The program uses some

The A.J.Broscoe theory is well known as the theory of the "Mean Stream Drop" and it says that, for the extraction by DEM of a stream network, exists a threshold value wich makes

By definig the

for streams in each Strahler order.

The

Using the Leopold and Miller relation (1964):

where C and t are constat values; the area we are searching (A) is the lowest that gives S to find H costant for each Strahler order (w).

where H

The area can be found by making some attempts for different area thresholds, doing some statistical tests (the suggested ADTDTM test and t-test), and choosing the

For the ADTDTM test the parameter

An output graphs is generated as PDF in the working folder.

The command syntax:

r.broscoe.sh dem=dem_abt 'thresholds=2000 3000 4000 5000' xcoor=2320378.547 ycoor=4779694.770 lt=3 result=broscoe_chiascio

threshold n1 n2 Mean 1 Mean >1 diff sd 1 sd >1 TrMean 1 Tr Mean >1 diff Test t eq var Perm Test eq var Perm Test noeq var Perm Test diff TrMean 2000 127 47 59.3228346456693 64.1063829787234 -4.78354833305411 71.8789637294643 62.2363077459624 52.2869565217391 58.3953488372093 -6.10839231547018 0.687063371319418 0.663366336633663 0.712871287128713 0.534653465346535 3000 87 32 67.9885057471264 63.78125 4.20725574712644 79.5933698087265 68.0449255651095 60.1139240506329 57.1666666666667 2.94725738396625 0.791240399171673 0.801980198019802 0.801980198019802 0.693069306930693 4000 74 21 72.0945945945946 51.6190476190476 20.475546975547 100.947724016344 42.6104167903533 57.6764705882353 49.8421052631579 7.8343653250774 0.368259756306302 0.405940594059406 0.198019801980198 0.623762376237624 5000 60 16 76.4833333333333 61.0625 15.4208333333333 108.929224676854 52.2193690118906 59.0555555555556 61.0625 -2.00694444444444 0.585538501927895 0.683168316831683 0.623762376237624 0.920792079207921

..and an "output.pdf" file of the graphics where threshold values are natural (left) and logaritmic (right):

The program uses the module

D. G. Tarboton and D. P. Ames, (2001). *Advances in the mapping of flow networks from digital elevation data.*** World Water and Environment Resources Congress**, presentation (2001).

J. J. Flint, (1974). *Stream gradient as a function of order, magnitude, and discharge.*** Water Resources Research**, vol.10, n.5, p.969-973.

NIST, (2006). *Engineering statistical handbook: confidence limits for the mean.*

URL: *http://www.itl.nist.gov/div898/handbook/eda/section3/eda352.htm*

J. C. Davis, (1990). *Statistics and Data Analysis in Geology*. John Wiley \& Sons editors (New York, NY, USA).

A. J. Broscoe, (1959). *Quantitative analysis of longitudinal stream profiles of small watersheds*. Department of Geology, Columbia University, NY.

*Last changed: $Date$*