The article excerpted below is a useful summary of the discussion about solar influences on climate. Climate skeptics will know the first part of it well. It is the second part -- putting the Warmist case -- that seems of some interest. So that is the section I excerpt below and discuss here.
The article is unsigned but is written by a "moderate" skeptic (possibly Pat Michaels) who accepts that CO2 can have SOME influence on climate -- rather than CO2 levels being a RESULT of climate. The author may adopt that stance for political reasons, given the poor empirical evidence for it. How come, for instance, that CO2 levels have risen greatly over the past 15 years, while temperature has flatlined or maybe even cooled?
A notable difference between the skeptical and Warmist cases is that the skeptical case -- as articulated by Svensmark -- is a theory that has been confirmed by direct experimental observations, while the Warmist case relies on a very dubious temperature record. The "hiding the decline" (in proxies) episode was a vivid demonstration of how unreliable temperature proxies are and the thermometer record has been blatantly corrupted by Jim Hansen and others with their various "adjustments". What the thermometers originally showed in aggregate is unknown. The data has been hopelessly compromised in an attempt to show temperature rises where no rise was previously shown.
So it is no wonder that Warmist scientists find no correlation with solar fluctuations and the temperature record. The temperature record is a false representation of reality.
But some facts from the past do not rely on a hokey temperature record. Events like the Little Ice Age or the Medieval Warm Period are well known from history. So we do have SOME information about past temperatures that we can rely on. And that data is very clearly correlated with solar activity. When both sides of the correlation are firmly established, we find that the correlation is strong. The "harder" the data the more we see a solar influence
The idea that solar variability exerts little-to-no influence on the global average surface temperature is based upon several lines of reasoning.
The first is that the difference in the amount of total incoming radiation from the peak of the well-known 11-yr solar sunspot cycle to the trough of the cycle is very low, only about one-quarter of Watt per square meter at the earth's surface. Depending on the climate sensitivity to incoming radiation that you prefer, this works out to a change in the global average temperature of maybe a tenth of a degree Celsius, give or take a few hundredths of a degree. Detecting such a small "signal" amidst other forms of climate "noise" (such as El Ni¤o, volcanoes, and a myriad of circulation patterns) becomes rather challenging.
The second, is that over a period spanning several solar cycles (several decades), the direct correlation between the solar variability and global temperature variability (after accounting for volcanoes and El Ni¤o/La Ni¤a cycles) is basically zero ( it even switches signs from time to time). This means that knowing what the sun is doing gives you little information as to what the global temperatures are doing. But notice the use of the word "direct". In Case #1 the mechanism is "indirect" with the sun modulating cloud formation via cosmic rays and not timed precisely with the more common measures of solar output (e.g. sunspot counts).
However, if your analysis is confined to last two of solar cycles, then it appears as if a decline/rise in solar output over the course of the 11-yr cycle is tied to a decline/rise in global temperatures. Such a correlation leads to the conclusion that declining solar output over the past decade has been, in part, responsible for the contemporaneous slowdown in the rate of global warming-accounting for maybe 0.05 to 0.1 degree of cooling over the course of past 10 years or so. This explanation is currently en vogue with respect to the obvious lack of strong warming in almost fifteen years. It is interesting to note that a solar explanation was largely absent (and in fact was pretty much pooh-pooed) by this same group of people during earlier periods when the warming rate was more to their liking.
A string of papers in the scientific literature have reported that even over the time period of the past several centuries that the influence of solar variability on the earth's average temperature has been slight. For example, Judith Lean and David Rind found that, although they could identify a persistent solar signal in the temperature record during the past century, the signal was small and little-changed over the course of the past 100 years. In other words, solar variability could not explain the observed warming trend. And another just-published paper by Gifford Miller and colleagues even makes the case that the cold period known as the Little Ice Age, long thought to have been the result of an extended period of low solar output, was primarily caused by a concurrence of large volcanic eruptions and feedback processes resulting therefrom. Currently, that paper is an outlier in the field and time will tell whether or not it is correct.
So in very general terms, what buoys the little-to-no solar variability influence reasoning is that straightforward empirical analyses trying to relate solar changes (both directly observed and inferred from proxies such as sunspots) to changes in the global temperature (both directly observed and inferred from proxies) fail to find a large direct influence on the latter from the former.
Even within the "little-influence" community, though, the science is not settled.