ATM Grid Resolution Summary

Note about the "NE" variable. This is the name of a Fortran variable and also used in CIME XML files to refer to cubed sphere grids. It is meaningless jargon to most people. For written documents we recommend referring to grids by their resolution in km. For the quasi-uniform cubed-sphere grid, average grid spacing at the equator is a good measure of the resolutions.

For cubed sphere grids (CAM-SE Grid Overview ), NE is the Number of spectral Elements along each cube face. Thus the total number of elements N = 6 NE^2.

For regionally refined grids, internally in the code NE=0 and the number of elements N is read in from the Exodus RRM mesh file. RRM grids can be any quadrilateral tiling of the sphere and may not be based on cubed-sphere grids.

For any spectral element grid with N elements, the number of unique points (physics columns) is (np-1)^2 * N + 2, where each element contains a np x np tensor product of Gauss-Lobatto points.

NE	common name	Resolution degrees	Resolution at equator (km)	Resolution at equator (miles)	N elements	N columns	factor over ne30 N columns

NE	common name	Resolution degrees	Resolution at equator (km)	Resolution at equator (miles)	N elements	N columns	factor over ne30 N columns
4	ultra low	7.5	835	520	96	866
11		2.7	304	190	726	6536
16		1.9	210	130	1536	13826
30	low	1.0	110	70	5400	48602	1x
120	high	0.25	28	17.25	86400	777602	16x
240		0.125	14	8.65	345600	3110402 (3.1M)	64x
256		0.1171875	13	8.1	393216	3538946 (3.5M)	73x
512		0.05859	6.5	4	1572864 (1.57M)	14155778 (14.16M)	291x
1024	ultra high	0.029297	3.25	2	6291456 (6.29M)	56623106 (56.6M)	1165x
2048		0.014648	1.63	1	25165824 (25.2M)	226492418 (226.5M)	4660x
3600		0.0083333	0.925	0.58	77760000 (77.76M)	699840002 (688.85M)	14400x

*All reported resolutions are average distances based on a third order cubed sphere spectral element domain using 4x4 Gauss-Labotto points (np=4).

**Standard vertical resolution for E3SM is 72 vertical levels.

For cubed sphere grids with np=4:

Resolution degrees = 360/4/NE/3
Resolution km = 40075/4/NE/3
Resolution miles = 24901/4/NE/3
Number elements = NE*NE*6
Number columns = 54*NE*NE + 2

For quick reference, one RRM grid being tested ne0np4_northamericax4v1 has 14454 elements and 130088 physics columns.

Now that we are moving to the physgrid (i.e. pg2) it is useful to have a table that compares various aspects of typical pg2 and np4 grids.

For the formulas, note that NP is normally 4 (ex. ne30np4) and NPG is normally 2 (ex. ne30pg2)

NE	np4 # physics columns *(NP-1)^2 6 * NE^2 + 2**	pg2 # physics columns *NE^2 6 * NPG^2**	np4 approx grid spacing [degrees] *360 / ( 4 NE * (NP-1) )**	pg2 approx grid spacing [degrees] *360 / ( 4 NE * NPG )**	np4 approx grid spacing [km] *40075 / ( 4 NE * (NP-1) )**	pg2 approx grid spacing [km] *40075 / ( 4 NE * NPG )**

NE	np4 # physics columns *(NP-1)^2 6 * NE^2 + 2**	pg2 # physics columns *NE^2 6 * NPG^2**	np4 approx grid spacing [degrees] *360 / ( 4 NE * (NP-1) )**	pg2 approx grid spacing [degrees] *360 / ( 4 NE * NPG )**	np4 approx grid spacing [km] *40075 / ( 4 NE * (NP-1) )**	pg2 approx grid spacing [km] *40075 / ( 4 NE * NPG )**
4	866	384	7.50	11.25	834.9	1252.3
8	3,458	1,536	3.75	5.63	417.4	626.2
11	6,536	2,904	2.73	4.09	303.6	455.4
16	13,826	6,144	1.88	2.81	208.7	313.1
30	48,602	21,600	1.00	1.50	111.3	167.0
45	109,352	48,600	0.67	1.00	74.2	111.3
60	194,402	86,400	0.50	0.75	55.7	83.5
120	777,602	345,600	0.25	0.38	27.8	41.7
256	3,538,946	1,572,864	0.12	0.18	13.0	19.6
512	14,155,778	6,291,456	0.06	0.09	6.5	9.8
1024	56,623,106	25,165,824	0.03	0.04	3.3	4.9
2048	226,492,418	100,663,296	0.01	0.02	1.6	2.4