Deriving distributed roughness values from satellite radar data for flood inundation modelling

Journal of Hydrology (2007) 344, 96– 111

available at www.sciencedirect.com

journal homepage: www.elsevier.com/locate/jhydrol

Deriving distributed roughness values from satellite radar data for flood inundation modelling G. Schumann a,b,*, P. Matgen a, L. Hoffmann a, R. Hostache e, F. Pappenberger c,d, L. Pfister a a

Department of Environment and Agro-biotechnologies, Public Research Centre-Gabriel Lippmann, Belvaux L-4422, Luxembourg b Environmental Systems Research Group, Dundee University, Dundee DD14HN, UK c Hydrology and Fluid Dynamics Group, Lancaster University, Environmental Science Department, Lancaster LA14YQ, UK d European Centre for Medium-Range Weather Forecasts, Reading RG29AX, UK e ´le ´de ´tection, Cemagref, Montpellier F-34093, France Maison de la Te Received 22 December 2006; received in revised form 8 May 2007; accepted 30 June 2007

KEYWORDS Remote sensing; Flood inundation model error; Monte Carlo-based computation; Spatially distributed parameter; Behavioural criteria; Parameter identifiability

Because of a lack of spatially distributed evaluation data flood inundation modelling is commonly performed with simplified flood propagation models that very often consider only one channel roughness parameter value to be calibrated. This concept as such is debatable, as friction values are known to be spatially heterogeneous. Moreover, with (over-) simplified model structures, it is clear that distributed simulations may consistently perform well at a given location whilst underperforming at another. Using only limited field data in model calibration, it is not possible to gather enough information on local model errors to improve the modelling concept. However, new processing procedures of remotely sensed flood imagery allow model calibration to be performed at any desired location. Such spatially distributed data can provide enough information to assess models locally. This local evaluation enables the modeller to define and set spatially distributed patterns of model parameters. Using the 2003 River Alzette (G.D. of Luxembourg) flood event recorded by the ENVISAT satellite, this study demonstrates that by directing the flood-modelling concept towards spatially clustered roughness parameters conditioned on remote sensing, it is possible to identify a model structure that generates acceptable model simulations not only at the reach scale but also locally. Applying the same procedure on earlier events with larger magnitude generates similar parameter clusters that are correlated with those obtained with the 2003 ENVISAT flood event. This

Summary

* Corresponding author. Address: Department of Environment and Agro-biotechnologies, Public Research Centre-Gabriel Lippmann, Belvaux, L-4422, Luxembourg. Tel.: +352 470261x417; fax: +352 470264. E-mail address: [email protected] (G. Schumann). 0022-1694/$ - see front matter ª 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jhydrol.2007.06.024

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illustrates the great potential that remote sensing holds in terms of identifying new ways to test existing model concepts and to contribute to the development of improved flood inundation models. The findings thus support the long-debated hypothesis that remote sensing improves our understanding and thus modelling of complex environmental processes, such as floods. ª 2007 Elsevier B.V. All rights reserved.

Introduction Floods are among the most devastating natural disasters and cost many lives every year (Dilley et al., 2005). The frequency with which they occur is on the up-rise in many regions of the world (Drogue et al., 2004) and due to ever increasing human activities on natural floodplains, the economical and socially destructive impact of floods is likely to worsen in the near future. With an increasing public awareness of the impacts of climate change and the more recent flood events throughout Europe and the rest of the world there is the need to establish more effective flood risk management plans and strategies (ICE, 2001). Future flood prevention and response measures will require a stronger emphasis on integrated approaches incorporating prediction and risk uncertainties (Pappenberger et al., 2006b). Altering flood risk mitigation strategies can result from researching improved methods on how to reduce uncertainty (Samuels et al., 2002). In the best-case scenario, this might be the case if the modeller comes up with a more area-representative model that generates predictions that are also acceptable locally. However, surprisingly few modelling approaches, at least in practice, include uncertainty (Pappenberger and Beven, 2006). Studies on GLUE (Beven and Binley, 1992) and other uncertainty estimation techniques have therefore recently gained popularity among modellers (Pappenberger et al., 2006a). Flood inundation models contain several effective parameters that may be adjusted as part of the calibration process. In particular the channel roughness is used, as this parameter determines the water stage which in return determines overtopping and thus, in many cases exhibits the highest sensitivity (Bates, 2000; Bates et al., 2003; Hall et al., 2005; Horritt, 2000). The evaluation of model predictions against observed or measured data can be performed at the reach scale or locally, e.g. with hydrographs. However, it has been shown that distributed simulations may consistently perform well at a given location whilst underperforming at another (Freer et al., 2004; Pappenberger et al., 2007). Pappenberger et al. (2007) and Pappenberger et al., 2006b have shown that a (two dimensional) model cannot be expected to perform well everywhere due to current model and data limitations. They further argue that one obvious solution would be to introduce spatially disaggregated model parameters, as a model with higher degrees of freedom may be able to reproduce local as well as reachscale (global) phenomena. However, they hypothesise that even with a maximum number of degrees of freedom it may be impossible to find models that fit everywhere. This study proposes a novel methodology to identify distributed functional classes of channel conveyance from remotely sensed data, which optimally balances the number

of distributed channel roughness parameters with the need to fit data globally and locally. Most work on researching roughness characteristics with remote sensing has been undertaken on floodplain roughness related to land use types (e.g. Werner et al., 2005; Straatsma and Middelkoop, 2006). Measuring effective roughness, particularly channel roughness distributions in the field is a very difficult and time and cost consuming task (if it is possible at all on the scale required). Therefore, trying to integrate distributed information from remotely sensed data in flood inundation and hydrological models has recently gained popularity due to its tremendous promise to provide new types of data that help make such models easier to use as well as improve their performance (Engman and Schultz, 2000). Remote sensing, especially synthetic aperture radar (SAR) with its all weather capability and its sensitivity towards smooth open water surfaces, can provide useful spatially distributed flood information that may be integrated with models (Aronica et al., 2002; Matgen et al., 2004; Pappenberger et al., 2005; Schumann et al., 2005; Horritt, 2006; Matgen et al., 2007; Schumann et al., 2007). This study presents a step-based approach that makes use of area-specific SAR flood information to group localised model error characteristics. This additional information is then used to derive spatial clusters of roughness parameters. By applying spatial distributions of important model parameters, the objective of this study is to obtain locally acceptable flood predictions. The methodology is developed on a flood event that occurred in early January 2003 on the River Alzette (G.D. of Luxembourg).

Study site and available data Study site The study reach of the River Alzette (G.D. of Luxembourg) north of Luxembourg City between Steinsel and Mersch (Fig. 1) has a long history of severe flooding (Schumann et al., 2007). The study reach is characterized by a relatively large and flat floodplain. The reach length is approximately 10 km and the average floodplain width 300 m. The average channel depth is 4 m and the average slope is 0.08%. The Alzette catchment has an area of 1175 km2, of which the study reach drainage area represents 34% (404 km2). Although some larger villages lie within the natural floodplain of the river, no severe damages were recorded for the early January 2003 flood, which had a peak discharge of around 70.5 m3 s1 corresponding to a return period of 5 years. This gives a specific peak discharge of 0.63 mm h1 for the 2003 event.

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Figure 1 Map of study site showing the ASAR image subset of the flooded reach. The extracted extent and the locations of the field-based high water marks are overlain.

Available data Hydraulic flow routing model The hydraulic flow routing model, HEC-RAS (USACE, 2002), used in this study is capable of performing unsteady flow calculations in the direction of the flow, which is oriented along the channel. Unsteady flow calculations are based on the continuity and momentum equations. A horizontal water surface at each cross-section normal to the direction of flow is assumed, such that the exchange of momentum between the channel and the floodplain is negligible and the discharge is distributed according to conveyance (USACE, 2002). Finally, the friction forces acting on the sys-

tem incorporate the well-known Manning equation that defines the friction slope, Sf, according to: Sf ¼

Q 2 n2 R4=3 A2

ð1Þ

where Q denotes discharge (m3 s1), A the cross-section area (m2), R the hydraulic radius (A divided by the wetted perimeter of the channel), and n represents an empirical roughness coefficient, the value of which is usually taken from tables. Hence, the only model parameters that need calibration in order to fit simulations to observations are the roughness coefficients, n, for the channel and the floodplain.

Deriving distributed roughness values from satellite radar data for flood inundation modelling The HEC-RAS database for the River Alzette comprises topographic data in the form of a high resolution digital elevation model (DEM), geometric data for 76 river cross sections, and a flood hydrograph as an upstream boundary condition. Model calibration and validation data Model evaluation data included remotely sensed data in the form of radar imagery and aerial photography as well as LiDAR elevation data and field-recorded high water marks: ENVISAT-ASAR data: The Advanced Synthetic Aperture Radar (ASAR) instrument onboard ENVISAT operating in Cband recorded a high-magnitude flood event on the River Alzette on January 2, 2003. The image was acquired in dual polarization mode (VV and VH) near the time of peak discharge (Fig. 2), which represents an opportunity for objective and distributed flood inundation model calibration. For successful flood extent extraction, VH-polarisation is superior to VV-polarisation (Henry et al., 2006) due to the lower sensitivity of VH to waves on the smooth surface and emergent vegetation that may hinder flood detection. Prior to flood area extraction, an image subset of the reach was filtered with a Frost 5 · 5 pixel window. This filter proves appropriate for subsequent flood boundary delineation, as it reduces the speckle present in the SAR scene while preserving information on the edges (Matgen et al., 2007). ERS-SAR data: The Synthetic Aperture Radar (SAR) instrument onboard ERS operating in C-band and VV-polarisation mode acquired a flood image of the 2003 event around ten hours before the peak (Fig. 2). This pre-flood event, which had a specific discharge of 0.47 mm h1 (i.e. 53 m3 s1), is used as a validation set for the spatial roughness clusters. Applying the radar-derived parameter configuration to another event and evaluating spatial correlation allows testing the robustness of the spatial arrangement of the parameter(s). Aerial photograph: A black and white aerial photograph of the 1995 flood event is used as an additional validation

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set for the spatial roughness clusters, as it represents a different remote sensing instrument. Using two independent validation sets, model over-fitting can be tested more objectively and above all the confidence in the results and conclusions increases. The 1995 event had a much higher peak discharge (modelled at 95.6 m3 s1) and caused more socio-economic damage than the 2003 event. The specific peak discharge for the 1995 event was 0.85 mm h1. The photograph was acquired on January 23, 1995 at around noon, approximately at peak discharge. LiDAR data: During low flow conditions, LiDAR data was also acquired over the study reach, from which a high-resolution high-precision DEM of the natural floodplain of the Alzette was generated with an average elevation RMSE of ±15 cm, after vegetation and buildings had been removed from the surface model. Its spatial resolution is 2 m. The vertical accuracy of the LiDAR DEM proves appropriate for flood management purposes. In situ high water marks: Field-based high water marks, evenly distributed across the study site, are used as an independent validation set to assess model performance at both the reach and the local scale. Setting behavioural criteria at the reach scale and local scale: Model evaluation is done using field-based high water marks. Evaluation at the reach scale is represented by a mean performance of the model over the study reach. In this case, a model is said to be behavioural if it performs at least as well as a simple linear interpolation between the reach uppermost and lowermost recorded high water mark (Bates et al., 1998). Refsgaard et al. (2006) state that a good reference for model performance is to compare it with uncertainties of the available field observations. In this sense, for local scale evaluation, a behavioural model has to reach the level of uncertainty that is set for each of the seven distributed field-based high water marks, given data measurement uncertainties (Beven, 2006). Floodplain water stages were obtained by intersecting GPS marks of wrack lines with the LiDAR DEM. Elevation variance within an assumed 5 m positional uncertainty buffer of the GPS marks

High water marks

80 Radar (ERS) image

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Q (m3 s—1)

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Figure 2

2—Jan—03 00:00

3—Jan—03 00:00 4—Jan—03 00:00 Date and time

5—Jan—03 00:00

2003 flood hydrograph. Acquisition date and time of remotely sensed data and field measurements are also shown.

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added to the DEM uncertainty (r of 0.15 m), revealed a total uncertainty at the floodplain water stage value of ±2r, i.e. ±0.3 m.

Methodology The methodology follows the procedure illustrated in Fig. 3. The subsections below explain the different methodological steps (P1–P4) in detail.

marks of the maximum flood boundary give a satisfactory agreement with the ASAR-derived flood extent (see Schumann et al., 2007) in the order of one ground resolution (i.e. 25 m), meaning two image pixel resolutions of 12.5 m. An intersection of the left and right flood boundary with the high-resolution high-precision LiDAR DEM at every HECRAS cross-section gave two water levels for each cross-section. Assuming a horizontal water level surface across the floodplain, as is also the case in 1D hydrodynamic models, the mean between the left and right boundary elevation denotes the water stage used for model evaluation.

SAR image processing (P1): radar-derived water elevation data

Spatially distributing roughness (P2–P3)

The HEC-RAS calibration data for the 2003 flood event are water levels derived from the ASAR image data at model cross sections through integration of remotely sensed flood boundaries and elevation data (see Schumann et al., 2007). The ENVISAT radar image of the 2003 flood event on the River Alzette provided an event-representative flood extent. After successful geo-referencing and image speckle removal, the flooded area was extracted with the widely used thresholding method (Fig. 1). Numerous (91) field-based GPS

In an ideal case, a ‘perfectly’ calibrated model should generate a simulation or prediction that meets the requirements not only at the reach scale but also at any desired location. This condition suggests that a model setup would be needed which reflects the local characteristics of a reach area that incorporates all possible relevant characteristics of that place (Beven, 2000). This is particularly important in flood risk assessment studies.

Radar image of flood 1

Key Input

P1: SAR image processing

Processing step Output

Flood extent

LiDAR DEM

Remotely sensed water levels

P2: Identifying area-specific model behaviour

Flood inundation model (HEC-RAS)

Performing simulations over realistic parameter ranges

CDFs for the roughness parameter

P3: Grouping spatial variations in model parameters

Roughness clusters

P4: Iterative calibration of flood inundation model with spatially distributed parameter configurations

Local area and reachscale evaluation data

Acceptable predictions at the local scale at parameter configuration X

NO YES

Stop iteration

Figure 3 Step-based approach to identify distributed functional classes of channel conveyance from remotely sensed data for fitting data locally. The processing steps P1–P4 are explained in detail in the text.

Deriving distributed roughness values from satellite radar data for flood inundation modelling One possible model setup could be one with spatially distributed parameter patterns (Werner et al., 2005; Pappenberger et al., 2006b). In fact, this study builds upon the discussion and conclusion of an innovative study by Pappenberger et al. (2006b) who investigate the spatial and temporal shift of ‘behavioural’ surface roughnesses. They varied independently from each other several different flood model cross-sections that are thought to have an influence on model output. Then, they computed the cumulative distribution function (CDF) at each cross-section for the Manning surface roughness based on the performance of the model and analysed correlations between cross-sections. They found that different cross-sections require different Manning values and that the model is influenced by a complex interaction of parameters but suggested that the results should be used with care, as it is difficult to pin point how parameter values should be changed locally and to define appropriate evaluation and acceptability criteria. By analysing local model errors to cluster spatial distributions of parameter values using satellite radar data of a flood event, it is expected that model predictions can be obtained which produce reach-scale acceptable models that also meet local behavioural criteria. Moreover, if model performance is such that radar remote sensing allows a model parameter configuration to be determined which leads to predictions that are locally adequate, the response may be to produce flood extent and depth maps or vulnerability and risk maps (Pappenberger et al., 2007) with low and thus probably acceptable uncertainties for more or less every location. Also, remote sensing, in particular radar remote sensing, would prove a vital tool in the study of physical parameter behaviour and its impact on models used to reproduce a simplified real world environmental process. At present, determining parameter configuration locally and without changing the model setup a priori seems only likely with the fully distributed nature of remotely sensed data. Furthermore, to assess model performance for a given parameter configuration at both the reach and the local scale, an independent data set, other than that used to distribute a model parameter, should preferably be used. In this study, the spatially distributed in situ measured high water marks are used as an independent evaluation. Identification of area-specific model behaviour (P2) Some studies have shown that model failure suggests inadequacies in the functioning of the model (e.g. Wagener et al., 2003). Thus, identifying model behaviour locally is expected to help lead to improved models. Radar remote sensing has the potential to offer model performance evaluation at any desired location of the image coverage. In other words, implementing and evaluating area-specific model behaviour becomes possible; however, only at locations where remote sensing based flood detection is relatively certain, i.e. at locations where there is (i) flooding present on the image and (ii) no considerable distortion of the signal response to flooding, such as e.g. near higher sloping terrain, trees or other higher vegetation, roads or buildings. By assessing models locally at each of the selected HECRAS cross sections (55 cross sections in total), local parameter configuration is analysed through the generation of cross-section CDFs of roughness based on area-specific model

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errors. As an initial step, ranges for the floodplain and channel roughness parameters, which are iteratively used in each model run in a Monte Carlo computation environment, are determined. Eq. (2) that gives the error between the water levels simulated with each model run and those derived from the radar image is of the form: LEH ¼ jHM  HR j

ð2Þ

where LEH stands for local absolute error in water level and reflects model performance, HM is the water level simulated by the model and HR is that derived from the ASAR image. Then, at each cross-section, CDF curves are generated for the roughness based on model performance (Eq. 2). These area-specific roughness distributions are compared to a CDF line of a uniform distribution for which model functioning, reflected by the magnitude of prediction errors, is the same across the sampled parameter space. Thus, in this study, the measure of parameter sensitivity is defined as the deviation from the initial sampling distribution (in this case uniform, see Krykacz-Hausmann, 2001 for details). It is worth noting here, that other ways to compare area-specific parameter sensitivity can be adopted. Then, all differences between an individual CDF curve and the uniform distribution line are summed for each cross-section to reflect the functioning of that local ‘model’, LM. Eq. 3 gives the formula that provides information on the local parameter effects (at a HEC-RAS cross-section): LM ¼

n X ðx CDFi  x dui Þ

ð3Þ

i¼1

where xdu denotes the CDF value of the discrete uniform line at model run i and xcdf represents the CDF value of the actual parameter distribution at model run i, with n being the number of runs performed. Sets of parameter values for which errors in model predictions are minimal (or close to zero) are represented by a (near-) horizontal line. Grouping functional spatial behaviour of model parameters (P3) CDFs representing similar model error characteristics based on different local parameter effects are clustered to a given class using the k-means clustering algorithm. Establishing similar functional classes (of parameters) has already been performed on hydrographs using multicomponent mapping by Pappenberger and Beven (2004). In the present study, classification of the functional behaviour of the roughness parameter is achieved by using the Euclidean squared distance measure of the k-means algorithm, which tries to minimize the total intra-cluster variance, or the function: V¼

k X X i¼1

jx j  li j2

ð4Þ

j2Si

where there are k clusters Si, i = 1,2, . . . , k and li is the mean point of all the points xj 2 Si. Fig. 4 illustrates a simplified representation of CDF curves that would be classified in four different clusters according to their deviation from uniform distribution representing maximum uncertainty. Of course, other methods to group or classify model functioning similarities can be used. The k-means algorithm is applied to all roughness CDFs derived for the 55 model cross sections analysed within

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Figure 4 Simplified representation of CDFs for the channel roughness at four cross sections, which would require different parameter values to increase prediction accuracy. The double arrows indicate the parameter range for each cluster that yields equally acceptable simulations.

the reach. A nearest neighbour algorithm is applied to find the appropriate cluster for the cross sections at which no flood was detected by the ASAR instrument.

Iterative model evaluation with spatially distributed parameters (P4) HEC-RAS is re-evaluated iteratively with spatially distributed parameters based on their functional spatial behaviour. The right value for the variable k (Eq. 4), which assigns k number of channel roughness clusters to the reach according to the local parameter effects, is determined iteratively. The number of k clusters is increased until the acceptability (or behavioural) criterion set for the reach scale and local scale (see ‘‘Model calibration and validation data’’ section), is satisfied (at nk clusters). In other words, first, during a high number of simulations run in a Monte Carlo environment, randomly chosen roughness values are attributed to one single cluster (k = 1) for the entire reach, i.e. the same roughness value at every model cross-section is used. Then, k is increased by one, and for each model simulation, the same randomly chosen roughness value within a pre-defined range is attributed to all cross sections within one cluster. Each model simulation is evaluated with the high water marks dataset, thereby applying the behavioural criteria. The procedure is stopped when nk clusters allow the generation of locally acceptable models.

Results and discussion The following subsections outline the findings of this study and discuss their implications. After initial observations are stated, the results of the cluster algorithm to find lo-

cally and reach-scale (globally) acceptable models are presented. These findings lead on to the identification of spatial patterns of parameter distributions to set different parameter arrangements. Finally, the results and consequences of applying a parameter configuration conditioned on satellite radar data are presented and discussed.

Initial observations on model calibration The ASAR-derived water levels at each HEC-RAS cross section, for which flood extraction is possible, are shown in Fig. 5. These spatially distributed data have been used in the Monte Carlo-based calibration environment to assess model behaviour in specific areas. The field-based high water marks, which are also shown in Fig. 5, have been used as an independent calibration data set. The water level data derived from the radar flood image are able to identify an acceptable range of the channel roughness parameters clearer than the field-recorded high water marks (Fig. 6). Highly spatially distributed data, assumed accurate thereby implicitly omitting any observational error range, may lead to a stronger constraining of sensitive model parameters. Moreover, it should be noted that the retained range represents effective rather than actual roughness coefficients, given that they compensate for all sorts of model errors and other processes assumed out of analysis (Lane, 2005). The radar-derived water levels are quite successful indeed in constraining the model predictions to an effective channel roughness of around 0.04 (Fig 6a). It is important to note that this range is different to effective channel roughness values for the Alzette River reach obtained in previous studies (e.g. Matgen et al., 2004; Schumann

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0.4 0.2 0 0.04 0.06 0.08 Channel roughness, n

0.6 0.4 0.2 0 0.04 0.06 0.08 Channel roughness, n

Flood depth error (m)

0.6

Flood depth error (m)

Flood depth error (m)

Flood depth error (m)

Figure 5 ASAR-derived water levels and field-recorded high water marks. The level of uncertainty associated with each fieldrecorded high water mark shown in Fig. 1 is also given.

1

0.5

0 0.05 0.1 Floodplain roughness, n 1

0.5

0 0.05 0.1 Floodplain roughness, n

Figure 6 Evaluation of HEC-RAS simulations of the 2003 event based on (a) ASAR-derived water stages and (b) field-recorded high water marks.

et al., 2005; Pappenberger et al., 2006b). This difference is caused by an updated rating curve used in this study and thus confirms the importance of rating curve uncertainties analysed and discussed by Pappenberger et al. (2006b). Fig. 6 also indicates that model predictions are insensitive to changes in floodplain roughness values (see Matgen et al., 2004; Pappenberger et al., 2006b). Therefore, to simplify, the floodplain roughness parameter is omitted in subsequent analysis and only channel roughness considered for spatial distribution. Also, other model parameters or input data such as inflow and hydraulic structures (e.g.

bridges) have been omitted from the analysis, as it is thought that (i) altering inflow will not significantly change the proposed roughness distribution and (ii) hydraulic structures, such as bridges, have only localised influence (Pappenberger et al., 2006b) but no relevant information on local parameter effects could be obtained from SAR observations for the 2003 flood. There was no backwater effect that could have created a significantly larger flood extent to be visible on the image and from which a local effect in the vicinity of the two bridges could have been deduced.

A first attempt to find acceptable predictions at both the reach scale and local scale For this study, reach-scale and local scale behavioural criteria have been defined: Reach scale behavioural criterion: As stated at the beginning, an acceptable model for the entire reach is one that outperforms a simple linear interpolation between the reach uppermost and lowermost measured high water mark. In this study, a behavioural model simulation has to generate a mean absolute error (MAE) in water level (compared to the measured high water marks) smaller than that of the interpolated model. For the 2003 event this means that a model simulation has to generate an MAE of less than 0.18 m in order to be acceptable at the reach scale. This rather rigorous threshold value suggests that it is possible to get a more or less appropriate estimate even with simple linear regression analysis (see Schumann et al., 2007). Local behavioural criterion: In order to be considered locally behavioural, a model must not exceed the specified uncertainty of the high water marks at any single location. In other words, the absolute error at each location between a given model simulation and the measured high water mark

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HEC-RAS cross-section (downstream)

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0.95

40 0.9

35 30

0.85

25 20 0.8

15 10

0.75

5 0.7

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10

15 20 25 30 35 40 HEC-RAS cross-section (downstream)

45

50

Figure 7 Correlation between cross-section CDFs for the channel roughness parameter. Higher correlations correspond to lighter grey tones.

1 0.9 0.8 0.7

CDF

0.6 0.5 0.4 0.3 0.2 0.1 0 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06 0.065 0.07 0.075 Channel n

Figure 8 Cross-section CDF curves implicitly demonstrating different channel roughness behavior for different cross sections (i.e. spatial regions).

must not be larger than the associated uncertainty of that mark (see Fig. 5). A level of uncertainty as low as 0.1 m for the automatically registered water level at the two bridges and of 0.3 m for the maximum water level recorded in the floodplain ensure that a model run performs well at every location with respect to the measurement uncertain-

ties. Defining measurement uncertainties is a rather difficult and often subjective procedure but some sort of acceptability threshold needs to be set for uncertain model evaluation, as both model and measurements are known to be inaccurate (or uncertain) to some extent. As high water marks in the floodplain were recorded by GPS on wrack lines

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and high water marks at the bridges were measured automatically during turbulent high flows, threshold values in stages of 30 and 10 cm, respectively, seem appropriate (cf. Pappenberger et al., 2006b). Given the modelling problem that performance may differ considerably from one area to another, a given model setup is appropriate for the reach under study if it generates simulations that meet both the reach and local scale behavioural criteria. A first attempt to obtain such simulations without changing the commonly used HEC-RAS model parameter configuration (i.e. one roughness value for the entire reach) was without success. Five thousand model simulations were performed in a Monte Carlo simulation environment over a channel roughness range of 0.025– 0.08 and a floodplain roughness range of 0.04–1.0. Although, 19% of all model runs met the behavioural criterion set for the reach scale, no model simulations were acceptable locally. Obtaining locally as well as reach-scale acceptable models is important, in particular for flood inundation modelling and prediction where acceptable model performance is of prime importance locally. A major issue related to scale distinction (i.e. local vs. reach-scale) is that of roughness parameter identifiability (e.g. Werner et al., 2005). Parameter sensitivity or identifiability can depend on many localised factors, such as topography, hydraulic structure (Pappenberger et al., 2006b), cross-section and bank geometry and coverage, and, or flow characteristics. The sensitivity of given parameter sets may be categorised into high or low identifiability quite easily and even statistically quantified (Saltelli et al., 2004).

Deriving patterns of spatial parameter distributions Following the approach of Pappenberger et al. (2006b), the Pearson correlation coefficient, between the generated (roughness) CDFs, is assessed to justify the need to cluster the roughness parameter(s). Fig. 7, which shows the degree of correlation between cross-sectional CDFs, clearly illustrates that varying roughness values are required. However, a sensitivity analysis based on correlation cannot capture higher order factor interaction, as it is prone to the multicollinearity problem (Frey and Patil, 2002; Helton and Davis, 2003). Although neither the exact number of different clusters required nor the parameter values in each cluster can be derived using correlation coefficients, the spatial allocation of different roughness clusters could nonetheless be approximated from a simple correlation matrix (compare Fig. 7 with Fig. 9b). The need to set a number of different parameter configurations in the studied reach also becomes obvious when looking at the different CDFs in Fig. 8. To get closest to the radar evaluation data at each cross section, the model would require different sets of channel roughness values. Any increase in model complexity has to strike the fine balance between over-parameterization and fitting the model to the data. However, keeping model complexity to a minimum (i.e. one channel roughness parameter for the entire reach) does not provide any locally acceptable models. Only by applying two different channel roughness parameter clusters (nk = 2) to the reach (Fig. 9), can satisfy-

Figure 9 The CDF curves in Fig. 8 are classified into two clusters according to the deviation from the discrete uniform distribution line (dotted 1 to 1 line), for which any channel roughness value yields equally good model simulations (a). (b) shows the two cross section clusters mapped into real space.

ing models be obtained also at the local scale. When distributing channel roughness spatially, 23% of the this time 10 000 model simulations meet the reach scale behavioural criterion and 0.1% the local one. The number of clusters needed is consistent with the number of different CDF structures observed in Fig. 8. Moreover, when the two cross-section clusters in Fig. 9a are mapped into real space (Fig. 9b), it is demonstrated that the spatial allocation of cross sections is regionally grouped, which reflects the functioning of the physically based model. A roughness value at one cross-section influences water stages at adjacent cross sections upstream and downstream. No field-based roughness

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estimates were available to verify the SAR-derived roughness allocation.

Selecting roughness values: the issue of identifiable parameters

0.05 0.04 0.03 1 2 Channel n cluster

Channel roughness (n) value

Reach-scale models 0.07 0.06 0.05 0.04 0.03 1

2 Channel n cluster

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Reach-scale models 0.07 0.06 0.05 0.04 0.03 1

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5000 10000 Distance downstream (m) Uncertainty bounds (local scale)

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5000 10000 Distance downstream (m) Uncertainty bounds (local scale)

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Water level (m a.s.l.)

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Reach-scale models

Channel roughness (n) value

c

Channel roughness (n) value

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Many hydrologists recognise that over-parameterisation makes parameter identification difficult (Kirchner, 2006). At the reach scale, the problem of identifying parameter importance or sensitivity in case of multiple (behavioural) model parameters reflecting high model complexity becomes indeed observable. In fact, the box plots in Fig. 10 illustrate that it is not possible to select a common roughness range for any of the two clusters with reasonable confidence. Although it can be seen that most values lie within a range of [0.035, 0.045] for cluster 1 and [0.05, 0.06] for cluster 2, the level of associated uncertainty is overlapping and thus there is no considerable difference between the two clusters. This means that model outcome would be too uncertain to be used in practise. Also, the low parameter identifiability in both clusters does not illustrate the real

need to cluster parameters across a reach. This is also reflected by the 19% of model simulations that perform better than a simple interpolated model with a mean absolute error of 18.4 cm, without spatially distributing channel roughness (see ‘‘A first attempt to find acceptable predictions at both the reach scale and local scale’’ section). An additional constraint needs to be put on the model if uncertainty is to be significantly reduced. This parameter tuning makes the model more flexible to fit data locally but this might be at the expense to compensate for model structural errors (Kirchner, 2006). Local acceptability criteria for models present a powerful constraint only if spatial variation in model functioning is considered. The box plots on the right in Fig. 10a show that when searching for local behavioural models, parameters become distinctive with a remarkable reduced level of uncertainty. The question that remains is: what happens to parameter identifiability at the local scale if additional parameters are added? Clustering local model behaviour inevitably sets more parameters for the model. In fact, the over-parameterisation problem is believed to grow rapidly and nonlinearly with the number of free parameters (Kirchner,

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Deriving distributed roughness values from satellite radar data for flood inundation modelling 2006). Given the fact that this increase in complexity gives a higher degree of freedom to the model, it is quite sensible to expect parameters and their interactions to become less clear and thus less identifiable. This would make the model too complex to be used most efficiently in practice. Fig. 10b and c illustrate the impact three and four channel roughness parameters have on parameter identifiability and predictive uncertainty bounds. As they all generate local behavioural models, they are performing equally well. However, it is clear that: • more local scale models are retained with an increase in the channel roughness parameter (0.1%, 0.4% and 13% for 2, 3 and 4 additional parameters, respectively), • parameter identifiability decreases dramatically if nk > 2, as there is more room for flexibility, • there is not really any need to go beyond two channel roughness parameters, as locally acceptable models are already generated. So the fine balance between model complexity and fitting the data is actually found with nk = 2, • for flood forecasting systems and flood risk application, it is desirable not only to constrain predictive uncertainty but also to increase parameter identifiability as much as possible and to come up with a robust configuration. Generally speaking, unidentifiable parameters in the case of reach-scale acceptable models become identifiable when searching for locally acceptable models. From this, it can be argued that in order to obtain acceptable model simulations at the reach scale, one single channel roughness parameter would suffice. However, for model simulations to become also locally acceptable, and this is at each of the seven locations (Fig. 11), a given cluster plays an important part in determining the model setup in such a way as to

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meet local behavioural criteria, thereby providing identifiable parameters while constraining predictive uncertainty most effectively (Fig. 11).

Event correlation: a proof of concept? When evaluating model predictions locally for a given flood event, there may be the danger of over-fitting the model such that the local calibration will not be robust in prediction to other events of different magnitude (Pappenberger et al., 2007). Moreover, the model setup (i.e. the configuration of spatially distributed parameters) derived from a radar remote sensing image for the 2003 event may not be similar to other events on the same reach acquired with a different or even the same instrument. In such a case, patterns of parameter distributions would reflect remote sensing data uncertainty, which is for obvious reasons not desirable. If, however, the spatial arrangement of the channel roughness parameter proves to be robust for other events of different magnitude, remotely sensed flood inundation characteristics can be used to pin point different roughness regions. Two datasets are available for validation: (a) a SAR instrument onboard the ERS satellite acquired an image around ten hours prior to peak in 2003 (see Fig. 2); (b) a flood event on the same reach with a much higher magnitude than that of 2003 occurred in 1995 and was recorded on aerial photography, acquired near the time of flood peak. As no instruments for discharge measurement were present in 1995, the peak discharge of 95.6 m3 s1 has been simulated using a rainfall-runoff model developed by Van den Bos et al. (2006). Both the ERS-recorded event prior to peak in 2003 and the 1995 event acquired by aerial photography are considered a very valuable source to test the robustness

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Figure 11 Significant difference in constraining uncertainty bounds (95th and 5th quantiles) and performances between reachscale and locally behavioural models (nk = 2).

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of the parameter arrangement and the possibility of model over-fitting. At a first stage, for robustness testing, the HEC-RAS model is evaluated for the 1995 event with water levels derived from aerial photography and for the prior-to-peak event in 2003 with water levels derived from the ERS SAR image. During a second stage, simulating the two validation events with the parameter configuration obtained for the ENVISATrecorded event assesses model over-fitting. The extracted flood maps for both validation events are shown in Fig. 12.

Figure 12

Assessing robustness of approach via correlation between events of different magnitude The spatially distributed local model error (LEH) analysis using Eq. 2 allows the assessment of local model error (or cross section) structures, LM (Eq. 3). Fig. 13 illustrates that the best performing simulations for both validation events are situated around a channel roughness value of 0.04. The similarity in terms of roughness between the three events is obvious. From this comparison it can be presumed that nearly identical channel roughness values for different events in terms of magnitude may indicate that (i) model

2003 and 1995 observed flood extents of the River Alzette study reach.

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as that found for the ASAR-recorded event, 65% of all crosssections are allocated to the same cluster when comparing two events and the spatial correlation between all three events is still as much as 50%. These spatial correlation values indicate in general a good agreement between events of different magnitudes, meaning that the parameter arrangement identified with the radar remote sensing image for one event ensures that model inundation predictions are also reliable both at the reach and local scale for other events. Disagreement between the different events is the result of a changing pattern of the spatially distributed clusters from one event to another. The reason for this is not really because the events are of different magnitudes but rather that the flood inundation process itself differs in some locations for each of the three events. During an event of lower magnitude, in order to flood areas that are not connected to the channel, i.e. where flooding originates from sources other than that of channel overtopping (e.g. groundwater resurgence and/or complex 2D floodplain flow interactions, see Matgen et al. (2006)), a simplified flood inundation model is forced to employ higher channel roughness values in order to get closer to the observed water level. If, during an event of a higher magnitude, these places become suddenly connected to the stream, the channel roughness characteristics will change of course. As a result, in those areas the spatial correlation of local parameter effects (LM) between events of different magnitude decreases. When ignoring such areas, spatial correlation of course increases considerably. Such a particular localised phenomenon is present but not predominant.

B. Simulating events of different magnitude to test model over-fitting

Figure 13 Similarities in channel roughness coefficients between three events of different magnitude. The black square indicates the channel roughness for minimal error.

calibration is robust (i.e. independent from event magnitude and remote sensing acquisition method), (ii) input data (i.e. discharge) is reliable, and (iii) both calibration and validation data sets can be considered to be of relatively high quality. Also in terms of local model errors, reflected by the structure of the LM curves, both validation events are nearly identical to the ASAR-recorded event. From this, it can be inferred that the same number of clusters of the channel roughness parameter (i.e. nk = 2) would be obtained. Indeed, when forcing the k-means algorithm, given by Eq. 4, to group the deviation of the cross-section CDF curves from a uniform distribution line into the same number of clusters

It is important to note that, as no quasi-distributed independent data sets (other than the aerial photography and the ERS SAR image) are available for both validation events, no objective behavioural criteria can be set for either event, making it difficult to determine the exact number of clusters that would increase model performance for each event. Hence, the same spatial distribution of clusters is forced on the two validation events and model results are evaluated with water levels recorded automatically at bridges. Fig. 14 demonstrates that for the ERS-recorded event, the simulated flood water line matches the automatically recorded water levels quite well. For the 1995 event, no recorded water levels are available. This event thus requires further, more detailed analysis. Nevertheless, as the aim is to get an initial impression of the robustness and over-fitting of the newly proposed model setup rather than finding absolute channel roughness values for each cluster, validating the clustering procedure with only limited data on the two events is thought a reasonable and valid approach.

General conclusions Freer et al. (2004) argue that a pragmatic approach to modelling should recognise that all models, regardless of their complexity, are to some extent in error. Such error information has been used in this study to derive patterns of spatial

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G. Schumann et al. 227 ERS-recorded event Aerial photography-recorded event ENVISAT-recorded event High water mark at bridge (ERS event) High water mark at bridge (ENVISAT event)

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distributions of the channel roughness for a well-documented reach of the River Alzette (G.D. of Luxembourg). The aim has been to find a model configuration with which to obtain acceptable models at the local scale. For the studied reach, two different clusters of channel roughness are required to find model predictions that perform well at each location of field-based measurements. At the reach scale, many flood simulations are already acceptable without spatially distributing the roughness parameter. However, when distributing channel roughness, parameters (need to) become identifiable in order to obtain locally acceptable models. It is shown that the ENVISAT-derived distributions are spatially well correlated with two other events on the same reach. Moreover, the suggested coefficient value or value range for each channel roughness cluster do not change considerably from one event to the next (i.e. not magnitude dependent), which is desirable, as in practical flood applications or climate change scenarios a complete re-calibration of the model is not preferred, unless we are talking in terms of model verification via dynamic parameter updating for example. Some further research is needed to find supporting evidence of the spatial allocation of clusters from radar imagery in the field. This could be done using correlation analysis of a classification of riverbank vegetation pictures at cross sections and the radar derived clusters. This study illustrates well the great potential that remote sensing holds in terms of improving flood model configuration. Hence, the findings support the long-debated hypothesis that remote sensing improves our understanding and thus modelling of complex environmental processes, such as floods.

Acknowledgements This study is supported by the ‘Ministe `re de la Culture, de l’Enseignement Supe ´rieur et de la Recherche’ of Luxembourg and has partly been funded by the National Research Fund (FNR) of Luxembourg through the VIVRE programme (FNR/VIVRE/06/36/04). Florian Pappenberger has been funded by the Flood Risk Management Research Consortium, FRMRC (http://www.floodrisk.org.uk), which is supported by Grant GR/S76304 from the Engineering and Physical Sciences Research Council, in partnership with the Natural Environment Research Council, the DEFRA/EA Joint Research Programme on Flood and Coastal Defence, UKWIR, the Scottish Executive and the Rivers Agency (N.I.). Moreover, additional financial support has been provided by the PREVIEW project, a European Commission FP6 programme. The LiDAR DEM was made available by the ‘Ministe `re de l’Inte ´rieur et de l’Ame ´nagement du Territoire’ of Luxembourg. Mark Cutler and Andrew Black from Dundee University are thanked for their comments.

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