## DESCRIPTION

Spread phenomena usually show uneven movement over space. Such unevenness is due to two reasons:
1) the uneven conditions from location to location, which can be called SPATIAL HETEROGENEITY, and
2) the uneven conditions in different directions, which can be called ANISOTROPY.
The anisotropy of spread occurs when any of the determining factors have directional components. For example, wind and topography cause anisotropic spread of wildfires.

One of the simplest spatial heterogeneous and anisotropic spread is elliptical spread, in which, each local spread shape can be thought as an ellipse. In a raster setting, cell centers are foci of the spread ellipses, and the spread phenomenon moves fastest toward apogees and slowest to perigees. The sizes and shapes of spread ellipses may vary cell by cell. So the overall spread shape is commonly not an ellipse.

r.spread simulates elliptically anisotropic spread phenomena, given three raster map layers about ROS (base ROS, maximum ROS and direction of the maximum ROS) plus a raster map layer showing the starting sources. These ROS layers define unique ellipses for all cell locations in the current geographic region as if each cell center was a potential spread origin. For some wildfire spread, these ROS layers can be generated by another GRASS raster program r.ros. The actual locations reached by a spread event are constrained by the actual spread origins and the elapsed spread time.

r.spread optionally produces raster maps to contain backlink UTM coordinates for each raster cell of the spread time map. The spread paths can be accurately traced based on the backlink information by another GRASS raster program r.spreadpath.

Part of the spotting function in r.spread is based on Chase (1984) and Rothermel (1983). More information on r.spread, r.ros and r.spreadpath can be found in Xu (1994).

## Flags:

-v
  Run verbosely, printing information about program progress to standard output.
-d
  Display the "live" simulation on screen. A graphics window must be opened and selected before using this option.
-s
  For wildfires, also consider spotting.

## Parameters

max=name
  Name of an existing raster map layer in the user's current mapset search path containing the maximum ROS values (cm/minute).
dir=name
  Name of an existing raster map layer in the user's current mapset search path containing directions of the maximum ROSes, clockwise from north (degree).
base=name
  Name of an existing raster map layer in the user's current mapset search path containing the ROS values in the directions perpendicular to maximum ROSes' (cm/minute). These ROSes are also the ones without the effect of directional factors.
start=name
  Name of an existing raster map layer in the user's current mapset search path containing starting locations of the spread phenomenon. Any positive integers in this map are recognized as starting sources.
spot_dist=name
  Name of an existing raster map layer in the user's current mapset search path containing the maximum potential spotting distances (meters).
w_speed=name
  Name of an existing raster map layer in the user's current mapset search path containing wind velocities at half of the average flame height (feet/minute).
f_mois=name
  Name of an existing raster map layer in the user's current mapset search path containing the 1-hour (<.25") fuel moisture (percentage content multiplied by 100).
least_size=odd int An odd integer ranging 3 - 15 indicating the basic sampling window size within which all cells will be considered to see whether they will be reached by the current spread cell. The default number is 3 which means a 3x3 window.
comp_dens=decimal A decimal number ranging 0.0 - 1.0 indicating additional sampling cells will be considered to see whether they will be reached by the current spread cell. The closer to 1.0 the decimal number is, the longer the program will run and the higher the simulation accuracy will be. The default number is 0.5.
init_time=int A non-negative number specifying the initial time for the current spread simulation (minutes). This is useful when multiple phase simulation is conducted. The default time is 0.
lag=int A non-negative integer specifying the simulating duration time lag (minutes). The default is infinite, but the program will terminate when the current geographic region/mask has been filled. It also controls the computational time, the shorter the time lag, the faster the program will run.
backdrop=name
  Name of an existing raster map layer in the user's current mapset search path to be used as the background on which the "live" movement will be shown.
output=name
  Name of the new raster map layer to contain the results of the cumulative spread time needed for a phenomenon to reach each cell from the starting sources (minutes).
x_output=name
  Name of the new raster map layer to contain the results of backlink information in UTM easting coordinates for each cell.
y_output=name
  Name of the new raster map layer to contain the results of backlink information in UTM northing coordinates for each cell.

## OPTIONS

The user can run r.spread either interactively or non- interactively. The program is run interactively if the user types r.spread without specifying flag settings and parameter values on the command line. In this case, the user will be prompted for input.

Alternately, the user can run r.spread non-interactively, by specifying the names of raster map layers and desired options on the command line, using the form:

r.spread [-vds] max=name dir=name base=name start=name [spot_dist=name] [w_speed=name] [f_mois=name] [least_size=odds int] [comp_dens=decimal] [init_time=int (>=0)] [lag=int (>= 0)] [backdrop=name] output=name [x_output=name] [y_output=name] The -d option can only be used after a graphics window is opened and selected.

Options spot_dist=name, w_speed=name and f_mois=name must all be given if the -s option is used.

## EXAMPLE

Assume we have inputs, the following simulates a spotting- involved wildfire on the graphics window and generates three raster maps to contain spread time, backlink information in UTM northing and easting coordinates:

r.spread -ds max=my_ros.max dir=my_ros.maxdir base=my_ros.base start=fire_origin spot_dist=my_ros.spotdist w_speed=wind_speed f_mois=1hour_moisture backdrop=image_burned output=my_spread x_output=my_spread.x y_output=my_spread.y

## NOTES

1. r.spread is a specific implementation of the shortest path algorithm. r.cost GRASS program served as the starting point for the development of r.spread. One of the major differences between the two programs is that r.cost only simulates ISOTROPIC spread while r.spread can simulate ELLIPTICALLY ANISOTROPIC spread, including isotropic spread as a special case.

2. Before running r.spread, the user should prepare the ROS (base, max and direction) maps using appropriate models. For some wildfire spread, a separate GRASS program r.ros based on Rothermel's fire equation does such work. The combination of the two forms a simulation of wildfire spread.

3. The relationship of the start map and ROS maps should be logically correct, i.e. a starting source (a positive value in the start map) should not be located in a spread BARRIER (zero value in the ROS maps). Otherwise the program refuses to run.

4. r.spread uses the current geographic region settings. The output map layer will not go outside the boundaries set in the region, and will not be influenced by starting sources outside. So any change of the current region may influence the output. The recommendation is to use slightly larger region than needed. Refer to g.region to set an appropriate geographic region.

5. The inputs to r.spread should be in proper units.

6. r.spread is a computationally intensive program. The user may need to choose appropriate size of the geographic region and resolution.

7. A low and medium (i.e. <= 0.5) sampling density can improve accuracy for elliptical simulation significantly, without adding significantly extra running time. Further increasing the sample density will not gain much accuracy while requiring greatly additional running time.

## SEE ALSO

g.region, r.cost, r.spreadpath, r.ros

## REFERENCES

Chase, Carolyn, H., 1984, Spotting distance from wind-driven surface fires -- extensions of equations for pocket calculators, US Forest Service, Res. Note INT-346, Ogden, Utah.

Rothermel, R. C., 1983, How to predict the spread and intensity of forest and range fires. US Forest Service, Gen. Tech. Rep. INT-143. Ogden, Utah.

Xu, Jianping, 1994, Simulating the spread of wildfires using a geographic information system and remote sensing, Ph. D. Dissertation, Rutgers University, New Brunswick, New Jersey.

## AUTHOR

Jianping Xu and Richard G. Lathrop, Jr., Center for Remote Sensing and Spatial Analysis, Rutgers University.

Last changed: $Date: 2006-04-13 12:25:42 -0700 (Thu, 13 Apr 2006) $