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
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.
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.
--
+-----------------------------------------------------------+
Carlos Henrique Grohmann - Guano
Geologist M.Sc - Doctorate Student at IGc-USP - Brazil
Linux User #89721 - carlos dot grohmann at gmail dot com
+-----------------------------------------------------------+
_________________
"Good morning, doctors. I have taken the liberty of removing Windows
95 from my hard drive."
--The winning entry in a "What were HAL's first words" contest judged
by 2001: A SPACE ODYSSEY creator Arthur C. Clarke
> 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.