Calculating Each Cell's Area in a Raster

[maisehhh]

Hi,

    I have a dataset that was originally in a decimal degrees projection. It is a raster of the globe, in 5 arc minute resolution.

    The final product I need is the same raster, with the each individual cell's value being its area, in hectares. These would essentially be highest around the equator (at around 8,000), and smooth out gradually to ~5,000 near the poles.

    After doing a lot of research on the forums, I've reprojected the dataset into an equal area projection (cylindrical equal area) as some have recommended. I am however stumped on how to use the raster calculator (or any other tool) to now calculate the area of each cell and assign this value to it in a new raster.

    Any ideas?
    Happy to elaborate more if any part of the above is unclear.

    Thank you!

[DanPatterson_Retired]

Each cell in a projected raster represents the exact same area on the ground.  How well the projection maintains area is another issue

[maisehhh]

Hi Dan,

Thanks for answering. In decimal degrees, yes, the cells are all the same size (0.0833x0.0833) however I would like to have those measurements in hectares. I was under the impression that latitude would have an effect of how many hectares are in each grid cell, once projected. Is this incorrect? I've measured out the areas using the measuring tool, once I reproject the data, and the cells no longer have equal area: there are higher values near the equator and lower values with increasing latitudes.

Is there some kind of way I can use the raster calculator to imprint the area of each cell as it's value, in projected units?  (sort of like [shape].ReturnArea, but for pixels?)

Thanks again!

[DanPatterson_Retired]

Ok, now when the cell size is in decimal degrees (ie 0.1 x 0.1 decimal degrees), then you are correct that the area of each square decreases as you go poleward.  However, when you project data, it converts if from decimal degrees to a planar system (usually meters) and the cell size would be X meters by X meters and you could need more cells in the southern portion of the study area than the northern part of the study area (assuming the N hemisphere here, flip that if you live south of the equator).  The point I was trying to make is that the cell sizes in projected data will be identical regardless of where you are, but, how well does the projection represent area in the first place.

[maisehhh]

I figured out the solution (not an exact estimate as it assumes the earth is a perfect sphere - not the case) and thought I should post it to help others that come across this thread.

This is the raster calculator formula to use:

85.7476 * Cos($$YMap * 0.0174532925)

The 85.7476 km2 comes from ~9.24 km squared, which is the cell area at the equator. This applies to 5 arc minutes and will change depending on your original cellsize. The 0.0174532925 is a conversion factor to convert degrees (from YMap) to radians, in order to satisfy the cosine argument.

[DanPatterson_Retired]

Others note for future reference the $$YMap doesn't work in arcmap 10, but can be emulated.  This will enable you to provide a value for the projected grid, however, the actual grid cell area in the projected data doesn't change.