r.sim.watergrass - Online in the Cloud

PROGRAM:

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 [-t] 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]
[output_step=integer] [diffusion_coeff=float] [hmax=float] [halpha=float]
[hbeta=float] [--overwrite] [--help] [--verbose] [--quiet] [--ui]

Flags:
-t
Time-series output

--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

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 (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 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_value 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 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 discharge 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 output_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 distribution of numerical error associated
with path sampling solution can be analysed using the output error raster file [m]. This
error is a function of the number of particles used in the simulation and can be reduced
by increasing the number of walkers given by parameter nwalkers. Duration of simulation
is controled 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).
Monitoring 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 region the water depth is logged each time step in the
logfile. The logfile 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 equations include a diffusion term
(diffusion_coeff 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 raster=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 elevation=elevation.10m dx=elev_dx dy=elev_dy \
rain=rain man=manning infil=infilt \
nwalkers=5000000 depth=depth

Water depth map in the Spearfish (SD) area

ERROR MESSAGES

If the module fails with
ERROR: nwalk (7000001) > maxw (7000000)!
then a lower nwalkers parameter value has to be selected.

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