EASE-DGGS: a hybrid discrete global grid system for Earth sciences

Figures & data

Table 1. Example of common Earth observation systems and their respective pixel sizes.

EO System	On-ground resolutions (m)
WorldView-3	0.31/1.24/3.70
Planet	0.50
SPOT-7	1.5/6
Sentinel-2	10/20/60
Landsat-8	15/30/100
MODIS	250/500/1000
VIIRS	375/750

Table 2. Comparison of cell sizes between H3 and rHEALPix at various refinement ratios. For this comparison, H3 cells are treated as a circle with an equivalent diameter.

DGGS	H3	rHEALPix	rHEALPix	rHEALPix
Ref. Ratio	7	4	9	14
Level	Equiv. diameter (m)	Cell Width (m)	Cell Width (m)	Cell Width (m)
0	2,326,362.90	10,013,169.15	10,013,169.15	10,013,169.15
1	879,282.53	5,006,584.58	3,337,723.05	2,503,292.29
2	332,337.56	2,503,292.29	1,112,574.35	625,823.07
3	125,611.79	1,251,646.14	370,858.12	156,455.77
4	47,476.79	625,823.07	123,619.37	39,113.94
5	17,944.54	312,911.54	41,206.46	9778.49
6	6782.40	156,455.77	13,735.49	2444.62
7	2563.51	78,227.88	4578.50	611.16
8	968.91	39,113.94	1526.17	152.79
9	366.22	19,556.97	508.72	38.20
10	138.42	9778.49	169.57	9.55
11	52.32	4889.24	56.52	2.39
12	19.77	2444.62	18.84	0.60
13	7.48	1222.31	6.28	0.15
14	2.83	611.16	2.09	0.04
15	1.07	305.58	0.70	0.01

Figure 1. Comparison of the discontinuities and distortions of two equal area representations of the Earth’s surface: a) representation using the rHEALPix hexadron datum; and b) projected representation using EASE Grid version 2. Note that the Orange ellipses are Tissot’s indicatrices, which indicate the amount and direction of surface distortion at various locations.

Table 3. Refinement ratio for each level of EASE-DGGS and corresponding cell resolution. Refinement ratio is currently not defined below Level 6.

Level	Ref. Ratio	Num. Cells	Cell dimensions [meters]
0	16	391,384	36,032.22084 × 36,032.22084
1	9	1,565,536	9008.05521 × 9008.05521
2	9	4,696,608	3002.68507 × 3002.68507
3	100	14,089,824	1000.89502 × 1000.89502
4	100	140,898,240	100.08950 × 100.08950
5	100	1,408,982,400	10.00895 × 10.00895
6	N.D.	14,089,824,000	1.000895 × 1.000895

Table 4. Longitude, latitude, and EASE-Grid coordinates (x, y) for the upper left and lower right of the EASE-DGGS.

Grid locations	Longitude	Latitude	EASE X [m]	EASE Y [m]
Upper-left	−180.0	85.04456640	−17,367,530.445161372	7,314,540.830638504
Lower-right	180.0	−85.04456640	17,367,530.445161372	−7,314,540.830638504

Figure 2. Hierarchical schema and decomposition of the Grid ID naming convention.

Figure 3. Representation of the address-indexing scheme underpinning EASE-DGGS. Note that all coordinate pairs are in y, x (row, column) order.

Table 5. The address-indexing scheme is compatible with a 64-bit address space representation.

Bit Range	Type	Description
0–6	Bit flag	Indicates hierarchy level.
7–15	Integer	Indicates Level 0 row.
16–25	Integer	Indicates Level 0 column.
26–29	Integer	Indicates Level 1 pixel location in Level 0 cell.
30–33	Integer	Indicates Level 2 pixel location in Level 1 cell.
34–37	Integer	Indicates Level 3 pixel location in Level 2 cell.
38–45	Integer	Indicates Level 4 pixel location in Level 3 cell.
46–52	Integer	Indicates Level 5 pixel location in Level 4 cell.
53–59	Integer	Indicates Level 6 pixel location in Level 5 cell.
60–63	–	Unused.

Table 6. Initial functions supported by GEMS Grid API.

Function Name	Description
points_to_grid	Map points (and optional values) to GEMS Grid cells at provided resolution.
poly_to_grid	Given a GeoJSON polygon and a specified grid resolution level, return the corresponding GEMS grid cell IDs.
grids_to_geom	Given a list of GEMS grid cell IDs, return a list of lon/lat values corresponding to the grid cell centroids and a polygon. Output points provided in GeoJSON.
get_grid_parents	Given a list of GEMS grid cell IDs, return a list of the parents of those grid IDs.
get_grid_children	Given a list of GEMS grid cell IDs, return a nested list of the children of each input grid ID
aggregate	Given GEMS grid cell IDs with a value associated with each Grid ID, return corresponding GEMS grid cell IDs with aggregated values at a specified grid resolution level coarser than that provided.

Data availability statement

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