r.sim.water(1grass) GRASS GIS User's Manual r.sim.water(1grass)
NAME
r.sim.water - Overland flow hydrologic simulation using path sampling
method (SIMWE).
KEYWORDS
raster, hydrology, soil, flow, overland flow, model
SYNOPSIS
r.sim.water
r.sim.water --help
r.sim.water [-ts] elevation=name dx=name dy=name [rain=name]
[rain_value=float] [infil=name] [infil_value=float] [man=name]
[man_value=float] [flow_control=name] [observation=name]
[depth=name] [discharge=name] [error=name] [walkers_output=name]
[logfile=name] [nwalkers=integer] [niterations=integer] [out-
put_step=integer] [diffusion_coeff=float] [hmax=float] [hal-
pha=float] [hbeta=float] [random_seed=integer] [nprocs=integer]
[--overwrite] [--help] [--verbose] [--quiet] [--ui]
Flags:
-t
Time-series output
-s
Generate random seed
Automatically generates random seed for random number generator
(use when you don’t want to provide the seed option)
--overwrite
Allow output files to overwrite existing files
--help
Print usage summary
--verbose
Verbose module output
--quiet
Quiet module output
--ui
Force launching GUI dialog
Parameters:
elevation=name [required]
Name of input elevation raster map
dx=name [required]
Name of x-derivatives raster map [m/m]
dy=name [required]
Name of y-derivatives raster map [m/m]
rain=name
Name of rainfall excess rate (rain-infilt) raster map [mm/hr]
rain_value=float
Rainfall excess rate unique value [mm/hr]
Default: 50
infil=name
Name of runoff infiltration rate raster map [mm/hr]
infil_value=float
Runoff infiltration rate unique value [mm/hr]
Default: 0.0
man=name
Name of Manning’s n raster map
man_value=float
Manning’s n unique value
Default: 0.1
flow_control=name
Name of flow controls raster map (permeability ratio 0-1)
observation=name
Name of sampling locations vector points map
Or data source for direct OGR access
depth=name
Name for output water depth raster map [m]
discharge=name
Name for output water discharge raster map [m3/s]
error=name
Name for output simulation error raster map [m]
walkers_output=name
Base name of the output walkers vector points map
Name for output vector map
logfile=name
Name for sampling points output text file. For each observation
vector point the time series of sediment transport is stored.
nwalkers=integer
Number of walkers, default is twice the number of cells
niterations=integer
Time used for iterations [minutes]
Default: 10
output_step=integer
Time interval for creating output maps [minutes]
Default: 2
diffusion_coeff=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
random_seed=integer
Seed for random number generator
The same seed can be used to obtain same results or random seed can
be generated by other means.
nprocs=integer
Number of threads which will be used for parallel compute
Default: 1
DESCRIPTION
r.sim.water is a landscape scale simulation model of overland flow de-
signed 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 con-
cept 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 con-
ditions and high resolutions (Mitas and Mitasova 1998). The key inputs
of the model include elevation (elevation raster map), flow gradient
vector given by first-order partial derivatives of elevation field (dx
and dy raster maps), rainfall excess rate (rain raster map or
rain_value single value) and a surface roughness coefficient given by
Manning’s n (man raster map or man_value single value). Partial deriva-
tives raster maps can be computed along with interpolation of a DEM us-
ing the -d option in v.surf.rst module. If elevation raster map is al-
ready provided, partial derivatives can be computed using r.slope.as-
pect 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 de-
rivatives 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 prede-
fined flow using its direction given by aspect and slope.
Figure: Simulated water flow in a rural area showing the areas with
highest water depth highlighting streams, pooling, and wet areas during
a rainfall event.
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 pro-
vided in [mm/hr]. Rainfall intensities are usually available from me-
teorological 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 val-
ues which can be found in literature. Optionally, user can provide an
overland flow infiltration rate map infil or a single value infil_value
in [mm/hr] that control the rate of infiltration for the already flow-
ing water, effectively reducing the flow depth and discharge. Overland
flow can be further controlled 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 flow_control 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 dis-
charge raster map discharge in [m3/s]. Error of the numerical solution
can be analyzed using the error raster map (the resulting water depth
is an average, and err is its RMSE). The output vector points map out-
put_walkers 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). The spatial distribu-
tion of numerical error associated with path sampling solution can be
analysed using the output error raster file [m]. This error is a func-
tion of the number of particles used in the simulation and can be re-
duced by increasing the number of walkers given by parameter nwalkers.
Duration of simulation is controlled by the niterations 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 walker, water depth and discharge
maps can be saved during simulation using the time series flag -t and
output_step 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 minutes (e.g. wdepth.05, wdepth.10). Moni-
toring of water depth at specific points is supported. A vector map
with observation points and a path to a logfile must be provided. For
each point in the vector map which is located in the computational re-
gion the water depth is logged each time step in the logfile. The log-
file is organized as a table. A single header identifies the category
number of the logged vector points. In case of invalid water depth
data the value -1 is used.
Overland flow is routed based on partial derivatives of elevation field
or other landscape features influencing water flow. Simulation equa-
tions include a diffusion term (diffusion_coeff parameter) which en-
ables 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 ad-
vection 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 kine-
matic wave approximation, but we include a diffusion-like term to in-
corporate 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 reformula-
tion, 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 re-
ciprocal 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 discon-
tinuities 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 Schrodin-
ger equation (Schmidt and Ceperley, 1992, Hammond et al., 1994; Mitas,
1996)). It is assumed that these equations are a representation of sto-
chastic processes with diffusion and drift components (Fokker-Planck
equations).
The Monte Carlo technique has several unique advantages which are be-
coming even more important due to new developments in computer technol-
ogy. Perhaps one of the most significant Monte Carlo properties is ro-
bustness 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 solu-
tions 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 tai-
lored to the new generation of computers as they provide scalability
from a single workstation to large parallel machines due to the inde-
pendence of sampling points. Therefore, the methods are useful both for
everyday exploratory work using a desktop computer and for large, cut-
ting-edge applications using high performance computing.
EXAMPLE
Using the North Carolina full sample dataset:
# set computational region
g.region raster=elev_lid792_1m -p
# compute dx, dy
r.slope.aspect elevation=elev_lid792_1m dx=elev_lid792_dx dy=elev_lid792_dy
# simulate (this may take a minute or two)
r.sim.water elevation=elev_lid792_1m dx=elev_lid792_dx dy=elev_lid792_dy depth=water_depth disch=water_discharge nwalk=10000 rain_value=100 niter=5
Now, let’s visualize the result using rendering to a file (note the
further management of computational region and usage of d.mon module
which are not needed when working in GUI):
# increase the computational region by 350 meters
g.region e=e+350
# initiate the rendering
d.mon start=cairo output=r_sim_water_water_depth.png
# render raster, legend, etc.
d.rast map=water_depth_1m
d.legend raster=water_depth_1m title="Water depth [m]" label_step=0.10 font=sans at=20,80,70,75
d.barscale at=67,10 length=250 segment=5 font=sans
d.northarrow at=90,25
# finish the rendering
d.mon stop=cairo
Figure: Simulated water depth map in the rural area of the North Car-
olina sample dataset.
ERROR MESSAGES
If the module fails with
ERROR: nwalk (7000001) > maxw (7000000)!
then a lower nwalkers parameter value has to be selected.
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 Confer-
ence 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 mul-
tiscale 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 simula-
tions for land use management, In: Landscape erosion and land-
scape evolution modeling, Harmon R. and Doe W. eds., Kluwer
Academic/Plenum Publishers, pp. 321-347.
• Hofierka, J, Mitasova, H., Mitas, L., 2002. GRASS and modeling
landscape processes using duality between particles and fields.
Proceedings of the Open source GIS - GRASS users conference
2002 - Trento, Italy, 11-13 September 2002. PDF
• Hofierka, J., Knutova, M., 2015, Simulating aspects of a flash
flood using the Monte Carlo method and GRASS GIS: a case study
of the Malá Svinka Basin (Slovakia), Open Geosciences. Volume
7, Issue 1, ISSN (Online) 2391-5447, DOI:
10.1515/geo-2015-0013, April 2015
• Neteler, M. and Mitasova, H., 2008, Open Source GIS: A GRASS
GIS Approach. Third Edition. The International Series in Engi-
neering and Computer Science: Volume 773. Springer New York
Inc, p. 406.
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
SOURCE CODE
Available at: r.sim.water source code (history)
Accessed: unknown
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