While this post was previously removed for publication purposes, the publication guidelines do allow discussion of papers under review on private blogs. The also allow submission of manuscripts to archives. The full text of an early version of the accumulation theory can be read here.

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I hate to throw a spanner in the works but observed cloud changes during the satellite era caused a direct 0.7w/m2 forcing in a mere 13 years. Ocean atmosphere response times looks to be about 5 years, hence declining OHC since 03.

While there is still room for ocean current driven lag from solar i’m struggling to see to see slow ocean equilibrium response times.

Rob, please do throw spanners at it! The longest response time is the deep ocean obviously, that I get to be 3500 years. With integration dynamics the 0.1C annual standard deviation, natural variation that is, can produce glacial-interglacial swings. The response time of the system gets less from there up. 5 years is about the surface ocean level. There is no one response time, it is graduated from 0 in the upper troposphere to 10 years at the surface to 3500 in the Deep.

DavidS99us

On time constants, you may be interested in Nicola Scafetta

“Comment on “Heat capacity, time constant, andsensitivity of Earth’s climate system” by Schwartz”sensitivity of Earth’s climate system” by Schwartz”GEOPHYSICAL RESEARCH LETTERS, VOL. ???, XXXX, DOI:10.1029/,

PS Thanks for the abstract, but don’t jeoparadise acceptance.

I can’t spea

Opps, okay, try that again: I can’t speak for David, but I think that there is a serious weakness in Scafetta’s comment: Namely the use of a GCM “hindcast” to de-trend and check the simpler detrend method. I also note that his second time constant is suspiciously close to the length of a typical solar cycle and this method is based on autocorrelation…but even discounting that the curve fit appears to be very poor for longer lags which makes me think that the estimate of the second time constant is not likely to be very certain.

The sensitivities implied also appear to be a little high with respect to the radiation flux data, especially if Scafetta’s short time period bias is taken seriously.

I think there are multiple sensitivities/characteristic decay times (tau not lags) depending on where you are in the system. As Hansen reports the tau vary from short to very long when the deep ocean is concerned. The sensitivites of the deep ocean appear to be very high, but so is the attenuation from the mixing.

No doubt there are multiple response times! I just doubt if Scafetta’s method of estimating them is quite right.

How to measure a specific response time when they are continuous? If you take the annual autocorrelation, then surface temperature is 0.9 giving a decay time and gain of 10. The lower troposphere UAH or TLT is 0.45 or about gain=2. The surface record is tied up with the greater mass of the ocean mixed zone. The dominant behavior of the system follows the largest eigenvalue, which is the deep ocean, that I put at a gain of 3500 but could be more. So its not right to say, the climate sensitivity is either of those values, and also the attenuation of the forcing needs to be considered. The gain of the deep ocean is so high, the attenuation must be very great, or we would have massive swings. But over the century time scale, the ocean mixed zone and a gain of 10 could well be dominant.

From what I remember of Scafetta model, its a linear sum of exponential filters, which is more clumsy than an AR recursive model, but I would have to look more closely at it. Its a lot less wrong than simple regression of TSI against temperature, which is essentially a zero response time assumption.

This sounds to me like an order of approximation problem, where each time scale involves more contribution to the response determination, but the refinement of the estimate becomes smaller. Scafetta is using something like a second order model for the response. It’s kind of a Taylor problem, in many ways, and I suspect that like those situations, one can safely neglect the very high order response times. But are just two response times sufficient? Dunno. It depends on many factors, including how accurate you want to be.

I think the long response times determine the dominant response of the system. The short ones become irrelevant. See Reversible Markov chain models http://www.scholarpedia.org/article/1/f_noise.

Then consider how to handle if the decay time is practically infinite. Not diffiicult actually.

Sadly I think that you have official gone beyond my current understanding of mathematics! Contributing further to this discussion will require further study on my part. Time to hit the books!

Hi David,

It must be disappointing to return from hibernation to a freezing winter! Well it’s freezing in Sydney anyway.

Anyway, do we not get any more details of the new paper (e.g. title/abstract) or is that likely to prejudice the peer review?

Best,

Alex

I would like to get it up somewhere before I release the paper, but I suppose the abstract would be ok.

Here we present evidence and theory in support of the view that the dynamics of global temperature change, from the annual to the glacial time scale, is dominated by the accumulation of variations in solar irradiance. In a simple recurrence matrix model of the atmosphere/surface/deep ocean system, temperature changes are due to (1) the size of a forcing, (2) its duration (due to accumulation of heat), and (3) the depth in the atmosphere/surface/deep ocean system where a forcing is applied (due to increasing mixing losses and increasing intrinsic gain with depth). The model explains most of the rise in temperature since 1950, and more than 70% of the variance with correct phase shift of the 11-year solar cycle. Global temperature displays the characteristics of an accumulative system over 6 temporal orders of magnitude, as shown by a linear $f^{-1}$ log-log relationship of frequency to temperature range, and other statistical relationships such as near random-walk and distribution asymmetry. Over the last century, annual global surface temperature rises or falls $0.063pm 0.028C/W^2$ per year when solar irradiance is greater or less than an equilibrium value of $1356.9W/m^2$ at top-of-atmosphere, which is consistent with the accumulation of heat into an ocean layer 159 meters deep. The notion of ‘climate sensitivity’ is superfluous in the model inasmuch as system behavior is dominated by a very slow characteristic time scale of the order of 3500 years, and so does not require a range of special feedback and lag parameters, and atmospheric forcings by greenhouse gasses are greatly attenuated by mixing losses. Thus recent warming may be explained without recourse to increases in heat-trapping gases produced by human activities.

Very cryptic Nik; a visual blancmange of your various fetishes perhaps?

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