Guest Post by Willis Eschenbach
I stumbled across an interesting journal study the other day entitled “Solar forcing of the semi‐annual variation of length‐of‐day” It makes the following chain of claims:
• Solar sunspot-related variations somehow affect the speed of the “zonal” winds. These are the components of the winds that blow parallel to the Equator. Whether said variations affect the “meridional” winds, the component of the winds perpendicular to the equator, the study sayeth not.
• Said variations in zonal winds then affect, not the length of the day (LOD), but per the study, the “amplitude A of the semi‐annual variation of the length‐of‐day”.
This chain of effects seemed rather … mmm … let me call it “tenuous” to me, so I decided to take a look. Let me start with the overall length-of-day (LOD) data.
Figure 1. Length of Day Anomaly
As you can see, the length of the day varies on a number of time scales. Per the study:
The length‐of‐day (lod) undergoes a wide spectrum of fluctuations.
The decadal fluctuations (10 to 30 years) are mainly attributed to exchanges of angular momentum between the core and mantle of the planet [e.g., Lambeck, 1980; Jault and Le Mouël, 1991; Gross, 2007].
Seasonal changes, which include semi‐annual, annual and biennial components, are almost entirely due to variations in atmospheric zonal wind circulation (apart from an important tidal component). The amplitudes of seasonal variations are not constant from year to year, and different hypotheses have been proposed to account for this variability.
Of interest to their study are the semi-annual variations. Here’s an overlay of each of the annual anomalies in the length of day, with the anomaly taken around each year’s mean. I’ve repeated each year so we can take a look at the overall cycle.
Figure 2. Length of Day Anomaly
As the authors discussed, there is indeed a strong semi-annual swing in the length of day. It’s generally longest around April 15 with a second peak in November, and lowest in July with a second trough in January.
Now, me being a simple fellow, I figured that if you are interested in the “amplitude A of the semi‐annual variation of the length‐of‐day”, you’d, you know, measure from the peak to the trough each year. Isn’t that what “amplitude” means?
But not these good folks. Here’s their procedure:
Figure 3. Authors’ amplitude calculation method
I can only shake my head in awe. They are using a four-year centered Fourier analysis to get the amplitude of the 6-month cycle … which seems to me that they’re claiming that the sunspot-related variations can affect the future.
In addition, there’s a huge problem with their method—there is no actual six-month cycle. The distance from the November peak to the April peak is five months, not six … and as a result, we could get a stronger Fourier 6-month result both by a change in amplitude and a change in timing of the peaks.
But I was born yesterday, what do I know?
In any case, I don’t like to engage in such a procedure without looking at individual years. Here are a few of said years, with a LOWESS smooth (black/yellow lines) and an indication of the semi-annual variation (black/red lines).
Figure 4. Authors’ amplitude calculation method
I doubt greatly that a Fourier analysis of that kind of variation will tell us anything. It’s not even clear what we can call the “amplitude A of the semi‐annual variation of the length‐of‐day”
So I set that whole question aside to look at the question of zonal winds. Unfortunately, the only long-term information on this are the results of a reanalysis computer model … but “needs must when the devil drives”, so that’s what I’ve used. Here are the average zonal winds:
Figure 5. Average zonal winds, Atlantic and Pacific centered views.
Hmmm … you can see what the strong winds are doing in the Southern Ocean, the latitudes that sailors like me call the “Roaring Forties”, and the “Screaming Fifties”.
Note that on average the wind value is negative, meaning on average an easterly wind. And the direction of the rotation of the earth means that stronger easterlies will tend to slow the rotation, and thus increase the length of the day.
So what does the annual cycle of the zonal winds look like? I’ve taken a monthly average of both the zonal wind torque and the LOD. Here’s the comparison.
Figure 6. Average monthly zonal wind torque and monthly LOD.
As you can see, the zonal winds clearly do speed up and slow down the rotation of the earth on an annual basis.
So … is there a correlation between sunspots and zonal wind speeds? To examine that, I used a CEEMD analysis which breaks out the underlying frequencies of the two signals. Here’s a comparison of the periodograms of the CEEMD analysis of the two datasets, zonal winds and sunspots.
Figure 7. Periodograms of sunspots and zonal winds, 1948 to present
Now, the first thing you have to understand about spectral analysis is that old Joe Fourier proved hundreds of years ago that ANY time series can be broken down into individual signals which, when added together, reconstitute the original time series. So the presence of such individual signals doesn’t necessarily mean that they are externally driven.
Looking at the different signals in Figure 7 above, you can see that the sunspots (black) have a clear 11-year signal in the Empirical Modes C6 and C7, with a smaller signal at 14 years. The zonal winds (red), on the other hand, have a signal at about 12 years, with a smaller signal at 9 years.
What this means becomes evident when we plot up the two actual empirical mode 7 signals, shown as “C7” in the figure above.
Figure 7. Periodograms of sunspots and zonal winds, 1948 to present
As you can see, both signals show an ~ 11-year component … but because they do not have same period, they start out in phase and end up totally out of phase.
In other words, although the annual variations in zonal winds are clearly responsible for some part of the annual variation in LOD, I’m not finding any evidence that sunspot-related variations in solar energy are driving the zonal winds.
In closing, my excursion into the zonal and meridional winds got me to thinking about global average wind speeds in general. The actual wind speed is the square root of the sum of the squares of the zonal and meridional winds. Here’s a global view of the long-term average wind speed.
Figure 8. Average wind speed, 1948 to present, Atlantic and Pacific centered views
Wind speed over the ocean is greater than over the land, and wind speed over the tropics is greater than wind speed over the ocean. And here’s the change in wind speed over the period.
Figure 9. Monthly average wind speed, 1948 to present
And why is the small increase in wind speed of a few percent important?
Well, evaporation basically varies linearly with wind speed. And globally, evaporation cools the surface by something on the order of 80 watts per square meter (W/m2) per year. So a 4.7% increase in wind speed should convert to additional surface cooling of about 3.7 W/m2 … just saying, there are a whole lot of things going on in this immense heat engine we call the “climate” that don’t have anything to do with CO2.
Here on our northern California hillside on Boxing Day, we have rain … blessed rain, life-giving rain. I had a wonderful Christmas with the people I live with in this rambling house I built with my own hands—my gorgeous ex-fiancee, my daughter and her husband, our two-year-old granddaughter, and our two-month-old grandson. (The walls don’t slope, it’s from the camera lens.)
Me, I’m the luckiest guy on the planet …
With wishes that your life be full of joy, sunshine, and just enough rain,
w.
PS—Here are my “Letters From Mexico To My Future Ex-Fiancee“.
PPS—When you comment, please quote the exact words you are referring to, so we can all be clear on the exact topic you are discussing.
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At what height is the windspeed measured? It’s not clear to me how this is dealt with.
I believe the standard height is 10 meters for “ground” measurements.
But if it was measured at, say, 5000 meters, in the jet stream, would that change the results?
If the poles are indeed warming faster than the equator, the reduction in temperature difference will reduce wind speeds in a Carnot heat engine.
This contradiction stronly argues that either the poles are not warming as reported or the wind speed observations are wrong.
Thanks, Ed. Actually, said polar warming should reduce the meridional winds, not the zonal winds. However, in a large complex system such as the Earth, this may not be a direct relationship.
w.
Humidity changes could also affect wind speed, by changing convection rates due to the buoyancy of water vapor.
Intriguing as always.
How robust is the science that “winds cause the earth to slow down”?
It is fairly clear differential heating causes wind. This heating being due to the rotation of the earth and the terminator sweeping over the surface of the earth.
However, the mass of air, moved by whatever cause, must be replaced with an equal(ish) mass of air from another region. One could view this on a small scale of farmers fields causing thermals plus wind and a large scale of land warming faster than ocean.
How any of this wind movement can interact with the near vacuum of space, I do not understand.
Friction between the surface and the surface touching air, is irrelevant. You only need to experience a still day to realize the air about you is traveling along at exactly the same speed as the surface you stand on. Only local winds, as described above, will disturb that.
I can understand trade winds caused by the daily terminator sweep, ‘stroking’ the surface.
I can understand the El Nina etc causing the earth to change speed due to the conservation of angular momentum if wide areas of the sea-level change. But these must average out. El Nina are cyclic warm currents probably caused by the terminator sweep with a long cyclic term.
What am I missing?
It’s surprising how little the authors understand about practical application of DSP theory…and the reviewers too. For example, consider all the apparent noise on the blue curves in their Figure 1. This is caused by the authors’ failure to properly window the 4-year data segments prior to FFT calculations.
They prove their ignorance in note [7] following figure 1, saying about segments only 1 or 2 years in length, “short period noise becomes larger.”
It appears they increased the segment size to 4 years in an attempt to swamp out the spectral noise from the non-windowed discontinuity between ends of the data. Properly windowing the data gives perfectly smooth results for 1 year segments.
But that’s not the real issue, I think. The real problem is that none of the data is truly periodic. What it is, is a random variable from a random process. Okay, there are some periodic components in there but they are so heavily modulated by processes we don’t understand (and cannot predict) that it may as well be random.
If you want to know about correlation, how about just computing the cross correlation sequences beetween LOD and SSN or LOD cosmic ray flux? You’re making way fewer assumptions with that approach. Just for fun, I did that and the attached image shows the result.
The correlation coefficient isn’t all that large, but there is a roughly 11-year periodicity in the cross-correlation.
Thanks, Observer. You have to be very careful with a cross-correlation of a strongly cyclical signal like say sunspots. You’ll find, for example, a strong cross-correlation with a unit impulse, or in fact with just about any complex signal … which means nothing.
w.
I’m not sure I understand your point. Even though the sunspot and cosmic ray data contains strong cyclical content, the cross correlation with LOD data would not be cyclical unless LOD also contained similar cyclical content. What am I missing?
Okay, never mind…I see it now.
Ozone blockade of the polar vortex in the lower stratosphere over Kamchatka.
Do you see an impact on the meridional jet stream over the west coast?
https://earth.nullschool.net/#2021/12/29/2200Z/wind/isobaric/250hPa/orthographic=-131.13,46.40,562
In four days, a powerful stratospheric intrusion will bring severe cold to the central states.
“So … is there a correlation between sunspots and zonal wind speeds?”
There should be a phase shift from the 1990’s, because the zonal winds would be responding to changes in the solar wind strength rather than sunspot cycles.
Not sure what you are calling “solar wind strength”. Do you have a link to a dataset?
Thanks,
w.
I have been through this on more than one occasion in the past with you, in response to the false claim that the solar wind variability follows sunspot cycles. The major lows in the solar wind shifted from around sunspot cycle maximum in 1969 and 1979-80, to just after sunspot cycle minimum in 1997 and 2009. The solar wind strength is a combination of speed/temperature and pressure. Note how in your figure 9 that the wind speeds shift faster from the mid 1990’s, which is when the solar wind weakened from, and of course when the AMO warmed from. There is probably also an ENSO influence on wind speeds.
https://omniweb.gsfc.nasa.gov/form/dx1.html
Thanks for the link, Ulric. You say “solar wind strength is a combination of speed/temperature and pressure”. The OMNIWeb site lists the following:
How are you “combining” them to give you “solar wind strength”? And what are the units of the final combination?
Regards, and best of the New Year,
w.
I just love it when a mathematical exersize actually has a point to itself.
Like crushing nonsense arguments and driving “scientists” mad.
Oddgeir