Hack’s Stream-Length

Hack’s Stream-Length Index (1973):

SL = (Δheight / Δlength) x L

* Δlength must always be smaller than L

Thanks to R.K. Kaushal for correcting my formulas! I’m such a dope.





Click for PDF of figure below.

Hacks SL Index_Cooley

Mapping of SL Index values at the landscape scale is done, first by calculating index values for all streams in a region, second by using Inverse Distance Weighting (IDW) or another interpolation tool on the point values, and third by breaking the IDW surface into 5-10 classes for display. Use natural breaks or another means of assigning class break values.


Etchebehere et al. (2004) Revista do Instituto de Geociências da USP – Série Científica 4
Fonseca & Augustin (2011)
Hack (1957) USGS Professional Paper 294-B
Hack (1973) USGS report
McKeown et al. (1988) USGS Bulletin 1807
Monteiro et al. (2010) UNESP Geociências 29
Perez-Pena et al. (2009) ESP&L 34
Seeber & Gornitz (1983) Tectonophysics 92
Troiani (2008) Geomorphology 102
Zhang et al. (2011) Geomorphometry.org

Zhang et al. (2011)