Tuesday 23 August 2005

G2

PT0011
Using personal computers in spherical harmonic synthesis of high degree Earth Geopotential Models
Bethencourt, Abelardo¹, Wang, Jinling², Rizos, Chris², Kearsley, Arthur²
1 Politechnic University Of Madrid, Spain
2 School of Surveying & Spatial Information System
Author email: abeth@euitto.upm.es
At the end of this year (2005) it is expected a new Earth Geopotential Model (EGM) complete to degree and order 2159, with ±15 cm of global Root Mean Square (RMS) precision for the undulation of the Geoid. This EGM will improve considerably the resolution and precision of the current EGMs, thus, besides its natural use by the scientific community, it is expected also that it will be used by the public in general, especially in connection with the determination of the Orthometric Heights (by calculating Geoid Undulation by means of EGM and the ellipsoidal height with the GPS). To take into consideration the fact that the gravimetric quantities obtainable by Spherical Harmonic Synthesis of this EGM will be used by a wide range of people, we have revised and tested different algorithms and methods to computing them and their associated errors in view of its implementation in a Personal Computer (PC) of general use and, in consequence, of general standard. We have analysed the advantages and drawbacks of each one regarding its computational stability, time used for the PC in their execution, and problems related to the numerical underflow of the Associate Legendre Functions and their derivatives.

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