Sensitivity Analysis of Spatial Scale and Particle Density on Overland Flow Pattern Accuracy and Computational Demand

Water flows according to the shallow water bivariate continuity equation (mass conservation), incorporating drift and diffusion, which allows the elevation model to remain unmodified (e.g., no sink and fill processing).

Path Sampling Method

Solution of SWF equation incorporates spatially variable flow velocity

Variable rainfall excess (impact of soils and land cover on infiltration),
Topography (slope steepness)
Land cover (Mannings roughness coefficient)

Computational Demands of Overland Flow Modeling?

The accuracy of overland flow simulations using path sampling methods depends heavily on particle density. However, varying particle density and spatial scale can be computationally demanding.

Error is proportional to \(1/\sqrt{N}\) where \(N\) is number of particles.

Why is this a problem?

Restrictive for research and policy development

Emergency management applications require rapid response times

Accuracy depends on particle density

Spatial scale influences particle density required for accurate results

How did we approach this problem?

Software

GRASS GIS v8.5
Geospatial Processing Engine
C and Python APIs
Open Source GPL v3
Parallelized (OpenMP)
SIMWE implemented as GRASS module r.sim.water

Computational Resources

Component	Specification
Laptop	System76 Serval WS
OS Name	Pop!_OS 22.04 LTS
OS Type	64-bit
Memory	64.0 GiB
Processor	13th Gen Intel® Core™ i9-13900HX × 32
Graphics	NVIDIA Corporation / Mesa Intel® Graphics (RPL-S)
Disk Capacity	8.0 TB

Model Parameterization

Spatially Uniform Parameters

Rainfall: 50 \(mm/hr\)

Infiltration Rate: 0 \(mm/hr\)

Manning’s C: 0.1

Temporal Parameters

Time Step: 5 min

Event Duration: 30 min

Resolution and Particle Density

Resolution: [1, 3, 5, 10 ,30]

Particle Density: [0.25, 0.5, 1, 2, 4]

    gs.run_command(
        "r.sim.water",
        elevation=elevation,
        dx=dx,
        dy=dy,
        rain_value=50,  # mm/hr
        infil_value=0.0,  # mm/hr
        man_value=0.1,
        nwalkers=particles,
        niterations=niterations,  # duration (minutes)
        output_step=OUTPUT_STEP,  # minutes
        depth=depth,  # m
        discharge=disch,  # m3/s
        random_seed=random_seed,
        nprocs=30,
        flags="t",
    )

GRASS GIS Python API

Area Ruggedness Scale (ARS)

TRI (Terrain Ruggedness Index): measures the differnce in elevation between cells using a moving window (Riley et al., 1999).
- TRI ran with a 5x5 Neighborhood
Area Ruggedness Scale (ARS): is the mean TRI (Terrain Ruggedness Index) for the entire study area.
- Less Rugged: Low Values
- More Rugged: High Values