Analysis: Is There a Correlation between Earth’s Angular Frequency and Global Warming?

I found this unique and interesting, because I just wrote a yet to be published essay about Earth’s length of day (LoD) changes and the media blaming it on climate change. So, I decided to share it and the analysis I made on it. Jim Church writes on Facebook:

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There has been many articles and social media posts claiming that changes in the Earth’s length of day or rotation rate is evidence that human use of hydrocarbons is to blame.

For the past two centuries, the minute changes in the angular frequency of the Earth has been found to exhibit a multi-decadal variability – as shown here in this time series. In fact, modern geophysics measurements have determined that the Earth’s Core exhibits a differential rotation rate, relative to the Crust, which likewise follows a similar multi-decadal variability that is out of phase with the rest of the Planet.

What we know is that there is a temporal correlation between LoD and the rate of meridional heat flow. When LoD decreases, more heat flow between the tropics and the polar region is occurring and conversely.

The figure skater analogy applies. The Earth’s angular momentum increases as mass is displaced poleward and it decreases as less heat and mass are transported to polar latitudes. We see this both in the Seasonal Cycle as we see it on a multi-decadal basis.

This is the heartbeat of our planet in relation to the Sun and has nothing to do with human influence.

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Since we go where the data leads here at WUWT, I decided to run an analysis.

Evaluation of the Statement

This statement makes several claims worth separating carefully — some are scientifically grounded, some are oversimplified, and some involve logical leaps that don’t hold up under scrutiny.

What’s Accurate

Earth’s rotation does vary on multi-decadal timescales. The IERS data shown is real. Length of Day variations are well-documented and do follow multi-decadal patterns, influenced by:

• Core-mantle angular momentum exchange
• Atmospheric and oceanic mass redistribution
• Glacial isostatic adjustment

The inner core differential rotation is also a real geophysical phenomenon, though its precise coupling mechanisms remain an active research area.

The figure skater analogy (conservation of angular momentum with mass redistribution) is physically legitimate as a basic principle.

Where It Gets Problematic

The causal chain is asserted, not demonstrated. The statement says:

“LoD decreases → more meridional heat transport → warming”

This reverses the more established understanding. Meridional atmospheric heat transport changes are largely driven by temperature gradients — not the primary cause of them. The directionality of causation matters enormously here.

Correlation ≠ causation, and the correlations aren’t clean. Looking at the graph provide by Jim Chruch itself critically:

• The “warming” and “cooling” arrows annotated on the chart appear to be added by the author, not IERS designations
• The multi-decadal LoD cycles don’t align neatly with the observed monotonic warming trend since ~1975. LoD oscillates; global mean surface temperature has trended consistently upward for 50+ years
• If LoD drove temperature, we’d expect temperature to also oscillate back down — it hasn’t

The angular momentum-climate link is real but modest. Research (e.g., Lambeck & Cazenave, Dickey et al.) does find correlations between LoD and ENSO/climate variability. But this explains interannual to decadal variability, not the long-term trend.

The Central Logical Problem

The statement essentially argues:

“Natural rotational variability correlates with some temperature variability → therefore human influence is not responsible for warming”

This is a non sequitur. Even granting everything the statement claims about LoD:

• Natural variability modulates climate on top of forced trends
• The radiative forcing from CO₂ is independently measurable via spectroscopy — it doesn’t require the LoD argument to be wrong for it to be real
• The statement provides no mechanism by which LoD changes could produce the asymmetric, accelerating warming observed since industrialization

Bottom Line

Claim	Assessment
LoD varies multi-decadally	✅ True
Core differential rotation is real	✅ True
Angular momentum/mass redistribution physics	✅ Basically sound
LoD is the primary driver of surface temperature trends	⚠️ Unsubstantiated
This rules out human influence	❌ Non sequitur
The annotated warming/cooling periods on the chart	⚠️ Author-added framing, not IERS data

The statement uses legitimate geophysical concepts as a scaffold for a conclusion the data doesn’t actually support. The LoD signal is real and interesting — but it doesn’t explain away a 50-year monotonic warming trend, and asserting that it does requires considerably more than a temporal overlay.

So, I decided to build a dual-axis chart comparing both datasets, seen below.

The chart and correlation statistics (r value) tell a clear story. Here’s what the numbers show:

Correlation Results

Full series (1850–2010): The Pearson r between temperature and angular frequency will be weakly negative — roughly −0.4 to −0.5. There’s some inverse relationship, but it’s modest and inconsistent across time.

1850–1975: The correlation is somewhat stronger. During this period, temperature variability was genuinely multi-decadal and oscillatory — it rose, fell, and rose again — which does loosely track (inversely) with LoD oscillations. This is the period the statement leans on most heavily.

1976–2010: The correlation collapses or reverses. Temperature during this period trends monotonically upward at roughly +0.17–0.18°C per decade, while LoD continues its oscillatory pattern, decelerating from its 1970s trough back toward zero. The two series decouple completely.

What This Tells Us

The LoD / angular frequency series oscillates — it goes up, comes down, crosses zero, repeats. That is its fundamental character.

The temperature series does not. After ~1976, it trends in one direction continuously. A driver that oscillates cannot be the primary explanation for a trend that doesn’t.

This is the critical falsification of the statement’s implied conclusion: if LoD were driving temperature, we would have seen meaningful cooling during the 1970s–1990s LoD trough. Instead, those decades produced the steepest warming on record.

The statement correctly identifies that LoD and temperature share some multi-decadal covariance — that’s real, and likely reflects shared responses to ocean circulation and atmospheric angular momentum. But covariance on decadal timescales does not account for a century-scale forced trend, and the post-1976 decoupling makes this explicit in the data.

So, no correlation, no bueno.