The closing section's coordinates must belong to the river network generated by r.stream.extract. It is suggested to run it beforehand.

The main parameters are:

- The coordinates of the vertices of the rectangle containing the basin.
- The center of gravity of the basin: the coordinates of the pixel nearest to the center of gravity of the geometric figure resulting from the projection of the basin on the horizontal plane.
- The area of the basin: is the area of a single cell multiplied by the number of cells belonging to the basin.
- The perimeter: is the length of the contour of the figure resulting by the projection of the basin on the horizontal plane.
- Characteristic values of elevation: the highest and the lowest altitude, the difference between them and the mean elevation calculated as the sum of the values of the cells divided by the number of the cells.
- The mean slope, calculated averaging the slope map.
- The length of the directing vector: the length of the vector linking the outlet to the center of gravity of the basin.
- The prevalent orientation: in Grass GIS the aspect categories represent the number degrees of east and they increase counterclockwise: (90deg is North, 180 is West, 270 is South 360 is East). The aspect value 0 is used to indicate undefined aspect in flat areas with slope=0. We instead calculate the orientation as the number of degree from north, increasing counterclockwise.
- The length of main channel: is the length of the longest succession of segments that connect a source to the outlet of the basin.
- The mean slope of main channel: it is calculated as follows

where N is the topological diameter, i.e. the number of links in which the main channel can be divided on the basis of the junctions. - The circularity ratio: is the ratio between the area of the basin and the area of the circle having the same perimeter of the basin.
- The elongation ratio: is the ratio between the diameter of the circle having the same area of the basin and the length of the main channel.
- The compactness coefficient: is the ratio between the perimeter of the basin and the diameter of the circle having the same area of the basin.
- The shape factor: is the ratio between the area of the basin and the square of the length of the main channel.
- The concentration time (Giandotti, 1934):

Where A is the area, L the length of the main channel and H the difference between the highest and the lowest elevation of the basin. - The mean hillslope length: is the mean of the distances calculated along the flow direction of each point non belonging to the river network from the point in which flows into the network.
- The magnitudo: is the number of the branches of order 1 following the Strahler hierarchy.
- The max order: is the order of the basin, following the Strahler hierarchy.
- The number of streams: is the number of the branches of the river network.
- The total stream length: is the sum of the length of every branches.
- The first order stream frequency: is the ratio between the magnitudo and the area of the basin.
- The drainage density: is the ratio between the total length of the river network and the area.
- The Horton ratios (Horton, 1945; Strahler, 1957).

- The distance-area function, also known as Width Function: in x axis is the length and in y axis is the area.
- The hypsographic curve provides the distribution of the areas at different altitudes. Each point on the hypsographic curve has on the y-axis the altitude and on the x-axis the percentage of basin surface placed above that altitude.
- The ipsometric curve has the same shape but is dimensionless.

- Matplotlib
- r.stream.basins
- r.stream.extract
- r.stream.stats
- r.stream.distance
- r.stream.order
- r.wf
- r.ipso

*Rodriguez-Iturbe I., Rinaldo A. — Fractal River Basins, Chance and Self-Organization. Cambridge Press (2001)*

*In Italian: Di Leo M., Di Stefano M., Claps P., Sole A. — Caratterizzazione morfometrica del bacino idrografico in GRASS GIS
(Morphometric characterization of the catchment in GRASS GIS environment), Geomatics Workbooks, n. 9 (2010)*

Margherita Di Leo (dileomargherita AT gmail DOT com), Massimo Di Stefano

*Last changed: $Date$*