I never looked at the Hadley and compared to GISS. I’d figured out the GISS LAND Ocean went from 5-8 years by adding the white and doing it my way. I’ve also run enough “Monte Carlo” type runs to see that the results are variable both under “my way” (whith white noise) and the original way (as we already knew from FASM.

So, the difference could just be the portion of the variability due to the measurement error. Or not– I’ll know better when I get back to checking how much variability you get when the “weather” part stays the same but the white noise changes.

If this turns out to be within the scatter for the measurement uncertainty, averaging the two might help. (In which case, it will be useful to figure out if we should average the temperaure first, the do the correlation, or run the correlations and then average!)

( Yep, I’m going to check this even if, at his blog, James Annan posts that he’s “amused” that I’m checking how the bias he pointed out as affecting Schwartz’s method translates to my method. FWIW, the properties of the bias look different when you add white noise. For example, based on small amounts of fiddling, the bias for the first lag one term tends to give correlations that are too high compared to the average values “expected” for a process that is the sum of red noise and white noise. The later lags do have correlations that are too low. )

For fun, I’ve repeated the analysis with the HadCRUT3 annual temperature series downloaded a couple of days ago from http://hadobs.metoffice.com/ha.....+sh/annual (using 1850 to 2007 data, so the linear trend is fit to a different time period here). Comparing with the GISS numbers, the autocorrelation of the Hadley data is clearly stronger:

and the time constant by Schwartz’ method is clearly larger:

at least 8 years. Any ideas why the difference?

== Lucia, if you could embed the images, thanks!

http://inlinethumb45.webshots......600Q85.jpg

http://inlinethumb34.webshots......600Q85.jpg

http://inlinethumb45.webshots......600Q85.jpg

Second one is here (time constant):

http://inlinethumb34.webshots......600Q85.jpg

Thanks if you can embed them. How did John V do it?

This link gives some info about thermal conductivity and capacity for land. It turns out that moisture content can have a huge effect.

http://www.geo4va.vt.edu/A1/A1.htm

This next curve is the time constant tau calculated by Schwartz’s method, again blue curve is the GISS Land/Ocean temperature series, and red is the Met station which Schwartz apparently used. Note that the blue curve shows time constants of at least a year longer in the early period:

By the way, I was trying to embed the above graphic links in the page here – how do I do that?

Because water has a large thermal mass and half way decent mixing of the upper layers, the world may act more “massive” at that point.

But… I could be full of it on this because obviously, dirt also has lots of mass etc.

Do you know whether the peak of summer is nearer the solstice over the ocean in the mid latitudes? Or does it lag the peak over land?

I’ve re-done his calculation using the data he used (GISS MET station annual data through 2004), and then compared it with the same calculation using the GISS Land/Ocean series (annual data through 2007). The Land/Ocean numbers are definitely more auto-correlated, and give you a consistently higher time constant, at least a year more (i.e. 6 years +, instead of 5, for the original Schwartz approach):

http://inlinethumb32.webshots......425Q85.jpg

http://inlinethumb02.webshots......425Q85.jpg

The first this suggests is, as with your analysis Lucia, and Scafetta’s comment, additional short-term variability (measurement noise or something else – the MET station data has a 30% higher rms residual from the trend than the land/ocean data) biases Schwartz’s method to give you too low a time constant. Or maybe it’s just that the time constant appropriate for land is shorter than for oceans?

That can’t be the right thing to do though, can it? Maybe it doesn’t matter much, but I would have thought if you were arguing about the ocean heat capacity and how it may or may not be causing autocorrelation in temperatures, you ought to include the ocean surface temperature data in your analysis!

So, if Schwartz’s data differs from the data by that much, I can’t really guess why. But, I do know someone who posted at Climate Audit has been downloading data regularly. When they first started, it created a bit of a brou-ha-ha. In the end, he got lots of data.

So, if Schwartz just made a mistake that’s an issue.

I’m going to be going back to looking at this now that I got together a response post.

But, one of the things I’m going to post may illustrate a different reason not to trust the single lump model! ( I fit it to model E, which we know was forced with that forcing file. )

Climate audit has discussed this, and Steve has been archiving past versions of historic GISS data. It changes. . .

To find out the exact data set Schwartz used, you might need to contact Schwartz!

I don’t know if Hadley temperature change backwards.

First pass I got a quite different auto-correlation curve (dips negative at lag of 13 years), so I was trying to track back the source of the trouble. And I realized his fig 5a that is supposed to be the “Original time series, GISS, [Hansen et al., 1996]“, doesn’t agree with the GISTEMP January-December global (land-ocean) mean temperature numbers, from the start. In particular, it comes close to a 0.0 anomaly in 1883 or so, and again in 1890. But if I look at the GISTEMP series here:

http://data.giss.nasa.gov/gist.....s+dSST.txt

which was also in Lucia’s spreadsheet, column N of the raw GISS data, that doesn’t come close to 0 until 1926, and doesn’t go above 0 until 1937.

The closest match I could find is the monthly data for February (column C). But that has much higher ups and downs than is shown in Schwartz’s figure 5a – in particular there’s a deep dip in February 1951 to -0.39, which isn’t there at all. And when you detrend, the root mean square residual is almost twice as large for the monthly series as for the annual one, so a lot of extra noise in there that probably isn’t useful for this purpose.

So what data set is he actually using there? Or has something changed with GISTEMP since he made those figures? This seems very strange…

I am not sure whether it would help much to complicate the heat capacity in terms of layers because, like you, I suspect that convection may be at least as important as conduction. However if I wanted to try, I would simply make my capacitor into a series of smaller ones separated by resistances. The capacitors would be the heat capacity per layer and the resistances would represent the conduction between the layers. At high frequency, only the surface capacitor would have much effect and at low frequency they would behave as though they were all in parallel.

I would think that we would not need an infinite number of these, as at some depth we can assume that no temperature changes occur at frequencies of interest. No doubt you can find some kind of transmission line type of equation to describe this behaviour, treating the layers as zero thickness but that is beyond my capability.

This more complicated version of my model capacitor would not alter the value of R as that represents the heat flow moving from the surface when the surface temperature deviates from some equilibrium value.

I don´t think this more detailed version of the capacitor really adds more free parameters to the model as the ratio between the heat capacity of a layer and the conduction between layers is a physical property.

As I mentioned to Lucia, I am used to solving these kinds of equation with a signal generator and a scope. My ability to do it with pencil and paper is rather limited.