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Algorithme pour le calcul de Shreve order dans la CCM

Shreve order

Stream order allows us to rank the size and the flow regime of streams. It is a measure of the position of the stream in the tributary hierarchy and is sensitive to the accuracy of the drainage pattern delineation.
Stream order increases with catchment size, tributary number and drainage network density (Crave, 1995). Crave, A., 1995. Quantification de l'organisation des réseaux hydrodynamiques. Thèse, Géosciences Rennes.

Strahler order

The methods proposed by Strahler (1957): All links with no tributaries are assigned an order of one and are referred to as first order. When two first-order links intersect, the downslope link is assigned an order of two. When two second-order links intersect, the downslope link is assigned an order of three, and so on. When two links of the same order intersect, the order will increase. This is the most common method.
This method does not take into consideration the final discharge of the river.

• Strahler, A. N. 1957. Quantitative analysis of watershed geomorphology. Transactions of the American Geophysical Union (38):913-920.
  

Strahler, A. N. 1964. Quantitative geomorphology of drainage basins and channel networks. in Handbook of Applied Hydrology, Ven Te Chow (Editor). McGraw Hill, New York. pp 4-39 - 4-76.
L’algorithme est le suivant : soient un arc A de rang m et un arc B de rang n confluant au noeud amont d’arc C de rang o. Alors : o= max{m,n,int((m+n+2)/2)}

Shreve order

The Shreve method accounts for all links in the network. As with the Strahler method, all exterior links are assigned an order of 1. By starting at the headwaters, numbers are assigned but are always added together at the confluence of each stream. So even if there is a 1st order joining a 2nd order stream the result is a 3rd order stream. This could quickly go into larger, even double, figures than the Strahler Method.

Because the orders are additive, the numbers from the Shreve method are sometimes referred to as magnitudes instead of orders. The magnitude of a link in the Shreve method is the number of upstream links.

• Shreve, R. (1966). Statistical Law of Stream Numbers, J. Geol., 74, , 17-37.
  

• Shreve, R. (1974). Variation of Mainstream Length With Basin Area in River Networks. Water Resources Research, vol.10, no.6
  

Shreve Algorithm

Scheidegger order

The order X of a stream formed by two rivers of different orders, say N and M, should be computed by the formula : X= [log([2^{N] +[2}M])]/log(2) #Problème avec l'écriture sur le trac de la formule !!! 2 exposant N + 2 exposant M !! s'écrit encore log2(2^{N + 2}M)

Scheidegger, A.E. (1965). The algebra of stream-order numbers: lIS. Geo/.SlIrl'ey Prot: Paper, 525B, pp. BI87-BI89.

• Scheidegger, A.E.(1966) 'EFFECT OF MAP SCALE ON STREAM ORDERS', Hydrological Sciences Journal, 11: 3, 56 — 61
  

​http://pdfserve.informaworld.com/338214__918243090.pdf[[BR]]

Horton order

Horton, R. E. (1945), Erosional development of streams and their drainage basins: hydro-physical approach to quantitative morphology, Geological Society of America Bulletin 56 (3): 275-370

​https://svn.osgeo.org/grass/grass-addons/raster/r.stream.order/description.html

Gravelius order

The first order is given to the main river of a drainage system that flows into a sea, lake or ocean. All the tributaries that flow directly into the first order water-course are considered to be second order and so on, to the tiniest water-courses, which will have the highest order. Gravelius, H., 1914. Flusskunde. Goschen Verlagshandlung Berlin. In Zavoianu, I (1985). Morphometry of drainage bassins. Amsterdam, Elsevier.