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       r.sim.water  - Overland flow hydrologic simulation using path sampling method (SIMWE).


       raster, flow, hydrology


       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]

           Time-series output

           Allow output files to overwrite existing files

           Verbose module output

           Quiet module output

           Name of the elevation raster map [m]

           Name of the x-derivatives raster map [m/m]

           Name of the y-derivatives raster map [m/m]

           Name of the rainfall excess rate (rain-infilt) raster map [mm/hr]

           Rainfall excess rate unique value [mm/hr]
           Default: 50

           Name of the runoff infiltration rate raster map [mm/hr]

           Runoff infiltration rate unique value [mm/hr]
           Default: 0.0

           Name of the Mannings n raster map

           Mannings n unique value
           Default: 0.1

           Name of the flow controls raster map (permeability ratio 0-1)

           Output water depth raster map [m]

           Output water discharge raster map [m3/s]

           Output simulation error raster map [m]

           Number of walkers, default is twice the no. of cells

           Time used for iterations [minutes]
           Default: 10

           Time interval for creating output maps [minutes]
           Default: 2

           Water diffusion constant
           Default: 0.8

           Threshold water depth [m] (diffusion increases after this water depth is reached)
           Default: 0.3

           Diffusion increase constant
           Default: 4.0

           Weighting factor for water flow velocity vector
           Default: 0.5


       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 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

       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.


       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.


       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


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

SEE ALSO, r.slope.aspect, r.sim.sediment


       Helena Mitasova, Lubos Mitas
       North Carolina State University

       Jaroslav Hofierka
       GeoModel, s.r.o. Bratislava, Slovakia

       Chris Thaxton
       North Carolina State University


                      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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