Hydraulic modeling of river floods has received a significant boost during the last 10 years; not only thanks to improved computers and hydraulic modeling software, but also to the capabilities and user-friendliness of geographical information systems (GIS). During the same period, new legislation, such as EU’s flood directive, demands that flood risks are incorporated into risk and management plans, and together, this has led to production of numerous flood risk maps. Although these maps may have been produced by professionals who are aware of the different inaccuracies and uncertainties underlying the maps, they are often used by people who have little or no experience of neither hydraulic nor digital elevation modeling. Furthermore, as these maps tend to form the basis for many decisions in spatial and physical planning of the built environment, there is a need for tools that can communicate the intrinsic uncertainties always present in the maps.
There are different types of uncertainties involved in flood risk mapping (see e.g. Pappenberger et al. 2008 and Merwade et al. 2008, for general treatise on this subject). The most immediate is which model to be used (e.g. Wagener and Gupta 2005), but in practice, the most commonly treated uncertainty is which magnitude of flow to use for a certain flood return period. This can be handled by running the model with different water discharges and thereby get a range of flood inundation areas. Other ways of treating uncertainty is through Monte Carlo simulations, i.e., feeding the model with slightly varied input of all input parameters, and where the large number of output maps in turn can be related to flood prediction uncertainty on how accurate the modeled results are (e.g. Apel et al. 2008). Obviously, specific objects and parameters in the hydraulic model can also influence the accuracy of the produced results. For example Koivumäki et al. (2010) studied the effects of buildings in the model, Pappenberger et al. (2006) looked at the effects of boundary conditions and bridges, and Cook and Merwade (2009) and Castellarin et al. (2009) treated the effects of cross-section location and spacing. As the hydraulic modeling usually involves calibration against a previous flood event, the importance of roughness is also widely known. By varying river bed and floodplain roughness values in a range that theoretically can be expected, minimum and maximum extents of the flooded area can be modeled. Although modelers have acknowledged the implications of roughness for a long time, it is not until recent years that any efforts have been made to see how much this type of uncertainty affects the results (see e.g. Pappenberger et al. 2005; Werner et al. 2005; Casas et al. 2006; Schumann et al. 2007; Wilson and Atkinson 2007; Brandt 2009; Warmink et al. 2013; Wu in press). This is probably due to the type of uncertainty which earlier has been considered the main constraint for successful modeling, viz. the quality of the digital elevation model (DEM).
Previous research on delineation uncertainties related to DEMs
Before the advent of LiDAR, the results from hydraulic models, which could be based on detailed surveyed cross sections, were overlain on DEMs of poor resolution. In Sweden, e.g., up to only a couple of years ago, the only elevation database of national coverage has been Lantmäteriet’s (the Swedish mapping, cadastral and land registration authority) with 50 m cell resolution (other countries have had similar resolutions). Very rarely, there have been DEMs of higher quality available. Due to the poor quality of the elevation models, in Sweden all such maps were given a notification that they should not be used for detailed planning. Hence, there have been some studies with the specific objective to study how the quality of DEMs affects the accuracy of inundation boundary delineation from 1D hydraulic models, which end products are water levels at each modeled cross section. By comparing these modeled levels with measured levels, several studies have shown that the accuracy of predicting correct levels is surprisingly high, irrespectively of the quality of DEM (e.g. Casas et al. 2006; Yacoub and Sanner 2006; Brandt 2009). Only with poor DEMs (i.e., cell sizes bigger than 10–25 m) together with steep river slopes, or abrupt slope change, the water levels may deviate significantly between modeled and real conditions (Brandt 2009). However, when it comes to the spatial extent, which is important when the inundation extents are transferred to maps, high-resolution DEMs of high quality may also produce inaccurate results.
An early attempt to look at spatial deviations was done by Zhang and Montgomery (1994) on two areas in the USA. They gridded spot elevation data to DEMs of 2, 4, 10, 30, and 90 m resolution. They noticed that better resolution than 10 m lead to improved modeling results. However, the best two DEMs did not produce any significant improvements; most probably due to the catchments being characterized by moderately to steep terrain gradients. Later, Werner (2001) used laser altimetry data for a reach of the river Saar in Germany. The original cell resolution was 2.5 m, which then was aggregated by averaging neighboring cell values to cell sizes of 5, 10, and 25 m. He concluded that a cell resolution of 10 m indicated the break when flood extents started to deviate significantly.
When the modeled areas are big, high-resolution DEMs usually contain enormous amounts of data. Therefore, it is of interest to see how much the original laser data can be filtered, without losing predictability performance. For an area around Leith Creek, North Carolina, Omer et al. (2003) looked at the angle α between two surveyed data points (Fig. 1). If a pre-determined angle is exceeded, the point will be preserved, but if it is not exceeded it will be removed from the dataset. In this way the number of points will be reduced, leading to less computer storage, faster analysis times, but also a DEM of poorer quality. The original dataset had ca 0.0288 points/m2, equivalent to 5.89 m cell size. By testing different threshold values of α, their recommendation is that α should be less than 4°, which in their case represented about 38 % of the original number of points, i.e., ca 0.0111 points/m2, equivalent to 9.50 m cell sizes.
Another study was undertaken by Casas et al. (2006). They looked at an area next to the Ter River, Spain, and tested different DEMs ranging from 1 to 4 m in cell size. The DEMs were derived from laser altimetry data, GPS surveyed data, 5 m contour data (scale 1:5000), as well as combinations between them, together with or without bathymetric data. They concluded that for a 500 m3/s discharge, the 4 m resolution DEM yielded inundated area differences up to 7.3 %. However, if higher discharges were used (3000 m3/s), the differences were reduced to 2.6 %. Therefore they argued that coarser resolution will have less consequence in floodplain areas.
Raber et al. (2007) looked at Reedy Fork Creek, North Carolina, and started with laser altimetry data with a mean point distance of 1.35 m, which later were filtered in several steps down to 9.64 m. By comparing statistics over the modeled inundated areas, they concluded that it is enough with 4 m mean point spacing. For better DEMs they did not see any significant differences between the model results.
Cook and Merwade (2009) studied the Brazos River, Texas, and Strouds Creek, North Carolina, for different resolutions (laser altimetry data of 3 m for Brazos River and 6 m for Strouds River, as well as 10 and 30 m USGS data for both rivers) combined with different qualities of cross-section resolutions. Although their research focus was on inundated area differences, they did notice that for the smaller Strouds River (with a width of 9.5 m during normal conditions) the average width of a modeled flood where 25 % wider when poor DEMs were used. Similarly, the larger Brazos River’s (with a width of 175 m during normal conditions) average width was 5 % wider. This effect was doubled when laser altimetry data were integrated in the cross-section profiles.
Aim and objectives
Nowadays flood risk maps are usually based on DEMs with quite high quality. In Sweden, a new national elevation dataset of 2 m resolution is under production, and thanks to the detailed appearance of the maps, many users as well as hydraulic modelers tend to put high confidence in them and consider the results to be very accurate, i.e., with a flood-boundary position accuracy of just one or two raster cells. However, there are a few studies available that have shown that these maps may also suffer severely from DEM-derived uncertainties, but despite the recognition of the problem, it seems that practically no attempts have been made to actually visualize the uncertainties of these maps (cf. Lim et al. 2016). Considering the fact that there still are accuracy and uncertainty issues due to the quality of the DEMs, together with the absence of effective visualization techniques to represent these issues, the general aim of this paper is to provide insights into the importance of DEMs influence on 1D hydraulic modeling. The specific objectives are to produce: (1) a general equation capable of describing the uncertainties related to the DEM resolution and the floodplain characteristics, here represented by the slope perpendicular to the flow direction, and (2) an algorithm capable of illustrating the uncertainties of flood boundary mapping, related to the quality of the DEMs.