The physics of climate modeling

From Jan. 07 Physics Today

The physics in climate models can be divided into three categories. The first includes fundamental principles such as the conservation of energy, momentum, and mass, and processes, such as those of orbital mechanics, that can be calculated from fundamental principles. The second includes physics that is well known in theory, but that in practice must be approximated due to discretization of continuous equations. Examples include the transfer of radiation through the atmosphere and the Navier–Stokes equations of fluid motion. The third category contains empirically known physics such as formulas for evaporation as a function of wind speed and humidity.

For the latter two categories, modelers often develop parameterizations that attempt to capture the fundamental phenomenology of a small-scale process. For instance, the average cloudiness over a 100-km2 grid box is not cleanly related to the average humidity over the box. Nonetheless, as the average humidity increases, average cloudiness will also increase. That monotonic relationship could be the basis for a parameterization, though current schemes are significantly more complex than my example.

Given the nature of parameterizations among other features, a climate model depends on several expert judgment calls. Thus, each model will have its own unique details. However, much of the large-scale behavior projected by climate models is robust in that it does not depend significantly on the specifics of parameterization and spatial representation.

The most interesting behavior of the climate system is emergent. That is, the large-scale phenomena are not obvious functions of the small-scale physics but result from the complexity of the system. For instance, no formula describes the Intertropical Convergence Zone of tropical rainfall, which arises through a combination of the seasonal cycle of solar radiation, the properties of moist convection, Earth's rotation, and so on. Emergent qualities make climate modeling fundamentally different from numerically solving tricky equations.

Climate modeling is also fundamentally different from weather forecasting. Weather concerns an initial value problem: Given today's situation, what will tomorrow bring? Weather is chaotic; imperceptible differences in the initial state of the atmosphere lead to radically different conditions in a week or so. Climate is instead a boundary value problem—a statistical description of the mean state and variability of a system, not an individual path through phase space. Current climate models yield stable and nonchaotic climates, which implies that questions regarding the sensitivity of climate to, say, an increase in greenhouse gases are well posed and can be justifiably asked of the models. Conceivably, though, as more components—complicated biological systems and fully dynamic ice-sheets, for example—are incorporated, the range of possible feedbacks will increase, and chaotic climates might ensue....