A relaxation to equilibrium response in surface sea temperature to a hypothesised radiative “forcing” proportional to SSN is calculated by convolution with a exponential decay having a time-constant : tau = 5 years
Such a time constant corresponds to near equilibrium being reached in 15 years.
The calculation is effectively a weighted integration and this kind of system response has low-pass filter characteristics while also introducing a lag.
The result is different to a fix time lag and depends upon the frequency content of the data. For the simple case of a constantly rising driver, the lag will be equal to the time constant.
The long term ( interdecadal ) variability matches sea surface temperatures quite closely but with a notable divergence near since around 1990. This suggests that there maybe a long term cumulative effect of solar activity on surface temperatures.
It is noted that the short term ( decadal ) variability does not correlate with the solar cycles. Avoiding the large, speculative adjustments made to hadSST3 just after WWII and taking the last six peaks on the graph to estimate the period:
( 1996.46 – 1952.28 ) / 5.0 = 8.836 years
This is strongly suggestive of a the lunar perigee cycle of 8.85 years, caused by the precession of the line of apsides, and accounts for the often noted phase drift when decadal variability is incorrectly attributed to variations in the solar cycle.
The line of apsides is the orientation of axis of eccentricity of the lunar orbit and is one of the factors determining the Earth latitude over which the maximum tidal forces occur a lunar perigee.
The difference of the earth-moon distance between perigee and apogee is about 15% leading to a variation of about 45% in the tidal force of the moon.
A similar graph comparing SSN to CET land temp record from central England:
A 75 month low-pass Lanczos filter was applied to SST. This almost totally removes any variation at or below 5 years in period.
Relaxation response with time-constant of 5y:
Svalgaard proposition of TSI proportional to SSN. SSN adjusted for variations in Wolf number.