IGRF model Implementation (Calculating the Partial Derivatives of the Legendre Polynomials)

I was implementing the IGRF-13 Geomagnetic model, and a parts of the equation (3 a, b, and c) requires calculating the Associated Legendre polynomials with Schmidt quasi-Normalization and its partial derivatives.

For the Associated Legendre polynomials, I used the function Legendre(n, x, 'sch') and it works perfectly. But now how would I calculate their partial derivatives?

Equations 19 a, b, and c provides some recursive formulae, but I am not getting the correct result possibly because I might have implemented them incorrectly. Even the sample MATLAB code provided in the paper is not producing the proper results.

I would really appreciate it if someone could provide a proper implementation for calculating the Partial derivatives of these Legendre Polynomials.

Thank you,

Abinay Brown

Reference: https://hanspeterschaub.info/Papers/UnderGradStudents/MagneticField.pdf

Answer 1

[Bjorn Gustavsson]

Have a look at the IGRF implementations available on the file exchange: international-geomagnetic-reference-field-igrf-model, international-reference-ionosphere-iri-model, earth-magnetic-field-with-igrf-13th-gen and igrf-magnetic-field. I've used one of the packages bby Drew Compston.

HTH

[Abinay Brown]

I checked out the package by Drew Compston earlier, he happened to use a similar set of recursive equations for calculating the Partial Derivative but he hasn't explained the source of the equations.