The module automatically converts horizontal distances from feet to metric system using
database/projection information. Rainfall excess is defined as rainfall intensity
- infiltration rate and should be provided in [mm/hr].
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.
Optionally, user can provide an overland flow infiltration rate map
infil or a single value infil_val in [mm/hr]
that control the rate of infiltration for the already flowing water, effectively
reducing the flow depth and discharge.
Overland flow can be further controled by permeable check dams or similar type of structures,
the user can provide a map of these structures and their permeability ratio
in the map traps that defines the probability of particles to pass
through the structure (the values will be 0-1).
Output includes a water depth raster map depth in [m],
anda water discharge raster map disch in [m3/s]. Error of the numerical
solution can be analyzed using the err raster map (the resulting water depth is an average,
and err is its RMSE). The output vector points map 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 the output walkers is controled by the density parameter, which controls
how many walkers used in simulation should be written into the output.
Duration of simulation is controled by the niter parameter. The default value
is 10 minutes, reaching the steady-state may require much longer time,
depending on the time step, complexity of terrain, land cover and size of the area.
Output water depth and discharge maps can be saved during simulation using
the time series flag -t and outiter parameter
defining the time step in minutes for writing output files.
Files are saved with a suffix representing time since the start of simulation in seconds
(e.g. wdepth.500, wdepth.1000).
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), given in [m]. 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 hbeta number 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.
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., Proceedings of the XVth International Conference on Computational Methods in Water Resources (CMWR XV), June 13-17 2004, Chapel Hill, NC, USA, Elsevier, pp. 1479-1490.
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., 2008, Open Source GIS: A GRASS GIS Approach. Third Edition. The International Series in Engineering and Computer Science: Volume 773. Springer New York Inc, p. 406.
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