I found something quite interesting about Tamino Foster’s latest post. He did a Fourier analysis of measured temp data. He started with a difference in measurements between RSS and UAH, — Interesting coincidence that he just now started looking at the “difference” between measurement types this week. Odd considering that my posts last week weren’t worth reading and belonged in the dump. Anyway he found something quite interesting. A regular one year signal hidden in the temp data.
Here is the original data.
Here is the difference between UAH and RSS data. These two show the significance to the highest degree, I copied the graph from his post but I did verify it.
Note the sinusodial up-down pattern imprinted on the years from 1998 on.
Seeing this trend he did an FFT analysis,
Ok, for those who aren’t familiar, FFT means fast Fourier transform. It is an operation which stems from the fact that any signal (graph) can be replicated by adding together an infinite number of sine waves. A Fourier transform is a method for finding the component sine waves which make up a signal. A fast Fourier transform is an expedient method for computers to find these component functions.
In practice, if you have a graph with a repeated pattern you can identify the main frequencies comprising the pattern. I wrote my own Fourier transform algorithm back in college in the days before R existed.
In the graph above the huge spike at 1 year intervals is quite dominant. I also verified this graph. The spike is quite real. Grant Tamino then made this plot of individual temp trends not the subtracted data.
Most of the one year variation exists in the UAH (blue) trend it turned out. My FFT’s came out a bit different but I think close enough to verify his result.
My graphs are quite a bit chunkier but still accurate. The R FFT function didn’t have any option for sub-measurement frequency accuracy that I could find.
From all of these graphs of temp FFT rather than temp difference FFT, the one thing I notice is a strong half year trend. Clearly there is a strong signal present in all 3 datasets at 0.5 years. Because we have so many points of data we can do another analysis. We can find the phase of the temp. If temps are annually varying when do they peak?
This next graph requires a bit of explanation.
I took a one year period sinusoid and did a correlation analysis to the three datasets from 2003-2008, I then phase shifted the sine wave (started the peak a bit later) and checked the correlation again. 100 correlations later I had the graph above. The higher the correlation, the better the match to temperature data. On the x axis is months. Jan is 0-1 months. I used R to locate the max of each correlation.
RSS = 0.96 months after Jan 1
Giss 1.32 months after Jan 1
UAH 0.6 months after Jan 1
Now how is that for an interesting result. For all three temp metrics I got a peak time for the one year trend between 0.6 and 1.32 months after the first of the year. Well you know the first thing I looked up, when is the earth the closest to the sun. Jan 3 is the number I found with a quick search. You would expect annual temps to be higher when we get closer to the sun. You would also expect them to lag behind the closest point. I want to spend more time verifying this but it might have an interesting meaning beyond closer to the sun means hotter.
These are the graphs over a longer term set of temps from 2000-present. Again they agree pretty closely.
RSS = 0.48 months after Jan 1
GISS 0.12 months after Jan 1
UAH 0.36 months after Jan 1
I couldn’t be this lucky. Well, I really don’t know the history of temp measurement well enough but even the unreasonable GISS corrections can’t hide this trend because it is built into the instruments.
Here’s what I’m thinking.
1-One big question in climatology is the response of the planet to changes in solar output.
2-We seem to have a signal created by our distance from the sun
3-We should be able to calculate the (short term) response of the climate system to net solar input. This would include solar particle as well as other forms of energy.
Hell this probably has already been done as far as I know, but Tamino Foster made it sound like nobody’s noticed this before. If the studies have not been done, we must be careful because the planet has an unknown thermal inertia based on a number of unquantified parameters including feedback from natural cloud systems there are all kinds of pitfalls I can see which would be easy for a scientist with motive to exaggerate. Still, if it hasn’t been done we should be able to make an estimate from actual data rather than models.
I’ll do the half year trend tomorrow.
Does anyone know of an analysis of year trend studies in temp signal? Does anyone know if it has been applied to solar forcing?
the Air Vent 
See comment #132 on Tsonis and Teleconnections Climate Audit by Steve McIntyre on October 20th, 2007 for the cycles. Keep in mind that several anomolies are based on the month … Mar 99,00,01, etc Apr 99,00,02, etc etc. It may be that the does not do this well or some may not do this at all. If they do, perhaps it is a bias. Sometimes finding a bias can be quite revealing.You will need someone who knows the different temperature methodologies in detail.
John,
Thanks for the fast reply, I will look for the link. I have read quite a bit of the different temp methodologies but am no expert. What I see though is that all 3 reveal the same thing. Peak temps shortly after January 1. The magnitude of the peak is I think where the methodologies become nearly incomprehensible.
Note that unless you account for it, using January as an example, the temperature rises in January (average of 1 – 31), then plateaus until end of March. Is it moving, or what?? I am curious also.
Some of the time shift may be due to data averaging. When the data are averaged, it causes a phase shift since the end result isn’t available until all of the samples have been taken and averaged. That would line up about perfect with the just less than 1 month shift (since the closest day is the 3rd, if the data are based on monthly average temperatures.
Jeff, you may have something interesting here. Is it possible to email you?
IIRC, the one of the differences between RSS and UAH is how they handle land and SST. This can cause an apparent problem because, the yearly bias of temperature is effected by the difference in the hemisphere land masses. Of course, relative to that will be the handling of the smaller land masses in the southern hemisphere about 6 months later. However, I read somewhere that because of the differences in the land masses of southern versus northern, the lag was different. It should be every six months, if equal, but it is not, since they aren’t. So it could be that what is being discussed is well known to the RSS/UAH people. Since the standard seems to be more of yearly than monthly, I do not think they would see this as a real problem.
James H,
I would expect some lag even if the data was perfect due to the thermal mass of Earth and reaction times of the feedback mechanisms. I still don’t know weather to believe this is caused by the sun because I don’t have the experience with the metrics although I have done a bunch of reading on them.
I copied this post from the thread at Watts Up With That. Lief is a solar physicist and computer programmer from stanford. — Correct me if I’m wrong.
Leif Svalgaard (18:35:16) :
Jeff Id (17:50:08) :
From that post I did some math and found out that when the earth is closest to the sun we get hotter. — Sounds like a kindergarten class but there is a small possibility from my less experienced perspective that this effect has never been quantified.
In January we receive 90 W/m2 more TSI than in July, or 7%. That should translate into a 7%/4 = 1.7% of 300K = 5K temperature difference. Because of the uneven land/sea distribution the effect is a bit smaller, but easily discernible. However, when you deal with temperature anomalies, this seasonal variation should disappear, if you do it correctly, i.e. deal with the two hemispheres separately [computing and subtracting the mean for each month [or day, whatever they use]]. If that is not done, or if the coverage is not the same in both hemispheres, or if there are any other little asymmetries, then you very easily get this kind of annual wave. For instance, the geomagnetic Dst-index [that measures the strength of magnetic storms] suffers from being based on 3 Northern and only 1 Southern station. This introduces an artificial annual cycle, see e.g. page 8 of http://www.leif.org/research/AGU%20Fall%202005%20SA12A-04.pdf
I don’t think [don’t know – more precisely] your effect has been noticed before. Good work.
Another comment
Leif Svalgaard (18:57:40) :
Jeff Id (17:50:08) :
Tamino Foster makes it sound like it’s a revelation.
He may be on to something, for once. I took a look at his posting:
http://tamino.wordpress.com/2008/10/21/rss-and-uah/#more-1145
“The RSS data show about what we’d expect, given the red-noise character of the data. The UAH data show the same, plus a strong response at a period of 1 year”, so the effect depends on the series [a good sign that it is artificial]. There is also the step in 1992. This is, indeed, interesting. Now, it is too early in the game to jump to conclusions [Tamino even had a ‘brain fart’ – his words…].
Here’s a third comment from Leif
Leif Svalgaard (19:17:20) :
Jeff Id (17:50:08) :
From that post I did some math and found out that when the earth is closest to the sun we get hotter.
1-One big question in climatology is the response of the planet to changes in solar output.
2-We seem to have a signal created by our distance from the sun
3-We should be able to calculate the (short term) response of the climate system to net solar input. This would include solar particle as well as other forms of energy.
Unfortunately it won’t work with the data you have. The ’signal’ is an artifact because of incomplete compensation for the seasons and the orbit. To investigate the real ’signal’ you have to work with actual temperatures [and not subtract the average to get the anomaly]. You see, it’s the average that is not determined ‘correctly’ and that bleeds through to the anomalies.
But, the principle is sound. I have often asked the modelers [e.g. Gavin Schmidt] to see if their model could handle the 90 W/m2 and what would be computed differently if you changed the 90 to 0 or to 180, but he never seems to be interested enough to do something about it [too busy?!].
So that left me with a bunch of questions. I made this post which is currently still in moderation.
Lief,
Thanks for the reply, you might be the perfect person to answer my questions about this.
When you say the signal is an artifact of incomplete compensation I wonder how do they make compensation for the seasons. And if the seasonal compensations were done perfectly, wouldn’t that still leave the effects of solar forcing.
I found the same phase angle for all three temp metrics?? GISS, UAH and RSS within a few weeks. Are they all using the same correction techniques?
I see both 1 year and half year variations in the signal. I’m working on half year today.
I am going to copy your comments over to my blog for my visitors to read. If you don’t mind, could you answer the questions there, Anthony has a very interesting post here on a different topic.
#5 you can email me at biounit69@gmail.com
Regarding Lief’s comments, I still haven’t found the temp corrections for annual variation but I wonder if it is a phase angle correction rather than a magnitude correction that is the problem.
It is interesting that in all three metrics the correction is underestimated too.
Jeff Id (06:36:02) :
When you say the signal is an artifact of incomplete compensation I wonder how do they make compensation for the seasons. And if the seasonal compensations were done perfectly, wouldn’t that still leave the effects of solar forcing.
I don’t KNOW how they compensate, but as far as I can tell the compensation is empirical: you just calculate the average temperature for each day of the year [or month?] over a baseline period and subtract the resulting curve from subsequent measurements. This takes care [it is thought] of the seasonal variation of solar forcing [incl. varying distance]. Apparently, there are some problems with that assumption [as per Tamino and you].
Thanks Leif,
I also had done the calc for 5K change in surface temp based on distance in the past, I couldn’t remember the number I got but before. I’m going to have to investigate this further because there must be a way to calculate the effects of albedo and feedback.
If we use the method you suggest in the calculation of temps (averaging over months) and the response of the climate system changes over time to become more sensitive to heat input. i.e. greenhouse gasses or something. The difference in response could also be a direct measurement of the global warming through changes in the climate system (i.e. CO2).
What I’m trying to say is, if we capture a higher percentage of the heat difference from the sun due to greenhouse gasses we will see a stronger annual variation now than we did in the past. The average for anomaly corrections would show a net positive (with some lag) correlation to solar input compared to past data. The difference between before and today should give a direct method for quantifying the effects of solar driving as well as greenhouse gasses. Again, it might have already been done somewhere but I haven’t seen it.
I’m going to look at historic GISS data and see if the effect disappears or inverts in phase.
Giss may not have increased the solar signal in their models for Leif but Hadley did:
Click to access StottEtAl.pdf
and the results were apparently interesting.
Thanks due to the person (I forget who) who pointed this one out to me.
JamesG Says:
October 26, 2008 at 9:19 pm
Giss may not have increased the solar signal in their models for Leif but Hadley did.
The reference starts out with this:
“Reconstructions of solar irradiance are uncertain and based on differing assumptions about how solar observations can be used as proxies for long-term solar irradiance variations. They are supported by observations of the aa geomagnetic activity index (Lockwood et al. 1999) and of the cosmogenic isotopes 10Be and 14C that show an inverse correlation with reconstructions of solar irradiance, as would be expected if increasing solar activity is coupled with increases in the interplanetary magnetic field that shields the earth from cosmic rays. Although a variety of reconstructions employing different assumptions (Lean 2000; Hoyt and Schatten 1993; Solanki and Fligge 2002) all show long-term secular changes in solar irradiance, a recent solar model indicates that solar irradiance might be decoupled from the interplanetary magnetic field and that total solar irradiance might have increased very little since the Maunder minimum (Lean et al. 2002).”
Note that Judith Lean [2002 and 2008] is agreeing with me that TSI hasn’t changed significantly over time. Nevertheless, the model-paper you reference, uses the old Lean [1995] and Hoyt and Schatten [1993] TSI-reconstructions that are simply wrong. Therefore the result is spurious and cannot be trusted. I have asked Gavin to use modern TSI series but to no avail, so far. My colleague Ed Cliver is going into the Lion’s den this November to give a seminar on the modern TSI, sunspot numbers, and interplanetary magnetic field data, and will urge them to use the latest and greatest. We shall see.
Thanks Leif,
I have been running R correlations to find the best fit for 1 year sine waves across the 30 year satellite data and GISS data to find a trend. The giss is the most consistent. All three metrics are consistent since about 2000, I need to nail down the year because something changed.
Anyway, my preliminary analysis shows that without less manipulated data I can’t conclude anything reliably.
I am convinced however that there might be some value in study of the 1 year solar forcing and response in temp data through history. I say that because it nearly eliminates the change in solar output through the comparison of response on a 6 month difference.
It might be possible to look at the differences in response and correlate them to CO2 to calculate warming from direct measurement rather than by the weak models currently being used. I think there are too many hurdles for me to pull it off, but I get excited when I think of how many variables we can eliminate.
If only we could get a good, not-necessarily-very-deep “core” sample from the Moon, most of our questions on the history of the Sun would be easy to answer…