Search

Knowledge of drought onset and its relationship with drought severity (deficit volume) is crucial for providing timely information for reservoir operations, irrigation scheduling, devising cropping choices and patterns and managing surface and groundwater water resources. An analysis of the relationship between drought onset timing and deficit volume can help in drought hazard assessments and associated risks. Despite its importance, little attention has been paid to understand the drought onset timing and its potential linkage with deficit volume for effective drought monitoring and its impact assessment. Further, only a few studies have explored the role of environmental controls, encompassing the interaction between climate, catchment and land‐surface processes in influencing streamflow droughts and associated characteristics such as onset time and severity. This study leverages quality‐controlled streamflow observations from 1965 to 2018 to unveil regional patterns of streamflow drought onset, at‐site trends in deficit volume and detect non‐linear relationships between onset timing and deficit volume across 82 rain‐fed catchments in peninsular India (8°–24° N, 72°–87° E). We show that around 12% of catchments show an earlier onset of streamflow droughts in conjunction with a decreasing trend in deficit volume. Further, approximately one‐third of the catchments show a significant non‐linear dependency between drought deficit volume and onset time. Among catchment controls, such as soil and topographic properties, we found soil organic carbon stock and stock as dominant drivers controlling the streamflow drought onset time. Likewise, sand content and vertical distance to channel network control the streamflow deficit volume. Finally, the linkages between inferred dominant low‐flow generation mechanisms and the specific combinations of environmental controls are synthesized in a conceptual diagram that might assist in developing appropriate models for low‐flow simulations and predictions, especially across ungauged sites. The new insights add value to understanding the chain of physical processes linking climatic and physiographic controls on streamflow droughts, which can support drought forecasting and climate impact assessment efforts. [ABSTRACT FROM AUTHOR]

Braided rivers can provide substantial recharge to regional aquifers, with flow exchange between surface water and groundwater occurring at a range of spatial and temporal scales. However, the difficulty in measuring and modelling these complex and dynamic river systems has hampered process understanding and the upscaling necessary to quantify these fluxes. This is due to an incomplete understanding of the hydrogeological structures that control river–groundwater exchange. In this paper, we present a new conceptualisation of subsurface processes in braided rivers based on observations of the main losing reaches of three braided rivers in Aotearoa / New Zealand. The conceptual model is based on a range of data, including lidar, bathymetry, coring, particle size distribution, groundwater level and temperature monitoring, radon-222, electrical-resistivity tomography and fibre-optic cables. The combined results indicate that sediments within the recently active river braidplain are distinctive, with sediments that are poorly consolidated and better sorted compared with adjacent deposits from the historical braidplain that become successively consolidated and intermixed with flood silt deposits due to overbank flow. A distinct sedimentary unconformity, combined with the presence of geomorphologically distinct lateral boundaries, suggests that a "braidplain aquifer" forms within the active river braidplain through the process of sediment mobilisation during flood events. This braidplain aquifer concept introduces a shallow storage reservoir to the river system, which is distinct from the regional aquifer system, and mediates the exchange of flow between individual river channels and the regional aquifer. The implication of the new concept is that surface water–groundwater exchange occurs at two spatial scales: the first is hyporheic and parafluvial exchange between the river and braidplain aquifer; the second is exchange between the braidplain aquifer and regional aquifer system. Exchange at both scales is influenced by the state of hydraulic connection between the respective water bodies. This conceptualisation acknowledges braided rivers as whole "river systems", consisting of channels and a gravel aquifer reservoir. This work has important implications for understanding how changes in river management (e.g. surface water extraction, bank training and gravel extraction) and morphology may impact groundwater recharge (and potentially flow, temperature attenuation and ecological resilience) under dry conditions. [ABSTRACT FROM AUTHOR]

Hydrogeological models require reliable uncertainty intervals that honestly reflect the total uncertainties of model predictions. The operation of a conventional Bayesian framework only produces realistic (interpretable in the context of the natural system) inference results if the model structure matches the data‐generating process, that is, applying Bayes' theorem implicitly assumes the underlying model to be true. With an imperfect model, we may obtain a too‐narrow‐for‐its‐bias uncertainty interval when conditioning on a long time‐series of calibration data, because the assumption of a quasi‐true model becomes too strict. To overcome the problem of overconfident posteriors, we propose a non‐parametric Bayesian method, called Tau‐averaging method: it applies Bayesian analysis on sliding time windows along the data time series for calibration. Thus, it obtains so‐called transitional posteriors per time window. Then, we average these into a wider predictive posterior. With the proposed routine, we explicitly capture the time‐varying impact of model error on prediction uncertainty. The length of the calibration window is optimized to maximize goal‐oriented statistical skill scores for predictive coverage. Our method loosens the perfect‐model‐assumption by conditioning only on small windows of the data set at a time, that is, it assumes that "the model is sufficient to follow the system dynamics for a smaller duration." We test our method on two cases of soil moisture modeling and show how it improves predictive coverage as compared to the conventional Bayesian approach. Our findings demonstrate that the proposed method convincingly overcomes the overconfidence drawback of Bayesian inference under model misspecification and long calibration time‐series. Plain Language Summary: Mathematical models mimic environmental systems to match what we see, and to predict what will happen. Unfortunately, such models are always simplifications of reality, balancing their complexity between manageability and accuracy. Consequently, interpreting model‐based conclusions requires caution. Assume a model has ten adjustable parameters to make it match with a system. The best‐possible achievable fit to observations is imperfect. Yet, statistical tools indicate we knew these parameters perfectly well after adjustment, especially when adjusting on long data series. Then, we might start believing that this model's adjusted predictions are perfect. We call this "overconfidence." Ways to overcome overconfidence include extending models by statistical components, making them predict intervals and probabilities rather than exact numbers. However, adjusting these additional statistical components has been difficult to date. In our new approach, we force the model only to match short time windows of the data, and move this window through the whole data set. As we use little data per window, we reduce the overconfidence effect. Instead, the model adjusts parameters and predicts outputs differently in each window. To make predictions, we combine the outputs into a more robust result, such that the testing data fall inside the intervals generated by our method. Key Points: We propose a data‐driven Bayesian method to obtain realistic uncertainty estimates despite model errorsOur method builds on a statistically rigorous, time‐windowed Bayesian framework without prior assumptions about error sources or patternsThe method is confirmed to provide realistic predictive coverage with two synthetic test cases and a real‐world lysimeter case study [ABSTRACT FROM AUTHOR]

Braided rivers can provide substantial recharge to regional aquifers, with flow exchange between surface water and groundwater occurring at a range of spatial and temporal scales. However, the difficulty of measuring and modelling these complex and dynamic river systems has hampered process understanding and the upscaling necessary to quantify these fluxes. This is due to an incomplete understanding of the hydrogeological structures which control river-groundwater exchange. In this paper, we present a new conceptualisation of subsurface processes in braided rivers based on observations of the main losing reaches of three braided rivers in New Zealand. The conceptual model is based on a range of data including: lidar, bathymetry, coring, particle size distribution, groundwater, temperature monitoring, radon-222, electrical resistivity tomography, and fibre optic cables. The combined results indicate that sediments within the recently active river braidplain are distinctive, with sediments that are poorly consolidated and better sorted compared to adjacent deposits from the historical braidplain, which become successively consolidated and intermixed with flood silt deposits due to overbank flow. A distinct sedimentary unconformity, combined with the presence of geomorphologically distinct lateral boundaries, suggests that a "braidplain aquifer" forms within the active river braidplain through the process of sediment mobilisation during flood events. This braidplain aquifer concept introduces a shallow storage reservoir to the river system, which is distinct from the regional aquifer system, and mediates the exchange of flow between individual river channels and the regional aquifer. The implication of the new concept is that surface water-groundwater exchange occurs at two spatial scales. The first is hyporheic and parafluvial exchange between the river and braidplain aquifer. The second is exchange between the braidplain aquifer and regional aquifer system. Exchange at both scales is influenced by the state of hydraulic connection between the respective water bodies. This conceptualisation acknowledges braided rivers as whole "river systems", consisting of channels, and gravel aquifer. This work has important implications for understanding how changes in river management (e.g., surface water extraction, bank modification and gravel extraction) and morphology may impact groundwater recharge, and potentially river flow, temperature attenuation, and ecological resilience during dry conditions. [ABSTRACT FROM AUTHOR]

Hydraulic nonequilibrium in soil during water infiltration and drainage is a well‐known phenomenon. During infiltration, water initially invades easily accessible pores before it slowly redistributes towards some state of energetic minimum. In analogy, during drainage, easily drainable pores are emptied more rapidly than those blocked by bottlenecks. The consequence is that the water content is lagging behind the water potential and both state variables do not follow a unique water retention curve as typically assumed when applying Richards equation. Current models that account for nonequilibrium allow for the required decoupling of water content and water potential; however, they do not consider the consequences for the hydraulic conductivity. In this contribution, we present a physically based approach to estimate hydraulic conductivity during nonequilibrium, which depends on both water content and water potential during nonequilibrium conditions. This approach of a dynamic hydraulic conductivity function is demonstrated for an infiltration process into relatively dry soil and for a stepwise drainage and rewetting with decreasing and increasing water fluxes (i.e., multistep flux experiment). The new approach reproduces well‐known phenomena such as pressure overshoot and preferential flow across infiltration fronts using a unified concept for hydraulic conductivity. This was not possible with existing models assuming some fixed unsaturated conductivity function depending on either water content or water potential. Core Ideas: Soils are rarely in hydraulic equilibrium.We show consequences for their effective hydraulic conductivity.We present a physically based concept how to better describe the unsaturated conductivity function.The new approach describes pressure overshoot across fronts and the emergence of preferential during infiltration. [ABSTRACT FROM AUTHOR]

Transmission losses are the loss in the flow volume of a river as water moves downstream. These losses provide crucial ecosystem services, particularly in ephemeral and intermittent river systems. Transmission losses can be quantified at many scales using different measurement techniques. One of the most common methods is differential gauging of river flow at two locations. An alternative method for non-perennial rivers is to replace the downstream gauging location by visual assessments of the wetted river length on satellite images. The transmission losses are then calculated as the flow gauged at the upstream location divided by the wetted river length. We used this approach to estimate the transmission losses in the Selwyn River (Canterbury, New Zealand) using 147 satellite images collected between March 2020 and May 2021. The location of the river drying front was verified in the field on six occasions and seven differential gauging campaigns were conducted to ground-truth the losses estimated from the satellite images. The transmission loss point data obtained using the wetted river lengths and differential gauging campaigns were used to train an ensemble of random forest models to predict the continuous hourly time series of transmission losses and their uncertainties. Our results show that the Selwyn River transmission losses ranged between 0.25 and 0.65 m3s-1km-1 during most of the 1-year study period. However, shortly after a flood peak the losses could reach up to 1.5 m3s-1km-1. These results enabled us to improve our understanding of the Selwyn River groundwater–surface water interactions and provide valuable data to support water management. We argue that our framework can easily be adapted to other ephemeral rivers and to longer time series. [ABSTRACT FROM AUTHOR]

Transmission losses are the loss in the flow volume of a river as water moves downstream. These losses provide crucial ecosystem services, particularly in ephemeral and intermittent river systems. Transmission losses can be quantified at many scales using different measurement techniques. One of the most common methods is differential gauging of river flow at two locations. An alternative method for non-perennial rivers is to replace the downstream gauging location by visual assessments of the wetted river length on satellite images. We used this approach to estimate the transmission losses in the Selwyn River (Canterbury, New Zealand) using 147 satellite images collected between March 2020 and May 2021. The location of the river drying front was verified in the field on five occasions and seven differential gauging campaigns were conducted to ground-truth the losses estimated from the satellite images. The transmission loss point data obtained using the wetted river lengths and differential gauging campaigns were used to train an ensemble of random forest models to reconstruct the hourly time series of transmission losses and their uncertainties. Our results show that the Selwyn river transmission losses ranged between 0.25 and 0.65 m3/s/km during most of the 1-year study period. However, shortly after a flood peak the losses could reach up to 1.5 m3/s/km. These results enabled us to improve our understanding of the Selwyn River groundwater – surface water interactions and provide valuable data to support water management. We argue that our framework can easily be adapted to other ephemeral rivers and to longer time series. [ABSTRACT FROM AUTHOR]

Lateral subsurface flow (LSF) is a phenomenon frequently occurring in the field induced by local water saturation along horizon boundaries under nonequilibrium conditions. However, observations of LSF in undisturbed soils under controlled irrigation in the laboratory are limited but needed for model improvement, prediction, and quantification of LSF. We present a method for extracting an undisturbed soil monolith along a soil horizon boundary and introduce an experimental setup for the measurement of LSF and an irrigation device for simulating rainfall. An experimental test run was simulated using HYDRUS 2D. Water infiltrating into the monolith and flowing either laterally along the horizon boundary or vertically through the bottom horizon could be separately captured by suction discs at the side and the bottom. Thus, a clear distinction between lateral and vertical flow was possible. Pressure heads and water contents were recorded by tensiometers and frequency domain reflectometry (FDR) sensors distributed across the monolith in a regular two‐dimensional, vertical, cross‐sectional pattern. Sensor readings indicated the presence of nonequilibrium conditions within the monolith. Modeling results could reproduce the lateral and vertical outflow of the monolith under constant irrigation, thus showing that water flow within the monolith under steady‐state conditions can be explained by the Richards equation and the van Genuchten–Mualem model. The presented method can be used to improve and verify models designed for the prediction of the onset of LSF including that induced by local nonequilibrium conditions. Core Ideas: A Laboratory method to induce and quantify lateral subsurface flow (LSF) is presented.The experimental setup is verified by modeling with HYDRUS 2D.Sampling of rectangular soil monoliths for 2D flow experiments is improved.Lateral subsurface flow and hydraulic nonequilibrium conditions are observed.The experimental data allow for improving models on the onset of LSF. [ABSTRACT FROM AUTHOR]

Deterministic hydrological models with uncertain, but inferred‐to‐be‐time‐invariant parameters typically show time‐dependent model errors. Such errors can occur if a hydrological process is active in certain time periods in nature, but is not resolved by the model or by its input. Such missing processes could become visible during calibration as time‐dependent best‐fit values of model parameters. We propose a formal time‐windowed Bayesian analysis to diagnose this type of model error, formalizing the question "In which period of the calibration time‐series does the model statistically disqualify itself as quasi‐true?" Using Bayesian model evidence (BME) as model performance metric, we determine how much the data in time windows of the calibration time‐series support or refute the model. Then, we track BME over sliding time windows to obtain a dynamic, time‐windowed BME (tBME) and search for sudden decreases that indicate an onset of model error. tBME also allows us to perform a formal, sliding likelihood‐ratio test of the model against the data. Our proposed approach is designed to detect error occurrence on various temporal scales, which is especially useful in hydrological modeling. We illustrate this by applying our proposed method to soil moisture modeling. We test tBME as model error indicator on several synthetic and real‐world test cases that we designed to vary in error sources (structure and input) and error time scales. Results prove the successful detection errors in dynamic models. Moreover, the time sequence of posterior parameter distributions helps to investigate the reasons for model error and provide guidance for model improvement. Key Points: We propose a data‐driven method for model‐structural error detectionOur method rests on a statistically rigorous Bayesian framework without prior assumptions about error sources or patternsWe confirm successful error detection on various temporal scales in synthetic test cases and present insights from a real‐world case study [ABSTRACT FROM AUTHOR]

Highly detailed physically based groundwater models are often applied to make predictions of system states under unknown forcing. The required analysis of uncertainty is often unfeasible due to the high computational demand. We combine two possible solution strategies: (1) the use of faster surrogate models; and (2) a robust data worth analysis combining quick first‐order second‐moment uncertainty quantification with null‐space Monte Carlo techniques to account for parametric uncertainty. A structurally and parametrically simplified model and a proper orthogonal decomposition (POD) surrogate are investigated. Data worth estimations by both surrogates are compared against estimates by a complex MODFLOW benchmark model of an aquifer in New Zealand. Data worth is defined as the change in post‐calibration predictive uncertainty of groundwater head, river‐groundwater exchange flux, and drain flux data, compared to the calibrated model. It incorporates existing observations, potential new measurements of system states ("additional" data) as well as knowledge of model parameters ("parametric" data). The data worth analysis is extended to account for non‐uniqueness of model parameters by null‐space Monte Carlo sampling. Data worth estimates of the surrogates and the benchmark suggest good agreement for both surrogates in estimating worth of existing data. The structural simplification surrogate only partially reproduces the worth of "additional" data and is unable to estimate "parametric" data, while the POD model is in agreement with the complex benchmark for both "additional" and "parametric" data. The variance of the POD data worth estimates suggests the need to account for parameter non‐uniqueness, like presented here, for robust results. [ABSTRACT FROM AUTHOR]

Hyporheic exchange is the interaction of river water and groundwater, and is difficult to predict. One of the largest contributions to predictive uncertainty for hyporheic exchange has been attributed to the representation of heterogeneous subsurface properties. Our study evaluates the trade‐offs between intrinsic (irreducible) and epistemic (reducible) model errors when choosing between homogeneous and highly complex subsurface parameter structures. We modeled the Steinlach River Test Site in Southwest Germany using a fully coupled surface water‐groundwater model to simulate hyporheic exchange and to assess the predictive errors and uncertainties of transit time distributions. A highly parameterized model was built, treated as a "virtual reality" and used as a reference. We found that if the parameter structure is too simple, it will be limited by intrinsic model errors. By increasing subsurface complexity through the addition of zones or heterogeneity, we can begin to exchange intrinsic for epistemic errors. Thus, the appropriate level of detail to represent the subsurface depends on the acceptable range of intrinsic structural errors for the given modeling objectives and the available site data. We found that a zonated model is capable of reproducing the transit time distributions of a more detailed model, but only if the geological structures are known. An interpolated heterogeneous parameter field (cf. pilot points) showed the best trade‐offs between the two errors, indicating fitness for practical applications. Parameter fields generated by multiple‐point geostatistics (MPS) produce transit time distributions with the largest uncertainties, however, these are reducible by additional hydrogeological data, particularly flux measurements. Article impact statement: Choosing structure for subsurface parameter distributions leads to trade‐offs in intrinsic (aleatoric) and epistemic model structural errors. [ABSTRACT FROM AUTHOR]

Numerical models for reactive transport can be used to estimate the breakthrough of a contaminant in a pumping well or at other receptors. However, as natural aquifers are highly heterogeneous with unknown spatial details, reactive transport predictions on the aquifer scale require a stochastic framework for uncertainty analysis. The high computational demand of spatially explicit reactive‐transport models hampers such analysis, thus motivating the search for simplified estimation tools. We suggest performing an electron balance between the reactants in the infiltrating solution and in the aquifer matrix to obtain the hypothetical time of dissolved‐reactant breakthrough at a receptor if the reaction with the matrix was instantaneous. This time we denote as the advective breakthrough time for instantaneous reaction (τinst). It depends on the amount of the reaction partner present in the matrix, the mass flux of the dissolved reactant, and the stoichiometry. While the shape of the reactive‐species breakthrough curve depends on various kinetic parameters, the overall timing scales with τinst. We calculate the latter by particle tracking. The effort of computing τinst is so low that stochastic calculations become feasible. We apply the concept to a two‐dimensional test case of aerobic respiration and denitrification. A detailed spatially explicit reactive‐transport model includes microbial dynamics. Scaling the time of local breakthrough curves observed at individual points by τinst decreased the variability of electron‐donor breakthrough curves significantly. We conclude that the advective breakthrough time for instantaneous reaction is efficient in estimating the time over which an aquifer retains its degradation potential. Article impact statement: Estimate the time of contaminant breakthrough at a receptor within a stochastic framework without solving reactive transport. [ABSTRACT FROM AUTHOR]

This study determines the aspects of river bathymetry that have the greatest influence on the predictive biases when simulating hyporheic exchange. To investigate this, we build a highly parameterized HydroGeoSphere model of the Steinlach River Test Site in southwest Germany as a reference. This model is then modified with simpler bathymetries, evaluating the changes to hyporheic exchange fluxes and transit time distributions. Results indicate that simulating hyporheic exchange with a high‐resolution detailed bathymetry using a three‐dimensional fully coupled model leads to nested multiscale hyporheic exchange systems. A poorly resolved bathymetry will underestimate the small‐scale hyporheic exchange, biasing the simulated hyporheic exchange towards larger scales, thus leading to overestimates of hyporheic exchange residence times. This can lead to gross biases in the estimation of a catchment's capacity to attenuate pollutants when extrapolated to account for all meanders along an entire river within a watershed. The detailed river slope alone is not enough to accurately simulate the locations and magnitudes of losing and gaining river reaches. Thus, local bedforms in terms of bathymetric highs and lows within the river are required. Bathymetry surveying campaigns can be more effective by prioritizing bathymetry measurements along the thalweg and gegenweg of a meandering channel. We define the gegenweg as the line that connects the shallowest points in successive cross‐sections along a river opposite to the thalweg under average flow conditions. Incorporating local bedforms will likely capture the nested nature of hyporheic exchange, leading to more physically meaningful simulations of hyporheic exchange fluxes and transit times. Article impact statement: Three‐dimensional fully coupled surface water‐groundwater models with detailed river bathymetry contrasts lead to nested multiscale hyporheic exchange systems. [ABSTRACT FROM AUTHOR]

Abstract: New Zealand's gravel‐bed rivers have deposited coarse, highly conductive gravel aquifers that are predominantly fed by river water. Managing their groundwater resources is challenging because the recharge mechanisms in these rivers are poorly understood and recharge rates are difficult to predict, particularly under a more variable future climate. To understand the river‐groundwater exchange processes in gravel‐bed rivers, we investigate the Wairau Plain Aquifer using a three‐dimensional groundwater flow model which was calibrated using targeted field observations, “soft” information from experts of the local water authority, parameter regularization techniques, and the model‐independent parameter estimation software PEST. The uncertainty of simulated river‐aquifer exchange flows, groundwater heads, spring flows, and mean transit times were evaluated using Null‐space Monte‐Carlo methods. Our analysis suggests that the river is hydraulically perched (losing) above the regional water table in its upper reaches and is gaining downstream where marine sediments overlay unconfined gravels. River recharge rates are on average 7.3 m3/s, but are highly dynamic in time and variable in space. Although the river discharge regularly hits 1000 m3/s, the net exchange flow rarely exceeds 12 m3/s and seems to be limited by the physical constraints of unit‐gradient flux under disconnected rivers. An important finding for the management of the aquifer is that changes in aquifer storage are mainly affected by the frequency and duration of low‐flow periods in the river. We hypothesize that the new insights into the river‐groundwater exchange mechanisms of the presented case study are transferable to other rivers with similar characteristics. [ABSTRACT FROM AUTHOR]

Abstract: Selecting a “best” model among several competing candidate models poses an often encountered problem in water resources modeling (and other disciplines which employ models). For a modeler, the best model fulfills a certain purpose best (e.g., flood prediction), which is typically assessed by comparing model simulations to data (e.g., stream flow). Model selection methods find the “best” trade‐off between good fit with data and model complexity. In this context, the interpretations of model complexity implied by different model selection methods are crucial, because they represent different underlying goals of modeling. Over the last decades, numerous model selection criteria have been proposed, but modelers who primarily want to apply a model selection criterion often face a lack of guidance for choosing the right criterion that matches their goal. We propose a classification scheme for model selection criteria that helps to find the right criterion for a specific goal, i.e., which employs the correct complexity interpretation. We identify four model selection classes which seek to achieve high predictive density, low predictive error, high model probability, or shortest compression of data. These goals can be achieved by following either nonconsistent or consistent model selection and by either incorporating a Bayesian parameter prior or not. We allocate commonly used criteria to these four classes, analyze how they represent model complexity and what this means for the model selection task. Finally, we provide guidance on choosing the right type of criteria for specific model selection tasks. (A quick guide through all key points is given at the end of the introduction.) [ABSTRACT FROM AUTHOR]

Abstract: Many groundwater contaminants react with components of the aquifer matrix, causing a depletion of the aquifer's reactivity with time. We discuss conceptual simplifications of reactive transport that allow the implementation of a decreasing reaction potential in reactive‐transport simulations in chemically and hydraulically heterogeneous aquifers without relying on a fully explicit description. We replace spatial coordinates by travel‐times and use the concept of relative reactivity, which represents the reaction‐partner supply from the matrix relative to a reference. Microorganisms facilitating the reactions are not explicitly modeled. Solute mixing is neglected. Streamlines, obtained by particle tracking, are discretized in travel‐time increments with variable content of reaction partners in the matrix. As exemplary reactive system, we consider aerobic respiration and denitrification with simplified reaction equations: Dissolved oxygen undergoes conditional zero‐order decay, nitrate follows first‐order decay, which is inhibited in the presence of dissolved oxygen. Both reactions deplete the bioavailable organic carbon of the matrix, which in turn determines the relative reactivity. These simplifications reduce the computational effort, facilitating stochastic simulations of reactive transport on the aquifer scale. In a one‐dimensional test case with a more detailed description of the reactions, we derive a potential relationship between the bioavailable organic‐carbon content and the relative reactivity. In a three‐dimensional steady‐state test case, we use the simplified model to calculate the decreasing denitrification potential of an artificial aquifer over 200 years in an ensemble of 200 members. We demonstrate that the uncertainty in predicting the nitrate breakthrough in a heterogeneous aquifer decreases with increasing scale of observation. [ABSTRACT FROM AUTHOR]

Monitoring networks are expensive to establish and to maintain. In this paper, we extend an existing data-worth estimation method from the suite of PEST utilities with a global optimization method for optimal sensor placement (called optimal design) in groundwater monitoring networks. Design optimization can include multiple simultaneous sensor locations and multiple sensor types. Both location and sensor type are treated simultaneously as decision variables. Our method combines linear uncertainty quantification and a modified genetic algorithm for discrete multilocation, multitype search. The efficiency of the global optimization is enhanced by an archive of past samples and parallel computing. We demonstrate our methodology for a groundwater monitoring network at the Steinlach experimental site, south-western Germany, which has been established to monitor river-groundwater exchange processes. The target of optimization is the best possible exploration for minimum variance in predicting the mean travel time of the hyporheic exchange. Our results demonstrate that the information gain of monitoring network designs can be explored efficiently and with easily accessible tools prior to taking new field measurements or installing additional measurement points. The proposed methods proved to be efficient and can be applied for model-based optimal design of any type of monitoring network in approximately linear systems. Our key contributions are (1) the use of easy-to-implement tools for an otherwise complex task and (2) yet to consider data-worth interdependencies in simultaneous optimization of multiple sensor locations and sensor types. [ABSTRACT FROM AUTHOR]

We simulate aquifer-scale reactive transport using an approach based on travel times and relative reactivity. The latter quantifies the intensity of the chemical reaction relative to a reference reaction rate with identical concentrations and can be interpreted as the strength of electron-donor (or electron-acceptor) release by the matrix, scaled by a reference release. In general, the relative reactivity is a spatially variable property reflecting the geology of the formation. In the proposed approach, we track the path of individual water parcels through the aquifer and evaluate the age of the water parcels and the relative reactivity integrated along their trajectories. By switching from spatial discretization to cumulative relative reactivity, advective-reactive transport can be simulated by solving a single system of ordinary differential equations for each combination of concentrations in the inflow. We test the validity of the approach in a two-dimensional test case of steady state groundwater flow and reactive transport involving aerobic respiration and denitrification. Here we compare steady state concentration distributions of the spatially explicit virtual truth, accounting for dispersive mixing, with the approximation based on cumulative relative reactivity and show that the errors introduced by neglecting dispersive mixing are minor if the target quantities are the mass fluxes crossing a control plane or being collected by a well. We further demonstrate the efficiency of the approach in a synthetic three-dimensional case study. The proposed approach is computationally so efficient that ensemble runs to assess statistical distributions of concentration time series of reactive solutes become feasible, which is not practical with a spatially explicit model. [ABSTRACT FROM AUTHOR]

Droughts are serious natural hazards, especially in semi-arid regions. They are also difficult to characterize. Various summary metrics representing the dryness level, denoted drought indices, have been developed to quantify droughts. They typically lump meteorological variables and can thus directly be computed from the outputs of regional climate models in climate-change assessments. While it is generally accepted that drought risks in semi-arid climates will increase in the future, quantifying this increase using climate model outputs is a complex process that depends on the choice and the accuracy of the drought indices, among other factors. In this study, we compare seven meteorological drought indices that are commonly used to predict future droughts. Our goal is to assess the reliability of these indices to predict hydrological impacts of droughts under changing climatic conditions at the annual timescale. We simulate the hydrological responses of a small catchment in northern Spain to droughts in present and future climate, using an integrated hydrological model calibrated for different irrigation scenarios. We compute the correlation of meteorological drought indices with the simulated hydrological time series (discharge, groundwater levels, and water deficit) and compare changes in the relationships between hydrological variables and drought indices. While correlation coefficients linked with a specific drought index are similar for all tested land uses and climates, the relationship between drought indices and hydrological variables often differs between present and future climate. Drought indices based solely on precipitation often underestimate the hydrological impacts of future droughts, while drought indices that additionally include potential evapotranspiration sometimes overestimate the drought effects. In this study, the drought indices with the smallest bias were the rainfall anomaly index, the reconnaissance drought index, and the standardized precipitation evapotranspiration index. However, the efficiency of these drought indices depends on the hydrological variable of interest and the irrigation scenario. We conclude that meteorological drought indices are able to identify years with restricted water availability in present and future climate. However, these indices are not capable of estimating the severity of hydrological impacts of droughts in future climate. A wellcalibrated hydrological model is necessary in this respect. [ABSTRACT FROM AUTHOR]

Bayesian model averaging (BMA) ranks the plausibility of alternative conceptual models according to Bayes' theorem. A prior belief about each model's adequacy is updated to a posterior model probability based on the skill to reproduce observed data and on the principle of parsimony. The posterior model probabilities are then used as model weights for model ranking, selection, or averaging. Despite the statistically rigorous BMA procedure, model weights can become uncertain quantities due to measurement noise in the calibration data set or due to uncertainty in model input. Uncertain weights may in turn compromise the reliability of BMA results. We present a new statistical concept to investigate this weighting uncertainty, and thus, to assess the significance of model weights and the confidence in model ranking. Our concept is to resample the uncertain input or output data and then to analyze the induced variability in model weights. In the special case of weighting uncertainty due to measurement noise in the calibration data set, we interpret statistics of Bayesian model evidence to assess the distance of a model's performance from the theoretical upper limit. To illustrate our suggested approach, we investigate the reliability of soil-plant model selection following up on a study by Wöhling et al. (2015). Results show that the BMA routine should be equipped with our suggested upgrade to (1) reveal the significant but otherwise undetected impact of measurement noise on model ranking results and (2) to decide whether the considered set of models should be extended with better performing alternatives. [ABSTRACT FROM AUTHOR]

A Bayesian model averaging (BMA) framework is presented to evaluate the worth of different observation types and experimental design options for (1) more confidence in model selection and (2) for increased predictive reliability. These two modeling tasks are handled separately because model selection aims at identifying the most appropriate model with respect to a given calibration data set, while predictive reliability aims at reducing uncertainty in model predictions through constraining the plausible range of both models and model parameters. For that purpose, we pursue an optimal design of measurement framework that is based on BMA and that considers uncertainty in parameters, measurements, and model structures. We apply this framework to select between four crop models (the vegetation components of CERES, SUCROS, GECROS, and SPASS), which are coupled to identical routines for simulating soil carbon and nitrogen turnover, soil heat and nitrogen transport, and soil water movement. An ensemble of parameter realizations was generated for each model using Monte-Carlo simulation. We assess each model's plausibility by determining its posterior weight, which signifies the probability to have generated a given experimental data set. Several BMA analyses were conducted for different data packages with measurements of soil moisture, evapotranspiration ( ETa), and leaf area index (LAI). The posterior weights resulting from the different BMA runs were compared to the weight distribution of a reference run with all data types to investigate the utility of different data packages and monitoring design options in identifying the most appropriate model in the ensemble. We found that different (combinations of) data types support different models and none of the four crop models outperforms all others under all data scenarios. The best model discrimination was observed for those data where the competing models disagree the most. The data worth for reducing prediction uncertainty depends on the prediction to be made. LAI data have the highest utility for predicting ETa, while soil moisture data are better for predicting soil water drainage. Our study illustrates, that BMA provides an objective framework for data worth analysis with respect to both model discrimination and model calibration for a wide range of applications. [ABSTRACT FROM AUTHOR]

Bayesian model selection or averaging objectively ranks a number of plausible, competing conceptual models based on Bayes' theorem. It implicitly performs an optimal trade-off between performance in fitting available data and minimum model complexity. The procedure requires determining Bayesian model evidence (BME), which is the likelihood of the observed data integrated over each model's parameter space. The computation of this integral is highly challenging because it is as high-dimensional as the number of model parameters. Three classes of techniques to compute BME are available, each with its own challenges and limitations: (1) Exact and fast analytical solutions are limited by strong assumptions. (2) Numerical evaluation quickly becomes unfeasible for expensive models. (3) Approximations known as information criteria (ICs) such as the AIC, BIC, or KIC (Akaike, Bayesian, or Kashyap information criterion, respectively) yield contradicting results with regard to model ranking. Our study features a theory-based intercomparison of these techniques. We further assess their accuracy in a simplistic synthetic example where for some scenarios an exact analytical solution exists. In more challenging scenarios, we use a brute-force Monte Carlo integration method as reference. We continue this analysis with a real-world application of hydrological model selection. This is a first-time benchmarking of the various methods for BME evaluation against true solutions. Results show that BME values from ICs are often heavily biased and that the choice of approximation method substantially influences the accuracy of model ranking. For reliable model selection, bias-free numerical methods should be preferred over ICs whenever computationally feasible. [ABSTRACT FROM AUTHOR]