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r.sim.water
r.sim.water is a landscape scale, simulation model of overland flow designed for spatially variable terrain, soil, cover and rainfall excess conditions. A 2D shallow water flow is described by the bivariate form of Saint Venant equations. The numerical solution is based on the concept of duality between the field and particle representation of the modeled quantity. Green’s function Monte Carlo method, used to solve the equation, provides robustness necessary for spatially variable conditions and high resolutions (Mitas and Mitasova 1998). The key inputs of the model include elevation (elevin raster file), flow gradient vector given by first-order partial derivatives of elevation field (dxin and dyin raster files), rainfall excess rate (rain raster file) and a surface roughness coefficient given by Manning’s n (manin raster file). Partial derivatives raster files can be computed along with the interpolation of a DEM using the -d option in v.surf.rst module. If elevation raster is already provided, partial derivatives can be computed using r.slope.aspect module. Partial derivatives determine the direction and magnitude of water flow. Partial derivatives computed from terrain can be modified to include pre-defined water flow (e.g. channels).
The module automatically converts data from feet to metric system using database/projection information. Rainfall excess is defined as rainfall intensity - infiltration rate. Rainfall intensities are usually available from meteorological stations. Infiltration rate depends on soil properties and land cover. It varies in space and time. For saturated soil and steady-state water flow it can be estimated using saturated hydraulic conductivity rates based on field measurements or using reference values which can be found in literature.
Output includes water depth raster file depth in [m], water discharge raster file disch in [m3/s]. Error of the numerical solution can be analyzed using err raster file (the resulting water depth is an average, and err is its RMSE). Output site file outwalk can be used to analyze and visualize spatial distribution of walkers at different simulation times (note that the resulting water depth is based on the density of these walkers). Number of theese output walkers is controled by density parameter, which says how many walkers used in simalution should be used in the output Duration of simulation is controled by niter parameter. The default value is 1000 iterations, to reach the steady-state may require, depending on the time step, complexity of terrain and land cover and size of the area, several thousand iterations. Output files can be saved during simulation using outiter parameter defining the time step for writing output files. This option requires the time series flag -t. Files are saved with suffix containing iteration number (e.g. name.500, name.1000, etc.).
Overland flow is routed based on partial derivatives of elevation field or other landscape features influencing water flow. Simulation equations include a diffusion term (diffc parameter) which enables water flow to overcome elevation depressions or obstacles when water depth exceeds a threshold water depth value (hmax). When it is reached, diffusion term increases as given by halpha and advection term (direction of flow) is given as "prevailing" direction of flow computed as average of flow directions from the previous hbetanumber of grid cells.
A 2D shallow water flow is described by the bivariate form of Saint Venant equations (e.g., Julien et al., 1995). The continuity of water flow relation is coupled with the momentum conservation equation and for a shallow water overland flow, the hydraulic radius is approximated by the normal flow depth. The system of equations is closed using the Manning’s relation. Model assumes that the flow is close to the kinematic wave approximation, but we include a diffusion-like term to incorporate the impact of diffusive wave effects. Such an incorporation of diffusion in the water flow simulation is not new and a similar term has been obtained in derivations of diffusion-advection equations for overland flow, e.g., by Lettenmeier and Wood, (1992). In our reformulation, we simplify the diffusion coefficient to a constant and we use a modified diffusion term. The diffusion constant which we have used is rather small (approximately one order of magnitude smaller than the reciprocal Manning’s coefficient) and therefore the resulting flow is close to the kinematic regime. However, the diffusion term improves the kinematic solution, by overcoming small shallow pits common in digital elevation models (DEM) and by smoothing out the flow over slope discontinuities or abrupt changes in Manning’s coefficient (e.g., due to a road, or other anthropogenic changes in elevations or cover).
Green’s function stochastic method of solution. The Saint Venant equations are solved by a stochastic method called Monte Carlo (very similar to Monte Carlo methods in computational fluid dynamics or to quantum Monte Carlo approaches for solving the Schrodinger equation (Schmidt and Ceperley, 1992, Hammond et al., 1994; Mitas, 1996)). It is assumed that these equations are a representation of stochastic processes with diffusion and drift components (Fokker-Planck equations). The Monte Carlo technique has several unique advantages which are becoming even more important due to new developments in computer technology. Perhaps one of the most significant Monte Carlo properties is robustness which enables us to solve the equations for complex cases, such as discontinuities in the coefficients of differential operators (in our case, abrupt slope or cover changes, etc). Also, rough solutions can be estimated rather quickly, which allows us to carry out preliminary quantitative studies or to rapidly extract qualitative trends by parameter scans. In addition, the stochastic methods are tailored to the new generation of computers as they provide scalability from a single workstation to large parallel machines due to the independence of sampling points. Therefore, the methods are useful both for everyday exploratory work using a desktop computer and for large, cutting-edge applications using high performance computing.
v.surf.rst r.slope.aspect r.sim.sediment
Helena Mitasova, Lubos Mitas
North Carolina State University
hmitaso AT unity DOT ncsu DOT edu
Jaroslav Hofierka
GeoModel, s.r.o. Bratislava, Slovakia
hofierka AT geomodel DOT sk
Chris Thaxton
North Carolina State University
csthaxto AT unity DOT ncsu DOT edu
csthaxto AT unity DOT ncsu DOT edu
Mitasova, H., Thaxton, C., Hofierka, J., McLaughlin, R., Moore, A., Mitas L., 2004, Path sampling method for modeling overland water flow, sediment transport and short term terrain evolution in Open Source GIS. In: C.T. Miller, M.W. Farthing, V.G. Gray, G.F. Pinder eds., Computational Methods in Water Resources, Elsevier.
Mitasova H, Mitas, L., 2000, Modeling spatial processes in multiscale framework: exploring duality between particles and fields, plenary talk at GIScience2000 conference, Savannah, GA.
Mitas, L., and Mitasova, H., 1998, Distributed soil erosion simulation for effective erosion prevention. Water Resources Research, 34(3), 505-516.
Mitasova, H., Mitas, L., 2001, Multiscale soil erosion simulations for land use management, In: Landscape erosion and landscape evolution modeling, Harmon R. and Doe W. eds., Kluwer Academic/Plenum Publishers, pp. 321-347.
Neteler, M. and Mitasova, H., 2004, Open Source GIS: A GRASS GIS Approach, Second Edition, Kluwer International Series in Engineering and Computer Science, 773, Kluwer Academic Press / Springer, Boston, Dordrecht, 424 pages.
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