How Accurate Are Climate Models?

A recent post by Doug L. Hoffman addresses the fundamental question of the accuracy of climate models in Climate Models Irreducibly Imprecise stating:

• A number of recent papers analyzing the nature of climate models have yielded a stunning result little known outside of mathematical circles—climate models like the ones relied on by the IPCC contain irreducible imprecision. 
• According to one researcher, all interesting solutions for atmospheric and oceanic simulation (AOS) models are chaotic, hence almost certainly structurally unstable. 
• Further more, this instability is an intrinsic mathematical property of the models which can not be eliminated. 
• Analysis suggests that models should only be used to study processes and phenomena, not for precise comparisons with nature.
• The ability to predict the future state of the Earth climate system, given its present state and the forcings acting upon it, is the holly grail of climate science. 
• What is not fully appreciated by most is that, in the prediction of the evolution of that system, we are severely limited by the fact that we do not know with arbitrary accuracy the evolution equations and the initial conditions of the system. 
• By necessity climate models work with a finite number of equations, from initial data determined with finite resolution from a finite set of observations. 
• These limitations are further exacerbated by the addition of structural instability due to finite mesh discretization errors (the real world isn't divided into boxes 10s or 100s of kilometers on a side; the impact of changing mesh size has been well documented in a number of recent studies).

A pessimistic view based on the argument that since the global weather is a chaotic system, it is impossible to predict because of an irreducible imprecision of computational modeling.

But is this a valid argument? Not necessarily, as I discuss in previous posts listed in Mathematics of Global Warming: Weather and climate dynamics results from turbulent motion of air and water and even if turbulent flow is chaotic or unpredictable in a pointwise sense, certain mean-values are computationally predictable. The conclusion of irreducible imprecision thus may be valid for pointwise quantities, but not necessarily for mean-values of interest in climate prediction, of course depending on what imprecision for what mean-value carries meaningful information. Imprecision of 50% may useless, 10% may say something, while 1% may be best possible and carry definite information. 

Our experience from computational simulation of turbulent flow indicates that mean-values such as drag and lift of bluff bodies may be computable up to an irreducible imprecision of 1%.  

We do not have to give up the hope of and work towards meaningful computational climate simulation and prediction. The irreducible imprecision because of chaos of turbulence may be acceptable. But to reach this limit requires advancing the computational technology of climate simulation, and here adaptive finite element methods with a posteriori error estimation offers new tools for progress...