Translating Trig Expressions into Code

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?

[Joseph Cheng]

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]

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?

Answer 1

[Roger Stafford]

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.

[Stephanie Goldstein]

Thanks for your response.

The two deltas are small and are measured in degrees. Unfortunately, when I enter this into matlab, I receive the error "Error using * Inner matrix dimensions must agree." Could this be because the latitude vector is 224 X 1 and the longitude vector is 240 X 1? How would I correct for this? Thanks.

[Roger Stafford]

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]

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.

Answer 2

[Image Analyst]

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?

[Stephanie Goldstein]

Hi, alright my fault. Thanks for catching that problem. Unfortunately I am still told "Error using * Inner matrix dimensions must agree" after entering this into matlab. How do I correct this problem?

[Image Analyst]

You must be using arrays. Just use a scalar for delta.

http://mathforum.org/library/drmath/view/63767.html

[Stephanie Goldstein]

Great. Thanks for your help!

[Roger Stafford]

No, the cos(theta) factor is needed! If you cut the earth with a plane parallel to the equator's plane but at a higher latitude, the circle you get has a smaller circumference than 2*pi*R, and that is the plane the longitude angle is measured in. The cos(theta) is the required correction.

[Roger Stafford]

@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]

Alright, thanks for clearing that up Roger!