Translating Trig Expressions into Code

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Stephanie Goldstein
评论： Stephanie Goldstein 2014-8-25
Hello everyone! I am a beginner at matlab and am attempting to calculate the area of each individual grid cell of climate data. I know that the area can be calculated with ((2*pi*R)/360)^2)*cos(theta)*delta_latitude*delta*longitude but am lost as to how to translate this into code. Can anyone offer suggestions please?
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Joseph Cheng
Joseph Cheng 2014-8-22
编辑：Joseph Cheng 2014-8-22
well unless there is something complicated what you typed in should work. if any of those are an array (more than 1x1) then you may want to look into the element by element multiplication '.*'
also did you make a typo? should it be delta_longitude?
((2*pi*R)/360)^2)*cos(theta)*delta_latitude*delta_longitude
and make sure theta is in radians or use cosd() for cosine with input of degrees.
Stephanie Goldstein
Stephanie Goldstein 2014-8-22
Hmm the only problem is that when I put this into matlab I get the error "Error using * Inner matrix dimensions must agree." Any clue as to how to fix this?

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回答（2 个）

Roger Stafford
Roger Stafford 2014-8-22
Your formula is only a valid approximation if the two delta's are small and are measured in degrees. Also theta must be the latitude. If it is measured in degrees, in matlab you would use either cosd(theta) or cos(theta*pi/180). Otherwise you can copy it directly into a matlab assignment.
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Roger Stafford
Roger Stafford 2014-8-22
编辑：Roger Stafford 2014-8-22
Yes, that would produce a complaint from matlab. If you have a 224 x 1 size vector first multiplied by a 1 x 240 size vector second, it would give you a 224 x 240 matrix of products. Is that what you are after? You haven't adequately explained what you are really attempting to do.
Stephanie Goldstein
Stephanie Goldstein 2014-8-25
Hi Roger, I'm attempting to find the area of each grid cell using latitude and longitude arrays which are 224 X 1 and 240 X 1 respectively. Does this help at all? How would I go about calculating the area using the formula I initially gave when the two vectors I am using differ in size? Thanks.

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Image Analyst
Image Analyst 2014-8-22
编辑：Image Analyst 2014-8-22
I think you both made a typo. There should be no ) after the R. You have three ( and four ).
degreeToRadiansConversionFactor = pi / 180; % Call it out so people know what it is.
area = (R * degreeToRadiansConversionFactor)^2 * delta_latitude * delta_longitude;
I also took out the cos(theta) since I don't know why it's there. Since the arc length on the surface of a circle is S=R*theta, if the patch is rectangular, you'd get an area of length * width = R^2 * delta_latitude * delta_longitude, where delta_latitude & delta_longitude are in radians, so where do you get the cos(theta) from?
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Roger Stafford
Roger Stafford 2014-8-22
@Image Analyst. If you have ever used USGS topographical maps, you will note that maps in the U.S. of the seven-and-a-half-minute series are not squares but are rectangles, even though the two angle delta's are the same. That illustrates the need for the cosine correction.
Stephanie Goldstein
Stephanie Goldstein 2014-8-25
Alright, thanks for clearing that up Roger!

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