Calibration Of Hydrological Models Research Articles

A Clustering Preprocessing Framework for the Subannual Calibration of a Hydrological Model Considering Climate‐Land Surface Variations

AbstractOne model structural deficiency is that some dynamic characteristics (such as seasonal dynamics) in catchment conditions are not explicitly represented by hydrological models. This study integrates data mining techniques to develop a clustering preprocessing framework for the subannual calibration of hydrological models to simulate seasonal dynamic behaviors. The proposed framework aims to solve the problems caused by missing processes and deficiencies of hydrological models, providing guidance for future model development. A set of climatic‐land surface indices is provided and preprocessed using the maximal information coefficient and the principal component analysis. Two clustering operations are performed based on the preprocessed climatic index and land‐surface index systems. Hydrological data are clustered into subannual periods for calibration. The parameters are independently optimized for each subperiod using a modified parallel calibration scheme and are then combined to generate a continuous simulation. The framework is applied in calibrating the TOPMODEL. The results show that the performance of the model with a clustering preprocessing framework in the middle‐ and low‐flow conditions is significantly improved without reducing the simulation accuracy for high flows. The transposability of the model parameters from the calibration to validation period has been improved significantly as well. The anomalous parameter values may be attributed in part to the convergence problem when using an optimization algorithm. Though well applied in the TOPMODEL, the framework has the potential to be used in other hydrological models.

A Ranking of Hydrological Signatures Based on Their Predictability in Space

AbstractHydrological signatures are now used for a wide range of purposes, including catchment classification, process exploration, and hydrological model calibration. The recent boost in the popularity and number of signatures has however not been accompanied by the development of clear guidance on signature selection. Here we propose that exploring the predictability of signatures in space provides important insights into their drivers and their sensitivity to data uncertainties and is hence useful for signature selection. We use three complementary approaches to compare and rank 15 commonly used signatures, which we evaluate in 600+ U.S. catchments from the Catchment Attributes and MEteorology for Large‐sample Studies (CAMELS) data set. First, we employ machine learning (random forests) to explore how attributes characterizing the climatic conditions, topography, land cover, soil, and geology influence (or not) the signatures. Second, we use simulations of the Sacramento Soil Moisture Accounting model to benchmark the random forest predictions. Third, we take advantage of the large sample of CAMELS catchments to characterize the spatial autocorrelation (using Moran's I) of the signature field. These three approaches lead to remarkably similar rankings of the signatures. We show (i) that signatures with the noisiest spatial pattern tend to be poorly captured by hydrological simulations, (ii) that their relationship to catchments attributes are elusive (in particular they are not well explained by climatic indices), and (iii) that they are particularly sensitive to discharge uncertainties. We suggest that a better understanding of the drivers of hydrological signatures and a better characterization of their uncertainties would increase their value in hydrological studies.

A Robust Gauss‐Newton Algorithm for the Optimization of Hydrological Models: Benchmarking Against Industry‐Standard Algorithms

AbstractOptimization of model parameters is a ubiquitous task in hydrological and environmental modeling. Currently, the environmental modeling community tends to favor evolutionary techniques over classical Newton‐type methods, in the light of the geometrically problematic features of objective functions, such as multiple optima and general nonsmoothness. The companion paper (Qin et al., 2018, https://doi.org/10.1029/2017WR022488) introduced the robust Gauss‐Newton (RGN) algorithm, an enhanced version of the standard Gauss‐Newton algorithm that employs several heuristics to enhance its explorative abilities and perform robustly even for problematic objective functions. This paper focuses on benchmarking the RGN algorithm against three optimization algorithms generally accepted as “best practice” in the hydrological community, namely, the Levenberg‐Marquardt algorithm, the shuffled complex evolution (SCE) search (with 2 and 10 complexes), and the dynamically dimensioned search (DDS). The empirical case studies include four conceptual hydrological models and three catchments. Empirical results indicate that, on average, RGN is 2–3 times more efficient than SCE (2 complexes) by achieving comparable robustness at a lower cost, 7–9 times more efficient than SCE (10 complexes) by trading off some speed to more than compensate for a somewhat lower robustness, 5–7 times more efficient than Levenberg‐Marquardt by achieving higher robustness at a moderate additional cost, and 12–26 times more efficient than DDS in terms of robustness‐per‐fixed‐cost. A detailed analysis of performance in terms of reliability and cost is provided. Overall, the RGN algorithm is an attractive option for the calibration of hydrological models, and we recommend further investigation of its benefits for broader types of optimization problems.

A TOPSIS-Based Multicriteria Approach to the Calibration of a Basin-Scale SWAT Hydrological Model

Calibration is one of the most important steps of hydrological modeling and applications. Observed data availability and model parameterization are two important factors affecting the calibration efficiency of the models. This study focuses on the assessment of the effects of the number and location of sites (LoS), number of parameters (NoP), and the calibration method (CM) on the performance of the SWAT hydrological model of a basin. Accordingly, twelve different models with respect to LoS, NoP, and CM are built for the Sirwan River Basin in Iran. NS, R-factor and P-factor efficiency criteria are then used to evaluate how well the models perform both in calibration and validation stages. In order to prioritize the models, TOPSIS multi-criteria decision analysis approach is applied to aggregate different efficiency criteria and to discriminate between the models. Results show the usefulness of the proposed MCDA-based approach to rank different alternatives (settings) of model calibration. Additionally, multi-site calibration is not always better than single-site calibration, and the locations of the sites included in the calibration procedure are also important in this respect.

Modelling precipitation uncertainties in a multi-objective Bayesian ecohydrological setting

Recent studies have demonstrated that hydrological model calibrations are impaired by uncertainties in observations and model structures. For a rainfall-driven model, the error in precipitation observations can lead to biased parameter estimates and predictions. For a conceptual ecohydrological model, an appropriate description of input error is essential because rainfall controls both hydrological processes and vegetation growth in the model. However, to date the impact of precipitation uncertainty on ecohydrologic model parameters and outputs has not been widely explored (Fuentes et al., 2006; Shields and Tague, 2012). The increased dimensionality of these types of models and the uncertainties associated with calibration data can make traditional approaches for characterizing precipitation errors problematic. Our study aims to investigate the impact of precipitation uncertainty for a Bayesian multi-objective calibration approach in an ecohydrological modeling study. A conceptual model that combines a hydrologic model and a modified bucket grassland model is implemented for a forested catchment in Australia. In the study, different input error descriptions are used in both single and multi-objective Bayesian calibration case studies aimed at simulating streamflow and Leaf Area Index (LAI). The emphasis on each objective is represented as different prior distributions defined for error parameters for multi-objective cases. Results show better parameter estimates and predictions for the cases including input error. Comparing the results from the cases in which different input error descriptions are used, a simple bias term works well for both streamflow and LAI estimations. Although a more complex rainfall multiplier approach to represent input error performs best for streamflow predictions, increasing the dimensionality of the input error model is not always justified given the information content of the data. In addition, some of the rainfall multipliers values are not meaningful in the real case, reflecting an overfitting problem.

Parameter uncertainty assessment of a flood forecasting model using multiple objectives

The calibration of hydrological models used for flood forecasting is a difficult task that has received widespread attention. Assessing the uncertainty of flood forecasting models is fundamental to properly support decision‐making activities. Because of the demand of the different decision‐making objectives of a flood management system, we assess the uncertainty of flood forecasting models from a multiobjective perspective. Multicriteria decision analysis (MCDA) is adopted to evaluate the flood likelihood within a generalised likelihood uncertainty estimation (GLUE) framework. By combining four criteria representing different flood characteristics, the acceptability of the simulations is fully examined. The method is applied to an uncertainty analysis of a variable infiltration capacity model for the Xitiaoxi catchment. The results of 10,000 Monte Carlo simulations show that no single criterion can describe the characteristics of floods. Compared with two single‐criterion methods using the Nash–Sutcliffe efficiency, the multicriteria method shows advantages not only in assessing the prediction bounds but also in providing median GLUE estimates. The results indicate that a single criterion may be inadequate in parameter identification within the GLUE framework and that MCDA is an alternative approach to reduce the prediction uncertainty in flood forecasting.

Reducing Computational Costs of Automatic Calibration of Rainfall-Runoff Models: Meta-Models or High-Performance Computers?

Robust calibration of hydrologic models is critical for simulating water resource components; however, the time-consuming process of calibration sometimes impedes the accurate parameters’ estimation. The present study compares the performance of two approaches applied to overcome the computational costs of automatic calibration of the HEC-HMS (Hydrologic Engineering Center-Hydrologic Modeling System) model constructed for the Tamar basin located in northern Iran. The model is calibrated using the Particle Swarm Optimization (PSO) algorithm. In the first approach, a machine learning algorithm, i.e., Artificial Neural Network (ANN) was trained to act as a surrogate for the original HMS (ANN-PSO), while in the latter, the computational tasks were distributed among different processors. Due to inefficacy of preliminary ANN-PSO, an efficient adaptive technique was employed to boost training and accelerate the convergence of optimization. We found that both approaches were helpful in improving computational efficiency. For jointly-events calibrations schemes, meta-models outperformed parallelization due to effective exploration of calibration space, where parallel processing was not practical owing to the time required for data sharing and collecting among many clients. Model approximation using meta-models becomes highly complex, particularly in the presence of combining more events, because larger numbers of samples and much longer training times are required.

Computationally Efficient Multivariate Calibration and Validation of a Grid-Based Hydrologic Model in Sparsely Gauged West African River Basins

The prediction of freshwater resources remains a challenging task in West Africa, where the decline of in situ measurements has a detrimental effect on the quality of estimates. In this study, we establish a series of modeling routines for the grid-based mesoscale Hydrologic Model (mHM) using Multiscale Parameter Regionalization (MPR). We provide a computationally efficient application of mHM-MPR across a diverse range of data-scarce basins using in situ observations, remote sensing, and reanalysis inputs. Model performance was first screened for four precipitation datasets and three evapotranspiration calculation methods. Subsequently, we developed a modeling framework in which the pre-screened model is first calibrated using discharge as the observed variable (mHM Q), and next calibrated using a combination of discharge and actual evapotranspiration data (mHM Q/ET). Both model setups were validated in a multi-variable evaluation framework using discharge, actual evapotranspiration, soil moisture and total water storage data. The model performed reasonably well, with mean discharge KGE values of 0.53 (mHM Q) and 0.49 (mHM Q/ET) for the calibration; and 0.23 (mHM Q) and 0.13 (mHM Q/ET) for the validation. Other tested variables were also within a good predictive range. This further confirmed the robustness and well-represented spatial distribution of the hydrologic predictions. Using MPR, the calibrated model can then be scaled to produce outputs at much smaller resolutions. Overall, our analysis highlights the worth of utilizing additional hydrologic variables (together with discharge) for the reliable application of a distributed hydrologic model in sparsely gauged West African river basins.

Constraining Conceptual Hydrological Models With Multiple Information Sources

AbstractThe calibration of hydrological models without streamflow observations is problematic, and the simultaneous, combined use of remotely sensed products for this purpose has not been exhaustively tested thus far. Our hypothesis is that the combined use of products can (1) reduce the parameter search space and (2) improve the representation of internal model dynamics and hydrological signatures. Five different conceptual hydrological models were applied to 27 catchments across Europe. A parameter selection process, similar to a likelihood weighting procedure, was applied for 1,023 possible combinations of 10 different data sources, ranging from using 1 to all 10 of these products. Distances between the two empirical distributions of model performance metrics with and without using a specific product were determined to assess the added value of a specific product. In a similar way, the performance of the models to reproduce 27 hydrological signatures was evaluated relative to the unconstrained model. Significant reductions in the parameter space were obtained when combinations included Advanced Microwave Scanning Radiometer ‐ Earth Observing System and Advanced Scatterometer soil moisture, Gravity Recovery and Climate Experiment total water storage anomalies, and, in snow‐dominated catchments, the Moderate Resolution Imaging Spectroradiometer snow cover products. The evaporation products of Land Surface Analysis ‐ Satellite Application Facility and MOD16 were less effective for deriving meaningful, well‐constrained posterior parameter distributions. The hydrological signature analysis indicated that most models profited from constraining with an increasing number of data sources. Concluding, constraining models with multiple data sources simultaneously was shown to be valuable for at least four of the five hydrological models to determine model parameters in absence of streamflow.

The hazards of split-sample validation in hydrological model calibration

This paper investigates the issues related to the use of validation in hydrological model calibration. Traditionally, models are calibrated and then assessed on an independent period (split-sample) to determine their adequacy in simulating streamflow as compared to observations. In this study, two hydrological models and three North American catchments are used to evaluate the effects of using validation to assess the model parameters’ robustness on the model’s actual simulation capabilities and accuracy in simulating streamflow. The length of the calibration period is increased from 1 to 16 years, and for each case a large number of randomly selected combinations of years are used for calibration and for validation using the Nash-Sutcliffe Efficiency metric. The calibrated model is then run on an independent 8-year test-period to assess the model’s actual performance in simulation mode in unknown conditions. The process is bootstrapped 30 times to ensure the robustness of the results. The tests pit the calibration/validation methods on increasing calibration period lengths against a full calibration on the entire available dataset. Results show that the calibration on the full dataset is the optimal strategy as it generates the most robust parameter sets, provides the best model accuracy on an independent testing period and does not require assumption-making on the modeler’s part. The calibrated parameter sets for each test-case were evaluated using the relative bias and correlation metrics, which revealed that the method transfers well to these two other metrics. Results also demonstrate the pitfalls of the commonly used split-sampling strategy, where good parameter sets may be discarded due to model performance discrepancies between calibration and validation periods. The conclusions point to the need to use as many years as possible in the calibration step and to entirely disregard the validation aspect under certain conditions.

How good are hydrological models for gap-filling streamflow data?

Abstract. Gap-filling streamflow data is a critical step for most hydrological studies, such as streamflow trend, flood, and drought analysis and hydrological response variable estimates and predictions. However, there is a lack of quantitative evaluation of the gap-filled data accuracy in most hydrological studies. Here we show that when the missing data rate is less than 10 %, the gap-filled streamflow data obtained using calibrated hydrological models perform almost the same as the benchmark data (less than 1 % missing) when estimating annual trends for 217 unregulated catchments widely spread across Australia. Furthermore, the relative streamflow trend bias caused by the gap filling is not very large in very dry catchments where the hydrological model calibration is normally poor. Our results clearly demonstrate that the gap filling using hydrological modelling has little impact on the estimation of annual streamflow and its trends.

Evaluation of the impacts of hydrologic model calibration methods on predictability of ecologically-relevant hydrologic indices

Due to the significant costs associated with stream health monitoring, hydrological modeling is widely used to calculate ecologically-relevant hydrologic indices to better understand the overall condition of streams within large and diverse watersheds. However, hydrologic modeling’s ability to replicate these indices is limited, especially when calibrating models by optimizing a single objective function or when selecting a single optimal solution. Hence, this study evaluates the performance of multi-objective model calibration in representing 167 hydrologic indices of ecological interest using the median values of different Pareto-optimal solution sets. For this purpose, two strategies based on three Nash-Sutcliffe Efficiencies (NSE), and root-mean-squared error (RMSE) with explicit hydrograph partitioning, were implemented. Additionally, the k-means clustering technique was employed to define subsets of Pareto-optimal solutions representing high, medium, and low flow conditions. The Soil and Water Assessment Tool (SWAT) was set up for the Honeyoey Creek-Pine Creek Watershed, located in Michigan, USA, and was calibrated using a single streamflow gauging station and the recently proposed multi-objective optimization algorithm – Non-dominated Sorting Genetic Algorithm III (NSGA-III). The results show that the NSE- and RMSE-based calibration strategies can represent 128 and 123 indices within a range of ±30% relative errors, respectively. In addition, the results of this study demonstrated that using different set of solutions, instead of a single optimal solution, introduces more flexibility in the predictability of different hydrologic indices of ecological interest. Moreover, it is suggested that a multi-objective calibration approach allows the systematic identification of groups of poorly represented and closely related indices. Knowing these poorly represented indices would facilitate the formulation of additional objective functions intended to improve model performance or to detect structural inadequacies.

COMPARISON OF AUTOMATIC CALIBRATION TECHNIQUES FOR SIMULATING STREAMFLOW IN TROPICAL CATCHMENT

Efficacy of hydrological model strongly depends on model calibration. A number of methods has been developed and employed for optimization of hydrological model so that model can replicate the observed streamflow accurately. A study has been carried out in this paper to find the best parameter optimization method for the calibration of a daily rainfall-runoff model for streamflow simulation of a tropical catchment. For the purpose, seven well known parameter optimization methods namely, Uniform Random Search, Pattern Search, Multi Start Pattern Search, Rosenbrock Method, Multi Start Rosenbrock Search, Genetic Algorithm and Suffled Complex Evaluation are used for the calibration of a conceptual hydrological model known as SIMHYD. Performance of the methods is evaluated by using Nash-Sutcliff coefficient and correlation coefficient. The result indicates that evolutionary algorithm based optimization techniques can optimize the model parameters more accurately for precise calibration of model and reliable prediction of daily streamflow in a tropical catchment.

Modeling and Combined Application of Orthogonal Chaotic NSGA-II and Improved TOPSIS to Optimize a Conceptual Hydrological Model

Conceptual rainfall-runoff modelling is a widely-used approach for rainfall-runoff simulation in streamflow forecasting. The objective of this paper is to introduce an improved non-dominated sorting genetic algorithm-II (NSGA-II) for multi-objective automatic calibration of a hydrologic model. The orthogonal design based initialization technique is exploited to produce a more uniformly-distributed initial population. At the same time, a chaotic crossover operator as well as a chaotic mutation operator are presented to avoid trapping into local minima and to obtain high quality solutions. Finally, a multi-criteria decision-making (MCDM) approach combing Shannon entropy weighting method and an improved technique for order preference by similarity to ideal solution (ITOPSIS) based on projection is introduced to prioritize the Pareto optimal solutions and select the comprehensive optimal solution as a follow-up step. Hydrological data from two river basins named the Leaf and Muma River basins are exploited to test the ability of the orthogonal chaotic NSGA-II (OCNSGA-II) for solving the multi-objective HYMOD (MO-HYMOD) problem. The results demonstrate that the OCNSGA-II can obtain better-distributed Pareto optimal front and thus can be exploited as an effective alternative approach for the multi-objective automatic calibration of hydrologic model.

Signature‐Domain Calibration of Hydrological Models Using Approximate Bayesian Computation: Theory and Comparison to Existing Applications

AbstractThis study considers Bayesian calibration of hydrological models using streamflow signatures and its implementation using Approximate Bayesian Computation (ABC). If the modeling objective is to predict streamflow time series and associated uncertainty, a probabilistic model of streamflow must be specified but the inference equations must be developed in the signature domain. However, even starting from simple probabilistic models of streamflow time series, working in the signature domain makes the likelihood function difficult or impractical to evaluate (in particular, as it is unavailable in closed form). This challenge can be tackled using ABC, a general class of numerical algorithms for sampling from conditional distributions, such as (but not limited to) Bayesian posteriors given any calibration data. Using ABC does not avoid the requirement of Bayesian inference to specify a probability model of the data, but rather exchanges the requirement to evaluate the pdf of this model (needed to evaluate the likelihood function) by the requirement to sample model output realizations. For this reason ABC is attractive for inference in the signature domain. We clarify poorly understood aspects of ABC in the hydrological literature, including similarities and differences between ABC and GLUE, and comment on previous applications of ABC in hydrology. An error analysis of ABC approximation errors and their dependence on the tolerance is presented. An empirical case study is used to illustrate the impact of omitting the specification of a probabilistic model (and instead using a deterministic model within the ABC algorithm), and the impact of a coarse ABC tolerance.

Hydrological similarity approach and rainfall satellite utilization for mini hydro power dam basic design (case study on the ungauged catchment at West Borneo, Indonesia)

An approach on flow duration and flood design estimation on the ungauged catchment with no rainfall and discharge data availability was been being develop with hydrological modelling including rainfall run off model implemented with watershed characteristic dataset. Near real time Rainfall data from multi satellite platform e.g. TRMM can be utilized for regionalization approach on the ungauged catchment. Watershed hydrologically similarity analysis were conducted including all of the major watershed in Borneo which was predicted to be similar with the Nanga Raun Watershed. It was found that a satisfactory hydrological model calibration could be achieved using catchment weighted time series of TRMM daily rainfall data, performed on nearby catchment deemed to be sufficiently similar to Nanga Raun catchment in hydrological terms. Based on this calibration, rainfall runoff parameters were then transferred to a model. Relatively reliable flow duration curve and extreme discharge value estimation were produced with reasonable several limitation. Further approach may be performed in order to deal with the primary limitations inherent in the hydrological and statistical analysis, especially to give prolongation to the availability of the rainfall and climate data with some novel approach like downscaling of global climate model.

Application research of multi-objective Artificial Bee Colony optimization algorithm for parameters calibration of hydrological model

Parameter optimization methods for hydrological models have an important impact for the hydrological forecasting. To achieve the parameters’ optimization and calibration for the distributed, conceptual watershed Xinanjiang model effectively and accurately, a multi-objective Artificial Bee Colony algorithm named RMOABC which adopts the mechanisms of regulation operator and Adaptive Grid is introduced in the paper. In the evolution of the algorithm, the regulation operator mechanism can balance the weights of local search and global search, and the Adaptive Grid mechanism is utilized to evaluate and maintain the Pareto solutions in the external archive. In the experiments, three commonly used multi-objective optimization algorithms, the NSGA-II, the e-MOEA and the SMPSO, with the RMOABC algorithm were applied in Heihe River Basin, and the parameter optimization problem of Xinanjiang hydrological model was taken as the application case for long-term runoff prediction to validate and compare their performance. The experiments results showed the RMOABC algorithm can provide more comprehensive and reliable parameters sets for practical hydrological forecasting in the study area with lower execution time.

Statistics for sample splitting for the calibration and validation of hydrological models

Hydrological models have been widely applied in flood forecasting, water resource management and other environmental sciences. Most hydrological models calibrate and validate parameters with available records. However, the first step of hydrological simulation is always to quantitatively and objectively split samples for use in calibration and validation. In this paper, we have proposed a framework to address this issue through a combination of a hierarchical scheme through trial and error method, for systematic testing of hydrological models, and hypothesis testing to check the statistical significance of goodness-of-fit indices. That is, the framework evaluates the performance of a hydrological model using sample splitting for calibration and validation, and assesses the statistical significance of the Nash–Sutcliffe efficiency index (Ef), which is commonly used to assess the performance of hydrological models. The sample splitting scheme used is judged as acceptable if the Ef values exceed the threshold of hypothesis testing. According to the requirements of the hierarchical scheme for systematic testing of hydrological models, cross calibration and validation will help to increase the reliability of the splitting scheme, and reduce the effective range of sample sizes for both calibration and validation. It is illustrated that the threshold of Ef is dependent on the significance level, evaluation criteria (both regarded as the population), distribution type, and sample size. The performance rating of Ef is largely dependent on the evaluation criteria. Three types of distributions, which are based on an approximately standard normal distribution, a Chi square distribution, and a bootstrap method, are used to investigate their effects on the thresholds, with two commonly used significance levels. The highest threshold is from the bootstrap method, the middle one is from the approximately standard normal distribution, and the lowest is from the Chi square distribution. It was found that the smaller the sample size, the higher the threshold values are. Sample splitting was improved by providing more records. In addition, outliers with a large bias between the simulation and the observation can affect the sample values of Ef, and hence the output of the sample splitting scheme. Physical hydrology processes and the purpose of the model should be carefully considered when assessing outliers. The proposed framework in this paper cannot guarantee the best splitting scheme, but the results show the necessary conditions for splitting schemes to calibrate and validate hydrological models from a statistical point of view.

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

AbstractFinding 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 (DREAMZS) 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.

Variance analysis of forecasted streamflow maxima in a wet temperate climate

Coupling global climate models, hydrologic models and extreme value analysis provides a method to forecast streamflow maxima, however the elusive variance structure of the results hinders confidence in application. Directly correcting the bias of forecasts using the relative change between forecast and control simulations has been shown to marginalize hydrologic uncertainty, reduce model bias, and remove systematic variance when predicting mean monthly and mean annual streamflow, prompting our investigation for maxima streamflow. We assess the variance structure of streamflow maxima using realizations of emission scenario, global climate model type and project phase, downscaling methods, bias correction, extreme value methods, and hydrologic model inputs and parameterization. Results show that the relative change of streamflow maxima was not dependent on systematic variance from the annual maxima versus peak over threshold method applied, albeit we stress that researchers strictly adhere to rules from extreme value theory when applying the peak over threshold method. Regardless of which method is applied, extreme value model fitting does add variance to the projection, and the variance is an increasing function of the return period. Unlike the relative change of mean streamflow, results show that the variance of the maxima’s relative change was dependent on all climate model factors tested as well as hydrologic model inputs and calibration. Ensemble projections forecast an increase of streamflow maxima for 2050 with pronounced forecast standard error, including an increase of +30(±21), +38(±34) and +51(±85)% for 2, 20 and 100 year streamflow events for the wet temperate region studied. The variance of maxima projections was dominated by climate model factors and extreme value analyses.