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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