land area on sloping surfaces

[Stephen B. King]

> > 
> > In mountainous terrain on a sloping surface the planimetric land area
> > is less than the actual surface area on the ground.  Is there an easy
> > way to use a DEM in GRASS to find the actual surface area?  Maybe I'm
> > asking for a 3-D GIS...
> > 
> > 	Bill
> > 	bakerwl at uwyo.edu
> > 
> Interesting problem. It should be possible to use r.mapcalc to look for four
> neighboring DEM measurements, calculate distances and angles along the 
> surface between them, and the surface area of the enclosed lozenge from
> that. This would create a new map, which can then be used to derive
> aggregate surface measurements a la r.average.
> 
> 	Martijn
> 	p.m.van-leusen at bham.ac.uk
> 
> 

I missed the original thread, and perhaps I don't understand the problem,
but I would think that area of a sloping cell could be found by: 

	(CELL WIDTH)^2/cos(slope)

r.average would then do the rest.

Steve King					
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