1.) How do you explain the correlation between what is happening on earth and recent sunspot activity?
2.) What is your view on the discovery that the polar ice caps on Mars are also receding, indicating that any planetary rise in average temperature is indicative of solar influence, versus earth-bound/man-made influence?
Part 1:
Before getting started, I need to point out that material found on the web is often misleading and sometimes completely wrong. One should always try to obtain scientific information from articles published in refereed journals. The info posted here is based upon my training which includes reading refereed journals. I will post some web sites (primarily from NASA) that represent current scientific thinking on these subjects. The material on these websites are accurate to the best of my knowledge and written by (actual) solar astronomers and solar physicists.
I apologize for being so long winded in this response, but solar physics is a bit complicated and there is a lot to explain. Since I worked at SOHO at NASA/Goddard for a few years, I'll point you to some interesting links at the SOHO website
http://sohowww.nascom.nasa.gov/ along the way for further information). I'll try to keep my explanations here as non-technical and as short as possible.
Sunspot numbers on the Sun vary from minimum to maximum to minimum values over an approximate 11 year cycle. Sunspots are dark regions on the Sun and mark what are called "active regions" -- regions of enhanced magnetic activity. Whereas one cycle might have sunspot pairs where north lead the south pole in an active region as the Sun rotates, the next cycle will have the reverse, south leading north. Hence the Sun's magnetic cycle is approximately 22 years. Note that the length of these cycles can vary by a few months from cycle to cycle. Also, these cycles have stopped in the Sun in the past, called the Maunder Minimum (see below), for a period of time and then restarted.
A new cycle starts when a minimum number of sunspots is noted from observations. We have just started a new sunspot cycle in January of 2008 (cycle number 24 -- i.e., the number of cycles since records have been kept on sunspot numbers) and the next maximum will occur in the summer of 2013. Based on past cycles, predictions suggest that this current cycle will have slightly less sunspot numbers than the last cycle.
The Sun emits energy at all wavelengths of the electromagnetic (E/M) spectrum. Though sunspots are dark at visible wavelengths, they are bright at ultraviolet (UV) and X-ray wavelengths. The visible part of the Sun's spectrum arises from the deepest layers of the solar atmosphere called the
photosphere -- the average temperature in the photosphere is 6000 K (K = Kelvin, the absolute temperature scale, zero Kelvin = -459 deg-F is as cold as you can get, room temperature is about 300 K). "Atmosphere" in the Sun and other stars has a slightly different meaning than it does for the terrestrial (i.e., Earth-like) planets -- there is no solid surface on the Sun or on stars, the gas just gets denser and denser (and hotter and hotter) as one goes deeper. As one travels out of the Sun through the photosphere, the temperature continuously drops until a point is reached where the temperature reverses itself and starts to climb. This enhanced temperature region (about 10,000 K) of the solar atmosphere is called the
chromosphere (seen as a red ring around the Moon during a solar eclipse, the light is reddish due to emission from a hydrogen transition going from the 3rd to the 2nd excited state in this atom, the so-called H-alpha line). This temperature rise results from sound waves and magnetic waves generated from the convection zone that sits just below the solar photosphere. The gas density in the chromosphere is a lot lower than it is in the photosphere and due to its relatively high temperature, emissions lines from singly ionized metals at UV wavelengths are very strong, such as singly-ionized magnesium and iron (note that in astronomy, every atom heavier than helium is called a metal).
As we get to the top of the chromosphere, there is a sharp increase in temperature up to one or two million Kelvins. This hot region is called the
corona because its light is seen as a halo (or crown) around the Moon during a solar eclipse. The gas in the corona is of very low density, hence it does not produce a lot of light as compared to the photosphere. But the light it does produce is brightest at X-ray wavelengths due to its high temperature. This coronal gas is completely ionized and is trapped in big magnetic loops for days (even weeks) at a time. In between the coronal loops are coronal holes, it is through these "holes" where the solar wind originates (note that all of these facts on the structure of the corona were discovered by the solar telescope onboard Skylab).
In order to measure the energy budget of solar radiation falling on the Earth, we need to integrate over the entire E/M spectrum, this then tells us the bolometric flux of the Sun on the Earth. This bolometric flux is also called the Total Solar Irradiance (TSI) and the "solar constant," the latter since this flux varies by less than 0.1% over a sunspot cycle (measured by VIRGO on SOHO from 1996 to present, by other spacecraft prior to this, and by ground-based measurement prior to the space program) and its average over a sunspot cycle hasn't changed (to within the uncertainties of the observations, which are small by the way) over the time these measurements have been made. The Sun's energy output is smallest during sunspot minimum and largest during maximum (see
http://sohowww.nascom.nasa.gov/gallery/Helioseismology/vir010.html and
http://sohowww.nascom.nasa.gov/hotshots/1999_12_20/). The reason for this is that even though sunspots are dark, hence reducing the visible light output by a small amount, the UV and X-ray flux is enhanced causing the TSI to increase. Measurements made by spacecraft over the past three decades have shown that the irradiance at extreme UV (EUV) wavelengths (i.e., just shy of the X-ray region) can vary over 30% within weeks and by a factor of 2 to 100 (depending upon wavelength) over a solar cycle (see
http://sohowww.nascom.nasa.gov/publications/ESA_Bull126.pdf, pages 30 & 31).
As I had mentioned above, the Sun experienced a time from 1645 to 1715 when sunspots were virtually absent from the Sun. This was first noted by E.W. Maunder in his refereed article in the Monthly Notices of the Royal Astronomical Society in 1890 (volume 50, page 251). Coincidentally, the northern hemisphere experienced a "Little Ice Age" during a portion of this time period. It has been suggested that the lack of sunspots might have been the cause of the cold temperatures.
This leads us now to the physics of the solar-terrestrial interactions, which is also a very complicated subject. The Sun is continuously shining E/M radiation on us and blowing its wind upon us (including high energy events such as solar flares and coronal mass ejections from time to time). The Earth's magnetic field blocks the solar wind and these high energy flows from the Sun (though they do cause aurorae). However it is possible for a few very high energy particles to make it through the magnetic field and reach the ground. The Earth's atmosphere is transparent to visible light, some bands in the infrared (IR) and microwave regions, and a large portion of the radio part of the spectrum. X-rays are absorbed by ionized nitrogen and oxygen in the Earth's ionosphere (outermost part of the Earth's atmosphere) and UV light is absorbed by ozone in the stratosphere. CO2 and H2O (and trace amounts of other gases) in the Earth's atmosphere absorb portions of the IR part of the spectrum. In terms of heating the surface directly by the Sun, visible light supplies the largest portion of this energy budget. As the Earth's surface is warmed by the Sun, its temperature increases. The Earth reradiates some this energy back into space at IR wavelengths following Wien's radiation law. Increasing CO2 and H2O abundances in the atmosphere increases the absorption of this reradiate heat, hence heating the atmosphere (the so-called greenhouse effect).
How can a lack of sunspots affect the Earth's surface temperature? With no sunspots on the solar disk, one would expect more visible light reaching the ground hence a temperature increase. But just the opposite happened during the Little Ice Age. As mentioned earlier, active regions produce enhanced UV and X-ray flux. Higher amounts of this flux should heat the stratosphere and ionosphere, respectively. Unfortunately, there is not much mixing between the various layers of the Earth's atmosphere and the thermal coupling between these higher layers and the lowest layer, the troposphere, is not very high. However, it may be high enough such that changing the temperatures in these upper layers could change the temperature at the lowest layer (though very inefficiently). It has been suggested that perhaps the lack of sunspots during the Maunder Minimum caused a decrease in UV and X-ray solar flux, hence cooling the ionosphere and stratosphere, and hence the troposphere. At this point, this is mere speculation since this Earth's surface and atmosphere are a very non-linear and dynamic system.
Note that I have seen passages on the web that claim that solar activity has been dimishing over the past 20 years. As a one time solar astronomer, this is 100% false! All you need to do is to look around on the SOHO website and look at the sunspot numbers. They change, but in their standard 11 year cycle. The TSI data also show this statement to be false.