Provided by: grass-doc_6.4.3-3_all 
NAME
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:
-t
Time-series output
--overwrite
Allow output files to overwrite existing files
--verbose
Verbose module output
--quiet
Quiet module output
Parameters:
elevin=name
Name of the elevation raster map [m]
dxin=name
Name of the x-derivatives raster map [m/m]
dyin=name
Name of the y-derivatives raster map [m/m]
rain=name
Name of the rainfall excess rate (rain-infilt) raster map [mm/hr]
rain_val=float
Rainfall excess rate unique value [mm/hr]
Default: 50
infil=name
Name of the runoff infiltration rate raster map [mm/hr]
infil_val=float
Runoff infiltration rate unique value [mm/hr]
Default: 0.0
manin=name
Name of the Mannings n raster map
manin_val=float
Mannings n unique value
Default: 0.1
traps=name
Name of the flow controls raster map (permeability ratio 0-1)
depth=name
Output water depth raster map [m]
disch=name
Output water discharge raster map [m3/s]
err=name
Output simulation error raster map [m]
nwalk=integer
Number of walkers, default is twice the no. of cells
niter=integer
Time used for iterations [minutes]
Default: 10
outiter=integer
Time interval for creating output maps [minutes]
Default: 2
diffc=float
Water diffusion constant
Default: 0.8
hmax=float
Threshold water depth [m] (diffusion increases after this water depth is reached)
Default: 0.3
halpha=float
Diffusion increase constant
Default: 4.0
hbeta=float
Weighting factor for water flow velocity vector
Default: 0.5
DESCRIPTION
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
map), flow gradient vector given by first-order partial derivatives of elevation field (dxin and dyin
raster maps), rainfall excess rate (rain raster map or rain_val single value) and a surface roughness
coefficient given by Manning's n (manin raster map or manin_val single 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 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], and a 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.
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 -t
Water depth map in the Spearfish (SD) area
ERROR MESSAGES
If the module fails with
ERROR: nwalk (7000001) > maxw (7000000)!
then a lower nwalk parameter value has to be selected.
SEE ALSO
v.surf.rst, r.slope.aspect, r.sim.sediment
AUTHORS
Helena Mitasova, Lubos Mitas
North Carolina State University
hmitaso@unity.ncsu.edu
Jaroslav Hofierka
GeoModel, s.r.o. Bratislava, Slovakia
hofierka@geomodel.sk
Chris Thaxton
North Carolina State University
csthaxto@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 14:18:09 -0800 (Sun, 28 Nov 2010) $
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