-optimization (SO) approach for identifying water management strategies in such settings. Our approach combines three key features for increased exploration of strategies. First, minimum environmental flow requirements are treated as a decision variable in the optimization model, yielding more flexibility than existing approaches that either treat it as a precomputed constraint or as an objective to be maximized. Second, conjunctive use is included as a management option by using dynamically coupled surface water (WEAP) and groundwater (MODFLOW) simulation models. Third, multi-objective optimization is used to yield entire Pareto sets of water management strategies that trade off between meeting environmental and agricultural water demand. The methodology is applied to the irrigated Miyandoab Plain, located upstream of endorheic Lake Urmia in Northwestern Iran. Results identify multiple strategies, i.e., combinations of minimum environmental flow requirements, deficit irrigation, and crop selection, that simultaneously increase environmental flow (up to 16 %) and agricultural profit (up to 24 %) compared to historical conditions. Results further show that significant temporary drops in agricultural profit occur during droughts when long-term profit is maximized, but that this can be avoided by increasing groundwater pumping capacity and temporarily reducing the lake's minimum environmental flow requirements. Such a strategy is feasible during moderate droughts when resulting declines in groundwater and lake water levels fully recover after each drought. Overall, these results demonstrate the usefulness and flexibility of the methodology in identifying a range of potential water management strategies in complex irrigated endorheic basins like the Lake Urmia basin.

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This study develops and applies the first coupled surface water-groundwater (SW-GW) flow model for the irrigated Miyandoab plain located in the Urmia basin, in the northwest of Iran. The model is implemented using a dynamic coupling between MODFLOW and WEAP and consists of spatially distributed monthly water balances for the aquifer, root-zone, rivers, canals, and reservoirs. Multi-objective calibration of the model using river discharge and GW level data yields accurate simulation of historical conditions, and results in better constrained parameters compared to using either data source alone. Model simulations show that crop water demand cannot be met during droughts due to limited GW pumping capacity, and that increased GW pumping has a relatively strong impact on GW levels due to the small specific yield of the aquifer. The SW-GW model provides a unique tool for exploring management options that sustain agricultural production and downstream flow to the shrinking Urmia Lake.@en

Post-glacial climate, vegetation and fire history were reconstructed from a sediment record from Begbie Lake, British Columbia, Canada, located in a municipal water supply area servicing > 350,000 people. Watershed managers have identified wildfire as a threat to water supply and seek to understand how vegetation and fire have varied through time with climate. In the cold late-glacial, open Pinus woodlands, periodically disturbed by fire, transitioned to mixed conifer forests subject to high-severity fire. The early Holocene is of interest to watershed managers because climate was warmer and drier than present. During this interval, low streamflow, abundant fire-adapted taxa, elevated background charcoal and regional increases in biomass burning indicate that fire seasons were longer and that fire was an important disturbance mechanism. Climate moistened in the mid Holocene, facilitating canopy closure and decreased fire disturbance. However, surface fires prevailed in Quercus ecosystems, which were expanding locally. Charcoal increased between 6180–2500 cal yr BP as climate further cooled and moistened, likely reflecting human activity and/or increased climate variability. Modern conditions arose within the last few millennia, impacted most recently by European settlement. In combination with paleoclimate modelling, modern management practices and forecast simulations, the Begbie Lake record informs about ecosystem changes within the watershed, yielding insights for management.

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In many regions of the world, intensive livestock farming has become a significant source of organic river pollution. As the international meat trade is growing rapidly, the environmental impacts of meat production within one country can occur either domestically or internationally. The goal of this paper is to quantify the impacts of the international meat trade on global organic river pollution at multiple scales (national, regional and gridded). Using the biological oxygen demand (BOD) as an overall indicator of organic river pollution, we compute the spatially distributed organic pollution in global river networks with and without a meat trade, where the without-trade scenario assumes that meat imports are replaced by local production. Our analysis reveals a reduction in the livestock population and production of organic pollutants at the global scale as a result of the international meat trade. However, the actual environmental impact of trade, as quantified by in-stream BOD concentrations, is negative; i.e. we find a slight increase in polluted river segments. More importantly, our results show large spatial variability in local (grid-scale) impacts that do not correlate with local changes in BOD loading, which illustrates: (1) the significance of accounting for the spatial heterogeneity of hydrological processes along river networks, and (2) the limited value of looking at country-level or global averages when estimating the actual impacts of trade on the environment.

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What is the “best” model? The answer to this question lies in part in the eyes of the beholder, nevertheless a good model must blend rigorous theory with redeeming qualities such as parsimony and quality of fit. Model selection is used to make inferences, via weighted averaging, from a set of K candidate models, (Formula presented.), and help identify which model is most supported by the observed data, (Formula presented.). Here, we introduce a new and robust estimator of the model evidence, (Formula presented.), which acts as normalizing constant in the denominator of Bayes’ theorem and provides a single quantitative measure of relative support for each hypothesis that integrates model accuracy, uncertainty, and complexity. However, (Formula presented.) is analytically intractable for most practical modeling problems. Our method, coined GAussian Mixture importancE (GAME) sampling, uses bridge sampling of a mixture distribution fitted to samples of the posterior model parameter distribution derived from MCMC simulation. We benchmark the accuracy and reliability of GAME sampling by application to a diverse set of multivariate target distributions (up to 100 dimensions) with known values of (Formula presented.) and to hypothesis testing using numerical modeling of the rainfall-runoff transformation of the Leaf River watershed in Mississippi, USA. These case studies demonstrate that GAME sampling provides robust and unbiased estimates of the evidence at a relatively small computational cost outperforming commonly used estimators. The GAME sampler is implemented in the MATLAB package of DREAM and simplifies considerably scientific inquiry through hypothesis testing and model selection.

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Organic pollution of rivers by wastewater discharge from human activities negatively impacts people and ecosystems. Without treatment, pollution control relies on a combination of natural degradation and dilution by natural runoff to reduce downstream effects. We quantify here for the first time the global sanitation crisis through its impact on organic river pollution from the threats of (1) increasing wastewater discharge due to urbanization and intensification of livestock farming, and (2) reductions in river dilution capacity due to climate change and water extractions. Using in-stream Biochemical Oxygen Demand (BOD) as an overall indicator of organic river pollution, we calculate historical (2000) and future (2050) BOD concentrations in global river networks. Despite significant self-cleaning capacities of rivers, the number of people affected by organic pollution (BOD >5 mg/l) is projected to increase from 1.1 billion in 2000 to 2.5 billion in 2050. With developing countries disproportionately affected, our results point to a growing need for affordable wastewater solutions.

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