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2. What is a Climate Model?

A model is a set of mathematical equations that represent a process. Thus, a global climate model is a set of mathematical equations that represent the interacting processes of the Earth System. These equations are tremendously complex and are only able to be solved by a computer. Some simple models can be run on a desktop computer, whereas the most complex ones can still only be run using room-sized supercomputers.

There are two main uses of these climate models. The first is to understand processes of the current and past climate system. A certain process is changed in the model to see how it affects the model climate or the model is run in the past to understand what processes contributed to climate changes seen in the paleoclimate or historical record. The second is to try to predict the future climate state as for the Intergovernmental Panel on Climate Change (IPCC) Assessment Reports (ARs).

A Short History of the Development of Climate Models

Climate models have a lot in common with models that are used to predict the weather. In fact, they both have the same roots. Numerical modeling of the atmosphere had been envision as early as the early 20th Century. In 1904, the Norwegian meteorologist Vilhelm Bjerknes first proposed the possibility of the numerical prediction of weather if the initial state and the physical laws were known accurately. Then, the English scientist Lewis Fry Richardson made a weather prediction using equations describing the physics of the atmosphere that he calculated by hand. In 1922, Richardson explained his forecast in his book Weather Prediction by Numerical Process. Unfortunately, his forecasts were horribly incorrect, because the observations that he used for the initial conditions were not very reliable. Also, the equations he used were too complex, allowing atmospheric waves of all kinds including sound waves. These high frequency waves grew to be very large. Later in the 1930s, Carl Gustav Rossby discovered this fatal mistake and reconfigured the equations to filter out these high frequency waves (Washington and Parkinson 2005).

With the development of modern computers in the late 1940s, the idea of direct numerical modeling of the atmosphere could be revisited. At Princeton University's Institute for Advanced Studies, John von Neumann supervised the construction of one of these early computers, and he realized the potential of using it for weather forecasting. He subsequently established a team of scientist led by Jule Charney to develop a numerical weather prediction model. This team of scientists used Rossby's simplified equations (Washington and Parkinson 2005). By this time, there were better data. What was missing from the set of observational data at Richardson's time were data from above the surface. By the 1940s, there were regular upper-air soundings made over land (Weart 2011, http://www.aip.org/history/climate/index.htm).

However, the first models had to be two-dimensional and regional for weather prediction purposes for the rudimentary computers of the time. Norman Phillips at the University of Chicago took a step towards global climate modeling. Inspired by his dishpan experiments of features that resembled weather in a rotating pan of water, he developed a two-layer model on a cylinder instead of a sphere that produced features that resembled a jet stream and weather systems (Weart 2011, http://www.aip.org/history/climate/index.htm).

Encouraged by Phillips's results, Joseph Smagorinsky at the U.S. Weather Bureau, the predecessor to the National Weather Service, established a team to develop a general circulation model (GCM), a global three-dimensional model of the atmosphere. A key member of this team was Syukuro "Suki" Manabe. Smagorinsky and Manabe developed a nine-layer model that was the first to include physical processes that are explained in the next chapter as well as moisture fluxes from a global damp surface (Weart 2011, http://www.aip.org/history/climate/index.htm). This group grew to become the Geophysical Fluid Dynamics Laboratory now housed at Princeton University.

Another group developing a GCM at about the same time was Yale Mintz's group at the University of California-Los Angeles (UCLA). Mintz recruited Akio Arakawa to help in the development of numerical schemes for a GCM. One of those schemes was a staggered vertical grid to resolve complications that develop when calculating all quantities at the same grid points. Together, Mintz and Arakawa developed a two-layer model with separate land and ocean surfaces (Weart 2011, http://www.aip.org/history/climate/index.htm).

With the advancement of computers, the GCMs became increasingly more complex with the inclusion of more processes and even a return to the original equations that Richardson used. Over the years, separate models began to be developed for the oceans, land surface, and sea ice that were eventually coupled to the atmospheric model for more accurate simulations of the whole Earth system (or as close to the whole system as possible). Also, more and more groups started developing their own GCMs first in the U.S. and then in other countries, but many of the later models are really offshoots from earlier models. A "family tree" of atmospheric GCMs can be found at http://www.aip.org/history/climate/xAGCMtree.htm.

The Difference Between Climate Modeling and Numerical Weather Prediction

As we saw in the last section, numerical weather prediction and climate models have much in common, and climate models are in fact derived in essence from weather models. But everybody knows that weather prediction is notroiously unreliable after a few days. Then, how can we expect to predict the climate decades or centuries into the future? The reason is that climate prediction is inherently different.

An example of the difference in forecasting the near-future versus the distant future can be gleamed from the realm of economics. The direction of the stock market is hard for economists to forecast on a few days in advance, but everybody knows that the stock market will be higher 10 years from now. The day-to-day variations in the stock market are based on a number of factors that could change how the stock market reacts even if these factors change just a little bit. On the other hand, the long-term upward trend of the stock market is due to the inherent nature of the system (X. Zeng, personal communication).

The same is true for weather versus climate. Weather is influenced by the state of the atmosphere at any moment. Thus, a small perturbation in the atmospheric state can have a dramatic effect on the weather. This is the so-called "butterfly effect:" a butterfly beating its wings in Beijing could produce a tornadic thunderstorm in Oklahoma or a major hurricane that hits Miami. This is known as chaos. Chaos was first discovered by Edward Lorenz who found that differing results were being produced by different runs of a very simple model. It turns out that very slight changes in the input to the model would radically change the output. This also occurs in more complex models. Slight perturbations to the input data to a numerical weather prediction model can produce different weather conditions. This is important, because even though observations are greatly improved, there is still uncertainties in those observations. Thus, many weather models are now run as ensembles of runs with differing perturbations to the input observations. This sensitivity to the initial conditions is known as an initial value problem.

However, climate is a boundary value problem. The small day-to-day weather has little effect on the large scale climate. Instead, the climate is forced by the state of the Earth system: the composition of the atmosphere, how much solar radiation is received, the geographic distribution of the continents and oceans, and so on. A small change in the input data set is not going to have as dramatic of an effect on the results of a climate model as it would a weather model. If the climate is in a stable state, that state would not be changed nor would a trend be substantially different if the climate is transitioning to a different state. An excellent example of this is the 20th century trend in carbon dioxide as measured at Mauna Loa, Hawaii (http://en.wikipedia.org/wiki/File:Mauna_Loa_Carbon_Dioxide-en.svg). The seasonal cycle in concentration can be seen in the data, but the long-term average trend is constantly upward. Thus, we can have confidence in any trend such as the temperature change after 100 or so years or the mean temperature change per year, decade, or century that is predicted by a global climate model. In fact, recent research has found that the model trends are most reliable for very large horizontal and time scales (Sakaguchi et al. 2011).

The Ensemble of Climate Models

The international assessment of climate is done by the IPCC. Periodically the panel puts out assessment reports which includes climate model predictions. The climate models that were included in the latest assessment (Randall et al. 2007, Table 8.1, http://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch8s8-2.html#table-8-1) include models from groups from around the world. Together, these models can be thought of as an "ensemble" of climate models.

These models are first assessed. Their simulated climate is compared to observations and reanalyses, model hindcasts that have been continuously constrained by observations. The group that heads this assessment is the Program for Climate Model Diagnosis and Interception (PCMDI) at Lawrence Livermore National Laboratory. The group compares not only the fully coupled model results but also the results from some of the individual components, most notably the atmospheric model, and results from special situations and uses. Such a comparison allows the models to be compared with each other on a level playing field, because PCMDI prescribes how they are all to be forced to be included in their comparison.

References

Randall, D. A., R. A. Wood, S. Bony, R. Colman, T. Fichefet, J. Fyfe, V. Kattsov, A. Pitman, J. Shukla, J. Srinivasan, R. J. Stouffer, A. Sumi, and K. E. Taylor, 2007: Climate models and their evaluation in Climate Change 2007: The Physical Science Basis, Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Solomon, S., D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor, and H. L. Miller, eds. Cambridge Univ. Press: Cambridge, UK.

Washington, W. M., and C. L. Parkinson, 2005: An Introduction Three-Dimensional Climate Modeling. University Science Books: Sausalito, Calif.

Weart, S. R., 2011: The Discovery of Global Warming. http://www.aip.org/history/climate/index.htm.

1. What is Climate?
Radiation: What Drives the Climate
The Components of the Earth System
2. What is a Climate Model?
A Short History of the Development of Climate Models
The Difference Between Climate Modeling and Numerical Weather Prediction
The Ensemble of Climate Models
3. The Components of a Climate Model
Atmospheric Models
Ocean and Sea Ice Models
Land Models
Offline Mode
4. What is Next for Global Climate Modeling?
Transitioning to Earth System Modeling
The Need for Increased Resolution