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Abflusssimulation - Flow Simulation

The "flood of the century" on the river Elbe in August 2002 hit vast areas along the river and some of its tributaries unprepared. Though the flood on the neighbouring river Oder in the summer of 1997 should have been a warning, an efficient alarm scheme had not been established. The demand, that state administration should implement a coherent river basin management, was raised afterwards.

The following considerations outline a model, to calculate the resulting flow from a watershed from the properties of terrain and landuse. The geografical information system (GIS) "Idrisi" (version 2 for WINDOWS) was used to create the model.

Rain falling within a watershed will reach the exit of the river basin after some time, which depends on the distance of an unit of area to the exit, the slope (the steeper the faster), and the orientation of the slope area unit towards the exit point. An arbitrary landscape was created of 40 x 30 area units (pixels), with a rim of 100 units (meters) to the west, and 50 units to the east, and a river meandering from north to south through a valley to the exit at a level of 0 units. The digital elevation model (DEM) was produced from digitized contours by the contours interpolation module of Idrisi, refined by mean and median filtering. An area is scetched in the DEM, where different landuses will be simulated, later.

Simple demonstration Digital Elevation Model

Picture 1: DEM model

From the DEM, slope and ascpect are derived. Idrise offers a module "VARCOST", that calculates the least time it will take to reach each pixel in the DEM from a set of target pixels. In this case, one target pixel at the south exit of the valley is set. In addition to distance, slope, and aspect, an isotropic friction is assumed, to move from one pixel to another. On land, the friction is set to an arbitrary value of  2. The riverbed, where water flows much faster, is set to a value of 0.1.

As the most simple case, a uniform precipitation for the duration of 1 time unit is assumed. In relative time units from 0 = the target pixel, to 46 = the most remote pixel in the northeast corner, VARCOST yields picture 2

Animated GIF of time, when water arrives at valley exit

Picture 2: animation in 3D-view of arrival of the water flow, displayed in steps of 5 time units

The area delineated in picture 1 was overlayed to the isotropic friction image, that either an urban surface with a roughness of 1, or a forested surface with a roughness of 3 replaced the general value of 2. Pictures 3 and 4, and picture 5, show the results.

water from the western slope with an urban area arrives earlier

Picture 3: water from the western slope with an urban area arrives earlier

water from the western slope with a forest area arrives later

Picture 4: water from the western slope with a forest area arrives later

diagram of frequency of pixels per time unit arriving at exit of catchment, 3 landuse scenarios

Picture 5: diagram of frequency of pixels per time unit arriving at exit of catchment,
3 landuse scenarios
yellow line =  homogenous
red line =  urban area on the western valley slope
blue-green = forest area on the western valley slope

Compared to a homogenous landuse, from an urban area more water arrives at one time at the exit, while with a forested area the peak flow is lowered and distributed to later time units.

The upper part of the Elbe catchment, the Bohemian Basin, was chosen to apply the idea to the real world. The US Geological Survey provides DEM and landuse maps, derived from satellite imagery, for all parts of the world. The river net was taken from ESRI.

3D-DEM cut from USGS world dem, 1km2 grid

Picture 6: The original DEM from USGS was imported to Idrisi, and the Elbe catchment cut like a cookie. Geografic projection is set by USGS to Lamber Azimuthal Equal Area, with a center at 20 East, 55 North. Pixel width measures 1 km, elevation is in meters, from sea level = 0 to the highest of 1457 m. Actually, the Riesengebirge (Giant Mountains, south-east corner, source of the Elbe, Czech: Labe) peak at 1600 m, however, in a coarse grid, accuracy of elevation is limited. In the Bohemian bowl,  the Elbe is joined by Moldau/Vltava and Eger/Ohre, breaks through the northern rim, and after passing the North German Lowlands, discharges into the North Sea.

USGS Land Use/Land cover system

Picture 7: Landuse derived from satellite imagery, according to USGS Land Use/Land Cover System; dominant landuse is cropland/pasture, followed by forests.

A flow calculation by the varcost-function was done for the Bohemian Basin, where frictions were assigned to landuse in this arbitrary scheme: 

friction Frequency=km2 landuse
0.1 1291 riverbed
1.0 471 urban
2.0 33153 Cropland/Pasture
3.0 2797 Cropland/Grassland Mosaic
4.0 1 Grassland
5.0 683 Cropland/Woodland Mosaic
7.0 56 Shrubland
8.0 12159 Forest
Along the major riverbeds, water from these pixels readily arrive at the target = exit at the break through the north rim, while from the western Eger valley, with a high share of forest area, time consumption is highest.

Simulation of flow from Bohemian basin, function of DEM and landuse, arbitrary units

Picture 8a: time consumption (relative units)  for each pixel in the Bohemian watershed, to reach the exit pixel, as a function of slope and aspect (from DEM), and friction (from landuse)

Histogramm of flow simulation from Bohemian basin

Picture 8b: corresponding histogram of flow from the Bohemian watershed

The calculations, so far, yield flow-curves qualitatively similar to measured flood levels, but they are not meant to make realistic predictions. However, any model, any computer software, would start with basic parameters, a DEM, the river net, and a landuse map. The capacity of soil, to subtract trickle water from the surface flow, has to be added. The accuracy of the maps has to be improved, and real friction factors have to replace those chosen arbitrarily, here. Precipitation scenarios that vary in time and space should be introduced (in Idrisi this can be done by crosstabulation). The simulation has to be calibrated.

In the middle of that month of August 2002, the Bohemian bowl was covered by extreme precipitation. From Prague, over Dresden, far down the Elbe valley the flood wave innundated numerous cities and villages. The water level curves are compiled from data provided by the German federal institute of hydrology (Bundesanstalt für Gewässerkunde). The data are not complete on the internet.

Water levels August 2002, data from Bundesanstalt f. Gewaesserkunde

Picture 9: Water levels of the Elbe flood in August 2002, German part from Czech border (Schoena) to Darchau, few kilometers upstream Hamburg.

Schoena, located on the Czech-German border, was hit by the highest water level on August 16. The historic downtown of Dresden was innundated one day later. On its way downstream Torgau, Wittenberg, Magdeburg, and Darchau, the flood wave flattened and became broader. At Hamburg, the flood volume dissipated into the branched harbour area and the broad estuary, and did no harm.

One experience from the desastrous flood in August 2002 is, that reliable and fast predictions are needed. No one could tell, when and where how much water would arrive in the flood plain, and if the capacity of the flood plain would be exceeded. Second, a flow model is needed for planning, to prevent rapid and steep accumulation of flow. Forested areas as buffer zones should be increased, urbanisation avoided at risk sites, rivers and creeks no longer channelized, but their natural "roughness" and length restored.

Klaus Baumgardt


Download simulation model Idrisi-files

zum Inhaltsverzeichnis- Index Environmental Atlas Hamburg



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