## Polar Stereographic Projection and Grid

NSIDC's polar stereographic projection specifies a projection plane or grid tangent to the Earth's surface at 70 degrees northern and southern latitude. This planar grid is designed so that the grid cells at 70 degrees latitude are exactly the nominal grid resolution. For more information on this topic, please refer to Pearson (1990) and Snyder (1987). It is common in polar stereographic projections to set the plane or grid tangent to the Earth's surface at the pole. Since there is a one-to-one mapping between the Earth's surface and the grid at the tangent point, there is no distortion at the pole. Distortion in the grid increases as the latitude decreases because more of the Earth's surface falls into any given grid cell, which can be quite significant at the edge of the northern SSM/I grid where distortion reaches 31 percent. For the southern grid, the SSM/I grid has a maximum distortion of 22 percent. To minimize the distortion, NASA and NSIDC made this polar stereo projection true at 70 degrees rather than at the poles. While this increases the distortion at the poles by six percent, the latitude of 70 degrees was selected so that little or no distortion would occur in the marginal ice zone. Another result of this assumption is that fewer grid cells will be required, as the Earth's surface is more accurately represented. This saves approximately 100 megabytes per year in data storage.

The polar stereographic formulae for converting between latitude/longitude and x-y grid coordinates have been taken from map projections used by the U.S. Geological Survey (Snyder 1982). Several different ellipsoids were compared to the Hughes ellipsoid; and in each case, differences were less than 1 km over the SSM/I grids. However, differences of up to 9 km were found if a sphere rather than an ellipsoid was used. Thus, it is an explicit requirement that an ellipsoid be used in processing the data.

An ellipsoid is defined by equatorial radius and eccentricity. The ellipsoid used in the Hughes software assumes a radius of 3443.992 nautical miles or 6378.273 km and an eccentricity (e) of 0.081816153. To properly convert these coordinates to a polar stereographic grid, the conversion should assume the Hughes ellipsoid.

### Polar Stereographic Grid Definitions

#### Grid Dimensions

The grid size varies depending on the region and channel, as shown in Table 1.

Table 1: Grid Dimensions
Region
Nominal Gridded Resolution (km)
Columns
Rows
North 6.25 1216 1792
North 12.5 608 896
North 25 304 448
South 6.25 1264 1328
South 12.5 632 664
South 25 316 332

Latitude/longitude pairs are geodetic, with positions on the Earth based on an ellipsoid rather than a sphere.

#### SSM/I Polar Spatial Coverage Maps

Northern Hemisphere
Southern Hemisphere

#### Grid Coordinates

The origin of each x, y grid is the respective pole. The approximate outer boundaries of the Northern and Southern grids are defined in Table 2 and Table 3, respectively. Corner points are listed; apply values to the polar grids reading clockwise from upper left. Interim rows define boundary midpoints.

Table 2: Northern Hemisphere Grid Coordinates
X (km)
Y (km)
Latitude (deg)
Longitude (deg)
-3850 5850 30.98 168.35 corner
0 5850 39.43 135.00 midpoint
3750 5850 31.37 102.34 corner
3750 0 56.35 45.00 midpoint
3750 -5350 34.35 350.03 corner
0 -5350 43.28 315.00 midpoint
-3850 -5350 33.92 279.26 corner
-3850 0 55.50  225.00 midpoint

Table 3: Southern Hemisphere Grid Coordinates
X (km)
Y (km)
Latitude (deg)
Longitude (deg)
-3950 4350 -39.23 317.76 corner
0 4350 -51.32  0.00  midpoint
3950 4350 -39.23 42.24 corner
3950 0 -54.66 90.00 midpoint
3950 -3950 -41.45 135.00 corner
0 -3950 -54.66 180.00 midpoint
-3950 -3950 -41.45 225.00 corner
-3950 0 -54.66 270.00 midpoint

### Grid Transformation Tools

The Mapx: Map Transformations Library is a coordinate transformation library. Users of this tool will need the following map projection parameter (.mpp) and grid parameter definition (.gpd) files to work with the DMSP SSM/I Daily Polar Gridded Brightness Temperatures data. See Table 4 for information on which MPP and GPD file to use for a given grid.

Table 4: MPP and GPD File Use
MPP and GPD File
Grid
Access Data
Nps.mpp Polar stereographic north
Sps.mpp Polar stereographic south
N3B.gpd SSM/I grids, north polar region, 25 km
N3A.gpd SSM/I grids, north polar region, 12.5 km
S3B.gpd SSM/I grids, south polar region, 25 km
S3A.gpd SSM/I grids, south polar region, 12.5 km

### References

Knowles, Kenneth W. 1993. Points, Pixels, Grids, and Cells: A Mapping and Gridding Primer. Unpublished report to the National Snow and Ice Data Center, Boulder, CO USA.

Maslanik, J., and J. Stroeve. 1990. DMSP SSM/I brightness temperature grids for the polar regions on CD-ROM: user's guide. Boulder, CO USA: National Snow and Ice Data Center.

Pearson, F. 1990. Map projections: Theory and applications. CRC Press. Boca Raton, Florida. 372 pages.

Snyder, J. P. 1987. Map projections - a working manual. U.S. Geological Survey Professional Paper 1395. U.S. Government Printing Office. Washington, D.C. 383 pages.

Snyder, J. P. 1982. Map Projections Used by the U.S. Geological Survey. U.S. Geological Survey Bulletin 1532.