I was wondering if there really was some natural variation that keeps getting cited by climate-change skeptics that predicts a warming? The only such variation I can think of would be the milankovitch cycles, however this predicts cooling not warming at present (as far as I recall).
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First off, let me preface this answer with a disclaimer: I do not deny climate change.
From what I've read, the skeptics for the most part don't claim to have an alternative explanation for the recent warming. Their arguments (not mine!) are fourfold:
Those are not my arguments.
With regard to point #1,
The above image speaks for itself. The global temperature change over the last forty years is very real, and is not noise.
That the farmer's field might turn into a mountain or be washed out to sea several millions of years from now is irrelevant. What's relevant is that his good or bad practices have an impact on the world food supply. That nature can do far worse does not negate those bad farming practices. Bad farming practices are bad for humanity.
Getting back to climate change, if higher global temperatures are bad for humanity, it doesn't matter matter one bit how close ice came to the equator or how far north dinosaurs roamed in the past. What matters is that modern humanity is sensitive to climate change, be it natural or induced by humans.
With regard to point #4, it is CO2. It was amusing to follow the skeptic response to Richard Muller's Berkeley Earth Surface Temperature project. Muller was a self-proclaimed skeptic, and he was going to prove those leftist climatologists wrong. The skeptic community cheered at the start. "He's going to prove them wrong!" A funny thing happened on the way to proving them wrong: He proved them to be correct. Muller was an honest scientist in this regard. His own work caused him to switch from being a skeptic to ascribing to AGW.
Many natural cycles are known and understood even though "skeptics" like to point to them. For example, we can predict Milankovitch cycles, and we have good solar records for over 200 years. Although we might not necessarily know the magnitude of these effects a priori, we can look for these patterns in the climate record. eg. Does the Earth get warmer when the sun becomes more energetic, and get cooler when it becomes less energetic.
We do see these effects in the Earth's climate (let's face it, it would a big surprise if the Earth did not get warmer when the Sun got warmer!), but they cannot account for all of these changes. For example, when the Sun might become less energetic the Earth does not cool as much as it warmed when the sun became more energetic.
I can list the cycles and possible cycles that I know of.
You mentioned the Milankovich cycles, 26,000 (or 21,000), 41,000 and about 100,000 (with some fluctuation), are pretty much like clockwork and are timed pretty well with historical ice ages, so those are confirmed cycles, but they also occur very slowly. The Sahara desert may cycle from lush rain forest to desert back to rain forest every 26,000 years.
That said, the orbital changes are not thought to be a big factor today. We're likely in the middle of a warm period between ice ages, perhaps in a gradual cooling.
The sun cycles between high and low sunspot periods on roughly an 11 year cycle. High sunspot activity does give the Earth slightly more energy but the effect of this is pretty small, maybe 1/4 of 1 degree C maximum to minimum, less than the 1 degree plus that the CO2 has already warmed the earth. Still 1/4 of 1 degree can have an effect if the sun enters an extended minimum. This may be the cause of the little ice age.
A recent study suggested that the sun might enter a new long term (Maunder like) minimum and that it may happen every few hundred years, but the cooling from this is likely smaller than the warming already experienced from CO2. (I have a link, need to track it down)
This is very complex and difficult to predict. We know that El Ninos and La Nina's tend to roughly alternate. El Nino's are associated with a warmer ocean current on the surface that warms teh air (and has numerous other global weather effects) and La Nina is a cooler ocean current on the surface that warms the air less/cools it more and there are also predictible weather effects all over the planet. La Nina and El Nino aren't exactly on a cycle any more than heavy snow fall winters and light snow fall winters are on a cycle, they're more like chance, for lack of a better word, though they must be caused by something but as far as I know there's no good predictive methods beyond a few months ahead of time. I think it's unlikely that La Nina and El Nino play key roles in global climate change though, but there's no definitive evidence.
Longer term ocean currents are often used by climate change skeptics, like 30 year ocean cycles, because, if you squint just right, they can argue that the global temperature has risen and fallen on a 30 year cycle. (They really haven't), but it looks like there could be some truth to that. See chart here (for some reason I couldn't embed)
Now it looks like the Earth cooled 1880-1910, warmed 1910-early 1940s, cooled a little / stayed about flat 1940-1975 and warmed 1975 to present. It sounds like a good argument but 2 periods is much too short a time period to draw any good conclusions, especially if the argument is largely circumstantial without a clear cause and effect, and lets not forget, the warming since the 1970s has blown out of the water any measured 30 year period before then, so the current warming doesn't fit the model.
While not really a "cycle" volcanoes can have measurable effects on climate, but only very large ones, so this happens maybe 1-2 times a century. The last cooling volcano happened in 1991 and may have cooled the earth about 1/2 of 1 degree, which is actually a lot, but it's also, quite temporary. A few years after the Volcano the Earth was setting heat records again and by 1998 with the large El Nino, global temperatures blew the previous records out of the water.
Roy Spencer suggests that during the medieval warm period it was 1 or 2 degrees hotter than today. I think he's basically lying because he's the only person producing charts like this. There's another scientist (I forget his name) who only studies the Greenland ice sheet which can be prone to local variations and not give a good picture of global temperatures.
Locally there can be fairly significant temperature variation but, and this is important, there's a difference between natural variation and cycles. Cycles by definition have causes. Natural variation tends to be more local than global, though there are global variations year to year, where the biggest drivers are probably El Nino/La Nina and the occasional once in a century volcanic eruption. Other smaller effects like cloud cover and snow cover/reflection probably play roles too.
But in a certain sense, all this is just movement of temperature and (OK clouds and snow can reflect solar energy away directly) but oceans, the primary cause used for cycles don't change the total heat in the system so much as they move it around. The sun, another commonly misused cause for cycles, doesn't vary enough to explain the current warming, so it's likely that most of the people saying "it's a cycle" are simply wrong. Though it's possible that part of the warming is riding a so far unexplained cycle, it's very unlikely that most of it is.
The simplest way to look at climate change is energy in and energy out.
This is grossly over simplified but 29% of the suns energy is reflected directly back into space, 23% warms the atmosphere and 48% warms the surface. The earth, when in equilibrium, gives back the same amount of energy that it receives, of that 71%, only 12% radiates from the surface of the earth and 59% radiates into space from the atmosphere. Small changes in radiation away from the earth (which is how greenhouse gas works) gradually increase the total heat of the earth, and most of this heat goes into the oceans, some melts ice and only about 3% stays in the atmosphere, which slowly warms the atmosphere, the current estimate is about 2 degrees C every 100 years (and the ocean warming, likely even slower than that, maybe 1 degree on the surface every 100 years or more and even more gradual warming in the middle and deeper oceans. All that is very one-dimensional as it doesn't take into account evaporation and cloud formation, changes in plant transporation, changes in desert vs green land cover, changes in ice cover, humidity etc. It's a hugely complicated system, BUT, there is very good evidence that the atmosphere is trapping heat and the earth is taking in more energy from the sun than it is currently returning to space and that's the single most important bit of evidence. So called 30 year ocean cycles are very much worth studying but likely not causing and unlikely to prevent man made climate change. Solar cycles are worth studying and may even exist over every few centuries, but they are probably too small to prevent the greenhouse gas warming. Other "undiscovered" cycles, well, sounds good, but without a testable theory, that's not real science.
That was probably too long, but there it is.
The natural variation of astrophysical cycles that affect climate (collectively known as Malenkovitch cycles; http://en.wikipedia.org/wiki/Milankovitch_cycles) can be seen in ice core records.
An image of the EPICA and Vostok ice cores versus age obtained from http://en.wikipedia.org/wiki/Ice_age , clearly shows influence of the Malenkovitch cycles. The most notable of which is the strong cycle that is approximately 70,000 years and is associated with geologic ice ages. In fact, the Earth is historically on average much cooler than it is now, and the retreat of glaciers has been periodic but not sustained. We were supposed to have cooled off some time ago, but clearly we are not in a global cooling period. Many would even argue that humans started affecting the climate over 7,000 years ago when land management and fire was wielded prevalently.
I would rather not get into what a climate-change skeptic might say. However, we can use climate models to determine natural variation without anthropogenic forcings. Below is an image of this from the IPCC AR5 Technical Summary draft which shows a full climate simulation and one without anthropogenic climate forcers. Note that currently the climate is changing much faster than it would naturally.