A statistically significant cooling trend in RSS and UAH satellite data

Statistical Significance in Satellite Data

Guest post by Jeff Id of The Air Vent

If you’ve been following along here you probably suspected the difference between UAH and RSS are substantial enough to reach 95% significance. In this short post, you can see you were right. Significance is a measure of likelihood that the short term noise is creating the slope we see. Now since we’re looking at a difference between two series measuring the same thing, a simple reasonable method is to take the difference between the two series and look at the residuals for significance.

Global RSS and UAH temperature anomalies look like this.

UAH full

RSS full

By taking the difference between the two anomalies, the graph below is calculated. You can see that if 95 significance in trend is 0.0104 the trend of 0.027 is almost 3 times outside of what is created by noise in the data. Much of this was created by a well known and still contested step at 1992 which was a particularly difficult satellite transition point.

UAH-RSS full

Now recently UAH and RSS started using different datasets for the first time. RSS continued using the old NOAA style satellites which decay in orbit over time while UAH switched to the AQUA station keeping satellite. The obital decay of NOAA-15 causes the instruments to measure different parts of earth at different times of day, gradually shifting over years. Imagine the difficulty in correcting temperature for all locations on earth based on time of day. You would need to quantify how the land, mountains, oceans, forests and even ice react over a day of heating. Each day being different over a year. RSS solved the problem with computer modeling of each grid square while UAH did it by measurement employing other satellites measuring at different times in the same day. I vastly prefer measurement to modeling in this case but that doesn’t mean RSS is wrong, just that there’s another black box step which is exceptionally difficult to verify.

The new AQUA satellite used in UAH has a station keeping thruster which keeps the measurement time of each gridcell constant for years at a time. The thing I think some miss about this is that the huge massive corrections which must be implemented over a day are suddenly the same correction value from day to day – no change. Therefore errors in corrections no longer create artificial trends. We’ve got our first high accuracy global trend measurement –ever. The record only extends from June 2002 though and RSS is already experiencing a large divergence over that time.

The last figure is UAH minus RSS for June 2002 until present. The data was re-anomalized after subtracting but the trend difference between the correct trend UAH and the old style calculation RSS is just past 95% significance.

UAH-RSS after 2002

RSS is showing too low of a trend over this timeframe. Dr. Christy mentioned that it’s a result of overcorrection for diurnal shift of the old style satellites orbit. Either way the UAH with the better quality trend since 2002 is below.

UAH after 2002UAH negative trend nearly reached 95% significance. So of course we have to look at RSS.

RSS after 2002

RSS is cooling outside of 95% significance for the past 8ish years. That’s the first statistically significant cooling I’ve seen so far. A short check of RSS on an annual basis shows that in 1978 over an 8 year window the trend is significantly negative. This means that by RSS there is a 95% certainty that cooling is occurring outside of weather variation since 2002. Not that it’s that big of a big deal, but cooling is cooling right?

My opinion is that UAH is the superior metric still, remember though I’m just an aeronautical engineer and not an expert. As a side note I’ve got a beauty of a quote in a private email from a specialist saying that nobody outside of Alabama prefers UAH. I wonder if the fickle tides of science will be turning.

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George E. Smith
November 10, 2009 1:21 pm

Jeff,
I’m not sure I have a clear image in my head of what it is you chaps do with this data.
But looking at your very first graph of the UAH from about 1978 to present; which I presume from the start date is about the sum total of the satellite data set (that they have).
The black line appears to be a straight line. Am I to assume that the rms value of the point by point deviations from that one straight line reaches its absolute minimum value for just that slope and vertical location; the only other constraint being that it is a straight line ?
If that is not the case; then just how is that line defined ?
Any particular reason why a straight line is presumed; since many of these plots seem to show clear indications of some cyclic behavior.
What would the Fourier transform frequency spectrum of that data look like ? I’m wondering if it might reveal the presence of periodic components that are of comparable significance to the zero frequency component.

Richard
November 10, 2009 1:36 pm

John Finn (12:39:11) : I haven’t got a hypothesis. I’m just interpreting the data as I see it and I don’t see any evidence that the earth is in a long term cooling phase. Temperatures dipped in response to the 2007/08 La Nina but they now look to be recovering. The next few years will tell us if this represents a return to the previous warming trend or something else.
How could you EVER possibly see evidence of the Earth being in a “long term cooling phase”? You would have to firstly define “long term”. Secondly even if by your definition there was a linear cooling trend over this defined period, you would only be able to “see the evidence” after the period was over and then it would tell you nothing about the next period.
As it happens there is a hypothesis put forward by the alarmists and adopted by the western nations that unstoppably dangerous warming is being caused by anthropogenic CO2. The evidence of the temperature records of the last 7 years, at least, among other evidence, does not seem to support this. But ignoring this and assuming AGW to be gospel we are nonetheless committing to a suicidal battle against this imaginary foe.

November 10, 2009 2:19 pm

George E. Smith (13:21:52) :
I wasn’t sure how to answer the longer comment. The line is an RMS fit which I’m sure you’re familiar with of the equation y = a x + b to the data x.
The straight line is the trend of course as without it there is no definition of trend. Regarding the Fourier spectrum of UAH and RSS I’ve done some work with that from last year. It’s taken a year to figure out why the cyclic variations were occurring in UAH.
http://noconsensus.wordpress.com/2008/10/26/half-year-cyclic-variaition-in-rssuah-and-giss-anomaly/
This linked post above also has implications that UAH may require additional corrections as well.
For those interested, Lucia confirmed the results in the last graph at this link.
http://rankexploits.com/musings/2009/satellite-trends-rss-and-uah/

Gary Hladik
November 10, 2009 2:41 pm

evanmjones (12:48:18) : “Yes, the next few years will tell us a lot.”
Yes, the next few years will tell us what the calculated “average temperature of the earth” was for those few years. 🙂
They’ll also give us the trend(s) for the preceding years.
As for the future…eeeh, not so much.

Evan Jones
Editor
November 10, 2009 3:08 pm

Yes, much. It will tell us about the progression of the negative PDO and possibly other cycles. (Not to mention solar issues.) That is very much indeed. The next few years are critical.

November 10, 2009 4:24 pm

Jeff Id (06:22:04) :
John Finn (03:27:21)
Actually this isn’t about el nino as much as this

You’re right – my original comment was a bit off topic. Sorry.

November 10, 2009 4:53 pm

George E. Smith (11:20:09) : “…I subtract my arbitrary reference form my real Temperature,a nd since my arbitrary zero was considered normal; the difference is considered abnormal; so I call it an abnormality…
The process I have performed when plotted as a time function is somewhat similar to applying the differential calculus. My abnormality is analagous to the derivative of my temperature; arbitrarily scaled to some easily plottable range. I just subtract a fixed offset, rather than a variable one.”
What you have is NOT analogous to the derivative or anything even remotely close to it. Sorry. Back to Calculus I.

Jeff Alberts
November 10, 2009 6:38 pm

Like those claiming warming in a short period, this is much ado about nothing.

Brian Dodge
November 10, 2009 8:29 pm

I downloaded the UAH and RSS data from woodfortrees so that I could plot the difference on the same graph as the 2 datasets, and I noticed that the difference seemed to have an annual periodicity starting around 2000, By simply subtracting a scaled and phased annual sinusoid from the RSS-UAH difference signal, I was able to reduce the Standard deviation from 6.7e-2 to 5.0e-2, or a 25% reduction in the apparent annual fluctuation. I went back to woodfortrees and plotted the fourier transforms of the RSS, UAH, and, to generate a reference annual signal, the Fourier transform of the arctic ice extent. see http://www.woodfortrees.org/plot/rss/from:1990/mean:2/fourier/magnitude/window/from:2/to:40/plot/uah/from:1990/mean:2/fourier/magnitude/window/from:2/to:40/plot/nsidc-seaice-n/from:1990/scale:0.01/offset:-0.1/fourier/magnitude/window/from:2/to:40
It is apparent that the UAH data has more signal than RSS coincident with the peak at 20 of the ice extent, which has a large annual signal. Could the decline in arctic sea ice and exposed ocean in the arctic be affecting the UAH signal, either directly or through changes in water vapor over the newly exposed ocean? Any other thoughts on what could be causing this annual signal to appear in the UAH data?

November 11, 2009 8:03 am

Brian Dodge (20:29:34) :
Nice work by the way. The ice does affect the sensors, the satellites don’t measure the poles but UAH does some infilling. You can see the actual data area though in this video of RSS and UAH
http://noconsensus.wordpress.com/2009/11/03/rss-and-uah-videos/
The reason for the annual signal is the errors in diurnal correction which were also present in UAH before the UAH 2002 change to AQUA. This is why UAH is likely to also require a correction – it’s a more subtle point though and I haven’t heard that from Dr. Christy — yet.
This post should answer some of your questions.
http://noconsensus.wordpress.com/2009/10/26/bias-in-satellite-temperature-metrics/

November 11, 2009 8:48 am

Brian: Interesting idea.. but I should just point out that “window” is supposed to be used in time space, before “fourier”, to remove edge effects when looking at frequency spectra. The effect of using it after, in frequency space, will be to reduce the peaks at the left and right edges.
Also, I’m not quite sure why you’re doing a “mean:2” on the temperature signal first.
Here’s your graph with this tidied up a bit:
http://www.woodfortrees.org/plot/rss/from:1990/window/fourier/magnitude/from:2/to:40/plot/uah/from:1990/window/fourier/magnitude/from:2/to:40/plot/nsidc-seaice-n/from:1990/scale:0.01/offset:-0.1/window/fourier/magnitude/from:2/to:40
I’m afraid in this case the two harmonic 20 (approx 1 year) peaks look rather more similar… Sorry!
Best wishes
Paul

Roger Knights
November 11, 2009 10:26 am

” Jeff Alberts (18:38:55) :
Like those claiming warming in a short period, this is much ado about nothing.

It’s significant because it casts doubt on the CAWG hypothesis, which strongly links increases in CO2 to increases in temperature, and on the robustness of the IPCC’s predictions. The disconnect that is being observed becomes more and more awkward for the CAWGers with each passing year, so our side is right to harp on it.

Brian Dodge
November 11, 2009 4:03 pm

I was averaging the signal to reduce the high frequency bias that I introduced by misusing the “window” function.
If one starts the dataset from 2002 when the UAH was changed to the Aqua satellite, (and doesn’t screw up the “window” function &;>), the difference in energy at the yearly harmonic(~7.5) between RSS & UAH is even more pronounced. I wonder if the peaks at 5 and ~16 that both RSS and UAH see are shared processing artifacts or represent real periodic temperature variations?
to save y’all from some typing, the URL is
http://www.woodfortrees.org/plot/rss/from:2002/window/fourier/magnitude/from:2/to:40/plot/uah/from:2002/window/fourier/magnitude/from:2/to:40/plot/nsidc-seaice-n/from:2002/scale:0.01/window/fourier/magnitude/from:2/to:40

November 12, 2009 6:13 am

I suspect the peak at 15-16 is a harmonic of 7.5 produced by ‘ringing’; not sure about the one at 4-5 (18 months-2 years) though.
Here’s the raw(-ish) data you’re analysing:
http://www.woodfortrees.org/plot/uah/mean:6/from:2002/plot/rss/mean:6/from:2002
It looks to me like there’s actually quite a strong 18-month-ish signal here, in both series, which I don’t have any explanation for – but it’s a short sample, and it could just be weather noise! But note it also exists in HADCRUT:
http://www.woodfortrees.org/plot/uah/mean:6/from:2002/plot/rss/mean:6/from:2002/plot/hadcrut3vgl/mean:6/from:2002
so whatever it is, it isn’t satellite-specific!