Comparison of hydrodynamic models of different complexities to model floods with emergency storage areas

HYDROLOGICAL PROCESSES Hydrol. Process. 22, 4695– 4709 (2008) Published online 16 June 2008 in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/hyp.7079 Comparison of hydrodynamic models of different complexities to model floods with emergency storage areas Chandranath Chatterjee,1 * Saskia Förster2 and Axel Bronstert2 1 Agricultural & Food Engineering Department, Indian Institute of Technology Kharagpur, Kharagpur - 721302, West Bengal, India 2 University of Potsdam, Department of Geo-ecology, Karl-Liebknecht-Str. 24-25, 14476 Golm, Germany Abstract: A flood emergency storage area (polder) is used to reduce the flood peak in the main river and hence, protect downstream areas from being inundated. In this study, the effectiveness of a proposed flood emergency storage area at the middle Elbe River, Germany in reducing the flood peaks is investigated using hydrodynamic modelling. The flow to the polders is controlled by adjustable gates. The extreme flood event of August 2002 is used for the study. A fully hydrodynamic 1D model and a coupled 1D–2D model are applied to simulate the flooding and emptying processes in the polders and flow in the Elbe River. The results obtained from the 1D and 1D–2D models are compared with respect to the peak water level reductions in the Elbe River and flow processes in the polders during their filling and emptying. The computational time, storage space requirements and modelling effort for the two models are also compared. It is concluded that a 1D model may be used to study the water level and discharge reductions in the main river while a 1D-2D model may be used when the study of flow dynamics in the polder is of particular interest. Further, a detailed sensitivity analysis of the 1D and 1D–2D models is carried out with respect to Manning’s n values, DEMs of different resolutions, number of cross-sections used and the gate opening time as well as gate opening/closing duration. Copyright  2008 John Wiley & Sons, Ltd. KEY WORDS flood; emergency storage area; hydrodynamic models; 1D-model; 1D-2D model Received 25 September 2007; Accepted 23 April 2008 INTRODUCTION Flood storage areas form part of the flood management strategy at many lowland rivers. They are used to store excess floodwater temporarily in order to reduce peak flood flows downstream. In the last few years various studies have been conducted to predict the flood peak reduction in the main river and to simulate the inundation process in the flood storage areas. These studies represent a special case of hydrodynamic floodplain modelling because of the controlled manner of detention and release of flood water. Flow may be controlled by spillways, adjustable inlet and outlet structures or engineered dike breaches. Various researchers have used the hydrodynamic modelling approach to simulate flood inundation in the floodplains (Werner, 2004; Bates et al., 2005). The hydrodynamic modelling approach of flood inundation simulation essentially involves the solution of onedimensional and two-dimensional Saint Venant equations using numerical methods. Various numerical models have been developed for flood plain delineation/flood inundation and flow simulation. These numerical models essentially involve solving the governing equations for * Correspondence to: Chandranath Chatterjee, Agricultural & Food Engineering Department, Indian Institute of Technology Kharagpur, Kharagpur - 721302, West Bengal, India. E-mail: cchatterjee@agfe.iitkgp.ernet.in Copyright  2008 John Wiley & Sons, Ltd. flow in rivers and floodplains using certain computational algorithms. Based on the approximations used, the numerical models are categorized into (a) onedimensional (1D) models, (b) two-dimensional (2D) models, and (c) one-dimensional river flow models coupled with two-dimensional floodplain flow (1D–2D) models. Software, such as HEC-RAS (HEC River Analysis System) from the US Army Corps of Engineer’s Hydrologic Engineering Center (HEC, 2002), US National Weather Service’s (NWS) DWOPER and FLDWAV (Fread et al., 1998), MIKE11 developed at the Danish Hydraulic Institute, Denmark (DHI, 1997), SOBEK-1D developed at Delft Hydraulics, Delft (Werner, 2001), etc., has been used extensively for dynamic 1D flow simulation in rivers. The 1D models, although simple to use and providing information on bulk flow characteristics, fail to provide detailed information regarding the flow field. Hence, attempts have been made to model the 2D nature of floodplain flow. Some of the most widely used software for 2D modelling are FLO 2D (O’Brien, 2006), RMA2 (King et al., 2001), MIKE-21 (DHI, 2000), DELFT-FLS (Hesselink et al., 2003), DELFT-3D (Stelling and Duinmeijer, 2003) and TELEMAC-2D (Horritt and Bates, 2001). The 1D models fail to provide information on the flow field while the 2D models require substantial computer 4696 C. CHATTERJEE, S. FÖRSTER AND A. BRONSTERT time; hence, attempts have been made to couple 1D river flow models with 2D floodplain flow models. In the coupled 1D–2D models, the flow in the main river channel is simulated using the 1D equations, while the 2D equations are solved for the water spilling over the banks to the floodplains. The link between the two kinds of flow is usually made by a mass conservation equation. Dhondia and Stelling (2002) describe the 1D–2D model SOBEK (Rural/Urban) developed by the laboratory at Delft Hydraulics. The MIKE-21 model has been dynamically linked to the MIKE-11 model, into a single package called MIKE FLOOD developed at the Danish Hydraulic Institute (Rungo and Olesen, 2003). Hydrodynamic models of different complexity have been used to simulate flow situations with flood storage areas. 1D models for the river coupled with storage cells that represent the polders have been used to simulate the peak capping effect. The storage cells are usually characterised by the relationship between volume or area as a function of elevation or by a series of cross-sections (Kúzniar et al., 2002; Minh Thu, 2002; Faganello and Attewill, 2005). Also, there are a few studies applying combined 1D–2D model, where the flow in the river is solved in 1D whereas the flow in the storage area is simulated using a 2D approach (Baptist et al., 2006). Further, since full 2D or combined 1D–2D models are generally computationally very extensive, quasi-2D model approaches have been applied in order to give a simplified 2D representation of the storage area combined with a fast computation process (Aureli et al., 2005; Huang et al., 2007). As far as floodplain inundation is concerned, several studies have been carried out to compare the predictive performances of hydrodynamic models of different complexities (Horritt and Bates, 2002; Tayefi et al., 2007). However, there has been no such detailed comparative study for simulating floods with emergency storage areas. In this study, a comparison of 1D MIKE11 and 1D–2D MIKEFLOOD models to simulate flows for a proposed flood emergency storage area at the middle Elbe River, Germany is carried out. STUDY AREA AND DATA USED The proposed emergency storage area is located in the lowland area at the Middle Elbe River, Germany (Figure 1). It extends 7 km along the right bank of the Elbe River. The overall area is 17 km2 with a maximum storage capacity of approximately 40 ð 106 m3 . The storage area is divided into a northern and a southern polder basin by an already existing dike road running through the area. The two basins are connected by a sluice gate of 50 m width and 2 m depth. This gate is termed the connecting gate. The filling and emptying process of the storage area is controlled by two adjustable overflow weirs, each of 25 m width. The gate for the north polder is termed the north gate while Figure 1. Map of the proposed flood emergency storage area at the Middle Elbe River, Germany Copyright  2008 John Wiley & Sons, Ltd. Hydrol. Process. 22, 4695– 4709 (2008) DOI: 10.1002/hyp HYDRODYNAMIC MODELS TO MODEL FLOODS WITH EMERGENCY STORAGE AREAS the gate for the south polder is termed the south gate. The emergency storage area is designed for reducing flood peaks of not less than 100 years return period. It has to be emphasized that the emergency storage area is a potential retention site and hence, at present neither the dikes surrounding the polder basins nor any control structures exist. Topographic data, river flow data and information on control structures and polder dikes were provided by the local water authorities according to the current planning stage. In this study, the flood event for the period 5 August to 17 September 2002, i.e. a duration of 44 days, is considered to study the effectiveness of the proposed polder. For this flood event, the peak discharge is 4420 m3 s
1 , which occurred on 18 August 2002 at the Torgau gauge. Four other flood events are used for model calibration and validation as described later. Currently about 90% of the area is under intensive agricultural use. The rest is taken up by watercourses and forests, most of which are under nature protection. It is expected that the land will retain its original purpose after designation as an emergency storage area. METHODOLOGY The 1D model MIKE 11 and the coupled 1D–2D model MIKEFLOOD are applied to simulate the flooding and emptying processes in the polders and flow in the Elbe River. The governing flow equations of MIKE 11 are 1D and are of shallow water types, which are modifications of the Saint Venant equations (DHI, 1997, 2000). MIKEFLOOD integrates topographic data of the 1D MIKE 11 river network with the 2D MIKE 21 floodplain (bathymetry data) through four different linkages: (i) standard link where one or more MIKE21 cells are linked to the end of a MIKE11 branch; (ii) lateral link where a string of MIKE21 cells are laterally linked to a specified reach of MIKE11; (iii) structure link consisting of a three-point (upstream cross-section, structure and downstream cross-section) MIKE11 branch whose ends are linked to MIKE21 cells; and (iv) zero flow link specified to a MIKE21 cell will have zero flow passing across the cell (DHI, 2004). For this study, the standard link is the only relevant link that can be used and hence, it is selected. One-dimensional model setup The 1D model MIKE 11 is set up to represent an18Ð6 km reach of the Elbe River (Figure 2), which is described by a series of 34 cross-sections. These crosssection data are provided by the local water authority. The cross-section data available downstream of Elbe 187 km are not only very sparse but are available for the main channel only. Hence, these cross-sections were extended to the dikes using elevation data from airborne laser altimetry. The boundary condition at the upstream end of the reach at 175Ð0 Elbe-km is a discharge hydrograph of Copyright  2008 John Wiley & Sons, Ltd. 4697 the Torgau gauging station. Although this gauge is located approximately 20 km upstream of the upper model boundary, utilisation of these discharge data is justified as there are only minor tributaries to the Elbe River between Torgau and the modelled river stretch. The downstream boundary condition at 193Ð6 Elbe-km is provided as a rating curve. The emergency storage area is schematized in the model by two storage cells each representing one polder basin. The storage cells are described by their area–elevation curves (Figure 2). The curves are derived from a high-resolution digital elevation model (DEM) that was obtained from airborne LiDAR survey. The gates are implemented as control structures that operate under certain pre-set conditions as mentioned later. Calibration and validation of model. Calibration of the hydrodynamic models for emergency flood storage areas is difficult as emergency storage areas are usually designed to be used for flood peak capping during rare flood events. The storage area may have never been in operation before and hence, observation data for calibration purpose may not be available. This is true for the present study, which investigates a proposed flood storage area that is not yet constructed. However, the MIKE11 model is calibrated and validated for the flow in the Elbe River and its floodplain within the embankments. The MIKE11 model is calibrated and validated against water levels recorded at the Mauken gauging station at 184Ð4 Elbe-km. Because of the different nature of bed materials two hydraulic roughness classes are distinguished, one for the main channel and one for the adjacent floodplain. In order to identify the two roughness coefficients, a two-stage calibration and validation procedure is adopted. In the first stage, the roughness coefficient for the main channel is identified and in the second stage the roughness coefficient for the floodplain is identified. Four flood events during the period 1 October to 30 November 1999, 1 January to 31 March 2002, 1 August to 27 September 2004 and 1 March to 30 June, 2005 are selected for the process of calibration and validation. Of these, water does not spill over to the floodplains for the first and third events and hence, these are used for calibration and validation for the main channel. Initially, the roughness information in the form of Manning’s n values is taken from the literature (Chow, 1959) and similar studies (Horritt and Bates, 2002) which are then modified during the calibration process. Two goodness of fit criteria are used to compare the simulated water levels with the observed values. These are (i) the Nash–Sutcliffe coefficient (Ens ) and (ii) the index of agreement (d), which are as follows:
⊲Qo
Qs ⊳2 ⊲1⊳ Ens D 1

⊲Qo
Qav ⊳2
⊲Qo
Qs ⊳2 dD1

⊲2⊳ ⊲jQo
Qav j C jQs
Qav j⊳2 Hydrol. Process. 22, 4695– 4709 (2008) DOI: 10.1002/hyp 4698 C. CHATTERJEE, S. FÖRSTER AND A. BRONSTERT Figure 2. MIKE 11 model layout for the proposed flood emergency storage area where, Ens D modelling efficiency, Qo D observed discharge (m3 s
1 ), Qs D simulated discharge (m3 s
1 ), Qav D mean of the observed discharge (m3 s
1 ) and d D index of agreement. One-/ two-dimensional model setup In the MIKEFLOOD model layout, the Elbe River and the three gates (inlet or south gate, connecting gate and outlet gate) are represented in the 1D model MIKE11. The polders are represented in the form of a DEM in the 2D model MIKE21. Both the 1D MIKE11 and 2D MIKE21 models are dynamically coupled by standard links. This coupled model is run with the same boundary conditions, flood scenario (i.e. for the August Copyright  2008 John Wiley & Sons, Ltd. 2002 flood event) and gate operation as the 1D model. Thus, the essential difference between the 1D MIKE11 setup and MIKEFLOOD setup is in the representation of the polders. In this study, three different DEMs are used which are obtained by resampling the LIDAR DEM to grid sizes of 8 m, 25 m and 50 m. Initially, the LIDAR DEM is processed to remove non-permanent objects, such as dung hills or vehicles, and to correctly represent line structures, such as dikes and ditches. While generating a DEM by interpolation of point data obtained by laser scanning, there is a risk that line structures are not continuous in the DEM. Thus, the following procedure is used to correct the representation of line structures: Hydrol. Process. 22, 4695– 4709 (2008) DOI: 10.1002/hyp HYDRODYNAMIC MODELS TO MODEL FLOODS WITH EMERGENCY STORAGE AREAS (i) line structures are digitised as line objects using topographic maps; (ii) height information is attached to the digitised line objects; (iii) a large number of points are generated along the line objects; and (iv) the DEM is generated by interpolating point data that were collected by the laser scanner and generated from the line objects using GIS. As the laser scanner only collects water surface elevation, bottom height of ditches was obtained by terrestrial measurements and included in the DEM generation procedure. While aggregating LIDAR data to other grid sizes, the DEM gets ‘smoother’, i.e. dikes have lower elevation and ditches become shallower. In order to preserve the flooding characteristics, post-processing is done in the aggregated DEM by converting the line objects (with correct height information) to grid objects of the same grid size as the aggregated DEM. Subsequently, the corresponding grid cells in the aggregated DEM are replaced by grid cells of the line object. While aggregating the DEM to grid sizes of 8 m, 25 m and 50 m, it is ensured that water does not spill over the dikes (Elbe dike and polder dikes) by setting the dike cells to their true elevations. However, the correct depths of the ditches inside the polders are not included in the aggregated DEMs as these ditches are very narrow (about 3 to 5 m wide) and hence, would be overrepresented when converting them into grid sizes of 8 m, 25 m and 50 m. Sensitivity analysis A detailed sensitivity analysis is carried out for the different hydrodynamic models with respect to a number of input parameters such as (i) Manning’s n values, (ii) DEM’s of different resolutions, (iii) number of cross-sections used and (iv) gate opening time and opening/closing duration. The conditions under which the sensitivity analyses are carried out for each of these input parameters is presented below. Manning’s n. First, the sensitivity analysis of the MIKE11 model setup for only the Elbe River (i.e. without the polders) is carried out with respect to Manning’s n values. For this purpose, two cases of Manning’s n values are considered. In the first case, the n values are decreased by 5% from the mean/calibrated values while in the second case, the n values are increased by 5% (Table I). Subsequently, the sensitivity analysis of the MIKE11 model setup to the Manning’s n values is carried out by including the polders. Again, the same two cases of n values stated above are considered (Table I). Table I. Range of Manning’s n values for different land-use classes considered in sensitivity analysis Class River channel River floodplain Polder Ł Calibrated values are indicated in brackets. Copyright  2008 John Wiley & Sons, Ltd. Manning’s nŁ 0Ð0361–0Ð0399 (0Ð038) 0Ð0475–0Ð0525 (0Ð050) 0Ð0475–0Ð0525 (0Ð050) 4699 The sensitivity analysis of the MIKEFLOOD setup to the Manning’s n values is also carried out. In this case the n values for the river as well as the river floodplain are kept at their calibrated values while the n values for the polders are varied, i.e. increased and decreased by 5% (Table I). DEMs of different resolutions. The sensitivity of the 1D MIKE11 model to the use of different DEM resolutions is studied. Two DEMs of horizontal resolution 8 m and 50 m are used to derive the area-elevation curves. The MIKE11 model is simulated for the August 2002 flood event with the area-elevation curves derived from the two different DEMs. The sensitivity of the MIKEFLOOD model to the use of different DEM resolutions is also studied. The sensitivity analysis is carried out considering three DEMs of different horizontal resolutions for the polders, namely, 8 m, 25 m and 50 m. The sensitivity of the use of these different DEMs to the water level and discharge reduction in the Elbe River as well as the flow dynamics in the polders is studied. The flood inundation extent and depth in the polders at a particular instant of time for the different DEM’s is also studied. Number of cross-sections used. The sensitivity of the 1D MIKE11 model to different numbers of cross-sections used is also studied. In this case also, only the Elbe River is modeled and the polders are not considered. As stated earlier, a total of 34 cross-sections are used to define the Elbe River in the MIKE11 model (Figure 2). These cross-sections are in general 400 m to 800 m apart but the cross-section spacing is more in the downstream side with a maximum spacing of 2Ð4 km between Elbe River 189Ð6 km and 192 km. In order to study the sensitivity of the results to the number of cross-sections used, two different cases are considered in which different numbers of cross-sections are used: (i) Case-I: Only 20 out of 34 cross-sections are used, i.e. 14 cross-sections (nos. 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27 and 29 (Figure 2)) are removed. Here, the 14 cross-sections which are removed are in the stretch of the Elbe River 175 km to 187Ð6 km. In this stretch of the river, the cross-section spacing varies from 400 to 800 m, i.e. they are closely spaced. Thus, the results obtained from the removal of these cross-sections would indicate the closeness at which the cross-sections are to be provided. (ii) Case-II: Again another set of 20 cross-sections are used, i.e. a different set of 14 cross-sections are removed (nos. 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26 and 28 (Figure 2)) in the same stretch of the Elbe River 175 km to 187Ð6 km. Gate opening time and opening/closing duration. The sensitivity of the 1D MIKE11 model to the time of opening of the south gate during the polder filling process Hydrol. Process. 22, 4695– 4709 (2008) DOI: 10.1002/hyp 4700 C. CHATTERJEE, S. FÖRSTER AND A. BRONSTERT is studied. For this the following two gate opening times are considered for the south gate: (i) Case-I. 6 h ahead of the actual opening time. (ii) Case-II. 6 h after the actual opening time. The sensitivity of the 1D MIKE11 model to different gate opening and closing duration during the polder filling process is also studied. In this study all the gates (i.e. the south and north as well as the connecting gates) open or close over a time of 30 min (based on information from local water authority). In order to study the sensitivity of the gate opening and closing duration to the water level and discharge reduction in the Elbe River, two different gate opening and closing durations are considered: gauging site during calibration and validation for the floodplains. Table III. Performance indices for MIKE11 simulated water levels at the Mauken gauging site during calibration and validation (for the floodplains) Events ! Manning’s n For river 0.038 Calibration Jan-Mar, 2002 For floodplain 0.035 0.040 0.045 0.050 Validation Mar-Jun, 2005 Ens d Ens d 0.976 0.980 0.981 0.979 0.724 0.728 0.732 0.736 — — 0.979 0.982 — — 0.584 0.594 (i) Case-I: All the gates take 5 min to open or close. (ii) Case-II: All the gates take 60 min to open or close. (a) RESULTS AND DISCUSSIONS Calibration and validation of the one-dimensional model Table II shows the performance indices for different trial values of Manning’s n for MIKE11 simulated water levels at the Mauken gauging site during calibration and validation for the main channel only. The Ens and d values are found to be highest for n equal to 0Ð038 during calibration. Using this n the Ens and d values are also found to be very high during validation. Hence, a Manning’s n value of 0Ð038 is chosen for the main channel. Different trial values of Manning’s n for the floodplain are chosen keeping the main channel n value equal to 0Ð038. Table III shows the performance indices for the MIKE11 simulated water levels at the Mauken gauging site during calibration and validation for the floodplain. For the January–March, 2002 event, the Ens value is found to be the highest for floodplain n value equal to 0Ð045 while the d value is found to be highest for a floodplain n value equal to 0Ð050. But during validation with the March–June, 2005 event, both the Ens and d values are found to be highest for floodplain n value equal to 0Ð050. Hence, a Manning’s n value of 0Ð050 is chosen for the floodplains. Figure 3 shows a comparison of the observed and simulated water levels at the Mauken (b) Table II. Performance indices for MIKE11 simulated water levels at the Mauken gauging site during calibration and validation (for the main channel only) Events ! Manning’s n (for river) 0.037 0.038 0.039 Calibration Oct-Nov, 1999 Validation Aug-Sep, 2004 Ens d Ens d 0Ð662 0Ð925 0Ð844 0Ð931 0Ð984 0Ð967 — 0Ð920 — — 0Ð983 — Copyright  2008 John Wiley & Sons, Ltd. Figure 3. Comparison of observed and simulated water levels at the Mauken gauging site during (a) calibration for the flood event of 1 January to 31 March 2002; (b) validation for the flood event of 1 March to 30 June, 2005 Hydrol. Process. 22, 4695– 4709 (2008) DOI: 10.1002/hyp HYDRODYNAMIC MODELS TO MODEL FLOODS WITH EMERGENCY STORAGE AREAS (a) (b) (c) Figure 4. MIKE11 simulation results for the proposed emergency storage area for the August 2002 flood event (positive discharge in flow direction from South to North): (a) simulated discharge and water levels; (b) gate levels; (c) gate discharge One-dimensional model results for flooding and emptying processes in the polder Figure 4a to c shows the results obtained from MIKE11 simulation for the flooding and emptying processes in the polders and flow in the Elbe River for the August 2002 flood event. The peak discharge for this flood event is 4420 m3 s
1 . Here, the area–elevation Copyright  2008 John Wiley & Sons, Ltd. 4701 curves for the storage areas are derived from a 50 m grid DEM. It is observed from these figures that the south gate opens when the water level in the Elbe River reaches a threshold value of 76Ð94 m corresponding to a discharge of 4100 m3 s
1 (Figure 4a and b). At this instant of time a discharge of about 440 m3 s
1 enters through the south gate (Figure 4c) and this results in a sharp reduction in the Elbe discharge and water level (Figure 4a). Subsequently, the connecting gate and the south gates close when the water level reaches the design value in the north and south polders, respectively. The entire filling process takes about 30 h. After the gates close, the discharge and water level in the Elbe River rise again. The water level reduction at the Elbe River 184Ð4 km (i.e. at the Mauken gauge) is 25 cm while the corresponding discharge reduction at this point is 310 m3 s
1 (Figure 4a). In order to achieve the maximum water level reduction in the Elbe River for given polder volumes, the discharge in the Elbe River should be as close as possible to a straight line after the filling process starts in the polder. The factors affecting the magnitude of water level reduction in the Elbe River for given polder volumes are (i) time of opening of the gates during the polder filling process, (ii) gate opening/closing duration (iii) gate width or partitioning of the gates and (iv) shape of the flood hydrograph. A detailed investigation of the effect of (i) sequential operation of the north and south gates during the filling process (ii) partitioning of the gates and (iii) shape of the flood hydrograph, on the magnitude of water level reduction in the Elbe River is reported in Förster et al. (2008). In this study, only the south and the connecting gates (and not the north gate) operate during the polder filling process. The gate opening/closing durations are 30 min and the gate widths are 25 m (based on information collected from local water authority). Further, as stated earlier, the August 2002 flood hydrograph is considered here. Thus, in this study, the time of opening of the south gate during the start of the filling process of the polders is the only crucial factor for obtaining the maximum possible water level reduction in the Elbe River. The time of opening of the south gate during the filling process of the polder is decided manually based on a trial and error process so as to maximize the water level reduction in the Elbe River. Several trial runs are carried out with different opening times for the south gate (specified in MIKE11 for each trial run) while the connecting and south gates close when the design water level is reached in the north and south polders, respectively. For each run the water level reduction in the Elbe River is noted. It is observed that when the south gate is opened corresponding to a water level of 76Ð94 m at Elbe River chainage 184Ð4 km (i.e. on 17 August 2002 at 15Ð40 hrs for the August 2002 flood event), a maximum water level reduction of 25 cm occurs in the Elbe River. The gate operation during the polder emptying process is also decided manually. The objective is to empty the polders as soon as possible. Thus, it is decided to release the water from the polders into the Elbe River Hydrol. Process. 22, 4695– 4709 (2008) DOI: 10.1002/hyp 4702 C. CHATTERJEE, S. FÖRSTER AND A. BRONSTERT as soon as the water level in the river falls below the water level in the polders. Accordingly, it is decided that the emptying process starts when the water level in the Elbe River near the south gate falls to 75Ð64 m (Figure 4a), i.e. 2 days after the filling process ends, which allows for safe release of the flood water. The south gate is opened first followed by the north gate 8 h later. The connecting gate is opened 7 h after the north gate is opened (Figure 4b). Immediately after the connecting gate is opened, the south gate is closed as the flow direction reverses and water starts entering the polders again. As per the MIKE11 simulation, the entire emptying process takes about 24 days. The long duration of the emptying process is because after a certain time the water level of the polders become the same as the water level in the Elbe and hence, the water levels in the polder fall along with the river water level. It is to be mentioned here that all gate operations are automatically executed in the MIKE11 model simulations based on the selected decision criteria. As mentioned earlier the storage area under investigation is yet to be constructed and hence, only calibration data for the river is available. Due to lack of calibration/validation data sets for the storage area the simulation results obtained herein are compared with a similar study. In IWK (2003) the peak attenuation effect for several proposed flood storage areas along the Middle Elbe River was simulated considering floods with peak discharges ranging between 4000 m3 s
1 and 5000 m3 s
1 . For the same storage area as investigated in the present study a peak reduction between 262 m3 s
1 (14 cm) and 497 m3 s
1 (23 cm) at the Wittenberg gauge was simulated. These results are very similar to the range of water level reduction obtained in the present study. Comparison of 1D and 1D–2D model results The DEM grid size used for MIKEFLOOD is 50 m and the area–elevation curves for MIKE11 are also extracted from 50 m grid DEM. A comparison of the results obtained from MIKE11 and MIKEFLOOD simulation runs shows that there is absolutely no difference in the water level and discharge reduction in the Elbe River. This is because the discharge through the south gate is the same for both models. The identical discharge is because it is a case of free flow discharge controlled by the upstream water level, and the upstream water level for the south gate for both models is the same even though the downstream water level differs. The differences between MIKE11 and MIKEFLOOD results are that for MIKE11 the water front reaches the connecting gate at the instant at which the south gate is opened while for MIKEFLOOD the water front takes about an hour to reach the connecting gate. Further, due to the different treatment of polder filling in the models, the water levels upstream and downstream of the connecting gate differ for the two models. As a result there is a slight difference in the discharge through the connecting gate for the two models. Copyright  2008 John Wiley & Sons, Ltd. In the polders emptying process there is a significant difference between MIKE11 and MIKEFLOOD results. For the MIKEFLOOD model, the emptying process continues until the water level in the polders lowers to about 73Ð25 m. The emptying process takes about 4 days with most of the emptying taking place in the first day and a half. The emptying process stops after the water level reaches 73Ð25 m because the ground elevations near the north gate are higher than its sill elevation (70Ð8 m) and this does not permit further draining of the water to take place. However, for the MIKE11 model, the emptying process continues until the water level in the polders lowers to the sill elevation of the north gate (70Ð8 m) along with the river water level. The emptying process takes about 24 days. This emptying result of MIKE11 is in fact incorrect since practically the draining process cannot continue below the water level 73Ð5 m because of the ground elevation conditions near the north gate, as mentioned above. Such an error is expected to occur in MIKE11 because the area–elevation curves that describe the polders do not take care of the spatial variations of ground elevations. However, a ‘work around’ is possible in MIKE11 by raising the sill level of the north gate to 73Ð5 m when the water level in the north polder lowers to 73Ð5 m during the emptying process. However, this would require the use of the MIKEFLOOD model to ascertain the required water level (73Ð5 m in this study) prior to using MIKE11. Such an approach was not adopted as this paper aims at an independent comparison of the 1D and 1D–2D models to model floods with emergency storage areas. MIKEFLOOD results for the polders show that large tracts of agricultural land, particularly in the northern side of the north polder (with depths of water as high as 1Ð5 to 2 m in some places) remain inundated after the emptying process through the north and south gates. Because of the topography, this water cannot drain using the gravity process through the gates. Hence, some of the water may be drained using a small gate in a stream on the northern boundary (not considered here in the modelling process) and the rest of it has to be pumped out or gradually evaporate or seep away. Additional information obtained from MIKEFLOOD is the water velocities in the polders. It is observed that at some places in the polder near the south gate, the velocity is higher than the mean velocity of 1Ð5 m s
1 (for 50 m grid size DEM). This type of information will be of particular help in studying erosion and sedimentation problems in the polder as well as in the subsequent risk analysis. Computation time, storage space requirements and modelling effort A comparison of the computation time requirements for the two models was carried out. For this the models were run in a personal computer having an AMD Athlon(tm) 64 3500C processor with 2Ð2 GHz speed and 2GB RAM. The models were run for the filling and emptying processes in the polders as well as flow Hydrol. Process. 22, 4695– 4709 (2008) DOI: 10.1002/hyp HYDRODYNAMIC MODELS TO MODEL FLOODS WITH EMERGENCY STORAGE AREAS in the Elbe River for the same August 2002 flood event. The MIKEFLOOD (with 8 m grid DEM for the polders) model was run for shorter durations because of the very high computation time and storage space requirements. The simulation time step intervals and result storing frequencies for the different runs are shown in Table IV. The computation time as well as storage space requirements for the model runs is shown in Table V. It is observed that the computation time and storage space requirements for the MIKE11 model are very low while they are very high for the MIKEFLOOD model. As expected, for MIKEFLOOD the computation time and storage space requirements increase drastically when finer resolution DEMs are used. Table IV. Model run details for the August 2002 flood event Model MIKE11 MIKEFLOOD Simulation time step interval (s) Result storing frequency (min) 5 s MIKE11–2 s MIKE21–2 s 5 2 15 Table V. Computation time and storage space requirement for different model runs Model MIKE11 MIKEFLOOD DEM grid size Computation time (h : min) Storage space 50 m DEM 25 m DEM 8 m DEMŁ 2 min 3 h 43 min 14 h 23 min 12 h 40 min 22 MB 1Ð1 GB 3Ð1 GB 1Ð3 GB Ł The MIKEFLOOD model with 8 m grid DEM is simulated only for the polder filling process, i.e. from 5 August to 21 August 2002. 4703 As far as the modelling effort is concerned, considerable effort is required in setting up the MIKEFLOOD model. For MIKEFLOOD, quite a few adjustments had to be made in the DEM near its links with the MIKE11 structures to bring about model stability. The DEM is cut and levelled near the structures and provided with an initial water level. In comparison, considerably less effort is required in setting up the MIKE11model. Sensitivity analysis Manning’s n. Figure 5 shows the maximum water levels along the longitudinal section of Elbe River as obtained from MIKE11 (when only the Elbe River is modelled and the polders are not considered) for different ‘n’ values for the August 2002 flood event. It is seen that as the n values are decreased the water level decreases and vice versa. When the n values are decreased by 5%, maximum water level difference occurs at the upstream end, at 16 cm, while the water level differences at the points of interest, i.e. at the south gate is 15 cm and at the Mauken gauging site is 13 cm. Similarly, when the n values are increased by 5%, the maximum water level difference still occurs at the upstream end, and is 15 cm, while the water level differences at the points of interest, i.e. at the south gate is 14 cm and at the Mauken gauging site is 12 cm. Considering the fact, that the maximum water level reduction at the Mauken gauging site is 25 cm (as stated earlier), these water level differences of 12–15 cm due to a change of n values seem to be significant. Figure 6a and b shows the results of sensitivity analysis of the MIKE11 model to the Manning’s n values when the polders are included. It is observed that when the n values are decreased by 5%, the water level reduction is only 12Ð3 cm and discharge reduction is 137 m3 s
1 80 n (river) = 0.0361; n (floodplain) = 0.0475 n (river) = 0.038; n (floodplain) = 0.05 79 n (river) = 0.0399; n (floodplain) = 0.0525 Water level, m 78 77 South Gate at 182.6 km Mauken Gauge at 184.4 km 76 75 74 174 177 180 183 186 189 192 195 River chainage, km Figure 5. Maximum water levels along longitudinal section of Elbe River as obtained from M11 (polders are not considered) for different ‘n’ values for the August 2002 flood event Copyright  2008 John Wiley & Sons, Ltd. Hydrol. Process. 22, 4695– 4709 (2008) DOI: 10.1002/hyp 4704 C. CHATTERJEE, S. FÖRSTER AND A. BRONSTERT (a) (b) Figure 6. Sensitivity of MIKE11 model to Manning’s n values when polders are considered (a) n D 0Ð0361 for river and 0Ð0475 for floodplain; (b) n D 0Ð0399 for river and 0Ð0525 for floodplain (Figure 6a). The water level reduction is only 17Ð0 cm and discharge reduction is 218 m3 s
1 when the n values are increased by 5% (Figure 6b). This happens because though the south gate is still opened at the same water level value of 76Ð94 m, the river discharge corresponding to this water level is different for the two cases due to different n values. As stated earlier, the water level reduction is 25 cm and discharge reduction is 310 m3 s
1 when the calibrated values of n are used. Thus, the model is quite sensitive to changes in n values. In this study, as mentioned earlier, the Manning’s n values obtained during the calibration and validation process are 0Ð038 and 0Ð05 for the main channel and adjacent floodplain, respectively. The corresponding normal values Copyright  2008 John Wiley & Sons, Ltd. of Manning’s n for the prevailing land-use mentioned in the literature (Chow, 1959) are 0Ð035 (for natural streams—major rivers) and 0Ð05 (for floodplains—light brush). As the calibrated values are very close to those mentioned in the literature and the land-use in the study area is quite uniform, a lower range (š5%) of Manning’s n is used in the sensitivity analysis. The uncertainty associated with the roughness values in modelling floods has been the subject of continuous research (Werner et al., 2005). Horritt (2005) states the difficulty in specifying the hydraulic roughness values in spite of having a reasonable idea of the land-use. The author further suggests the use of a calibration approach to remove this difficulty. Hence, it is proposed that a more detailed calibration Hydrol. Process. 22, 4695– 4709 (2008) DOI: 10.1002/hyp HYDRODYNAMIC MODELS TO MODEL FLOODS WITH EMERGENCY STORAGE AREAS and validation procedure be adopted considering a large number of flood events in order to reduce the uncertainties associated with Manning’s n values. However, it is also expected that the sensitivity to n values would decrease when more than one polder is used and the consequent peak water level reduction in the Elbe River is much higher. The results of sensitivity analysis of the MIKEFLOOD model show that it is insensitive to the variation of n values in the polders. This is quite expected because (i) the inflow to the polder remains the same as it is not influenced by the polder water level and (ii) n is proportional to the velocity which in the bulk characteristic is low. This finding justifies using only one roughness value for the polders rather than differentiating into several roughness classes. Similar results are also reported by Werner et al. (2005). DEM’s of different resolutions. The results of sensitivity analysis of the MIKE11 model to area–elevation curves derived from different grid size DEMs show that the water level and discharge reduction in the Elbe River remains unchanged. However, when the south gate is closed after the filling process, the discharge in the Elbe River for the 8 m DEM case increases to a lesser extent than that of the 50 m DEM case. For both DEM cases the polders are filled to their design levels, i.e. 76Ð14 m for the south polder and 75Ð35 m for the north polder. Although the discharge through the south and connecting gates are the same for both cases, the gates close a little earlier for the 50 m DEM case than the 8 m DEM case. This minor difference in the result is due to the slightly different volume–elevation curves derived from the two DEMs. Because of averaging, the 50 m DEM has slightly lesser volume for the design water level compared to the 8 m DEM. For the 50 m DEM, the volume of water corresponding to the design water levels are 20Ð24 Mm3 in the north polder and 20Ð32 Mm3 in the south polder (i.e. a total volume of 40Ð56 Mm3 ). Whereas for the 8 m DEM, the volume of water corresponding to the design water levels are 20Ð44 Mm3 in the north polder and 20Ð54 Mm3 in the south polder (i.e. a total volume of 40Ð98 Mm3 ). Thus, the total difference in volume of the polders for the two cases is 0Ð42 Mm3 . But this does not produce significantly different results. Hence, a 50 m DEM can be used to derive the area–elevation curves for the 1D MIKE11 model and yet give accurate results. The results of sensitivity analysis of the MIKEFLOOD model to the use of different DEM resolutions for the polders also show that the water level and discharge reduction in the Elbe River remain the same. However, when the south gate is closed after the filling process, the discharge in the Elbe River for the 8 m DEM case increases to a lesser extent than that of the 25 m DEM case, which in turn increases to a lesser extent than that of the 50 m DEM case. This is because, for the design water level, the volume of the 8 m grid DEM is slightly higher than that of the 25 m grid DEM, which in turn is higher than that of the 50 m grid DEM. As a result, Copyright  2008 John Wiley & Sons, Ltd. 4705 for the 50 m DEM case the south gate closes ahead of the 25 m DEM case, which in turn closes ahead of the 8 m DEM case. The south gate discharge is the same in all cases because of the same upstream water level. So, even though the downstream water levels differ, the discharge remains the same as it is a case of free flow discharge governed by upstream water level. The water front takes about an hour to reach the connecting gate for all cases. However, the discharge through the connecting gate is slightly different for the three grid size DEMs because of varying upstream and downstream water levels for the three cases. The upstream water level for the 8 m case remains lower than for the other two since the 8 m DEM has the same volume of water at a lower elevation compared with that of the 25 m and 50 m DEM. Figure 7a to c shows the flood inundation extent and depth in the south polder for the three DEM cases (8 m, 25 m and 50 m) on 17 August 2002 at 16Ð30 hours, i.e. 40 min after the filling process starts through the south gate. At this instant of time, the volume of water that enters the south polder is the same for all three cases as the discharge through the south gate is the same for all cases. For the 50 m DEM, the inundation extent is 1Ð35 km2 and the maximum water depth is 3Ð01 m (Figure 7c). For the 25 m DEM, the inundation extent is 1Ð23 km2 and the maximum water depth is 3Ð36 m (Figure 7b). For the 8 m DEM, the inundation extent is 1Ð23 km2 and the maximum water depth is 3Ð64 m (Figure 7a). For the 50 m DEM, the surface elevations are higher than the 25 m and 8 m DEM. Hence, the maximum water depth is lowest for the 50 m DEM and the resulting inundation extent is the greatest. Further, although the total inundation extents for the 8 m and 25 m DEMs are the same, their spatial variation is different, particularly at the fringes (Figure 7a and b). Unlike floodplain inundation studies, for polder studies, the analysis of the inundation extent and depth for different DEMs is not of much significance since after the initial phase where the water front progresses, the polders begin to fill up and DEM resolution does not play a major role. Number of cross-sections used. Figure 8 shows the maximum water levels along the longitudinal section of the river as obtained from MIKE11 for the case when all 34 cross-sections are used and for the two different cases of cross-sections used for the August 2002 flood event. It is observed that for case I, the water levels are sometimes a little higher and sometimes a little lower than the case when all 34 cross-sections are used. The water levels for case-II are, in general, a little lower than the case when all 34 cross-sections are used. However, for the lower reaches of the river, the water levels for both cases I and II almost coincide with the water level for the case when all 34 cross-sections are used. The water level differences at the points of interest, i.e. south gate and Mauken gauging site for the different cases are shown in Table VI. It is seen that the water Hydrol. Process. 22, 4695– 4709 (2008) DOI: 10.1002/hyp 4706 C. CHATTERJEE, S. FÖRSTER AND A. BRONSTERT (b) (a) Inundation area = 1.23 km2 Maximum water depth = 3.64 m Inundation area = 1.23 km2 Maximum water depth = 3.36 m (c) Inundation area = 1.35 km2 Maximum water depth = 3.01 m Figure 7. Flood inundation extent and depth on 17 August 2002 at 16Ð30 hours in south polder as obtained from MIKEFLOOD for DEM with grid sizes (a) 8 m (b) 25 m and (c) 50 m level differences are not that significant considering that 14 cross-sections are removed. These results indicate that for the two cases when 14 cross-sections are removed, the shape of the river including its depth and width are very well represented by the remaining 20 cross-sections. Thus, in general it can be seen that the number of cross-sections used in this study to model the Elbe water level is reasonably sufficient. Copyright  2008 John Wiley & Sons, Ltd. Gate opening time and opening/closing duration. As mentioned earlier, during the polder filling process, the south gate is opened at 15Ð40 hours on 17 August 2002 in order to obtain a maximum water level reduction of 25 cm in the Elbe River. When the south gate opens 6 h ahead of this opening time at 9Ð40 hours on 17 August 2002 (corresponding to the Elbe water level of 76Ð71 m at the Mauken gauge instead of 76Ð94 m), the water level reduction decreases to 14Ð8 cm (from Hydrol. Process. 22, 4695– 4709 (2008) DOI: 10.1002/hyp HYDRODYNAMIC MODELS TO MODEL FLOODS WITH EMERGENCY STORAGE AREAS 25Ð0 cm), which corresponds to a discharge reduction of 182 m3 s
1 . Similarly, when the south gate opens 6 h after the actual opening time at 21Ð40 hours on 17 August 2002 (corresponding to the Elbe water level of 77Ð10 m at the Mauken gauge instead of 76Ð94 m), the water level reduction decreases to 8Ð6 cm (25Ð0 cm), which corresponds to a discharge reduction of 93 m3 s
1 . This shows the importance of a very good forecast for effective reduction of water levels in the main river. The results of sensitivity analysis of the MIKE11 model to different gate opening/closing durations during the polder filling process show that for case I, there is a sudden fall in the Elbe River discharge (compared with the 30 min duration case) when the south gate opens. This is because the south gate opens faster and hence, the initial discharge through the south gate is higher. Also, the south gate closes earlier (than for the 30 min duration case). This is because both the south and connecting gates are closed when the respective design water levels are reached in the polders. As the gates close very fast for case I, the water level (and hence, the volume) in both polders after the gates are fully closed are lower compared with the 30 min case. The final volume of water in the north and south polders for case I are 20Ð10 Mm3 and 20Ð08 Mm3 , respectively; while the final volumes of water in the north and south polders for the 30 min case are 20Ð32 Mm3 and 20Ð24 Mm3 , respectively. Thus, as the storage volume in the polders Table VI. Water level differences (in m) in the Elbe River due to use of different sets of cross-section data Case No. of cross-sections removed I II 14 14 Water level difference (m) at river chainage 182Ð6 km 184Ð4 km
0Ð05
0Ð09
0Ð02
0Ð08 80 All 34 c/s (Actual) 14 c/s removed (Case I) 14 c/s removed (Case II) Water level, m 79 78 South Gate at 182.6 km 77 Mauken Gauge at 184.4 km 76 75 74 174 177 180 183 186 189 River chainage, km 192 195 Figure 8. Maximum water levels along longitudinal section of Elbe River as obtained from M11 for different sets of cross-sections for the August 2002 flood event Copyright  2008 John Wiley & Sons, Ltd. 4707 is a little less for case I, the discharge and water level at Elbe River 184Ð4 km rise a little higher than for the 30 min case. However, the total discharge and water level reduction in the Elbe River for case I is the same as that for the 30 min case, because the total discharge and water level reductions are still governed by the threshold discharge and water levels at which the south gate opens, and this threshold discharge and water level are the same for both cases. Similarly, for case II, as the gates open and close slowly the final volume of water in the north and south polders are 20Ð58 Mm3 and 20Ð43 Mm3 , respectively. Thus, as the storage volume in the polders is a little more, the discharge and water levels at Elbe River 184Ð4 km rise a little less than the 30 min case. However, in this case also, the discharge and water level reductions are the same as for the 30 min case. CONCLUSIONS For the August 2002 flood event, the polder with the proposed gate dimensions and gate control strategy is capable of reducing the peak water levels near the Mauken gauging site in the Elbe River by about 25 cm while the corresponding discharge reduction is about 310 m3 s
1 . The time of opening of the south gate during the polder filling process is decided using a trial and error process so as to maximize the water level reduction in the Elbe River. The water level reduction can be further improved through different gate control strategies. This aspect, as well as the effectiveness of the polders in reducing the water levels in the Elbe River for floods of different magnitudes and duration, is discussed in a separate paper by the same authors (Förster et al., 2008). As far as the emptying of the polders are concerned, there are no intricacies involved. The emptying process starts when the discharge in the main river falls to a low threshold value. Both the 1D and coupled 1D–2D model simulations for the polder yield the same water level and discharge reductions in the Elbe River. However, due to difference in treatment of the polders in the two models, the results for the flow processes in the polders are slightly different. For example, there are differences in the time for the water front to reach the connecting gate as well as the discharge through the connecting gate. Also, the emptying process of the polders differs significantly for the two models. While the 1D model drains the polders completely in 24 days, the 1D–2D model drains it only partially in 4 days. The 1D–2D model result is practically correct as the polders cannot be drained below a certain water level because of ground elevation conditions near the gates. The 1D–2D model provides additional information in terms of the areal extent as well as depth of water in the polders after the emptying process as well as the water velocities in the polders. The information on velocities will be particularly useful in studying erosion and sedimentation problems and Hydrol. Process. 22, 4695– 4709 (2008) DOI: 10.1002/hyp 4708 C. CHATTERJEE, S. FÖRSTER AND A. BRONSTERT subsequent risk analysis in the polders. The computation time and storage requirements for the 1D model are very low, and are significantly higher for the 1D–2D model and more so when finer resolution DEMs are used. Further, unlike the 1D model, considerable effort is required in setting up and simulating the 1D–2D model. In view of this, it is recommended to use a 1D model for studying the flooding processes of polders, particularly the water level and discharge reductions in the main river. The computation time requirement suggests that a 1D model may be used in a near real time mode. However, a 1D–2D approach may be used when the study of flow dynamics in the polder is of particular interest. The 1D model is quite sensitive to changes in the values of Manning’s n for the river and its floodplain within the embankments. Thus, there is a need for rigorous calibration and validation of the model before it is put to use. The 1D–2D model is not so sensitive to change in Manning’s n values for the polders. This is because the ‘n’ values do not have a role to play once the water front reaches the boundary of the polders and the water level in the polders starts rising. A coarse resolution DEM can be used to derive the area–elevation relationship for the polders for use in the 1D model and yet obtain accurate results. The same holds true for a coupled 1D–2D model, wherein a coarse resolution DEM for the polders can be effectively used. This would result in significant reduction of the computational time and storage space requirements. In this study, the use of a 50 m grid DEM was found to yield good results. The number of cross-sections should be chosen such that the shape of the river including its depth and width are very well represented by them. In this study, it is seen that the 34 cross-sections used to model the Elbe water levels are quite sufficient. A different gate opening time for the south gate causes the water level reduction to decrease drastically. This indicates that it is essential to have a good flood forecast in order to effectively reduce the water levels in the main river. The change in gate opening and closing durations from 5 min to 60 min does not have an effect on the water level reductions in the Elbe River. In this study, a gate opening and closing duration of 30 min is selected based on information provided by the local water authorities. ACKNOWLEDGEMENTS The research was jointly funded by the Alexander-vonHumboldt Foundation Fellowship Programme and the Sixth Framework Programme of the European Commission (FLOODsite project, EC Contract number: GOCECT-2004-505420). This paper reflects the authors’ views and not those of the European Community. Neither the European Community nor any member of the FLOODsite Consortium is liable for any use of the information in this paper. Copyright  2008 John Wiley & Sons, Ltd. Data were kindly provided by the following authorities: Landesbetrieb für Hochwasserschutz und Wasserwirtschaft Sachsen-Anhalt, Wasser- und Schifffahrtsamt Dresden and Landesvermessungsamt Sachsen-Anhalt. The authors are also grateful to the Danish Hydraulic Institute (DHI), Denmark for providing an evaluation copy of the MIKE software. REFERENCES Aureli F, Maranzoni A, Mignosa P, Ziveri C. 2005. Flood hazard mapping by means of fully-2D and quasi-2D numerical modelling: a case study. In Floods, from Defence to Management, Van Alphen J, van Beek E and Taal M (eds). Taylor & Francis: London; 389– 399. Baptist MJ, Haasnoot M, Cornelissen P, Icke J, van der Wedden G, de Vriend H, Gugic G. 2006. Flood detention, nature development and water quality in a detention area along the lowland river Sava, Coratia. Hydrobiologia 565: 243–257. Bates PD, Lane SN, Ferguson RI. 2005. Computational Fluid Dynamics: Applications in Environmental Hydraulics. John Wiley & Sons Ltd. Chow VT. 1959. 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A comparison of oneand two-dimensional approaches to modelling flood inundation over complex upland floodplains. Hydrological Processes 21: 3190– 3202. Werner M. 2001. Impact of grid size in GIS based flood extent mapping using a 1-D flow model. Physics and Chemistry of the Earth, Part B: Hydrology, Oceans and Atmosphere 26: 517– 522. Werner M. 2004. Spatial flood extent modelling—A performance based comparison. PhD thesis, Delft University, Netherlands. Werner MGF, Hunter NM, Bates PD. 2005. Identifiability of distributed floodplain roughness values in flood extent estimation. Journal of Hydrology 314: 139– 157. Hydrol. Process. 22, 4695– 4709 (2008) DOI: 10.1002/hyp