torsdag 24 september 2009

Short-Time vs Long-Time Accuracy 1

The question of short-time vs long-time accuracy of climate models  is discussed in a recent article in New York Times by Andrew Revkin. What does the plateau in global temperature seen over the last decade tell us? That global warming is over? Maybe, maybe not. But it tells that climate models are inaccurate over a decade since the plateau was not predicted. Does it then follow that climate models are accurate over long-time over a century?  Not necessarily. A short-time inaccurate model may be long-time inaccurate as well.

What is then the mathematical nature of models which are short-time inaccurate but long-time accurate. Are there such models? Yes, if you put a rapid short-time oscillation on top of a long-time slow motion, then a model that discards the rapid short-time oscillation will have this property. 

Can you then draw the conclusion that a simple model with some form of damping of short-time variations, will be long-time accurate? Sometimes yes, but then only under very special conditions: regular short-time oscillation and linearity, which allows a lot of cancellation to take place. But in a non-linear system this may not be the case at all, since cancellation maybe lost.

The idea that climate models can be allowed to be short-time inaccurate, without jeopardizing long-time accuracy,  thus seems questionable. Of course, a climate model will be short-time inaccurate if some unknown major natural variation is not taken into account, and if that unknown natural variation would disappear, then the model may recover long-time accuracy but then together with short-time accuracy. The combination of short-time-inaccurate with long-time-accurate seems very special.

Altogether, it seems reasonable to ask climate models to be short-time accurate. If they are not, it probably signals that they are also long-time inaccurate. Compare the recent post by Roger Pielke Sr.  stating in particular:
  • Societally useful (i.e., reliable, accurate, etc.) climate  prediction requires that all of the feedbacks and other physical processes included in weather prediction be  presented in the climate prediction model. In addition, longer-term feedback and physical processes must  be included. This makes climate prediction amuch more difficult problem than weather prediction.
We learn that climate models also have to be weather models, and thus have to be short-time accurate in order to have a chance to be long-time accurate. It follows that the accuracy of 
climate models can be tested over short-time. What is the result of such tests? 

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