Paul L. Vaughan, M.Sc.
Without a good handle on its simple geometry, a seemingly complex time series can appear as a changeling yielding to the pressures of mysterious statistical manipulation.
For example, a fundamentally important seminal observation reported by Le Mouël, Blanter, Shnirman, & Courtillot (2010) revealed the quasistationary 11 year solar cycle in the rate of change of length of day (LOD’), but newcomers taking a preliminary look at daily resolution LOD’ are more likely to fixate on the 18.6 year lunisolar envelope.
Multiscale variance summaries highlight obvious envelopes:
Zooming in, a semi-annual envelope is also evident:
(WIDE GRAPH ABOVE –Click to view elongate graph^1 & then click again to magnify.)
(WIDE GRAPH ABOVE –Click to view elongate graph^2 & then click again to magnify.)
A parsimonious weekly-to-monthly timescale model of daily LOD’, explaining ~93% of the variance (r = 0.965), can be constructed using the following information (with model terms in bold italics):
| Year | Period (days) | Half-Period (days) | Defined by… |
| Tropical | 365.24219 | 182.621095 | equinoxes |
| Lunar Month | Period (days) | Half-Period (days) | Defined by… |
| Tropical | 27.321582 | 13.660791 | equator/equinoxes |
| Nodal or Draconic | 27.212221 | 13.6061105 | ecliptic |
| Anomalistic | 27.55455 | 13.777275 | apogee/perigee |
| Synodic | 29.530589 | 14.7652945 | new/full moon |
(27.321582)*(27.212221) / (27.321582 – 27.212221)
= 6798.410105 days = 18.61343046 years
(6798.410105)*(13.6061105) / (6798.410105 – 13.6061105)
= 13.63339592 days
(27.55455)*(13.660791) / (27.55455 + 13.660791)
= 9.132933018 days
Noteworthy envelopes apparent in the variance structure of LOD’ relate to:
1) lunar nodal cycle (LNC) = 18.6 years
2) lunar apse cycle (LAC) = 8.85 years
3) terrestrial year (1 year)
4) harmonics (e.g. 0.5 years & 4.42 years)
| Beat Period | (years) | Tropical | Nodal | Anomalistic | Synodic |
| 27.321582 | 27.212221 | 27.55455 | 29.530589 | ||
| Tropical | 27.321582 | – | 18.6134 | 8.8475 | 1.0000 |
| Nodal | 27.212221 | 18.6134 | – | 5.9970 | 0.9490 |
| Anomalistic | 27.55455 | 8.8475 | 5.9970 | – | 1.1274 |
| Synodic | 29.530589 | 1.0000 | 0.9490 | 1.1274 | – |
| Beat Period | (years) | Tropical/2 | Nodal/2 | Anomalistic/2 | Synodic/2 |
| 13.660791 | 13.6061105 | 13.777275 | 14.7652945 | ||
| Tropical/2 | 13.660791 | – | 9.3067 | 4.4238 | 0.5000 |
| Nodal/2 | 13.6061105 | 9.3067 | – | 2.9985 | 0.4745 |
| Anomalistic/2 | 13.777275 | 4.4238 | 2.9985 | – | 0.5637 |
| Synodic/2 | 14.7652945 | 0.5000 | 0.4745 | 0.5637 | – |
Beat Period = (A*B) / ( |A-B| )
| | indicates absolute value
The model:
| Relative | Cumulative | ||||
| Term | Period (days) | Amplitude | r^2 | r | Contribution |
| 1 | 13.660791 | 1 | 0.713 | 0.844 | | polarity | |
| 2 | 13.63339592 | 0.41 | 0.824 | 0.908 | LNC |
| 3 | 9.132950896 | 0.30 | 0.881 | 0.939 | LAC alternation |
| 4 | 27.55455 | 0.26 | 0.926 | 0.962 | LAC alternation |
| 5 | 14.7652945 | 0.08 | 0.931 | 0.965 | semi-annual |
(WIDE GRAPH ABOVE – Click to view elongate graph^3 & then click again to magnify.)
eLOD’ = estimated LOD’
The above tables & figures, while certainly nothing new to science, have been summarized here for the benefit of those striving to efficiently develop the foundations necessary to appreciate and build upon the recent seminal work of Le Mouël, Blanter, Shnirman, & Courtillot (2010). From their conclusions:
“The solid Earth behaves as a natural spatial integrator and time filter, which makes it possible to study the evolution of the amplitude of the semi-annual variation in zonal winds over a fifty-year time span. We evidence strong modulation of the amplitude of this lod spectral line by the Schwabe cycle (Figure 1a). This shows that the Sun can (directly or undirectly) influence tropospheric zonal mean-winds over decadal to multi-decadal time scales. Zonal mean-winds constitute an important element of global atmospheric circulation. If the solar cycle can influence zonal mean-winds, then it may affect other features of global climate as well […]”
[Typos: 1) “evidence” should read “observe”. 2) “undirectly” should read “indirectly”.]
Caution
Exclusive &/or excessive focus on the first moment (the mean) should not be at the expense of attention to higher moments (such as the variance), as the following graph should emphasize:
SOI = Southern Oscillation Index (an index of El Nino / La Nina)
[ ] indicates boxcar averaging [applied here to highlight interannual variability]
When studying the preceding graph, it is important to understand that the blue line is the normalized interannual average of the black line. (Take a minute to think about this carefully.)
To reinforce this point, here is another graph of the normalized mean at the semi-annual to annual timescale:
The occurrence of such patterns in the mean despite the maintenance of stationary variance limits suggests a need to carefully consider which equators (geographic, celestial, magnetic, meteorological, etc.) are relevant to the phenomena under study. (See for example Leroux (1993).)
Multimoment multiscale spatiotemporal integration reveals nonrandom harmonic pattern-summary discontinuities, exposing the comedy tragically advocated by deceitful &/or naive theoreticians who are in part constrained by a dominant culture that clings seemingly religiously to maladaptive traditions such as unjustifiable assumptions of randomness, independence, uniformity, linearity, etc. that are routinely misapplied (for example to conveniently render abstract conceptions mathematically tractable).
Bear in mind that for some phenomena, such as ice-jacking freeze/thaw cycles, the properties of the variance play a critically fundamental role in dynamics.
Conclusion
With awareness of key wavelengths and a solid conceptual understanding of the effect of integration across harmonics, we arrive at something truly simple: Earth, Sun, Moon.
Both of the ~11 year waves summarize the semi-annual wave, which summarizes biweekly & monthly LOD’ variations bounded by lunisolar limits.
While the magenta wave is isolated via complex wavelet methods, the sky-blue wave is accessible to any member of the general public with an understanding of this article, 5 minutes to spare, & a spreadsheet.
Acknowledgement
Tim Channon generously shared LOD’ models developed using his synthesizer software. Access to Tim’s models facilitated expeditious cross-checking of lunisolar theory, mainstream literature, & data.
Suggestion
I encourage responsible readers to download & archive daily LOD data. Scientifically-engaged citizens can keep a vigilant watch on potentially-arising future data vandalism.
Data
LOD
International Earth Rotation Service (IERS)
http://www.iers.org/IERS/EN/DataProducts/EarthOrientationData/eop.html
Related Reading
Li, G.-O.; & Zong, H.-F. (2007). 27.3-day and 13.6-day atmospheric tide. Science in China Series D – Earth Sciences 50(9), 1380-1395.
http://www.scichina.com:8080/sciDe/fileup/PDF/07yd1380.pdf
Sidorenkov, N.S. (2007). Long-term changes in the variance of the earth orientation parameters and of the excitation functions.
http://syrte.obspm.fr/journees2005/s3_07_Sidorenkov.pdf
Sidorenkov, N.S. (2005). Physics of the Earth’s rotation instabilities. Astronomical and Astrophysical Transactions 24(5), 425-439.
http://images.astronet.ru/pubd/2008/09/28/0001230882/425-439.pdf
Gross, R.S. (2007). Earth rotation variations – long period. In: Herring, T.A. (ed.), Treatise on Geophysics vol. 11 (Physical Geodesy), Elsevier, Amsterdam, in press, 2007.
http://geodesy.eng.ohio-state.edu/course/refpapers/Gross_Geodesy_LpER07.pdf
http://geodesy.geology.ohio-state.edu/course/refpapers/Gross_Geodesy_LpER07.pdf
Schwing, F.B.; Jiang, J.; & Mendelssohn, R. (2003). Coherency of multi-scale abrupt changes between the NAO, NPI, and PDO. Geophysical Research Letters 30(7), 1406. doi:10.1029/2002GL016535.
Maraun, D.; & Kurths, J. (2005). Epochs of phase coherence between El Nino-Southern Oscillation and Indian monsoon. Geophysical Research Letters 32, L15709. doi10.1029-2005GL023225.
http://www.cru.uea.ac.uk/~douglas/papers/maraun05a.pdf
Leroux, M. (1993). The Mobile Polar High: a new concept explaining present mechanisms of meridional air-mass and energy exchanges and global propagation of palaeoclimatic changes. Global and Planetary Change 7, 69-93.
http://ddata.over-blog.com/xxxyyy/2/32/25/79/Leroux-Global-and-Planetary-Change-1993.pdf
Trenberth, K.E.; Stepaniak, D.P.; & Smith, L. (2005). Interannual variability of patterns of atmospheric mass distribution. Journal of Climate 18, 2812-2825.
http://www.cgd.ucar.edu/cas/Trenberth/trenberth.papers/massEteleconnJC.pdf
Abarca del Rio, R.; Gambis, D.; & Salstein, D.A. (2000). Interannual signals in length of day and atmospheric angular momentum. Annals Geophysicae 18, 347-364.
http://hal-insu.archives-ouvertes.fr/docs/00/32/91/24/PDF/angeo-18-347-2000.pdf
Abarca del Rio, R.; Gambis, D.; Salstein, D.; Nelson, P.; & Dai, A. (2003). Solar activity and earth rotation variability. Journal of Geodynamics 36, 423-443.
http://www.cgd.ucar.edu/cas/adai/papers/Abarca_delRio_etal_JGeodyn03.pdf
Le Mouël, J.-L.; Blanter, E.; Shnirman, M.; & Courtillot, V. (2010). Solar forcing of the semi-annual variation of length-of-day. Geophysical Research Letters 37, L15307. doi:10.1029/2010GL043185.
Vaughan, P.L. (2010). Semi-annual solar-terrestrial power.
Technical Aside
For those interested in exploring LOD’ variance patterns that are not necessarily evident at first glance, another noteworthy envelope is the following:
(13.777275)*(13.63339592) / (13.777275 – 13.63339592)
= 1305.478517 days = 3.574281812 years
This polar-equatorial eclipse cycle is evident in the sequence of diagrams here:
http://eclipse.gsfc.nasa.gov/5MCLE/5MCLE-Figs-10.pdf (1733-2151)
From:
Espenak, F.; & Meeus, J. (2009). Five millennium canon of solar eclipses: -1999 to +3000 (2000 BCE to 3000 CE). NASA Technical Publication TP-2009-214172.
http://eclipse.gsfc.nasa.gov/SEpubs/5MCLE.html
h/t to WUWT commenter “lgl” for initially drawing attention to this pattern some time ago.
Earlier & Future Articles
I wrote the following articles before (a) acquiring access to Le Mouël, Blanter, Shnirman, & Courtillot (2010), (b) coming across Leroux (1993), and (c) re-reading Sidorenkov (2005) with consequently improved awareness:
1) http://wattsupwiththat.com/2010/08/18/solar-terrestrial-coincidence/
2) http://wattsupwiththat.com/2010/09/04/the-north-pacific-solar-cycle-change/
3) http://wattsupwiththat.com/2010/09/11/solar-cycle-length-its-rate-of-change-the-northern-hemisphere/
Related articles could have been written on All India Rainfall Index & other variables, but the audiences’ handle on the solar, lunisolar, & spatiotemporal nature of interannual variations was revealed to be inadequate in comments here:
4) http://wattsupwiththat.com/2010/10/11/atlantic-hurricanes-the-sun/
[Some audience members may benefit from careful consideration of issues raised by Tomas Milanovic at Dr. Judith Curry’s blog Climate Etc.]
Le Mouël, Blanter, Shnirman, & Courtillot’s (2010) game changing observation rendered earlier results much less mysterious:
For capable individuals striving to render these & related findings disgestible by a mainstream audience, I strongly recommend:
A) gleaning the primary point made by Schwing, Jiang, & Mendelssohn (2003) about the effect of windowing parameters on apparent phase, which can be reversed by spatial patterns, not just temporal evolution.
B) heeding the advice of Maraun & Kurths (2005) about “periods of coupling which are invisible to linear methods.”
Future posts in this series (if it continues) may draw attention to:
a) nonrandom relations between interannual terrestrial oscillations and interannual [not to be confused with decadal] rates of change of solar variables.
b) the guaranteed potential for naive investigators to be irrecoverably derailed by Simpson’s Paradox due to stubborn &/or blind adherence to seriously misguided conventional mainstream statistical inference paradigms & malpractices that rigidly & dogmatically insist on falsely assuming independence when none exists.
c) the [counterintuitive &/or paradoxical for some] influence of grain & extent – & aggregation criteria more generally – on summaries of spatiotemporal pattern.
“Grain” & “extent“?…
Grain is another term for spatiotemporal resolution. Important: Extent is a term which concisely encompasses the properties of spatiotemporal summary windows. The vast majority of mainstream researchers are either absolutely ignorant or insufficiently cognizant of the effect of extent on integrals across spatiotemporal harmonics (including the nonstationary variety). The consequences are serious: blindness and rejection of valid findings on nonsensical grounds.
Best Regards to All.
George says:
No. Simply that the earth is approximately a shere rotating on its axis.
The ice is predominately located towards the poles, or at higher latitudes. When it melts it distributes roughly uniformly across the surface of the globe and contributes about the same sea-level rise everywhere (its actually an oblate spheroid with a bulge around the equator which would seem to improve my argument).
The ice that was at higher latitudes contributes less angular momentum than the water that is now at lower latitudes. I guess it will depend on where the ice was. If it was all at 30 degrees on either side it would seem to be a wash, but most of it seems to be further away than 30 degrees. Of course ice melting on Kilimanjaro will be different and will lead to a shortening of the LOD, I imagine.
However, if the discussion was predominately about ice at lower latitudes melting, then I am wrong.
The LOD varies during the year as the earth speeds up and slows down in its orbit round the Sun but its rotation period is not affected by its solar orbit.I think that graphs are showing the apparent LOD during the year not just the actual rotation of the Earth.
Let’s just start with the basics.
Where is the ftp with the code and data.
Same question we asked Jones.
Until then you have an advertisement for science, not the science itself.
And no, verbal descriptions of algorithms will not be enough. Hansen used that
excuse.
I always knew the global economy was run by Lunatics! Every 9 years (approx) there is a collapse in the world’s domestic land markets (corresponding to the Lunar Apse Cycle = 8.85 years) and every 18 years there is a huge collapse into economic depression as the commercial, agricultural and (again) domestic land markets die more or less together (which corresponds to the Lunar Nodal Cycle= 18.6 years).
In 1801, Herschel announced he had spotted a correlation between sunspots and wheat prices. Now we have a correlation between economic cycles and rates of change in Length of Day Lunar cycles (sunspots involved too!—gosh, they do get around!)
🙂
It’s all driven by sunspots and the moon!
Leif Svalgaard misleading readers: “irrelevant for the Le Mouel paper”
“Not even wrong” (a category worse than wrong) as you would say Leif. You really do not understand extent (nor do you even seem to make an effort to understand).
“”””” Richard Sharpe says:
April 11, 2011 at 1:45 pm
George says:
Tut tut Richard; I know you are sharper than that. You are contemplating that the melt water unaided, by human hand can actually run uphill to a higher potential energy location.
No. Simply that the earth is approximately a shere rotating on its axis. “””””
Well of course the earth is not a rotating sphere; it is an oblate spheroid, that is flatter at the poles. I’m sure this flattening is largely a direct result of the earth rotating on its axis. If the earth wqas not rotating on its axis at 1000 mph at the equator it would not be oblate it would be more speherical. The earth’s shape is such that on average it is not uphill in any direction. There is no reason for ocean water to run north and south to the poles becaue the altitude there is lower. Gravitationally, the poles are not any lower than the equator, and there is no gravitation reason for water to run from the equator tyo the poles. Well it does on the surface of course; but then it returns towards the bottom depths, so that there is no net flow. The ocean surface at the equator is as far downhill as it can possibly get on the long term averaged earth. So melting of ice on land, or precipitation from the atmosphere can only decrease the moment of inertia, so the rotation speeds up as land ice melts, and runs down to sea level. It doesn’t matter whether it is Antarctic polar ice, or tropical ice from Mt Kilimajaro, it will go down hill locally, and the zero datum is the same everywhere due to the earth not being a rigid body, on geological time scales.
Carla says:
April 11, 2011 at 1:16 pm
The ionosphere is suggested to be directly coupled with the polar vortex and may vary it by strong variations of ionospheric winds. Seems lately we have seen a stalling of regional weather systems moving across the N. Hem, causing an unusually shaped jetstream.
Now your talking about something realistic. This may also have something to do with LOD. There could be a ionosphere/vortex coupling, but what is controlling it is not obvious. There has been wild swings in the AO/AAO over the past 6 months that suggests a seasonal factor or something else controlling the strength of the planetary wave.
Paul Vaughan says:
April 11, 2011 at 4:13 pm
Leif Svalgaard misleading readers: “irrelevant for the Le Mouel paper”
I think most of the readers here cannot be misled. Let the ones who are prone to be misled speak up now.
“Not even wrong” (a category worse than wrong) as you would say Leif. You really do not understand extent (nor do you even seem to make an effort to understand).
The case is one of direct and simple comparison of two heavily smoothed [and for one, fudged] time series. This is straight forward. How the time series are constructed is irrelevant.
Lots of confusion around here. One poster confuses LOD=sunrise to sunset with sidereal LOD, equals one spin of the earth relative to a star. I’m surprised at George Smith, but I will try to enlighten him. When polar ice melts the earth changes shape: mass (ice) which was concentrated at the poles, with a short arm of inertia, is spread evenly around the ocean surface, averaging something like 63 degrees latitude. If the the mantel were totally elastic nothing would happen, but it isn’t. It is part elastic, part plastic, so there is an instantaneous change of shape (more oblate) followed by slow inelastic recovery (back to round, or oblate spheroid). The earth has been speeding up in recent years due to Glacial Isostatic Adjustment from a combination of the Last Glacial Maximum and the Little Ice Age. The GIA due to the LGM is insufficient to counteract tidal deceleration, but rebound from the LIA is apparently adequate to the task. Barring unknown interference from the likes of core/mantle coupling the LOD decrease of the last 40 years indicates that melting has decreased and GIA from the LIA is now winning.
Get that? Melting is decreasing. End of LIA. Insignificanat GW, AGW, CAGW, etc. I’m not the first to make the claim. See the more careful remarks of Walter Munk at http://www.pnas.org/content/99/10/6550.full. –AGF
Thanks to all who have contributed to the discussion.
Best Regards,
Paul Vaughan.
” “Grain” & “extent“?…
Grain is another term for spatiotemporal resolution. Important: Extent is a term which concisely encompasses the properties of spatiotemporal summary windows.”
This confirms my argument against comparing average temperature with solar variabilty. The grain is different. You should be comparing temperature change with solar variability.
solar variability = energy/time
temperature change = temperture/time
average temperature = temperature
Temperature change and solar variability are at the same grain. Average temperature is not. As the author quotes:
“The vast majority of mainstream researchers are either absolutely ignorant or insufficiently cognizant of the effect of extent on integrals across spatiotemporal harmonics (including the nonstationary variety). The consequences are serious: blindness and rejection of valid findings on nonsensical grounds.”
Here here. Climate Science has missed the boat. They have rejected solar variability as a significant climate forcing due to the use of the wrong gain in their analysis. They made this mistake 60 years ago with Milankovitch, they have done it again with CO2.
Does this remind anyone of global temperature sets? And the argument that Global Average temperature is robust because it has been averaged over many samples?
http://www.intuitor.com/statistics/SimpsonsParadox.html
Simpsons’s Paradox – When Big Data Sets Go Bad
It’s a well accepted rule of thumb that the larger the data set, the more reliable the conclusions drawn. Simpson’ paradox, however, slams a hammer down on the rule and the result is a good deal worse than a sore thumb. Unfortunately Simpson’s paradox demonstrates that a great deal of care has to be taken when combining small data sets into a large one. Sometimes conclusions from the large data set are exactly the opposite of conclusion from the smaller sets. Unfortunately, the conclusions from the large set are also usually wrong.
ferd berple says:
April 11, 2011 at 9:16 pm
This confirms my argument against comparing average temperature with solar variabilty. The grain is different. You should be comparing temperature change with solar variability.
solar variability = energy/time
temperature change = temperature/time
average temperature = temperature
No, as wrong as can be. In another thread you said solar variability was in Watt/square meter*times area. This is solar irradiance*area. The irradiance, TSI, is proportional to temperature to the 4th power, so are of the same ‘grain’, if you want to use that useless concept. In physics we deal in dimensions [units], not grain. Temperature is just another way of expressing the Wattage per unit area.
Both TSI and average temperature can be determined at any given time and two time series can be formed, so both vary in time [one as the fourth power of the other].
ferd berple says:
April 11, 2011 at 9:31 pm
Simpson’ paradox, however, slams a hammer down on the rule and the result is a good deal worse than a sore thumb.
Nonsense, the paradox comes from combining unequal group sizes, and no real scientists [but many economists] do such a silly thing.
In general, the forward transform of the Morlet wavelet is well defined but in general the inverse transform is ill defined (since support for the Gaussian is the entire real line.) The inverse transform can be made well defined but without knowing the number of oscillations in the Gaussian window, I view the smoothing (inverse) as Morlet art :).
In any case, since you’re never going to post the phase or energy plots of the forward Morlet transform, would it be possible to get a spreadsheet dump of the LOD data you used?
Its always a little disappointing if you ask a question that gets no answer. You suspect the question was ‘wrong’ or irrelevant in some way…
But it is FAR more frustrating when you ask a question and you get an reply that appears to avoid giving a meaningful answer.
@-Paul Vaughan says:
April 11, 2011 at 8:10 am
“The vertical scales are normalized to optimize visualization. As a contribution to this multidisciplinary discussion, I explore data, leaving physics to physicists & other qualified parties.”
I had asked what time-period was represented by the vertical scale on the graphs and what amount of energy variation this implied. This on the basis that as in politics its follow the money, in science its follow the energy.
This reply clearly does nothing to answer the question – very disappointing.
Perhaps somebody else can answer what amount of time all these curves actually represent ?
Paul Vaughan says:
April 10, 2011 at 11:10 pm
Don’t use a running mean if you are looking for time/phase correlations between different datasets. RM introduces significant distortions other than the simple low pass filter you are assuming you get.
Peaks will be shifted left or right depending on the surrounding data. The frequency response of this as a filter is very poor, the phase distortion is even worse. It is a particularly bad choice for this kind of analysis.
“But it is FAR more frustrating when you ask a question and you get an reply that appears to avoid giving a meaningful answer.”
Agreed.
“Normalising” to a non-dimensional scale does not in any way change the graph , hence it in no way “optimize visualization”. What it does do is make interpretation of the data impossible. Labelling an axis [-1:1] is meaningless , it may as well have no scale or label.
I have no time at all for graphs without meaningful quantities on the axes.
The changes in LOD are probably something like microseconds per year , which makes the idea that it affects climate laughable. I expect such a presentation to tell me that not hide it.
The fact that you did not get a clear reply to a simple question and the false “optimisation” argument says a lot about the author’s objectivity and openness.
He should probably apply some of his vitriolic criticism of mainstream science to his own efforts.
wikipedia.org/wiki/Day
Hope that link works it say that the length of day noon to noon over the year is about + or- 7.9 seconds.
Leif Svalgaard says:
Where I studies physics temperature was measured in kelvin which is in no way “just another way of expressing” watt/metre*2 . I don’t know what you are trying to say here but the way you said it is clearly wrong.
Equally TSI may be simplistically said to be related to T*4 of the sun. But where the “average temperature” in question is that of the earth your comment is “as wrong as can be”.
As a supposed correction to ferd berple’s comment that is a surprisingly messy effort from someone of your level of competence.
Leif Svalgaard says:
April 11, 2011 at 10:03 pm
Isn’t that exactly fred’s point? That what is being done with
climateweather station data is combining a whole lot of very unequal data sets.So it looks like your comment is says that compiling a global average is not the kind of thing real scientists would do (only economists). Despite declaring fred’s comment “nonsense” you appear to endorse what he is saying.
oops, that should have read:
Isn’t that exactly fred’s point? That what is being done with
climateweather station data is combining a whole lot of very unequal data sets.So it looks like your comment is says that compiling a global average is not the kind of thing real scientists would do (only economists). Despite declaring fred’s comment “nonsense” you appear to endorse what he is saying.
Leif Svalgaard says:
April 11, 2011 at 8:08 pm
That would be me. I hope I haven’t missed the deadline for “now.” Does that depend on Length of Day? ‘Cause something led me to believe that it might.
The agenda dances,
and personal stances,
of all become clear,
reading down to here,
nice to see all present,
have their own mindset.
P. Solar says:
April 12, 2011 at 12:22 am
Where I studies physics temperature was measured in kelvin which is in no way “just another way of expressing” watt/metre*2 . I don’t know what you are trying to say here but the way you said it is clearly wrong.
Perhaps I was not clear enough. “The Stefan–Boltzmann law, also known as Stefan’s law, states that the total energy radiated per unit surface area of a black body per unit time (known variously as the black-body irradiance, energy flux density, radiant flux, or the emissive power), j*, is directly proportional to the fourth power of the black body’s thermodynamic temperature T (also called absolute temperature):
The constant of proportionality σ, called the Stefan–Boltzmann constant or Stefan’s constant, derives from other known constants of nature. The value of the constant is
5.67×10^-8 W/m2. Thus at 100 K the energy flux density is 5.67 W/m2, at 1000 K 56,700 W/m2, etc.”
Watt/Square-meter is just another measure of temperate. This holds for both the sun and the earth [the earth is radiating too]. Fred is trying to convince you that TSI is a measure of the rate of change of T. Unfortunately, he may have succeeded.
P. Solar says:
April 12, 2011 at 12:37 am
Isn’t that exactly fred’s point? That what is being done with climate weather station data is combining a whole lot of very unequal data sets.
In doing so, the data is weighted by area to avoid Simpson’s paradox. If there are 1000 stations in Europe with an average temperature of 15C, and 10 stations in North Africa with an average temperature of 25C, then if you calculate the average as T = (15*1000 + 25*10)/(1000+10) = 15.099C you run into Simpson’s paradox, but if you do it correctly [assuming for the sake of the argument that Europe and North Africa have the same area], then you get the correct T=(15+25)/2 = 20C. This is how the average temperature is constructed.