# Section 2.2

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## 2.2 Earth Locating the Polar Satellite Data

The Earth viewing instruments on the NOAA satellites (with one exception) are cross-track scanners; i.e., they scan perpendicular to the direction of movement of the satellite. For each instrument several quantities are important for Earth viewing:

1. The angular field of view for a single observation - instantaneous field of view (IFOV) - not needed to compute Earth locations.

2. The step angle between consecutive observations.

3. The step time.

4. The number of steps.

These values are all measured at the satellite position. A scan angle of zero corresponds to the midpoint of the scan. It may not correspond to an actual IFOV. Values for the scan data for each instrument can be found in Appendix J.

The actual area on the Earth observed in an IFOV or encompassed within the width of a scan swath depends on the height of the satellite above the Earth surface. This height is not constant for two reasons. Even if the satellite were in a perfectly circular orbit, the Earth is approximately an ellipsoid, the radius of which varies by 21.4 kilometers from equator to pole. Additionally, the satellite orbit, while very close to circular, is not exactly so. Since the Earth center is at one focus of the elliptic orbit, it is displaced to one side of the ellipse. While the combined effects of these two factors must be considered for correct Earth location, for generalized approximations they may be neglected, and the orbit considered to be perfectly circular about a spherical Earth.

Within a single scan, the area on the Earth within an IFOV will increase with the angle from nadir, due to the combined effects of an oblique viewing angle and the curvature of the Earth. The nadir direction is defined by a line through the satellite which is perpendicular to the surface of the Earth ellipsoid. This point of intersection of this line with the ellipsoid is defined as the sub-satellite point (SSP).

Using the satellite position, the scan angle, and any pertinent attitude angles (in Section 2.3), the direction in inertial space in which a given instrument is looking - the Line of Sight (LOS) - is found. The intersection of the LOS with the ellipsoid may then be found. In order to determine the longitude of the intersection, the Greenwich Hour Angle (GHA) must be found for the time of the observation. This is the longitude difference between the Greenwich meridian and the zero "longitude" of the inertial coordinate system - the Vernal Equinox. Once this is done the exact Earth location which the instrument is viewing (geodetic latitude and longitude) may be found. See Appendix I for the Earth location algorithm.