CSALT model and the Hale cycle

The CSALT model is able to pick out the TSI component of the average global temperature, matching the predicted value of about 0.05C thermal forcing over the last 130 years.

As an interesting experiment, I replaced the empirically observed and measured TSI profile with a set of harmonics representing the Hale cycle of solar activity.  This essentially described a pure sine wave with period of 22 years and five harmonics with periods of 11, 7.3, 5.5, 4.4, and 3.7 years. Each of these has an arbitrary phase and amplitude that is fitted by the CSALT multiple linear regression algorithm.

The result is shown in Figure 1 below.

Fig 1 : Replacing the TSI with sinusoidal harmonics with a fundamental frequency of the solar Hale cycle improved the fit of the CSALT model significantly (top panel). The bottom panel shows the 22 and 11 year contributions alone. Red arrows indicate the 22 year peaks associated with the Hale cycle. Note that the CSALT fitting model adjusts the major Hale phase to that of the TSI. A strong 7.3 year harmonic increases the correlation significantly.

What is significant about alignment is that the GISS temperature profile does not clearly show the Hale cycle, yet the CSALT regression model is able to dig the primary peaks out of the signal, showing the correct phase and relative amplitude corresponding to the TSI.   Note that the TSI does not provide any hints as that component was removed. The actual assistance was provided by the compensating removal of the other forcing components consisting of CO2, SOI, volcanic aerosols, and LOI corrections. In addition, the orbital and tidal parameters recently added to CSALT provided further discrimination.   Significantly, the CSALT tidal factors also showed an exact phase registration with the observed diurnal tides observed.

A critical harmonic in the series is the 1/3 period of the Hale cycle of approximately 7.3 years.  This appears to be an important factor in interpreting the North Atlantic oscillation dynamics, with the Hale “family” of harmonics as described in [1].   The 7.3 year period also has a relationship to the tidal precession, as it describes the duration of time it takes for the spring tides to realign with the calendar date — which is close to the perigee cycle of 7.7 years. As [1] states, “whole year multiples are important because, ultimately, climate cycles have to be tied to seasons”.   So this may in fact be a resonance that ties the tides to the solar cycle.

The 6 Hale frequencies also match those observed from solar neutrino experiments [2], as Mandal and Rachauduri find from the Homestake solar neutrino flux data:

“Wavelet amplitude versus periodicities graphs have been presented and it is observed that clear peaks are arising around the 22 years, 11 years, 7.3 years, 5.5 years, 4.4 years & 3.7 years periodicities. Among the height of the peaks shows that the periodicities of 5.5 years, 7.3 years, 11 years, 22 years are above the 95% confidence level, which strongly favours the existence of periodicities in the Homestake solar neutrino flux data. These type of periodicities are observed in the other forms of solar activities (i.e. sunspot number data, solar flare data etc.).”

Higher-order harmonics are evidently important in periodically pulsed dynamos as they provide the high-frequency content necessary to create the spikes while maintaining the observed periodic content.

What is fascinating about the CSALT model approach is that as the correlation between temperature data and model nears unity (nearing 0.995 now with limited filtering) the ability to discriminate fine features in the factoring increases markedly. This is not about being able to model a system given enough parameters, but closer to the idea that all these minor factors play a role and we are simply exposing them with the CSALT approach.

It also appears that the ongoing work presented by  Judith Lean at the recent AGU work parallels this approach. The NRL statistical climate model shown below and described by David Appel here builds on her previous work [3][4]. The truth is uncovered by looking at the statistics and mean value of the compensating natural factors, and not by GCMs and other analyses that allow the non-determinism of individual runs to suggest the outcome.

All these factors need to be taken together in a statistical fashion, and the truth will continue to emerge.



[1] G. Wefer, Climate Development and History of the North Atlantic Realm. Springer, 2002, p. 113.
[2]  A. Mandal and P. Raychaudhuri, “A Proof of Chaotic Nature of the Sun through Neutrino Emission,” presented at the International Cosmic Ray Conference, 2005, vol. 9, p. 123.  PDF
[3] J. L. Lean and D. H. Rind, “How natural and anthropogenic influences alter global and regional surface temperatures: 1889 to 2006,” Geophysical Research Letters, vol. 35, no. 18, 2008.
[4] J. L. Lean, “Cycles and trends in solar irradiance and climate,” Wiley Interdisciplinary Reviews: Climate Change, vol. 1, no. 1, pp. 111–122, 2010.

Tidal component to CSALT

As we look at attribution of global warming to various physical mechanisms, one of the puzzling observations we can make is that many researchers place too much emphasis on a single cause. This is especially true of the research from those that have skeptical views of GHG-caused warming.  For instance, Scafetta is convinced that the orbital forces are the key, and may also prove to be the cause of any long-term trends we are seeing — yet he makes a concerted effort to downplay the effects of the CO2 control knob, giving the CO2 TCR a very low value.  That is OK if he is truly being skeptical but not so good if he wants to retain objectivity.

From a previous post, we added Scafetta’s orbital cyclic parameters to the CSALT model. These include orbital parameters that are lunar as well as solar and planetary.  If we look at the periods that control lunar tides — the 18.613 year period and the 8.848 period  — CSALT generates an amplitude and phase that lines up remarkably well with the diurnal tidal analysis of R.Ray at NASA Goddard [1], whose work has been referenced by skeptic Clive Best  here [2] .  See Figure 1 below:


Fig 1: The top panel shows the CSALT extracted 18.6-year diurnal tidal period amplitude (right axis) along with the temperature phasing. The left axis shows the yearly averaged actual tidal amplitude from R.Ray[1], which is completely in-phase with the temperature factor.  The middle panel shows a higher resolution look at the tidal amplitudes over a shorter time interval.  Both the 18.6 year and a faint 8.85/2 year extracted temperature signal are in phase and of comparable relative amplitudes as the data.  The bottom panel shows the semidiurnal amplitude with a 8.85/2 temperature signal which has a different sign than the diurnal signal.

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Dealing with the Dynamics of Diffusional Sequestration

A WUWT post (with comments invoking yours truly) is arguing over the merits of the BERN model to describe the sequestration of CO2.  In the past, I have described the sum of multiple exponentials of varying time constants in the BERN model as a heuristic approximation to the full diffusional model (see Figure 1) in several places — see the book “The Oil ConunDrum”, the “Diffusive Growth” paper  (both available in the menu), and several blog posts here.

Fig. 1: Impulse Response of the sequestering of Carbon Dioxide to a normalized stimulus. The solid blue curve represents the generally accepted model, while the dashed and dotted curves represent the dispersive diffusion model

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Orbital forcings in the CSALT model : explain the pause?

A set of orbital forcing cycles inspired by the persistent publications of Scafetta [1] was added to the CSALT model (also see Related).  This set was grouped into two parts. The first set comprises the identified luni-solar periods identified by Scafetta and others. These are pure sine waves with a phase giving the best residual fit. Interesting that they do indeed have a significant impact on the model fit, raising the correlation coefficient above 0.992 for a Pratt 12-9-7 triple running filter [2]. The other factor is a sun barycentric velocity that Scafetta has identified.  This also has an impact on improving the fit as seen in Figure 1.

Fig. 1:  CSALT interface including the orbital periods.  See Figure 5 for a description of the Pratt filter.

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