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 … 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 winds and the LOD. Here’s the comparison.
Figure 6. Average monthly zonal winds 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,
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.