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### r.sim.water: Overland flow hydrologic simulation using path sampling method (SIMWE)

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r.sim.water- Overland flow hydrologic simulation using path sampling method (SIMWE)## KEYWORDS

raster, flow, hydrology## SYNOPSIS

r.sim.water r.sim.water help r.sim.water[-t]elevin=name dxin=name dyin=name[rain=name] [rain_val=float] [infil=name] [infil_val=float] [manin=name] [manin_val=float] [traps=name] [depth=name] [disch=name] [err=name] [nwalk=integer] [niter=integer] [outiter=integer] [diffc=float] [hmax=float] [halpha=float] [hbeta=float] [--overwrite] [--verbose] [--quiet]Flags: -tTime-series output--overwriteAllow output files to overwrite existing files--verboseVerbose module output--quietQuiet module outputParameters: elevin=nameName of the elevation raster map [m]dxin=nameName of the x-derivatives raster map [m/m]dyin=nameName of the y-derivatives raster map [m/m]rain=nameName of the rainfall excess rate (rain-infilt) raster map [mm/hr]rain_val=floatRainfall excess rate unique value [mm/hr] Default:50 infil=nameName of the runoff infiltration rate raster map [mm/hr]infil_val=floatRunoff infiltration rate unique value [mm/hr] Default:0.0 manin=nameName of the Mannings n raster mapmanin_val=floatMannings n unique value Default:0.1 traps=nameName of the flow controls raster map (permeability ratio 0-1)depth=nameOutput water depth raster map [m]disch=nameOutput water discharge raster map [m3/s]err=nameOutput simulation error raster map [m]nwalk=integerNumber of walkers, default is twice the no. of cellsniter=integerTime used for iterations [minutes] Default:10 outiter=integerTime interval for creating output maps [minutes] Default:2 diffc=floatWater diffusion constant Default:0.8 hmax=floatThreshold water depth [m] (diffusion increases after this water depth is reached) Default:0.3 halpha=floatDiffusion increase constant Default:4.0 hbeta=floatWeighting factor for water flow velocity vector Default:0.5## DESCRIPTION

r.sim.wateris 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 (elevinraster map), flow gradient vector given by first-order partial derivatives of elevation field (dxinanddyinraster maps), rainfall excess rate (rainraster map orrain_valsingle value) and a surface roughness coefficient given by Manning's n (maninraster map ormanin_valsingle value). Partial derivatives raster maps can be computed along with interpolation of a DEM using the -d option in v.surf.rst module. If elevation raster map is already provided, partial derivatives can be computed using r.slope.aspect module. Partial derivatives are used to determine the direction and magnitude of water flow velocity. To include a predefined direction of flow, map algebra can be used to replace terrain-derived partial derivatives with pre-defined partial derivatives in selected grid cells such as man-made channels, ditches or culverts. Equations (2) and (3) from this report can be used to compute partial derivates of the predefined flow using its direction given by aspect and slope. 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 mapinfilor a single valueinfil_valin [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 maptrapsthat defines the probability of particles to pass through the structure (the values will be 0-1). Output includes a water depth raster mapdepthin [m], and a water discharge raster mapdischin [m3/s]. Error of the numerical solution can be analyzed using theerrraster map (the resulting water depth is an average, and err is its RMSE). The output vector points mapoutwalkcan 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 thedensityparameter, which controls how many walkers used in simulation should be written into the output. Duration of simulation is controled by theniterparameter. 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-tandoutiterparameter 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 (diffcparameter) 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 byhalphaand advection term (direction of flow) is given as "prevailing" direction of flow computed as average of flow directions from the previoushbetanumber of grid cells.## NOTES

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.## EXAMPLE

Spearfish region: g.region rast=elevation.10m -p r.slope.aspect elevation=elevation.10m dx=elev_dx dy=elev_dy # synthetic maps r.mapcalc "rain = if(elevation.10m, 5.0, null())" r.mapcalc "manning = if(elevation.10m, 0.05, null())" r.mapcalc "infilt = if(elevation.10m, 0.0, null())" # simulate r.sim.water elevin=elevation.10m dxin=elev_dx dyin=elev_dy \ rain=rain manin=manning infil=infilt \ nwalk=5000000 depth=depth # visualize r.shaded.relief elevation.10m d.mon x0 d.font Vera d.rast.leg depth pos=85 d.his i=elevation.10m.shade h=depth d.barscale at=4,92 bcolor=none tcolor=black -tWater depth map in the Spearfish (SD) areaERROR MESSAGES

If the module fails with ERROR: nwalk (7000001) > maxw (7000000)! then a lowernwalkparameter value has to be selected.## SEE ALSO

v.surf.rst, r.slope.aspect, r.sim.sediment## AUTHORS

Helena Mitasova, Lubos Mitas North Carolina State Universityhmitaso@unity.ncsu.eduJaroslav Hofierka GeoModel, s.r.o. Bratislava, Slovakiahofierka@geomodel.skChris Thaxton North Carolina State Universitycsthaxto@unity.ncsu.edu## REFERENCES

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. Last changed: $Date: 2010-11-28 23:18:09 +0100 (Sun, 28 Nov 2010) $ Full index (C) 2003-2010 GRASS Development Team R.SIM.WATER(1)

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