For inter-calibrations between geostationary and sun-synchronous satellites, the orbits provide collocations near the GEO Sub-Satellite Point (SSP) within fixed time windows every day and night. In this case, we adopt the simple approach outlined in general option v0.1.
We define the GEO Field of Regard (FoR) as an area close to the GEO Sub-Satellite Point (SSP), which is viewed by the GEO sensor with a zenith angle less than a threshold. Wu [2009] defined a threshold angular distance from nadir of less than 60^\circ based on geometric considerations, which is the maximum incidence angle of most LEO sounders. This corresponds to \approx \pm 52^\circ in latitude and longitude from the GEO SSP. The GEO and LEO data is then subset to only include observations within this FoR within each inter-calibration period.
Mathematically, the GEO FoR is the collection of locations whose arc angle (angular distance) to nadir is less than a threshold or, equivalently, the cosine of this angle is larger than min_cos_arc. We chose the threshold min_cos_arc = 0.5, i.e., angular distance less than 60 degree.
Computationally, with known Earth coordinates of GEO nadir G (0, geo_nad_lon) and granule centre P (gra_ctr_lat, gra_ctr_lon) and approximating the Earth as being spherical, the arc angle between a LEO pixel and LEO nadir can be computed with cosine theorem for a right angle on a sphere (see Figure 3):
Equation 1:\cos (GP) = \cos (gra\_ctr\_lat) \cos (geo\_nad\_lon - gra\_ctr\_lon)
If the LEO pixel is outside of GEO FoR, no collocation is considered possible. Note the arc angle GP on the left panel of Figure 3, which is the same as the angle \angle GOP on the right panel, is smaller than the angle \angle SPZ (right panel), the zenith angle of GEO from the pixel. This means that the instrument zenith angle is always less than 60 degrees for all collocations.
Figure 3: Computing arc angle to satellite nadir and zenith angle of satellite from Earth location