Spencer: Record January warmth is mostly sea

Jordan (14:32:48) :
“No demonstration of how a statistical analysis can provide a test of aliasing in the above aliased sinusoid? No statistical analysis of an aliased series which points us to the required sampling rate then?”
Your sinusoid was purely in the time domain – it has limited relevance the spatial sampling of temporal signals. The Hansen analysis is to look at temporal correlations in the time domain as a function of sample spacing. If there was a problem of aliasing you would see the correlations falling off and then increasing as the spacing was increased. In fact the correlations in temperature anomalies fall off gently, and are the decrease is comparable to the scatter in the data out to about 1000 km. This confirms there is not an aliasing problem.

I think this data should be looked at very closely. How has it been corrected or manipulated. The lesson of the previous few months is, do not take ANYTHING at face value.
My gut feeling is, the anomolously high snow coverage of the northern land areas is biasing the satellite data somehow.

Tom P: “Your sinusoid was purely in the time domain – it has limited relevance the spatial sampling of temporal signals.”
OK, but I did suggest the sinusoid could be in space or in time (just change of units if the oscilloscope). That said, perhaps you’re saying you believe there is a method based on correlation when there are multiple dimensions.
I have my doubts, and here are some reasons…
There is no way to saparate the components of the samples into those labelled “genuine” and those labelled “folded” (aliased). As George Smith correctly says, the central limit theorem does nothing to help get us out of aliasing (statistics are also unable to separate genuine from aliased). I’d be extremely reluctant to rely on any statistical aggregate without assurance that aliasing is out of the question.
Hansen and Lebedeff do not even address the issue of aliasing. It is not the subject of their paper – they don’t mention the sampling theorem or aliasing. The only person who links this paper to the sampling thorem appears to be you Tom.
If Hansen and Lebedeff had addressed the question of aliasing, they ought to have referred to the relevant mathematics and literature, and then explained why a different method was required. They make no attempt to do so.
The the method you appear to be suggesting is completely silent when it comes to suggesting a required sampling rate (time or space). Or any criterion for determining that a required sampling rate has been achieved. Odd that the method would not even come up with an answer.
The Hansen and Lebdeff paper is concerned with gridding the surface, carrying out grid averages and, where there is no data, in-filling using data from distant sources. The correlation calculation is a method seeking to justify the use of data from “neighbouring” sites. There is no theoretical basis to suggest whether a given correlation is acceptable or not:
“The 1200-km limit is the distance at which the average correlation coefficient of temperature variations falls to 0.5 at middle and high
latitudes and 0.33 at low latitudes. Note that the global coverage defined in this way does not reach 50% until about 1900; the northern hemisphere obtains 50% coverage in about 1880 and the southernh emisphere in about 1940. Although the number of stations doubled in about 1950, this increased
the area coverage by only about 10%, because the principal deficiency is ocean areas which remain uncovered even with the greater number of stations. For the same reason, the decrease in the number of stations in the early 1960s, (due to the shift from Smithsonian to Weather Bureau records),
does not decrease the area coverage very much. If the 1200-km limit described above, which is somewhat arbitrary, is reduced to 800 km, the global area coverage by the stations in recent decades is reduced from about 80% to about 65%.”
I could have some sympathy with this analysis – the authors are trying to make the best of a bad lot (past temperature methods that just happen to have been gathered). But that doens’t make it correct.
There is a straightforward answer to all of this Tom: a detailed survey of the global tempertature field and a design specification for sampled data acquisition systems.
We expect no less from the digital control systems in a chocolate factory – this gives you the assurance of consistent quality when you buy a bar of chocolate. Why not the same for climate data?
If the design tells us that past data is of inferior quality, at least we will know whether or not to “buy” those temperature reconstructions.

Bob Tisdale (18:28:53):
It’s the precisely the great intensity of the now-fading South Pacific warm pool (~4K at its peak development in January) that makes me suspect a genesis quite apart from ENSO. It’s certainly far greater than anything seen in the equatorial zone during the same time period. Do you have your own speculations why this is so?
anna v (22:40:13):
You’re quite correct! Aliasing does not make the data series “meaningless,” any more than the individual snapshots in the videos here are devoid of information. It’s just that the information can be highly misleading when strung together in a series. Aliasing can change the entire spectral structure of the underlying analog signal, but only in an analytically prescribed way. With adequately long series the average value and the total variance of a random or chaotic signal are not affected in the general case, as shown by the Parseval Theorem. Only in highly contrived examples–sampling a pure sinusoid at exactly its own frequency, instead of twice that, does it produce quite meaningless results.

Jordan (00:07:52) :
You don’t understand a paper, so you throw it in the bin. I suppose it’s one way to avoid having to consider your own faulty analysis.

Tom P: ” It might not frame the problem in a way you like, but that does not make its analysis any less valid.”
There is an established methodology for helping to deal with the issues of data sampling and discrete signal processing. It acutally does give us theoretically grounded criteria for determining when data is corrupted by inadequate sampling.
The H&L paper fails to discuss why it doens’t use those techniques. It doesn’t even acknowledge that they exist or that aliasing could be an issue. And you want to talk about faulty analysis?
So the paper plunges into a new technique without referring its techniques back to relevant theory and/or literature. Perhaps you could provide the missing references to the mathematical theory which supports your assertions with respect to correlation of the sampled as a mechanism to alert us to aliasing, and to produce criteria for sampling rate. So far you have failed to do so.
If not, then we could all agree that this would be another example of climatology venturing into the realms of inventing new techniques without interacting with the relevant specialist communities (ref Wegman).
Besides Tom, I did not want to get into this debate. All I have said is that there appears to be no evidence of the survey and sampling design study which would have determined the necessary sampling strategy for the global temperature field. Such a study would have become the “handbook” for all attempts to produce these temperature reconstructions.
Sorry Tom, but you are simply defending an unhelpful distraction in a paper which pretty well confirms the issue I rasied. Unless you can deliver a convincing reference to those missing mathematics, I see no further reason to entertain you.

sky: These are good points.
I’m not very familiar with argumens about chaos. I’m more familiar with signal components we might refer to as “noise” or perhaps “error” in statistics.
There may well be an issue with sationarity and ergodicity of the climate. That might cause problems when we assess the frequency spectra with a finite data sample. But surely the same problem would apply to statistical analysis over finite intervals?
It is appealing to say that climate processes are not stationary ergodic processes, and I can see where you are coming from. But surely that means that statistical analysis of the data we have collected over finite sample intervals would have no particular significance?
Returning to the topic of noise – this can be characterised by a frequency spectrum. Red noise is concentrated at the lower frequencies – each has a finite component – we could sample red noise and get an aliased signal. For example zero mean noise could be sampled to produce a bias (offset) due to the coincidence beteen certain frequency components and the sample rate.
I understand a stochastic process as being one with a rendom component, but also with a deterministic element. If we don’t have the latter, then I would struggle to see any scope for making predictions. And if we don’t have the latter, would there not be an issue in trying to give meaning to past observations?
If we were to concluded that climate signals are basically unobservable, there could well be a lack of logic in seeking to explain changes like January 2010.
“The satellite anomlies are much too coherent with the surface record.”
I’m not too sure that this can be used to argue that aliasing does not exist an any one or all of the temperature series. Bear in mind how aliasing can produce plausible signals and statisitcal analysis (which is invalidated by aliasing) could well latch onto those appealing similarities.