In Chapter 12 of the book, the math model behind the equatorial Pacific ocean dipole known as the ENSO (El Nino /Southern Oscillation) was presented.  Largely distinct to that, the climate index referred to as the Pacific Decadal Oscillation (PDO) occurs in the northern Pacific. As with modeling the AMO, understanding the dynamics of the PDO helps cross-validate the LTE theory for dipoles such as ENSO, as reported at the 2018 Fall Meeting of the AGU (poster). Again, if we can apply an identical forcing for PDO as for AMO and ENSO, then we can further cross-validate the LTE model. So by reusing that same forcing for an independent climate index such as PDO, we essentially remove a large number of degrees of freedom from the model and thus defend against claims of over-fitting.

The new research by Professor Michael Mann in his peer-reviewed article called “Absence of internal multidecadal and interdecadal oscillations in climate model simulations” asks whether the decadal >10 year (and perhaps faster cycles) in the AMO and PDO behave as an internal property of the ocean or whether the cycles are externally forced. The quandary is that Mann does not deny that the ENSO behavior has a strong internal oscillation, so what if anything makes ENSO special?

Like the AMO, the characteristic of PDO that distinguishes it from ENSO is in the longer decadal variation that it exhibits. In Fig 1 below, we show a model fit to PDO that relies on essentially the same input tidal forcing that was applied to the ENSO model. What is most impressive about the fit is how naturally the interdecadal cyclic variation emerges.

Figure 1: LTE model fit of PO using the forcing from ENSO

The comparison between the ENSO and PDO tidal forcing is shown in Fig 2 below. As with AMO, the clue to where the interdecadal cycle arises from is in the slight modulated curvature in the profile.

Figure 2: The tidal forcing applied to the PDO LTE model is very close to the ENSO model. It was allowed to vary from the same starting state during the fitting process but did not stray far, resulting in correlation coefficient near 0.99 (see inset). The slight concave-down curvature in the time-series is due to a fortnightly vs monthly interference.

What is causing the curvature is the interference between two closely aliased primary tidal forcings. These are the fortnightly tropical cycle of 13.66 days and the monthly anomalistic cycle of 27.55 days as described here in LOD characterization and see Fig A2 at the end of the AMO post.

The two primary forcings acting mutually are also observed in tidal tables, in what is known as the long-period 9-day tide labelled “Mt” . The period of this tide is ~9.133 days and so when applied to an annual impulse we get 365.242/9.133 = 39.99146. This number is very close to an integral value but not quite, so it will only reach a constructive interference against an annual impulse every 1/(40-39.99146) ~ 120 years.

Since the LTE model is nonlinear, the 120 year underlying cycle can readily transform into a 60 year harmonic. So — just as for the AMO — the ~60 year cycle emerges in the PDE time series with the appropriate LTE modulation as in Fig 3 below.

Figure 3 : LTE modulation applied to the PDO forcing. This is mainly comprised of a higher wavenumber modulation than that for ENSO. There is a lower wavenumber envelope that is comparable to the classic dipole wavenumber of ENSO, but the higher value seen is closer to that of the tropical instability wave (TIW) modulation of ENSO. These TIW wavelengths show up as the pair of downward excursions in the amplitude spectra in the inset. This generates what appears to be a noisier cycling of PDO, even though the model provides an excellent fit especially in being able to reproduce the interdecadal variation.

Although this analysis is slightly different than what we presented at the 2018 AGU meeting, the same bottomline stands, in that the tidal forcing is nearly equivalent for the ENSO, PDO, and AMO climate indices as show in Fig 4 below. This also applies to the IOD index, so that any long-term predictability may arise solely due to the ability to precisely refine this forcing along with the LTE modulation for the appropriate oceanic dipole.

Figure 4 : Nearly identical tidal forcing for the climate indices

The reality is that with the combination of AGW and the additive impact of multiple concurrently peaking oceanic dipoles, extremes in temperature can occur that may be larger than any time in modern times. Consider the possibility in Fig 4 of the IOD, ENSO, and SAM peaking simultaneously and the impact that has in Australia. And that is at least partly what is happening now.

Figure 4: What happens when peaks in surrounding climate dipoles concurrently occur with the ongoing secular AGW?

3 thoughts on “The PDO

  1. Pingback: PDO is even, ENSO is odd | GeoEnergy Math

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s