The Threat of Computed Climate

Suppose a team of mathematicians today announces that the Earth will be hit by a large meteor in 5 years and 20 days, according to their computations. How should we react?Ask about the reliability of their computations, I guess. If we then get the answer that the computations are so complicated that there is no way we can check that they are correct. How are we then to react? Should be panick and launch a massive exodus to Mars? Well, this is all fiction and has not yet happened, so we don't have to worry.

Suppose a couple of teams of mathematicians today are telling us that according to their computations, in a few decades the sea level will rise by 5 meters and 20 centimeters and billions of people will have to move to avoid getting drowned, in a great exodus. Again we ask about how the computations are performed and what their reliability may be? But again we get the answer that the computations are so complicated that nobody outside the teams of mathematicians involved, can understand them. How are we then to react?

And this is not fiction: Global warming from burning of fossil fuels is today predicted by a couple of computer codes simulating the global climate. One of these codes is the National Center for Atmospheric Research Community Atmosphere Model CAM 3.0 also referred to as CCSM  presented as follows:

• CCSM belongs to an elite category of computer-based simulation models known as general-circulation models. Such models use mathematical formulas to recreate the chemical and physical processes that drive Earth's climate. What emerges from trillions of computer calculations is a picture of the world's climate in all its complexity. 

The future of mankind seems to be governed by this code. What is then the reliability/accuracy of CCSM? Is there anyway we can tell or is CCSM so complex that its beyond scrutiny by people outside the coding team?

Well, the first thing is to take a look at the documentation to learn that the numerics involves 

the following fixes of an otherwise unstable or overly stable useless code: 

• time filter
  
• horisontal diffusion correction
• initial divergence damping
• mass fixers
• energy fixer
• monotonicity fixer.

Further, the codes uses mathematical formulas to model the following physics:

• deep convection
• moist convection
• precipitation
• cloud fraction
• short wave radiation
• long wave radiation
• surface exchange
• vertical diffusion
• boundary layers
• sulfur chemistry
• prognostic of greenhouse gases

plus a number of other fixes and models. The most advanced version CCSM3 uses a horisontal computational grid of mesh size of about 150 km x 150 km and about 30 vertical levels, which must be regarded as a coarse grid requiring a lot of difficult mathematical modeling. The numerics seems to be a concoction of rather old-fashioned techniques.

Looking at this information, as an expert of computational fluid dynamics, my scientific self protests. It does not seem right to base far-reaching limitations on energy consumption on such a code. Or is the accuracy of the code irrelevant, as long as it serves to limit the use of energy?

What if a code tomorrow shows that CO2 can increase without negative climate effects? What if this code is wrong, but we don't understand that?

Of course we should be careful how we use resources on our only Earth, but believing that we will be hit by a meteor in 5 years and 20 days may not be the best basis for rational decisions, if the meteor is only fiction predicted by an incorrect computer simulation.

The numerics could be upgraded using modern adaptive finite element methods with flexible meshing and a posteriori error control. This may not do wonders, but the effort can not be spared...For the first time in history the future of mankind is in the hands of computational mathematicians...