ellipsoid or sphere in area calculations of terra?

Question

How the calculations of area are made in terra, when using geographical coordinates (lon/lat)?

1 - On a sphere or an ellipsoid?

2 - Using a constant width of the cells (the median width) as it was done in raster package, or using a more accurate algorithm?

My questions concern both the expanse and cellSize functions.

I tried to find the answers in the terra manual and the help pages, but I was not successful. Thank you for your help.

Answer 1

According to Robert Hijmans’ (@RobertHijmans) answer to this existing question (Why do terra::cellSize() and raster::area() produce different estimates of raster cell area?):

raster uses the product of the width (longitude) and height (latitude) of a cell. terra is more precise, it computes the spherical area of a cell (as defined by its four corners). This matters most at high latitudes, where the width of a cell changes most, and can be different between the bottom and the top of a cell. So the difference will be largest at high latitudes and with cells with a low vertical resolution.”

Dr. Hijmans also says:

"The bigger change in terra is that it also computes actual cell-size for projected (i.e. not lon-lat) rasters."

See the existing question linked above for examples from his answer. Hope that helps!

Answer 2

On a sphere or an ellipsoid?

The WGS84 ellipsoid

Using a constant width of the cells or a more accurate algorithm?

More accurate. See Christopher Crawford's answer