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NAME - Calculates Horton's statistics for Strahler and Horton ordered networks created with


raster, hydrology, stream network, Horton's statistics

SYNOPSIS --help [-mco] stream_rast=name direction=name elevation=name [memory=integer] [output=name] [--overwrite] [--help] [--verbose] [--quiet] [--ui]


Use memory swap (operation is slow)
Print only catchment's statistics
Print only orders' statistics
Allow output files to overwrite existing files
Print usage summary
Verbose module output
Quiet module output
Force launching GUI dialog


stream_rast=name [required]
Name of input raster map with stream network
direction=name [required]
Name of input flow direction raster map
elevation=name [required]
Name of input elevation raster map
Max memory used in memory swap mode (MB)
Default: 300
Name for output file (if omitted output to stdout)

Table of contents


The module is prepared to calculate Horton's statistics of drainage network.


Print only catchment's characteristics. Useful for shell script calculation or collecting data in external tables.
Print only parameters for every order. Useful to visualise Horton's law with external software (see example bellow).
Only for very large data sets. Use segment library to optimise memory consumption during analysis.
Stream network: name of input stream raster map produced by r.watershed or, on which ordering will be performed. Because stream network produced by r.watershed and may slighty differ in detail, it is required to use both stream_rast and direction map produced by the same module. The stream_rast background shall have NULL value or zero value. Background values of NULL are by default produced by r.watershed and If not 0 or NULL use r.mapcalc to set background values to NULL.
Flow direction: name of input direction raster map produced by r.watershed or If output raster map is used, it only has non-NULL values in places where streams occur. NULL (nodata) cells are ignored, zero and negative values are valid direction data if they vary from -8 to 8 (CCW from East in steps of 45 degrees). Direction map shall be of type CELL values. Region resolution and map resolution must be the same. Also stream_rast network map must have the same resolution. It is checked by default. If resolutions differ the module informs about it and stops. Region boundary and maps boundary may differ but it may lead to unexpected results.
Elevation: name of input elevation map. Map can be of type CELL, FCELL or DCELL. It is not restricted to resolution of region settings as stream_rast and direction raster map.


Output statistics are send to standard output. To redirect output to file use redirection operators: < or << (Unix only). If redirection is used, output messages are printed on stderr (usually terminal) while statistics are written to the file. Statistics can be print as a formatted summary information with number of parameters or as a catchement's descriptive statistics and table with statistics for every order.


These statistics are calculated according to formulas given by R.Horton (1945). Because Horton do not defined precisely what is stream slope, 2 different approaches have been proposed: the first (slope) uses cell-by-cell slope calculation; the second (gradient) uses the difference between elevation of outlet and source of every channel to its length to calculate formula. Bifurcation ratio for every order is calculated acording to the formula: n_streams[1]/n_stream[i+1] where i is the current order and i+1 is the next higher order. For max order of the cell value of streams is zero. Rest of the ratios are calculated in similar mode. The bifurcation and other ratios for the whole catchment (map) is calculated as mean i.e. sum of all bifurcation ratio / max_order-1 (for max_order stream bifurcation ratio = 0). It is strongly recommended to extract the stream network using basin map created with If the whole stream order raster map is used, the calculation will be performed but results may not have hydrological sense. For every order (std) means that statistics are calculated with standard deviation: Ratios: For the whole basin: Ratios:

For the whole basins ratios are calculated acording two formulas: as a mean of ratios for every order, or as a antilog of slope coefficient of the regression model: order vs. log10(parameter)

The module calculates statistics for all streams in input stream_rast map. It is strongly recommended to extract only network of one basin, but it is not necessary for computation. Streams for the desired basin can be extracted by the following r.mapcalc formula:

#xxx category of desired basin
r.mapcalc "sel_streams = if(basin==xxx,streams,null())"

It is also possible to calculate Horton's statistics for Shreve ordering but it has no hydrological sense. Hack (or Gravelius hierarchy) main stream is not the same what so called Horton's reverse ordering (see: Horton 1945).

The module can work only if direction raster map, stream_rast map and region have the same settings. It is also required that stream_rast map and direction map come from the same source. For lots of reason this limitation probably cannot be omitted. This means that if stream_rast map comes from also direction map from must be used. If the stream network was generated with MFD method also MFD direction map must be used.


Create table with order statistics. This table can easily be sent to external program (like R) to be visualised:
g.region -p -a raster=elevation
r.watershed elevation=elevation threshold=10000 drainage=direction stream=streams stream_rast=horton direction=direction elevation=elevation
# export for processing in R -o stream_rast=horton direction=direction elevation=elevation > tmp_file

	main="Sperafish area", 
	sub=paste("Bifurcation ratio: ",


r.mapcalc,,,,,,,, r.watershed

See also r.streams.* modules wiki page.


Jarek Jasiewicz, Adam Mickiewicz University, Geoecology and Geoinformation Institute.

Last changed: $Date: 2014-12-27 14:30:46 +0100 (Sat, 27 Dec 2014) $


Available at: source code (history)

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