How to calculate the area under a curve in km^2?

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GIACOMO MELCHIORI 2023-5-22

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https://ww2.mathworks.cn/matlabcentral/answers/1970334-how-to-calculate-the-area-under-a-curve-in-km-2

评论： Torsten 2023-5-22

Hello everyone!

I am a geologist working on this area of the Moon characterized by this fault-related landforms (see image), for some future calculations I need to know the so-called "excess area", so I need to quantify in m^2 or km^2 the area under the red line (this is a topographic profile across one of the above-mentioned structures) and above the black line whiich is my reference level. Since I am working on a GIS-based software with a known coordinate system I can measure all the distances I want to have a reference for calculation.

I read in a paper that "cross-sectional area of ridges was calculated from each profile by using a trapezoidal numerical integration" but I really don't know where to start...

Thank you in advance,

Jack

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GIACOMO MELCHIORI 2023-5-22

I can extract these coordinates I think

Torsten 2023-5-22

在 MATLAB Online 中打开

Then

trapz(x,y-ybase)

is the area where x and y are as above and ybase is the y-coordinate of the black line.

The unit of the area will be [unit_x]*[unit_y].

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Answer 1

Nathan Hardenberg 2023-5-22

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https://ww2.mathworks.cn/matlabcentral/answers/1970334-how-to-calculate-the-area-under-a-curve-in-km-2#answer_1241684

编辑：Nathan Hardenberg 2023-5-22

在 MATLAB Online 中打开

Check out the trapz-function (https://de.mathworks.com/help/matlab/ref/trapz.html). This is exactly what you need.

You have to cut of the data from your starting point to your endpoint. And your "black line" has to be 0 level. because the trapz-function is just integrating numerically. If your data is not euqally spaced, you can also provide this in the function (see documentation)

% creating radom data

y = zeros(1,20);

y(5:14) = rand(1,10)+5

y = 1×20

0 0 0 0 5.0174 5.1231 5.1924 5.7921 5.4807 5.5166 5.2084 5.1917 5.7500 5.7148 0 0 0 0 0 0

plot(y); % visualizing

xline(4, '--');

xline(15, '--');

y_cut = y(4:15); % cutting off data

area = trapz(y_cut)

area = 53.9872