Rating curve estimation under epistemic uncertainty

River discharge values, estimated using a rating curve, are subject to both random and epistemic errors. We present a new likelihood function, the ‘Voting Point’ likelihood that accounts for both error types and enables generation of multiple possible multisegment power‐law rating curve samples that aim to represent the total uncertainty. The rating curve samples can be used for subsequent discharge analysis that needs total uncertainty estimation, e.g. regionalisation studies or calculation of hydrological signatures. We demonstrate the method using four catchments with diverse rating curve error characteristics, where epistemic uncertainty sources include weed growth, scour and redeposition of the bed gravels in a braided river, and unconfined high flows. The results show that typically, the posterior rating curve distributions include all of the gauging points and succeed in representing the spread of discharge values caused by epistemic rating errors. We aim to provide a useful method for hydrology practitioners to assess rating curve, and hence discharge, uncertainty that is easily applicable to a wide range of catchments and does not require prior specification of the particular types and causes of epistemic error at the gauged location. Copyright © 2014 John Wiley & Sons, Ltd.     

The impact of epistemic uncertainty on an earthquake loss model

Models capable of estimating losses in future earthquakes are of fundamental importance for emergency planners, for the insurance and reinsurance industries, and for code drafters. Constructing a loss model for a city, region or country involves compiling databases of earthquake activity, ground conditions, attenuation equations, building stock and infrastructure exposure, and vulnerability characteristics of the exposed inventory, all of which have large associated uncertainties. Many of these uncertainties can be classified as epistemic, implying—at least in theory—that they can be reduced by acquiring additional data or improved understanding of the physical processes. The effort and cost involved in refining the definition of each component of a loss model can be very large, for which reason it is useful to identify the relative impact on the calculated losses due to variations in these components. A mechanically sound displacement‐based approach to loss estimation is applied to a test case of buildings along the northern side of the Sea of Marmara in Turkey. Systematic variations of the parameters defining the demand (ground motion) and the capacity (vulnerability) are used to identify the relative impacts on the resulting losses, from which it is found that the influence of the epistemic uncertainty in the capacity is larger than that of the demand for a single earthquake scenario. Thus, the importance of earthquake loss models which allow the capacity parameters to be customized to the study area under consideration is highlighted. Copyright © 2005 John Wiley & Sons, Ltd.     

Incorporating structural uncertainty of hydrological models in likelihood functions via an ensemble range approach

ABSTRACT

Model ensembles are possibly the most powerful tool to assess uncertainties in runoff predictions stemming from inadequacies in model structure. But in many applications little knowledge is gained about the specific weaknesses of the individual models. Here we introduce the ensemble range approach (ERA). Compared to other ensemble techniques, ERA is primarily intended to facilitate hydrological reasoning about model structural uncertainty. This is attempted by separate modelling of data uncertainty and structural uncertainty with two different error density functions that are combined in one likelihood function. The width of the structural error density is in accordance with the range of runoff predictions calculated by a small model ensemble at each individual time step. Albeit not the only choice, this study is restricted on the use of a modified beta density to represent structural uncertainty. The performance of ERA is assessed in some synthetic and real data case studies. Ensembles of two structurally identical models are applied, made possible by estimating the parameters of ERA and both models simultaneously.

Editor D. Koutsoyiannis; GUEST editor S. Weijs     

A method for uncertainty constraint of catchment discharge and phosphorus load estimates

River discharge and nutrient measurements are subject to aleatory and epistemic uncertainties. In this study, we present a novel method for estimating these uncertainties in colocated discharge and phosphorus (P) measurements. The “voting point”‐based method constrains the derived stage‐discharge rating curve both on the fit to available gaugings and to the catchment water balance. This helps reduce the uncertainty beyond the range of available gaugings and during out of bank situations. In the example presented here, for the top 5% of flows, uncertainties are shown to be 139% using a traditional power law fit, compared with 40% when using our updated “voting point” method. Furthermore, the method is extended to in situ and lab analysed nutrient concentration data pairings, with lower uncertainties (81%) shown for high concentrations (top 5%) than when a traditional regression is applied (102%). Overall, for both discharge and nutrient data, the method presented goes some way to accounting for epistemic uncertainties associated with nonstationary physical characteristics of the monitoring site.     

Implications of model uncertainty for the mapping of hillslope‐scale soil erosion predictions

An integrated modelling approach (MIRSED) which utilizes the process‐based soil erosion model WEPP (Water Erosion Prediction Project) is presented for the assessment of hillslope‐scale soil erosion at five sites throughout England and Wales. The methodology draws upon previous uncertainty analysis of the WEPP hillslope soil erosion model by the authors to qualify model results within an uncertainty framework. A method for incorporating model uncertainty from a range of sources is discussed as a first step towards using and learning from results produced through the GLUE (Generalized Likelihood Uncertainty Estimation) technique. Results are presented and compared to available observed data, which illustrate that levels of uncertainty are significant and must be taken into account if a meaningful understanding of output from models such as WEPP is to be achieved. Furthermore, the collection of quality, observed data is underlined for two reasons: as an essential tool in the development of soil erosion modelling and also to allow further constraint of model uncertainty. Copyright © 2001 John Wiley & Sons, Ltd.     

Transferability of hydrological model parameters between basins in data-sparse areas, subarctic Canada

Hydrological models used for the simulation of runoff are often calibrated only on the basis of data obtained at the catchment outlet but the parameters thus derived are then applied to the simulations for the subbasins. Such a practice is common for the data-sparse areas such as the subarctic. However, it may yield erroneous results when the calibrated model parameters are applied to basins of various sizes, or with divergent physical characteristics. This study assesses the feasibility of transferring parameter estimates derived for one basin of a particular size to other basins of different dimensions, using the SLURP model for simulation and the Liard and two of its subbasins as an example. Results indicate that other than the snowmelt factor, the parameter values obtained from the subbasins are similar, but values of several parameters (e.g. maximum capacity of the soil water and groundwater storage, and snowmelt factor) are different from those derived for the large basin. Compared with applying the Liard basin parameters, the subbasins parameter sets generate higher evapotranspiration, earlier termination of the snowmelt period, more soil water storage, a shorter period with significant soil water storage and a better overall agreement between the observed and simulated runoff. It is recommended that adequate attention be given to the transferability of the parameter values to improve the simulation of subbasins hydrology.     

Assessment of the SWMM model uncertainties within the generalized likelihood uncertainty estimation (GLUE) framework for a high‐resolution urban sewershed

This research incorporates the generalized likelihood uncertainty estimation (GLUE) methodology in a high‐resolution Environmental Protection Agency Storm Water Management Model (SWMM), which we developed for a highly urbanized sewershed in Syracuse, NY, to assess SWMM modelling uncertainties and estimate parameters. We addressed two issues that have long been suggested having a great impact on the GLUE uncertainty estimation: the observations used to construct the likelihood measure and the sampling approach to obtain the posterior samples of the input parameters and prediction bounds of the model output. First, on the basis of the Bayes' theorem, we compared the prediction bounds generated from the same Gaussian distribution likelihood measure conditioned on flow observations of varying magnitude. Second, we employed two sampling techniques, the sampling importance resampling (SIR) and the threshold sampling methods, to generate posterior parameter distributions and prediction bounds, based on which the sampling efficiency was compared. In addition, for a better understanding of the hydrological responses of different pervious land covers in urban areas, we developed new parameter sets in SWMM representing the hydrological properties of trees and lawns, which were estimated through the GLUE procedure. The results showed that SIR was a more effective alternative to the conventional threshold sampling method. The combined total flow and peak flow data were an efficient alternative to the intensive 5‐min flow data for reducing SWMM parameter and output uncertainties. Several runoff control parameters were found to have a great effect on peak flows, including the newly introduced parameters for trees. Copyright © 2013 John Wiley & Sons, Ltd.     

Hydrological modelling,process understanding and uncertainty in a southern African context: lessons from the northern hemisphere

During the four decades of Keith Beven's career there have been many developments in the science of hydrological modelling. Some have focused on the links between hydrological process understanding and the structure and complexity of hydrological models, others on the related issues of modelling uncertainty. The southern Africa region continues to be generally less well endowed with the resources required to contribute to these research developments, but they are critical for successful water resources management decision‐making in data scarce areas, and go beyond academic interest. Consequently, the focus in the region has been on adding a local context to northern hemisphere research as well as trying to put it into practice. The challenge in southern Africa has always been to extrapolate from published research ideas and decide how they can be effectively used in larger scale practical applications in data‐poor areas. The paper examines the issues of model complexity, links with process understanding and the broad topic of model uncertainty estimation in the context of data scarce areas and how the science questions relate to improvements in water resources decision making. The conclusions suggest that the southern African region has benefited a great deal from several decades of northern hemisphere research (including those by Beven) and that some values have been added through the focus on practical implementation. The region should also embrace the opportunities presented by the need to link realistic uncertainty estimates with risk‐based water resources decision‐making, thereby contributing to the international debate on this important topic. Copyright © 2015 John Wiley & Sons, Ltd.     

Quantifying the relative impact of hydrological and hydraulic modelling parameterizations on uncertainty of inundation maps

ABSTRACT

Flood risk management strongly relies on inundation models for river basin zoning in flood-prone and risk-free areas. Floodplain zoning is significantly affected by the diverse and concurrent uncertainties that characterize the modelling chain used for producing inundation maps. In order to quantify the relative impact of the uncertainties linked to a lumped hydrological (rainfall–runoff) model and a FLO-2D hydraulic model, a Monte Carlo procedure is proposed in this work. The hydrological uncertainty is associated with the design rainfall estimation method, while the hydraulic model uncertainty is associated with roughness parameterization. This uncertainty analysis is tested on the case study of the Marta coastal catchment in Italy, by comparing the different frequency, extent and depth of inundation simulations associated with varying rainfall forcing and/or hydraulic model roughness realizations. The results suggest a significant predominance of the hydrological uncertainty with respect to the hydraulic one on the overall uncertainty associated with the simulated inundation maps.     

Standardized uncertainty analysis for hydrometry: a review of relevant approaches and implementation examples

Abstract

The water-centric community has continuously made efforts to identify, assess and implement rigorous uncertainty analyses for routine hydrological measurements. This paper reviews some of the most relevant efforts and subsequently demonstrates that the Guide to the expression of uncertainty in measurement (GUM) is a good candidate for estimation of uncertainty intervals for hydrometry. The demonstration is made by implementing the GUM to typical hydrometric applications and comparing the analysis results with those obtained using the Monte Carlo method. The results show that hydrological measurements would benefit from the adoption of the GUM as the working standard, because of its soundness, the availability of software for practical implementation and potential for extending the GUM to hydrological/hydraulic numerical simulations.

Editor D. Koutsoyiannis

Citation Muste, M., Lee, K. and Bertrand-Krajewski, J.-L., 2012. Standardized uncertainty analysis for hydrometry: a review of relevant approaches and implementation examples. Hydrological Sciences Journal, 57 (4), 643–667.     

The influence of parametric uncertainty on the relationships between HBV model parameters and climatic characteristics

Abstract

An HBV rainfall–runoff model was applied to test the influence of climatic characteristics on model parameter values. The methodology consisted of the calibration and cross-validation of the HBV model on a series of 5-year periods for four selected catchments (Axe, Kamp, Wieprz and Wimmera). The model parameters were optimized using the SCEM-UA method which allowed for their uncertainty also to be assessed. Nine climatic indices were selected for the analysis of their influence on model parameters, and divided into water-related and temperature-related indices. This allowed the dependence of HBV model parameters on climate characteristics to be explored following their response to climate change conditioned on the catchment’s physical characteristics. The Pearson correlation coefficient and weighted Pearson correlation coefficient were used to test the dependence. Most parameters showed a statistically significant dependence on several climatic indices in all catchments. The study shows that the results of the correlation analysis with and without parametric uncertainty taken into account differ significantly.     

Testing new sources of topographic data for flood propagation modelling under structural,parameter and observation uncertainty

ABSTRACT

This study assessed the utility of EUDEM, a recently released digital elevation model, to support flood inundation modelling. To this end, a comparison with other topographic data sources was performed (i.e. LIDAR, light detection and ranging; SRTM, Shuttle Radar Topographic Mission) on a 98-km reach of the River Po, between Cremona and Borgoforte (Italy). This comparison was implemented using different model structures while explicitly accounting for uncertainty in model parameters and upstream boundary conditions. This approach facilitated a comprehensive assessment of the uncertainty associated with hydraulic modelling of floods. For this test site, our results showed that the flood inundation models built on coarse resolutions data (EUDEM and SRTM) and simple one-dimensional model structure performed well during model evaluation.

Editor Z.W. Kundzewicz; Associate editor S. Weijs     

Projections of hydrology in the Tocantins-Araguaia Basin,Brazil: uncertainty assessment using the CMIP5 ensemble

ABSTRACT

A semi-distributed hydrological model is developed, calibrated and validated against unregulated river discharge from the Tocantins-Araguaia River Basin, northern Brazil. Climate change impacts are simulated using projections from the 41 Coupled Model Intercomparison Project Phase 5 climate models for the period 2071–2100 under the RCP4.5 scenario. Scenario results are compared to a 1971–2000 base line. Most climate models suggest declines in mean annual discharge although some predict increases. A large proportion suggest that the dry season experiences large declines in discharge, especially during the transition to the rising water period. Most models (>75%) suggest declines in annual minimum flows. This may have major implications for both current and planned hydropower schemes. There is greater uncertainty in projected changes in wet season and annual maximum discharges. Two techniques are investigated to reduce uncertainty in projections, but neither is able to provide more confidence in the simulated changes in discharge.

Editor D. Koutsoyiannis Associate editor F. Hattermann     

GCM-related uncertainty for river flows and inundation under climate change: the Inner Niger Delta

ABSTRACT

A semi-distributed hydrological model of the Niger River above and including the Inner Delta is developed. GCM-related uncertainty in climate change impacts are investigated using seven GCMs for a 2°C increase in global mean temperature, the hypothesised threshold of “dangerous” climate change. Declines in precipitation predominate, although some GCMs project increases for some sub-catchments, whilst PET increases for all scenarios. Inter-GCM uncertainty in projected precipitation is three to five times that of PET. With the exception of one GCM (HadGEM1), which projects a very small increase (3.9%), river inflows to the Delta decline. There is considerable uncertainty in the magnitude of these reductions, ranging from 0.8% (HadCM3) to 52.7% (IPSL). Whilst flood extent for HadGEM1 increases (mean annual peak +1405 km²/+10.2%), for other GCMs it declines. These declines range from almost negligible changes to a 7903 km² (57.3%) reduction in the mean annual peak.

Editor Z.W. Kundzewicz; Associate editor not assigned     

A predictive model for Arias intensity at multiple sites and consideration of spatial correlations

Arias intensity, I_a, has been identified as an efficient intensity measure for the estimation of earthquake‐induced losses. In this paper, a new model for the prediction of Arias intensity, which incorporates nonlinear site response through the use of the average shear‐wave velocity and a heteroskedastic variance structure, is proposed. In order to estimate the effects of ground motions on spatially‐distributed systems, it is important to take into account the spatial correlation of the intensity measure. However, existing loss‐estimation models, which use I_a as an input, do not take this aspect of the ground motion into account. Therefore, the potential to model the spatial correlation of Arias intensity is also investigated. The empirical predictive model is developed using recordings from the Pacific Earthquake Engineering Research Center Next Generation of Attenuation database whereas the model for spatial correlation makes use of the well‐recorded events from this database, that is the Northridge and Chi‐Chi earthquakes. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

Incorporating uncertainty in hydrological predictions for gauged and ungauged basins in southern Africa

Abstract

The increasing demand for water in southern Africa necessitates adequate quantification of current freshwater resources. Watershed models are the standard tool used to generate continuous estimates of streamflow and other hydrological variables. However, the accuracy of the results is often not quantified, and model assessment is hindered by a scarcity of historical observations. Quantifying the uncertainty in hydrological estimates would increase the value and credibility of predictions. A model-independent framework aimed at achieving consistency in incorporating and analysing uncertainty within water resources estimation tools in gauged and ungauged basins is presented. Uncertainty estimation in ungauged basins is achieved via two strategies: a local approach for a priori model parameter estimation from physical catchment characteristics, and a regional approach to regionalize signatures of catchment behaviour that can be used to constrain model outputs. We compare these two sources of information in the data-scarce region of South Africa. The results show that both approaches are capable of uncertainty reduction, but that their relative values vary.

Editor D. Koutsoyiannis

Citation Kapangaziwiri, E., Hughes, D.A., and Wagener, T., 2012. Incorporating uncertainty in hydrological predictions for gauged and ungauged basins in southern Africa. Hydrological Sciences Journal, 57 (5), 1000–1019.     

Probabilistic and ensemble simulation approaches for input uncertainty quantification of artificial neural network hydrological models

Artificial neural network (ANN) has been demonstrated to be a promising modelling tool for the improved prediction/forecasting of hydrological variables. However, the quantification of uncertainty in ANN is a major issue, as high uncertainty would hinder the reliable application of these models. While several sources have been ascribed, the quantification of input uncertainty in ANN has received little attention. The reason is that each measured input quantity is likely to vary uniquely, which prevents quantification of a reliable prediction uncertainty. In this paper, an optimization method, which integrates probabilistic and ensemble simulation approaches, is proposed for the quantification of input uncertainty of ANN models. The proposed approach is demonstrated through rainfall-runoff modelling for the Leaf River watershed, USA. The results suggest that ignoring explicit quantification of input uncertainty leads to under/over estimation of model prediction uncertainty. It also facilitates identification of appropriate model parameters for better characterizing the hydrological processes.     

Effect of rainfall uncertainty on the performance of physically based rainfall–runoff models

This paper analyses the effect of rain data uncertainty on the performance of two hydrological models with different spatial structures: a semidistributed and a fully distributed model. The study is performed on a small catchment of 19.6 km² located in the north‐west of Spain, where the arrival of low pressure fronts from the Atlantic Ocean causes highly variable rainfall events. The rainfall fields in this catchment during a series of storm events are estimated using rainfall point measurements. The uncertainty of the estimated fields is quantified using a conditional simulation technique. Discharge and rain data, including the uncertainty of the estimated rainfall fields, are then used to calibrate and validate both hydrological models following the generalized likelihood uncertainty estimation (GLUE) methodology. In the storm events analysed, the two models show similar performance. In all cases, results show that the calibrated distribution of the input parameters narrows when the rain uncertainty is included in the analysis. Otherwise, when rain uncertainty is not considered, the calibration of the input parameters must account for all uncertainty in the rainfall–runoff transformation process. Also, in both models, the uncertainty of the predicted discharges increase in similar magnitude when the uncertainty of rainfall input increase.