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.

11 thoughts on “CSALT model and the Hale cycle

  1. This is very interesting but not at all surprising. A few thoughts…

    Given the high dependency of tropospheric temperatures on sensible and latent heat flux from ocean to atmosphere, but also, the dependency of that same flux to noncondensing GH gas concentrations in the atmosphere, we need to explore further the “control valve” relationship and negative feedback components in this ocean to atmosphere heat flux. That is, an atmosphere warmed by GH gases will act to restrict the amount of heat flowing to the atmosphere from the ocean (increasing ocean heat content) but also therefore causing the atmosphere to not warm as much. Given that we know GH gas concentrations and the positive forcing are continually increasing, that means the oceans will continual to warm as the control valve that regulates the flow from ocean to space is shut down more and more, but likewise, less heat will be available to warm the atmosphere. How does the CSALT model take this negative feedback into account?


  2. RG, The OHC is wrapped into the C * dT CSALT component, where C is the heat capacity of the system.

    I could conceivably take the heat capacity of the ocean separately and use that along with the measure of the ocean temps, but the data going back to 1880 is not the best quality, as it seems to get more noisy the further back its goes (likely due to how they inferred temp from SLR alone instead of the modern-day methods).


  3. WHT,

    How do other greenhouse gases fit into the CSALT model? I have been in some discussions about methane flux increases in the arctic. David Archer at real climate does not think this is of great concern, if I am understanding him correctly. Curious if you have looked into this at all.



    • DC, I am assuming that the other GHG’s “ride along” with CO2. The log sensitivity is then an effective value based on the CO2 control knob. This is plausible because water vapor is also a GHG and this is also considered to scale with CO2.


      • Aren’t some of the other GHG’s independent of CO2 such as methane? There seems to be some concern by the arctic methane emergency group that methane is a problem,
        David Archer at Real Climate says no problem, I tend to believe what Real Climate says on these matters, but thought I would check with you because clearly you follow climate change closely.



      • DC, You are right. In terms of the details, methane doesn’t track co2 exactly.

        However, I don’t think there are decent data sets that measure methane back to 1880, which is what I am using for the full regression.


  4. From Excel my CSALT model (no orbital or AAM):
    Coefficients Standard Error t Stat P-value
    Intercept -0.404400428 0.009149007 -44.20156428 1.316E-279
    c 3.047060996 0.043290998 70.38555749 0
    l -0.050081403 0.002327833 -21.51417332 2.17346E-90
    s -0.020315513 0.001694975 -11.98572964 9.22819E-32
    a -0.982259984 0.132386903 -7.419616031 1.89715E-13
    t 0.079510583 0.010015976 7.938375738 3.8212E-15

    I will add an image with 12 month centered moving average, click on image to enlarge.



    • DC,
      It’s getting there. I think your SOI coefficient is low by a factor of 50%. This may be because you are not using the SOI differential signal as outlined in another comment. It is critical to use the difference between Tahiti and Darwin pressures.


    • Hi Paul,

      I am indeed using the SOI data from


      SOI.signal.annstd.ascii is the file I downloaded from that page
      which is decscibed as follows:
      “contains the SOI (Standardized Tahiti — Standardized Darwin) where the standardizing is done using the approach outlined by Trenberth (1984). To maximize the signal, the monthly anomalies were standardized using standard deviations of annual means. ”

      I agree that there is a difference between our analyses, my assumption is that I have done something incorrectly, I am just trying to uncover my error. Thanks.



  5. Better formatting for coeficients below:

                   Coefficients	Standard Error	t Statistic     P-value
    Intercept	-4.044E-01	9.149E-03	-4.420E+01	1.316E-279
    c	        3.047E+00	4.329E-02	7.039E+01	0.000E+00
    l	        -5.008E-02	2.328E-03	-2.151E+01	2.173E-90
    s	        -2.032E-02	1.695E-03	-1.199E+01	9.228E-32
    a	        -9.823E-01	1.324E-01	-7.420E+00	1.897E-13
    t	       7.951E-02	1.002E-02	7.938E+00	3.821E-15


  6. Pingback: Reverse Forecasting via the CSALT model | context/Earth

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