On Sun, Mar 1, 2015 at 8:15 PM, Helmut Kudrnovsky <hellik@web.de> wrote:
Hi,
in the book "Geomorphometry - Concepts, Software, Applications" I've found a
short paragraph about the Stream power Index (SPI).
the SPI can be used to describe potential flow erosion related to landscape
processes.
in the book SPI is defined as:
SPI = A x tan(beta)
where A is the specific catchment area and beta is the local slope angle.
in link [1] there is the SAGA GIS formula.
sometimes SPI is also defined as:
SPI = ln(A x tan(beta))
This is also known as Topographic Convergence Index (TCI) or
Topographic Wetness Index (TWI). You can calculate this index with
r.watershed and r.terraflow. If you need the non-logarithmic form, you
can use r.mapcalc "SPI = exp(TCI)".
Markus M
my idea for SPI calculation in GRASS GIS may be:
A = {accumulation flow by r.watershed} x {ns resolution x ew resolution}
beta = r.slope slope
anyone ever used/calculated SPI in GRASS GIS? any hints for calculation?
where A is the specific catchment area and beta is the local slope angle.
in link [1] there is the SAGA GIS formula.
sometimes SPI is also defined as:
SPI = ln(A x tan(beta))
This is also known as Topographic Convergence Index (TCI) or
Topographic Wetness Index (TWI). You can calculate this index with
r.watershed and r.terraflow. If you need the non-logarithmic form, you
can use r.mapcalc "SPI = exp(TCI)".
Disclaimer: The views expressed are purely those of the writer and may not in any circumstance be regarded as stating an official position of the European Commission.
On Wed, Mar 4, 2015 at 9:46 AM, Helmut Kudrnovsky <hellik@web.de> wrote:
in the book SPI is defined as:
SPI = A x tan(beta)
where A is the specific catchment area and beta is the local slope angle.
in link [1] there is the SAGA GIS formula.
sometimes SPI is also defined as:
SPI = ln(A x tan(beta))
This is also known as Topographic Convergence Index (TCI) or
Topographic Wetness Index (TWI). You can calculate this index with
r.watershed and r.terraflow. If you need the non-logarithmic form, you
can use r.mapcalc "SPI = exp(TCI)".
TCI is definded as: Topographic index ln(a / tan(b))
divison vs. multiplication
OK. You can get SPI with a little math:
exp(TCI) = a / tan(b)
tan(b) = a / exp(TCI)
a = flow accumulation / res
or a bit more precise, for flow direction to direct neighbors:
a = flow accumulation / ((ns_res + ew_res) / 2)
and diagonal neighbors:
a = flow accumulation / sqrt(ns_res * ns_res + ew_res * ew_res)
now you have a, can calculate tan(b) and SPI
note that slope from r.slope.aspect could be used but does not
necessarily point to the predominant flow direction. r.slope.aspect
calculates slope for a given cell from its 3x3 neighborhood whereas
TCI uses the slope from the current cell to the next downstream cell.
Thus for TCI and SPI the upstream slope does not matter so much, it is
important how it continues immediately downstream (e.g. waterfall).
Since a and tan(b) are already calculated by r.watershed for TCI,
implementing SPI (as yet another option to r.watershed) would be
relatively easy.