If you throw a ball down a rocky hill, what happens? Of course, we know it'll bounce off some rocks, skid off some others and end up somewhere at the bottom of the hill. What if we want to try to represent this in a computer model? Well, we know from basic physics that if we can determine all of the forces on an object, we know where it will go.

So what are the forces (i.e. what might alter the movement of the ball?)? Let's start with the simple ones:

The "primary" forces (the most important ones)

gravity is always pulling the ball downwards
the ground/rocks will have a force upwards when the ball hits (i.e. the ball bouncing)
the initial force when you throw the ball

These are the easy ones, but are there others? Yes:

The "secondary" forces (the "less" important ones)

air friction that slows the ball
friction between the ball and the ground/rocks upon impact
air motions around the ball
perhaps imperfections in the ball that alter how it bounces
others (this is just a crude list)

However, these secondary forces usually do not have a major impact on the ball's motion. What does this mean? Let's say you throw a ball 50 times. The model, given the input of the primary forces, could accurately represent how the ball moves 45 of the 50 times (45 is arbitrary, but it's a majority). What about the other 5? Well think about this: what if one of your throws catches the very back edge of one of the rocks? You could easily imagine in this case that the small effect of air friction may slow the ball down just enough to cause this to occur (instead of missing the rock entirely)--and because of it, the model's ball bounces a bit differently off the next rock, more differently off the next rock etc. until perhaps the model is wrong.

So how can we avoid these 5 bad model runs? In the case of air friction, it is not possible to model these effects using equations directly for mathematical reasons that wont be discussed here (they are what is called "non-linear"). But we can estimate the effects of air friction via a parameterization. A parameterization is a means of simplifying the math involved by approximation (for air friction we can do physical tests that show that it is approximately proportional to the velocity squared). This way, instead of ignoring the effects of such forces, at least we can put its approximate value into the model, thus making the model more accurate.

Important point: A parameterization is not a random guess; it is an educated guess based on observations that can always be shown to make a model more accurate than ignoring the forcing it represents entirely. However, "more accurate" does not always imply "close to reality" either.

Climate models work in a similar, but far more complex manner: attempt to determine and accurately represent as many forces that exist in reality as possible.

Now that you have some idea of the concept of a model, it's time to learn about how these models can help us. There are really three types of climate models: Paleoclimate models, Global climate models, and Regional climate models. They are somewhat interrelated but are separated here in order to distinguish their uses. The primary difference between the models relate to which forcings are the important ones for what the model is trying to show.

Paleoclimate models

Paleoclimate models attempt to recreate our past climate, especially the period of cyclic glaciations over the past 500,000 years. This type of model does this simply by examining the energy balance of the Earth over long time scales. So in this case, the important forcings are the ones that would alter the overall amount of energy (i.e. radiation) entering or leaving the atmosphere. The primary forcings are: incoming solar radiation and outgoing longwave radiation. What might alter these two types of radiation? On such long time scales, one must take into account the Milankovich solar cycles, locations of continents, amount of ice (related to temperature), as well as changes in concentrations of gases in the atmosphere (recall the Greenhouse Effect!). When all of these important forcings on the global energy balance are accounted for, the model should demonstrate temperature trends and cycles similar to that observed in our climate history.

What do Paleoclimate models tell us? Paleoclimate models have difficulty recreating the observed ice age cycles without accounting for the effects of carbon dioxide. This suggests that carbon dioxide likely plays an important role in the dramatic shifts in our climate that are associated with ice ages.

Global climate models

Global climate models (GCMs) are used to predict the future of our global climate system over the next 10-500 years. They are similar to paleoclimate models in the sense that they attempt to assess the Earth's energy balance (including the Greenhouse Effect). However, global climate models are not concerned with long-term cycles such as solar cycles that do not change too much over a 100 year span. Instead, a GCM must take into account forcings that may alter our climate on shorter time scales since they're purpose is to tell us how the energy balance will change over decades rather than millenia. For example, rather than simply accounting for an ice-free ocean appearing within a few thousand years, which a paleoclimate model can do, a global climate model must attempt to assess the rate at which the ice might melt. If the ice melts slowly, then there would be a slower feedback onto the overall warming (because ice reflects incoming solar radiation back to space), which might mean that the climate might take 100 years rather than 50 years to shift dramatically. Thus, these and other short-term changes to the energy balance are taken into account in a GCM.

GCMs are tuned until they are found to accurately represent our climate history over at least the past 100 years (if it can't get what we already know occurred correct, it's obviously wrong). Also, natural cycles (e.g. El Nino) should be seen in the models (i.e it should be able to represent natural variations within the Earth system).

What do Global climate models tell us? Global climate models give us an outlook on the overall temperature trend of the Earth. These projections are somewhat trustworthy in terms of general trends, but should really be used as a guide to our potential future rather than as the hard numbers for what will occur. There are still important interactions and even natural cycles (such as the Madden-Julian Oscillation) that do not appear in GCMs but are being actively researched today. In any case, they have unquestionably become far more complex over the past decade, accounting for interactions between air and sea, clouds, and even changes in land-use such as crops and vegetation and their impacts. Thus, they are not really comparable to the old (and inaccurate) models of the 80s and 90s.

What are the current predictions? They currently project a 3.6-8.1F increase by 2100 (see below), with some models actually projecting an 8-12F increase by 2100 (the upper portion of the light gray envelope), although these are largely ignored as too extreme for now. In other words, the range commonly stated is actually closer to the low end of the current range of possibilities and is thus not merely an "extreme" case! The range of the models is derived from the fact that models are often run under several different scenarios of future CO₂ emissions. For example, a scenario of rapid technological progress and thus a great reduction in CO₂ emissions results in a slower warming.

Climate model projections. The IPCC (Intergovernmental Panel on Climate Change) currently states the most likely scenario is 3.6-8.1F warming by 2100, although some models show an 8-12F warming (upper light gray region) that are largely ignored for now. The different models vary based on internal dynamics, as well as future scenarios of carbon emission reduction, changes in land use, population growth etc.
Source: http://www.abc.net.au/rn/bigidea/features/deakins/img/projection.gif

Regional climate models

Regional climate models (RCMs) are used to predict the future climate for a specific region of the world. In general, these models use the output of a GCM to determine the overall global climate and energy budget and then apply dynamical principles to the new climate regime. A simple example: what might the climate be in the Pacific Northwest US? A GCM may show that it should be significantly warmer inland in the US. Since warm air rises, this would create a low pressure center in the central US, which would result in increased flow onshore from the Pacific ocean (where it doesn't warm as much and so the pressure is higher), thus increasing precipitation.

In my opinion, RCMs are not yet trustworthy. We are still learning fundamental ways--those primary forces on the bouncing ball--in which the climate can be affected by smaller-scale events, such as hurricanes. These are undoubtedly very important, so without them an RCM model output is nothing more than the climate future for a region of a different world. Nonetheless, current RCMs and GCMs are important stepping stones towards highly-advanced and more precise models in the future.

What do current climate models do well?

Useful for El Nino predictions
"Emerging Constraints": What is observed has been predicted by the models (from Professor Vimont, UW-Madison Dept. of Atmos. Sci)

The Arctic regions (towards the North Pole) are warming much faster than elsewhere
Water cycle: in general, wet regions are getting wetter and dry regions are getting drier

Given these "emerging constraints," the models must be doing something right

What are some current problems with GCMs and RCMs? (This is scientific but necessary to defend my statements)

They cannot reproduce some observed natural cycles, such as the Madden-Julian Oscillation
They do not incorporate short time-scale and spatial-scale events, such as hurricanes, which are now being shown to have a significant impact on the climate.
Cloud feedback modeling is very poorly understood; clouds are extremely important in the energy balance
They produce two Intertropical Convergence Zones
Some argue that parameterization of convection, which is a key driver of tropical/global circulations, is a poor representation of the process
Some argue that the Earth's climate is simply too complex to model (see NY Times Feb 26, 2007 article "The Problems in Modeling Nature, With Its Unruly Natural Tendencies")

How can we improve them?

The latest research seeks to model the "unified Earth system": weather, climate, and everything in between. For them to be truly reliable, they need to take into account all dynamics and processes that exist in the Earth system given emerging research into the important interactions that occur between small and large spatial and temporal scales.

Overall

Paleoclimate models are very important in demonstrating the role carbon dioxide plays in our climate system--a possible gatekeeper of rapid climate shifts. Current global and regional climate models are important steps towards reaching a goal of a more accurate climate model of the unified climate system and provide insight into the overall effects and trends due to global warming. However, current regional climate models are not yet well-enough equipped to properly handle the complexity of our climate at regional scales.

Alright, climate models aren't perfect but at least they give us insight into our past, as well as an idea of the future that is certainly worth listening to. What's this I hear about Global Dimming?