1. Fritz R. Fiedler University of Idaho Department of Civil Engineering Simulation of Shallow Discontinuous Flow over Complex Infiltrating Terrain

2. What is shallow discontinuous flow?  Shallow: depth << wavelength o vertical acceleration negligible o depth-averaged NS equations  Discontinuous: both dry and wet areas o shocks o topographic control o infiltration variability

3. What is complex terrain?  Topography with characteristic length scales (amplitude and wavelength) similar to flow depth o two-dimensional flow

4. Examples  Flooding o inundation mapping o dam breaks  Overland Flow o hydraulics o hydrologic response  Wetlands and Estuaries, and Tidal Flats

5. Physical Objectives  Determine how Dynamic Surface Interactions affect Hydrologic Response  Evaluate the Effects of Grazing – degenerates plant community changes infiltration changes microtopography

6. Study Area Description  Central Plains Experimental Rangeland  Light- and heavy-grazed enclosures  1/2-hour, 100-year rain: ~100 mm/hr 1-hour, 100-year rain: ~75 mm/hr  Patchy vegetation

7. CPER

8. Outline  Field Measurements  Mathematical Model  Results

9. Infiltration Measurements  Disc infiltrometers  Light- and heavy-grazed areas  Bare and vegetated

10. Infiltration Variability  High K vegetated (locally high elevation)  Low K bare (locally low elevation)

11. Microtopography The ground surface topography with approximately the same order amplitude and frequency as the overland flow depth in a given situation: –related to rainfall intensity –related to infiltration characteristics –caused by vegetation growth

12. Ground Microtopography

13. Shaded Relief Map

14. Mathematical Modeling  Infiltration spatial variability (G-A model)  Microtopography (2-D dynamic equations)  Uniform rainfall  Simplified flow resistance

15. Surface Water Equations

16. Numerical Challenges  Non-linear hyperbolic system  Strong source terms (sometimes “stiff”)  Small depths / dry areas (discontinuous)  Large gradients in dependent variables

17. Vector Form

19. Basic MacCormack Scheme Lx1 Operator :

20. Friction Slope: Point-Implicit Treatment

21. Convective Acceleration Upwinding

22. Smoothing Function

23. Lateral Inflow

24. ponded:

25. not ponded:

26. High-performance computing  Fortran  Loop optimizations o most dependencies eliminated o unrolling, fusion o single-stride memory access  Shared-memory parallel processing o PC environment

27. Comparative Numerical Examples  Steady state kinematic wave solution (analytical)  Dam break problem (analytical)  Published results  Iwagaki, 1955 (experimental)  Woolhiser et al., 1996 (characteristics- based)

28. Dam Break Problem

29. Microtopographic Surface

30. Overland Flow Depths

31. Flow Depths and Velocity

32. Spatial Distribution of Infiltration Parameters

33. Flow Channels

34. Overland Flow Depths

35. Cumulative Infiltration

36. Simulated vs. Measured

37. Simulated Grazing Effects

38. Spatial Distribution of Reynolds Number and log(f )

39. Cross-Sectional Mean Reynolds Number vs. Friction Factor

40. Distribution of log(K S )

41. Plane Slope, Variable Ks

42. Mean Depth vs Discharge Variable K S

43. Effect of Microtopographic Amplitude

44. Mean Depth vs Discharge Variable Microtopography

45. Conclusions  Plane approximation gross distortion  Vegetation controls response  Average/effective K not applicable  Interactive infiltration important  Reynolds No. - Friction Factor  K-W assumption

46. Watch Your Step!