Multi‐method global sensitivity analysis (MMGSA) for modelling floodplain hydrological processes

When studying hydrological processes with a numerical model, global sensitivity analysis (GSA) is essential if one is to understand the impact of model parameters and model formulation on results. However, different definitions of sensitivity can lead to a difference in the ranking of importance of the different model factors. Here we combine a fuzzy performance function with different methods of calculating global sensitivity to perform a multi‐method global sensitivity analysis (MMGSA). We use an application of a finite element subsurface flow model (ESTEL‐2D) on a flood inundation event on a floodplain of the River Severn to illustrate this new methodology. We demonstrate the utility of the method for model understanding and show how the prediction of state variables, such as Darcian velocity vectors, can be affected by such a MMGSA. This paper is a first attempt to use GSA with a numerically intensive hydrological model. Copyright © 2007 John Wiley & Sons, Ltd.     

Estimation of uncertainty propagation in flood inundation mapping using a 1‐D hydraulic model

A need for more accurate flood inundation maps has recently arisen because of the increasing frequency and extremity of flood events. The accuracy of flood inundation maps is determined by the uncertainty propagated from all of the variables involved in the overall process of flood inundation modelling. Despite our advanced understanding of flood progression, it is impossible to eliminate the uncertainty because of the constraints involving cost, time, knowledge, and technology. Nevertheless, uncertainty analysis in flood inundation mapping can provide useful information for flood risk management. The twin objectives of this study were firstly to estimate the propagated uncertainty rates of key variables in flood inundation mapping by using the first‐order approximation method and secondly to evaluate the relative sensitivities of the model variables by using the Hornberger–Spear–Young (HSY) method. Monte Carlo simulations using the Hydrologic Engineering Center's River Analysis System and triangle‐based interpolation were performed to investigate the uncertainty arising from discharge, topography, and Manning's n in the East Fork of the White River near Seymour, Indiana, and in Strouds Creek in Orange County, North Carolina. We found that the uncertainty of a single variable is propagated differently to the flood inundation area depending on the effects of other variables in the overall process. The uncertainty was linearly/nonlinearly propagated corresponding to valley shapes of the reaches. In addition, the HSY sensitivity analysis revealed the topography of Seymour reach and the discharge of Strouds Creek to be major contributors to the change of flood inundation area. Copyright © 2014 John Wiley & Sons, Ltd.     

When does spatial resolution become spurious in probabilistic flood inundation predictions?

Advances in remote sensing have enabled hydraulic models to run at fine scale resolutions, producing precise flood inundation predictions. However, running models at finer resolutions increase their computational expense, reducing the feasibility of running the multiple model realizations required to undertake uncertainty analysis. Furthermore, it is possible that precision gained by running fine scale models is smoothed out when treating models probabilistically. The aim of this paper is to determine the level of spatial complexity that is required when making probabilistic flood inundation predictions. The Imera basin, Sicily is used as a case study to assess how changing the spatial resolution of the hydraulic model LISFLOOD‐FP impacts on the skill of conditional probabilistic flood inundation maps given model parameter and boundary condition uncertainties. We find that model performance deteriorates at resolutions coarser than 50 m. This is predominantly caused by changes in flow pathways at coarser resolutions which lead to non‐stationarity in the optimum model parameters at different spatial resolutions. However, although it is still possible to produce probabilistic flood maps that contain a coherent outline of the flood extent at coarser resolutions, the reliability of these maps deteriorates at resolutions coarser than 100 m. Additionally, although the rejection of non‐behavioural models reduces the uncertainty in probabilistic flood maps the reliability of these maps is also reduced. Models with resolutions finer than 50 m offer little gain in performance yet are more than an order of magnitude computationally expensive which can become infeasible when undertaking probabilistic analysis. Furthermore, we show that using deterministic, high‐resolution flood maps can lead to a spurious precision that would be misleading and not representative of the overall uncertainties that are inherent in making inundation predictions. Copyright © 2015 The Authors Hydrological Processes Published by John Wiley & Sons Ltd.     

A data based mechanistic approach to nonlinear flood routing and adaptive flood level forecasting

Operational flood forecasting requires accurate forecasts with a suitable lead time, in order to be able to issue appropriate warnings and take appropriate emergency actions. Recent improvements in both flood plain characterization and computational capabilities have made the use of distributed flood inundation models more common. However, problems remain with the application of such models. There are still uncertainties associated with the identifiability of parameters; with the computational burden of calculating distributed estimates of predictive uncertainty; and with the adaptive use of such models for operational, real-time flood inundation forecasting. Moreover, the application of distributed models is complex, costly and requires high degrees of skill. This paper presents an alternative to distributed inundation models for real-time flood forecasting that provides fast and accurate, medium to short-term forecasts. The Data Based Mechanistic (DBM) methodology exploits a State Dependent Parameter (SDP) modelling approach to derive a nonlinear dependence between the water levels measured at gauging stations along the river. The transformation of water levels depends on the relative geometry of the channel cross-sections, without the need to apply rating curve transformations to the discharge. The relationship obtained is used to transform water levels as an input to a linear, on-line, real-time and adaptive stochastic DBM model. The approach provides an estimate of the prediction uncertainties, including allowing for heterescadasticity of the multi-step-ahead forecasting errors. The approach is illustrated using an 80 km reach of the River Severn, in the UK.     

Sampling-based flood risk analysis for fluvial dike systems

A dike system of moderate size has a large number of potential system states, and the loading imposed on the system is inherently random. If the system should fail, in one of its many potential failure modes, the topography of UK floodplains is usually such that hydrodynamic modelling of flood inundation is required to generate realistic estimates of flood depth and hence damage. To do so for all possible failure states may require 1,000s of computationally expensive inundation simulations. A risk-based sampling technique is proposed in order to reduce the computational resources required to estimate flood risk. The approach is novel in that the loading and dike system states (obtained using a simplified reliability analysis) are sampled according to the contribution that a given region of the space of basic variables makes to risk. The methodology is demonstrated in a strategic flood risk assessment for the city of Burton-upon-Trent in the UK. 5,000 inundation model simulations were run although it was shown that the flood risk estimate converged adequately after approximately half this number. The case study demonstrates that, amongst other factors, risk is a complex function of loadings, dike resistance, floodplain topography and the spatial distribution of floodplain assets. The application of this approach allows flood risk managers to obtain an improved understanding of the flooding system, its vulnerabilities and the most efficient means of allocating resource to improve performance. It may also be used to test how the system may respond to future external perturbations.     

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.     

Characterisation of flood inundated areas and delineation of poor drainage soil using ERS-1 SAR imagery

Recent years have been marked by a continuous availability of spatial SAR data since the launch of the European remote sensing satellite (ERS-1) in 1991. Consequently, remote sensing techniques now offer an opportunity to map flood inundation fields caused by river overflow or waterlogging in environments characterized by frequent cloud cover. Indeed, inundation fields can clearly be seen on ERS-1 SAR images taken during flooding periods. However, such an identification can be constrained by the similarity in behaviour between water surfaces and other features of the landscape such as extended asphalt areas, permanent water bodies and less illuminated slopes. For consistent flood inundation extent mapping a more robust approach is required. This is provided by a conceptual flood inundation index that is physically sound in relation to radar imaging. Moreover, this index has proved to be useful for highlighting soils located within inundation fields and having significantly different internal drainage. The results achieved in the framework of the research must be seen in the context of intensive use of remote sensing data to support decision methods for sustainable management of land and water resources. Such decision support methods could be provided by river hydraulic models aimed at assessing environmental effects of inundation floods and at early flood warning systems. © 1997 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.     

Joint Monte Carlo and possibilistic simulation for flood damage assessment

A joint Monte Carlo and fuzzy possibilistic simulation (MC-FPS) approach was proposed for flood risk assessment. Monte Carlo simulation was used to evaluate parameter uncertainties associated with inundation modeling, and fuzzy vertex analysis was applied for promulgating human-induced uncertainty in flood damage estimation. A study case was selected to show how to apply the proposed method. The results indicate that the outputs from MC-FPS would present as fuzzy flood damage estimate and probabilistic-possibilistic damage contour maps. The stochastic uncertainty in the flood inundation model and fuzziness in the depth-damage functions derivation would cause similar levels of influence on the final flood damage estimate. Under the worst scenario (i.e. a combined probabilistic and possibilistic uncertainty), the estimated flood damage could be 2.4 times higher than that computed from conventional deterministic approach; considering only the pure stochastic effect, the flood loss would be 1.4 times higher. It was also indicated that uncertainty in the flood inundation modeling has a major influence on the standard deviation of the simulated damage, and that in the damage-depth function has more notable impact on the mean of the fitted distributions. Through applying MC-FPS, rich information could be derived under various α-cut levels and cumulative probabilities, and it forms an important basis for supporting rational decision making for flood risk management under complex uncertainties.     

A probabilistic model for real‐time flood warning based on deterministic flood inundation mapping

Deterministic flood inundation mapping is valuable for the investigation of detailed flood depth and extent. However, when these data are used for real‐time flood warning, uncertainty arises while encountering the difficulties of timely response, message interpretation and performance evaluation that makes statistical analysis necessary. By incorporating deterministic flood inundation map outputs statistically by means of logistic regression, this paper presents a probabilistic real‐time flood warning model determining region‐based flood probability directly from rainfall, being efficient in computation, clear in message, and valid in physical meaning. The calibration and validation of the probabilistic model show a satisfactory overall correctness rate, with the hit rate far surpassing the false alarm rate in issuing flood warning for historical events. Further analyses show that the probabilistic model is effective in evaluating the level of uncertainty lying within flood warning which can be reduced by several techniques proposed in order to improve warning performance. Copyright © 2011 John Wiley & Sons, Ltd.     

洪湖分蓄洪区洪水淹没风险动态识别与可能损失评估

全球气候变化和社会经济快速发展,使长江流域面临越来越严重的防洪压力．在长江流域开展洪水淹没风险识别与洪水损失评估工作,对于长江流域洪水风险管理具有重大意义．本项研究以洪湖分蓄洪区为案例,采用基于GIS栅格数据整合于Arcview3．x的二维水文-水动力学模型进行洪水淹没风险动态识别,并且根据土地利用分类及其单位面积价值,建立洪水淹没损失函数,进行洪水淹没动态损失评估,建立了东洪湖分蓄洪区洪水淹没动态损失数据库,为东洪湖分蓄洪区的合理利用提供定量科学依据．洪水淹没动态风险识别基于数字高程模型进行,采用修正的1998年夏季洪水水位-时间水文过程线对模型参数进行调整,并以地面糙率反映不同地表覆盖形态对洪水演进过程的影响．     

Validation of a full hydrodynamic model for large‐scale hydrologic modelling in the Amazon

A key aspect of large river basins partially neglected in large‐scale hydrological models is river hydrodynamics. Large‐scale hydrologic models normally simulate river hydrodynamics using simplified models that do not represent aspects such as backwater effects and flood inundation, key factors for some of the largest rivers of the world, such as the Amazon. In a previous paper, we have described a large‐scale hydrodynamic approach resultant from an improvement of the MGB‐IPH hydrological model. It uses full Saint Venant equations, a simple storage model for flood inundation and GIS‐based algorithms to extract model parameters from digital elevation models. In the present paper, we evaluate this model in the Solimões River basin. Discharge results were validated using 18 stream gauges showing that the model is accurate. It represents the large delay and attenuation of flood waves in the Solimões basin, while simplified models, represented here by Muskingum Cunge, provide hydrographs are wrongly noisy and in advance. Validation against 35 stream gauges shows that the model is able to simulate observed water levels with accuracy, representing their amplitude of variation and timing. The model performs better in large rivers, and errors concentrate in small rivers possibly due to uncertainty in river geometry. The validation of flood extent results using remote sensing estimates also shows that the model accuracy is comparable to other flood inundation modelling studies. Results show that (i) river‐floodplain water exchange and storage, and (ii) backwater effects play an important role for the Amazon River basin hydrodynamics. Copyright © 2011 John Wiley & Sons, Ltd.     

An event simulation approach to the assessment of flood level frequencies: risk maps for the Warsaw reach of the River Vistula

Flood risk assessment is customarily performed using a design flood. Observed past flows are used to derive a flood frequency curve which forms the basis for a construction of a design flood. The simulation of a distributed model with the 1‐in‐T year design flood as an input gives information on the possible inundation areas, which are used to derive flood risk maps. The procedure is usually performed in a deterministic fashion, and its extension to take into account the design flood‐and flow routing model uncertainties is computer time consuming. In this study we propose a different approach to flood risk assessment which consists of the direct simulation of a distributed flow routing model for an observed series of annual maximum flows and the derivation of maps of probability of inundation of the desired return period directly from the obtained simulations of water levels at the model cross sections through an application of the Flood Level Frequency Analysis. The hydraulic model and water level quantile uncertainties are jointly taken into account in the flood risk uncertainty evaluation using the Generalized Likelihood Uncertainty Estimation (GLUE) approach. An additional advantage of the proposed approach lies in smaller uncertainty of inundation predictions for long return periods compared to the standard approach. The approach is illustrated using a design flood level and a steady‐state solution of a hydraulic model to derive maps of inundation probabilities. Copyright © 2016 John Wiley & Sons, Ltd.     

Assessing the uncertainty in distributed model predictions using observed binary pattern information within GLUE

In this paper we extend the generalized likelihood uncertainty estimation (GLUE) technique to estimate spatially distributed uncertainty in models conditioned against binary pattern data contained in flood inundation maps. Untransformed binary pattern data already have been used within GLUE to estimate domain‐averaged (zero‐dimensional) likelihoods, yet the pattern information embedded within such sources has not been used to estimate distributed uncertainty. Where pattern information has been used to map distributed uncertainty it has been transformed into a continuous function prior to use, which may introduce additional errors. To solve this problem we use here ‘raw’ binary pattern data to define a zero‐dimensional global performance measure for each simulation in a Monte Carlo ensemble. Thereafter, for each pixel of the distributed model we evaluate the probability that this pixel was inundated. This probability is then weighted by the measure of global model performance, thus taking into account how well a given parameter set performs overall. The result is a distributed uncertainty measure mapped over real space. The advantage of the approach is that it both captures distributed uncertainty and contains information on global likelihood that can be used to condition predictions of further events for which observed data are not available. The technique is applied to the problem of flood inundation prediction at two test sites representing different hydrodynamic conditions. In both cases, the method reveals the spatial structure in simulation uncertainty and simultaneously enables mapping of flood probability predicted by the model. Spatially distributed uncertainty analysis is shown to contain information over and above that available from global performance measures. Overall, the paper highlights the different types of information that may be obtained from mappings of model uncertainty over real and n‐dimensional parameter spaces. Copyright © 2002 John Wiley & Sons, Ltd.     

Influence of uncertain boundary conditions and model structure on flood inundation predictions

In this study, the GLUE methodology is applied to establish the sensitivity of flood inundation predictions to uncertainty of the upstream boundary condition and bridges within the modelled region. An understanding of such uncertainties is essential to improve flood forecasting and floodplain mapping. The model has been evaluated on a large data set. This paper shows uncertainty of the upstream boundary can have significant impact on the model results, exceeding the importance of model parameter uncertainty in some areas. However, this depends on the hydraulic conditions in the reach e.g. internal boundary conditions and, for example, the amount of backwater within the modelled region. The type of bridge implementation can have local effects, which is strongly influenced by the bridge geometry (in this case the area of the culvert). However, the type of bridge will not merely influence the model performance within the region of the structure, but also other evaluation criteria such as the travel time. This also highlights the difficulties in establishing which parameters have to be more closely examined in order to achieve better fits. In this study no parameter set or model implementation that fulfils all evaluation criteria could be established. We propose four different approaches to this problem: closer investigation of anomalies; introduction of local parameters; increasing the size of acceptable error bounds; and resorting to local model evaluation. Moreover, we show that it can be advantageous to decouple the classification into behavioural and non-behavioural model data/parameter sets from the calculation of uncertainty bounds.     

Interactions between subgrid‐scale resolution,feature representation and grid‐scale resolution in flood inundation modelling

Numerical modelling of flood inundation over large and complex floodplains often requires mesh resolutions coarser than the structural features (e.g. buildings) that are known to influence the inundation process. Recent research has shown that this mismatch is not well represented by conventional roughness treatments, but that finer‐scale features can be represented through porosity‐based subgrid‐scale treatments. This paper develops this work by testing the interactions between feature representation, subgrid‐scale resolution and mesh resolution. It uses as the basis for this testing a 2D diffusion‐based flood inundation model which is applied to a 2004 flood event in a topologically complex upland floodplain in northern England. This study formulated simulations with different grid mesh resolution and subgrid mesh ratio. The sensitivity of the model to mesh resolution and roughness specification was investigated. Model validation and verification suggest that the subgrid treatment with higher subgrid mesh ratio can give much improved predictions of flood propagation, in particular, in terms of the predicted water depth. This study also highlighted the limitation of using at‐a‐point in time inundation extent for validation of flood models of this type. Copyright © 2010 John Wiley & Sons, Ltd.     

Evaluation of groundwater resources in wide inundation areas of the Mekong River basin

Severe floods can have disastrous impacts and cause wide ranging destruction in the Mekong River basin. At the same time groundwater resources are significantly influenced and extensively recharged by flood water in inundation areas of the basin. This study determines the variation of groundwater resources caused by flooding over inundated areas located in lower part of the Mekong River basin using numerical modeling and field observations. The inundation calculations have been evaluated using satellite image outputs. Comparing large, medium and small flood events, we conclude that flood control which reduces the area of inundation, results in a reduction of groundwater resources in the area. In 1993, a 19% reduction in inundation areas resulted in a 31% reduction in groundwater storage. In 1998, a 44% reduction in inundation areas led to a 42% reduction in groundwater storage. Thus, while flood control activities are vital to reduce negative flood impacts in the Mekong River basin, they also negatively impact groundwater resources in the area.     

Estimating uncertainty associated with water stages from a single SAR image

It is the goal of remote sensing to infer information about objects or a natural process from a remote location. This invokes that uncertainty in measurement should be viewed as central to remote sensing. In this study, the uncertainty associated with water stages derived from a single SAR image for the Alzette (G.D. of Luxembourg) 2003 flood is assessed using a stepped GLUE procedure. Main uncertain input factors to the SAR processing chain for estimating water stages include geolocation accuracy, spatial filter window size, image thresholding value, DEM vertical precision and the number of river cross sections at which water stages are estimated. Initial results show that even with plausible parameter values uncertainty in water stages over the entire river reach is 2.8 m on average. Adding spatially distributed field water stages to the GLUE analysis following a one-at-a-time approach helps to considerably reduce SAR water stage uncertainty (0.6 m on average) thereby identifying appropriate value ranges for each uncertain SAR water stage processing factor. For the GLUE analysis a Nash-like efficiency criterion adapted to spatial data is proposed whereby acceptable SAR model simulations are required to outperform a simpler regression model based on the field-surveyed average river bed gradient. Weighted CDFs for all factors based on the proposed efficiency criterion allow the generation of reliable uncertainty quantile ranges and 2D maps that show the uncertainty associated with SAR-derived water stages. The stepped GLUE procedure demonstrated that not all field data collected are necessary to achieve maximum constraining. A possible efficient way to decide on relevant locations at which to sample in the field is proposed. It is also suggested that the resulting uncertainty ranges and flood extent or depth maps may be used to evaluate 1D or 2D flood inundation models in terms of water stages, depths or extents. For this, the extended GLUE approach, which copes with the presence of uncertainty in the observed data, may be adopted.     

Influential input classification in probabilistic multimedia models

 Monte Carlo analysis is a statistical simulation method that is often used to assess and quantify the outcome variance in complex environmental fate and effects models. Total outcome variance of these models is a function of (1) the variance (uncertainty and/or variability) associated with each model input and (2) the sensitivity of the model outcome to changes in the inputs. To propagate variance through a model using Monte Carlo techniques, each variable must be assigned a probability distribution. The validity of these distributions directly influences the accuracy and reliability of the model outcome. To efficiently allocate resources for constructing distributions one should first identify the most influential set of variables in the model. Although existing sensitivity and uncertainty analysis methods can provide a relative ranking of the importance of model inputs, they fail to identify the minimum set of stochastic inputs necessary to sufficiently characterize the outcome variance. In this paper, we describe and demonstrate a novel sensitivity/uncertainty analysis method for assessing the importance of each variable in a multimedia environmental fate model. Our analyses show that for a given scenario, a relatively small number of input variables influence the central tendency of the model and an even smaller set determines the spread of the outcome distribution. For each input, the level of influence depends on the scenario under consideration. This information is useful for developing site specific models and improving our understanding of the processes that have the greatest influence on the variance in outcomes from multimedia models.     

Sensitivity of a hydraulic model to channel erosion uncertainty during extreme flooding

Recent research into flood modelling has primarily concentrated on the simulation of inundation flow without considering the influences of channel morphology. River channels are often represented by a simplified geometry that is implicitly assumed to remain unchanged during flood simulations. However, field evidence demonstrates that significant morphological changes can occur during floods to mobilize the boundary sediments. Despite this, the effect of channel morphology on model results has been largely unexplored. To address this issue, the impact of channel cross‐section geometry and channel long‐profile variability on flood dynamics is examined using an ensemble of a 1D–2D hydraulic model (LISFLOOD‐FP) of the ~1 : 2000 year recurrence interval floods in Cockermouth, UK, within an uncertainty framework. A series of simulated scenarios of channel erosional changes were constructed on the basis of a simple velocity‐based model of critical entrainment. A Monte‐Carlo simulation framework was used to quantify the effects of this channel morphology together with variations in the channel and floodplain roughness coefficients, grain size characteristics and critical shear stress on measures of flood inundation. The results showed that the bed elevation modifications generated by the simplistic equations reflected an approximation of the observed patterns of spatial erosion that enveloped observed erosion depths. The effect of uncertainty on channel long‐profile variability only affected the local flood dynamics and did not significantly affect the friction sensitivity and flood inundation mapping. The results imply that hydraulic models generally do not need to account for within event morphodynamic changes of the type and magnitude of event modelled, as these have a negligible impact that is smaller than other uncertainties, e.g. boundary conditions. Instead, morphodynamic change needs to happen over a series of events to become large enough to change the hydrodynamics of floods in supply limited gravel‐bed rivers such as the one used in this research. Copyright © 2014 John Wiley & Sons, Ltd.