Department of Physical Geography, Faculty of Geographical Sciences, Utrecht University, Utrecht, Netherlands
Now at Ministry of Transport, Public Works and Water Management, Directorate-General of Public Works and Water Management, National Institute for Coastal and Marine Management, Middelburg, Netherlands.
 The inundation model Delft flooding system (Delft-FLS) was applied to simulating the historical flood of 1805 in the polder Land van Maas en Waal (Netherlands). Delft-FLS is a two-dimensional (2-D) hydrodynamic model that simulates overland flow. Sensitivity analyses show a large influence of floodplain topography and hydraulic friction on the propagation of the inundation. Because of the typical topography of Dutch polders, a virtually flat floodplain bordered by high dikes, the extent of the inundated area alone cannot be used for evaluating the model performance. Therefore the inundation time and water levels within the inundated area were used to test the model capabilities. This study shows that using historic data has a potential advantage over using contemporary data. Historic data allow evaluation of a model for real flood disasters that have long return periods and, fortunately, have not occurred in modern times.
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 Flooding is a severe potential risk in low elevated floodplains. To protect the densely populated lowlands from floodings, many rivers were embanked. As a result of the embankment in Netherlands, embanked floodplains and polders came into existence between 1000 and 1350 AD. The embanked floodplain is a 0.5 to 1.5 km wide stretch adjacent to the rivers Rhine and Meuse. Polders are low elevated, former floodplains, mostly surrounded by dikes, in which the water level is controlled by man.
 In the winters of 1993/1994 and 1994/1995 the embanked floodplains of the rivers Rhine and Meuse were flooded and large polders were about to be inundated. These near-catastrophic events were regarded by some as the first signs of a climate change, although the floods may still fall within the range of present-day variability of discharge. However, due to the expected climatic change, river discharge will increase in wintertime [Kwadijk, 1993; Middelkoop, 1997; Middelkoop et al., 2001], increasing the risk of flooding in the polders. Growing economic activities and changing land use also increase the risk of possible future inundations [Penning-Roswell and Tunstall, 1996]. Therefore variability, frequency and magnitude of floods but also the effect of inundation need to be analyzed. Especially in polders where even a small dike breaches resulted in major catastrophes [Gottschalk, 1971, 1975, 1977; Driessen, 1994].
 Several computer models have been developed to simulate and predict (future) inundations of floodplains and polders [e.g., Bates et al., 1992, 1998; Paquier and Farissier, 1998; Stelling et al., 1998; Testa et al., 1998; Darby, 1999; Bates and De Roo, 2000]. The models range from simple models, that predict inundation by the intersection of a water surface and a digital elevation model (DEM), to very complex models, in which the inundation is predicted using three-dimensional solutions of the Navier-Stokes equations. These latter models try to estimate the three-dimensional aspect of the complex transient out-of-bank flows [Knight and Shonio, 1996; Knight et al., 1989]. With respect to verification and validation of inundation models, there are basically two ways to test the models. The first way is to test the numerical scheme of the models. This is typically done by comparisons with analytic solutions, theoretical analyses of consistency, stability and convergence, and by laboratory experiments where the model simulation results are compared with the results of an inundation experiment. The second type is by comparing the model results with real-world flood events. This type of validation tries to answer the question, “What accuracy can we expect from inundation models for practical purposes?” Up till now, only few attempts have been undertaken to evaluate the performance of inundation models in the real world. This is due to model complexity and absence of field measurements. Nevertheless, managers and policy makers use model outcomes in designing evacuation plans and planning of new infrastructure on floodplains. It is therefore important to test the real-world reliability of inundation models and to assess the uncertainties in the simulation results.
 Many inundation models are designed to simulate the flooding of natural lowland floodplains in a wide valley. However, when a floodplain is protected against flooding by river dikes a model has to be able to simulate the inundation in the polder caused by dike breach events [Paquir and Farissier, 1998; Han et al., 1998]. This type of inundations can be simulated using Delft-FLS [Stelling et al., 1998]. Delft-FLS is developed at WL|Delft Hydraulics. It is a 2-D hydrodynamic inundation model, in which a dike breach tool is incorporated. Furthermore Delft-FLS incorporates numerical techniques to capture the hydrodynamics of the inundation of a polder. The model is suited to simulate the dynamic behavior of overland flow over initially dry land, as well as flooding and drying processes on every kind of geometry [cf. Stelling et al., 1998]. These full 2-D shallow water hydrodynamics are essential to simulate the propagation of the flow over the sloping land surface in the polder. Although a simple storage model would also be able to predict the volume and extent of an inundation from a given inflow through a dike breach, it does not consider the propagation of the inundation flow.
 So far, Delft-FLS has not been tested with field measurements, on a temporal scale of catastrophic discharge peaks and a spatial scale of polders. This is due to the scarcity of proper data sets, because fortunately inundations of Dutch river polders have not occurred in moderns times (since 1926). However, various historic sources present in Netherlands, contain information on the inundation of river polders, caused by dike breaches. Since the embankments, numerous eyewitness reports, damage reports, and dike board reports were made of these disastrous events. Together, these data provide quantitative information on the boundary conditions of an inundation, as well as of the inundation process itself. Moreover, with this data it is possible to validate computer simulation models and determine the required level of topographic detail in the model schematization. The aim of this study therefore is to validate simulation results of Delft-FLS with historic data of a real flood disaster of a river polder after a dike breach. Sensitivity analyses were carried out to explore the effect of varying the level of detail in the topography and surface roughness used in the modeling on the simulation results. The study also aims to highlight the potential advantage of historic data over contemporary data, by evaluating a model for real flood disasters with long return periods.
2. Inundation Model Delft-FLS
 Delft-FLS requires four types of information to simulate inundation due to dike breaches: (1) discharge (Q) or water depth (h) time series at the inflow boundary of the model and a Q(h) relation at the outflow boundary of the model, (2) dimensions of the dike breach and scour hole to determine the discharge to the floodplain or polder, (3) a DEM of the channel, embanked floodplain and polder, including the height and location of dikes, roads, ditches, and sluices, and (4) land surface cover in terms of hydraulic roughness, as well as hydraulic roughness of the main channel. The model produces raster maps of water height and level, flow velocity and direction, and calculates from these an inundation depth map at each time step.
 FLS is a 2-D grid-based inundation model using the finite difference method. The scheme used in Delft-FLS is based upon the following characteristics: The continuity equation is approximated such that (1) mass is conserved not only globally but also locally and (2) the total water depth is guaranteed to be always positive which excludes the necessity of “flooding and drying” procedures. The momentum equation is approximated such that a proper conservation laws are applied at rapid flow variations at dam breaches, submerged dams, hydraulic jumps and bores. The combination of positivity of water depths and mass conservation assures a stable numerical solution. To explain the principles it is sufficient to consider the following one-dimensional shallow-water equations:
where U is velocity, ζ is water level above plane of reference, C is the Chezy coefficient, d depth below plane of reference, h total water depth (h = ζ + d). The bottom is supposed not to be time varying. From this it follows that the continuity equations can be rewritten as:
Equation (2) can be considered as a transport equation of the scalar quantity h, which we rewrite as:
where h at i means hi, a(u, u) denotes some advection approximation, see later:
 The time integration is based upon the θ method [see, e.g., Lambert, 1991]. A simple locally linearized version this method, that does not require iterations for the solution of nonlinear equations, is given by:
where un+θ = θun + 1 + (1 − θ)un, xat (i + 1/2) = (hi + hi+1)/2, and ζn+θ is defined accordingly. To derive conditions for strict positivity we rewrite equation (5a), while we assume positive flow, as:
From this it follows that strict positivity is ensured if:
Similar conditions can be derived for other flow directions. Simply fulfilling equation (7) will prevent wet points from drying, i.e., no special drying and flooding procedures are required for this approach.
 It is to be noted that the description of the continuity equation in the primitive variables, instead of the integrated quantities, has important advantages: (1) it enables strict positive water levels, and (2) the upwinding yields artificial viscosity without influencing strict local mass conservation.
 For sufficiently smooth solutions advection approximations could well be based upon at least second order local truncation errors. In this case numerical viscosity is minimal. Near local discontinuities in the solution, due to sharp bottom gradients or hydraulic jumps, order of accuracy is a meaningless concept. Conservation properties are the most important aspect in such a case. The following quantities are considered: (1) mass, (2) momentum, and (3) energy head. The numerical approximation, given by equation (4a), is already mass conservative. For the advection approximation we only consider energy head and momentum. The so-called energy-head conserving formulation of equation (1b) is given by:
This means near rapidly varied flow, such that time variation and bottom friction can be neglected locally, = constant. Like wise the momentum conservative formulation is given by:
Both formulations (8) and (9) are completely equivalent for continuous and sufficiently smooth solutions. At local discontinuities however equations like (8) and (9) have no unique solution in general. Discontinuities can be due to (1) bores (as in dam break problems) and hydraulic jumps and (2) discontinuities in the bathymetry, for instance due to submerged dikes or dam breaches. Here “smoothness” is also related to numerical grid resolution. At discontinuities conservation properties are needed to connect the equations at both sides of the discontinuity. In case of dam breaches or submerged dams, a rough estimation of the energy loss follows from consecutive application of (specific) energy head conservation in the contraction followed by momentum conservation at the abrupt expansion (see Figure 2). A hydraulic jump is considered as an abrupt expansion. These are classical notions in open channel hydraulics [see, e.g., Chow, 1959; Chaudry, 1993; Roberson and Crowe, 1993].
 For numerical approximations that are applied for inundation simulations it is important that near rapidly varied flows, proper conservation properties are captured automatically. Mass conservation is imperative regardless of the nature of the discontinuity. In the following we will show two advection approximations, that were applied for the approximation of momentum advection and that are either energy head or momentum conservative. The first approximation is energy head conservative:
Here the expression for the advection approximation should be read as follows:
It is to be noted that, based on the definitions as given above, for positive values of u∀i the advection approximation yields:
In a similar way momentum conservative approximation are derived. For this purpose it is convenient to denote the following identities:
where: q = uhNow the second spatial discretization for conservation of momentum is given by:
where q = uh(u), and . After averaging equation (12a) over the grid points (i) and (i + 1) and multiplying the resulting equation by u one gets:
Equation (13b) is consistent with equation (9) and is thus momentum conservative. It is to be noted that for positive flow direction ∀i the advection approximation of equation (12b) yields a simple expression given by:
It is to be noted that each approach leads to consistent approximations. This means that for sufficiently smooth solutions the differences are minor. Only near discontinuities the differences play an important role. In locations of significant flow contractions equation (10b) is applied, everywhere else equation (12b) is applied. In Figure 3 an example of this approach is given of flow over a submerged dam.
 Integration in time is based upon the θ method [see Lambert, 1991]. Strict application for θ = 1/2 yields nonlinear equations. This necessitates the application of iterative solvers. By local linearization, iteration is avoided. In practice the linearized solutions proved to be sufficiently conservative.
 The principles here explained can be applied, without any alteration for more general 1D equations that include arbitrary cross sections.
 The method given by the equations (10) and (12) is only of first order of consistency. “Almost second order approximations,” including guaranteed positive water depth however can be constructed as well. A second order accurate approximation based upon central differences is likely to be subjected to spurious oscillations and even to instabilities in case of super critical flows. A positive water depth cannot be guaranteed and leads to many “flooding and drying procedures” [Stelling et al., 1998]. In stead a different approach is applied that is based upon flux limiters, such as the one defined by Van Leer as denoted by Pourquié  or the one given by Koren . The flux limited approximations guarantee positivity of the water levels for sufficiently small time steps. The local order of consistency depends on the solution. Near extremes the accuracy reduces to first order. The total number of possible flux limiters is large [see, e.g., Hirsch, 1990]. Stelling  gives examples for rapidly varied shallow water flows For the computations of this paper first order approximations proved to be sufficiently accurate.
2.2. Two-Dimensional Application
 The method described previously is extended to two dimensions. For this purpose we consider the 2-D shallow water equations as given by:
A staggered numerical “C” grid is defined by Figure 4.
 A momentum conservative spatial discretization of equation (14) is now given by:
where uq = uh(u), vq = vh(v), , , and all other values are define accordingly. The momentum conservation characteristics follow easily from multiplying equation (15b) and equation (15c) respectively by x and y.
 Time integration can be implemented with semi-implicit methods according to Wilders et al.  or Casulli  or with ADI (alternating direction implicit) according to Stelling . The Delft-FLS system contains all these options, however for the computations of this paper ADI time integration has been applied.
 For flooding over a dry bed a predictor corrector approach is applied for bottom friction. This prevents overshoot of the velocities if the velocity accellerates from zero during the passage of a flow discontinuity. An extensive comparison between simulations with DELFT-FLS and laboratory experiments of inundations due to dambreaks is given by Stelling . It is to be noted that to compute the flow in a breach correctly, only with 2-D models rather then fully 3D Navier Stokes, the subsequent application of energy head conservation followed by momentum conservation is imperative. This was found for the experiments mentioned by Stelling . The actual size of a breach ind a clay dike and also the growth of the breach as a function of time are very difficult to compute. These values were based upon empirical observations.
3. Study Area
 The validation of Delft-FLS was performed using data of the 1805 inundation of the polder Land van Maas(=Meuse) en Waal. This polder is a typical example of the Dutch polders, characterized by a complex network of drainage canals and polder dikes. Because this situation is different to floodplains elsewhere a data set concerning the inundation of a Dutch polder was used, instead of more recent data sets of, e.g., the inundation of the wide and simple Maas valley [Bates and De Roo, 2000] or the inundation of the Imera floodplain in Sicily [Aronica et al., 1998a, 1998b, 1998c], where the inundation is predominately a basin-filling problem controlled by embankments. The data set of the 1805 inundation is the best available, although the last inundation of a Dutch polder due to a river flood occurred in 1926 [Ploeger, 1992]. The 1805 inundation was selected because a detailed description of the dike breach and of the inundation exist [Driessen, 1994] which enabled the reconstruction of topographical characteristics of the polder, water levels of the rivers Rhine and Meuse, and dike breach dimensions. Therefore the data needed as input and for verifying the model results of the 1805 flood were similar in number and quality as the 1926 data, and in 1805, the topography of the polder was less complex than in 1926, only one dike breach occurred and only one polder inundated, which makes interpretation of the simulation results more straightforward. Still, we acknowledge the possible weaknesses of historic data: recent data would suffer from fewer conversion problems, be more accurate and have a greater number of observed points.
 The polder Land van Maas en Waal (Figure 5) is located in the eastern part of the Dutch river area. The embanked rivers Meuse and Waal enclose the polder, in the north, south, and west. An ice-pushed ridge south of Nijmegen borders the polder in the east. This ice-pushed ridge was formed during the Saalian glaciation (OIS-stage 6), and consists partly of Tertiary river sands [Zagwijn, 1974]. The polder is characterized by relatively large differences in elevation: from 20 m +NAP (Dutch Ordnance Datum, ≈ mean sea level) in the east, to 3.5 m +NAP in the west. In the center a complex of aeolian dunes is found; their elevation varies between 7.5 and 20 m +NAP. These dunes were formed during the waning stage of the Weichselian glaciation (OIS-stage 2) and are partly buried by flood basin sediments [Berendsen et al., 1995]. After the polder was completely embanked in 1350 AD [Pons, 1957], seepage water from the ice-pushed ridge and aeolian dunes collected in the lower western part of the polder. This water was artificially drained to the river Meuse. To control the drainage of the polder, small polder dikes, canals, and sluices were constructed, resulting in several drainage units [Pons, 1957]. The complex pattern of drainage canals and polder dikes may potentially have a major influence on the flow pattern of inundation water when a flood disaster occurs.
4. The 1805 Inundation
 The inundation of the polder in February 1805 was a result of accumulation of ice floes in the river Waal, downstream of Weurt. These floes obstructed the flow in the river Waal and caused the water level to rise rapidly until the morning of 13 February 1805 (Figure 6). At 5:00 AM the major river dike broke. Since the dike consisted of clay, a section of 190 m flushed away in a few seconds, and water began to flow into the polder [Thomkins, 1805]. Almost immediately, the water level of the river Waal at Nijmegen dropped (Figure 6). After the initial dike breach, the water flow eroded a large scour hole of 200 by 400 m with a maximum depth of 13 m [Hesselink, 2002]. The material from this scour hole (gravel, sand, and sandy clay) was deposited as a lobate splay behind the scour hole (Figure 7). After the dike breach, water flowed toward the lower western part of the polder. This flow inundated several sluices along its path. A second flow was directed to the east, overtopping the important Teersdijk (E in Figure 5), resulting in the inundation of the area south of this dike [Municipal Archive Nijmegen, 1805a]. The maximum water depth in the polder after the dike breach ranged from 0.8 m close to the dike breach to 2.0 m in the western part of the polder. An overview of water depth and water levels in the polder after the dike breach is given in Table 1. It is hard to indicate the return period of the 1805 inundation because it was due to a peak discharge in combination with an ice jam that further raised the water level in the river. The maximum water level during this flood occurred 7 times between 1780 and 1850; after the normalization works in 1850 this level never was reached again.
Table 1. Water Depth and Water Levels Based on Historic Data of the 1805 Inundation of the Polder Land van Maas en Waal
 Several measures were taken to alleviate the effects of the inundation. Immediately after the dike breach, people dug away the upper parts of the major river dike in the west near Dreumel (A in Figure 5). This resulted in a spillway that discharged water from the inundated polder into the river Meuse, which generally had lower water levels than the river Waal [Municipal Archive Nijmegen, 1805b]. From the reports of civil cases, it became clear that small sluices in the polder dikes were illegally opened to drain the inundated compartments as quickly as possible, to the disadvantage of lower downstream units [Municipal Archive Nijmegen, 1805c]. Damage reports indicate that houses were destroyed in Alphen, Appeltern, Dreumel and Weurt (Figure 5). To aid the victims, bakers whose ovens were not inundated (in Dreumel, Druten, Nijmegen and Wamel; Figure 5) were ordered to bake bread for people in the drowned villages [Driessen, 1994].
 Hydrological information was extracted from various historic sources (written sources, observation series, maps), expressed in old, nonmetric units relative to local ordnance datum. Therefore the historic data were converted to meters relative to NAP.
 1. Water levels of the rivers Meuse and Waal (Figure 6) were converted from “Rijnlandsche” feet and thumbs relative to the ordnance datum of Grave and Nijmegen, to meters relative to NAP(= Dutch Ordnance Datum ≈ mean sea level). The converted water levels were used at the inflow boundary of the model. At the outflow, the present stage-discharge relation of the rivers Meuse and Waal was used. Despite the presence of sluices in the river Meuse since 1954 [Ploeger, 1992], the stage-discharge relation during peak flows is hardly affected by the sluices. The sluices are open during high water.
 2. The dimensions of the dike breach and the dike breach scour hole were obtained from several historic maps made after the dike breach of 1805. These maps show plans for repair of the dike breach (Figure 7).
 3. The 1805 DEM was constructed, based on (1) a 1965 DEM [Wolters-Noordhoff Atlasproducties, 1987], (2) surface elevations measured around 1800 by Dibbets and by Fijnje in 1839 [see Fijnje, 1840], (3) level of the major river dike in 1801 [General State Archive, 1801] and the polder dikes, measured around 1800 by Dibbets and in 1839 by Fijnje , (4) location of polder dikes and canals in the beginning of the nineteenth century [Wolters-Noordhoff Atlasproducties, 1990]. The 1965 DEM consists of 35,868 elevation measurement points, and is based on a field survey with elevation measurements at 100 m distance intervals. The 1965 DEM is one of the oldest and most complete DEM's of the polder Land van Maas en Waal. It represents the natural relief, before major leveling and reallocation schemes were carried out between 1965 and present. The surface elevation measurements were interpolated to a 50 by 50 m raster grid, in 394 by 682 raster cells. After that, the 1965 surface elevation was compared to the 1805 surface elevation as far as known from five cross sections. This showed that subsidence of channel belts was virtually zero, whereas in flood basins, subsidence values of up to 60 cm were found. The amount of subsidence was strongly correlated to substrate composition. Hence a geological map [Berendsen et al., 1994, 1995] was used to interpolate subsidence (Figure 8). The contour lines follow the borderline of the geological units. Subsequently, dike elevation and canal depth were added to the DEM. The depth of the approximately 25 m wide drainage canals was reduced to 0.5 m, to preserve the correct cross sectional area on a raster coverage of 50 m.
Conversion from Manning n to Nikuradse k with a water depth of h = 1,0 m.
Grass, no brush
Medium to dense brush
6. Simulation Runs
 Dynamic simulation runs with Delft-FLS were carried out for a 15-day period between 0:00 AM on 11 February 1805 and 0:00 AM on 26 February 1805. To start the dynamic simulations with water depths and flow velocities in steady state, we defined a constant inflow at a water level of 11.9 m +NAP for the river Waal (a discharge of 3000 m3/s) and 10.8 m +NAP for the river Meuse (a discharge of 1400 m3/s), preceding the simulated period. These water levels are the measured water levels on 11 February 1805. The steady state condition was maintained for 24 h, after which the discharge at the inflow and outflow boundaries were equal and in equilibrium. The number of simulations was limited to 12 (Table 3), because of the high computational demands of the model (it took 2.5 days on a UNIX mainframe before one simulation was computed).
Table 3. Simulation Input Characteristics of the 1805 Inundation of the Polder Land van Maas en Waal
 Sensitivity analyses were carried out to explore the effect of (1) the uncertainties in the topography representation and (2) the friction factor on the simulation results. We envisaged that uncertainties in topography (presence of dikes) would strongly influence the dynamics of the inundation. Therefore the details of the polder dike network incorporated in the DEM should be taken into account when the model is used to predict the inundation dynamics [Aronica et al., 1998c]. Three topographic realizations with an increasing simplification of the polder dike network were generated (Figure 9). Uncertainties as result of unknown land surface cover types were explored through variations in the hydraulic roughness coefficient, assuming a complete grass cover and different situations of mixed land surface cover types: (1) one uniform vegetation roughness per land cover type (Figure 10a), (2) spatially random distribution of vegetation roughness cover of Figure 10a (Figure 10b), (3) vegetation roughness randomly varied per land cover type (Figure 10c), and (4) randomly varied vegetation roughness (Figure 10d). Uncertainty in the friction coefficient is caused by seasonal variation of the hydraulic roughness of one land surface cover type, annual variation of different land surface cover types due to rotation of land surface cover types, and variations of friction with the discharge during the event. The floodplain frictions used are two end-members of many more possible solutions. It is not implied that these combinations represent the “true” field situation.
 Although we recognize the paramount importance of the breach as a triggering event to what happened subsequently in the polder, no sensitivity analysis was carried out to explore the effect on the temporal evolution of the breach size on the discharge through the breach and consequently on the flooding of the polder. A linearly decreasing of the dike section was assumed because historic sources show that in case of failure of the dikes, a large dike section collapses simultaneously within a second [Driessen, 1994]. This is due to the internal composition of the dikes. In Netherlands the dikes consists of several layers of clay instead of sand [Driessen, 1994]. After the initial dike breach no further evolution of the breach occurs [Driessen, 1994]. This is endorsed by different historic sources on the 1805 dike breach [Municipal Archive Nijmegen, 1805a, 1805b, 1805c; Thomkins, 1805].
8. Influence of Topography on the Simulation Results
 The results of simulations R1 to R6 (Table 3) are shown for four different locations in the polder (Figure 11). Close to the dike breach (location 1 in Figure 11) the level of detail of the schematization does not affect the results of the model simulations. Simulations R1, R3, and R5 (Table 3) yielded similar results; location 1 is inundated after 1 hours. The time at which inundation occurs, generally increases with the distance to the dike breach. When no polder dikes are assumed (R5), the western part (location 4 in Figure 11) of the polder is inundated after 24 h. Including the major polder dikes in the DEM halves the propagation velocity of the inundation (R3, location 4); the western part (location 4 in Figure 11) of the polder is inundated after 49 h. Adding the remaining polder dikes in the DEM (R1), however, hardly further delays the inundation: at location 4 the difference in inundation between R1 and R3 is only 2 hours. South of the long east-west orientated waterways, a similar retardation of the inundation is simulated if dikes are incorporated in the DEM. At the Teersdijk (Figure 5), located upstream of the dike breach, almost no differentiation in propagation of the inundation front is seen for different simulations. The presence of the Teersdijk caused a delay of 3 h. Thus including the main objects of a polder dike network in the DEM considerably reduces the propagation velocity of the inundation front. Contrary to the propagation of the inundation front, the maximum water depth is not influenced by an increase in detail of the polder dike network.
 Simplification of the polder dike network accelerates discharge through the dike breach (Figure 12a), because it results in a decrease of the back-water effect. During the first hours of the inundation, discharge through the dike breach varies between 2500 (DEM with all polder dikes) and 3200 m3/s (DEM without any polder dikes). The mean discharge is 2700 ± 240 m3/s.
9. Influence of Land Surface Cover on the Simulation Results
 The increase in friction coefficient decelerates the propagation velocity of the inundation front. Location 1 (Figure 13) is only inundated in simulation R8 (maximum friction coefficient; Table 3). The time to inundation is 18 h. Location 2 (Figure 13) is inundated after 11 h with a low (R7, Table 3) and after 14h with a high (R8) friction coefficient. In the western part of the polder (location 4, Figure 13) the influence of variation in vegetation roughness is most pronounced. In case the friction coefficient is low (R7), location 4 is inundated 14 h earlier than when the friction coefficient is high (R8). While increasing roughness delays the inundation, differences in friction coefficient hardly influence water depth.
 Varying the friction coefficient between the minimum and maximum value (Table 2) hardly influences the discharge through the dike breach. During the first hours of inundation, discharge through the dike breach varies from 2400 (high floodplain friction coefficient) to 2600 m3/s (low floodplain friction coefficient); the mean discharge is 2500 ± 75 m3/s (Figure 12b).
 The level of detail of information on land surface cover hardly influences the simulated propagation velocity and final water depth of the inundation (Figure 14). It even hardly affects the moment the inundation water reaches the western part of the polder (location 4, Figure 14). In simulations R3 (floodplain friction coefficient known) and R10 (random friction coefficient), location 4 is inundated 102 h after the dike breach (Figure 14), while R9 (random floodplain friction per land surface cover) and R11 (land surface cover unknown) simulate the inundation of location 4 after 108 h (Figure 14). Here too the maximum water depth is not influenced.
 It is concluded that the detail of the polder dike network incorporated in the DEM and the vegetation roughness influence (1) the discharge through the dike breach, (2) the water level in time, and (3) the moment of inundation. They do not influence maximum water depth or maximum extent of the inundation. Because of the “bath-tub”-like topography of the polder, the maximum spatial extent of the inundation is constant for a large range of discharges through the dike breach.
10. Evaluation of Model Performance With Varying Degree of Topographic Detail
 In six model runs (R1 to R6, Table 3) we varied (1) the details of the polder dike network incorporated in the DEM and (2) the vegetation roughness (expressed as friction coefficient). We generated three topographic realizations with increasing simplification of the polder dike network. Two land surface cover assemblages were assumed: a complete grass cover and a situation of mixed land surface cover types. Because of the limited number of data for evaluation, analysis of the model results using a classic objective function as evaluation criterion [e.g., Nash and Sutcliffe, 1970] is not possible. Therefore a combination of accuracy in time and of water depth is used in this study. This means that the best simulation is the one with largest number of locations where the model predicted the timing and depth of the inundation correctly (R2, Table 4). From the historic data, the moment of inundation could not always be determined exactly, only within a time period of a few hours in which the location became inundated. The range of uncertainty has been considered in the model evaluations (Table 4) by calculating results for the indicated values in Table 1 (indicated between parentheses).
Table 4. Validation of Delft-FLS With Historic Dataa
R1 Time, h
R1 Water Level, m +NAP
R2 Time, h
R2 Water Level, m +NAP
R3 Time, h
R3 Water Level, m +NAP
R4 Time, h
R4 Water Level, m +NAP
R5 Time, h
R5 Water Level, m +NAP
R6 Time, h
R6 Water Level, m +NAP
Model Time, h
Water Level, m +NAP
Italic type indicates exact fitting model results. Bold type indicates the model results within the range of uncertainty.
The water level in the polder (Hp) exceeds the water level in the river Maas (HM).
The water level in river Maas (HM) exceeds the water level in the polder (Hp).
 According to the evaluation criteria defined in this study, the best prediction of the 1805 inundation is obtained when the most detailed polder dike network (Table 4) is incorporated in the DEM, and a complete grass cover is assumed (R2, Table 3). However, similar results can be obtained with different parameter sets. The chosen parameters were selected from a typical range of values suggested in literature [Chow, 1959; Acrement and Schneider, 1984] and historic data.
11. Simulated 1805 Inundation
 The best simulation (R2, Table 4) shows a stepwise compartment-like inundation of the polder (Figure 15). As soon as a compartment is completely filled with water, the next compartment downstream is inundated. This process of discontinuous inundation is due to the network of polder dikes. Water in the polder essentially flows to the lower western part of the polder and, eventually, the “bath-tub”-like polder fills completely. The inundation front propagates with a mean velocity of 0.9 km/h in a downstream direction. Mean water level rise in the western part of the polder (location 4) is 0.03 m/h. After 3 days the maximum water depth of 2.3 m is reached here. Water depth close to the dike breach and upstream of it falls shortly after recession of the discharge peak in the river. On the basis of the sequence of events and flow characteristics during the inundation, two zones can be distinguished.
 1. Near the dike breach, flow velocities reach a maximum of 2.5 m/s shortly after the breach. Here, the flow velocity slows to 1.8 m/s in the following twelve hours. Within 1 hour after the dike breach, flow velocity 300 m away from the dike breach diminishes to 1.3 m/s. Here, flow velocity is almost 0 m/s within 12 hours. Near the dike breach water depth quickly reaches a maximum of 0.8 m after which it falls, following the recession of the discharge peak in the river (Figure 16).
 2. The lowest parts of the polder became inundated two days after the dike breach. Water depth rises to a maximum of 2.3 m, and remains at this level for weeks until the polder is drained (Figure 16).
 Between zone 1 and 2 a third zone is found. This zone is characterized by a rapid inundation after which the water level falls back.
12.1. Sensitivity of Delft-FLS
 Delft-FLS appears very sensitive to the presence and dimensions of obstructing elements in inundation simulations of a polder. The same was found by Aronica et al. [1998b] using a different model. They showed that random changes in floodplain elevation data were statistically significant. A maximum delay of the inundation is caused by a perpendicular orientation of the polder dikes to the water flow. The effect of the major polder dikes on the inundation propagation velocity overshadows the effect of the smaller minor polder dikes on the inundation propagation velocity. Major polder dikes also control the discharge through the dike breach.
 The propagation velocity of the inundation and the discharge through the dike breach is less sensitive to the obstructing effects of the land surface cover types (expressed in floodplain friction) when compared to presence and dimensions of obstructing elements. The simulation results show a maximum retardation of the inundation propagation of 12 hours in the western part of the polder. Floodplain friction does not influence the maximum water level in the polder. As soon as the water level exceeds the vegetation height during the infilling of the polder, the controlling effect of the vegetation on the water level and the inundation propagation velocity diminishes. This means that the retardation of the inundation propagation occurred in the first moments of inundation of the initially dry land.
 Because discharge through the dike breach is very sensitive to obstructions in the polder, we assume that the model results are also very sensitive to the presence and dimensions of the dike breach gap. A dike breach gap acts as a conductor of the water flow and consequently its size determines the magnitude of the water flow through the dike breach. This is very important in case of sandy dikes where the temporal evolution of the breach size determines the discharge through the dike breach and thus the inundation of the polder.
12.2. Evaluation of Delft-FLS
 In general, inundation models are calibrated using the maximum extent of the inundation [Bates et al., 1998; Bates and De Roo, 2000]: the maximum extent of the inundation is determined from easily available high-resolution data, such as satellite synthetic aperture radar. This method is very promising, especially in large areas without a comprehensive data collection. However, in relatively flat areas surrounded by dikes or in valleys with nonembanked rivers where the valley floor is completely filled after a large inundation, the extent of the inundation is the same for each flood. Then the extent of the inundation is not a proper method to validate a computer inundation model. In these flat areas water levels and propagation velocities of the inundation are indispensable for this purpose. The locations with known water levels in time should be more or less evenly distributed over the inundated area.
 It was shown that it is possible to evaluate the simulation results of Delft-FLS for the inundation of river polders using historic data. The main advantage of the use of historic data in inundation modeling is that it allows evaluation of model performance for real inundations and for inundations with long return periods.
 Because of the “bath-tub” topography of these polders, the inundation is characterized by a rise in water level over time. Extent of the inundation is entirely controlled by the location of the dike breach and the position of the river dikes. Sensitivity analyses showed a strong influence of topography and floodplain friction coefficient on the inundation. Propagation velocity of the inundation front decreased by 50%, in case a polder dike network is present. Land use influences propagation velocity of the inundation but not the water level. Detailed polder dike network and high friction coefficients also influenced discharge through the dike breach. A detailed polder network and high friction coefficient reduced discharge through the dike breach by 20%.
 During inundation, two zones with different types of damage are distinguished. Close to the dike breach, the inundation is characterized by high flow velocity. Here, damage is caused by washing away of roads, buildings, livestock, crops, and trees. In the downstream part of the polder, the inundation is characterized by a high water level. This results in saturation of buildings and roads, drowning of livestock, and devastation of crops. In between, both types of damage can be expected. The extent of the zones depends on the location of the dike breach and the discharge through the dike breach. If the dike breach is located in the downstream part of the polder, damage will mainly be caused by saturation.
 We hereby thank WL|Delft Hydraulics, for providing their computer facilities and their model Delft-FLS. We also thank Gerard van de Ven who kindly provided old maps of the polder Land van Maas en Waal and Anneke Driessen who gave us access to interesting archives. Ron Agtersloot and Bert Jagers introduced us to the miracles of computers and computer models. Three anonymous reviewers, Ward Koster, Henk Berendsen, Jeroen Schokker and Sandra van der Linden of Utrecht University and Paul Bates of the University of Bristol kindly reviewed earlier drafts of this manuscript. We thank Jacqueline Franssens, for showing us the meaning of writing. This study was funded by the Netherlands Organization for Scientific Research (NWO), project number 750-19-611. The animation of the inundation can be downloaded from the Internet http://www.geog.uu.nl/fg/palaeogeography; click Ongoing research).