[GRASS-user] [GRASSLIST:1160] RE: Surface area of a DEM

I was thinking this, but does the fact that a DEM grid cell is square cause
complications in this formulation? A 45 degree slope to the west would have
a different surface area than a 45 degree slope to the southwest. I've come
across some solutions that use a set of 8 triangles created by the lines
between the center cell and each of its 8 neighbors to help in the
calculation, but I was hoping this ability might be buried in a GRASS
command someplace.

Thoughts?

--j

--

Jonathan A. Greenberg, PhD
NRC Research Associate
NASA Ames Research Center
MS 242-4
Moffett Field, CA 94035-1000
Phone: 415-794-5043
AIM: jgrn3007
MSN: jgrn3007@hotmail.com

  _____

From: Smith, Michael [mailto:Michael.Smith@maine.gov]
Sent: Wednesday, July 19, 2006 4:21 PM
To: Jonathan Greenberg
Subject: RE: [GRASSLIST:1159] Surface area of a DEM

Well wouldn't the true area be the length of one side x (length of other
side / cosine of slope (in degrees))?

And since it doesn't really matter which side you choose, it should be:
area of cell / cosine of slope = "real" area on the ground, or in your case
900/cos(slope).

Michael Smith
Maine DEP GIS Unit

  _____

From: owner-GRASSLIST@baylor.edu on behalf of Jonathan Greenberg
Sent: Wed 7/19/2006 6:24 PM
To: 'GRASS user list'
Subject: [GRASSLIST:1159] Surface area of a DEM

I'd like to estimate the surface area of each cell in a DEM (r.surf.area
seems to just give you the value for the entire dem, no?) -- by surface area
I am referring to the "true" ground area as opposed to the planar projected
ground area (which is constant for all cells) -- flat areas the area = the
planar projected area (e.g. a 30m cell that is flat has 900m2 of surface
area, but an inclined slope will have > 900m2). Is there a grass module to
do this, or any recommendation on how to calculate this? Thanks!

--j

--

Jonathan A. Greenberg, PhD
NRC Research Associate
NASA Ames Research Center
MS 242-4
Moffett Field, CA 94035-1000
Phone: 415-794-5043
AIM: jgrn3007
MSN: jgrn3007@hotmail.com

Jonathan Greenberg wrote:

I was thinking this, but does the fact that a DEM grid cell is square
cause complications in this formulation? A 45 degree slope to the
west would have a different surface area than a 45 degree slope to the
southwest. I've come across some solutions that use a set of 8
triangles created by the lines between the center cell and each of its
8 neighbors to help in the calculation, but I was hoping this ability
might be buried in a GRASS command someplace.

think of each cell as a spinning dinner plate on a stick.

you can rotate each cell in the direction of the aspect, and the
slope->projected area will be the same.

dx*dy is its own entity, or if you prefer, the r.mapcalc command doesn't
know about the aspect.

??

Hamish

Jonathan,

You can do that with r.mapcalc.

Calculations can be made with r.mapcalc, using the following formula
for a 50m regular grid:

50*(sqrt((exp((tan(A)*50), 2)) + 2500))
Where A is the slope map.

from: GROHMANN, C.H. 2004. Morphometric analysis in Geographic
Information Systems: applications of free software GRASS and R.
Computers & Geosciences, 30 (9-10):1055-1067.

cheers

Carlos Grohmann

On 7/20/06, Hamish <hamish_nospam@yahoo.com> wrote:

Jonathan Greenberg wrote:

> I was thinking this, but does the fact that a DEM grid cell is square
> cause complications in this formulation? A 45 degree slope to the
> west would have a different surface area than a 45 degree slope to the
> southwest. I've come across some solutions that use a set of 8
> triangles created by the lines between the center cell and each of its
> 8 neighbors to help in the calculation, but I was hoping this ability
> might be buried in a GRASS command someplace.

think of each cell as a spinning dinner plate on a stick.

you can rotate each cell in the direction of the aspect, and the
slope->projected area will be the same.

dx*dy is its own entity, or if you prefer, the r.mapcalc command doesn't
know about the aspect.

??

Hamish

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Linux User #89721 - carlos dot grohmann at gmail dot com
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by 2001: A SPACE ODYSSEY creator Arthur C. Clarke

Jonathan Greenberg wrote:

> I was thinking this, but does the fact that a DEM grid cell is
> square cause complications in this formulation? A 45 degree slope
> to the west would have a different surface area than a 45 degree
> slope to the southwest. I've come across some solutions that use a
> set of 8 triangles created by the lines between the center cell and
> each of its 8 neighbors to help in the calculation, but I was hoping
> this ability might be buried in a GRASS command someplace.

me:

think of each cell as a spinning dinner plate on a stick.

you can rotate each cell in the direction of the aspect, and the
slope->projected area will be the same.

that is all wrong of course.

take a cube of side "1", apply a plane in it of 45 degrees (W aspect)
to cut the cube in two parts. (each shaped like a monopoly-house roof)

one side is unit length of 1, the other sqrt(2). area=sqrt(2).

take the same cube, this time with an aspect of SW. when you cut the
cube this time you get two 4-sided pyramids. area of the plane is
sqrt(2)*sqrt(2) = 2.

Hamish