## table of contents

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, parallel

# 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*]
[**output_step**=*integer*] [**diffusion_coeff**=*float*]
[**hmax**=*float*] [**halpha**=*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 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.

*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 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 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 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 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). 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¶

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 Carolina 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 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.
- 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 Engineering 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: Saturday Jul 27 17:08:21 2024

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