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.