An old claim made by global warming deniers is that global warming can be attributed to the number of sunspots. They will point out that there was a general rise in the number of sunspots during the last few hundred years and the this number closely matches the temperature trend.
This is one of those claims that has just enough truth to sound credible. Basically, the Sun is responsible for all global warming. Without the Sun, Earth would be a big frozen, lifeless ball floating around in space. And, in fact, there is good evidence that solar activity at least contributes to variations in the climate. The Maunder Minimum is frequently pointed at as evidence of the effectiveness of solar activity towards global warming.
During the period between about 1645 and 1715 when there were very few sunspots. This period also coincided with what is dubbed the Little Ice Age, a period when North America and Europe experienced unusually severe winters. There is scientific evidence to show that the Sun's ultraviolet output varies more over a solar cycle than was previously thought. This seems to lend credence to the idea that the solar cycle is responsible for the recently observed global warming, as claimed by some people.
Unfortunately, there is a real flaw in the theory. Starting in the 1970s the Sun started becoming slightly more quiet, a trend that is still continuing. But, this was when we started to see the unprecedented rise in global temperatures. Never has there been any similar rise in global temperature in the recorded record, going back 800,000 years, as what we are witnessing today. And yet, the Sun actually got cooler during that time span.
One commenter to an earlier posting to this blog, Dan Pangburn, claims to have developed a mathematical equation to leads to a match between time-integrated sunspot numbers and global temperatures.You can read his write-up here. His write-up is very technical, which seems to give it some degree of credibility. However, after looking it over I can say I believe he would not be able to get it past any peer review.
Basically, he uses numerical analysis in order to get a correlation between his equation and the measured data. There is nothing wrong with numerical analysis and it is used frequently, I have personally used in my research. However, it is not evidence of any cause and effect. This is part of what is known as modeling.
Mr. Pangburn claims his modeling shows that carbon dioxide is not a driver of global warming because he can get the equations to fit the data with a great deal of correlation without using any CO2 input. In fact, he actually does use CO2 input, but without acknowledging it. He uses both cloud cover and ocean oscillations as input for his equations, along with the sunspot number. But, it must be noted that both cloud cover and ocean temperature are strongly affected by atmospheric greenhouse gases. CO2 is the most influential of these gases. What Mr. Pangburn is doing is the equivalent of claiming wear and tear on roads is not dependent on the number of cars driving on the roads, but is actually dependent on the number of tires sold.
So, what does this mean?
The historical record indicates there is probably some degree of climate dependence on solar activity. However, the evidence also shows this dependence should be causing a slight global cooling at the same time we have experienced a record-setting rise in global temperature.
So, we can conclude that the sunspot number is not what is responsible for what we have been witnessing the last 35 years. Mr. Pangburn can continue conducting his numerical analysis, but it will only make a nice graph without providing any kind of scientific evidence.
Here is an article in Scientific American about the topic. And, here is a good summary of the scientific literature.