Are secular correlations between sunspots, geomagnetic activity, and global temperature significant?

New paper by Love et al suggests no prominent role for solar‐terrestrial interaction in global climate change. I’m providing it here for discussion.

We are not convinced that the combination of sunspot‐number,

geomagnetic‐activity, and global‐temperature data can, with

a purely phenomenological correlational analysis, be used to

identify an anthropogenic affect on climate.

Abstract

Recent studies have led to speculation that solar‐terrestrial interaction, measured by sunspot number and geomagnetic activity, has played an important role in global temperature change over the past century or so. We treat this possibility as an hypothesis for testing. We examine the statistical significance of cross‐correlations between sunspot number, geomagnetic activity, and global surface temperature for the years 1868–2008, solar cycles 11–23. The data contain substantial autocorrelation and non-stationarity, properties that are incompatible with standard measures of cross-correlational significance, but which can be largely removed by averaging over solar cycles and first‐difference detrending. Treated data show an expected statistically significant correlation between sunspot number and geomagnetic activity, Pearson ρ < 10^−4, but correlations between global temperature and sunspot number (geomagnetic activity) are not significant, ρ = 0.9954, (ρ = 0.8171). In other words, straightforward analysis does not support widely‐cited suggestions that these data record a prominent role for solar‐terrestrial interaction in global climate change.

With respect to the sunspot‐number, geomagnetic‐activity, and global‐temperature data, three alternative hypotheses remain difficult to reject: (1) the role of solar‐terrestrial interaction in recent climate change is contained wholly in long‐term trends and not in any shorter‐term secular variation, or, (2) an anthropogenic signal is hiding correlation between solar‐terrestrial variables and global temperature, or, (3) the null hypothesis, recent climate change has not been influenced by solar‐terrestrial interaction.

Citation: Love, J. J., K. Mursula, V. C. Tsai, and D. M. Perkins (2011), Are secular correlations between sunspots, geomagnetic activity, and global temperature significant?, Geophys. Res. Lett., 38, L21703, doi:10.1029/2011GL049380.

Conclusions

One of the merits of using three separate data sets in a correlational analysis is that intercomparisons can be made. After treatment for removal of autocorrelation and nonstationarity through simple averaging and differencing, we find statistically‐significant secular correlation between sunspot number and geomagnetic activity. This is expected,

and it serves as important support for our analysis method. On the other hand, after making the same treatment to the global surface temperature, correlations between temperature and either sunspot number or geomagnetic activity are not significant.

We have not, in this study, considered derived proxy metrics of relevance to climate change, such as reconstructed total‐solar irradiance [e.g., Fröhlich and Lean, 2004] or

interplanetary magnetic field [e.g., Lockwood et al., 1999]. Still, we believe that our methods are general, that they could be used for other data sets, even though our analysis, here, is tightly focused on specific data sets. [15] From analysis of sunspot‐number, geomagneticactivity, and global‐temperature data, three hypotheses remain difficult to reject; we list them.

(1) The role of solarterrestrial interaction in recent climate change is wholly contained in the long‐term trends we removed in order to reduce autocorrelation and nonstationarity. This possibility seems artificial, but we acknowledge that our method requires a nontrivial time‐dependence in the data that is different from a simple trend. Still needed is a method for measuring the significance of correlation between data sets with trends.

(2) An anthropogenic signal is hiding correlation between solar‐terrestrial variables and global temperature. A phenomenological correlational analysis, such as that used here, is not effective for testing hypotheses when the data record a superposition of different signals. Physics is required to separate their sum.

(3) Recent climate change has not been influenced by solar‐terrestrial interaction. If this null hypothesis is to be confidently rejected, it will require data and/or methods that are different from those used here.

Paper: http://www.leif.org/EOS/2011GL049380.pdf

h/t to Dr. Leif Svalgaard

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November 16, 2011 7:18 am

Geoff Sharp says:
November 16, 2011 at 6:43 am
not make such grand statements that look to support the AGW crowd..
Since when should science be directed such as not to support any particular view? Your comment shows your bias and agenda. These have no place in science, neither pro nor con.

Dave Springer
November 16, 2011 7:25 am

Leif Svalgaard says:
November 16, 2011 at 6:52 am
“There most likely was no Modern Maximum ”
“Most likely”? Spare me the weasel words.

November 16, 2011 7:27 am

Geoff Sharp says:
November 16, 2011 at 6:43 am
not make such grand statements that look to support the AGW crowd..
Since when should science be directed such as not to support any particular view? Your comment shows your bias and agenda. They have no place in science, neither pro nor con.

Mikel Mariñelarena
November 16, 2011 7:30 am

Hi Leif,
Congratulations for your patience and willingness to engage in debate with scholars and laymen alike.
The other day I was speaking to an astronomer about the recent flatness in global temperatures and she thought that the cause may be the sun’s decreased activity (I don’t think she’s particularly interested in climate issues but the sun still seems to be an important climate driver in her community). Also I often debate with people in blogs who are totally unaware of the recent trend among solar specialists that you keep warning us about that diminish the TSI variations in past decades and centuries. They stick to data such as that presented by Solanski.
I’d like to ask a little favor please. Can you give me some credible reference on the current status of the TSI reconstruction debate that I can point people to?
Thanks,
Mikel

Dave Springer
November 16, 2011 7:36 am

http://scholar.google.com/scholar?hl=&sourceid=navclient-ff&rlz=1B3GGHP_en___US455&ie=UTF-8&q=%22modern+maximum%22+solar
The only one questioning the modern maximum appears to be Leif and his questioning evidently hasn’t risen above the bar of passing peer review.
Naturally he must attempt to discredit the observations. This is typical of those who find their pet computer models to be more compelling than reality thus when reality disagrees with the model then there must be something wrong with the observations of the real world because the fantasy world just can’t be incorrect.
Pfffffffffffffffffffft!!!!!!!!!!!!!!!!11111
FAIL

Yarmy
November 16, 2011 7:50 am

Some here are quick to dismiss this paper presumably because they don’t much like their own pet solar-climate theories being challenged. (A tad hypocritical, no?)
But there’s much of interest in the paper. For example, I’ve heard it said that in recent years the correlation between Temp and SSN has broken and that this is evidence of an anthropogenic signal. The authors, however, state that this conclusion cannot be drawn (see section 7 of the paper), mainly because the correlation wasn’t much cop before then!

November 16, 2011 8:14 am

Dave Springer says:
November 16, 2011 at 7:36 am
The only one questioning the modern maximum appears to be Leif and his questioning evidently hasn’t risen above the bar of passing peer review.
The normal procedure is the talk about research at conferences and seminars to get a feeling for how solid a finding is. If the feedback is positive one then proceeds with a formal paper for the record. My research on this has now reached such a point. If you want to get a preview, consult the references I gave you. And perhaps this one too: http://ssnworkshop.wikia.com/wiki/Home
Mikel Mariñelarena says:
November 16, 2011 at 7:30 am
Can you give me some credible reference on the current status of the TSI reconstruction debate that I can point people to?
A good one is this by Schrijver et al. http://www.leif.org/EOS/2011GL046658.pdf

G. Karst
November 16, 2011 8:55 am

Dr. Lurtz says:
November 16, 2011 at 6:43 am
But most important, the Earth is the center of the Universe!!

I have seen this line popping up in various places. Other than the fact that the universe appears to extend 15 billion light years to all sides, has there been new science which indicates more? If I am I behind the 8 ball on this, a reference would be nice? GK

Stephen Rasey
November 16, 2011 9:36 am

Leif 11/15 10:57am
Differencing is an effective method of removing trend from a time series.
Yes it does. Differencing is a High-Pass, Low-Cut Filter. It preserves high frequency (short period) and attenuates (to disregard and discard) low frequency (long period) signal.
This provides a clearer view of the true underlying behavior of the series.
Is that your view? It is clearly false if the true underlying behavior includes low frequency processes that slowly vary over long-periods, like climate or solar signals.
Differencing is a kin to listening to music with the treble maxed the mid range off and the woofer unplugged. Discard the baseline, smother the melody and bring out the hiss of the recording.

It is also possible to filter a series such that the low-frequency variations are reduced and the high-frequency variations unaffected. This type of filter is called a high-pass filter. Detrending is a form of high-pass filtering: the fitted trend line tracks the lowest frequencies, and the residuals from the trend line have had those low frequencies removed. – David M. Meko

Good reference: Dr. Meko has an excellent set of notes on line for his class:
GEOS 585A, Applied Time Series Analysis, with a main page at http://www.ltrr.arizona.edu/~dmeko/geos585a.html

2CentsWorth
November 16, 2011 9:46 am

Leif Svalgaard says:
November 16, 2011 at 8:14 am
Dave Springer says:
November 16, 2011 at 7:36 am
The only one questioning the modern maximum appears to be Leif and his questioning evidently hasn’t risen above the bar of passing peer review.
The normal procedure is the talk about research at conferences and seminars to get a feeling for how solid a finding is.
——–
Leif Svalgaard says:
November 16, 2011 at 7:18 am
Your comment shows your bias and agenda. These have no place in science, neither pro nor con.
——–
Pardon me, but… Something is now to be considered a “scientific fact” because someone got “a feeling for how solid” their own preferred personal point-of-view is during casual conversations at a conference??… LOL!… One wonders if it’s occured to Dr. Svalgaard that his comment at 7:18 am above, attempting to dismissivly wave-away others’ positions out-of-hand, would seem to apply just as equally to his own subsequent position as expressed by him at 8:14 am. 🙂

November 16, 2011 9:50 am

If Dr. Love (of Geomagnetism Program, USGS, Denver, Colorado, USA) would like to get in touch, I shall clearly demonstrate to him that there is a direct relationship between temperature and the heliospheric magnetic field. The extent of the temperature variation is about 2 degree C between the solar max and solar min (for this specific case – not the global temperature), as shown here:
http://www.vukcevic.talktalk.net/HMF-T.htm
Notice that both the peaks and troughs of the temperature follow the peaks and troughs of the HMF rather than those of the corresponding solar cycles.
There is some interference from the oceans. If anyone is interested in the two discontinuities, look up my recent article : http://www.vukcevic.talktalk.net/theAMO.htm you will find explanation on pages 10 &11.
Article with all details will be on line in a week or two.
Dave Springer says:
November 16, 2011 at 6:37 am
There is more to it than it is obvious to a casual observer:
http://www.vukcevic.talktalk.net/NFC1.htm

November 16, 2011 10:09 am

Stephen Rasey says:
November 16, 2011 at 9:36 am
“This provides a clearer view of the true underlying behavior of the series.”
Is that your view? It is clearly false if the true underlying behavior includes low frequency processes that slowly vary over long-periods, like climate or solar signals.

That was the view of the authors of the paper in question, and they note: “[15] From analysis of sunspot‐number, geomagnetic‐activity, and global‐temperature data, three hypotheses remain difficult to reject; we list them. (1) The role of solar‐terrestrial interaction in recent climate change is wholly contained in the long‐term trends we removed in order to reduce autocorrelation and nonstationarity.”
2CentsWorth says:
November 16, 2011 at 9:46 am
Pardon me, but… Something is now to be considered a “scientific fact” because someone got “a feeling for how solid” their own preferred personal point-of-view is during casual conversations at a conference??
Not casual conversations, but formal presentations and subsequent peer-review before inclusion in the conference proceedings, e.g. http://www.leif.org/research/SOHO23.pdf and http://www.leif.org/research/IAUS286-Mendoza-Svalgaard.pdf (under review)
The preliminary conclusion is considered so important that the National Solar Observatory (NSO), the Royal Observatory of Belgium (ROB), and the Air Force Research Laboratory (AFRL) are sponsoring a series of workshops [with participation of all stakeholders, such as SIDC, NOAA, NASA, etc] on this problem in order to provided the community with a vetted and agreed-upon new series of sunspot numbers. See http://ssnworkshop.wikia.com/wiki/Home
So, this has moved past my ‘personal point of view’. We realize it may take another decade or more to reduce reactions like yours to a suitably low level of just noise.

November 16, 2011 10:16 am

M.A.Vukcevic says:
November 16, 2011 at 9:50 am
Notice that both the peaks and troughs of the temperature follow the peaks and troughs of the HMF rather than those of the corresponding solar cycles.
The HMF follows closely the corresponding solar cycles. http://www.leif.org/research/Heliospheric%20Magnetic%20Field%201835-2010.pdf
http://www.leif.org/research/JASR_9142.pdf [figure 6]

JJThoms
November 16, 2011 10:43 am

Geoff Sharp says: November 16, 2011 at 6:43 am
“Leif Svalgaard says:November 16, 2011 at 5:20 am
There is a small 0.1 degree change related to solar activity.
This statement really doesn’t look good and severely exposes you to questioning. You are very aware of other solar influences that are currently being evaluated that provide a far greater range than the TSI only variant you peddle relentlessly (TSI also being subject to inconsistencies).”
======
TSI (TOTAL solar irradiance = ALL the “wavy energy” from the sun that can be absorbed by the satellite i.e. from 0.001nm to 1 mm wavelength) changes insignificantly to give less than 0.1C variation in the global temp.
http://www.scostep.ucar.edu/archives/scostep11_lectures/Woods.pdf
Are you postulating that there is some other energy that emanates from the sun? Please tell me what it is!
Do you believe that there is a magic effect of very small magnetic variations? (what on earth could this affect to cause a greater change than TSI). Please describe the influence.
Is it clouds? But there is no proof that cosmic rays can affect cloud cover. Why do the satellites not detect the significantly increased short wave radiation from the earth due to increased clouds?
The CLOUD experiment proved that proto CCN were formed but not they grew big enough to create a water droplet. Or do you know different and can therefore point me to an intelligent paper?
Even a massive CME that wipes out power grids, satellites, etc. has miniscule energy compared to TSI and even minisculer when integrated over a year.
Is it water sloshing about in ocean basins = energy==heat.?
Is it deep water overturning due to gravitation?
Then where is the evidence?
Is it wind patterns being nudged by the merest whiff of solar aether? But then this would not give 40 years of increase. No energy is entering the system so temperatures will rise and fall-back to the same level.
You are obviosly convinced that the sun is changing more that what is indicated by TSI. Please tell me what that change is and why it affects temperature

Dave Springer
November 16, 2011 10:52 am

Leif Svalgaard says:
November 16, 2011 at 8:14 am
“The normal procedure is the talk about research at conferences and seminars to get a feeling for how solid a finding is.”
I’ve been to a million of them. Except for the few most interesting presentations which are the main draw for the whole dog & pony show it’s a real snooze fest. Literally a snooze fest because most people are recovering from the free food and booze in the nightly after-parties. You’d pick up a stack of papers for each presentation that might possibly be of interest and plan on looking it over when you got back home. Invariably you never looked at the crap again with the sure knowledge that you’d miss nothing important because the important stuff graduates from the conference circuit. As usual I’ll hold off until your criticism of the inconvenient sunspot data that appears in every introduction to solar physics in the world is embraced by a larger audience. You’re an outlier in no man’s land as far as I’m concerned trying to win hearts and minds on a goofy blog of all places. This isn’t really the place for it unless you’re an amateur and have no other outlet or what you’re peddling is crap that your peers in more professional venues won’t waste their time on. Given you’re not an amateur that leaves a pretty short list of reasons why you’re pushing it on blogs.

Dave Springer
November 16, 2011 11:08 am

M.A.Vukcevic says:
November 16, 2011 at 9:50 am
“There is more to it than it is obvious to a casual observer:
http://www.vukcevic.talktalk.net/NFC1.htm
Indeed. That would be a real rib tickler if the vagaries of the earth’s magnetic field was playing a major role in climate trends. I mean I could scarcely believe my eyes when I looked at a graph of the rate of drift of the north magnetic pole and it struck me it bore more than a passing resemblance to the AMDO. Who’da thunk? I wasn’t looking for that. All I was doing was verifying your claim that NH geomagnetic field varies a lot more than SH and that declination rate of change resembling the AMDO jumped right off the page at me.

George E. Smith;
November 16, 2011 11:23 am

“”””” Leif Svalgaard says:
November 15, 2011 at 8:53 pm
George E. Smith; says:
November 15, 2011 at 8:20 pm
the sun only heats us by 0.1 deg, then I guess I must be wrong about that.
just silly. “””””
NO Dr Svalgaard; NOT silly at all; simply making a point.
It WAS you who said that the sun’s influence on earth climate was less than 0.1 deg C, NOT me.
I’m well aware that during a typical solar sunspot cycle, or half cycle depending on how you want to characterize it, the observed value of the TSI changes by about 0.1% peak to peak. If one simply calculates the change in the mean “black body” Temperature of earth, that should result from a 0.1% change in TSI, the result would be 0.025%. Transposing that to the supposed mean global surface Temperature of 288 K, would yield a 72 mdeg C change in Temperature; which is certainly less than your 0.1 deg C.
Now I am NOT claiming that such a simple calculation gives a correct result of a 0.1% change in TSI; it simply ignores ALL of the possible climate system feedbacks that might accompany a change in TSI; such as a change in cloud cover or a change in atmospheric water vapor, or any other change such as a CO2 change due to an ocean Temperature change..
You have stated many times; and I totally believe your assertion, that nobody has ever detected such a 70 millidegree global Temperature cycle that accompanies the 11 year or 22 year solar cycles; so I have never asserted that changes in TSI materially affect global climate CHANGES.
But I DO assert that the entire earth climate system IS driven, and powered by a nearly constant input of radiant energy from the sun, at a rate of about 1362 Watts per square meter; based on a recently published NASA revised value. Now I don’t really care whether TSI is 1368 or 1366, or 1362, or even my old history book value of 1353 Wm^-2 for the solar power input rate; but it certainly is NOT 342 or thereabouts Wm^-2 as is claimed by Trenberth et all and the whole climate science community.
And yes I do know that the area of a circle is pi R^2 while that of a sphere is 4pi R^2. The point is that energy input to a portion of the earth surface at a rate of 1362 Wm^-2 for a portion of the 24 hour day, WILL NOT produce the same local result, as a continuous 24 hour input of energy at a 342 Wm^-2 rate.
For a start, an input power of 1362 Wm^-2 to an icy surface could melt that ice even if the local air Temperature is less than zero deg C; whereas a power of 342 Wm^-2 will not, so the climatic result is quite different.
Also during the day, land Temperatures in some tropical regions such as equatorial deserts, can be as high as +60 deg C (even +90) and that will result in almost twice the power density of the LWIR emittance from such surfaces during the day; resulting in much greater cooling rates that would result from a constant 342 Wm^-2 and a resultant 288 K or thereabouts surface Temperature.
So my point is that solar TSI DOES drive the earth climate system (entirely); and I have NEVER said or implied, that small changes in TSI are or have caused CHANGES IN EARTH CLIMATE.
Such changes might, just as Svensmark’s cosmic or solar charged particle changes might affect cloud formation (to some extent); but I’ve never asserted that such changes are significant; just interesting; but maybe not observable in the data.
Well I also don’t believe that “the data” properly represents the true picture of such climate variables as the true mean global surface Temperature; the sampling regimen is laughable.
If so-called “climate scientists” actually observed the changes that occur in the ground (ocean) level solar incident power density(or irradiance), that result form changes in the system, such as CO2 abundance, H2O atmospheric content, cloud cover percentage, and geographical distribution, they might actually be able to construct some believable model for the system. But starting from the point that the sun plays no role in earth climate; well that is “just silly”.

November 16, 2011 11:26 am

Dave Springer says:
November 16, 2011 at 10:52 am
Given you’re not an amateur that leaves a pretty short list of reasons why you’re pushing it on blogs.
Giving you a heads-up what you’ll see in a “special Topical Issue of Solar Physics [Journal] for the eventual joint publication of the SSN series and the accompanying historical, procedural, and scientific papers” http://ssnworkshop.wikia.com/wiki/Home
But stick you head in the sand if you must.

George E. Smith;
November 16, 2011 11:44 am

“”””” George E. Smith; says:
November 15, 2011 at 8:02 pm
“”””” dallas says:
November 15, 2011 at 2:23 pm
Robert Brown Said, “It strikes me that there may be an additional source of actual heating that has been neglected so far (as far as I’ve been able to tell) that was once upon a time considered to be a cosmologically important heating process in the early solar system.”
That is interesting. Space does have a temperature and the energy of photons are unique to the temperature to the sourc. “”””” “””””
dallas says:
November 15, 2011 at 8:55 pm
George E. Smith, No actually. The lower temperature reduces the size and intensity of the spectrum.
“”””” Space does have a temperature and the energy of photons are unique to the temperature to the sourc. “””””
“”””” energy of photons “””””
Well from Max Planck’s relation; photon energy = h (Planck’s constant) x (nu (Greek letter for ferquency)), or you can use E = hc/(lambda (another Greek letter for wavelength)).
Neither Planck’s constant (h) nor photon wavelength or frequency is a function ot Temperature (of anything) let alone Temperature of the source (or sourc).
Also photon energy is not synonymous with the spectrum of some (presumably) thermal source of radiant energy.
WORDS HAVE MEANING; specially in science; so use the correct words, and you’ll get the correct meaning.

A. C. Osborn
November 16, 2011 11:49 am

Their conclusion states
(2) An anthropogenic signal is hiding correlation between
solar‐terrestrial variables and global temperature.
What anthropogenic signal??

November 16, 2011 11:59 am

Leif Svalgaard says: November 16, 2011 at 10:16 am
…………..
That’s all right then.
(HMF B sits on a LF on top of a DC, all together about 100% of the amplitude’s pp, the SSN’s troughs LF and DC are negligible compared to the amplitude’s pp (but the SSN’s peaks LF is high) , hence T is more like the HMF B than the SSN).
Any other comments on the AMO/NAO article except erroneous ma correlation.

November 16, 2011 12:19 pm

George E. Smith; says:
November 16, 2011 at 11:23 am
the sun only heats us by 0.1 deg, then I guess I must be wrong about that.
just silly.
NO Dr Svalgaard; NOT silly at all; simply making a point.

YES, silly as you and most people would know that was meant was the effect of the variation of solar output over a cycle.
would yield a 72 mdeg C change in Temperature; which is certainly less than your 0.1 deg C.
My number [as you should also know] was clearly an order of magnitude estimate. To think otherwise is the silly part. It is usual practice to give values with the number of decimals saying something about the uncertainty. If I had believe the number were 100 milliK with only a few milliK uncertainty, then I would have said 0.100K, and not 0.1K
So my point is that solar TSI DOES drive the earth climate system (entirely); and I have NEVER said or implied, that small changes in TSI are or have caused CHANGES IN EARTH CLIMATE.
If TSI drives the climate [entirely], then [I’ll tell you] changes of TSI will also change the climate.
But starting from the point that the sun plays no role in earth climate; well that is “just silly”.
It was clearly meant that the small variations in TSI play a small role [0.1K] in the Earth’s climate. So, your whole missive here is “just silly”. Of the same nature as “yeah, if we turn off the Sun, it would have no effect?”

November 16, 2011 12:31 pm

A. C. Osborn says:
November 16, 2011 at 11:49 am
Their conclusion states
(2) An anthropogenic signal is hiding correlation between
solar‐terrestrial variables and global temperature.
What anthropogenic signal??

They didn’t say that. They said that they cannot reject the hypothesis an anthropogenic signal is hiding correlation between solar‐terrestrial variables and global temperature. So, neither can you if you otherwise accept their analysis.
M.A.Vukcevic says:
November 16, 2011 at 11:59 am
That’s all right then.
(HMF B sits on a LF on top of a DC, all together about 100% of the amplitude’s pp, the SSN’s troughs LF and DC are negligible compared to the amplitude’s pp (but the SSN’s peaks LF is high) , hence T is more like the HMF B than the SSN).

No that is nonsense as the SSN is just an index with no direct physical meaning. If you measure solar activity by a real physical index like F10.7, you’ll find that the solar cycle variation is much like that of B. And T should be measured in Kelvin, so since B varies by a factor of two, T should also [according to your ‘logic’]
Any other comments on the AMO/NAO article
No, as it is not clear what the goal is [and here is not the place].

November 16, 2011 1:33 pm

JJThoms says:
November 16, 2011 at 10:43 am
You are obviosly convinced that the sun is changing more that what is indicated by TSI. Please tell me what that change is and why it affects temperature
You obviously are not aware of the parts of the spectrum that vary by more than 0.1%. Have a read of these links for a beginning to your education.
http://tinyurl.com/2dg9u22/?q=node/128
http://tinyurl.com/2dg9u22/?q=node/189
http://tinyurl.com/2dg9u22/?q=node/224

November 16, 2011 1:53 pm

Geoff Sharp says:
November 16, 2011 at 1:33 pm
You obviously are not aware of the parts of the spectrum that vary by more than 0.1%.
The total energy in these parts is small, so their larger variation does not have much effect. You are advocating judging changes in Bill Gates’s wealth by the variation of the number of coins in his pockets. Learn from this: http://lasp.colorado.edu/sorce/news/2011ScienceMeeting/docs/presentations/6b_Cahalan_Sedona_9-15-2011.pdf
These variations have almost no effect [0.05K].

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