Uncertainty analysis of flood inundation modelling using GLUE with surrogate models in stochastic sampling

A generalized likelihood uncertainty estimation (GLUE) method incorporating moving least squares (MLS) with entropy for stochastic sampling (denoted as GLUE‐MLS‐E) was proposed for uncertainty analysis of flood inundation modelling. The MLS with entropy (MLS‐E) was established according to the pairs of parameters/likelihoods generated from a limited number of direct model executions. It was then applied to approximate the model evaluation to facilitate the target sample acceptance of GLUE during the Monte‐Carlo‐based stochastic simulation process. The results from a case study showed that the proposed GLUE‐MLS‐E method had a comparable performance as GLUE in terms of posterior parameter estimation and predicted confidence intervals; however, it could significantly reduce the computational cost. A comparison to other surrogate models, including MLS, quadratic response surface and artificial neural networks (ANN), revealed that the MLS‐E outperformed others in light of both the predicted confidence interval and the most likely value of water depths. ANN was shown to be a viable alternative, which performed slightly poorer than MLS‐E. The proposed surrogate method in stochastic sampling is of practical significance in computationally expensive problems like flood risk analysis, real‐time forecasting, and simulation‐based engineering design, and has a general applicability in many other numerical simulation fields that requires extensive efforts in uncertainty assessment. Copyright © 2014 John Wiley & Sons, Ltd.     

Uncertainty and multiple objective calibration in regional water balance modelling: case study in 320 Austrian catchments

We examine the value of additional information in multiple objective calibration in terms of model performance and parameter uncertainty. We calibrate and validate a semi‐distributed conceptual catchment model for two 11‐year periods in 320 Austrian catchments and test three approaches of parameter calibration: (a) traditional single objective calibration (SINGLE) on daily runoff; (b) multiple objective calibration (MULTI) using daily runoff and snow cover data; (c) multiple objective calibration (APRIORI) that incorporates an a priori expert guess about the parameter distribution as additional information to runoff and snow cover data. Results indicate that the MULTI approach performs slightly poorer than the SINGLE approach in terms of runoff simulations, but significantly better in terms of snow cover simulations. The APRIORI approach is essentially as good as the SINGLE approach in terms of runoff simulations but is slightly poorer than the MULTI approach in terms of snow cover simulations. An analysis of the parameter uncertainty indicates that the MULTI approach significantly decreases the uncertainty of the model parameters related to snow processes but does not decrease the uncertainty of other model parameters as compared to the SINGLE case. The APRIORI approach tends to decrease the uncertainty of all model parameters as compared to the SINGLE case. Copyright © 2006 John Wiley & Sons, Ltd.     

Bayesian updating of flood inundation likelihoods conditioned on flood extent data

Previously we have detailed an application of the generalized likelihood uncertainty estimation (GLUE) procedure to estimate spatially distributed uncertainty in models conditioned against binary pattern data contained in flood inundation maps. This method was applied to two sites where a single consistent synoptic image of inundation extent was available to test the simulation performance of the method. In this paper, we extend this to examine the predictive performance of the method for a reach of the River Severn, west‐central England. Uniquely for this reach, consistent inundation images of two major floods have been acquired from spaceborne synthetic aperture radars, as well as a high‐resolution digital elevation model derived using laser altimetry. These data thus allow rigorous split sample testing of the previous GLUE application. To achieve this, Monte Carlo analyses of parameter uncertainty within the GLUE framework are conducted for a typical hydraulic model applied to each flood event. The best 10% of parameter sets identified in each analysis are then used to map uncertainty in flood extent predictions using the method previously proposed for both an independent validation data set and a design flood. Finally, methods for combining the likelihood information derived from each Monte Carlo ensemble are examined to determine whether this has the potential to reduce uncertainty in spatially distributed measures of flood risk for a design flood. The results show that for this reach and these events, the method previously established is able to produce sharply defined flood risk maps that compare well with observed inundation extent. More generally, we show that even single, poor‐quality inundation extent images are useful in constraining hydraulic model calibrations and that values of effective friction parameters are broadly stationary between the two events simulated, most probably reflecting their similar hydraulics. Copyright © 2004 John Wiley & Sons, Ltd.     

Probabilistic calibration of a distributed hydrological model for flood forecasting

Abstract

The complexity of distributed hydrological models has led to improvements in calibration methodologies in recent years. There are various manual, automatic and hybrid methods of calibration. Most use a single objective function to calculate estimation errors. The use of multi-objective calibration improves results, since different aspects of the hydrograph may be considered simultaneously. However, the uncertainty of estimates from a hydrological model can only be taken into account by using a probabilistic approach. This paper presents a calibration method of probabilistic nature, based on the determination of probability functions that best characterize different parameters of the model. The method was applied to the Real-time Interactive Basin Simulator (RIBS) distributed hydrological model using the Manzanares River basin in Spain as a case study. The proposed method allows us to consider the uncertainty in the model estimates by obtaining the probability distributions of flows in the flood hydrograph.

Citation Mediero, L., Garrote, L. & Martín-Carrasco, F. J. (2011) Probabilistic calibration of a distributed hydrological model for flood forecasting. Hydrol. Sci. J. 56(7), 1129–1149.     

One decade of multi-objective calibration approaches in hydrological modelling: a review

Abstract

One decade after the first publications on multi-objective calibration of hydrological models, we summarize the experience gained so far by underlining the key perspectives offered by such approaches to improve parameter identification. After reviewing the fundamentals of vector optimization theory and the algorithmic issues, we link the multi-criteria calibration approach with the concepts of uncertainty and equifinality. Specifically, the multi-criteria framework enables recognition and handling of errors and uncertainties, and detection of prominent behavioural solutions with acceptable trade-offs. Particularly in models of complex parameterization, a multi-objective approach becomes essential for improving the identifiability of parameters and augmenting the information contained in calibration by means of both multi-response measurements and empirical metrics (“soft” data), which account for the hydrological expertise. Based on the literature review, we also provide alternative techniques for dealing with conflicting and non-commeasurable criteria, and hybrid strategies to utilize the information gained towards identifying promising compromise solutions that ensure consistent and reliable calibrations.

Citation Efstratiadis, A. & Koutsoyiannis, D. (2010) One decade of multi-objective calibration approaches in hydrological modelling: a review. Hydrol. Sci. J. 55(1), 58–78.     

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     

Model structure exploration for index flood regionalization

Although the nonlinear power form model structure is widely accepted by practitioners in the flood regionalization modelling, there is a lack of studies on whether there is a room for further improvement, and if the answer is yes, what should be done to explore alternative model structures. A framework is proposed in this study towards investigating this issue by the following steps: (i) a universal data‐driven model is utilized to see if there is a room for improvement compared with the conventional model, and (ii) if improvement is achieved, this means that there should exist more effective model structures than the current form. However, because the universal data‐driven models are usually opaque, more explicit model structures should be explored, which are convenient for practical usage. In this study, the proposed framework is applied in a case study using the catchment characteristics from the Flood Estimation Handbook in conjunction with the gamma test, support vector machine (SVM) and genetic programming (GP). First, the gamma test is used for the purpose of input variables selection where no model structure needs to be defined as a priori, and therefore, the result can be applied to any model structures for model building. Second, an SVM, which is a powerful data‐driven nonlinear model capable of modelling a variety of nonlinear systems, is applied to the index flood model for the first time. Once the best model is determined using those two data‐driven tools, GP is employed to find an alternative model structure. As the SVM is not formulated for producing explicit model functional form, the GP offers an advantage at this point where it can infer an explicit mathematical model functional form. Copyright © 2012 John Wiley & Sons, Ltd.     

Near real time satellite imagery to support and verify timely flood modelling

The study investigates the capability of coarse resolution synthetic aperture radar (SAR) imagery to support flood inundation models. A hydraulic model of a 98‐km reach of the River Po (Northern Italy) was calibrated on the October 2000 high‐magnitude flood event with extensive and high‐quality field data. During the June 2008, low‐magnitude flood event a SAR image was acquired and processed in near real time (NRT) in order to provide adequate data for quick verification and recalibration of the hydraulic model. Copyright © 2009 John Wiley & Sons, Ltd.     

ROC‐based calibration of flood inundation models

The use of spatial patterns of flood inundation (often obtained from remotely sensed imagery) to calibrate flood inundation models has been widespread over the last 15 years. Model calibration is most often achieved by employing one or even several performance measures derived from the well‐known confusion matrix based on a binary classification of flooding. However, relatively early on, it has been recognized that the use of commonly reported performance measures for calibrating flood inundation models (such as the F measure) is hampered because the calibration procedure commonly utilizes only one possible solution of a wet/dry classification of a remote sensing image [most often acquired by a synthetic aperture radar (SAR)] to calibrate or validate models and are biased towards either over‐prediction or under‐prediction of flooding. Despite the call in several studies for an alternative statistic, to this date, very few, if any, unbiased performance measure based on the confusion matrix has been proposed for flood model calibration/validation studies. In this paper, we employ a robust statistical measure that operates in the receiver operating characteristics (ROC) space and allows automated model calibration with high identifiability of the best model parameter set but without the need of a classification of the SAR image. The ROC‐based method for flood model calibration is demonstrated using two different flood event test cases with flood models of varying degree of complexity and boundary conditions with varying degree of accuracy. Verification of the calibration results and optional SAR classification is successfully performed with independent observations of the events. We believe that this proposed alternative approach to flood model calibration using spatial patterns of flood inundation should be employed instead of performance measures commonly used in conjunction with a binary flood map. © 2013 California Institute of Technology. Hydrological Processes © 2013 John Wiley & Sons, Ltd.     

Mitigating parameter bias in hydrological modelling due to uncertainty in covariates

The uncertainty in hydrological model covariates, if ignored, introduces systematic bias in the parameters estimated. We introduce here a method to determine the true value of parameters given uncertainty in model inputs. This method, known as simulation extrapolation (SIMEX) operates on the basis of an empirical relationship between parameters and the level of input noise (or uncertainty). The method starts by generating a series of alternate model inputs by artificially adding white noise in increasing multiples of the known error variance. The resulting parameter sets allow us to formulate an empirical relationship between their values and the level of noise present. SIMEX is based on theory that the trend in alternate parameters can be extrapolated back to the notional error free zone.

We illustrate the strength of SIMEX in improving skills of predictive models that use uncertain sea surface temperature anomaly (SSTA) data over the NINO3 region as predictor to the southern oscillation index (SOI), an alternate measure of the strength of the El Nino southern oscillation. Our hypothesis is that the higher magnitude of noise in the pre 1960 data period introduces bias to model parameters where SSTA is the input variable. The relatively error invariant southern oscillation index (SOI) is regressed over SSTA and calibrated using a subset of the series from 1900 to 1960. We validate the resulting models using the less erroneous 1960–2003 data period. Overall the application of SIMEX is found to reduce the residual predictive errors during the validation period.     

Uncertainty in floodplain delineation: expression of flood hazard and risk in a Gulf Coast watershed

This paper investigates the development of flood hazard and flood risk delineations that account for uncertainty as improvements to standard floodplain maps for coastal watersheds. Current regulatory floodplain maps for the Gulf Coastal United States present 1% flood hazards as polygon features developed using deterministic, steady‐state models that do not consider data uncertainty or natural variability of input parameters. Using the techniques presented here, a standard binary deterministic floodplain delineation is replaced with a flood inundation map showing the underlying flood hazard structure. Additionally, the hazard uncertainty is further transformed to show flood risk as a spatially distributed probable flood depth using concepts familiar to practicing engineers and software tools accepted and understood by regulators. A case study of the proposed hazard and risk assessment methodology is presented for a Gulf Coast watershed, which suggests that storm duration and stage boundary conditions are important variable parameters, whereas rainfall distribution, storm movement, and roughness coefficients contribute less variability. The floodplain with uncertainty for this coastal watershed showed the highest variability in the tidally influenced reaches and showed little variability in the inland riverine reaches. Additionally, comparison of flood hazard maps to flood risk maps shows that they are not directly correlated, as areas of high hazard do not always represent high risk. Copyright © 2012 John Wiley & Sons, Ltd.     

正弦标定自动处理算法研究

由于种种原因, 地震计的周期、 阻尼、 灵敏度等参数在仪器运行的过程中会发生变化, 这些参数的变化直接影响到地震计的性能和观测数据的质量。 为了掌握地震计参数的变化, 通常采用定期标定的方法, 对运行中仪器的参数进行跟踪监测, 通过分析标定数据得到仪器的运行状态。 目前, 对于标定数据的处理通常采用人工分析的办法。 随着台站数量的增加, 对标定数据的处理工作变得日益繁重。 该文介绍一种正弦标定自动处理算法, 利用这种算法编写的自动处理程序, 在标定数据处理过程中不需要人工干预, 计算机可以自动提取有效的波形数据进行测量计算, 并可以对效果不好的数据进行修复, 最终给出仪器的频率响应特性。     

An assessment of large-scale flood modelling based on LiDAR data

Large-scale flood modelling approaches designed for regional to continental scales usually rely on relatively simple assumptions to represent the potentially highly complex river bathymetry at the watershed scale based on digital elevation models (DEMs) with a resolution in the range of 25–30 m. Here, high-resolution (1 m) LiDAR DEMs are employed to present a novel large-scale methodology using a more realistic estimation of bathymetry based on hydrogeomorphological GIS tools to extract water surface slope. The large-scale 1D/2D flood model LISFLOOD-FP is applied to validate the simulated flood levels using detailed water level data in four different watersheds in Quebec (Canada), including continuous profiles over extensive distances measured with the HydroBall technology. A GIS-automated procedure allows to obtain the average width required to run LISFLOOD-FP. The GIS-automated procedure to estimate bathymetry from LiDAR water surface data uses a hydraulic inverse problem based on discharge at the time of acquisition of LiDAR data. A tiling approach, allowing several small independent hydraulic simulations to cover an entire watershed, greatly improves processing time to simulate large watersheds with a 10-m resampled LiDAR DEM. Results show significant improvements to large-scale flood modelling at the watershed scale with standard deviation in the range of 0.30 m and an average fit of around 90%. The main advantage of the proposed approach is to avoid the need to collect expensive bathymetry data to efficiently and accurately simulate flood levels over extensive areas.     

Using historical source data to understand urban flood risk: a socio-hydrological modelling application at Gregório Creek,Brazil

ABSTRACT

The city of São Carlos, state of São Paulo, Brazil, has a historical coexistence between society and floods. Unplanned urbanization in this area is a representative feature of how Brazilian cities have developed, undermining the impact of natural hazards. The Gregório Creek catchment is an enigma of complex dynamics concerning the relationship between humans and water in Brazilian cities. Our hypothesis is that social memory of floods can improve future resilience. In this paper we analyse flood risk dynamics in a small urban catchment, identify the impacts of social memory on building resilience and propose measures to reduce the risk of floods. We applied a socio-hydrological model using data collected from newspapers from 1940 to 2018. The model was able to elucidate human–water processes in the catchment and the historical source data proved to be a useful tool to fill gaps in the data in small urban basins.     

Applying ANN emulators in uncertainty assessment of flood inundation modelling: a comparison of two surrogate schemes

Abstract

A generalized likelihood uncertainty estimation (GLUE) framework coupling with artificial neural network (ANN) models in two surrogate schemes (i.e. GAE-S1 and GAE-S2) was proposed to improve the efficiency of uncertainty assessment in flood inundation modelling. The GAE-S1 scheme was to construct an ANN to approximate the relationship between model likelihoods and uncertain parameters for facilitating sample acceptance/rejection instead of running the numerical model directly; thus, it could speed up the Monte Carlo simulation in stochastic sampling. The GAE-S2 scheme was to establish independent ANN models for water depth predictions to emulate the numerical models; it could facilitate efficient uncertainty analysis without additional model runs for locations concerned under various scenarios. The results from a study case showed that both GAE-S1 and GAE-S2 had comparable performances to GLUE in terms of estimation of posterior parameters, prediction intervals of water depth, and probabilistic inundation maps, but with reduced computational requirements. The results also revealed that GAE-S1 possessed a slightly better performance in accuracy (referencing to GLUE) than GAE-S2, but a lower flexibility in application. This study shed some light on how to apply different surrogate schemes in using numerical models for uncertainty assessment, and could help decision makers in choosing cost-effective ways of conducting flood risk analysis.     

Using model error in response history analysis to evaluate component calibration methods

This research is part of a larger effort to better understand and quantify the epistemic model uncertainty in dynamic response-history simulations. This paper focuses on how calibration methods influence model uncertainty. Structural models in earthquake engineering are typically built up from independently calibrated component models. During component calibration, engineers often use experimental component response under quasi-static loading to find parameters that minimize the error in structural response under dynamic loading. Since the calibration and the simulation environments are different, if a calibration method wants to provide optimal parameters for simulation, it has to focus on features of the component response that are important from the perspective of global structural behavior. Relevance describes how efficiently a calibration method can focus on such important features. A framework of virtual experiments and a methodology is proposed to evaluate the influence of calibration relevance on model error in simulations. The evaluation is demonstrated through a case study with buckling-restrained braced frames (BRBF). Two calibration methods are compared in the case study. The first, highly relevant calibration method is based on stiffness and hardening characteristics of braces; the second, less relevant calibration method is based on the axial force response of braces. The highly relevant calibration method consistently identified the preferable parameter sets. In contrast, the less relevant calibration method showed poor to mediocre performance. The framework and methodology presented here are not limited to BRBF. They have the potential to facilitate and systematize the improvement of component-model calibration methods for any structural system.     

Advancing isotope-enabled hydrological modelling for ungauged calibration of data-scarce humid tropical catchments

Realistic projections of the future climate and how this translates to water availability is crucial for sustainable water resource management. However, data availability constrains the capacity to simulate streamflow and corresponding hydrological processes. Developing more robust hydrological models and methods that can circumvent the need for large amounts of hydro-climatic data is crucial to support water-related decisions, particularly in developing countries. In this study, we use natural isotope tracers in addition to hydro-climate data within a newly developed version of the spatially-distributed J2000iso as an isotope-enabled rainfall-runoff model simulating both water and stable isotope (δ²H) fluxes. We pilot the model for the humid tropical San Carlos catchment (2500 km²) in northeastern Costa Rica, which has limited time series, but spatially distributed data. The added benefit of simulating stable isotopes was assessed by comparing different amounts of observation data using three model calibration strategies (i) three streamflow gauges, (ii) three gauges with stream isotopes and (iii) isotopes only. The J2000iso achieved a streamflow Kling–Gupta efficiency (KGE) of 0.55–0.70 across all the models and gauges, but differences in hydrological process simulations emerged when including stable water isotopes in the rainfall-runoff calibration. Hydrological process simulation varied between the standard J2000 rainfall-runoff model with a high simulated surface runoff proportion of 37% as opposed to the isotope version with 84%–89% simulated baseflow or interflow. The model solutions that used only isotope data for calibration exhibited differences in simulated interflow, baseflow and model performance but captured bulk water balances with a reasonable match between the simulated and observed hydrographs. We conclude that J2000iso has shown the potential to support water balance modelling for ungauged catchments using stable isotope, satellite and global reanalysis data sets.     

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.     

A reliability‐based selective index for regional flood frequency analysis methods

In this paper, a new index is proposed for the selection of the best regional frequency analysis method. First, based on the theory of reliability, the new selective index is developed. The variances of three regional T‐year event estimators are then derived. The proposed methodology is applied to an actual watershed. For each regional method, the reliability of various T‐year regional estimates is computed. Finally, the reliability‐based selective index graph is constructed from which the best regional method can be determined. In addition, the selection result is compared with that based on the traditional index, root mean square error. The proposed new index is recommended as an alternative to the existing indices such as root mean square error, because the influence of uncertainty and the accuracy of estimates are considered. Copyright © 2003 John Wiley & Sons, Ltd.