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r.convergence - Calculate convergence index.


raster, terrain


r.convergence --help
r.convergence [-cs] input=name output=name window=integer weights=string [--overwrite] [--help] [--verbose] [--quiet] [--ui]


Use circular window (default: square)
Add slope convergence (radically slows down calculation time)
Allow output files to overwrite existing files
Print usage summary
Verbose module output
Quiet module output
Force launching GUI dialog


input=name [required]
Digital elevation model map
output=name [required]
Output convergence index map
window=integer [required]
Window size
Default: 3
weights=string [required]
Method for reducing the impact of the cell due to distance
Options: standard, inverse, power, square, gentle
Default: standard

Table of contents


Increase convergence if slope value is high. Slope parameter radically slows down computation time, especially if the window parameter is high. If slope is used, a slope modifier is used according to the formula: sin(current)*sin(target) + cos(current)*cos(target). If the slope of current and target cells are equal, this modifier's value will be 1. The modifier is applied with the formula: acos(cos(convergence) * modifier)
Use circular window instead of square (default)
Digital elevation model. Data can be of any type and any projection. To calculate relief convergence, r.convergence uses real distances which is recalculated into cell distance, according formula:
distance_between_current_cell_and_target_cell/distance_between_current_cell_and_nearest_neighbour_cell. It is important if convergence is calculated for large areas in Lat/Lon projection.
Parameter describing the reduction of the impact of the cell due to its distance, where distance in cells:
  • standard: no decay
  • inverse: distance modifier is calculated as 1/x
  • power: distance modifier is calculated as 1/(x*x)
  • power: distance modifier is calculated as 1/(x*x)
  • gentle: distance modifier is calculated as 1/((1-x)/(1+x))
Window size. Must be odd. For now there are no limits in window size. r.convergence uses the window size instead of classical radius for compatibility with other GRASS GIS commands.
Map of convergence index. The values ranges from -100 (max divergent, real peaks and ridges) by 0 (planar areas) to 100 (max convergent, real pits and channels). Classical convergence index presented with degrees (-90 to 90)


How convergence index is calculated (3 x 3 window):

Illustrations of convergence index values.
     For divergent case, index is -100.
     For convergent case, index is +100.
     For planar case, index is 0.
Figure 1: Convergence index for maximum divergence, maximum convergence, and planar
Convergence index is a terrain parameter which shows the structure of the relief as a set of convergent areas (channels) and divergent areas (ridges). It represents the agreement of aspect direction of surrounding cells with the theoretical matrix direction. Convergence index is mean (or weighted mean if weights are used) aspect difference between real aspect and theoretical maximum divergent direction matrix representing ideal peak (see figure) minus 90 degrees. So if there is maximum agreement with divergent matrix the convergence index is (0 - 90) * 10/9 = -100. If there is ideal sink (maximum convergence) the convergence index is (180 -90) * 10/9 = 100. Slope and aspect are calculated internally with the same formula as in r.slope.aspect. Convergence index is very useful for analysis of lineaments especially represented by ridges or channel systems as well as valley recognition tool.


r.slope.aspect, r.param.scale, r.neighbors,


Claps, P., Fiorentino, M., Oliveto, G., (1994), Informational entropy of fractal river networks, Journal of Hydrology, 187(1-2), 145-156 .

Bauer J., Rohdenburg H., Bork H.-R., (1985), Ein Digitales Reliefmodell als Vorraussetzung fuer ein deterministisches Modell der Wasser- und Stoff-Fluesse, IN: Bork, H.-R., Rohdenburg, H., Landschaftsgenese und Landschaftsoekologie, Parameteraufbereitung fuer deterministische Gebiets-Wassermodelle, Grundlagenarbeiten zu Analyse von Agrar-Oekosystemen, 1-15.

Böhner J., Blaschke T., Montanarella, L. (eds.) (2008). SAGA Seconds Out. Hamburger Beiträge zur Physischen Geographie und Landschaftsökologie, 19: 113 s.


Jarek Jasiewicz


Available at: r.convergence source code (history)

Latest change: Monday Jan 30 19:52:26 2023 in commit: cac8d9d848299297977d1315b7e90cc3f7698730

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