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Polar Stereographic Projections and Grids

The polar stereographic projection specifies a projection plane or grid tangent to the Earth at 70 degrees. The planar grid is designed so that the grid cells at 70 degrees latitude are 25 km by 25 km. For more information on this topic please refer to Pearson (1990) and Snyder (1987). This projection often assumes that the plane is tangent to the Earth at the pole. Thus, since there is a one-to-one mapping between the Earth's surface and the grid at the pole, 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, the projection is true at 70 degrees rather than at the poles. This increases the distortion at the poles by three percent and decreases the distortion at the grid boundaries by the same amount. 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 about 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 kilometers (km) and an eccentricity (e) of 0.081816153. To properly convert these coordinates to a polar stereographic grid (the projection of choice), 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.

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 Northern and Southern grids' approximate outer boundaries 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.

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.

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.

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