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I have some NetCDF data where I have a few variables

lat : dimensions - (x,y)
lon : dimensions - (x,y)
x : dimensions - (x,)
y : dimensions - (y,)
temp : dimensions - (year, y, x)

I am struggling a bit to understand what a two dimensional latitude or longitude represent. To my knowledge latitude should be a 1 dimensional vector and not a 2D matrix, and the same for longitude.

From what I think, for a particular latitude value (i.e 51.34) should fall between some x and y coordinate range (y1,y2,x1,x2) in the lat variable and similarly in the lon variable (y3,y4,x3,x4) and that should represent the x and y range (perhaps something like bounding box) in the temperature variable.

What does this type of (x,y) for format for latitude represent?

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Referring to the answer of this question, the two dimensional representation is seen for projected coordinates. The projected coordinates are used to refer to the cartesian coordinates.

For instance, a cartesian system has a point (x, y). If it is projected, it will have a different location in the projected grid, since the origin and axis will change after projection. To refer the projected location of the point, we will need the grid location of x, which can be represented as (x', y'). The changed x will have a new coordinate comprising the x' and y' of the new projected system.

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