[CIG-MC] CitcomS Legendre polynomial normalization

Shijie Zhong Shijie.Zhong at Colorado.Edu
Wed Mar 3 17:13:39 PST 2010

Hi Joy,

For how the normalization or Legendre polynomials is defined, you can check 
the recent benchmark paper [Zhong et al., G^3, 2008] that also includes 
benchmarks of dynamic topography and geoid for CitcomS.
You are right that the recursion relation for the Legendre polynomials used in 
CitcomS is different from the standard in Numerical Recipes by Press. The 
standard one in Numerical Recipes blows up for spherical harmonic degree l > 
20 or something, even with double precision computation. I re-derived a 
recursion relation in 1997 that is stable for nearly all l's and is used in CitcomS. 


Shijie Zhong
Department of Physics
University of Colorado at Boulder
Boulder, CO 80309
Tel: 303-735-5095; Fax: 303-492-7935
Web: http://anquetil.colorado.edu/szhong

---- Original message ----
>Date: Wed, 3 Mar 2010 15:45:36 -0800
>From: cig-mc-bounces at geodynamics.org (on behalf of Joy Hines 
<jmhines at ucdavis.edu>)
>Subject: [CIG-MC] CitcomS Legendre polynomial normalization  
>To: cig-mc at geodynamics.org
>   Hello, 
>   I have been looking at the geoid output from
>   CitcomS, and am not sure why a non-standard
>   normalization is used for the Legendre polynomials
>   in the function modified_plgndr_a.  The recursion
>   used in CitcomS differs from the algorithm given in
>   Numerical Recipes in C (Press, 2nd Ed., p. 254).
>    Is there a reference for the modification of the
>   standard normalization?
>   Thanks very much,
>   Joy Hines
>   --
>   Graduate Student Researcher
>   Department of Geology
>   University of California, Davis
>   2205 Earth & Physical Sciences
>   Davis, CA 95616
>CIG-MC mailing list
>CIG-MC at geodynamics.org

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