Uncertainty in hydrologic modelling for estimating hydrologic response due to climate change (Santiam River,Oregon)

This paper explores the predicted hydrologic responses associated with the compounded error of cascading global circulation model (GCM) uncertainty through hydrologic model uncertainty due to climate change. A coupled groundwater and surface water flow model (GSFLOW) was used within the differential evolution adaptive metropolis (DREAM) uncertainty approach and combined with eight GCMs to investigate uncertainties in hydrologic predictions for three subbasins of varying hydrogeology within the Santiam River basin in Oregon, USA. Predictions of future hydrology in the Santiam River include increases in runoff in the fall and winter months and decreases in runoff for the spring and summer months. One‐year peak flows were predicted to increase whereas 100‐year peak flows were predicted to slightly decrease. The predicted 10‐year 7‐day low flow decreased in two subbasins with little groundwater influences but increased in another subbasin with substantial groundwater influences. Uncertainty in GCMs represented the majority of uncertainty in the analysis, accounting for an average deviation from the median of 66%. The uncertainty associated with use of GSFLOW produced only an 8% increase in the overall uncertainty of predicted responses compared to GCM uncertainty. This analysis demonstrates the value and limitations of cascading uncertainty from GCM use through uncertainty in the hydrologic model, offers insight into the interpretation and use of uncertainty estimates in water resources analysis, and illustrates the need for a fully nonstationary approach with respect to calibrating hydrologic models and transferring parameters across basins and time for climate change analyses. Copyright © 2012 John Wiley & Sons, Ltd.     

Investigating the uncertainty and transferability of parameters in SWAT model under climate change

ABSTRACT

There is an implicit assumption in most work that the parameters calibrated based on observations remain valid for future climatic conditions. However, this might not be true due to parameter instability. This paper investigates the uncertainty and transferability of parameters in a hydrological model under climate change. Parameter transferability is investigated with three parameter sets identified for different climatic conditions, which are: wet, intermediate and dry. A parameter set based on the baseline period (1961–1990) is also investigated for comparison. For uncertainty analysis, a k-simulation set approach is proposed instead of employing the traditional optimization method which uses a single best-fit parameter set. The results show that the parameter set from the wet sub-period performs the best when transferred into wet climate condition, while the parameter set from the baseline period is the most appropriate when transferred into dry climate condition. The largest uncertainty of simulated daily high flows for 2011–2040 is from the parameter set trained in the dry sub-period, while that of simulated daily medium and low flows lies in the parameter set from the intermediate calibration sub-period. For annual changes in the future period, the uncertainty with the parameter set from the intermediate sub-period is the largest, followed by the wet sub-period and dry sub-period. Compared with high and medium flows/runoffs, the uncertainty of low flows/runoffs is much smaller for both simulated daily flows and annual runoffs. For seasonal runoffs, the largest uncertainty is from the intermediate sub-period, while the smallest is from the dry sub-period. Apart from that, the largest uncertainty can be observed for spring runoffs and the lowest one for autumn runoffs. Compared with the traditional optimization method, the k-simulation set approach shows many more advantages, particularly being able to provide uncertainty information to decision support for watershed management under climate change.

EDITOR Z.W. Kundzewicz ASSOCIATE EDITOR not assigned     

Sources of uncertainty in estimating stream solute export from headwater catchments at three sites

Uncertainty in the estimation of hydrologic export of solutes has never been fully evaluated at the scale of a small‐watershed ecosystem. We used data from the Gomadansan Experimental Forest, Japan, Hubbard Brook Experimental Forest, USA, and Coweeta Hydrologic Laboratory, USA, to evaluate many sources of uncertainty, including the precision and accuracy of measurements, selection of models, and spatial and temporal variation. Uncertainty in the analysis of stream chemistry samples was generally small but could be large in relative terms for solutes near detection limits, as is common for ammonium and phosphate in forested catchments. Instantaneous flow deviated from the theoretical curve relating height to discharge by up to 10% at Hubbard Brook, but the resulting corrections to the theoretical curve generally amounted to <0.5% of annual flows. Calibrations were limited to low flows; uncertainties at high flows were not evaluated because of the difficulties in performing calibrations during events. However, high flows likely contribute more uncertainty to annual flows because of the greater volume of water that is exported during these events. Uncertainty in catchment area was as much as 5%, based on a comparison of digital elevation maps with ground surveys. Three different interpolation methods are used at the three sites to combine periodic chemistry samples with streamflow to calculate fluxes. The three methods differed by <5% in annual export calculations for calcium, but up to 12% for nitrate exports, when applied to a stream at Hubbard Brook for 1997–2008; nitrate has higher weekly variation at this site. Natural variation was larger than most other sources of uncertainty. Specifically, coefficients of variation across streams or across years, within site, for runoff and weighted annual concentrations of calcium, magnesium, potassium, sodium, sulphate, chloride, and silicate ranged from 5 to 50% and were even higher for nitrate. Uncertainty analysis can be used to guide efforts to improve confidence in estimated stream fluxes and also to optimize design of monitoring programmes. © 2014 The Authors. Hydrological Processes published John Wiley & Sons, Ltd.     

Uncertainty assessment in river flow projections for Ethiopia’s Upper Awash Basin using multiple GCMs and hydrological models

ABSTRACT

Uncertainty in climate change impacts on river discharge in the Upper Awash Basin, Ethiopia, is assessed using five MIKE SHE hydrological models, six CMIP5 general circulation models (GCMs) and two representative concentration pathways (RCP) scenarios for the period 2071–2100. Hydrological models vary in their spatial distribution and process representations of unsaturated and saturated zones. Very good performance is achieved for 1975–1999 (NSE: 0.65–0.8; r: 0.79–0.93). GCM-related uncertainty dominates variability in projections of high and mean discharges (mean: –34% to +55% for RCP4.5, – 2% to +195% for RCP8.5). Although GCMs dominate uncertainty in projected low flows, inter-hydrological model uncertainty is considerable (RCP4.5: –60% to +228%, RCP8.5: –86% to +337%). Analysis of variance uncertainty attribution reveals that GCM-related uncertainty occupies, on average, 68% of total uncertainty for median and high flows and hydrological models no more than 1%. For low flows, hydrological model uncertainty occupies, on average, 18% of total uncertainty; GCM-related uncertainty remains substantial (average: 28%).     

Sensitivity analysis and uncertainty assessment in water budgets simulated by the variable infiltration capacity model for Canadian subarctic watersheds

In this study, we evaluate uncertainties propagated through different climate data sets in seasonal and annual hydrological simulations over 10 subarctic watersheds of northern Manitoba, Canada, using the variable infiltration capacity (VIC) model. Further, we perform a comprehensive sensitivity and uncertainty analysis of the VIC model using a robust and state-of-the-art approach. The VIC model simulations utilize the recently developed variogram analysis of response surfaces (VARS) technique that requires in this application more than 6,000 model simulations for a 30-year (1981–2010) study period. The method seeks parameter sensitivity, identifies influential parameters, and showcases streamflow sensitivity to parameter uncertainty at seasonal and annual timescales. Results suggest that the Ensemble VIC simulations match observed streamflow closest, whereas global reanalysis products yield high flows (0.5–3.0 mm day⁻¹) against observations and an overestimation (10–60%) in seasonal and annual water balance terms. VIC parameters exhibit seasonal importance in VARS, and the choice of input data and performance metrics substantially affect sensitivity analysis. Uncertainty propagation due to input forcing selection in each water balance term (i.e., total runoff, soil moisture, and evapotranspiration) is examined separately to show both time and space dimensionality in available forcing data at seasonal and annual timescales. Reliable input forcing, the most influential model parameters, and the uncertainty envelope in streamflow prediction are presented for the VIC model. These results, along with some specific recommendations, are expected to assist the broader VIC modelling community and other users of VARS and land surface schemes, to enhance their modelling applications.     

The comparative study of multi‐site uncertainty evaluation method based on SWAT model

With the recent development of distributed hydrological models, the use of multi‐site observed data to evaluate model performance is becoming more common. Distributed hydrological model have many advantages, and at the same time, it also faces the challenge to calibrate over‐do parameters. As a typical distributed hydrological model, problems also exist in Soil and Water Assessment Tool (SWAT) parameter calibration. In the paper, four different uncertainty approaches – Particle Swarm Optimization (PSO) techniques, Generalized Likelihood Uncertainty Estimation (GLUE), Sequential Uncertainty Fitting algorithm (SUFI‐2) and Parameter Solution (PARASOL) – are taken to a comparative study with the SWAT model applied in Peace River Basin, central Florida. In our study, the observed river discharge data used in SWAT model calibration were collected from the three gauging stations at the main tributary of the Peace River. Behind these approaches, there is a shared philosophy; all methods seek out many parameter set to fit the uncertainties due to the non‐uniqueness in model parameter evaluation. On the basis of the statistical results of four uncertainty methods, difficulty level of each method, the number of runs and theoretical basis, the reasons that affected the accuracy of simulation were analysed and compared. Furthermore, for the four uncertainty method with SWAT model in the study area, the pairwise correlation between parameters and the distributions of model fit summary statistics computed from the sampling over the behavioural parameter and the entire model calibration parameter feasible spaces were identified and examined. It provided additional insight into the relative identifiability of the four uncertainty methods Copyright © 2014 John Wiley & Sons, Ltd.     

Parameter Uncertainty Propagation in a Rainfall–Runoff Model; Case Study: Karoon-III River Basin

Conceptual hydrological models are popular tools for simulating land phase of hydrological cycle. Uncertainty arises from a variety of sources such as input error, calibration and parameters. Hydrologic modeling researches indicate that parametric uncertainty has been considered as one of the most important source. The objective of this study was to evaluate parameter uncertainty and its propagation in rainfall-runoff modeling. This study tried to model daily flows and calculate uncertainty bounds for Karoon-III basin, Southwest of Iran, using HEC-HMS (SMA). The parameters were represented by probability distribution functions (PDF), and the effect on simulated runoff was investigated using Latin Hypercube Sampling (LHS) on Monte Carlo (MC). Three chosen parameters, based on sensitivity analysis, were saturated-hydraulic-conductivity (Ks), Clark storage coefficient (R) and time of concentration (t _c ). Uncertainty associated with parameters were accounted for, by representing each with a probability distribution. Uncertainty bounds was calculated, using parameter sets captured from LHS on parameters PDF of sub-basins and propagating to the model. Results showed that maximum reliability (11%) resulted from Ks propagating. For three parameters, underestimation was more than overestimation. Maximum sharpness and standard deviation (STD) was resulted from propagating Ks. Cumulative Distribution Function (CDF) of flow and uncertainty bounds showed that as flow increased, the width of uncertainty bounds increased for all parameters.     

Definitions of climatological and discharge days: do they matter in hydrological modelling?

The performance of hydrological models is affected by uncertainty related to observed climatological and discharge data. Although the latter has been widely investigated, the effects on hydrological models from different starting times of the day have received little interest. In this study, observational data from one tropical basin were used to investigate the effects on a typical bucket-type hydrological model, the HBV, when the definitions of the climatological and discharge days are changed. An optimization procedure based on a genetic algorithm was used to assess the effects on model performance. Nash-Sutcliffe efficiencies varied considerably between day definitions, with the largest dependence on the climatological-day definition. The variation was likely caused by how storm water was assigned to one or two daily rainfall values depending on the definition of the climatological day. Hydrological models are unlikely to predict high flows accurately if rainfall intensities are reduced because of the day definition.     

Predictive uncertainty of a nearshore bed evolution model

Predictions of nearshore depth evolution using process-based numerical simulation models contain inherent uncertainties owing to model structural deficiencies, measurement errors, and parameter uncertainty. This paper quantifies the parameter-induced predictive uncertainty of the cross-shore depth evolution model Unibest-TC by applying the Bayesian Generalised Likelihood Uncertainty Estimation methodology to modelling depth evolution at Egmond aan Zee (Netherlands). This methodology works with multiple sets of parameter values sampled uniformly in feasible parameter space and assigns a likelihood value to each parameter set. Acceptable simulations (i.e., based on parameter sets with a nonzero likelihood) were found for a wide range of parameter values owing to parameter interdependence and insensitivity. The 95% uncertainty prediction interval of bed levels after the 33 days prediction period was largest (0.5–1 m) near the sandbar crests that characterize the Egmond depth profile, reducing to near-zero values in the sandbar troughs and the offshore area. The prediction interval built up during storms (when sediment transport rates are largest) and remained the same or even reduced slightly during less-energetic conditions. The prediction uncertainty ranges bracket the observations near the inner-bar crest, its seaward flank, and at the seaward flank of the outer bar, suggesting that elsewhere model structural errors (and, potentially, measurement errors) dominate over parameter errors. The interdependence and the non-Gaussian marginal posterior distribution functions of the free model parameters cast doubt on the ability of commonly applied multivariate normal distribution functions to estimate parameter uncertainty.     

Multisource hydrologic modeling uncertainty analysis using the IBUNE framework in a humid catchment

Hydrologic cycle is a complex system associated with both certain and uncertain constituents. The propagation of confidence bounds from different uncertainty sources to model output is of great significance for hydrologic modeling. In this paper, we applied the integrated bayesian uncertainty estimator to quantify the effects of parameter, input and model structure uncertainty on hydrologic modeling progressively. Two hydrologic models (Xinanjiang model and TOPMODEL) were applied to a humid catchment under three scenarios. Case I: the shuffled complex evolution metropolis (SCEM-UA) algorithm was conducted to determine the posterior parameter distribution of hydrologic models and analyze the corresponding forecast uncertainty. Case II: input uncertainty was also considered by assuming rain depth bias follows a normal distribution, and integrated with SCEM-UA. Case III: Simulations from two models were combined by the Bayesian model averaging to fully quantify multisource uncertainty effects. Results suggested that, from Case I to II, the containing ratio (percentage of observed streamflow enveloped by 95% confidence interval) obviously increased by an average magnitude of 10% for the study period 2000–2006. Besides, it also found that the width of 95% confidence interval became wider and narrower for Xinanjiang model and TOPMODEL, respectively, from Case I to II. This may indicate that the uncertainty of TOPMODEL results was more remarkable than Xinanjiang model in Case I. By combining results from two models, model structure uncertainty was also considered in Case III. The accuracy of uncertainty bounds further improved with the containing ratio of 95% confidence interval >95%. In addition, the optimized deterministic results from the uncertainty analysis showed that the average Nash–Sutcliffe coefficient increased continually from Case I to II and III (0.82, 0.84 and 0.90, respectively) for the study period. The analysis demonstrated the improvement of modeling accuracy when extra uncertainty sources were also quantified, and this finding also proved the applicability of IBUNE framework in hydrologic modeling.     

Can climate variability information constrain a hydrological model for an ungauged Costa Rican catchment?

Long‐term hydrological data are key to understanding catchment behaviour and for decision making within water management and planning. Given the lack of observed data in many regions worldwide, such as Central America, hydrological models are an alternative for reproducing historical streamflow series. Additional types of information—to locally observed discharge—can be used to constrain model parameter uncertainty for ungauged catchments. Given the strong influence that climatic large‐scale processes exert on streamflow variability in the Central American region, we explored the use of climate variability knowledge as process constraints to constrain the simulated discharge uncertainty for a Costa Rican catchment, assumed to be ungauged. To reduce model uncertainty, we first rejected parameter relationships that disagreed with our understanding of the system. Then, based on this reduced parameter space, we applied the climate‐based process constraints at long‐term, inter‐annual, and intra‐annual timescales. In the first step, we reduced the initial number of parameters by 52%, and then, we further reduced the number of parameters by 3% with the climate constraints. Finally, we compared the climate‐based constraints with a constraint based on global maps of low‐flow statistics. This latter constraint proved to be more restrictive than those based on climate variability (further reducing the number of parameters by 66% compared with 3%). Even so, the climate‐based constraints rejected inconsistent model simulations that were not rejected by the low‐flow statistics constraint. When taken all together, the constraints produced constrained simulation uncertainty bands, and the median simulated discharge followed the observed time series to a similar level as an optimized model. All the constraints were found useful in constraining model uncertainty for an—assumed to be—ungauged basin. This shows that our method is promising for modelling long‐term flow data for ungauged catchments on the Pacific side of Central America and that similar methods can be developed for ungauged basins in other regions where climate variability exerts a strong control on streamflow variability.     

Use of spatially distributed water table observations to constrain uncertainty in a rainfall–runoff model

The Generalised Likelihood Uncertainty Estimation (GLUE) methodology is used to investigate how distributed water table observations modify simulation and parameter uncertainty for the hydrological model TOPMODEL, applied to the Sæternbekken Minifelt catchment in Norway. Errors in simulating observed flows, continuously-logged borehole water levels and more extensive, spatially distributed water table depths are combined using Bayes' equation within a `likelihood measure' L. It is shown how the distributions of L for the TOPMODEL parameters change as the different types of observed data are considered. These distributions are also used to construct corresponding simulation uncertainty bounds for flows, borehole water levels, and water table depths within the spatially-extensive piezometer network. Qualitatively wide uncertainty bounds for water table simulations are thought to be consistent with the simplified nature of the distributed model.     

Climate models and hydrological parameter uncertainties in climate change impacts on monthly runoff and daily flow duration curve of a Mediterranean catchment

ABSTRACT

Climate models and hydrological parameter uncertainties were quantified and compared while assessing climate change impacts on monthly runoff and daily flow duration curve (FDC) in a Mediterranean catchment. Simulations of the Soil and Water Assessment Tool (SWAT) model using an ensemble of behavioural parameter sets derived from the Generalized Likelihood Uncertainty Estimation (GLUE) method were approximated by feed-forward artificial neural networks (FF-NN). Then, outputs of climate models were used as inputs to the FF-NN models. Subsequently, projected changes in runoff and FDC were calculated and their associated uncertainty was partitioned into climate model and hydrological parameter uncertainties. Runoff and daily discharge of the Chiba catchment were expected to decrease in response to drier and warmer climatic conditions in the 2050s. For both hydrological indicators, uncertainty magnitude increased when moving from dry to wet periods. The decomposition of uncertainty demonstrated that climate model uncertainty dominated hydrological parameter uncertainty in wet periods, whereas in dry periods hydrological parametric uncertainty became more important.

Editor M.C. Acreman; Associate editor S. Kanae     

A general Bayesian framework for calibrating and evaluating stochastic models of annual multi-site hydrological data

Multi-site simulation of hydrological data are required for drought risk assessment of large multi-reservoir water supply systems. In this paper, a general Bayesian framework is presented for the calibration and evaluation of multi-site hydrological data at annual timescales. Models included within this framework are the hidden Markov model (HMM) and the widely used lag-1 autoregressive (AR(1)) model. These models are extended by the inclusion of a Box–Cox transformation and a spatial correlation function in a multi-site setting. Parameter uncertainty is evaluated using Markov chain Monte Carlo techniques. Models are evaluated by their ability to reproduce a range of important extreme statistics and compared using Bayesian model selection techniques which evaluate model probabilities. The case study, using multi-site annual rainfall data situated within catchments which contribute to Sydney’s main water supply, provided the following results: Firstly, in terms of model probabilities and diagnostics, the inclusion of the Box–Cox transformation was preferred. Secondly the AR(1) and HMM performed similarly, while some other proposed AR(1)/HMM models with regionally pooled parameters had greater posterior probability than these two models. The practical significance of parameter and model uncertainty was illustrated using a case study involving drought security analysis for urban water supply. It was shown that ignoring parameter uncertainty resulted in a significant overestimate of reservoir yield and an underestimation of system vulnerability to severe drought.     

Improvement and comparative assessment of a hydrological modelling approach on 20 catchments of various sizes under different climate conditions

Assessing water resources is an important issue, especially in the context of climatic changes. Although numerous hydrological models exist, new approaches are still under investigation. In this context, we propose a modelling approach based on the physical principle of least action. We present new hypotheses to develop the model further, to widen its application. The improved version of the model MODHYPMA was applied on 20 sub-catchments in Africa and the USA. Its performance was compared with two well-known lumped conceptual models, GR4J and HBV. The model could be successfully calibrated and validated. In calibration, GR4J performed better, while other models had similar performance. In validation, MODHYPMA and GR4J performed similarly and better than HBV. The parameter λ has medium sensitivity while parameters λ and TX have low sensitivity. The parameter uncertainty for MODHYPMA, analysed using the GLUE methodology, was higher during high flows but with good p and r factors.

EDITOR D. Koutsoyiannis ASSOCIATE EDITOR not assigned     

Stage‐discharge uncertainty derived with a non‐stationary rating curve in the Choluteca River,Honduras

Uncertainty in discharge data must be critically assessed before data can be used in, e.g. water resources estimation or hydrological modelling. In the alluvial Choluteca River in Honduras, the river‐bed characteristics change over time as fill, scour and other processes occur in the channel, leading to a non‐stationary stage‐discharge relationship and difficulties in deriving consistent rating curves. Few studies have investigated the uncertainties related to non‐stationarity in the stage‐discharge relationship. We calculated discharge and the associated uncertainty with a weighted fuzzy regression of rating curves applied within a moving time window, based on estimated uncertainties in the observed rating data. An 18‐year‐long dataset with unusually frequent ratings (1268 in total) was the basis of this study. A large temporal variability in the stage‐discharge relationship was found especially for low flows. The time‐variable rating curve resulted in discharge estimate differences of ? 60 to + 90% for low flows and ± 20% for medium to high flows when compared to a constant rating curve. The final estimated uncertainty in discharge was substantial and the uncertainty limits varied between ? 43 to + 73% of the best discharge estimate. Copyright © 2010 John Wiley & Sons, Ltd.     

Modelling the impacts of land-cover change on streamflow dynamics of a tropical rainforest headwater catchment

Abstract

A modelling experiment is used to examine different land-use scenarios ranging from extreme deforestation (31% forest cover) to pristine (95% forest cover) conditions and related Payment for Ecosystem Services (PES) schemes to assess whether a change in streamflow dynamics, discharge extremes and mean annual water balance of a 73.4-km² tropical headwater catchment in Costa Rica could be detected. A semi-distributed, conceptual rainfall–runoff model was adapted to conceptualize the empirically-based, dominant hydrological processes of the study area and was multi-criteria calibrated using different objective functions and empirical constraints on model simulations in a Monte Carlo framework to account for parameter uncertainty. The results suggest that land-use change had relatively little effect on the overall mean annual water yield (<3%). However, streamflow dynamics proved to be sensitive in terms of frequency, timing and magnitude of discharge extremes. For low flows and peak discharges of return periods greater than one year, land use had a minor influence on the runoff response. Below these thresholds (<1-year return period), forest cover potentially decreased runoff peaks and low flows by as much as 10%, and non-forest cover increased runoff peaks and low flows by up to 15%. The study demonstrated the potential for using hydrological modelling to help identify the impact of protection and reforestation efforts on ecosystem services.

Editor Z.W. Kundzewicz

Citation Birkel, C., Soulsby, C., and Tetzlaff, D., 2012. Modelling the impacts of land-cover change on streamflow dynamics of a tropical rainforest headwater catchment. Hydrological Sciences Journal, 57 (8), 1543–1561.     

Parameter estimation and uncertainty analysis of SWAT model in upper reaches of the Heihe river basin

Heihe river basin, the second largest inland river basin in China, has attracted more attention in China due to the ever increasing water resources and eco‐environmental problems. In this article, SWAT (Soil and Water Assessment Tool; http://www.brc.tamus.edu/swat/ ) model was applied to upper reaches of the basin for better understanding of the hydrological process over the watershed. Parameter uncertainty and its contribution on model simulation are the main foci. In model calibration, the aggregate parameters instead of the original parameters in SWAT model were used to reduce the computing effort. The Bayesian approach was employed for parameter estimation and uncertainty analysis because its posterior distribution provides not only parameter estimation but also uncertainty analysis without normality assumption. The results indicated that: (1) SWAT model performs satisfactorily in this watershed as a whole, although some low and high flows were under‐ or overestimated, particularly in dry (e.g. 1991) and wet (e.g. 1996) years; (2) all calibrated parameters were not normally distributed (essentially positively or negatively skewed) and the parameter uncertainties were relatively small; and (3) the contributions of parameter uncertainty on model simulation uncertainty were relatively small. Copyright © 2009 John Wiley & Sons, Ltd.     

Assessing uncertainties in a conceptual water balance model using Bayesian methodology / Estimation bayésienne des incertitudes au sein d’une modélisation conceptuelle de bilan hydrologique

Abstract

Abstract The aim of this study was to estimate the uncertainties in the streamflow simulated by a rainfall–runoff model. Two sources of uncertainties in hydrological modelling were considered: the uncertainties in model parameters and those in model structure. The uncertainties were calculated by Bayesian statistics, and the Metropolis-Hastings algorithm was used to simulate the posterior parameter distribution. The parameter uncertainty calculated by the Metropolis-Hastings algorithm was compared to maximum likelihood estimates which assume that both the parameters and model residuals are normally distributed. The study was performed using the model WASMOD on 25 basins in central Sweden. Confidence intervals in the simulated discharge due to the parameter uncertainty and the total uncertainty were calculated. The results indicate that (a) the Metropolis-Hastings algorithm and the maximum likelihood method give almost identical estimates concerning the parameter uncertainty, and (b) the uncertainties in the simulated streamflow due to the parameter uncertainty are less important than uncertainties originating from other sources for this simple model with fewer parameters.