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by M. J. Brodzik, NSIDC
Introduction
Map Parameters
Grid Parameters
References
All Polar Pathfinder grids are based on either a north or south polar azimuthal equal-area map, and differ only in grid resolution. This document describes the map coordinate transformations and the relationships of the various resolution grids.
The north polar azimuthal equal-area map is defined as
The south polar azimuthal equal-area map is defined as
Both projections are based on a spherical model of the Earth with radius R = 6371.228 km. This radius gives a sphere with the same surface area as an ellipsoid using the International Datum.
Aspect ratios are:
| Azimuthal Equal-Area | |
|---|---|
| lat | k/h |
| 90 | 1.00 |
| 75 | 1.02 |
| 60 | 1.07 |
| 45 | 1.17 |
| 30 | 1.33 |
| 15 | 1.59 |
| 0 | 2.00 |
The SSM/I NL and SL grids were defined with a nominal cell size of 25 km x 25 km, and all other Polar Pathfinder grid resolutions are calculated as exact multiples or factors of this cell size. (The actual cell size C=25.067525 km was chosen to make the SSM/I cylindrical 25km grid exactly span the equator, and was then used for the azimuthal projections for the sake of SSM/I EASE-Grid consistency.) Of course, few "25km" cells actually have these dimensions, but they all have the same area.
The SSM/I grids represent full hemispheric coverage, and the TOVS and AVHRR grids are proper subsets of the full hemispheres.
The TOVS and AVHRR subsets of the SSM/I full Northern Hemisphere grid are shown in Figure 1.
Figure 1: The TOVS and AVHRR Polar Pathfinder Northern hemisphere grid subsets.
The AVHRR subsets of the SSM/I full Southern hemisphere grid is shown in Figure 2.
Figure 2: The AVHRR Polar Pathfinder Southern hemisphere grid subset (there is no TOVS Southern Hemisphere grid).
Grid coordinates (r,s) start in the upper left corner with r increasing to the right and s increasing downward. Rounding the grid coordinates up at .5 yields the grid cell number. Grid cell i,j is centered at grid coordinates (i,j) and bounded by: i-.5 ltamp;= r ltamp; i+.5, j-.5 ltamp;= s ltamp; j+.5.
With the exception of the AVHRR 1.25km grids (Na1 and Sa1), each of the Polar Pathfinder grids is defined such that the grid coordinates are coincident (a.k.a. "bore-centered") at the respective pole. All of these grids are square, symmetric about the pole, with an odd number of rows and columns, and the location of the center pixel of each grid is the (North or South) pole. The AVHRR 1.25km grids are the only exceptions, being exact multiples of the AVHRR 5 km grids, and so location of the pole in each of these is at the intersection of the 4 center pixels.
There are four SSM/I grids, six AVHRR polar grids, and one TOVS grid, as follows.
| Grid Name | Sensor | Resolution (km) | Hemisphere |
|---|---|---|---|
| TOVS | TOVS | 100 | Northern |
| NL | SSM/I | 25 | Northern |
| SL | SSM/I | 25 | Southern |
| NA25 | AVHRR | 25 | Northern |
| SA25 | AVHRR | 25 | Southern |
| NH | SSM/I | 12.5 | Northern |
| SH | SSM/I | 12.5 | Southern |
| NA5 | AVHRR | 5 | Northern |
| SA5 | AVHRR | 5 | Southern |
| NA1 | AVHRR | 1.25 | Northern |
| SA1 | AVHRR | 1.25 | Southern |
The dimensions and latitude extent of each grid are summarized below. The map projections used for all grids are defined with the origin at the respective pole. For the AVHRR and TOVS grids, the latitude extent listed is the latitude of the center of the corner pixels on the grid. For the SSM/I grids, the latitude extent listed is the latitude of the center of the center pixel on a side.
| Grid Name | Dimensions | Latitude Extent | ||
|---|---|---|---|---|
| Width | Height | Minimum | Maximum | |
| TOVS | 67 | 67 | 46.90928 N | 90.00000 N |
| NL | 721 | 721 | 0.33836 S | 90.00000 N |
| SL | 721 | 721 | 90.00000 S | 0.33836 N |
| NA25 | 361 | 361 | 29.89694 N | 90.00000 N |
| SA25 | 321 | 321 | 90.00000 S | 37.13584 S |
| NH | 1441 | 1441 | 0.25845 S | 90.00000 N |
| SH | 1441 | 1441 | 90.00000 S | 0.25845 N |
| NA5 | 1805 | 1805 | 29.74956 N | 90.00000 N |
| SA5 | 1605 | 1605 | 90.00000 S | 36.99339 S |
| NA1 | 7220 | 7220 | 29.72191 N | 90.00000 N |
| SA1 | 6420 | 6420 | 90.00000 S | 36.96667 S |
The relationships of the various grids are shown in Figure 3.
Figure 3: Relationships of various Polar Pathfinder grid resolutions, in the center TOVS 100km pixel.
