DMD & HDMD of the Annular Modes

This repository contains scripts/codes to calculate Dynamic mode decomposition (DMD) and Hankel Dynamic Mode Decomposition (HDMD) of the Annular Modes based on Matlab and NCL

1. dmd_u_erainterim.m includes the codes to calculate dynamic mode decomposition of the zonal mean zonal wind anomalies (p, lat) from ERA-Interim.

2. eof_u_erainterim.ncl includes the codes to calculate empirical orthogonal functions of the zonal mean zonal wind anomalies from ERA-Interim.

3. corr_dmd_u_erainterim.ncl includes the codes to find pairs of DMD modes that are highly correlated with the EOF modes.

4. dmd_u_erainterim_plot.ncl includes the codes to plot the best pairs of DMD modes.

5. hdmd_u_erainterim.m includes the codes to calculate Hankel dynamic mode decomposition of the zonal mean zonal wind anomalies (p, lat) from ERA-Interim.

6. eof_u_erainterim.ncl includes the codes to calculate empirical orthogonal functions of the zonal mean zonal wind anomalies from ERA-Interim.

7. corr_hdmd_u_erainterim.ncl includes the codes to find pairs of HDMD modes that are highly correlated with the EOF modes.

8. hdmd_u_erainterim_plot.ncl includes the codes to plot the best pairs of HDMD modes.

9. GCM_HDMD.m is alculating the basis functions (EOFs or DMD modes or Hankel-DMD modes depending on the entries)

Figure 1. Principal oscillation patterns (POPs) or dynamical mode decomposition (DMD) patterns (color shading) superimposed with the two leading EOF modes (contour lines) for the Southern Hemisphere zonal mean large-scale circulation. (a) Real and (b) imaginary parts of the dominant Southern Hemisphere POPs from year-round ERA-Interim data, calculated at θ =11 days (representing the modes onto which the first two EOFs project the most strongly). The corresponding eigenvalue is λ = -0.0974 ± 0.0425i day−1. The contour lines denote the EOF1 (EOF2) pattern superimposed with the real (imaginary) parts of the POPs (Lubis and Hassanzadeh, in review).