### Stretched 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 pole of stretching
33-36 Longitude of the pole of stretching
37-40
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) 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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