Observational and predictive uncertainties for multiple variables in a spatially distributed hydrological model

In this study, uncertainty in model input data (precipitation) and parameters is propagated through a physically based, spatially distributed hydrological model based on the MIKE SHE code. Precipitation uncertainty is accounted for using an ensemble of daily rainfall fields that incorporate four different sources of uncertainty, whereas parameter uncertainty is considered using Latin hypercube sampling. Model predictive uncertainty is assessed for multiple simulated hydrological variables (discharge, groundwater head, evapotranspiration, and soil moisture). Utilizing an extensive set of observational data, effective observational uncertainties for each hydrological variable are assessed. Considering not only model predictive uncertainty but also effective observational uncertainty leads to a notable increase in the number of instances, for which model simulation and observations are in good agreement (e.g., 47% vs. 91% for discharge and 0% vs. 98% for soil moisture). Effective observational uncertainty is in several cases larger than model predictive uncertainty. We conclude that the use of precipitation uncertainty with a realistic spatio‐temporal correlation structure, analyses of multiple variables with different spatial support, and the consideration of observational uncertainty are crucial for adequately evaluating the performance of physically based, spatially distributed hydrological models.     

Understanding the time‐varying importance of different uncertainty sources in hydrological modelling using global sensitivity analysis

Simulations from hydrological models are affected by potentially large uncertainties stemming from various sources, including model parameters and observational uncertainty in the input/output data. Understanding the relative importance of such sources of uncertainty is essential to support model calibration, validation and diagnostic evaluation and to prioritize efforts for uncertainty reduction. It can also support the identification of ‘disinformative data’ whose values are the consequence of measurement errors or inadequate observations. Sensitivity analysis (SA) provides the theoretical framework and the numerical tools to quantify the relative contribution of different sources of uncertainty to the variability of the model outputs. In traditional applications of global SA (GSA), model outputs are aggregations of the full set of a simulated variable. For example, many GSA applications use a performance metric (e.g. the root mean squared error) as model output that aggregates the distances of a simulated time series to available observations. This aggregation of propagated uncertainties prior to GSA may lead to a significant loss of information and may cover up local behaviour that could be of great interest. Time‐varying sensitivity analysis (TVSA), where the aggregation and SA are repeated at different time steps, is a viable option to reduce this loss of information. In this work, we use TVSA to address two questions: (1) Can we distinguish between the relative importance of parameter uncertainty versus data uncertainty in time? (2) Do these influences change in catchments with different characteristics? To our knowledge, the results present one of the first quantitative investigations on the relative importance of parameter and data uncertainty across time. We find that the approach is capable of separating influential periods across data and parameter uncertainties, while also highlighting significant differences between the catchments analysed. Copyright © 2016 The Authors. Hydrological Processes. Published by John Wiley & Sons Ltd.     

Observational uncertainties in hypothesis testing: investigating the hydrological functioning of a tropical catchment

Hypothesis testing about catchment functioning with conceptual hydrological models is affected by uncertainties in the model representation of reality as well as in the observed data used to drive and evaluate the model. We formulated a learning framework to investigate the role of observational uncertainties in hypothesis testing using conceptual models and applied it to the relatively data‐scarce tropical Sarapiqui catchment in Costa Rica. Observational uncertainties were accounted for throughout the framework that incorporated different choices of model structures to test process hypotheses, analyses of parametric uncertainties and effects of likelihood choice, a posterior performance analysis and (iteratively) formulation of new hypotheses. Estimated uncertainties in precipitation and discharge were linked to likely non‐linear near‐surface runoff generation and the potentially important role of soils in mediating the hydrological response. Some model‐structural inadequacies could be identified in the posterior analyses (supporting the need for an explicit soil‐moisture routine to match streamflow dynamics), but the available information about the observational uncertainties prevented conclusions about other process representations. The importance of epistemic data errors, the difficulty in quantifying them and their effect on model simulations was illustrated by an inconsistent event with long‐term effects. Finally we discuss the need for new data, new process hypotheses related to deep groundwater losses, and conclude that observational uncertainties need to be accounted for in hypothesis testing to reduce the risk of drawing incorrect conclusions. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Impacts of uncertain river flow data on rainfall‐runoff model calibration and discharge predictions

In order to quantify total error affecting hydrological models and predictions, we must explicitly recognize errors in input data, model structure, model parameters and validation data. This paper tackles the last of these: errors in discharge measurements used to calibrate a rainfall‐runoff model, caused by stage–discharge rating‐curve uncertainty. This uncertainty may be due to several combined sources, including errors in stage and velocity measurements during individual gaugings, assumptions regarding a particular form of stage–discharge relationship, extrapolation of the stage–discharge relationship beyond the maximum gauging, and cross‐section change due to vegetation growth and/or bed movement. A methodology is presented to systematically assess and quantify the uncertainty in discharge measurements due to all of these sources. For a given stage measurement, a complete PDF of true discharge is estimated. Consequently, new model calibration techniques can be introduced to explicitly account for the discharge error distribution. The method is demonstrated for a gravel‐bed river in New Zealand, where all the above uncertainty sources can be identified, including significant uncertainty in cross‐section form due to scour and re‐deposition of sediment. Results show that rigorous consideration of uncertainty in flow data results in significant improvement of the model's ability to predict the observed flow. Copyright © 2010 John Wiley & Sons, Ltd.     

Discharge and nutrient uncertainty: implications for nutrient flux estimation in small streams

The measurement of discharge is fundamental in nutrient load estimation. Because of our ability to monitor discharge routinely, it is generally assumed that the associated uncertainty is low. This paper challenges this preconception, arguing that discharge uncertainty should be explicitly taken into account to produce robust statistical analyses. In many studies, paired discharge and chemical datasets are used to calculate ‘true’ loads and used as the benchmark to compare with other load estimates. This paper uses two years of high frequency (daily and sub‐hourly) discharge and nutrient concentration data (nitrate‐N and total phosphorus (TP)) collected at four field sites as part of the Hampshire Avon Demonstration Test Catchment (DTC) programme. A framework for estimating observational nutrient load uncertainty was used which combined a flexible non‐parametric approach to characterising discharge uncertainty, with error modelling that allowed the incorporation of errors which were heteroscedastic and temporally correlated. The results showed that the stage–discharge relationships were non‐stationary, and observational uncertainties from ±2 to 25% were recorded when the velocity–area method was used. The variability in nutrient load estimates ranged from 1.1 to 9.9% for nitrate‐N and from 3.3 to 10% for TP when daily laboratory data were used, rising to a maximum of 9% for nitrate‐N and 83% for TP when the sensor data were used. However, the sensor data provided a better representation of the ‘true’ load as storm events are better represented temporally, posing the question: is it more beneficial to have high frequency, lower precision data or lower frequency but higher precision data streams to estimate nutrient flux responses in headwater catchments? Copyright © 2015 John Wiley & Sons, Ltd.     

Unpacking some of the linkages between uncertainties in observational data and the simulation of different hydrological processes using the Pitman model in the data scarce Zambezi River basin

The main objective of this study was to use an uncertainty version of a widely used monthly time step, semi-distributed model (the Pitman model) to explore the equifinalities in the way in which the main hydrological processes are simulated and any identifiable linkages with uncertainties in the available observational data. The study area is the Zambezi River basin and 17 gauged sub-basins have been included in the analyses. Unfortunately, it is not generally possible to quantify some of the observational uncertainties in such a data scarce area and mostly we are limited to identifying where these data are clearly deficient (i.e., erroneous or non-representative). The overall conclusion is that the equifinalities in the model are hugely dominant in terms of the uncertainties in the relative occurrence of different runoff generating processes, although water use uncertainties in the semi-arid parts of the basin can contribute to these uncertainties. The identification of landscape features that suggest the occurrence of saturation excess surface runoff provides some information to constrain the model. Improved independent estimates of groundwater recharge is also identified as a key source of observational data that would help a great deal in constraining the model parameter space and therefore reducing some of the model equifinality.     

Uncertainty Analysis of Strong-Motion and Seismic Hazard

In this article we present the modelling of uncertainty in strong-motion studies for engineering applications, particularly for the assessment of earthquake hazard. We examine and quantify the sources of uncertainty in the basic variables involved in ground motion estimation equations, including those associated with the seismological parameters, which we derive from a considerable number of strong-motion records. Models derived from regression analysis result in ground motion equations with uncertain parameters, which are directly related to the selected basic variables thus providing an uncertainty measure for the derivative variable. These uncertainties are exemplified and quantified. An alternative approach is presented which is based on theoretical modelling defining a functional relationship on a set of independent basic variables. Uncertainty in the derivative variable is then readily obtained when the uncertainties of the basic variables have been defined. In order to simplify the presentation, only the case of shallow strike-slip earthquakes is presented. We conclude that the uncertainty is approximately the same as given by the residuals typical for regression modelling. This implies that uncertainty in ground motion modelling cannot be reduced below certain limits, which is in accordance with findings reported in the literature. Finally we discuss the implications of the presented methodology in hazard analyses, which is sensitive to the truncation of the internal error term, commonly given as an integral part of ground motion estimation equations. The presented methodology does not suffer from this shortcoming; it does not require truncation of the error term and yields realistic hazard estimates. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

Model uncertainty analysis by variance decomposition

Errors and uncertainties in hydrological, hydraulic and environmental models are often substantial. In good modelling practice, they are quantified in order to supply decision-makers with important additional information on model limitations and sources of uncertainty. Several uncertainty analysis methods exist, often with various underlying assumptions. One of these methods is based on variance decomposition. The method allows splitting the variance of the total error in the model results (as estimated after comparing model results with observations) in its major contributing uncertainty sources. This paper discusses an advanced version of that method where error distributions for rainfall, other inputs and parameters are propagated in the model and the “rest” uncertainties considered as model structural errors for different parts of the model. By expert knowledge, the iid assumption that is often made in model error analysis is addressed upfront. The method also addresses the problems of heteroscedasticity and serial dependence of the errors involved. The method has been applied by the author to modelling applications of sewer water quantity and quality, river water quality and river flooding.     

The integrated effects of climate and hydrologic uncertainty on future flood risk assessments

This work examines future flood risk within the context of integrated climate and hydrologic modelling uncertainty. The research questions investigated are (1) whether hydrologic uncertainties are a significant source of uncertainty relative to other sources such as climate variability and change and (2) whether a statistical characterization of uncertainty from a lumped, conceptual hydrologic model is sufficient to account for hydrologic uncertainties in the modelling process. To investigate these questions, an ensemble of climate simulations are propagated through hydrologic models and then through a reservoir simulation model to delimit the range of flood protection under a wide array of climate conditions. Uncertainty in mean climate changes and internal climate variability are framed using a risk‐based methodology and are explored using a stochastic weather generator. To account for hydrologic uncertainty, two hydrologic models are considered, a conceptual, lumped parameter model and a distributed, physically based model. In the conceptual model, parameter and residual error uncertainties are quantified and propagated through the analysis using a Bayesian modelling framework. The approach is demonstrated in a case study for the Coralville Dam on the Iowa River, where recent, intense flooding has raised questions about potential impacts of climate change on flood protection adequacy. Results indicate that the uncertainty surrounding future flood risk from hydrologic modelling and internal climate variability can be of the same order of magnitude as climate change. Furthermore, statistical uncertainty in the conceptual hydrological model can capture the primary structural differences that emerge in flood damage estimates between the two hydrologic models. Copyright © 2014 John Wiley & Sons, Ltd.     

Parameter and rating curve uncertainty propagation analysis of the SWAT model for two small Mediterranean catchments

Abstract

The SWAT model was tested to simulate the streamflow of two small Mediterranean catchments (the Vène and the Pallas) in southern France. Model calibration and prediction uncertainty were assessed simultaneously by using three different techniques (SUFI-2, GLUE and ParaSol). Initially, a sensitivity analysis was conducted using the LH-OAT method. Subsequent sensitive parameter calibration and SWAT prediction uncertainty were analysed by considering, firstly, deterministic discharge data (assuming no uncertainty in discharge data) and secondly, uncertainty in discharge data through the development of a methodology that accounts explicitly for error in the rating curve (the stage?discharge relationship). To efficiently compare the different uncertainty methods and the effect of the uncertainty of the rating curve on model prediction uncertainty, common criteria were set for the likelihood function, the threshold value and the number of simulations. The results show that model prediction uncertainty is not only case-study specific, but also depends on the selected uncertainty analysis technique. It was also found that the 95% model prediction uncertainty interval is wider and more successful at encompassing the observations when uncertainty in the discharge data is considered explicitly. The latter source of uncertainty adds additional uncertainty to the total model prediction uncertainty.

Editor D. Koutsoyiannis; Associate editor D. Gerten

Citation Sellami, H., La Jeunesse, I., Benabdallah, S., and Vanclooster, M., 2013. Parameter and rating curve uncertainty propagation analysis of the SWAT model for two small Mediterranean watersheds. Hydrological Sciences Journal, 58 (8), 1635?1657.     

Evaluation of safety of hydraulic structures affected by migrating pits

Because it can be carried by flowing water, a sand/gravel pit on the river bed could migrate downstream. Consequently, the presence of pits on river beds could pose a safety threat to in-stream hydraulic structures such as bridge piers. A pit migration model can be used to predict progressive changes of pit geometry as it migrates downstream. However, due to the existence of many uncertainties, the maximum pit depth cannot be predicted with certainty. This paper adopted a simple pit migration model and evaluated the uncertainty associated with the calculated maximum pit depth. Such information is essential for evaluating the probability that a migrating pit could pose a safety threat to a downstream hydraulic structure. Three reliability analysis techniques were applied and their performances were compared.     

Evaluation of safety of hydraulic structures affected by migrating pits

Because it can be carried by flowing water, a sand/gravel pit on the river bed could migrate downstream. Consequently, the presence of pits on river beds could pose a safety threat to in-stream hydraulic structures such as bridge piers. A pit migration model can be used to predict progressive changes of pit geometry as it migrates downstream. However, due to the existence of many uncertainties, the maximum pit depth cannot be predicted with certainty. This paper adopted a simple pit migration model and evaluated the uncertainty associated with the calculated maximum pit depth. Such information is essential for evaluating the probability that a migrating pit could pose a safety threat to a downstream hydraulic structure. Three reliability analysis techniques were applied and their performances were compared.     

Probabilistic-fuzzy health risk modeling

Health risk analysis of multi-pathway exposure to contaminated water involves the use of mechanistic models that include many uncertain and highly variable parameters. Currently, the uncertainties in these models are treated using statistical approaches. However, not all uncertainties in data or model parameters are due to randomness. Other sources of imprecision that may lead to uncertainty include scarce or incomplete data, measurement error, data obtained from expert judgment, or subjective interpretation of available information. These kinds of uncertainties and also the non-random uncertainty cannot be treated solely by statistical methods. In this paper we propose the use of fuzzy set theory together with probability theory to incorporate uncertainties into the health risk analysis. We identify this approach as probabilistic-fuzzy risk assessment (PFRA). Based on the form of available information, fuzzy set theory, probability theory, or a combination of both can be used to incorporate parameter uncertainty and variability into mechanistic risk assessment models. In this study, tap water concentration is used as the source of contamination in the human exposure model. Ingestion, inhalation and dermal contact are considered as multiple exposure pathways. The tap water concentration of the contaminant and cancer potency factors for ingestion, inhalation and dermal contact are treated as fuzzy variables while the remaining model parameters are treated using probability density functions. Combined utilization of fuzzy and random variables produces membership functions of risk to individuals at different fractiles of risk as well as probability distributions of risk for various alpha-cut levels of the membership function. The proposed method provides a robust approach in evaluating human health risk to exposure when there is both uncertainty and variability in model parameters. PFRA allows utilization of certain types of information which have not been used directly in existing risk assessment methods.     

Rating curve uncertainty and change detection in discharge time series: case study with 44‐year historic data from the Nyangores River,Kenya

The intersection of the developing topic of rating curve and discharge series uncertainty with the topic of hydrological change detection (e.g., in response to land cover or climatic change) has not yet been well studied. The work herein explores this intersection, with consideration of a long‐term discharge response (1964–2007) for a ~650‐km² headwater basin of the Mara River in west Kenya, starting with stream rating and daily gauge height data. A rating model was calibrated using Bayesian methods to quantify uncertainty intervals in model parameters and predictions. There was an unknown balance of random and systemic error in rating data scatter (a scenario not likely unique to this basin), which led to an unknown balance of noise and information in the calibrated statistical error model. This had implications on testing for hydrological change. Overall, indications were that shifts in basin's discharge response were rather subtle over the 44‐year period. A null hypothesis for change using flow duration curves (FDCs) from four different 8‐year data intervals could be either accepted or rejected over much of the net flow domain depending on different applications of the statistical error model (each with precedence in the literature). The only unambiguous indication of change in FDC comparisons appeared to be a reduction in lowest baseflow in recent years (flows with >98% exceedance probability). We defined a subjective uncertainty interval based on an intermediate balance of random and systematic error in the rating model that suggested a possibility of more prevalent impacts. These results have relevance to management in the Mara basin and to future studies that might establish linkages to historic land use and climatic factors. The concern about uncertain uncertainty intervals (uncertainty²) extends beyond the Mara and is relevant to testing change where non‐random rating errors may be important and subtle responses are investigated. Copyright © 2013 John Wiley & Sons, Ltd.     

Assessing hydrological model predictive uncertainty using stochastically generated geological models

In distributed and coupled surface water–groundwater modelling, the uncertainty from the geological structure is unaccounted for if only one deterministic geological model is used. In the present study, the geological structural uncertainty is represented by multiple, stochastically generated geological models, which are used to develop hydrological model ensembles for the Norsminde catchment in Denmark. The geological models have been constructed using two types of field data, airborne geophysical data and borehole well log data. The use of airborne geophysical data in constructing stochastic geological models and followed by the application of such models to assess hydrological simulation uncertainty for both surface water and groundwater have not been previously studied. The results show that the hydrological ensemble based on geophysical data has a lower level of simulation uncertainty, but the ensemble based on borehole data is able to encapsulate more observation points for stream discharge simulation. The groundwater simulations are in general more sensitive to the changes in the geological structure than the stream discharge simulations, and in the deeper groundwater layers, there are larger variations between simulations within an ensemble than in the upper layers. The relationship between hydrological prediction uncertainties measured as the spread within the hydrological ensembles and the spatial aggregation scale of simulation results has been analysed using a representative elementary scale concept. The results show a clear increase of prediction uncertainty as the spatial scale decreases. Copyright © 2015 John Wiley & Sons, Ltd.     

Can global sensitivity analysis steer the implementation of models for environmental assessments and decision-making?

 We illustrate a method of global sensitivity analysis and we test it on a preliminary case study in the field of environmental assessment to quantify uncertainty importance in poorly-known model parameters and spatially referenced input data. The focus of the paper is to show how the methodology provides guidance to improve the quality of environmental assessment practices and decision support systems employed in environmental policy. Global sensitivity analysis, coupled with uncertainty analysis, is a tool to assess the robustness of decisions, to understand whether the current state of knowledge on input data and parametric uncertainties is sufficient to enable a decision to be taken. The methodology is applied to a preliminary case study, which is based on a numerical model that employs GIS-based soil data and expert consultation to evaluate an index that joins environmental and economic aspects of land depletion. The index is used as a yardstick by decision-makers involved in the planning of highways to identify the route that minimises the overall impact.     

Diagnostic evaluation of multiple hypotheses of hydrological behaviour in a limits‐of‐acceptability framework for 24 UK catchments

Testing competing conceptual model hypotheses in hydrology is complicated by uncertainties from a wide range of sources, which result in multiple simulations that explain catchment behaviour. In this study, the limits of acceptability uncertainty analysis approach used to discriminate between 78 competing hypotheses in the Framework for Understanding Structural Errors for 24 catchments in the UK. During model evaluation, we test the model's ability to represent observed catchment dynamics and processes by defining key hydrologic signatures and time step‐based metrics from the observed discharge time series. We explicitly account for uncertainty in the evaluation data by constructing uncertainty bounds from errors in the stage‐discharge rating curve relationship. Our study revealed large differences in model performance both between catchments and depending on the type of diagnostic used to constrain the simulations. Model performance varied with catchment characteristics and was best in wet catchments with a simple rainfall‐runoff relationship. The analysis showed that the value of different diagnostics in constraining catchment response and discriminating between competing conceptual hypotheses varies according to catchment characteristics. The information content held within water balance signatures was found to better capture catchment dynamics in chalk catchments, where catchment behaviour is predominantly controlled by seasonal and annual changes in rainfall, whereas the information content in the flow‐duration curve and time‐step performance metrics was able to better capture the dynamics of rainfall‐driven catchments. We also investigate the effect of model structure on model performance and demonstrate its (in)significance in reproducing catchment dynamics for different catchments. Copyright © 2013 John Wiley & Sons, Ltd.