URBAN FLOOD MODELING Simulation of flood in a dense urban area using 2D Shallow water equations

2 Flood Event City: Southern French city of Nimes Event : 03 Oct 1988 Cause: Downpour of 420 mm in 8 hours Return period: years Depths observed: 3 m

3 Modeled Zone Suburban area:‘Richelieu’ Dimensions: 1400 m along N-S, m along E-W Boundaries: Northern and eastern side by railway embankment, western by hills Building type: Military barracks, hospital, regular network of narrow streets Long. slope: >1% Flood cause:Storm runoff

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5 Data for Model Development X-sections : 200 of 60 streets Typical profile : 11 points Flood marks : Map and 99 marls Hydrograph : Rainfall-Runoff transformation No. of hydrographs : Two, east and west Sewage network : Decoupled; interaction capacity<10% Qmax

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8 Mesh Generation Junction profiles: Generated, linear interpolation on altitude Buildings:Impermeable DEM: pts

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10 Reference Calculation Dx streets: 25 m Mesh density: 100 cells at crossroads, in each street Manning’s ‘n’ and  and 0.1 m2/s Time step: 0.01 sec Simulation time: 10 hrs Outflow b.c: Fr=1 Initial condition: dry bed

11 Flood Progression High velocity (3-4 m/s) and supercritical flow on streets aligned along N-S axis. Small velocities( m/s) and subcritical flow occurs in streets aligned along E-W axis. The time to peak in streets correspond with time to peak of the eastern hydrograph. Flow at crossroads is generally complex with mixed flow regime.

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13 Comparison Parameter

14 Comparison with Observations Flooded zone extent correctly simulated. Measurement with peak values of depth. About 40% overestimated and 60% underestimated. The max. difference is 1.6 m and the average difference is 0.41 m Good agreement in the northern zone Strong underestimated in the narrow streets (43 cm) Slight overestimation in the southern part (16 cm)

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17 Sensitivity Tests 1: Inflow and Storage Effects 1A: Inflow increased by 20% To check hydrological uncertainties. Depths increase by 12.5 cm Higher increase in the upstream zone than in the downstream and the southern part.

18 Sensitivity Tests 1: Inflow and Storage Effects 1B: Rainfall vol. taken into account Rainfall (61 mm/hr) falling over the simulated zone added to the inflow hydrographs The rainfall vol. (212,000 cu.m) is very small compared to the flood hydrographs (3600,000 cu.m) Limited effect. Peak water depths increased by about 4 cm.

19 Sensitivity Tests 1: Inflow and Storage Effects 1C: Creation of a Storage Zone Reference case computation assumed watertight buildings with no storage in lawns, parks, basements etc. The military barracks (l’ecole d’artillerie aerienne) are the largest open space. Volume stored is about 80,000 cu.m. A very small reduction of peak water depths at d/s is observed (about 1 cm)

20 Sensitivity Tests 2: Roughness and Kinematic Viscosity Coefficients 2A: Effect of Kin. Viscosity  represents turbulence and the heterogeneity over the vertical.  =khu*, k=0.01, k=0.1 m2/s. Small to no effect on computed depths.

21 Sensitivity Tests 2: Roughness and Kinematic Viscosity Coefficients 2B: Effect of Manning’s ‘n’ ‘n’ represents the effect of friction on the bottom, walls, irregularities, obstacles to flow. n increased to from Depths overall increase by 10 cm. Depth increased at Faita-Sully junction thus decreasing the discharge in the d/s sections. Flow regime strongly altered at crossroads and changes from supercritical to subcritical (fig).

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23 Underestimation decreased in the central zone, overestimated depths in the northern zone and in the southern zone. Globally the depths increase and improve but locally there is worsening.

24 Sensitivity Tests 2: Roughness and Kinematic Viscosity Coefficients 2C: Different Manning’s ‘n’ n=0.05 selected for the central part comprising of narrow streets meeting at right angle to each other. This accounts for increased friction due to walls and presence of parked cars. Elsewhere n is same as that of reference calculation Results improved significantly in the central zone where dh reduced to 23 cm from 43 cm.

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26 Sensitivity Tests 3: Downstream Boundary Conditions 3A: Zero depth gradient boundary The d/s b.c is changed to a zero depth gradient condition for subcritical flow and no d/s influence for supercritical flow. Depth increases in the streets in the vicinity of the d/s boundary

27 Sensitivity Tests 3: Downstream Boundary Conditions 3B: Representation of backwater effect To simulate backwater effect of the outlying areas upon the modeled zone, flow prevented from leaving through S1, S2 and S10. Flow strongly affected in the whole southern zone and flow depths increase as far up as the southern part of the central zone

28 Whereas the choice of b,c affects the flow only in the close vicinity of the exit the choice of exit has a far greater influence in the upstream zone extending upto four streets backwards.

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30 Sensitivity Tests 4: Simplification of the Street Profile 3B: 4 point, 5 point and 7 point profiles To reduce the data requirement and calculation times For 11, 7, 5, 4 points cells at the junction are 64, 16, 4 and 1 respectively. The general form of the results remains same except that depths are increased by about 10 cm.

31 The 7 and 11 point calculation results are very similar In 5 and 4 point versions of the calculations flow detail at a junction is averaged out e.g if a flow at a junction is mainly subcritical with a small supercritical area. The model calculates an average subcritical flow depth.

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33 RESULTS SUMMARY

34 Conclusions 2D Shallow water equations in complete form were used, without interaction with sewage network to model urban flood. The results showed a standard deviation of 50 cm which is on the higher side but reflects the uncertainty in flood marks, insufficient topographical data, missing information about mobile obstructions, wall irregularities etc.

35 Kinematic viscosity seems to exercise negligible to no influence on he results. Manning,s ‘n’ strongly affects the flow but no single value can be determined to correctly represent all the zones. Assigning each zone an ‘n’ reflecting its structural characteristics seems to be the best strategy.

36 Recommendations The input hydrographs should be precisely calculated for an accurate peak water depth map creation. If the rainfall volume is small compared to the input hydrograph volume than there effect is going to be negligible and can be neglected. If the storage volume is small compared to the input hydrograph volume they can be safely neglected.

37 Different friction coefficients should be applied to various homogeneous urban zones, depending on the width of the streets and fixed and mobile obstacles that may increase the resistance to flow. Collecting information about the flooded areas just downstream from the studied zone is important in establishing an accurate outflow boundary condition.

38 A 5 point representation for a street profile can represent a fairly good estimate for the general overview of the flood dynamics reducing data needed and calculation times However, if information about local depths is available than a more precise description of the streets is required to calibrate the model. Use of a 2d code to assess the flood progression through an urban zone is a convenient tool for hydraulic engineers and urban planners.