Constraining water table depth simulations in a land surface model using estimated baseflow

Several recent studies have shown the significance of representing groundwater in land surface hydrologic simulations. However, optimal methods for model parameter calibration in order to realistically simulate baseflow and groundwater depth have received little attention. Most studies still use globally constant groundwater parameters due to the lack of available datasets for calibration. Moreover, when models are calibrated, various parameter combinations are found to exhibit equifinality in simulated total runoff due to model parameter interactions. In this study, a simple lumped groundwater model is incorporated into the Community Land Model (CLM), in which the water table is interactively coupled to soil moisture through the groundwater recharge fluxes. The coupled model (CLMGW) is successfully validated in Illinois using a 22-year (1984–2005) monthly observational dataset. Baseflow estimates from the digital recursive filter technique are used to calibrate the CLMGW parameters. The advantage obtained from incorporating baseflow calibration in addition to traditional calibration based on measured streamflow alone is demonstrated by a Monte Carlo-type simulation analysis. Using the optimal parameter sets identified from baseflow calibration, flow partitioning and water table depth simulations using CLMGW are improved, and the equifinality problem is alleviated. For other regions that lack observations of water table depth, the baseflow calibration approach can be used to enhance parameter estimation and constrain water table depth simulations.     

Comparison of parameter uncertainty analysis techniques for a TOPMODEL application

Parameter uncertainty in hydrologic modeling is crucial to the flood simulation and forecasting. The Bayesian approach allows one to estimate parameters according to prior expert knowledge as well as observational data about model parameter values. This study assesses the performance of two popular uncertainty analysis (UA) techniques, i.e., generalized likelihood uncertainty estimation (GLUE) and Bayesian method implemented with the Markov chain Monte Carlo sampling algorithm, in evaluating model parameter uncertainty in flood simulations. These two methods were applied to the semi-distributed Topographic hydrologic model (TOPMODEL) that includes five parameters. A case study was carried out for a small humid catchment in the southeastern China. The performance assessment of the GLUE and Bayesian methods were conducted with advanced tools suited for probabilistic simulations of continuous variables such as streamflow. Graphical tools and scalar metrics were used to test several attributes of the simulation quality of selected flood events: deterministic accuracy and the accuracy of 95 % prediction probability uncertainty band (95PPU). Sensitivity analysis was conducted to identify sensitive parameters that largely affect the model output results. Subsequently, the GLUE and Bayesian methods were used to analyze the uncertainty of sensitive parameters and further to produce their posterior distributions. Based on their posterior parameter samples, TOPMODEL’s simulations and the corresponding UA results were conducted. Results show that the form of exponential decline in conductivity and the overland flow routing velocity were sensitive parameters in TOPMODEL in our case. Small changes in these two parameters would lead to large differences in flood simulation results. Results also suggest that, for both UA techniques, most of streamflow observations were bracketed by 95PPU with the containing ratio value larger than 80 %. In comparison, GLUE gave narrower prediction uncertainty bands than the Bayesian method. It was found that the mode estimates of parameter posterior distributions are suitable to result in better performance of deterministic outputs than the 50 % percentiles for both the GLUE and Bayesian analyses. In addition, the simulation results calibrated with Rosenbrock optimization algorithm show a better agreement with the observations than the UA’s 50 % percentiles but slightly worse than the hydrographs from the mode estimates. The results clearly emphasize the importance of using model uncertainty diagnostic approaches in flood simulations.     

Internal catchment process simulation in a snow‐dominated basin: performance evaluation with spatiotemporally variable runoff generation and groundwater dynamics

Hydrologic models have increasingly been used in forest hydrology to overcome the limitations of paired watershed experiments, where vegetative recovery and natural variability obscure the inferences and conclusions that can be drawn from such studies. Models are also plagued by uncertainty, however, and parameter equifinality is a common concern. Physically‐based, spatially‐distributed hydrologic models must therefore be tested with high‐quality experimental data describing a multitude of concurrent internal catchment processes under a range of hydrologic regimes. This study takes a novel approach by not only examining the ability of a pre‐calibrated model to realistically simulate watershed outlet flows over a four year period, but a multitude of spatially‐extensive, internal catchment process observations not previously evaluated, including: continuous groundwater dynamics, instantaneous stream and road network flows, and accumulation and melt period spatial snow distributions. Many hydrologic model evaluations are only on the comparison of predicted and observed discharge at a catchment outlet and remain in the ‘infant stage’ in terms of model testing. This study, on the other hand, tests the internal spatial predictions of a distributed model with a range of field observations over a wide range of hydroclimatic conditions. Nash‐Sutcliffe model efficiency was improved over prior evaluations due to continuing efforts in improving the quality of meteorological data collection. Road and stream network flows were generally well simulated for a range of hydrologic conditions, and snowpack spatial distributions were well simulated for one of two years examined. The spatial variability of groundwater dynamics was effectively simulated, except at locations where strong stream–groundwater interactions exist. Model simulations overall were quite successful in realistically simulating the spatiotemporal variability of internal catchment processes in the watershed, but the premature onset of simulated snowmelt for one of the simulation years has prompted further work in model development. Copyright © 2011 John Wiley & Sons, Ltd.     

Assessing the hydrological and geomorphic behaviour of a landscape evolution model within a limits-of-acceptability uncertainty analysis framework

Landscape evolution models (LEMs) have the capability to characterize key aspects of geomorphological and hydrological processes. However, their usefulness is hindered by model equifinality and paucity of available calibration data. Estimating uncertainty in the parameter space and resultant model predictions is rarely achieved as this is computationally intensive and the uncertainties inherent in the observed data are large. Therefore, a limits-of-acceptability (LoA) uncertainty analysis approach was adopted in this study to assess the value of uncertain hydrological and geomorphic data. These were used to constrain simulations of catchment responses and to explore the parameter uncertainty in model predictions. We applied this approach to the River Derwent and Cocker catchments in the UK using a LEM CAESAR-Lisflood. Results show that the model was generally able to produce behavioural simulations within the uncertainty limits of the streamflow. Reliability metrics ranged from 24.4% to 41.2% and captured the high-magnitude low-frequency sediment events. Since different sets of behavioural simulations were found across different parts of the catchment, evaluating LEM performance, in quantifying and assessing both at-a-point behaviour and spatial catchment response, remains a challenge. Our results show that evaluating LEMs within uncertainty analyses framework while taking into account the varying quality of different observations constrains behavioural simulations and parameter distributions and is a step towards a full-ensemble uncertainty evaluation of such models. We believe that this approach will have benefits for reflecting uncertainties in flooding events where channel morphological changes are occurring and various diverse (and yet often sparse) data have been collected over such events.     

Uncertainty in water resource model parameters used for climate change impact assessment

Despite their acknowledged limitations, lumped conceptual models continue to be used widely for climate‐change impact assessments. Therefore, it is important to understand the relative magnitude of uncertainties in water resource projections arising from the choice of model calibration period, model structure, and non‐uniqueness of model parameter sets. In addition, external sources of uncertainty linked to choice of emission scenario, climate model ensemble member, downscaling technique(s), and so on, should be acknowledged. To this end, the CATCHMOD conceptual water balance model was used to project changes in daily flows for the River Thames at Kingston using parameter sets derived from different subsets of training data, including the full record. Monte Carlo sampling was also used to explore parameter stability and identifiability in the context of historic climate variability. Parameters reflecting rainfall acceptance at the soil surface in simpler model structures were found to be highly sensitive to the training period, implying that climatic variability does lead to variability in the hydrologic behaviour of the Thames basin. Non‐uniqueness of parameters for more complex model structures results in relatively small variations in projected annual mean flow quantiles for different training periods compared with the choice of emission scenario. However, this was not the case for subannual flow statistics, where uncertainty in flow changes due to equifinality was higher in winter than summer, and comparable in magnitude to the uncertainty of the emission scenario. Therefore, it is recommended that climate‐change impact assessments using conceptual water balance models should routinely undertake sensitivity analyses to quantify uncertainties due to parameter instability, identifiability and non‐uniqueness. Copyright © 2005 John Wiley & Sons, Ltd.     

Données isotopiques (8786/Sr) et changements hydrologiques depuis 15 000 ans sur l'Altiplano andin

Abstract

In catchments characterized by spatially varying hydrological processes and responses, the optimal parameter values or regions of attraction in parameter space may differ with location-specific characteristics and dominating processes. This paper evaluates the value of semi-distributed calibration parameters for large-scale streamflow simulation using the spatially distributed LISFLOOD model. We employ the Shuffled Complex Evolution Metropolis (SCEM-UA) global optimization algorithm to infer the calibration parameters using daily discharge observations. The resulting posterior parameter distribution reflects the uncertainty about the model parameters and forms the basis for making probabilistic flow predictions. We assess the value of semi-distributing the calibration parameters by comparing three different calibration strategies. In the first calibration strategy uniform values over the entire area of interest are adopted for the unknown parameters, which are calibrated against discharge observations at the downstream outlet of the catchment. In the second calibration strategy the parameters are also uniformly distributed, but they are calibrated against observed discharges at the catchment outlet and at internal stations. In the third strategy a semi-distributed approach is adopted. Starting from upstream, parameters in each subcatchment are calibrated against the observed discharges at the outlet of the subcatchment. In order not to propagate upstream errors in the calibration process, observed discharges at upstream catchment outlets are used as inflow when calibrating downstream subcatchments. As an illustrative example, we demonstrate the methodology for a part of the Morava catchment, covering an area of approximately 10 000 km². The calibration results reveal that the additional value of the internal discharge stations is limited when applying a lumped parameter approach. Moving from a lumped to a semi-distributed parameter approach: (i) improves the accuracy of the flow predictions, especially in the upstream subcatchments; and (ii) results in a more correct representation of flow prediction uncertainty. The results show the clear need to distribute the calibration parameters, especially in large catchments characterized by spatially varying hydrological processes and responses.     

A Linking Test to reduce the number of hydraulic parameters necessary to simulate groundwater recharge in unsaturated soils

In environmental studies, numerical simulation models are valuable tools for testing hypothesis about systems functioning and to perform sensitivity studies under scenarios of land use or climate changes. The simulations depend upon parameters which are not always measurable quantities and must be calibrated against observations, using for instance inverse modelling. Due to the scarcity of these observations, it has been found that parameter sets allowing a good matching between simulated and measured quantities are often non-unique, leading to the problem of equifinality. This can lead to non-physical values, erroneous fluxes and misleading sensitivity analysis. Therefore, a simple but robust inverse method coined the Linking Test is presented to determine if the parameters are linked. Linked parameters are then sub-divided into classes according to their impact on water fluxes. The Linking Test establishes the causes of non-uniqueness of parameter sets and the feasibility of the inverse modelling.     

How do hydrologic modeling decisions affect the portrayal of climate change impacts?

End users face a range of subjective decisions when evaluating climate change impacts on hydrology, but the importance of these decisions is rarely assessed. In this paper, we evaluate the implications of hydrologic modelling choices on projected changes in the annual water balance, monthly simulated processes, and signature measures (i.e. metrics that quantify characteristics of the hydrologic catchment response) under a future climate scenario. To this end, we compare hydrologic changes computed with four different model structures – whose parameters have been obtained using a common calibration strategy – with hydrologic changes computed with a single model structure and parameter sets from multiple options for different calibration decisions (objective function, local optima, and calibration forcing dataset). Results show that both model structure selection and the parameter estimation strategy affect the direction and magnitude of projected changes in the annual water balance, and that the relative effects of these decisions are basin dependent. The analysis of monthly changes illustrates that parameter estimation strategies can provide similar or larger uncertainties in simulations of some hydrologic processes when compared with uncertainties coming from model choice. We found that the relative effects of modelling decisions on projected changes in catchment behaviour depend on the signature measure analysed. Furthermore, parameter sets with similar performance, but located in different regions of the parameter space, provide very different projections for future catchment behaviour. More generally, the results obtained in this study prompt the need to incorporate parametric uncertainty in multi‐model frameworks to avoid an over‐confident portrayal of climate change impacts. Copyright © 2015 John Wiley & Sons, Ltd.     

Inverse modelling for freshwater lens in small islands: Kish Island,Persian Gulf

A number of challenges including instability, nonconvergence, nonuniqueness, nonoptimality, and lack of a general guideline for inverse modelling have limited the application of automatic calibration by generic inversion codes in solving the saltwater intrusion problem in real‐world cases. A systematic parameter selection procedure for the selection of a small number of independent parameters is applied to a real case of saltwater intrusion in a small island aquifer system in the semiarid region of the Persian Gulf. The methodology aims at reducing parameter nonuniqueness and uncertainty and the time spent on inverse modelling computations. Subsequent to the automatic calibration of the numerical model, uncertainty is analysed by constrained nonlinear optimization of the inverse model. The results define the percentage of uncertainty in the parameter estimation that will maintain the model inside a user‐defined neighbourhood of the best possible calibrated model. Sensitivity maps of both pressure and concentration for the small island aquifer system are also developed. These sensitivity maps indicate higher sensitivity of pressure to model parameters compared with concentration. These sensitivity maps serve as a benchmark for correlation analysis and also assist in the selection of observations points of pressure and concentration in the calibration process. Copyright © 2012 John Wiley & Sons, Ltd.     

Calibration of hydrological models in ungauged basins based on satellite radar altimetry observations of river water level

This paper proposes a new orientation to address the problem of hydrological model calibration in ungauged basin. Satellite radar altimetric observations of river water level at basin outlet are used to calibrate the model, as a surrogate of streamflow data. To shift the calibration objective, the hydrological model is coupled with a hydraulic model describing the relation between streamflow and water stage. The methodology is illustrated by a case study in the Upper Mississippi Basin using TOPEX/Poseidon (T/P) satellite data. The generalized likelihood uncertainty estimation (GLUE) is employed for model calibration and uncertainty analysis. We found that even without any streamflow information for regulating model behavior, the calibrated hydrological model can make fairly reasonable streamflow estimation. In order to illustrate the degree of additional uncertainty associated with shifting calibration objective and identifying its sources, the posterior distributions of hydrological parameters derived from calibration based on T/P data, streamflow data and T/P data with fixed hydraulic parameters are compared. The results show that the main source is the model parameter uncertainty. And the contribution of remote sensing data uncertainty is minor. Furthermore, the influence of removing high error satellite observations on streamflow estimation is also examined. Under the precondition of sufficient temporal coverage of calibration data, such data screening can eliminate some unrealistic parameter sets from the behavioral group. The study contributes to improve streamflow estimation in ungauged basin and evaluate the value of remote sensing in hydrological modeling. Copyright © 2011 John Wiley & Sons, Ltd.     

Application of the patient rule induction method to detect hydrologic model behavioural parameters and quantify uncertainty

Finding an operational parameter vector is always challenging in the application of hydrologic models, with over‐parameterization and limited information from observations leading to uncertainty about the best parameter vectors. Thus, it is beneficial to find every possible behavioural parameter vector. This paper presents a new methodology, called the patient rule induction method for parameter estimation (PRIM‐PE), to define where the behavioural parameter vectors are located in the parameter space. The PRIM‐PE was used to discover all regions of the parameter space containing an acceptable model behaviour. This algorithm consists of an initial sampling procedure to generate a parameter sample that sufficiently represents the response surface with a uniform distribution within the “good‐enough” region (i.e., performance better than a predefined threshold) and a rule induction component (PRIM), which is then used to define regions in the parameter space in which the acceptable parameter vectors are located. To investigate its ability in different situations, the methodology is evaluated using four test problems. The PRIM‐PE sampling procedure was also compared against a Markov chain Monte Carlo sampler known as the differential evolution adaptive Metropolis (DREAM_ZS) algorithm. Finally, a spatially distributed hydrological model calibration problem with two settings (a three‐parameter calibration problem and a 23‐parameter calibration problem) was solved using the PRIM‐PE algorithm. The results show that the PRIM‐PE method captured the good‐enough region in the parameter space successfully using 8 and 107 boxes for the three‐parameter and 23‐parameter problems, respectively. This good‐enough region can be used in a global sensitivity analysis to provide a broad range of parameter vectors that produce acceptable model performance. Moreover, for a specific objective function and model structure, the size of the boxes can be used as a measure of equifinality.     

Practical Postcalibration Uncertainty Analysis: Yucca Mountain, Nevada

The values of parameters in a groundwater flow model govern the precision of predictions of future system behavior. Predictive precision, thus, typically depends on an ability to infer values of system properties from historical measurements through calibration. When such data are scarce, or when their information content with respect to parameters that are most relevant to predictions of interest is weak, predictive uncertainty may be high, even if the model is "calibrated." Recent advances help recognize this condition, quantitatively evaluate predictive uncertainty, and suggest a path toward improved predictive accuracy by identifying sources of predictive uncertainty and by determining what observations will most effectively reduce this uncertainty. We demonstrate linear and nonlinear predictive error/uncertainty analyses as applied to a groundwater flow model of Yucca Mountain, Nevada, the United States' proposed site for disposal of high-level radioactive waste. Linear and nonlinear uncertainty analyses are readily implemented as an adjunct to model calibration with medium to high parameterization density. Linear analysis yields contributions made by each parameter to a prediction's uncertainty and the worth of different observations, both existing and yet-to-be-gathered, toward reducing this uncertainty. Nonlinear analysis provides more accurate characterization of the uncertainty of model predictions while yielding their (approximate) probability distribution functions. This article applies the above methods to a prediction of specific discharge and confirms the uncertainty bounds on specific discharge supplied in the Yucca Mountain Project License Application.     

Prediction uncertainty of conceptual rainfall-runoff models caused by problems in identifying model parameters and structure

Abstract

The uncertainties arising from the problem of identifying a representative model structure and model parameters in a conceptual rainfall-runoff model were investigated. A conceptual model, the HBV model, was applied to the mountainous Brugga basin (39.9 km”) in the Black Forest, southwestern Germany. In a first step, a Monte Carlo procedure with randomly generated parameter sets was used for calibration. For a ten-year calibration period, different parameter sets resulted in an equally good correspondence between observed and simulated runoff. A few parameters were well defined (i.e. best parameter values were within small ranges), but for most parameters good simulations were found with values varying over wide ranges. In a second step, model variants with different numbers of elevation and landuse zones and various runoff generation conceptualizations were tested. In some cases, representation of more spatial variability gave better simulations in terms of discharge. However, good results could be obtained with different and even unrealistic concepts. The computation of design floods and low flow predictions illustrated that the parameter uncertainty and the uncertainty of identifying a unique best model variant have implications for model predictions. The flow predictions varied considerably. The peak discharge of a flood with a probability of 0.01 year^?1, for instance, varied from 40 to almost 60 mm day^?1. It was concluded that model predictions, particularly in applied studies, should be given as ranges rather than as single values.     

Choosing an arbitrary calibration period for hydrologic models: How much does it influence water balance simulations?

The selection of calibration and validation time periods in hydrologic modelling is often done arbitrarily. Nonstationarity can lead to an optimal parameter set for one period which may not accurately simulate another. However, there is still much to be learned about the responses of hydrologic models to nonstationary conditions. We investigated how the selection of calibration and validation periods can influence water balance simulations. We calibrated Soil and Water Assessment Tool hydrologic models with observed streamflow for three United States watersheds (St. Joseph River of Indiana/Michigan, Escambia River of Florida/Alabama, and Cottonwood Creek of California), using time period splits for calibration/validation. We found that the choice of calibration period (with different patterns of observed streamflow, precipitation, and air temperature) influenced the parameter sets, leading to dissimilar simulations of water balance components. In the Cottonwood Creek watershed, simulations of 50-year mean January streamflow varied by 32%, because of lower winter precipitation and air temperature in earlier calibration periods on calibrated parameters, which impaired the ability for models calibrated to earlier periods to simulate later periods. Peaks of actual evapotranspiration for this watershed also shifted from April to May due to different parameter values depending on the calibration period's winter air temperatures. In the St. Joseph and Escambia River watersheds, adjustments of the runoff curve number parameter could vary by 10.7% and 20.8%, respectively, while 50-year mean monthly surface runoff simulations could vary by 23%–37% and 169%–209%, depending on the observed streamflow and precipitation of the chosen calibration period. It is imperative that calibration and validation time periods are chosen selectively instead of arbitrarily, for instance using change point detection methods, and that the calibration periods are appropriate for the goals of the study, considering possible broad effects of nonstationary time series on water balance simulations. It is also crucial that the hydrologic modelling community improves existing calibration and validation practices to better include nonstationary processes.     

Equifinality and uncertainty in physically based soil erosion models: application of the GLUE methodology to WEPP–the Water Erosion Prediction Project–for sites in the UK and USA

Despite the wealth of soil erosion models available for the prediction of both runoff and soil loss at a variety of scales, little quantification is made of uncertainty and error associated with model output. This in part reflects the need to produce unequivocal or optimal results for the end user, which will often be an unrealistic goal. This paper presents a conceptually simple methodology, Generalized Likelihood Uncertainty Estimation (GLUE), for assessing the degree of uncertainty surrounding output from a physically based soil erosion model, the Water Erosion Prediction Project (WEPP). The ability not only to be explicit about model error but also to evaluate future improvements in parameter estimation, observed data or scientific understanding is demonstrated. This approach is applied to two sets of soil loss/runoff plot replicates, one in the UK and one in the USA. Although it is demonstrated that observations can be largely captured within uncertainty bounds, results indicate that these uncertainty bounds are often wide, reflecting the need to qualify results that derive from ‘optimum’ parameter sets, and to accept the concept of equifinality within soil erosion models. Attention is brought to the problem of under‐prediction of large events/over‐prediction of small events, as an area where model improvements could be made, specifically in the case of relatively dry years. Finally it is proposed that such a technique of model evaluation be employed more widely within the discipline so as to aid the interpretation and understanding of complex model output. Copyright © 2000 John Wiley & Sons, Ltd.     

Identifiability analysis: towards constrained equifinality and reduced uncertainty in a conceptual model

Abstract

Different sets of parameters and conceptualizations of a basin can give equally good results in terms of predefined objective functions. Therefore, a need exists to tackle equifinality and quantify the uncertainty bands of a model. In this paper we use the concepts of equifinality, identifiability and uncertainty to propose a simple method aimed at constraining the equifinal parameters and reducing the uncertainty bands of model outputs, and obtaining physically possible and reasonable models. Additionally, the uncertainty of equifinal solutions is quantified to estimate the amount by which output uncertainty can be reduced by knowing how to discard most of the equifinal solutions of a model. As a study case, a conceptual model of the Chillán basin in Chile is carried out. From the study it is concluded that using identifiability analysis makes it possible to constrain equifinal solutions with reduced uncertainty and realistic models, resulting in a framework that can be recommended to practitioners, especially due to the simplicity of the method.     

Multiple objective evaluation of a simple phosphorus transfer model

A simple phosphorus (P) transfer model of the Welland catchment, UK, is evaluated against multiple objective functions using a Monte Carlo approach that combines calibration, identifiability, sensitivity and uncertainty analysis. The model is based on simple conceptual rainfall‐runoff and river routing components, combined with estimates of the daily non‐point source load derived from annual landuse‐based export coefficients, disaggregated as a function of the runoff. The model has limited data requirements, consistent with data availability, and is parsimoneous with respect to the number of parameters identified through inverse modelling. The best performing parameter sets capture the main aspects of the observed flow and total P (TP) concentrations and provide a suitable basis for a decision‐support tool. However, a trade‐off is evident between matching the observed flow peaks, flow recessions and TP concentrations simultaneously, highlighting some limitations of the model structure and/or calibration data. Model analysis indicates that daily non‐point source load cannot be described as a function of near‐surface runoff and land use alone, but that other influences, including seasonality, are important. However, further model development to improve performance is likely to introduce additional complexity (in terms of parameter numbers), and hence additional problems of parameter identifiability and output uncertainty, which in turn raises issues of the information content of the available data. Copyright © 2004 John Wiley & Sons, Ltd.     

Hydrologic data assimilation using particle Markov chain Monte Carlo simulation: Theory,concepts and applications

During the past decades much progress has been made in the development of computer based methods for parameter and predictive uncertainty estimation of hydrologic models. The goal of this paper is twofold. As part of this special anniversary issue we first shortly review the most important historical developments in hydrologic model calibration and uncertainty analysis that has led to current perspectives. Then, we introduce theory, concepts and simulation results of a novel data assimilation scheme for joint inference of model parameters and state variables. This Particle-DREAM method combines the strengths of sequential Monte Carlo sampling and Markov chain Monte Carlo simulation and is especially designed for treatment of forcing, parameter, model structural and calibration data error. Two different variants of Particle-DREAM are presented to satisfy assumptions regarding the temporal behavior of the model parameters. Simulation results using a 40-dimensional atmospheric “toy” model, the Lorenz attractor and a rainfall–runoff model show that Particle-DREAM, P-DREAM_(VP) and P-DREAM_(IP) require far fewer particles than current state-of-the-art filters to closely track the evolving target distribution of interest, and provide important insights into the information content of discharge data and non-stationarity of model parameters. Our development follows formal Bayes, yet Particle-DREAM and its variants readily accommodate hydrologic signatures, informal likelihood functions or other (in)sufficient statistics if those better represent the salient features of the calibration data and simulation model used.