NOAA KLM User's Guide

Appendix I.1

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I.1 General

This document describes a general algorithm for computing Earth location values for data from scanning radiometers flown on three-axis stabilized polar orbiting satellites. Given the following information about any data point, a corresponding latitude and longitude on Earth can by computed:

Position and velocity of the satellite as a function of time

Position vector P sub sat of t is composed of componants X sub sat, Y sub sat and Z sub sat

where Postion Vector P sub sat at time t is the position vector of the satellite and its components are expressed in the earth-centered-inertial coordinate system I (e.g., equator and equinox of date) at a time t in a standard time system (such as UTC).

Velocity vector V sub sat of t is composed of componants X dot sub sat, Y dot sub sat and Z dot sub sat

where Velocity vector V sub sat of t is the velocity of the satellite relative to the same inertially fixed coordinate system I at time t with its components expressed in that system.

Rotation of the Earth in the same time system, t, relative to the earth-fixed-inertial coordinate system, I, with a rotation angle written G(t), commonly called the "Greenwich Hour Angle".

3) Misalignments of the instrument from the coordinate system in which the nadir position of the scanner points towards the subsatellite point and scanning is perpendicular to the scan-axis vector/satellite subpoint vector plane. (see note below.)

             a. the misalignments are constant instrument mounting and/or attitude errors

             b. misalignments or attitude errors as functions of time in the t system

4) The time difference between the t system and the time-tagging system of the satellite, (i.e., the onboard computer).

5) The timing and angular displacements of each data sample in the scanning cycle.


The constant instrument mounting and/or time dependent attitude errors for NOAA satellites are minimized by the Attitude Determination And Control System (ADACS) onboard the spacecraft. This system orients the satellite in such a way that the nadir position of the scanning instruments always points toward the geodetic satellite subpoint. The residual errors of this system are reported in the data stream and could be used to correct the earth locations calculations in the paper. However, the handling of these misalignment errors, as a function of time, is somewhat complicated and beyond the intended scope of this algorithm description. These misalignments are included here for the sake of completeness.

Amended May 8, 2006

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