I’ve been browsing through some articles on climate modeling and GCMs since even the Hockey Team no longer seems to try to base climate policy on multiproxy studies. I’m particularly interested in the approach of maximum entropy theorists, since they offer a very non-IPCC perspective on GCMs. Here are a few quotes from Holloway , “From Classical to Statistical Ocean Dynamics” which is online here. Holloway observed:
In principle we suppose that we know a good approximation to the equations of motion on some scale, e.g., the Navier-Stokes equations coupled with heat and salt balances under gravity and rotation. In practice we cannot solve for oceans, lakes or most duck ponds on the scales for which these equations apply.
He likened the GCM method for climate modeling to the following:
This enterprise is like seeking to reinvent the steam engine from molecular dynamics’ simulation of water vapour. What a brave, but bizarre, thing to attempt!
Here is a longer excerpt:
In principle we suppose that we know a good approximation to the equations of motion on some
scale, e.g., the Navier-Stokes equations coupled with heat and salt balances under gravity and rotation. In practice we cannot solve for oceans, lakes or most duck ponds on the scales for which these equations apply. For example, the length scales over which ocean salinity varies are often shorter than 1 mm. We try to solve for fields represented on grids (or other bases) that are far larger than the scales to which “known” equations apply. Then we are compelled to guess the equations of motion.
Guessing equations is uncomfortable, often causing us to assume without question the equations used by some previous author. When we are brave, we realize that this too is uncomfortable. It is natural to wish that, as computers grow ever more powerful, we guess less and less. What would be needed from the computer? In the oceans there are about 1.36 x 10^18 m3 of water. If we felt that variability was unimportant within volumes of O(10)9 m3) then the computer should track O(1027) volumes, each described by several degrees of freedom. Clearly one can fiddle these numbers. Today’s “big computer models”, e.g., for weather forecasting or turbulence research, may advance 10^7, 10^8 or 10^9 variables. Over time we are assured that computers will become bigger yet. Even if we imagine computer models advancing 10^12 variables (not on my desk in my lifetime!), we still face the situation that, for each one variable we track, we must guess how that variable interacts with 10^15 variables about which we are uninformed. Limiting ourselves to coastal oceans or lakes, the mismatch in degrees of freedom might reduce to 10^8 or less. Might computations for a suitably modest duck pond “someday ” be possible? Maybe. This enterprise is like seeking to reinvent the steam engine from molecular dynamics’ simulation of water vapour. What a brave, but bizarre, thing to attempt! For oceans, lakes and ponds the circumstance is even worse than the dismal numbers above suggest.
He was critical of some conventional parameterizations, pointing out:
traditional geophysical fluid dynamics (GFD), with traditional eddy viscosities, violates the Second Law of Thermodynamics, assuring the wrong answers.
I do not have an independent view of whether Holloway’s comments about traditional ocean models (which form one module of coupled GCMs) are right or not. I don’t know anything about Holloway, but he seems to have published a number of technical articles in respected journals on related topics. In this particular paper, he thanks Joel Sommeria, whose mathematical credentials strike me as far more imposing than those of the Hockey Team. The issues that he raises all seem plausible ones. I’ll post up some more comments on some articles raising similar issues in the next few days.
Reference: Greg Holloway, 2004. From Classical to Statistical Ocean Dynamics. Surveys in Geophysics 25: 203″€œ219, 2004. http://www.planetwater.ca/research/entropy/SurvGeophys.pdf