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What I mean by the question is if retrodiction has been attempted back to, say, 50 or 100 years starting with the presently known state of climate as initial conditions using the same equations and methods that are popularly used to predict climate 50 or 100 years ahead?

If yes, how well retrodiction turned out? If not, why not?

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    $\begingroup$ The Navier-Stokes equations are not time-reversible so I doubt it would be possible to use the same equations and methods. $\endgroup$ – tpg2114 Jan 26 '14 at 2:19
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    $\begingroup$ Of course you realize that the mathematical models have been fitted to the climate data up to the present and the predictions are extrapolations to the future. This means that any retrodiction using one of the existing models already contains the data and is invalid as a check. One should start from scratch taking lets say the last 50 years and fitting the parameters, and then retrodict from 50 to 100, or something like that. $\endgroup$ – anna v Jan 26 '14 at 6:16
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Very nice idea and question! Of course, also climate scientists have already come up with this idea. And an other similar idea, which is to take the available data on the climate from say 100 years ago and run the simulation for the next 50 years, and compare the obtained result with the real data from 50 years ago. These are the "backcasting" and "hindcasting" approaches. One recent paper is this:

A. Carlsson-Kanyama, H. Carlsen, Barriers in municipal climate change adaptation: results from case studies using backcasting, Futures (2013): http://dx.doi.org/10.1016/j.futures.2013.02.008

But you may find some more popular descriptions on the links here, here or here. I hope you were looking for some references like this.

Cheers, Zoltan

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Paleoclimatology Modeling at the National Climatic Data Center of NOAA is a good resource to start with.

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