Chapter 8: Modeling Physical Systems

FIGURES

Figure 8.1. Modeling steady state surface water depth h (shown as 200x exaggerated surface) in terrain with depressions and uniform soil and cover conditions: a) input 10m resolution DEM; b) h as a function of upslope contributing area computed by D8 algorithm: artificial flow pattern on hillslopes, geometrical flow through depressions (r.watershed in GRASS5); c) h as a function of upslope contributing area computed by vector-grid algorithm: depressions act as a sinks, (Mitasova et al. 1996, r.flow in GRASS5); d) 2D kinematic wave solution of continuity equation: water accumulates in depressions to infinity (SIMWE with diffussion->0); e) 2D approximate diffusive wave solution: water fills depressions creating ponds with subsequent outflow (SIMWE); f) 2D approximate diffusive wave solution with a channel with predefined gradient in one of the depressions: water flows rapidly through the depression (SIMWE). The SIMWE model is described by Mitas and Mitasova (1998).

BW version of Figure 8.1.

Figure 8.2. Path sampling method for solution of partial differential equations.

Figure 8.3 Land use and net erosion/deposition pattern computed by USPED (Mitasova and Mitas, 1999) using general GIS (GRASS5).

Figure 8.4 Snapshots from a 2D dynamic model of water depth distribution in a relatively flat field (0.8x1.5km) during steady uniform rainfall: a) 3 minutes, b) 15 minutes, c) 1 hour, d) 8 hours after the rainfall. Water depth, represented by color, is draped over exagerrated DEM. Time is approximate, modeling was performed by SIMWE.

BW version of Figure 8.4.

FIGURE 8.5 Modeling of water depth, sediment flow and net erosion/deposition for different land use designs using SIMWE. Land use without conservation measures: a) low water depth due to fast runoff; b) potential for gullies in areas of concentrated water flow. Land use with extended grasss cover including a grassway: c) increased water depth in grass covered areas; d) deposition in grassway with erosion along its edges. Sediment flow is represented as a surface with erosion/deposition draped over it as color.

Figure 8.6 Modeling surface water flow on a section of the Mississippi river. Surface-water Modeling System (SMS) was used to predict flow by the finite element two-dimensional hydrodynamic flow simulation program FESWMS http://www.ems-i.com/sms/ , 3D visualization of terrain model, land use and the river was done in GRASS5 using NVIZ tool. Figures courtesy Mingshi Chen, William M. Brown, RiverWeb Museum Consortium http://www.ncsa.uiuc.edu/Cyberia/RiverWeb/Projects/RWMuseum/

BW version of Figure 8.6.


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