måndag 7 september 2009

Short-Time Accuracy Test of Climate Models?

The climate of the Earth results from turbulent flow of air in the atmosphere and turbulent flow of water in the ocean, which is heated by incoming solar radiation and cooled by outgoing infrared radiation, both of which critically depend on cloud formation, which requires presence of particles in the air or aerosols acting as condensation kernels.

Burning of fossil fuels produces aerosols which can enhance cloud formation. Low clouds  can decrease incoming radiation and thus act as negative feedback to global warming from fossil fuels, while high clouds can decrease outgoing radiation and thus act as positive feed-back. The net effect appears to be unknown and uncertainties in modeling of cloud formation propagate to uncertainties in global climate modeling.

A main goal of climate modeling is to predict climate sensitivity, that is the increase of global temperature from doubling of CO2 in the atmosphere. In the  IPCC 4th Assessment Report climate sensitivity is predicted to likely be between 2 and 4.5 degrees Celcius, which thus could be the global warming in 2100 without CO2 emission control. The UK Met Office explains to us:
  • There have been major advances in the development and use of models over the last 20 years and the current models give us a reliable guide to the direction of future climate change.
  • Computer models cannot predict the future exactly...
  • Current models enable us to attribute the causes of past climate change, and predict the main features of the future climate, with a high degree of confidence.
  • As well as producing CO2, burning fossil fuels also produces small particles called aerosols which cool the climate by reflecting sunlight back into space. These have increased steadily in concentration over the 20th century, which has probably offset some of the warming we have seen.
IPCC and the Met Office thus inform us that even if climate model predictions are incorrect over year and decade, they can be correct over centennials. But is this really possible from a mathematical point of view? Are there dynamical systems which allow computational modeling with this surprising property? Long-time accurate while short-time inaccurate? We are familiar with models which are short-time pointwise accurate and long-time pointwise inaccurate, but the opposite?

There are trivial such systems, like modeling an oscillation between -1 and +1 by a constant 0 state, but is the climate such a trivial system? Probably not. 

There are dissipative systems which forget initial data over long-time, so if initial data are incorrect this affects accuracy only for short-time. Climate models are dissipative and thus partly forget initial data, but that is not enough to secure long-time accuracy. 

The previous blog Climate and Turbulence Modeling recalled the analysis of turbulent flow in Computational Turbulent Incompressible Flow, showing that long-time meanvalues of turbulent flow may be predictable even if pointvalues are predictable only over short time, because of cancellation effects.  It is likely that climate models can share this property, but it requires short-time accuracy.

Altogether, I see no real reason to expect that short-time inaccurate climate models can be long-time meanvalue accurate, as suggested by IPCC and the Met Office. 

If this observation is correct, one could require climate models to be short-time accurate, which can be tested in short-time,  as a necessary requirement for reliability of long-time meanvalue prediction of climate sensitivity. 

Concerning the predictive capabilities of current climate models, see the US Senate Report: Dissent over Global Warming Claims.

The lecture Considering the Human Influence on Climate by R. A. Pielke Sr, is also informative. 

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