Print Email Facebook Twitter Ultra-high degree spherical harmonic analysis and synthesis using extended-range arithmetic Title Ultra-high degree spherical harmonic analysis and synthesis using extended-range arithmetic Author Wittwer, T. Klees, R. Seitz, K. Heck, B. Faculty Aerospace Engineering Department Delft Institute of Earth Observation and Space Systems Date 2007-07-12 Abstract We present software for spherical harmonic analysis (SHA) and spherical harmonic synthesis (SHS), which can be used for essentially arbitrary degrees and all co-latitudes in the interval (0°, 180°). The routines use extended-range floating-point arithmetic, in particular for the computation of the associated Legendre functions. The price to be paid is an increased computation time; for degree 3,000, the extended-range arithmetic SHS program takes 49 times longer than its standard arithmetic counterpart. The extended-range SHS and SHA routines allow us to test existing routines for SHA and SHS. A comparison with the publicly available SHS routine GEOGFG18 by Wenzel and HARMONIC SYNTH by Holmes and Pavlis confirms what is known about the stability of these programs. GEOGFG18 gives errors <1 mm for latitudes [-89°57.5?, 89°57.5?] and maximum degree 1,800. Higher degrees significantly limit the range of acceptable latitudes for a given accuracy. HARMONIC SYNTH gives good results up to degree 2,700 for almost the whole latitude range. The errors increase towards the North pole and exceed 1 mm at latitude 82° for degree 2,700. For a maximum degree 3,000, HARMONIC SYNTH produces errors exceeding 1 mm at latitudes of about 60°, whereas GEOGFG18 is limited to latitudes below 45°. Further extending the latitudinal band towards the poles may produce errors of several metres for both programs. A SHA of a uniform random signal on the sphere shows significant errors beyond degree 1,700 for the SHA program SHA by Heck and Seitz. Subject Spherical harmonic analysisSpherical harmonic synthesisExtended-range arithmeticNumerical stability To reference this document use: http://resolver.tudelft.nl/uuid:99fb9dcf-e90e-4fa9-8deb-92c6d4e55593 Publisher Springer ISSN 1432-1394 Source Journal of Geodesy, 82 (4-5) Part of collection Institutional Repository Document type journal article Rights (c) 2007 The Authors; Springer Files PDF wittwer_2008.pdf 478.14 KB Close viewer /islandora/object/uuid:99fb9dcf-e90e-4fa9-8deb-92c6d4e55593/datastream/OBJ/view