Uncertainty in the calibration of effective roughness parameters in HEC-RAS using inundation and downstream level observations
Introduction
One-dimensional (1D) flow routing approaches such as Mike 11, ISIS or HEC, based on the St. Venant/Shallow Water Equations or variations, still form the majority of traditional numerical hydraulic models used in practical river engineering. The widespread usage in practice might be explained not only by the fact that 1D models are (in comparison to higher dimensional models) simpler to use and require a minimal amount of input data and computer power, but also because the basic concepts and programs have already been around for several decades (Stoker, 1957, Army, 2001).
However, these models have been criticised not only because of the expectation that representation of floodplain flow as a two-dimensional (2D) flow interacting with the channel flow will give more accurate predictions of flood wave propagation (Anderson et al., 1996, Aronica et al., 1998, Bates et al., 1992, Bates et al., 1998, Cunge, 1975, Dutta et al., 2000, Ervine and MacLeod, 1999, Gee et al., 1990, Hromadka et al., 1985), but also for the usage of the Manning equation (which can be also a criticism for higher dimensional models). This flow equation is computed:
- (1)
with an exponent of the wetted perimeter which Manning set to 2/3 despite the fact that his (and later) analysis of existing data showed that the value can vary (in his case between 0.6175 and 0.8395) (Laushey and 1989, 1989, Manning, 1891);
- (2)
is dimensionally inhomogeneous (Chow, 1959, Dooge, 1992, Manning, 1895);
- (3)
furthermore, was developed to represent uniform flow and not non-uniform conditions (see criticism of Laushey, 1989).
All model packages focus on the calibration of the roughness parameter which, together with the geometry, is considered to have the most important impact on predicting inundation extent and flow characteristics (Aronica et al., 1998, Bates et al., 1996, Hankin and Beven, 1998, Hardy et al., 1999, Rameshwaran and Willetts, 1999, Romanowicz et al., 1996, Schmidt, 2002).
Whether the model is more sensitive to either or both of the roughness and geometry uncertainty is in part a result of the dimensionality of the model structure, which represents geometry in different ways (Lane et al., 1999). Every model geometry is an approximation of the real geometry, with all its downstream variations, and therefore will have an implicit effect on the values of the effective roughness parameters. This also means that it should be possible to compensate to a certain degree for geometrical uncertainty, by varying the effective roughness values (Aronica et al., 1998, Marks and Bates, 2000). The extent to which this is possible varies with model dimensionality and discretisation.
Therefore, the focus of this study is an evaluation of the uncertainty of the roughness coefficients which is also driven by the fact that many modellers see the main problem in practical applications as a problem of choosing the ‘correct’ roughness (Barr and Das, 1986, Bathurst, 2002, Boss International, 2001, Dingman and Sharma, 1997, Graf, 1979, Rameshwaran and Willetts, 1999, Rice et al., 1998, Tinkler, 1997). Some studies (Trieste and Jarrett, 1987) have demonstrated discrepancies between calibrated effective model values and roughnesses which have been estimated based only on the nature of the channel and flood plain surfaces, despite many sources of guidance about how to choose a value, such as photographs (Arcement and Schneider, 1989, Chow et al., 1988), tables (Chadwick and Morfett, 1999, Chow, 1959, Chow et al., 1988, King, 1918), composite formulae (Barkau, 1997, Bathurst, 1994, Dingman and Sharma, 1997, Knight et al., 1989, Li and Zhang, 2001, Rice et al., 1998, Riggs, 1976) or measurement programs (Ackers, 1991, Dingman and Sharma, 1997, Ervine and MacLeod, 1999, Harunurrashid, 1990).
These estimates have usually been based on velocities measured for local velocity profiles or across a single cross-section. A flood routing model requires ‘effective’ values of roughness at the scale of the distance increment of the model (Beven and Carling, 1992), including all the effects of variable cross-sections, heterogeneous slopes and vegetation cover at that scale, as it is impossible to quantify every source of energy loss separately (Ervine et al., 1993). These parameters also have to compensate for the effects of man made structures on the flood plain neglected in the specification of the reach geometry, the method used to combine the roughness of the floodplain and channels (Bousmar and Zech, 1998), and possibly the particular numerical algorithms used. Any attempts, for example, to split the Manning roughness according to each of these component losses (Arcement and Schneider, 1989) will experience difficulties. It is problematic to quantify each loss in respect of the approximation of the model structure.
Several studies have been conducted to investigate the uncertainty in the structure of flood inundation models. Horritt and Bates (2002) compared 1D and 2D model codes (HEC-RAS, LISFLOOD-FP and TELEMAC-2D) in an optimisation framework without consideration of parameter uncertainty. They found that all models performed equally well, although different responses to changes in the friction parameterisation.
One methodological approach to formalise the uncertainty in the roughness parameters is presented in this study with the generalised likelihood uncertainty estimation (GLUE) methodology (Beven and Binley, 1992), which is explained in more detail later. This method has been applied by various researchers with one, two and quasi-two dimensional inundation codes (Romanowicz and Beven, 2003, Romanowicz et al., 1996; Aronica et al., 2002, Aronica et al., 1998). It could be shown that several sets of model roughness parameters perform equally well.
The first objective of this study is to extend the previous research of parameter uncertainty to the 1D model code HEC-RAS (US Army Corps of Hydraulic Engineers), because this type of inundation model is still widely used. It further compares the findings of two different sites (the River Morava in the Czech Republic and the River Severn in Great Britain) and two different data sets: elevation and inundation measurements for cross-sections only for the River Morava; and a full distributed inundation map for the River Severn. A new methodology to quantify the global performance of flood inundation within fuzzy set theory (extending Aronica et al., 2002, Horritt and Bates, 2001b) is utilised.
The paper also investigates the role of the accuracy of the numerical solution and its impact on model predictions. The role of parameters which control properties of the numerical solution are very often neglected, although a considerable impact has been found (Claxton, 2002).
Finally, a method to investigate the number of runs necessary within the GLUE framework to achieve consistent predictions is presented. This is a contribution to the common question on how many simulations are necessary within this type of Monte Carlo framework.
This paper discusses initially the model which has been applied, together with uncertainties faced in flood inundation modelling. Then the GLUE methodology is presented and how it has been applied within this framework. This is followed by a brief presentation of the catchments. Subsequently, the results of this study are discussed and a final conclusion is drawn at the end.
Section snippets
Uncertainties in flood inundation modelling using the example of HEC-RAS
In this section we explore some sources of uncertainties of a 1D flood inundation model. These are: structure, implementation of the numerical scheme, topography, model input/output and parameters.
The GLUE methodology
In this section the GLUE methodology is introduced, followed by the introduction of the measures used to evaluate model results. Finally, a stopping criteria, which indicates the number of runs necessary in performing such an analysis is presented.
Model case studies
This section briefly describes the two locations and the data available. It explains how the models have been set-up and explains in which way the river sections have been evaluated.
Stability
Many simulations, which have not been rejected as unstable by UNET itself, have been identified as physically impossible by visual inspection. The current version of UNET appears to have significant numerical problems that could not be associated with any particular cross-section, roughness combination or weighting parameter.
It must be pointed out that the user community is aware of some of these problems and avoids them by, e.g. cutting pilot channels in the original geometry and avoiding ‘low
Conclusions
In this study a 1D unsteady flow model (UNET, part of HEC-RAS 3.0) is analysed within a GLUE framework. In this Monte Carlo type analysis the weighting parameter of the numerical scheme (θ) and the Manning roughness parameters are varied using the model for cross-sections of the River Morava (Czech Republic) and the River Severn (United Kingdom). The results are evaluated with an absolute error criterion against maximum inundation level at cross-sections for a 25 km long stretch of the Morava
Acknowledgements
The data of the Morava have been made available by the Morava River Company and Czech Hydrometeorological Institute through the FRIEND project for which the authors are very grateful. The authors further would like to thank Paul Bates and Neil Hunter (both Bristol University) for valuable help. Financial support to Florian Pappenberger was provided by a European Union Grant (EU Framework 5 Proposal EVG1-CT-1999-00011). Matthew Horritt was supported by a UK Natural Research Council research
References (95)
- et al.
Uncertainty and equifinality in calibrating distributed roughness coefficients in a flood propagation model with limited data
Advances in Water Resources
(1998) At-a-site variation and minimum flow resistance for mountain rivers
Journal of Hydrology
(2002)- et al.
Statistical development and validation of discharge equations for natural channels
Journal of Hydrology
(1997) - et al.
Open channel profiles by Newton's iteration technique
Journal of Hydrology
(1971) - et al.
The importance of spatial resolution in hydraulic models for floodplain environments
Journal of Hydrology
(1999) Estimation of Manning roughness coefficient for basin and border irrigation
Agricultural Water Management
(1990)A statistical active contour model for SAR image segmentation
Image and Vision Computing
(1999)- et al.
Effects of spatial resolution on a raster based model of flood flow
Journal of Hydrology
(2001) - et al.
Evaluation of 1D and 2D numerical models for predicting river flood inundation
Journal of Hydrology
(2002) Modelling topography with SAR interferometry: illustrations of a favourable and less favourable environment
Computers and Geosciences
(2001)
The application of computational fluid dynamics to natural river channels: three-dimensional versus two-dimensional approaches
Geomorphology
Calculation of field Manning's roughness coefficient
Agricultural Water Management
River flow forecasting through conceptual models, part I—a discussion of principles
Journal of Hydrology
Criterion for location of downstream control for dynamic flood routing
Journal of Hydrology
Critical flow in rockbed streams with estimated values for Manning's n
Geomorphology
Understanding the radar backscattering from flooded and nonflooded Amazonian forests: results from canopy backscatter modeling
Remote Sensing of Environment
Toward a generalization of the TOPMODEL concepts: topographic indices of hydrological similarity
Water Resources Research
The general context for floodplain process research
Assessing the uncertainty in distributed model predictions using observed binary pattern information within GLUE
Hydrological Processes
Modeling floodplain flows using a 2-dimensional finite-element model
Earth Surface Processes and Landforms
Initial comparison of 2 2-dimensional finite-element codes for river flood simulation
Proceedings of the Institution of Civil Engineers-Water Maritime and Energy
Analysis and development of hydraulic models for floodplain flows
Investigating the behaviour of two-dimensional finite element models of compound channel flow
Earth Surface Processes and Landforms
Terrain information in geomorphological models: stability, resolution and sensitivity
Flow resistance estimation in mountain rivers
Journal of Hydraulic Engineering (ASCE)
Towards a coherent philosophy for modelling the environment
Proceedings of the Royal Society of London Series A—Mathematical Physical and Engineering Sciences
The future of distributed models: model calibration and uncertainty prediction
Hydrological Processes
Velocities, roughness and dispersion in the lowland River Severn
Quasi-two dimensional modelling of flood routing in rivers and flood plains by means of storage cells
On constraining TOPMODEL hydrograph simulations using partial saturated area information
Hydrological Processes
Water Profile computation in compound channels
Evaluation of light detection and ranging (LIDAR) for measuring river corridor topography
Journal of the American Water Resources Association
Synthetic aperture radar interferometry to measure Earth's surface topography and its deformation
Annual Review of Earth and Planetary Sciences
Two dimensional modeling of flood plain flows
The Manning formula in context
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