The reality is that a complex system has so many feedback functions with varying amplification factors that anyone can get completely lost in the noise. In trying to explain, I have used a variety of static models that indicate you can only get so close with the information available and that it is probably better just to accept the limits and focus on longer and longer time frames to reduce some of the noise. The Three Compartment Ocean Model indicates that there are likely settling time frames or constants of at least 500 years with shorter pseudo-cyclic patterns on the order of 62.5 years just due to the size and limited flow rate between ocean basins. Near the surface of the oceans, shorter time frame settling noise with periods of 5 to 10 years produce much of the "weather" which may be isolated from climate, zeroing out over a limited period, or an indication of longer term climate, awfully hard to tell one way or the other. Still, chaos theory implies that there is self similarity of the patterns on all time scales. Theories are theories though, not laws, just suggestions.
To figure out how small variations in solar can impact climate I have played with the TSI data from Sorce and the satellite data. There is an obvious solar impact, but correlations never are completely convincing.
Kind of interesting. A longer term "staycation" on either side of the threshold should cause a gradual change in "climate" as far as surface air temperature and sea surface temperature are concerned. Only one problem, solar reconstructions of the past are worse than most of the temperature reconstructions.
At the start of the IPCC series of reports, the solar "constant" was about 1366 Wm-2 and reconstructions by scientist like Judith Lean indicated that past solar variability was enough to drive climate until roughly 1950. Since then, the solar "constant" has become 1361.1 +/- 0.1 Wm-2 and past variation is only +/- 1 Wm-2, about the same as then maximum estimated energy imbalance. With the new and improved data, solar just can't do the job. ENSO though, that natural internal variability can have some impact on climate but no one can agree on how much and since ENSO is an "oscillation", it doesn't much matter anyway, it will average out. However, the comparison of of solar TSI and the imbalance between the northern Atlantic and Pacific oceans seems to indicate that solar can cause about 0.4C of variability with just the 11 years cycle so a prolonged solar minimum or modern solar maximum should be able to do about the same thing.
The typical way that solar impact is determined is TSI/4 since the Earth is a rotating sphere. The tropics though don't require half of that 4 divisor, about 1.414, the square root of two is more relevant to the tropics. In day mode, the ~1 Wm-2 of solar variation would be felt as ~0.7 Wm-2 of change at the ocean surface in the 30N to 30S latitude band. That is still a small amount, but compared to an ocean only imbalance of ~0.3 to 0.6 Wm-2, significant. "Proving" that solar drives ENSO or more realistically the tropical ocean regional imbalances is not a slam dunk, but there is enough evidence and close enough energy available to mark a fair argument to that effect. So what is the major malfunction?
Well, comparing two of the Solar "TSI" reconstructions, we don't have an agreement on what "Top of the Atmosphere" and "Surface" really is. The Svalgaard TSI reconstruction used above is scaled to the mean of the Bard et al. 1810 to 1966 mean value. The blue line is the "modern" mean and the orange would be the past 1200 year mean. Svalgaard's mean is actually 1361 Wm-2 +/- a touch which would be below the minimum chart value. The Solar "Constant" has dropped nearly 5 Wm-2 since the start of the CO2 mania.
The Bard et al. estimated "TSI" is based on "surface" impact of solar variation using Carbon 14 and Beryllium 10 isotope ratios, per the Bard et al. abstract:
ABSTRACT: Based on a quantitative study of the common fluctuations of 14C and 10Be production rates, we have derived a time series of the solar magnetic variability over the last 1200 years. This record is converted into irradiance variations by linear scaling based on previous studies of sun-like stars and of the Sun's behavior over the last few centuries. The new solar irradiance record exhibits low values during the well-known solar minima centered about 1900, 1810 (Dalton), and 1690 AD (Maunder). Further back in time, a rather long period between 1450 and 1750 AD is characterized by low irradiance values. A shorter period is centered about 1200 AD, with irradiance slightly higher or similar to present day values. It is tempting to correlate these periods with the so-called "little ice age" and "medieval warm period", respectively. An accurate quantification of the climatic impact of this new irradiance record requires the use of coupled atmosphere-ocean general circulation models (GCMs). Nevertheless, our record is already compatible with a global cooling of about 0.5 - 1 C during the "little ice age", and with a general cooling trend during the past millennium followed by global warming during the 20th century (Mann et al. 1999).
So one measures "surface" impact of solar variation and the other a "constant" at some point in the atmosphere that has changed for whatever reason since 2000. I am sure both groups are competent at their jobs, but which is more relevant to climate science, actual surface impact or potential impact at some not all that well defined "surface"?