Wednesday, May 28, 2008

Climate models: Their origin and nature

An infinite number of approximation schemes are available to turn the full climate theory into something tractable. In practice, approximation methods have fallen into a few distinct classes.

Textbook cases. There are very simple approximate models that can be solved exactly. These typically exclude convection and include evaporation, condensation, and clouds only in a very simplified form, if at all. Such models are frequently used in climate textbooks. A slightly more complex class of models require computers to achieve an approximate (but typically quite accurate) solution. (That is, the theory is replaced by an approximate model, which itself is then subject to further approximations in order to solve it.) The earliest versions of both classes of models date from the end of the 19th and the early decades of the 20th centuries.* Early versions of numerical approximations, which replace continuous time and space with a discretized "grid" of time instants and spatial points, were developed during these periods. The calculations to implement these approximation methods are tedious and had to be done by hand. (In the 19th century, a "calculator" was a person who carried out this arithmetic drudgery!) In the 1920s, 30s, and 40s, electromechanical calculators, forerunners of today's electronic handheld calculators, were pressed into service to carry out such work. It is worth stressing: the computers just implement a numerical approximation scheme; they do no physics and don't "know" the approximation method except to the extent that they are programmed by humans.

The rise of large-scale computer models. Around that time, the British physicist Lewis Fry Richardson, following up the suggestion of Norwegian Vilhelm Bjerknes, collected the pieces of the full climate theory as we know it today. The fluid dynamics and thermodynamics of air and water vapor were discovered during the 19th century, including the famous Navier-Stokes equation, which describes the motion of turbulent fluids. At the end of that century and the first decade of 20th, the nature of radiation and radiative heat transport came to be understood for the first time. With all these necessary pieces, Richardson wrote down a simplified version of the complete climate dynamics. He postulated that hundreds or thousands of human "calculators" could be set to doing the necessary arithmetic to implement a numerical "grid-ified" approximation scheme for the atmosphere.

From the start, Richardson's first attempts to predict weather ran into just the problems that would subsequently occupy climate and atmospheric scientists for the rest of the century. He could never piece together enough initial condition information to properly start the integration forward in time. He ran into a version of chaos, although he failed to understand the full nature of what he had stumbled into. The human-implemented arithmetic calculations needed to carry out the method were so slow that weather prediction could not be done in real time. Starting on day one, he got to making a prediction for the following day's weather only after six weeks - and it was wrong. Richardson had posed the full climate problem, for the first time, as a problem in mathematical physics, and it quickly came to be perceived as unsolvable.

At the end of the 1930s, the invention of the electronic computer (first built with vacuum tubes, later with transistors and transistors on "chips") promised to transform the entire problem by making possible a large number of fast, accurate calculations. Better numerical approximation schemes (many of them rooted in the work needed to design and test the first nuclear weapons) became available. By the 1950s, people were seriously talking about making accurate weather predictions, not just for tomorrow or next week, but long-term, months or even years. Weather was one of the first non-military applications of these computers. Fantasies about controlling weather were floated as well, since accurate prediction and control are closely related.

Modern climate models, called atmosphere-ocean general circulation models (AOGCMs, or GCMs for short) have their roots in the postwar decades, the 1950s and 60s. They were put into their contemporary form in the 1980s and continue to serve as the main basis for the most complex long-term climate predictions.

And then chaos happened. Readers of this blog know what also happened during that period: the discovery of chaos by Edward Lorenz at MIT. By the early 70s, it was clear that long-term weather forecasting was doomed. A chasm opened up between hope and reality and between "weather forecasting" in the popular sense (limited to a week or two ahead) and "climate prediction" for the long term. Modelers retreated to a fuzzy distinction between "weather" and "climate," a distinction that has never been properly defined. Climate had to be defined statistically, as a set (or ensemble) or possible weathers, with some attached probabilities. Long-term predictions of climate would have to sample this ensemble, then average the results weighted by their respective probabilities. Because the full climate theory equations could not be solved accurately, heavy use of repetitive past weather situations to make future predictions came into play: in ordinary weather forecasting, known as synoptic meteorology; in "climate" prediction, as "climate parameterizations."**

Climate models: Successes and failures. The accuracy and control embodied in these GCMs are very uneven if we disaggregate the models into the various pieces that come from the fundamental theory. Before the next couple postings explain what's wrong with the models, it's a good idea to step back and point out what's right about them.

Mechanical equilibrium (pressure gradient balancing the pull of gravity downward) is the best-respected part of the whole standard climate picture. This piece gives us the pressure and density profiles as functions of altitude, as well as the atmospheric motions we know as winds. It's the thermal and chemical parts (heat transport and water phase transformations, respectively) where things get much hairier, because there is intermediate-scale structure smaller than the whole Earth but bigger than little parcels of air that are close to thermodynamic equilibrium: clouds, storms, cyclones, anti-cyclones, fronts.

Radiation and evaporation are the best controlled approximations in that sector of the models. Convection is under much poorer control, and turbulence essentially not at all. Neither are condensation and precipitation. "Global warming" due to infrared (IR)-opaque gases arises from the first two pieces (radiation, and the major enhancement of clear-air water vapor due to the much smaller effect of increased CO2 and CH4 concentrations). Not surprisingly, conventional climate models currently get these parts pretty well.

But the other parts, not under good control, are just as important. Convection is a significant heat transport mechanism in its own right and plays an essential role in getting water vapor above the bottom-most layer of the atmosphere to higher altitudes where it condenses into clouds. Turbulence embodies the chaotic, unpredictable evolution of climate. Condensation and precipitation complete the hydrologic cycle, form a major part of heat transport, and encompass the formation and dispersal of clouds. These in turn have crucial effects back on the radiation. Climate models don't get these parts well or at all. Not surprisingly, therefore, standard climate models overstate the degree of "global warming" due to IR-opaque gases: they get the warming parts, but do poorly with the anti-warming compensatory mechanisms, clouds above all.

The final two postings on climate models will drill further into these problems.
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* It was during this period that the Swedish physicist Arrhenius first noticed the effect of IR-opaque gases such as carbon dioxide (CO2) on the temperature lapse rate.

** In weather forecasting, if limited to no more than about two weeks ahead, synoptic techniques have a limited but real justification. The time horizon of prediction is short enough that chaos does not come into full play.

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