[GRASSLIST:10563] Re: TOPIDX flow direction algorithm

[Dylan Beaudette]

T,

Good question.


According to some papers I have:


(Wilson and Gallant. Terrain Analysis Principles and Applications. 2000)
also in (Soil Science Society of America 64:2046-2056)
CTI (compound topographic index) is defined for steady-state
CTI = ln(As/tan(B))
where As = specific catchment area and
B = slope angle

(Wilson and Gallant. Terrain Analysis Principles and Applications. 2000)
CTI (compound topographic index) is also defined for non-steady state
CTI = ln(Ae/tan(B))
where Ae = effective catchment area and
B = slope angle

here is another one...
(Wilson and Gallant. Terrain Analysis Principles and Applications. 2000)
CIT = As(tan(B))^2

(Geoderma 103:249-272)
TCI (terrain characterization index)
TCI = C * log_10 (A)
where C = surface curvature and
A = upslope contributing area


However, I have heard and seen TCI and CTI used interchangeably, without 
reference to the actual equation...

in GRASS61-CVS

r.topidx reports that it is calculating 
ln(a/tanB)   
a: the area of the hillslope per unit contour length that drains through any 
point
which looks like it could be the As(Tan(B)) variant of the CTI as defined in 
Wilson and Gallant. 


subtracting "CTI" maps created with r.terraflow and r.topidx and running some 
quick stats:
r.mapcalc "t = abs(topidx-tci_9x9)"
r.stats -n -A -p t nsteps=15
r.stats:  100%
0.786645  70.09%     ****
2.359906  22.93%     ****
3.933167   2.66%
5.506428   0.30%
7.079689   0.02%
8.65295   0.00%
10.226211   0.01%
11.799472   0.91%
13.372733   1.69%
14.945993   0.98%
16.519254   0.31%
18.092515   0.06%
19.665776   0.04%
21.239037   0.01%
22.812298   0.00%


Looks like they are not much different.... however, it would be interesting to 
know exactly _how_ different the two approaches are. 

In my own work, I have found that the output from r.terraflow to be much 
better _looking_ for high resolution elevation data, or data where there is a 
lot of noise.

Cheers,

On Friday 24 February 2006 12:24 pm, twiens wrote:
> Dylan,
>
> I have a question about r.terraflow.
>
> r.terraflow computes the TCI or topographic convergence
> index. AFAIK this is not the same thing as CTI or compound
> topographic index or wetness index generated by r.topidx. Am
> I mistaken?
>
> T
>
> ----- Original Message Follows -----
> From: Dylan Beaudette <dylan.beaudette at gmail.com>
> To: twiens at interbaun.com
> Cc: GRASSLIST at baylor.edu, grass4u at gmail.com
> Subject: [GRASSLIST:10558] Re: TOPIDX flow direction
> algorithm
> Date: Fri, 24 Feb 2006 10:44:30 -0800
>
> > On Friday 24 February 2006 07:31 am, twiens wrote:
> > > I'm working with some ArcGIS users and in a note in the
> > > AML script to calculate the topographic index, the
> > > author notes that ArcInfo uses a D8 algorithm to
> > > calculate the contributing area. The concern is that for
> > > relatively flat areas, the index value will be
> > > inaccurate or inappropriate. I've noted in areas that I
> > > have generated a topographic index, that flat areas seem
> >
> > to be set to NULL by topidx. >
> >
> > > I've not been able to find any reference to this issue
> > > in the topidx documentation. Can someone tell me if this
> > > concern is valid for r.topidx?
> > >
> > > Thanks
> > >
> > > T
> > > --
> > > Trevor Wiens
> > > twiens at interbaun.com
> >
> > I would highly recommend enabling c++ support when you
> > compile GRASS, so that  you have access to the r.terraflow
> >  This will compute a TCI, and in many  cases I have found
> > the output from r.terraflow to be superior to the
> > analogous commands in GRASS.
> >
> > cheers,
> >
> >
> > --
> > Dylan Beaudette
> > Soils and Biogeochemistry Graduate Group
> > University of California at Davis
> > 530.754.7341

-- 
Dylan Beaudette
Soils and Biogeochemistry Graduate Group
University of California at Davis
530.754.7341