Hydrological Uncertainty Research Articles

From HUP to MCP: Analogies and extended performances

► This work compares two known Predictive Uncertainty (PU) approaches, HUP and MCP. ► Both processors imply same joint distribution of predictand-model-latest observation. ► Both processors provide same correct results if lag-1 Markov is not assumed in HUP. ► Lag-1 Markov assumption in HUP leads to under-predict uncertainty estimates. ► MCP correct estimator of PU and extendable to multi site, multi temporal applications. This paper discusses the analogies and the performances of two uncertainty post-processors, the Hydrologic Uncertainty Processor (HUP) introduced by Krzysztofowicz (1999) and the Model Conditional Processor (MCP), which was proposed by Todini (2008) for the assessment of predictive uncertainty, as an alternative to HUP. The paper shows analytically and through a numerical example that the two uncertainty processors are strongly related and explains why MPC results into improved performances with respect to the HUP, when used with the same level of information. The simplicity of its derivation, the extended capabilities of MCP at tackling multi-predictand, multi-site, multi-model, multi-time problems together with the possible use of Truncated Normal Distributions in order to overcome heteroscedasticity in the residuals make MCP more easily applicable than HUP to describe predictive uncertainty in real time flood forecasting applications.

Toward a statistical framework to quantify the uncertainties of hydrologic response under climate change

The cascade of uncertainty that underscores climate impact assessments of regional hydrology undermines their value for long‐term water resources planning and management. This study presents a statistical framework that quantifies and propagates the uncertainties of hydrologic model response through projections of future streamflow under climate change. Different sources of hydrologic model uncertainty are accounted for using Bayesian modeling. The distribution of model residuals is formally characterized to quantify predictive skill, and Markov chain Monte Carlo sampling is used to infer the posterior distributions of both hydrologic and error model parameters. Parameter and residual error uncertainties are integrated to develop reliable prediction intervals for streamflow estimates. The Bayesian hydrologic modeling framework is then extended to a climate change impact assessment. Ensembles of baseline and future climate are downscaled from global circulation models and are used to drive simulations of streamflow over parameters drawn from the posterior space. Time series of streamflow statistics are calculated from baseline and future ensembles of simulated flows. Uncertainties in hydrologic model response, sampling error, and the range of future climate projections are integrated to help determine the level of confidence associated with hydrologic alteration between baseline and future climate regimes. A case study is conducted on the White River in Vermont, USA. Results indicate that the framework can be used to present a reliable depiction of the range of hydrologic alterations that may occur in the future.

Dam overtopping risk using probabilistic concepts – Case study: The Meijaran Dam, Iran

Hydrologic risk assessment and uncertainty analysis by mathematical and statistical methods provide useful information for decision makers. This study presents the application of risk and uncertainty analysis to dam overtopping due to various inflows and wind speeds for the Meijaran Dam in the north of Iran. The procedure includes univariate flood and wind speed frequency analyses, reservoir routing, and integration of wind set-up and run-up to calculate the reservoir water elevation. Afterwards, the probability of overtopping was assessed by applying two uncertainty analysis methods (Monte Carlo simulation and Latin hypercube sampling), and considering the quantile of flood peak discharge, initial depth of water in the reservoir, and spillway discharge coefficient as uncertain variables. The results revealed that rising water level in the reservoir is the most important factor in overtopping risk analysis and that wind speed also has a considerable impact on reservoirs that are placed in windy areas.

On the sources of hydrological prediction uncertainty in the Amazon

Abstract. Recent extreme events in the Amazon River basin and the vulnerability of local population motivate the development of hydrological forecast systems using process based models for this region. In this direction, the knowledge of the source of errors in hydrological forecast systems may guide the choice on improving model structure, model forcings or developing data assimilation systems for estimation of initial model states. We evaluate the relative importance of hydrologic initial conditions and model meteorological forcings errors (precipitation) as sources of stream flow forecast uncertainty in the Amazon River basin. We used a hindcast approach that compares Ensemble Streamflow Prediction (ESP) and a reverse Ensemble Streamflow Prediction (reverse-ESP). Simulations were performed using the physically-based and distributed hydrological model MGB-IPH, comprising surface energy and water balance, soil water, river and floodplain hydrodynamics processes. The model was forced using TRMM 3B42 precipitation estimates. Results show that uncertainty on initial conditions plays an important role for discharge predictability, even for large lead times (∼1 to 3 months) on main Amazonian Rivers. Initial conditions of surface waters state variables are the major source of hydrological forecast uncertainty, mainly in rivers with low slope and large floodplains. Initial conditions of groundwater state variables are important, mostly during low flow period and in the southeast part of the Amazon where lithology and the strong rainfall seasonality with a marked dry season may be the explaining factors. Analyses indicate that hydrological forecasts based on a hydrological model forced with historical meteorological data and optimal initial conditions may be feasible. Also, development of data assimilation methods is encouraged for this region.

A blueprint for process‐based modeling of uncertain hydrological systems

We present a probability based theoretical scheme for building process‐based models of uncertain hydrological systems, thereby unifying hydrological modeling and uncertainty assessment. Uncertainty for the model output is assessed by estimating the related probability distribution via simulation, thus shifting from one to many applications of the selected hydrological model. Each simulation is performed after stochastically perturbing input data, parameters and model output, this latter by adding random outcomes from the population of the model error, whose probability distribution is conditioned on input data and model parameters. Within this view randomness, and therefore uncertainty, is treated as an inherent property of hydrological systems. We discuss the related assumptions as well as the open research questions. The theoretical framework is illustrated by presenting real‐world and synthetic applications. The relevant contribution of this study is related to proposing a statistically consistent simulation framework for uncertainty estimation which does not require model likelihood computation and simplification of the model structure. The results show that uncertainty is satisfactorily estimated although the impact of the assumptions could be significant in conditions of data scarcity.

Uncertainty assessment and optimization of hydrological model with the Shuffled Complex Evolution Metropolis algorithm: an application to artificial neural network rainfall-runoff model

Assessment of parameter and predictive uncertainty of hydrologic models is an essential part in the field of hydrology. However, during the past decades, research related to hydrologic model uncertainty is mostly done with conceptual models. As is accepted that uncertainty in model predictions arises from measurement errors associated with the system input and output, from model structural errors and from problems with parameter estimation. Unfortunately, non-conceptual models, such as black-box models, also suffer from these problems. In this paper, we take the artificial neural network (ANN) rainfall-runoff model as an example, and the Shuffled Complex Evolution Metropolis algorithm (SCEM-UA) is employed to analysis the parameter and predictive uncertainty of this model. Furthermore, based on the results of uncertainty assessment, we finally arrive at a simpler incomplete-connection artificial neural network (ICANN) model as well as with better performance compared to original ANN rainfall-runoff model. These results not only indicate that SCEM-UA can be a useful tool for uncertainty analysis of ANN model, but also prove that uncertainty does exist in ANN rainfall-runoff model. Additionally, in some way, it presents that the ICANN model is with smaller uncertainty than the original ANN model.

Uncertainty assessment of climate change impacts for hydrologically distinct river basins

Summary The hydrologic uncertainty of climate change impacts in two river basins in the Pacific Northwest of US is investigated. One basin is dominated by snowfall in winter, resulting in snowmelt in spring and early summer, and the other basin is dominated by rainfall in all seasons. In addition to hydrologic uncertainties, we consider the combined effect of two emission scenarios and eight general circulation models (GCMs) in our analyses. Latin Hypercube Sampling (LHS) is employed to sample the Precipitation Runoff Modeling System (PRMS) parameter space and the behavioral parameter sets were obtained according to a statistical performance measure. The results suggest that the relative impacts of uncertainties from different sources vary between the two basins. It is shown that changes in winter runoff are more affected by hydrologic model parameter uncertainty in the snow-dominated basin, while they are less influenced in the rain-dominated basin. The differences in the amount and timing of snowmelt as a result of model parameter uncertainty contribute to the variations of change in winter runoff in the snowfall-dominated basin. This result indicates that climate change impact studies for snow-dominated regions require more cautious interpretation of runoff projections due to considerable uncertainty in estimated hydrologic model parameters.

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

AbstractThis 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.

Statistical processing of forecasts for hydrological ensemble prediction: a comparative study of different bias correction strategies

Abstract. The aim of this paper is to investigate the use of statistical correction techniques in hydrological ensemble prediction. Ensemble weather forecasts (precipitation and temperature) are used as forcing variables to a hydrologic forecasting model for the production of ensemble streamflow forecasts. The impact of different bias correction strategies on the quality of the forecasts is examined. The performance of the system is evaluated when statistical processing is applied: to precipitation and temperature forecasts only (pre-processing from the hydrological model point of view), to flow forecasts (post-processing) and to both. The pre-processing technique combines precipitation ensemble predictions with an analog forecasting approach, while the post-processing is based on past errors of the hydrological model when simulating streamflows. Forecasts from 11 catchments in France are evaluated. Results illustrate the importance of taking into account hydrological uncertainties to improve the quality of operational streamflow forecasts.

추계학적 모의유량을 이용한 한강수계 용수공급시스템의 장기지속가뭄 영향 평가

The Uncertainty of drought events can be regarded as supernatural phenomena so that the uncertainty of water supply system will be also uncontrollable. Decision making for water supply system operation must be dealt with in consideration of hydrologic uncertainty conditions. When ultimate small quantity of precipitation or streamflow lasts, water supply system might be impacted as well as stream pollution, aqua- ecosystem degradation, reservoir dry-up and river aesthetic waste etc. In case of being incapable of supplying water owing to continuation of severe drought, it can make the damage very serious beyond our prediction. This study analyzes comprehensively sustained drought impacts on the Han River Basin Water Supply System. Drought scenarios consisted of several sustained times and return periods for 5 sub-watersheds are generated using a stochastic hydrologic time series model. The developed drought scenarios are applied to assess water supply performance at the Paldang Dam. The results show that multi-year drought events reflecting spatial hydrologic diversity need to be examined in order to recognize variation of the unexpected drought impacts.

Quantifying uncertainty in catchment-scale runoff modeling under climate change (case of the Huaihe River, China)

Abstract Climate change impact assessment on runoff plays a key role for catchment-scale water resources planning and adaptation. Quantification of impacts on water resources modeling at the catchment-scale is characterized by uncertainties of hydrological model parameters, emission scenarios, and global climate model outputs (including the downscaling techniques). The hydrological parameter uncertainty may show the different magnitude with that of Global Climate Models (GCMs). Much less systematic work has been done to estimate climatic uncertainty and to assess the climatic and hydrologic model outputs within an uncertainty perspective. In this study, based on the Generalized Likelihood Uncertainty Estimation (GLUE) methodology, a systematic uncertainty analysis framework is proposed in terms of a comparable variable. Climatic uncertainty was involved in an ensemble manner through combination of the results from emission scenarios A1B, A2 and B1 and global climate models (CSIRO, NCAR, MPI). The biases of downscaled temperature and precipitation simulations from GCMs were processed by a delta change approach method. Addressing into TOPMODEL, it was analyzed for the future runoff variation and uncertainties impact by climate change. The results indicate uncertainties introduced by different sources lie in different magnitudes, which highlights the new challenges to cope with the multi-scales uncertainty in decision-making process.

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

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

Evaluation of a nonparametric post‐processor for bias correction and uncertainty estimation of hydrologic predictions

AbstractThis paper evaluates a nonparametric technique for estimating the conditional probability distribution of a predictand given a vector of predictors. In the current application, the predictors are formed from a multimodel ensemble of simulated streamflows, such that the hydrologic uncertainties are modelled independently of any forcing uncertainties. The technique is based on Bayesian optimal linear estimation of indicator variables and is analogous to indicator cokriging (ICK) in geostatistics. By developing linear estimators for the conditional probability that the observed variable does not exceed several thresholds, ICK provides a discrete approximation of the full conditional probability distribution. The weights of the predictors can be chosen to minimize the expected error variance at each threshold (the Brier score) or, without loss of analytical tractability, a combination of the error variance and the expected square bias conditional upon the observation, i.e. the Type‐II conditional bias (CB). The latter is referred to as CB‐penalized ICK (CBP‐ICK) and is an important enhancement to ICK. Indeed, the biases in atmospheric and hydrologic predictions generally increase towards the tails of their probability distributions. The performance of CBP‐ICK is evaluated for selected basins in the eastern USA using a range of probabilistic verification metrics and associated confidence intervals for the sampling uncertainties. Overall, CBP‐ICK produces unbiased and skillful estimates of the hydrologic uncertainties, with some sensitivity to the calibration data period at high flow thresholds. More generally, we argue that the common aim in statistical post‐processing of ‘maximizing sharpness subject to reliability (Type‐I CB)’ should be recast to accommodate both the Type‐I and Type‐II CBs, as both are important for practical applications of hydrologic predictions. Copyright © 2012 John Wiley & Sons, Ltd.

Technical Note: The normal quantile transformation and its application in a flood forecasting system

Abstract. The Normal Quantile Transform (NQT) has been used in many hydrological and meteorological applications in order to make the Cumulated Distribution Function (CDF) of the observed, simulated and forecast river discharge, water level or precipitation data Gaussian. It is also the heart of the meta-Gaussian model for assessing the total predictive uncertainty of the Hydrological Uncertainty Processor (HUP) developed by Krzysztofowicz. In the field of geo-statistics this transformation is better known as the Normal-Score Transform. In this paper some possible problems caused by small sample sizes when applying the NQT in flood forecasting systems will be discussed and a novel way to solve the problem will be outlined by combining extreme value analysis and non-parametric regression methods. The method will be illustrated by examples of hydrological stream-flow forecasts.

Multi-Objective Optimization of Fusegates System under Hydrologic Uncertainties

Fusegates are independent units held only by the gravity installed on the free spillway of existing dams in order to increase reservoir storage and/or discharge capacity. Increasing reservoir storage in many dams can partly sacrifice dam’s reliabilities. So considering the failure risk of a dam together with the amount of increase in the reservoir capacity can prevent selecting fusegates which seriously endanger a dam safety. However, Lack of accurate information on various damage functions and difficulty in quantifying failure consequences are among principal limitations that hinder practical application of conventional approaches which account failure risk in real world hydrosystems problems. This study develops two effective multi-objective frameworks to optimize fusegates’ configuration in order to eliminate the need for such hard-to-get mathematical damage functions and provide valuable information on the failure risk, total cost, and increased water volume of a reservoir. The proposed models find trade-off solutions between two sets of conflicting objectives. The first competing objectives is investment cost and water storage and the second conflicting goals are water storage and failure probability under the inherent and parameter hydrologic uncertainties. Complicated flood routing phenomenon within a reservoir equipped with fusegates is explicitly taken into account to attain a more cost-effective and reliable design without jeopardizing the dam safety. Applicability and performance of the developed optimization schemes are discussed and demonstrated on a real life case study. The multi-objective optimization results represented as an ensemble of diverse trade-off solutions provide decision makers with more insight and understanding of system behavior and different design alternatives.

Uncertainties in Hydrologic and Climate Change Impact Analyses in Headwater Basins of British Columbia

Abstract Three headwater basins located across British Columbia (BC) were analyzed using a hydrologic model driven by five global climate models (GCMs) and three scenarios from the Special Report on Emissions Scenarios (SRES) to project future changes in seasonal water budgets and assess the uncertainty in the projections arising from GCMs, emissions scenarios, and hydrologic model parameterizations under two future time periods. Future projected changes in temperature are for annual increases of approximately +2°C by the 2050s and +3°C by the 2080s. The 2050s and 2080s precipitation projections are for increased winter precipitation in all basins and decreases in summertime precipitation for two of the three basins—with increases projected in the northeastern BC subwatershed. The study found that the hydrologic parameter uncertainty ranged up to 55%, (average 31%) for winter runoff anomalies, which was less than the uncertainty associated with GCMs and emissions scenarios that ranged up to 135% and 78% (average 84% and 58%, respectively). The uncertainty results were variable across the three hydroclimate regimes. Coastal headwater systems in British Columbia experience more uncertainty associated with changes during winter and the summer, whereas interior systems experience the greatest uncertainties during the winter and spring. Changes projected for the 2050s at the coastal site fell outside of the range of natural variability, a robust shift that may result in a very different regime for this basin within the short planning horizon of 50 years. A small, semiarid watershed located on the Chilcotin Plateau exhibited changes to the hydrologic regime that were projected to be small in absolute terms and fell within the range of natural variability.

Uncertainty assessment of hydrologic and climate forecast models in Northeastern Brazil

AbstractSeasonal streamflow forecasts based on climate information can guide water managers toward superior reservoir operations, leading to improved water resources management efficiency. Uncertainty, however, is always present in seasonal streamflow forecasts, affecting the forecast value. Thus, a forecast should not be considered complete without a description of its uncertainty, which is critical for climate risk and water resources management. This study investigates the uncertainties of a seasonal streamflow forecast system for Northeastern Brazil based on climate precipitation forecasts and hydrologic modeling. These two sources of uncertainty are treated independently and then compared in order to guide future investments in the forecast system. Sea surface temperature is considered to be the primary source of uncertainty for the seasonal precipitation forecasts, based upon a 10‐member climate model ensemble. Parameter uncertainty is considered to be the only source of uncertainty for the hydrologic model. Estimation of parameter uncertainty is estimated by the Shuffled Complex Evolution Metropolis algorithm, which employs a Markov Chain Monte Carlo scheme to provide the posterior distribution of the parameters and form uncertainty bounds on streamflow forecasts. Results indicate that uncertainties associated with the climate forecast are much larger than those from parameter estimation in the hydrologic model. Although model structure has not been considered in the evaluation of hydrologic uncertainties, this study indicates that future efforts to address the predominant source of uncertainty should focus on the climate prediction models. Copyright © 2011 John Wiley & Sons, Ltd.

Uncertainty in hydrological modelling of climate change impacts in four Norwegian catchments

Projections for the hydrological impacts of climate change are necessarily reliant on a chain of models for which numerous alternative models and approaches are available. Many of these alternatives produce dissimilar results which can undermine their use in practical applications due to these differences. A methodology for developing climate change impact projections and for representing the range of model outcomes is demonstrated based on the application of a hydrological model with input data from six regional climate scenarios, which have been further adjusted to match local conditions. Multiple best-fit hydrological model parameter sets are also used so that hydrological parameter uncertainty is included in the analysis. The methodology is applied to consider projected changes in the average annual maximum daily mean runoff in four catchments (Flaksvatn, Viksvatn, Masi and Nybergsund) which are characterised by regional differences in seasonal flow regimes. For catchments where rainfall makes the predominant contribution to annual maximum flows, hydrological parameter uncertainty is significant relative to other uncertainty sources. Parameter uncertainty is less important in catchments where spring snowmelt dominates the generation of maximum flows. In this case, differences between climate scenarios and methods for adjusting climate model output to local conditions dominate uncertainty.

Using precipitation data ensemble for uncertainty analysis in SWAT streamflow simulation

Summary Precipitation patterns in the tropics are characterized by extremely high spatial and temporal variability that are difficult to adequately represent with rain gauge networks. Since precipitation is commonly the most important input data in hydrological models, model performance and uncertainty will be negatively impacted in areas with sparse rain gauge networks. To investigate the influence of precipitation uncertainty on both model parameters and predictive uncertainty in a data sparse region, the integrated river basin model SWAT was calibrated against measured streamflow of the Pipiripau River in Central Brazil. Calibration was conducted using an ensemble of different precipitation data sources, including: (1) point data from the only available rain gauge within the watershed, (2) a smoothed version of the gauge data derived using a moving average, (3) spatially distributed data using Thiessen polygons (which includes rain gauges from outside the watershed), and (4) Tropical Rainfall Measuring Mission radar data. For each precipitation input model, the best performing parameter set and their associated uncertainty ranges were determined using the Sequential Uncertainty Fitting Procedure. Although satisfactory streamflow simulations were generated with each precipitation input model, the results of our study indicate that parameter uncertainty varied significantly depending upon the method used for precipitation data-set generation. Additionally, improved deterministic streamflow predictions and more reliable probabilistic forecasts were generated using different ensemble-based methods, such as the arithmetic ensemble mean, and more advanced Bayesian Model Averaging schemes. This study shows that ensemble modeling with multiple precipitation inputs can considerably increase the level of confidence in simulation results, particularly in data-poor regions.

Missouri River Watershed: the Object for Hydrological Study and Uncertainty of Models

Missouri River Watershed: the Object for Hydrological Study and Uncertainty of Models