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One of the projections that SMAP (Soil Moisture Active Passive) used is EPSG: 6933 (Global, Equal-Area; EASE-Grid 2.0). For the 9-km resolution grids, the earth data website says the grids has 3856 columns, 1624 rows, and the area of the grid is 9,008.05 m x 9,008.05 m.enter image description here

However, if multiply the 9km resolution with columns, it gets: 9008.05 * 3856 = 34735040.8 m, which is much smaller than the circumference of the earth at the equator: 2 * pi * R = 2 * pi * 6371000 = 40030173.6 m. Besides, the regular grids mean that at every latitude, the data will always cover 34735040.8 m, which seems contrary to the fact that the earth has different circumferences at different latitudes.

I wonder what the grids of SMAP data look like.

Does the 9,008.05 m x 9,008.05 m grids mean that every grid has a 9,008.05 m width and 9,008.05 m height or just indicate its area?

Are there any gaps or overlaps between the grids?

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The EASE-2.0 global grid definition uses the Lambert cylindrical equal area projection. It's a rectangular grid so distorted east-west (all latitude lines are equal length) but the north-south distances are reduced to maintain equal area.

They set a standard parallel at +/-30, thus reducing the length of the equator. If I multiply your calculation by 1/cos(30), the length's over 40 million meters. You also need to use R = 6378137.0, not 6371000, which also narrows the difference between the two calculations. It's not an exact match, but that may be due to the actual projection math which I haven't looked at recently.

Disclosure: I work for Esri and am on the subcommittee that maintains the EPSG geodetic registry.

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    Thank you for your answer! Yes, 2 * pi * 6378137.0 * cos(pi / 6) = 34705982.5 m, which is a very good match to rows * resolution = 3856 * 9008.05 = 34735040.8 m. The standard of latitude 30 is the key point. The grid is only accurately 9 km in width and 9 km in height at lat 30. I checked the latitude and longitude bands of SMAP data. It shows as latitudes become higher, the grid width is fixed to 0.0933685 degrees (shorter than 9 km above lat 30), but the grid height will increase (larger than 9 km above lat 30), thus keeping the total area of a grid to almost 81 km^2 (9km * 9km).
    – QRW
    May 16, 2023 at 6:17

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