I do not know the AR process that corresponds with a diffusive ocean as opposed to a slab (AR[1]) ocean.

I am prepared to work it out but I thought I would ask here to see if it is known.

In terms of filters it turns white into pink noise. (3db/octave & 45 degrees of phase).

In terms of circuit components it is a resistance feeding an impendence with a constant 45 degree (1-j) phase and magnitude that varies with the inverse of the square root of the frequency.

I know where I can get approximations (just Google) I am looking for a more analytical treatment.

Any offers?

************

BTW if anyone would like to turn a (ocean) temperature record into flux uptake by the oceans (slab & diffusive) and does not know how; or how to turn a flux forcing record into a SST record (slab & diffusive) I could let you know. I can provide the appropriate integrals and discrete approximations.

Best Wishes

Alexander Harvey

2 C is the mode of the distribution, but the probability that the true climate sensitivity is above 2 C is well over 50%: the distribution is heavily right-skewed. This has tremendous relevance for long term climate.

(You also missed the point of the “academic frou-frou” which you apparently dismissed; it gives an alternative argument which supports your position more strongly than does Fig. 7b.)

I was looking at the Schwartz paper and realized that if we had an estimate for forcing (rather than white noise) and someone knows how to do this fits properly, we should be able to come up with much better estimates for the time constant and the heat capacity of the earth.

If any of you are interested, could you contact me?

Mind, what they say is—

From Fig. 7b one can see that prior assumptions considerably
influence the upper tail of the posterior distribution.
Large climate sensitivities cannot be excluded
by means of the data alone. However, the use of
a uniform prior for the feedback parameter lambda would
imply a strongly informative prior for climate sensitivity
S, which would result, after Bayesian updating, in a
posterior distribution for climate sensitivity whose support
is almost exclusively bounded to the [1.5, 4.5]
range…

–obligatory academic frou-frou. But Fig. 7b speaks for itself.
2ºC, plus maybe a skosh

Best for 2008, Pete T

So, are we converging on a theoretical/empirical sensitivity value of 1 to 2ºC? Steve?

Best for 2008, PT

Thanks! Here’s the full text:
http://www.cgd.ucar.edu/ccr/knutti/papers/tomassini07jc.pdf

This one will take some digesting…

Cheers — Pete T

ABSTRACT
A Bayesian uncertainty analysis of 12 parameters of the Bern2.5D climate model is presented. This includes an extensive sensitivity study with respect to the major statistical assumptions. Special attention is given to the parameter representing climate sensitivity. Using the framework of robust Bayesian analysis, the authors first define a nonparametric set of prior distributions for climate sensitivity S and then update the entire set according to Bayes’ theorem. The upper and lower probability that S lies above 4.5°C is calculated over the resulting set of posterior distributions. Furthermore, posterior distributions under different assumptions on the likelihood function are computed. The main characteristics of the marginal posterior distributions of climate sensitivity are quite robust with regard to statistical models of climate variability and observational error. However, the influence of prior assumptions on the tails of distributions is substantial considering the important political implications. Moreover, the authors find that ocean heat change data have a considerable potential to constrain climate sensitivity.

See Tomassini et al. (2007) in J. Climate for a nice modern treatment of this problem, which attempts to use ocean heat uptake data to constrain the vertical diffusivity. They are not the first to do so, but I think it’s one of the best published analyses to date from the standpoint of physical modeling and parameter estimation methodology.

Do you have a full cite (or better, link) to this paper? Google isn’t finding it for me….

TIA, PT