Partly in response to Mikael Rittri's questions about compressing the

data files for the EGM models, I looked into seeing how well EGM2008 is

approximated by a few terms in its spherical harmonic expansion. The

quick answer is not very well. The bumps in EGM2008 are at all scales

and the coefficients in the spherical harmonic expansion decay very

slowly.

However, I thought it worth reporting on the magnitudes of the low order

terms. Recall that the range in geoid heights (in meters) relative to

WGS84 is about [-107, 86].

The lowest order terms, Y00, Y10, Y11, Y20, Y21 are all small (less than

0.5m), "by construction". (The volume if WGS84 is about right, the COM

of the geoid nearly matches WGS84, the flattening nearly matches WGS84.)

The biggest spherical harmonic component is the Y22 term, which is the

component that makes WGS84 into a triaxial ellipsoid. This makes the

equator an ellipse with major/minor equatorial axes

6378137 +/- 35 meters

The major axis is lon = -15, 165; the minor axis is lon = -105, 75. The

amount EGM2008 deviates from this triaxial shape (WGS84 + Y22 term) is

[-72, 70]. The reason that a triaxial model of the earth is not useful

is that you add a lot of mathematical complexity going from an oblate

ellipsoid to a triaxial ellipsoid and yet you have not gained much

(about 25%) in how well you approximate the geoid.

The next biggest contributions are the Y3m components which together

with their amplitudes (meters) above/below WGS84 are

Y31: +/- 29

Y33: +/- 21

Y30: +/- 16

Y32: +/- 14

These results were derived by taking spherical harmonic moments of the

gridded EGM2008 geoid numerically using the longitude and geographic

co-latitude as the independent variables.

I found it necessary to carry out these integrals directly rather than

using the spherical harmonic expansions provided by the NGA because the

NGA provides two expansions: one for the gravitational potential and

another for an undulation correction, and both of these use geocentric

co-latitude. I found it simplest just to perform the analysis on the

geoid height directly.

--

Charles Karney <

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SRI International, Princeton, NJ 08543-5300

Tel: +1 609 734 2312

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