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

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

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

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

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

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

CPER

Outline  Field Measurements  Mathematical Model  Results

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

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

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

Ground Microtopography

Shaded Relief Map

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

Surface Water Equations

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

Vector Form

Basic MacCormack Scheme Lx1 Operator :

Friction Slope: Point-Implicit Treatment

Convective Acceleration Upwinding

Smoothing Function

Lateral Inflow

ponded:

not ponded:

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

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

Dam Break Problem

Microtopographic Surface

Overland Flow Depths

Flow Depths and Velocity

Spatial Distribution of Infiltration Parameters

Flow Channels

Overland Flow Depths

Cumulative Infiltration

Simulated vs. Measured

Simulated Grazing Effects

Spatial Distribution of Reynolds Number and log(f )

Cross-Sectional Mean Reynolds Number vs. Friction Factor

Distribution of log(K S )

Plane Slope, Variable Ks

Mean Depth vs Discharge Variable K S

Effect of Microtopographic Amplitude

Mean Depth vs Discharge Variable Microtopography

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

Watch Your Step!