Annual Heating Signal from Solar Input
Posted by Jeff Id on October 25, 2008
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?