I have previously described a basic thermodynamic model for global average temperature that I call CSALT. It consists of 5 primary factors that account for trend and natural variability. The acronym C S A L T spells out each of these factors.

C obviously stands for excess atmospheric CO2 and the trend is factored as logarithm(CO2).

S refers to the ENSO SOI index which is known to provide a significant fraction of temperature variability, without adding anything by way of a long-term trend. Both the SOI and closely correlated Atmospheric Angular Momentum (AAM) have the property that they revert to a long-term mean value.

A refers to aerosols and specifically the volcanic aerosols that cause sporadic cooling dips in the global temperature measure. Just a handful of volcanic eruptions of VEI scale of 5 and above are able to account for the major cooling noise spikes of the last century.

L refers to the length-of-day (LOD) variability that the earth experiences. Not well known, but this anomaly closely correlates to variability in temperature caused by geophysical processes. Because of conservation of energy, changes in kinetic rotational energy are balanced by changes in thermal energy, via waxing and waning of the long-term frictional processes. This is probably the weakest link in terms of fundamental understanding, with  the nascent research findings mainly coming out of NASA JPL (and check this out too).

T refers to variations in Total Solar Irradiance (TSI) due mainly to sunspot fluctuations. This is smaller in comparison to the others and around the level predicted from basic insolation physics.

Taken together, these factors account for a correlation coefficient of well over 90% for a global temperature series such as GISTEMP.

Over time I have experimented with other factors such as tidal periodicities and other oceanic dipoles such as North Atlantic Oscillation, but these are minor in comparison to the main CSALT factors. They also add more degrees of freedom, so they can also lead one astray in terms of spurious correlation.  A factor such as AMO contains parts of the temperature record itself so also needs to be treated with care.

My biggest surprise is that more scientists don’t do this kind of modeling. My guess is that it might be too basic and not sophisticated enough in its treatment of atmospheric and climate physics to attract the General Circulation Model (GCM) adherents.

So what follows is a step-by-step decomposition of the NASA GISS temperature record shown below, applying the symbolic regression tool Eureqa as an alternative to the CSALT multiple linear regression algorithm. This series has been filtered and a World War II correction has been applied.

 

The first step is to add the factors to Eureqa as a set of time series, running from 1880 to 2010. (The AMO only runs to 2010 so was truncated there).  Then we instruct Eureqa to include the CSALT factors as algebraically manipulable symbolic terms, in addition to any number of sinusoidal components that it sees fit to include.

GISS = f(CO2, SOI, Aero, LOD, TSI, AAM, AMO)

The strongest component that Eureqa finds in Fig 1 is ln(CO2), immediately raising the correlation coefficient to above 0.93.

The next factor along the Pareto complexity curve  is LOD, raising the CC to 0.96 (Fig 2).

At this point, to improve the dynamic range, one can shift CO2 and LOD as known factors and then let Eureqa analyze the resultant residual.

GISS - CO2 - LOD = f(SOI, Aero, TSI, AAM, AMO)

It first suggests an AAM factor, giving a correlation coefficient of 0.61 on the residual (Fig 3).

Next the volcanic aerosol factor (Aero) raises the coefficient to 0.67 (Fig 4).

The SOI factor helps to register the peaks and valleys strongly as El Ninos and La Ninas modulate the earth’s temperature, raising the CC above 0.7 (Fig 5).

Next, the TSI raises the residual CC to 0.73 (Fig 6).

The remaining fluctuations show modulation aligned with the Atlantic Meridional Oscillation (Fig 7). This was only after the AMO was demodulated of its slowly-varying envelope, applying an 8-year isolation as shown here.

The last strong Pareto front contribution is one that Eureqa identified by itself. This is a ~19.5 year period sinusoidal factor that either accentuates the 21-22 year TSI Hale cycle or possibly related to a solar-tidal reinforcing Metonic cycle of 19 years (Fig 8).

Overall, it is clear that all the detail in the natural fluctuations are explained by a limited set of thermodynamic measures along with the influence of CO2.  The introduction of the AMO factor shows how an Atlantic dipole complements the SOI Pacific dipole.  Even if this factor, which is based on temperature, was not included, the fit would still be compelling.

Putting the factors together using the values up to 1960 as a training interval, the overall fit is shown in Fig 9.

Fig 10 is the observed versus predicted regression considering all the factors, showing how well factoring explains both the tend and natural variations. Then with a model such as the SOIM to explain and possibly project fluctuations in the SOI, the approach has potential predictive power as well.

Eureqa is a very easy tool to use and anyone can apply a CSALT-like of analysis without needing to get bogged sown in the details of mathematical regression techniques.