1. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 1 Yan DingResearch Assistant Professor National Center for Computational Hydroscience and Engineering, The University of Mississippi Mustafa S. AltinakarDirector and Research Professor Jaswant SinghResearch Scientist

2. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 2

3. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 3

4. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 4

5. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 5

6. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 6

7. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 7 Vector of conserved variables Vector of fluxes in x direction Vector of fluxes in y direction Source and sink terms 2D Shallow Water Equations (SWE) in vector notation Friction terms in X, Y direction Bottom elevation terms in X,Y direction R=Rainfall Intensity I=Infiltration Rate

8. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 8 B (nodes) w,u,v (nodes) Front view of the domain h w B Rain R(x,y,t) Infiltration (I)

9. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 9 a = local speed of wave propagation in X direction H= Numerical flux of w, hu, hv in x and y direction

10. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 10 C= Chezy’s coefficient N= manning coefficient

11. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 11

12. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 12 Green and Ampt method parameters L: Depth of the wetting zone η: Porosity Ks: Saturated hydraulic conductivity θ i : Initial moisture content of the soil Δθ : (θ s - θ i ) θ r : Residual moisture content of the soil after thoroughly drained. θ s : Saturated moisture content Ψ =wetting front dry suction head, This method is based on Darcy’s law.93 R(x,y,t) Infiltration variables definition in the Green Ampt method variables θ h0h0 L Saturated zone Z η Δθ θ i Wetting front θe θe θr θr Unsaturated zone Ponded water

13. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 13 Ψ = dry suction head F = total infiltration in time t Discretizing using Euler’s method Green and Ampt Method parameters: Porosity (n), Saturated moisture content (θ s ), wetting front dry suction head (Ψ), hydraulic conductivity (Ks), θ e effective porosity, S e = Effective saturation (0-1)

14. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 14 Gottardi and Venutelli (1993) AWR Domain = 500m X 400m Impervious bottom Slope (x)=0.0005 Slope (y) =0.0 R= 0.33mm/min, constant in time n= 0.02 m -1/3 s ∆x = ∆y = 0.05m. Outlet = cell (1 x 1)

15. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 15 Peugeot et. al. 1997 Niger (South Africa) Total plot area =71.25 m 2 Grid spacing = 0.25m R= Rainfall intensity (temporally varying storm) n= 0.02 m -1/3 s Outlet = downstream side (complete side) Storm simulated =4 Average slope X direction =0.0196 Average slope Y direction =0.064 Rainfall-Runoff Field experiment Surface profile of the experimental field at Niger, West Africa.

16. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 16 Field Experiment strom in Niger (Africa) experimental site Event No. Date Initial soil moisture Total rainfall depth (mm) Max. rainfall intensity (mm/h) Rainfall duration (s) 110 th August 940.10613.075.01520 27 th August 940.10031.0200.02055 325 th August 940.08524.5138.02446 44 th September 94 0.08262.5138.4612581 Green and Ampt parameters for fiele experiments Soil TypeLoamy Sand Manning’s n (s m -1/3 )0.02 Hydraulic Conductivity (cm/h)2.99 Porosity0.437 Effective Porosity0.401 Saturation water content0.296 Wetting front soil suction head (cm)6.13

17. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 17 Comparison of simulated runoff with field observed runoff for storm dated August 10, 1994 (calibration run).

18. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 18 Comparison of simulated runoff with field observed runoff for storm dated August 7, 1994.

19. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 19 Simulated water depth, velocity vectors over the experimental field at 750 seconds for the storm dated August 25, 1994.

20. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 20 Animation of overland flow with velocity vectors for storm 3

21. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 21 Comparison of simulated runoff with field observed runoff for storm dated September 4, 1994

22. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 22 Total area in DEM = 55 Km 2, Watershed area=21.3 Km 2 No. of Cells in the DEM =307 X202, Grid size= 30 meters No. of Rain Gauge Station=31 Solution Method= KP Model Infiltration method = Green and Ampt method. Infiltration parameters =Spatially variable Manning’s = Spatially variable Storm 1 Date =17-18, october-1981 2Date= January 20 th, 21 th, 22 nd and 23 rd, 1982 Rainfall-Runoff modeling at Goodwin Creek Watershed

23. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 23 Rain Gauge Stations Rainfall-Runoff modeling at Goodwin Creek Watershed

24. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 24 Rainfall-Runoff modeling at Goodwin Creek Watershed

25. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 25 Calibrated parameters for Green and Ampt method and Manning’s n for Goodwin creek soils and landuse Land use PastureForestSoybeanCotton Manning ‘s n0.070.110.05 Table 2 Sr. No. Infiltration parameters Soil type Porosity Effective Porosity Dry Suction (cm) Hydraulic Conductivity (cm/h) Effective Saturation 1Calloway0.450.44018.50.450.341 2Collins0.350.33017.350.550.335 3Fallaya0.330.30116.500.630.34 4Grenada0.350.31016.800.490.334 5Gullied land0.550.48616.680.650.336 6Loring0.520.48616.680.650.338 7Memphis0.510.48616.680.650.334 Rainfall-Runoff modeling at Goodwin Creek Watershed

26. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 26 Comparison of simulated and field observed runoff on 17 th and 18 th October 1981 Rainfall-Runoff modeling at Goodwin Creek Watershed

27. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 27 Comparison of simulated and field observed runoff on January 20 th, 21 th, 22 nd and 23 rd, 1982 Rainfall-Runoff modeling at Goodwin Creek Watershed

28. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 28 Rainfall-Runoff modeling at Goodwin Creek Watershed Overland flow depth (m) Wetting front depth (m) Velocity vectors Various maps at 15.9 hours for storm no. 2 in Goodwin creek watershed

29. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 29 Conclusions A 2D numerical model is developed using Kurganov and Petrova 2007 scheme for simulation of flush floods. The scheme is well balanced, robust and positivity preserving. The model is tested against the field level experimental data and found that the simulated results match well with the experimental result for runoff at the outlet of the field. The model is applied in real life case of Goodwin Creek watershed. Spatial and temporal variability of rainfall and spatial variability of soil properties and landuse is incorporated in the model. Two storm events simulated by the model match well with the observations at the watershed outlet

30. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 30 Acknowledgements This research was funded by the Department of Homeland Security-sponsored Southeast Region Research Initiative (SERRI) at the Department of Energy ’ s Oak Ridge National Laboratory, USA.

31. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 31 Flux computations Eq. 1 Eq. 2 Eq. 3

32. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 32 Subtracting B ij from both side of equation 1, and applying Eq. 4 Eq. 4 where

33. The University of MississippiNational Center for Computational Hydroscience and Engineering Rainfall runoff modeling in agricultural watershed using 2D shallow water equations Jaswant Singh, Mustafa S. Altinakar, Yan Ding. 33 Gottardi and Venutelli (1993) AWR Domain = 500m X 400m Impervious bottom Slope (x)=0.0005 Slope (y) =0.0 R= 0.33mm/min, constant in time n= 0.02 m -1/3 s ∆x = ∆y = 0.05m. Outlet = cell (1 x 1)