This code is an add-on to the OMI calculation package published in Hoffmann, C.G., Kiladis, G.N., Gehne, M. and von Savigny, C., 2021. A Python Package to Calculate the OLR-Based Index of the Madden- Julian-Oscillation (OMI) in Climate Science and Weather Forecasting. Journal of Open Research Software, 9(1), p.9. DOI: http://doi.org/10.5334/jors.331 which can be found on github in at https://github.com/cghoffmann/mjoindices.
The complete OMI algorithm is described in Kiladis, G.N., J. Dias, K.H. Straub, M.C. Wheeler, S.N. Tulich, K. Kikuchi, K.M. Weickmann, and M.J. Ventrice, 2014: A Comparison of OLR and Circulation-Based Indices for Tracking the MJO. Mon. Wea. Rev., 142, 1697–1715, https://doi.org/10.1175/MWR-D-13-00301.1
A description of the rotation algorithm can be found in Weidman, S., Kleiner, N., & Kuang, Z. (2022). A rotation procedure to improve seasonally varying empirical orthogonal function bases for MJO indices. Geophysical Research Letters, 49, e2022GL099998. https://doi.org/10.1029/2022GL099998
A FAIR compliant repository of this code can be found on Zenodo at https://doi.org/10.5281/zenodo.6870694
UPDATE 10/26/2022: The rotation algorithm has now been fully incorporated into the mjoindices package at https://github.com/cghoffmann/mjoindices. The documentation in that repository describes how to install the package and how to calculate OMI with the alternative rotation algorithm. The example files in this repository show exactly how the rotated EOFs in the Weidman et al. paper were calculated. The plotting functions in the ipynb file will reproduce the figures. The PCs calculated using the rotated EOFs (the modified OMI) are also included here.
If you use the OMI and rotation algorithm in your research, please cite the above three papers. Thank you!
The rotation post-processing method includes a projection and rotation postprocessing step that reduces noise in the original EOF calculation.
Postprocessing includes an alignment of EOF signs and a rotation algorithm that rotates the EOFs in three steps:
1. Projects EOFs at DOY = n-1 onto EOF space for DOY = n. This is done to reduce spurious oscillations
between EOFs on sequential days
2. Rotate the projected EOFs by 1/366 (or 1/365) per day to ensure continuity across January to December
3. Renormalize the EOFs to have a length of 1 (this is a small adjustment to account for small numerical
errors).
Figures from the EOF rotation paper can be reproduced using the eof_rotation_example.ipynb file, along with the functions in rotation_plotting_tools.py. An example of how to implement the rotation algorithm using the above packages can be found in either eof_rotation_example.ipynb or eof_rotation_example.py.
Adaptation written by Sarah Weidman, 2022. Contact: sweidman@g.harvard.edu if you have any questions or feedback!