Geomagnetic data assimilation under Plesio-Geostrophy

Plesio-Geostrophy Model, or PG, is a reduced-dimensional model for 3-D magnetohydrodynamics (MHD) in rapidly rotating sphere. This is proposed by Jackson and Maffei (2020), and also contituted part of the doctoral work of Holdenried-Chernoff (2021).

The current ongoing implementation of PG model is the Python package PlesioGeostroPy. Figure below visualizes an eigenmode solved using this code.

Theory paper and reference material

• Theory and concept paper, Jackson and Maffei (2020).
• Daria Holdenried-Chernoff’s doctoral thesis (2021).

Formulation, documentation and results

• [PDF] Formulations for PG model: missing ingredients and new recipes. Recent updates:
  • Energy calculation: in progress
  • Multi-precision calculation: in progress
• [PDF] Results of the PG model.. Recent updates:
  • Hydrodynamic results added, equations and numerical analysis complete.
  • Malkus field results added, equations complete.
  • Poloidal dipolar field results added, equations complete.
• [PDF] Regularity conditions for general tensors in polar coordinates.

Code and demos

• [Repo] PlesioGeostroPy.
• [Documentation] PlesioGeostroPy.
• [IPython notebook] Regularity conditions on tensor components in polar coordinates.
• [IPython notebook] Quickstart for PlesioGeostroPy, alternatively view using nbviewer. Further code-specific tutorials, please refer to the documentation page.
• [IPython notebook] Eigenvalue solver for PG model.
• [IPython notebook] Demonstrative tests, currently includes
  • Using recurrence relation for evaluation of Jacobi polynomials,
  • Using product form to calculate the inner product matrices,
  • Multi-precision libraries, precision and efficiency tests, and calculating matrices in multi-prec,
  • Basis functions for vorticity and velocity components.