[GRASS-user] Stream power Index calculation?

[Markus Metz]

On Wed, Mar 4, 2015 at 9:46 AM, Helmut Kudrnovsky <hellik at 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)".
>
> AFAIU from the manual:
>
> http://grass.osgeo.org/grass71/manuals/r.watershed.html
>
> 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.

Markus M

>
> -----
> best regards
> Helmut
> --
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