Phase Lag of Global Temperature

Lag or phase relationships are to me one of the most convincing pieces of evidence for the accumulative theory.

The solar cycle varies over 11 years on average like a sine wave. This property can be used to probe contribution of total solar insolation (TSI) to global temperature.

Above is a plot of two linear regression models of the HadCRU global temperature series since 1950. The time since 1950 is chosen because it is the period that the IPCC states that most of the warming has been caused by greenhouse gasses GHG, like CO2, and because the data is more accurate.

The red model is a linear regression using TSI and a straight line representing the contributions of GHGs. This could be called the conventional IPCC model. The green model is the accumulated TSI only, the model I am exploring. Accumulative TSI is calculated by integrating the deviations from the long-term mean value of TSI.

You can see that both models are indistinguishable by their R2 values (CumTSI is slightly better than GHG+TSI at R2=0.73 and 0.71 respectively).

You can also see a lag or shift in the phase of the TSI between the direct solar influence (in the red model) and the accumulated TSI (green model). This shift comes about because integration shifts a periodic like a sine wave by 90 degrees.

While there is nothing to distinguish between the models on fit alone, the shift provides independent confirmation of the accumulative theory. Volcanic eruptions in the latter part of the century obscure the phase relation over this period somewhat, so I look at the phase relationships over the whole period of the data since 1850.

Above is the cross-correlation of HacCRU and TSI (ccf in R) showing the correlation at all the shifts between -10 and +10 years. The red dashed line is at 2.75 years, a 90 degree shift of the solar cycle, or 11 years divided by 4. This is the shift expected if the relationship between global temperature and TSI is an accumulative one.

The peak of the cross-correlation lies at exactly 2.75 years!

This is not a result I thought of when I started working on the accumulation theory. The situation reminds me of the famous talk by Richard Feynmann on “Cargo Cult Science“.

When you have put a lot of ideas together to make an elaborate theory, you want to make sure, when explaining what it fits, that those things it fits are not just the things that gave you the idea for the theory; but that the finished theory makes something else come out right, in addition.

Direct solar irradiance is almost uncorrelated with global temperature partly due to the phase lag, and partly due to the accumulation dynamics. This is why previous studies have found little contribution from the Sun.

Accumulated solar irradiance, without recourse to GHGs, is highly correlated with global temperature, and recovers exactly the right phase lag.

Accumulation of TSI comes about simply from the accumulation of heat in the ocean, and also the land.

I think it is highly likely that previous studies have grossly underestimated the Sun’s contribution to climate change by incorrectly specifying the dynamic relationship between the Sun and global temperature.


0 thoughts on “Phase Lag of Global Temperature

  1. Does this have consequences for some styles of proxy calibrations, which should be regressed against the green curve rather than the red curve (assuming for the moment that the black line is valid)?
    I’ve had the fortune to feel the happiness that is in the Feynmann quote. It looks like your champagne cork should pop soon.

    • It does. In the wiki description of Cargo Cult Science ( it says

      “Feynman used the allegory of a cargo-cultist to argue against an inductive
      approach to scientific theory whereby the previous behavior of a system
      is taken in isolation to predict its future performance, rather than a deductive
      approach in developing theory based on an understanding of the
      principles of operation of the system, informed and confirmed by
      previous behavior.[1]The radioactive proxies of TSI like Be10 and C14 must have a model of accumulation and decay in them — I haven’t studied them though. 

  2. See: Using the oceans as a calorimeter to quantify the solar radiative forcing JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113, A11101, doi:10.1029/2007JA012989, 2008

    we use the oceans as a calorimeter to measure the radiative forcing variations associated with the solar cycle. This is achieved through the study of three independent records, the net heat flux into the oceans over 5 decades, the sea-level change rate based on tide gauge records over the 20th century, and the sea-surface temperature variations. . . .We find that the total radiative forcing associated with solar cycles variations is about 5 to 7 times larger than just those associated with the TSI variations, thus implying the necessary existence of an amplification mechanism, although without pointing to which one.

    Nir J. Shaviv similarly calculated the Pi/2 phase lag. See especially equation 12, Fig 3.

    We see that if the mixed layer is large, the phase lag approaches 90 deg. If the diffusion into the deep ocean is
    dominant, the preferred phase is 45 deg, while the lag will tend
    to disappear if l is large (climate sensitivity is small). . . .
    The frequency we use is of course that of the 11 year solar cycle: w = 2p/11 yr. . . .
    “Figure 3 it is apparent that the main uncertainty in determining the relation between the ocean flux and the SST is the diffusion coefficient beneath the mixed layer.

  3. The most convincing evidence for the importance of the Milankovitch cycles is the work that compares summer insolation at 65N to the rate of change (not level) of the temperature proxies in the ice cores — so the same accumulative idea there.

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