It’s the gradient, stupid!

How does the Sun drive climate change?

Guest Post by Javier

The dispute between scholars that favor a periodical interpretation of climate changes, mostly based on astronomical causes, and those that prefer non-periodical Earth-based explanations has a long tradition that can be traced to the catastrophism-uniformitarianism dispute and how the theory of ice ages (now termed glaciations) fitted in.

Prior to the scientific proposal of ice ages in 1834, most scholars that cared about the issue believed that the Earth had been progressively cooling from a hot start, as tropical fossils at high latitudes appeared to support. By 1860 scholars had been convinced by evidence that not one but several glaciations had taken place in the distant past. By then scientists trying to explain the cause of past glaciations were split in two. Those following Joseph Adhémar, who had already proposed orbital variations in 1842, and those following John Tyndall, who proposed that they were due to changes in GHGs (greenhouse gases) in 1859, particularly water vapor.

For a time, the anti-cyclical, pro-GHG camp had the advantage, after James Croll’s hypothesis was rejected, and Svante Arrhenius in 1894 proposed CO2 as the responsible GHG. But then, doubts about the CO2 effect and a new formulation of the cyclical astronomical hypothesis by Milankovitch appeared that fit popular geological reconstructions of past glaciations. This swung the field again.

By the late 1940’s Milankovitch theory was well established, particularly in Europe, but not so much in America where reconstruction of Laurentide ice-sheet changes did not match the theory very well. But in the 1950’s a new consensus formed. The GHG theory was reinforced by Suess, Revelle, and Keeling’s work, while carbon dating led to glacial reconstructions at odds with Milankovitch theory.

In the 1960’s and early 70’s Milankovitch theory was discredited with only a handful of followers left. The anti-cyclical, GHG explanation enjoyed wide consensus, but due to the cooling at the time, scholars believed other factors must be at play. Then disaster struck for the anti-cyclical camp. In 1976, Hays, Imbrie, and Shackleton, analyzing Indian Ocean benthic cores for the past 450,000 years and showed that glaciations followed some of Milankovitch frequencies within 5% error. A 140-year quest had ended, and the cyclical orbital supporters had won.

Of course, GHG supporters are bad players and did not accept the defeat graciously. Since it was soon discovered in ice cores that GHGs followed orbital changes (as they should), it was soon proposed (and accepted without evidence) that they were required to amplify the orbital changes and to maintain inter-hemispheric synchroneity. Trying to turn the defeat into a victory, they claim that the frequency is set by Milankovitch but a great deal of glacial-interglacial climate changes are due to GHG changes.

You would think that after showing that climate was cyclical and astronomically based, propositions that other astronomical phenomena (like lunar periodicities or solar variability periodicities), might affect climate would at least be given the benefit of doubt. But no. The anti-cyclical camp enjoys centennial beatings by the cyclical mavericks, so they are building up for the next one by flatly rejecting any significant climatic effect from periodical solar changes. Apparently, they are undeterred by the evidence showing most periods of low solar activity during the Holocene are associated with cooling and atmospheric circulation and precipitation changes, like the LIA. There are about 10 abrupt climate events (ACEs) associated with low solar activity during the Holocene. Some have names like the pre-boreal and boreal oscillations, or the 9.3 or 2.7 kyr events, showing that the most frequent cause for ACEs is prolonged low solar activity.

I have already shown some evidence for that in my previous articles:

Do-It-Yourself: The solar variability effect on climate

Do-It-Yourself: Solar variability effect on climate. Part II

I have also shown that ENSO is under solar control:

Solar minimum and ENSO prediction

Yet the anti-cyclical crowd (IPCC included) takes refuge in the bean-counting argument that solar variability is only 0.1% and therefore too small to produce much of a change. This only shows how narrowly focused their view of climate is. They think that Earth’s climate can be explained solely with terms of W/m2 and after all 0.1% is only 1.4 W/m2 over the 11-yr cycle (solar irradiation), adjusted to only 0.34 W/m2 annual average insolation change at top-of-the-atmosphere (TOA) at 1 AU. However, the Earth received the same TOA insolation during the Last Glacial Maximum as now, so climate is clearly not a case of bean-counting Watts.

Today I am going to show you how solar variability affects Earth’s rotation speed, and why it is important. This issue was raised several times in 2010, but it is not understood by most:

Changes in the rotation speed of the Earth are measured as variations in the length of day (ΔLOD) defined as the difference between the astronomically determined duration of the day and 86,400 Standard International (SI) seconds. ΔLOD has been measured daily down to a 20 microsecond (µs) precision by interferometry since 1962. Annual changes at 1 millisecond (ms) precision have been reconstructed for the telescope era from astronomical observations. Variations in ΔLOD on annual and seasonal (semi-annual) time scales are highly correlated with angular momentum fluctuations within the atmosphere, mainly due to changes in zonal winds. The averaged annual and semi-annual oscillations in ΔLOD feature almost equal amplitudes of approximately 0.36 ms.

The semi-annual oscillation in ΔLOD has the following characteristics:

From November to January the Earth accelerates to ~ 0.2 ms-day (ΔLOD changes by -0.2 ms). Then it decelerates by nearly the same amount by April. Afterwards it accelerates to ~ 1 ms-day by July (ΔLOD change of -1 ms), before decelerating back to the initial value by the next November. The average amplitude is ~ 0.35 ms, but the NH winter component is much smaller than the SH winter component (see figure 1, inset).

This change is caused by the angular momentum of the atmosphere being higher in winter because the meridional circulation is much stronger during that season. This is the result of the winter pole receiving very little insolation as the Sun is above the opposite hemisphere. The dark pole becomes colder and the latitudinal temperature gradient steeper, and as a result more heat needs to be transported poleward, activating the meridional circulation in that hemisphere. The asymmetry of the NH (Northern Hemisphere) winter and SH (Southern Hemisphere) winter components of ΔLOD is due to the asymmetry in land masses between hemispheres having a strong effect on wind circulation.

Le Mouël et al., 2010 showed that the semi-annual component of ΔLOD responds to solar variability. This is an extremely important result highlighted only by a few skeptics and ignored by everybody else. Part of the problem is that the article’s method to show it is quite complicated, and most people did not understand the article or its implications. Let’s try a simpler way.

Let’s concentrate only on the NH winter acceleration (ΔLOD decrease) that by being smaller, more clearly shows the effect. We start with LOD data from the International Earth Rotation and Reference System Service EOP C04 IAU2000A file:

This is a 20,700 data point file with daily ΔLOD values since 1962. It is converted to monthly values to work with only 680 points and eliminate all the oceanic and atmospheric tidal higher frequencies. The result is shown in figure 1.

Figure 1. Monthly ΔLOD. The inset shows two years of data with four semi-annual components. What I am going to measure every year is the acceleration (ΔLOD decrease) of the NH-winter component.


The NH winter trough in ΔLOD might take place in Dec-Jan-Feb (DJF), so for every year I select the lowest value among those three months, and then subtract from that value the highest value (ΔLOD fall peak) within the four prior months to the one selected. If there is no peak value in the 4 prior months this means there was no ΔLOD decrease the prior fall and I introduce a zero (it happened in 1983 and 1993, see figure 1). The result is a number for every year measuring the Earth’s acceleration from Oct-Nov to DJF in milliseconds, that varies between 0 and -0.9 ms.

As ΔLOD is affected by anything that affects the angular momentum of the atmosphere, like ENSO, the obtained NH winter acceleration yearly dataset is noisy, so we smooth it with a triangular filter (ΔLODsm[t] = 0.5*ΔLOD[t] + 0.25*ΔLOD[t-1] + 0.25*ΔLOD[t+1]). The result is then compared to solar activity, in this case monthly 10.7 cm flux smoothed with a gaussian filter. It is shown in figure 2.

Figure 2. NH winter ΔLOD vs. Solar activity

This is a simpler way to look at the dependence of the speed of rotation of the Earth on solar variability. Let’s remember that Le Mouël et al., 2010, and Paul Vaughan here at WUWT, showed that both semi-annual components respond to solar variability, and not only the NH winter one that I have shown. The agreement with solar data is even better using both components (see Le Mouël et al., 2010 or the WUWT links above).

Now we know how solar variability affects climate despite being only a 0.1% change in TSI. But before explaining that, let me explain why ΔLOD is so important for climate.

Changes in Earth’s rotation speed act as a climate integrator, reflecting changes in atmospheric circulation that then cause changes in temperature. ΔLOD is not known to be a cause for climate change, but a way of measuring it that responds in real time to changes in the angular momentum of the atmosphere. It is therefore a leading indicator of climate change. It is not known to respond to radiative changes and therefore to CO2, and thus it does not appear in the IPCC reports. I searched the WG1 AR5 report and could not find any mention of it. Yet, in 1976 Kurt Lambeck and Anny Cazenave reported that changes in ΔLOD for the past 150 years correlate well to a variety of climate indices, and they produced one of the few trend-change climate predictions that have proven accurate. They indicated that since ΔLOD had started accelerating in 1972 (see figure 1) the observed cooling trend was about to end. 1976 was the exact year when that happened.

Adriano Mazzarella in 2013, and Mazzarella and Scafetta in 2018 showed the good correlation between several climate indices and ΔLOD. In figure 3 I compare, as he did, yearly NH SST from HadSST3.1 and yearly ΔLOD (both linearly detrended for the period shown).

Figure 3. Detrended changes in Northern Hemisphere Sea Surface Temperature and detrended changes in Earth’s rotation speed (ΔLOD inverted).

On average changes in ΔLOD precede changes in SST by 4 years, indicating that atmospheric changes affecting ΔLOD are also responsible for cooling or warming the ocean surface.

So, how does the Sun affect ΔLOD? As figure 2 shows, when solar activity is high the winter NH acceleration does not take place, and when solar activity is low the winter NH acceleration is greater. So, the winter NH atmospheric circulation suffers more profound changes when solar activity is low. Low solar activity is also associated with a stronger activation of the winter meridional circulation that causes stronger meridional heat transport towards the poles and more frequent winter blocking. Further, low solar activity is associated with persistent winter negative NAO (North Atlantic Oscillation) conditions over high latitudes. The subpolar oceanic gyre then becomes weaker. A warmer North Atlantic current feeds more snow to Scandinavia (remember the great 2010 snowstorm that blanketed Great Britain and several other European countries), while weaker Westerlies result in a more southward winter storm track that dries Northern Europe and wets the Mediterranean.

During the LIA (Little Ice Age) the planet got stuck in this situation during years and decades of low solar activity. And every 200 years there was a Grand Solar Minimum that lasted for 80-150 years, so it got cooler and cooler and glaciers grew and grew, until solar activity returned to normal and there was a recovery. It was a slow cooling and it is a slow warming. Long-term solar activity has been growing to the late 20th century (figure 4). According to my calculations of solar periodicities, long-term solar activity should continue being high for at least another 100 years, but it won’t increase much more over the levels seen in the second half of the 20th-century. So, it should not significantly contribute to additional global warming.

Because of the land mass asymmetry between hemispheres, the atmospheric circulation changes caused by solar variability are proportionally smaller in the Southern Hemisphere. Although the effect is global it is stronger in the Northern Hemisphere, providing an explanation for the unexplained fact that climate change is more intense in that hemisphere. LIA effects were also stronger in the Northern Hemisphere, to the point of some suggesting it was a regional phenomenon. It is a feature of asymmetric solar variability effect on hemispheric atmospheric circulation, and the reason I selected NH-winter acceleration to show the effect.

Figure 4 shows how solar activity changed during the LIA and how it has been increasing since. Temperature has been trailing the recovery in solar activity with a delay. While solar activity started recovering after ~ 1700, temperature bottomed a second time in 1810-1840 and only started recovering after the cluster of large volcanic eruptions during the Dalton period (~1790-1840) ended. Temperature is affected by more things than just solar activity.

Figure 4. a) Solar activity reconstruction from 14C record (Muscheler et al., 2007), with a 2nd degree polynomial showing the long-term trend. b) Total solar irradiation reconstruction (Vieira et al., 2011) compared to Northern Hemisphere summer temperature reconstruction (Anchukaitis et al., 2017).

The planet’s climate is determined by the latitudinal temperature gradient, not the average global temperature. The poles are energy sinks to space (particularly in winter) and the efficiency of the poleward heat transport determines how much energy the planet retains, not the amount of CO2 in the atmosphere, which has a much smaller effect. We are studying the thickness of the glass in the windows, when it is the open door to the poles that matters regarding warming. The door has been closing, so the Earth has been warming, and solar variability is responsible, while CO2 is just contributing. Zonal wind vertical strength is proportional to the latitudinal temperature gradient and inversely proportional to the Coriolis factor. Solar variability, despite being only 0.1%, shows a demonstrable capacity to affect the zonal/meridional wind balance during winters. There are several possible mechanisms, but a strong possibility is through stratospheric latitudinal temperature gradients due to winter ozone distribution and UV changes with solar variability. These gradients could affect tropospheric wind circulation through changes in geopotential height. Alternatively, the atmosphere is known to expand and contract with solar activity, but this effect is dominated by the rarefied outer atmosphere that has very little mass, and the atmospheric angular momentum changes that affect Earth’s rotation are dominated by the effect of tropospheric winds in the lower 30 km. It could be a combination of solar variability effects over the entire atmosphere acting in the same direction and affecting zonal wind circulation.

The importance of the latitudinal temperature gradient cannot be overstated. Christopher Scotese has been reconstructing the climate of the distant past by reconstructing changes in the latitudinal temperature gradient on a 10-million-year scale over the Phanerozoic. The main difference between a hothouse climate and an icehouse climate is in the gradient, and the average temperature of the planet is just the result of how much energy is moved through the gradient.

When this is sufficiently researched, once again the cyclical climate camp will have given a sound beating to the GHG crowd, let’s hope that this time is for good. And the TSI bean counters will discover that the climate of the planet is a lot more complex than they think and it is not only a matter of W/m2. Simple answers are satisfying, but rarely solve complex questions.

And if you want to know how climate change is going to evolve over the next 4 years, you only have to look at how ΔLOD is evolving now. You will know more about it than the IPCC, Gavin Schmidt, and all the consensus builders looking at their models based on an incorrect paradigm.

I leave for another day how the Moon produces some of the most abrupt cyclical climate change events of the past.


Hays, J. D., Imbrie, J. and Nicholas J. Shackleton. 1976. Variations in the Earth’s orbit: pacemaker of the ice ages. Science 194 (4270), 1121-1132. Link.

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(15). Link.

Na, S. H., Kwak, Y., Cho, J. H., Yoo, S. M., & Cho, S. (2013). Characteristics of perturbations in recent length of day and polar motion. Journal of Astronomy and Space Sciences, 30, 33-41. Link.

Lambeck, K., & Cazenave, A. (1976). Long term variations in the length of day and climatic change. Geophysical Journal of the Royal Astronomical Society, 46(3), 555-573. Link.

Mazzarella, A. (2013). Time-integrated North Atlantic Oscillation as a proxy for climatic change. Natural Science, 5(01), 149. Link.

Mazzarella, A., & Scafetta, N. (2018). The Little Ice Age was 1.0–1.5° C cooler than current warm period according to LOD and NAO. Climate Dynamics, 1-12. Link.

Muscheler, R., Joos, F., Beer, J., Müller, S. A., Vonmoos, M., & Snowball, I. (2007). Solar activity during the last 1000 yr inferred from radionuclide records. Quaternary Science Reviews, 26(1-2), 82-97. Link.

Anchukaitis, K. J., Wilson, R., Briffa, K. R., Büntgen, U., Cook, E. R., D’Arrigo, R., … & Hegerl, G. (2017). Last millennium Northern Hemisphere summer temperatures from tree rings: Part II, spatially resolved reconstructions. Quaternary Science Reviews, 163, 1-22. Link.

Vieira, L. E. A., Solanki, S. K., Krivova, N. A., & Usoskin, I. (2011). Evolution of the solar irradiance during the Holocene. Astronomy & Astrophysics, 531, A6. Link.