### Stretched and Rotated Spherical Harmonic Coefficients

Created 07/29/2005

Octet No. Contents
15-18
J ― pentagonal resolution parameter
19-22 K ― pentagonal resolution parameter
23-26 M ― pentagonal resolution parameter
27
Representation type indicating the method used to define the norm (see Code Table 3.6)
28
Representation mode indicating the order of the coefficients (see Code Table 3.7)
29-32 Latitude of the southern pole of projection
33-36 Longitude of the southern pole of projection
37-40
Angle of rotation of projection
41-44
Latitude of pole of stretching
45-48
Longitude of pole of stretching
49-52
Stretching factor

 Notes: (1)   The pentagonal representation of resolution is general. Some common truncations are special cases of the pentagonal one:      Triangular: M = J = K      Rhomboidal: K = J + M      Trapezoidal: K = J, K > M (2)  Three parameters define a general latitude/longitude coordinate system, formed by a general rotation of the sphere. One choice for these parameters is:   (a) The geographic latitude in degrees of the southern pole of the coordinate system,06 for example.   (b) The geographic longitude in degrees of the southern pole of the coordinate system,λp for example.   (c) The angle of rotation in degrees about the new polar axis (measured clockwise when looking from the southern to the northern pole) of the coordinate system, assuming the new axis to have been obtained by first rotating the sphere through λpdegrees about the geographic polar axis and then rotating through (90 + 0p) degrees so that the southern pole moved along the (previously rotated) Greenwich meridian. (3) The stretching is defined by three parameters:       (a) The latitude in degrees (measured in the model coordinate system) of the "pole of stretching";       (b) The longitude in degrees (measured in the model coordinate system) of the "pole of stretching"; and       (c) The stretching factor C in units of 10-6 represented as an integer. The stretching is defined by representing data uniformly in a coordinate system with longitudeq λ and latitude θ1, where:         θ 1 = sin-1[(1- C2) + (1 + C2) sin θ] / [(1 + C2) + (1 - C2) sin θ ] and λ and θ are longitude and latitude in a coordinate system in which the "pole of stretching" is the northern pole. C = 1 gives uniform resolution, while C > 1 gives enhanced resolution around the pole of stretching.

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