The Divide and Conquer Method: How Climate Models Work
Potentates from King Philip II of Macedon (382 B.C.–336 B.C.) to the present day have espoused a philosophy of divide and conquer as a solution to the world’s problems. In computer science, a divide-and-conquer algorithm is one that splits a problem into an ever greater number of related subproblems until the solution to each becomes relatively simple.
GCMs follow this philosophy in several respects. First, GCMs divide the planet into a minimum of two compartments, atmosphere and ocean. Many GCMs also treat sea ice and land separately. Each compartment has its own model that characterizes processes intrinsic to the compartment and transfers of material and energy with other compartments. These models are in themselves large computer programs (having more than 100,000 lines of code) that undergo independent development. For example, atmosphere models may derive from any of ten distinct lineages, ocean models from at least five other lineages , and sea-ice models from yet again six others.  Integrating all the pieces into a coherent semblance of Earth requires another large computer program called a coupler that coordinates both the timing and the format of data exchange among the atmosphere, ocean, sea ice, and land models. 
Examples of grid box systems (A) A latitude–longitude grid with the pole on top, red lines at the equator and at two constant longitudes, and dots representing grid cell centers. (B) A geodesic grid with the continents in white and a color-coded plot of observed sea-surface temperatures. This grid has 10,242 cells, each of which is roughly 240 km across. Twelve of the cells are pentagons; the rest are hexagons. From Randall et al. 2002.
Second, each compartment model is further divided into submodels. In particular, an atmosphere model usually has discrete submodels for the dynamical core of fluid motions described in the following paragraphs; precipitation and cloud formation; atmospheric chemistry; aerosols such as smoke, smog, and haze; and characterization of physical processes such as radiation and convection. An ocean model usually has submodels for dynamical core of interior ocean fluid motions, wind stress on surface mixing layers, and, sometimes, fresh water inputs, such as river cycling, vegetation, and albedo. Each submodel may again be divided into sub-submodels, and so on until the processes that are being simulated sufficiently diminish in complexity to become mathematically straightforward.
Third, as mentioned previously, GCMs divide the world into a patchwork of small boxes operating over a relatively short period of time. There are several types of grid box systems and time steps, and sometimes a single GCM will use a different one for each submodel. No matter what grid box system or time step a GCM uses, the classical laws of physics apply to every grid box during every time step. These laws are the conservation of momentum (a mass changes its velocity only in proportion to the magnitude of outside forces), conservation of mass (the mass of a closed system will remain constant, regardless of the processes acting inside the system), and conservation of energy (the total amount of energy in a closed system remains constant).
At the core of every GCM, then, is a group of fundamental equations of fluid mechanics and often, a set of assumptions that simplify the mathematical representation of air, water, and ice movements. In practice, solving these systems of equations remains challenging. Air is not dry. Water is not pure. Net heat gain depends on the multifaceted energy budget of Earth’s surface and its atmosphere. Appropriate initial conditions for a model may not be obvious. Despite these difficulties, climate modelers approximate solutions to these systems of differential equations and create useful tools for studying climate and forecasting climate change.
 Washington, W. M. and C. L. Parkinson (2005) An introduction to three-dimensional climate modeling, 2nd Edition. University Science Books, Sausalito, CA.
 Craig, A. P., R. Jacob, B. Kauffman, T. Bettge, J. Larson, E. Ong, C. Dingo, and Y. He (2005) Cpl6: The new extensible, high performance parallel coupler for the Community Climate System Model. International Journal of High Performance Computing Applications 19:309-327.
This is an excerpt from the book Global Climate Change: Convergence of Disciplines by Dr. Arnold J. Bloom and taken from UCVerse of the University of California.
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