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<title>[GRASSLIST:1159] Surface area of a DEM</title>
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<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>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.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>Thoughts?<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>--j<o:p></o:p></span></font></p>
<div>
<p><font size=2 color=navy face="Times New Roman"><span style='font-size:10.0pt;
color:navy'>--<br>
<br>
Jonathan A. Greenberg, PhD<br>
NRC Research Associate<br>
<st1:place w:st="on"><st1:PlaceName w:st="on">NASA</st1:PlaceName> <st1:PlaceName
w:st="on">Ames</st1:PlaceName> <st1:PlaceName w:st="on">Research</st1:PlaceName>
<st1:PlaceType w:st="on">Center</st1:PlaceType></st1:place><br>
MS 242-4<br>
<st1:place w:st="on"><st1:City w:st="on">Moffett Field</st1:City>, <st1:State
w:st="on">CA</st1:State> <st1:PostalCode w:st="on">94035-1000</st1:PostalCode></st1:place><br>
Phone: 415-794-5043<br>
AIM: jgrn3007<br>
MSN: jgrn3007@hotmail.com</span></font><font color=navy><span style='color:
navy'> </span></font><o:p></o:p></p>
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<p class=MsoNormal><b><font size=2 face=Tahoma><span style='font-size:10.0pt;
font-family:Tahoma;font-weight:bold'>From:</span></font></b><font size=2
face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma'> Smith, Michael
[mailto:Michael.Smith@maine.gov] <br>
<b><span style='font-weight:bold'>Sent:</span></b> Wednesday, July 19, 2006
4:21 PM<br>
<b><span style='font-weight:bold'>To:</span></b> <st1:PersonName w:st="on">Jonathan
Greenberg</st1:PersonName><br>
<b><span style='font-weight:bold'>Subject:</span></b> RE: [GRASSLIST:1159]
Surface area of a DEM</span></font><o:p></o:p></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
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<p class=MsoNormal><font size=2 color=black face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:black'>Well wouldn't the true area be the length
of one side x (length of other side / cosine of slope (in degrees))?</span></font><o:p></o:p></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>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).<o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>Michael Smith<br>
<st1:State w:st="on"><st1:place w:st="on">Maine</st1:place></st1:State> DEP GIS
Unit<o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
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<p class=MsoNormal style='margin-bottom:12.0pt'><b><font size=2 face=Tahoma><span
style='font-size:10.0pt;font-family:Tahoma;font-weight:bold'>From:</span></font></b><font
size=2 face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma'>
owner-GRASSLIST@baylor.edu on behalf of <st1:PersonName w:st="on">Jonathan
Greenberg</st1:PersonName><br>
<b><span style='font-weight:bold'>Sent:</span></b> Wed 7/19/2006 6:24 PM<br>
<b><span style='font-weight:bold'>To:</span></b> 'GRASS user list'<br>
<b><span style='font-weight:bold'>Subject:</span></b> [GRASSLIST:1159] Surface
area of a DEM</span></font><o:p></o:p></p>
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<p style='margin-bottom:12.0pt'><font size=2 face="Times New Roman"><span
style='font-size:10.0pt'>I'd like to estimate the surface area of each cell in
a DEM (r.surf.area<br>
seems to just give you the value for the entire dem, no?) -- by surface area<br>
I am referring to the "true" ground area as opposed to the planar
projected<br>
ground area (which is constant for all cells) -- flat areas the area = the<br>
planar projected area (e.g. a 30m cell that is flat has 900m2 of surface<br>
area, but an inclined slope will have > 900m2). Is there a grass
module to<br>
do this, or any recommendation on how to calculate this? Thanks!<br>
<br>
--j<br>
<br>
--<br>
<br>
Jonathan A. Greenberg, PhD<br>
NRC Research Associate<br>
<st1:place w:st="on"><st1:PlaceName w:st="on">NASA</st1:PlaceName> <st1:PlaceName
w:st="on">Ames</st1:PlaceName> <st1:PlaceName w:st="on">Research</st1:PlaceName>
<st1:PlaceType w:st="on">Center</st1:PlaceType></st1:place><br>
MS 242-4<br>
<st1:place w:st="on"><st1:City w:st="on">Moffett Field</st1:City>, <st1:State
w:st="on">CA</st1:State> <st1:PostalCode w:st="on">94035-1000</st1:PostalCode></st1:place><br>
Phone: 415-794-5043<br>
AIM: jgrn3007<br>
MSN: jgrn3007@hotmail.com<br>
<br>
</span></font><o:p></o:p></p>
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