Given the way the components of the surface temperature record extracted from the SSA (singular spectrum analysis) line up with various potential causes of climate change in the previous post here, the temptation is to latch onto series 2, and say, aha, there is the forcing due to increase in CO2. It’s the right shape, exponential. Its the right size, about 0.6C.

But looking into fractal data is like seeing pictures in clouds. Be suspicious of magic methods that pull explanations out of the air. Below I have plotted SSA decompositions of the the monthly global temperature anomaly from the HadCRU dataset from 1976 to the present, the period of most recent rise, and attributed largely to GHGs. Kind of zooming in.

The similarities to the previous post are there in the initial series, although the year ranges are different. The thing I noticed was the first two series, the main ones, have very noticeable downturns at the end. Clearly, neither of series 1 or 2 could represent a signal due to steadily increasing GHG’s, with a hook in the end like that. Perhaps the downturn in the last few years is significant, and the exponential seen in the previous decomposition from 1900 on is due to something else, or nothing, an endogeneous trendiness!

I think I need to lie down. I need to understand a lot more about the limitations of SSA before jumping to conclusions. Can SSA reliably recover exponential signals anyway? Here is were you need to start running SSA on simulated data.

For reference I plotted the first series (red line) in the figure above onto the actual temperature data (black line). The hook down really only starts in the last few years.

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I’d love to see a longer series of this 67 & 9 look like a beat signal happening that does not relate to series 1 & 2.

For some reason I can’t unpack the mac version of ssa so I might have to get and compile from the source.

Yes, I downloaded, hand compiled, then moved the shared library to get it working. No biggie but be aware. Its good otherwise.

I'd love to see a longer series of this 67 & 9 look like a beat signal happening that does not relate to series 1 & 2. For some reason I can't unpack the mac version of ssa so I might have to get and compile from the source.

Yes, I downloaded, hand compiled, then moved the shared library to get it working. No biggie but be aware. Its good otherwise.

David,

I suspect the downturn at the end is an artefact. Any spectral analysis assumes you have an infinite data set. It just pads outside your range of data with zero values. So it fits as if from 2009 onwards, the anomaly is zero, Since by choice of base period, it was positive before that, this represents artificial cooling.

A test is to repeat the analysis subtracting 1 from all your Hadcrut anomalies. I suspect the downturn will become an upturn.

Nah, these things are invariant to constant shifts and scaling. The result with -1 subtracted is here.

Yes, indeed it looks the same. However, the technique uses autocorrelation matrices and has to make some assumption about values beyond, which gives some sort of end effect.

I think the major assumption is that the series is stationary. Then a trend is approximated by the sum of two periodic curves (periodicity being stationary as it has a constant mean). Hence the tendency to get the pictures above with a concave and a convex shape. These are artifacts.

The hook at the end shouldn’t be an artifact though. SSA should have factored all the periodic components out. And despite the fact it’s using two periodic curves to fit a general uptrend, the emergence of the hook down is evidence of a real downturn in the non-periodic component. This contradicts the doctrine of AGW, as the only explanation for a downturn in the presence of increasing forcing is ‘offsetting’ by PDO or other endogenous fluctuations.

David,

I hadn’t read your post of 26 June which clarifies it. I see now that you are extending beyond 2009 assuming that the last value continues unchanged, and then you get a downturn. This indeed won’t be affected by adding a constant.

The minimum roughness criterion uses the last value, but adds an uptrend equivalent to that historically observed. Then you don’t get a hook downturn.

That is what I mean by it being an artefact. It just depends on what you assume about the future. Since the last month in the data set was very cool, assuming that will continue unchanged is

assumingrather extreme future coolness, which then shows up as a “realised” downturn. Assuming historic growth, which is more reasonable, changes this. Actually even that is conservative, as projecting historic growth from a cool month still builds artificial coolness into the future and amplifies it back into the present in the fitted curve.Nick the Rahmstorf analysis you refer to has different parameters. The minimum roughness criterion (MRC) made by appending a new slope onto the dataset, and the 11 year embedding period.

Here, the data is not extended, just pure SSA, and the embedding period is L/2 by default. The amount of downturn would vary with the embedding parameter, so it is contingent, but not an artifact.

SSA is like a matrix of principle components that moves along the dataset, so the size of the matrix (embedding period) affects the bendiness of the first component. But it doesnt need an extension of data. That a Mann one-off designed specifically to ensure the continuation of increasing temperatures to the end of the data series (its in the paper).

David,

No, there is an implied extension of L/2 at each end of the range. You need that data to calculate the endpoint autocorrelation matrix that SSA finds the eigenvalues of. MRC makes an explicit extrapolation. As I said above, I imagined that if you don’t supply anything, it will assume it to be zero, and this will be shown up by shifting the reference point (by subtracting 1, say). However, this didn’t happen, so I can only assume SSA pads by extending the last value at each end as a constant.

I would need to study the linear algebra to say anything more intelligent on this topic. I am not saying you are wrong.

David,I suspect the downturn at the end is an artefact. Any spectral analysis assumes you have an infinite data set. It just pads outside your range of data with zero values. So it fits as if from 2009 onwards, the anomaly is zero, Since by choice of base period, it was positive before that, this represents artificial cooling.A test is to repeat the analysis subtracting 1 from all your Hadcrut anomalies. I suspect the downturn will become an upturn.

Nah, these things are invariant to constant shifts and scaling. Here is the result with -1 subtracted. <img src=”http://landshape.org/enm/wp-content/uploads/2009/06/t1a-300×192.png” alt=”t1a” title=”t1a” width=”300″ height=”192″ />

Have done some runs on simulated data with an exponential trend + noise. Seems like it will only reliably return the single exponential trend in series 1 with a relatively small proportion of noise. Otherwise it returns the exponential trend as the doublet pictured.

Have done some runs on simulated data with an exponential trend + noise. Seems like it will only reliably return the single exponential trend in series 1 with a relatively small proportion of noise. Otherwise it returns the exponential trend as the doublet pictured.

Yes, indeed it looks the same. However, the technique uses autocorrelation matrices and has to make some assumption about values beyond, which gives some sort of end effect.

I think the major assumption is that the series is stationary. Then a trend is approximated by the sum of two periodic curves (periodicity being stationary as it has a constant mean). Hence the tendency to get the pictures above with a concave and a convex shape. These are artifacts. The hook at the end shouldn't be an artifact though. SSA should have factored all the periodic components out. And despite the fact it's using two periodic curves to fit a general uptrend, the emergence of the hook down is evidence of a real downturn in the non-periodic component. This contradicts the doctrine of AGW, as the only explanation for a downturn in the presence of increasing forcing is 'offsetting' by PDO or other endogenous fluctuations.

David,I hadn't read your post of 26 June which clarifies it. I see now that you are extending beyond 2009 assuming that the last value continues unchanged, and then you get a downturn. This indeed won't be affected by adding a constant. The minimum roughness criterion uses the last value, but adds an uptrend equivalent to that historically observed. Then you don't get a hook downturn.That is what I mean by it being an artefact. It just depends on what you assume about the future. Since the last month in the data set was very cool, assuming that will continue unchanged is

assumingrather extreme future coolness, which then shows up as a “realised” downturn. Assuming historic growth, which is more reasonable, changes this. Actually even that is conservative, as projecting historic growth from a cool month still builds artificial coolness into the future and amplifies it back into the present in the fitted curve.Nick the Rahmstorf analysis you refer to has different parameters. The minimum roughness criterion (MRC) made by appending a new slope onto the dataset, and the 11 year embedding period. Here, the data is not extended, just pure SSA, and the embedding period is L/2 by default. The amount of downturn would vary with the embedding parameter, so it is contingent, but not an artifact. SSA is like a matrix of principle components that moves along the dataset, so the size of the matrix (embedding period) affects the bendiness of the first component. But it doesnt need an extension of data. That a Mann one-off designed specifically to ensure the continuation of increasing temperatures to the end of the data series (its in the paper).

David,No, there is an implied extension of L/2 at each end of the range. You need that data to calculate the endpoint autocorrelation matrix that SSA finds the eigenvalues of. MRC makes an explicit extrapolation. As I said above, I imagined that if you don't supply anything, it will assume it to be zero, and this will be shown up by shifting the reference point (by subtracting 1, say). However, this didn't happen, so I can only assume SSA pads by extending the last value at each end as a constant.

I would need to study the linear algebra to say anything more intelligent on this topic. I am not saying you are wrong.

David, I think it is a fun little result and a cool statistical tool but:

“But looking into fractal data is like seeing pictures in clouds. Be suspicious of magic methods that pull explanations out of the air.”

Is indeed good advice. I suspect most of it is just interesting looking nonsense-in scientific terms, noise

David, I think it is a fun little result and a cool statistical tool but:”But looking into fractal data is like seeing pictures in clouds. Be suspicious of magic methods that pull explanations out of the air.”Is indeed good advice. I suspect most of it is just interesting looking nonsense-in scientific terms, noise

I would need to study the linear algebra to say anything more intelligent on this topic. I am not saying you are wrong.

David, I think it is a fun little result and a cool statistical tool but:”But looking into fractal data is like seeing pictures in clouds. Be suspicious of magic methods that pull explanations out of the air.”Is indeed good advice. I suspect most of it is just interesting looking nonsense-in scientific terms, noise

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