Understanding how the carbon cycle affects the global climate is not a simple matter. And yet, scientists can do more to provide a better understanding to intelligent non-scientists. Here is my attempt.
At every step, a scientist would say "well its not exactly like that, because…" I'm taking a lot of shortcuts with the science to give a better flavor of what is important without getting to all the complexities.
How a greenhouse works:
To understand the "greenhouse" effect, let's review what a greenhouse does. Consider a glass house that is made with "low-emissivity" glass. The idea behind "low-E" glass is that it allows visible (high frequency) light to pass through, but traps infrared (low frequency) thermal energy - see http://en.wikipedia.org/wiki/Low-emissivity for more explanation. Let's not worry about plants for the moment, but imagine two glass houses - one with a floor of black asphalt and the other with a floor of perfectly white concrete. Everything else being equal, you might intuit that the glass house with the asphalt floor will be hotter - and you would be correct. The house with the concrete floor will reflect the visible light, which will pass back out through the glass. In contrast, the asphalt will absorb the visible light and re-emit the light in the infrared spectrum - which is trapped within the house by the glass. If you had high-emissivity glass (that passes infrared) then both houses would have similar interior temperatures.
Let us imagine that we have asphalt that absorbs every bit of visible light and turns it into infrared, and we have white concrete that reflects every bit of visible light. Since we are imagining, let us also imagine that the sun never sets and the outside temperature is a constant 70 degrees F and our glass has an "emissivity" of zero (traps all infrared light) How would the temperature behave in our two imaginary greenhouses? First, the greenhouse with the concrete floor should be at 70 F. All the solar radiation energy coming in is reflected back out, so the temperature of the house and the air inside should be the the same as that outside - i.e. simple conduction through the structure of the greenhouse leads to the temperatures reaching equilibrium.
But for the greenhouse with the asphalt floor, all the solar radiation coming in is trapped and raises the temperature of the asphalt and the air inside. As the air temperature rises, so does the temperature of the house structure itself, which then conducts/radiates thermal energy to the outside. How high will the temperature rise in the greenhouse? This depends upon when equilibrium is reached. Since the sun is shining constantly in our imaginary world, there is a constant supply of visible light that is being converted into infrared heat. The temperature will keep rising until the rate at which this thermal energy is conducted/radiated to the outside is exactly equal to the rate at which energy in visible light is being supplied. This process is exactly the same as what happens when you turn up the thermostat in your house - it takes more energy to maintain a house at 72 F during the winter than it does at 68 F because you lose energy from the house at a greater rate when you maintain the house at 72. Understanding this concept of equilibrium between heat transfer rates is critical to understanding the greenhouse effect. We will call the temperature in the greenhouse where all the heat transfers balance the "equilibrium temperature." We can think of this as the temperature that the greenhouse wants to be at once everything is in balance.
Now let's imagine that we have a special type of glass that allows us to control the percent of infrared light that is trapped - that is, we control the glass emissivity. By increasing the emissivity (allowing some infrared to pass through) we can control the temperature of the greenhouse. We can also modify the reflectivity of the floor to change the greenhouse temperature - we imagine a material that we can change from white through any shade of gray to completely black, so as to modify the amount of incoming visible light that is turned into infrared light. With these materials we exert control on the temperature of the greenhouse. Increasing the reflectivity of the floor or increasing the emissivity of the glass will both serve to reduce the equilibrium temperature of the greenhouse. In contrast, decreasing floor reflectivity and/or glass emissivity serves to increase the equilibrium temperature. Of course, whenever we make a change, there will be some adjustment period while the house warms up or cools down to the new equilibrium.
Water cycle in a greenhouse
Things get more complicated when you add water to a greenhouse. Let's imagine that we add a large pond to our greenhouse but otherwise have a gray floor that reflects part of the visible light and converts the other part to infrared. Assuming that the temperature in the greenhouse isn't above the boiling point, we will have a pond with liquid water and water vapor in the air. It turns out that water vapor will absorb some of the infrared released from the floor, preventing it from even reaching the glass. So even if we turn our glass emissivity to high (allowing all infrared that reaches it to pass through), we find that the water vapor will trap the infrared and lead to a higher equilibrium temperature than we would have without the water. You may have heard that water vapor is the dominant greenhouse gas. This is true - but it is also misleading. The skeptics want you to think that because water vapor is present in larger quantities than CO2, then it CO2 must not be important. We'll try to explain why this is not the case.
Here's where things also get a little ugly - we have what is known as a "feedback" mechanism that leads to cycling rather than a simple equilibrium state. When the temperature in the greenhouse increases, the air will hold more water vapor and more water vapor will be released from the pond. For example, put a pot of water on the stove and heat it up to 120 degrees (well below boiling) and you will notice a lot more moisture in the air. This increased water vapor in the air leads will trap more infrared, leading to a higher temperature and more water vapor - the cycle reinforces itself. We call a reinforcing cycle a "positive feedback." If you've ever heard a high pitched scream from a microphone and speaker system you've heard the results of positive feedback - this happens when sound from the speakers enters the mike, is then amplified and fed back into the speakers, then back into the mike and amplified again through the speakers and into the mike etc. However, for water vapor there is a compensating "negative feedback" mechanism: clouds. When the water vapor in the air gets sufficiently high, the vapor condenses into clouds. Due to their fluffy white nature, clouds reflect some of the incoming visible light before it ever reaches the floor where it would be changed into infrared and subject to trapping. Thus clouds, a product of a greenhouse gas (water vapor) are actually a limiting factor on the greenhouse effect from water vapor. So here's the picture when we add water to the greenhouse:
1. Water vapor absorbs infrared thereby raising the greenhouse temperature, which leads to more water vapor and an even higher temperature.
2. Clouds form and reflect some of the incoming solar radiation.
3. The clouds turn into rain, cooling and reducing water vapor in the atmosphere, which leads temporarily to less trapping of infrared, but now more solar radiation is reaching the floor and the pond.
4. Heating starts again and water goes back into the atmosphere as vapor, and we return to step 1.
So rather than having a simple equilibrium state, the water vapor cycle oscillates around some central temperature. Sometimes its warmer, sometimes its colder, but the system is essentially in a dynamic balance. Over a single cycle of vaporization/rain, the temperature evolution in our imaginary greenhouse will be such that the net solar energy input is exactly balanced by the net energy lost to the outside. If we change anything in the system then this central (or equilibrium) temperature will change. Understanding how such changes occur requires understanding the rates at which the processes cycle and leads to some of the mathematical complexities in analyzing climate data.
Summarizing the above: Reflecting white surfaces in the greenhouse will simply reflect solar radiation straight back out of the greenhouse. Absorbing black surfaces will convert solar radiation to infrared radiation, which can be trapped in the greenhouse either by the glass itself, or by water vapor in the atmosphere. With sufficient water vapor we get rain, which temporarily reduces greenhouse gas trapping my removing water vapor from the atmosphere, thereby leading to some cooling. Thus, even though water vapor itself is produced with a positive feedback mechanism (trapping more heat leading to more water vapor), there is a "negative feedback" mechanism in rainfall that clears out the water vapor and allows the greenhouse to cool down again. Thus, a nifty climate cycle in dynamic balance.
Adding CO2 to the greenhouse atmosphere
Much like water vapor, CO2 is a "greenhouse gas" in that it absorbs infrared energy that the floor converts from the visible light. However, unlike water vapor, the CO2 doesn't form clouds to reflect incoming visible light and doesn't rain out of the atmosphere. So if we take the greenhouse water cycle described above and add some CO2, we expect that after a rainstorm (when water vapor has been cleared) the CO2 will absorb some of the infrared that would have slipped out of the greenhouse if the CO2 hadn't been there. This increased trapping of energy results in an increase in the equilibrium temperature of the greenhouse. So if we take our imaginary greenhouse and dump in some CO2 we can expect higher temperatures. We understand this mechanism extremely well, and if this were all there were to the problem, scientists would have reached agreement in the early 1970s and the argument would have been over then. The key point here is that it doesn't matter that water vapor is the largest greenhouse gas, because it has a natural negative feedback mechanism through rainfall. If CO2 levels aren't a problem (which is the skeptics claim), then there must be some negative feedback for CO2 as well. So now we have to investigate the carbon cycle and what happens with CO2 in a greenhouse.
Carbon cycle in a greenhouse
Now let's add some plants to our greenhouse. Plants live and die in a cycle. When alive, plants take in visible light and scavenge carbon and oxygen from the air (in CO2) and the soil. The carbon is added to the plant stem and leaves while the oxygen is released back to the atmosphere. When a plant dies, bacteria work the opposite direction, eating the plant carbon and excreting CO2. Let's imagine our greenhouse has a fixed store of carbon that is continually being cycled. Some carbon is in the live plants, some is in the soil in dead plants and is being eaten by bacteria and some is in the greenhouse atmosphere in the form of CO2. If the total amount of carbon is fixed, then we will reach some equilibrium cycle in the plant life with some proportion of the carbon in each of these "pools". Once the proportion of carbon in each of the pools is established, we'll have some predictable amount in the atmosphere and some central "equilibrium" temperature about which the greenhouse cycle operates.
Adding fossil-fuel carbon
We can imagine introducing some new amount of carbon to the system. Let's say we take a barbecue into the greenhouse and light a small fire made from coal we dug from a nearby hillside. Initially, the smoke from the coal may prevent sunlight from entering the greenhouse, and reduce the incoming solar radiation. It is possible that this might initially cause a net cooling (if the solar radiation reflected is greater than the heat caused by burning). But after some time, the smoke clears and we have a new carbon cycle. Some of the carbon we introduced will be in new plants that have grown (because there is more carbon in the air). Some of the carbon will be in these soils, and some will be in the air. A new equilibrium system will be developed. This equilibrium will be at a higher temperature. When you added more carbon to the greenhouse, you can't just tell the carbon to "stay in the plants and the soil;" it's going to end up in all three pools: plants, soil and atmosphere. With more CO2 in the atmosphere, the temperature of the greenhouse will rise as more infrared is blocked from escaping.
The increased temperature due to CO2 heat tramping will feed back into the water cycle as well, leading to changes in vaporization, cloud cover and rainfall. This is an area where trying to understand the system gets really tricky and the biggest scientific uncertainties still lie. It is difficult for scientist to predict the exact amount of temperature rise because of all the feedbacks between the different effects. However, what is very clear is that increasing CO2 in the atmosphere increases the heat trapping in the atmosphere. The global temperatures will rise until a new equilibrium is reached. Note that if we don't level-off our CO2 emissions at some output that matches the intake of the plants, then we won't ever reach an equilibrium. That is, if we keep treating the atmosphere as an open sewer for an ever increasing amount of CO2, the temperature will simply keep rising until life, as we know it, is unsustainable.
The critical importance of fossil fuels
Our dependence on fossil fuels is the crux of the problem. If we were to heat our homes, power our cars, and generate our electricity by chopping down trees from sustainable forests, then we wouldn't be changing the amount of carbon in the global cycle. But, we are resurrecting carbon that was laid down in times when the world was much warmer and there was much more CO2 in the atmosphere. By digging out and adding the coal (and to some extent the oil) to the present carbon cycle we are pushing our climate back to a much warmer state.
The question for the skeptics
For all the skeptics out there (if any bothered to read this far), you have a responsibility to more than simply be cynical doubters. If you are an honest skeptic, then you need to be able to answer one very simple question: Where is the extra CO2 going to go such that it doesn't affect the climate? The science of global warming is built on an understanding of physical mechanism on how CO2 traps infrared radiation. The rise in CO2 levels is indisputable science. Any skeptic who tries to claim CO2 levels are not rising will be laughed out of any debate. Fact: CO2 levels are rising globally. Fact: CO2 traps infrared thermal energy. Thus, we are left with two possible conclusions:
1) The scientists who have studied the mechanisms of this are correct, and the earth will warm due to fossil-fuel CO2 emissions.
2) The global warming skeptics are hiding some brilliant understanding of a new physical mechanism that will naturally absorb CO2 and prevent global warming.
If you have some brilliant idea as to how the CO2 is actually going to be ameliorated by some negative-feedback mechanism that no one else has looked at, then please let the world know. You can prattle on about climate cycles over the last 10 thousand or 10 million years all that you want - but you've got to answer the key question: WHERE IS THE CO2 GOING AND WHY IS IT NOT AFFECTING THE CLIMATE? If you don't have any scientific explanation with a mechanism for how increasing CO2 doesn't warm the atmosphere, then shut the &!#*(;$ up. because you don't have any scientific basis for your skepticism. Without any scientific basis for your claims, you're either a selfish Luddite or a partisan hack.