Recent studies of observational climate data have shown that Earth’s climate system: has many abrupt climate shifts; is phase locked to an annual cycle of Solar origin; and is chaotic. These phenomena are related and are summarized below.
The climate shift of the mid-1970s is well known. Among the first to characterize this particular Climate Shift was Trenberth , who in a study of the Pacific mean sea level pressure reported a “different regime after 1976”. Numerous studies have confirmed this and many other Climate Shifts. A new innovative way to identify Climate Shifts using networks of climate indices was introduced by Swanson and Tsonis . Their method, which can be thought of as a different quantitative “teleconnections” scheme, consisted of two parts. The first part was a definition of a “distance” d between two indices involving the Pearson correlation function. Second, the correlation among more than two indices was defined by “synchronization”, which is a particular function of the individual distances. In a study of a network of four northern hemispheric climate indices (Nino; Pacific Decadal Oscillation, PDO; North Atlantic Oscillation, NAO; and the North Pacific Index, NPI) they reported “synchronization peaking” showing five Climate Shifts since 1900 including the mid-1970s Climate Shift.
Douglass  (here) improved the Swanson and Tsonis scheme in a number of ways. A different distance “d” was defined so that it satisfied the 3 triangle conditions to be in a mathematical metric space. This then allowed the correlation among 3 or more indices to be easily measured using the diameter D from Topology. Minima in D corresponds to high correlation. These new definitions were used to study of a different “more global” set (Nino3.4, north and south Pacific indices and Atlantic Multidecadal Oscillation, AMO) of climate indices that included both north and south hemispheres . The more sensitive D plots showed 18 strong minima (Climate Shifts) since 1870, which included the 5 of Swanson and Tsonis. The 3 most recent Climate Shifts occurred during 1976–77, 1986–87 and 2002–03. A further improvement in the scheme was made by Towsley, Pakianathan and Douglass  (here). They showed that the topological area A defined also from the distances d was even more sensitive.
Figure 1 below from Towesly et al. sums the results. Both the diameter D and the area A since 1940 are plotted. The minima which corresponds to the Climate Shifts are indicated by arrows. The three most recent Climate Shifts are: 1976-1977 (the mid-1970s shift); 1986-1987 (missed by Swanson and Tsonis); and 2001-2002 (this Climate Shift is seen to be particularly strong.
Phase-Locked Climate States
What is the nature of the climate state between Climate Shifts? In a later paper Douglass [2011a] (here) studied the Pacific sea surface temperatures in greater detail and showed that the climate system is frequently phase locked to an annual cycle. The abstract of that paper gives a summary.
The Pacific sea surface temperature data contains two components: NL, a signal that exhibits the familiar El Niño/La Niña phenomenon and NH, a signal of one-year period. Analysis reveals: (1) The existence of an annual solar forcing FS; (2) NH is phase locked directly to FS while NL is frequently phase locked to the 2nd or 3rd subharmonic of FS. At least ten distinct subharmonic time segments of NL since 1870 are found. The beginning or end dates of these segments have a near one-to-one correspondence with the abrupt climate changes reported by Douglass .
The plot below is a Figure from Douglass [2011a] of NL from 1990 to 2012. The plot shows two complete phase-locked segments. The first is a segment of 3 cycles of period 3-years from about Dec 1991 to Dec 1999. Note that the El Niño of 1997-98 is the third oscillation in this segment. The second segment shows 3 cycles of period 2-years from about June 2002 to Mar 2008. A new phase-locked segment began about April 2009; the period is not yet determined [as of Nov 2011] but may be 2-years. The explanation for the abrupt beginnings or endings is not known.
Figure 2 from Douglass [2011a]
Chaos of the climate system
Douglass [2011b] (here) also studied various ENSO time series and showed from a determination of the Lyapunov exponents that the underlying climate system is chaotic . See table below. In particular:
- dimensionality d = 3
- one exponent is positive, which by definition means that the system is chaotic
- the El Niño index NL has one exponent ≈ 0, which mean that the underlying dynamics are described by d (=3) first order differential equations
Since the time series are bounded and the phase-locked states are predominately 2nd and 3rd subharmonic of the annual forcing, then the chaos of the climate system is probably deterministic (bounded) of low order.
Table of Lyapunov exponents of ENSO indices. From Dougass [2011b]
Studies of various climate indices suggest that the global climate system is chaotic of low order. In particular, the ENSO indices show many time segment that are phase locked to an annual cycle probable of Solar origin. These phase locked states have abrupt beginnings and ending, which have occurred at least 18 times since 1870.
Predicting future climate phenomenon depends upon knowledge of the past and an extrapolation to the future that assumes continuity of the relevant climate variables. Continuity of climate indices of interest across an abrupt Climate Shift cannot be assumed and any analysis that does so may be meaningless.
Douglass D.H. (2010) Topology of Earth’s climate indices and phase-locked states. Physics Letters A 374 p4164-4168. doi:10.1016/j.physica.2010.08.025. (pdf)
Douglass D. H. (2011b) Separation of a Signal of Interest from a Seasonal Effect in Geophysical Data: I. El NiÃ±o/La NiÃ±a Phenomenon David H. Douglass International Journal of Geosciences, 2011, 2, **-** Published Online November 2011 (pdf)
Towsley A., J. Jonathan Pakianathan and D.H. Douglass.(2011) Correlation Angles and Inner Products: Application to a Problem from Physics International Scholarly Research Network, ISRN Applied Mathematics, Volume 2011, Article ID 323864, doi:10.5402/2011/323864 (pdf)
Swanson K. L. and A. A. Tsonis (2009) Has the climate recently shifted? Geophys Res. Letters 36 L06711, doi:10.1029/2008GL03022
Trenberth K. E. (1990) Recent observed interdecadal climate changes in the northern hemisphere. Bull. Amer. Meteorol. Soc. 71 p988–993
JC comment. This guest post arose from an email that David Douglass sent to me pursuant to the Santa Fe Conference about some of his recent papers. I invited him to do a guest post, since this has been a topic of interest at Climate Etc. Previous Climate Etc. posts on this topic include:
I would like to thank David Douglass for his post, and remind you that guests posts implies no particular endorsement by myself.