Jorge A. Ramirez (ed.), Proceedings of the Twenty-Second Annual American Geophysical Union Hydrology Days. April 1-4, 2002. Colorado State University, Fort Collins, CO 80523-1372, USA: 98-109.

GIS based distributed modeling for flood estimation

Seifu Gebremeskel∗, Yong Bo Liu, Florimond De Smedt Department of Hydrology and Hydraulic Engineering, Free University Brussels, Belgium. Laurent Pfister Centre de Recherche Public - Gabriel Lippmann, Grand-Duchy of Luxembourg.

Abstract. This paper presents a flood estimation method by combining geographical information systems with distributed hydrologic modeling. The main focus of the paper is on discussing a flood hydrograph estimation method by using physiographic characteristics and recorded meteorological data. Basin related parameters of the model are derived from a digital elevation model, a land use map and a soil map in raster format. Runoff is generated for each raster cell in relation to rainfall intensity and soil moisture content and is routed along the flow paths by using the diffusive wave approximation. The model is applied to the Alzette basin located in the Grand-duchy of Luxembourg. River discharges are estimated on hourly basis from December 1996 to March 2001 and good agreement is obtained with the measured data.

Key Words: Hydrological modeling, flood prediction, Alzette basin

1. Introduction The devastating floods of 1993 and 1995 in the Rhine and Meuse river

basins of Western Europe have urged the need for hydrologic models that

∗ Department of Hydrology and Hydraulic Engineering Faculty of Applied Sciences Free University Brussels Pleinlaan 2, 1050 Brussels, Belgium. Tel: +32 2 629 3548 Fax: +32 2 629 3022 Email: seifu.gebremeskel@vub.ac.be

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are transposable. In view of a large-scale management of floods, this issue clearly has a high priority. In this paper the model transposablity issue is addressed as: a) the applicability of models from the basin where they are developed and tested to other basins and b) the sensitivity of models to up– and/or downscaling. Because many hydrologic models are developed and tested on specific and small river basins, they often suffer from a lack of transposablity to larger basins. In such cases, models that can accurately describe and simulate the heterogeneity of large-scale river basins, such as the Rhine and the Meuse, are needed. The present day availability of detailed basin characteristics, together with advances in computer hardware and GIS software, allow this kind of studies.

The objective of the paper is to discuss the development and application of a spatially distributed hydrologic model, which is successfully applied to the 67 km2 Barebeek basin in Belgium by De Smedt et al., (2000) to the much larger Alzette basin in Luxembourg.

2. Description of the study area

Figure 1 shows the transnational Alzette river basin extending over 1176 km2 in France, Belgium and Luxembourg. The Alzette originates in France, approximately 4 km south of the French-Luxembourg border and extends downstream towards the city of Ettelbruck for about 65 km. At present, the valley accommodates almost two thirds of the population of Luxembourg as well as important industrial infrastructures. In its upstream part, the Alzette valley is up to 3 km wide before it cuts through a sand stone formation near the city of Luxembourg. In this natural bottleneck, the valley is only 75 to 100 m wide. Downstream of the Luxembourg city, the valley widens again before it reaches a second bottleneck near the city of Mersch.

Figure 2 shows the topographic elevation map of the Alzette basin. The minimum elevation is 195 m and the maximum is 545 m, with an average basin slope of 8.8 %. Figure 3 shows the spatial distribution of the different land uses in the Alzette basin. Forest with 33.7% is the dominant land use type; other land use types are agriculture (23.3%), grassland (30.7%) and urban areas (11.2%). The dominant soil types are clay (37.3%), silt (22.4%), loam (29.7%) and sand (16.6%).

The average annual precipitation of the Alzette basin varies between 800 mm to 1000 mm. In the western part of the basin the annual variability of the rainfall is characterized by distinctive winter and summer seasons. For this part of the basin, the highest monthly rainfall is 100 mm recorded during the months of December, January and February, while the lowest 70 mm rainfall is recorded during the months of April, August and September. Towards the eastern border, this seasonal rainfall distribution pattern is much less pronounced. The monthly potential evapotranspiration values in the basin vary from 13.5 mm in winter to 81.8 mm in mid summer.

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#

#

#

#

#

#

#

#

#G

ermany

Belg

ium

France

Wiltz

Mersch

Remich

Redange

Clervaux

Ettelbruck

Echternach

Esch/Alzette

Luxembourg-city

N

EW

S

0 20km

Luxembourg boundary

main riversAlzette boundary

Figure 1. Location of the Alzette basin.

N

EW

S

0 1

Elevation (m)150 - 200200 - 250250 - 300300 - 350350 - 400400 - 450450 - 500500 - 550550 - 600

0 km

Figure 2. Topography of the Alzette basin.

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N

EW

S

0 1

cropsgrasslandforesturban areassurface watermining areas

0 km

Figure 3. Land use map of the Alzette basin.

3. The WetSpa model

he WetSpa model is a grid-based distributed hydrologic model for wate

s follows:

S = CP (θ/θs) (1)

where, excess rainfall or surface runoff (mm)

m) 3 m-3)

Tr and energy transfer between soil, plants and atmosphere. The model

is originally developed by Wang et al., (1996) and adopted for flood prediction by De Smedt et al., (2000). The hydrologic processes considered in the model are precipitation, interception, evapotranspiration, excess rainfall, soil moisture storage, interflow, percolation, groundwater storage and discharge. The main outputs of the model are river flow hydrographs and spatially distributed hydrologic characteristics.

Surface runoff for each raster cell is calculated a

S =C = runoff coefficient P = net precipitation (mθ = soil moisture content (mθs = saturated soil moisture (m3 m-3)

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The surface runoff that is generated according to Eq. 1 is routed from a single cell to the outlet by using the diffusive waveform of the St. Venant equation, which is described in Eq. 2. This equation is used in the model to simulate both overland flow and channel flow.

xQc

xQD

tQ

2

2

∂∂

−∂∂

=∂∂ (2)

whe

discharge (m s ) ow path (m)

ity of the wave (m s )

oth the wave celerity c and dissipation coefficient D depend upon the flow

re,

3 -1Q =x = distance along the flt = time (s)

-1c = the celerD = dissipation coefficient (m2 s-1) B velocity, flow depth and terrain characteristics. If the flow velocity v

(m s-1) is computed with the Manning equation

2132 sRn1v //= (3)

where, hydraulic radius (m)

hness coefficient (m-1/3 s)

the celerity of the diffusion wave c is given as:

R =s = slope (m m-1) n = Manning roug

v23c = (4)

and the dispersion coefficient D is

s3

cRs2

vRD == (5)

it is assumed that the hydraulic radius is a static terrain characteristic that

Ifdoes not change during a flood event, it follows from Eq. 4 and Eq. 5

that c and D only depend upon position. In this case, an approximate solution of Eq. 2 relating the discharge at the end of a flow path to the available runoff at the start is given as follows (De Smedt et al., 2000):

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⎥⎦

⎤⎢⎣

⎡σ

−−

πσ+

≈0

2

2o

o

o

tt2tt

tt2t2ttVtQ

/)(exp

/)( (6)

where, the volume of surface runoff per cell (m3) calculated as S(∆x)2,

avel from any point to the

V =with ∆x the grid size (m) t = the total time required by the wave to trooutlet along the topographically derived flow path and given as

∑∫=

∆≈=

n

1i io c

xcdxt (7)

where, = is the number of grid cells along the flow path

And is the deviation of the flow time

n σ

xcD2dx

cD2 n

1i3i

i3 ∆≈=σ ∑∫

=

(8)

herefore, the flow routing consists of tracking the flow from a cell to

the o

4. Model Application

o illustrate the ability to predict the evolution of the flood hydr

Tutlet along the flow path with Eq. 6, and the total response is obtained

by convolution of the flow response from all grid cells. The advantage of this approach is that the response functions can be obtained using standard GIS techniques. First maps are produced of c and D with Eq. 4 and Eq. 5. Next, the contributing area is determined from topographic data for a particular downstream convergence point, and for each contributing grid cells the values of t0 and σ are calculated by using ARC/INFO’s FLOWLENGTH routine according to Eq. 7 and Eq. 8. The interflow and groundwater contribution to the discharge are taken into account by the method of linear reservoirs (Liu, 1999). Finally, the total river discharge at the downstream convergence point is obtained by superimposing the surface runoff, interflow, and groundwater flow from every grid cell.

Tographs, the model is applied to the Alzette basin. The simulation

period ranges from December 1996 to March 2001, using hourly time steps. First, all parameters of the model that are related to the basin are derived from a combination of a digital elevation model, a soil map and a land use map. From the 50 by 50 m pixel resolution digital elevation model of the basin, the flow direction, flow accumulation and the sub basins are delineated.

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N

EW

S

0 1

Velocity (m/s)0 - 0.010.01 - 0.020.02 - 0.030.03 - 0.040.04 - 0.20.2 - 1> 1

0 km

Figure 4. Runoff velocity map of the Alzette basin.

The Manning coefficients, maximum interception storages and root depth parameters are derived from the land use map. The Manning roughness grid is created using a three-stage process: first the Manning coefficient for the overland flow is derived from the land use grid reclassified with a lookup table that relates the roughness coefficient to the land use types; second, the Manning coefficient for river channels is constructed by assigning a constant value of 0.04 m-1/3s to all stream orders; third, the Manning coefficient map of the basin is constructed by merging the two grids. In the same way as the Manning coefficient, the hydraulic radius map of the basin is constructed for overland flow and channel flow. The hydraulic radius of channel flow is derived from the stream order, where it is assumed that the hydraulic radius varies depending on the order of a stream, i.e. lower orders have the lowest hydraulic radius and higher orders the highest hydraulic radius. The hydraulic radius for overland flow is assigned 5 mm. Figure 4 shows the velocity map of the Alzette basin with Eq. 3 constructed using the hydraulic radius grid, together with the slope and Manning coefficient grids.

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N

EW

S

0 1

Flow time (h)0 - 22 - 44 - 66 - 88 - 1010 - 1212 - 1414 - 16> 16

0 km

Figure 5. Travel time to the basin outlet.

N

EW

S

0 1

Runoff coefficients0 - 0.1

0.1 - 0.2

0.2 - 0.3

0.3 - 0.4

0.4 - 0.5

0.5 - 0.6

> 0.6

0 km

Figure 6. Distribution of runoff coefficients.

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Once the boundary of the basin is delineated, the downstream flow length from any cell to the outlet along the flow path is computed using the ARC/INFO FLOWLENGTH routine. The travel time is derived in the same way as the flow length, but using the reciprocal of the flow celerity as the flow resistance in each cell. Figure 5 shows the resulting travel time to the main outlet of the Alzette basin. Next, the runoff coefficient grid is created from the slope, land use and soil grids using values collected and compiled from literature (Dunne, 1978; Chow et al., 1988; Browne, 1990; and Mallants & Feyen, 1990). Figure 6 shows the resulting potential runoff coefficient of the Alzette basin. As can be seen in Figure 6, the values of the runoff coefficient are highest in the urban areas.

0

50

100

150

200

250

300

01/0

1/98

11/0

2/98

25/0

3/98

06/0

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16/0

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28/0

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1/00

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3/00

Q (m

3 /s)

0

10

20

30

40

50

P (m

m/h

)

simulated observed rainfall

Figure 7. Observed vs. simulated stream flows at the basin outlet. Finally, the WetSpa model is run using observed rainfall and potential

evapotranspiration time series together with physiogaphic parameters. Figure 7 shows the resulting time series plot of observed versus simulated stream flows for a selected period at the Ettelbruck stream gauge station. Figure 8 shows observed versus simulated stream flows in more detail for a rainfall event that occurred in February 1997. The maximum recorded rainfall intensity during this period is 4.8 mm/h, the maximum observed stream flow is 190 m3 s-1 and the maximum simulated peak flow is 188 m3

s-1. As can be seen in Figure 8, this storm is preceded by another storm. However, the previous storm did not lead to large flooding as it only saturated the soils, such that the second storm yielded large flood peaks and flood volumes in the river basin.

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0

50

100

150

200

250

17/0

2/97

19/0

2/97

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2/97

23/0

2/97

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14/0

3/97

Q (m

3 /s)

0

2

4

6

8

10

12

P (m

m/h

)

Rainfall Observed Simulated

Figure 8. Observed vs. simulated peak flood for a storm event.

Scatter plots of observed versus simulated peak discharges for twenty

different storm events that occurred during the simulation period are given in Figure 9. As can be seen in the figure, high floods are reproduced fairly although somewhat underestimated by the model.

0

40

80

120

160

200

240

0 40 80 120 160 200 240

Simulated (m3/s)

Obs

erve

d (m

3 /s)

Figure 9. Observed vs. simulated peak flows.

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Different hydrology model evaluation criteria are applied to the results from the Alzette basin to assess the performance of the model. These criteria are a) the ability to reproduce the water balance b) the ability to reproduce the time evolution of all discharges c) the ability to reproduce the time evolution of low discharges and d) the ability to reproduce the time evolution of high discharges. The WetSpa model is able to reproduce the observed water balance with 3.1% overestimation. The model efficiency for reproducing the river discharges is 74%. The ability of the model to reproduce low flows is 71%, but the for floods this is 86%, which proves that the model is very well suited for flood estimation.

5. Conclusions

In this paper an attempt is made to outline a method of estimating flood runoff in the Alzette basin by using detailed basin characteristics together with meteorological data as an input to the WetSpa spatially distributed model. To avoid the complexity inherent in estimating surface runoff, a simple but effective approach is presented where the whole basin is divided into grid cells, giving the possibility to simulate the hydrologic processes at a reasonably small scale. The fact that the WetSpa model parameters are derived from known basin characteristics, gives the advantage that long time stream flows can be simulated without model calibrations. In view of model transposability in large river basins as the Rhine and Meuse, such approaches could be useful. Acknowledgements. This research is partly financed by the European Interreg Rhine-Meuse Activities (IRMA) and managed by the Netherlands Center for River Studies (NCR). More detailed information about the program and other relevant issues can be found at the following website: http://www.irma-sponge.org

References Browne, F. X., 1990: Stormwater management. In: Standard Handbook of

Environmental Engineering (ed. by R. A. Corbitt), McGraw-Hill, New York, USA, 7.1-7.135.

Chow, V. T., Maidment, D. R. and Mays, L. W., 1988: Applied Hydrology. McGraw Hill Inc., New York, USA.

De Smedt, F., Yongbo, L., and Gebremeskel, S., 2000: Hydrologic modeling on a catchment scale using GIS and remote sensed land use information. In: Risk Analysis II (ed. by C. A. Brebbia), WTI press, Southampton, Boston, 295-304.

Dunne, T., 1978: Field studies of hillslope flow processes. In: Hillslope Hydrology (ed. by M. J. Kirkby). John Willey & Sons.

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Liu, Y. B., 1999: A GIS-based spatially distributed hydrological modelling of the Barebeek catchment. M.Sc. Thesis, Inter-University Programme in Water Resources Engineering, Katholieke Universiteit Leuven and Vrije Universiteit Brussel, Belgium.

Mallants D. and Feyen, J., 1990: Kwantitatieve en kwalitatieve aspecten van oppervlakte en grondwaterstroming (Quantitative and qualitative aspects of surface and groundwater flow) in Dutch, Volume 2., KUL, Leuven, Belgium.

Wang Z., Batelaan, O. and De Smedt, F., 1996: A distributed model for Water and Energy Transfer between Soil, Plants and Atmosphere (WetSpa). Phys. Chem. Earth, 21(3), 189-193.