What started as an effort to model the Atlantic Multidecadal Oscillation (AMO) using Laplace’s Tidal Equation (LTE) forcing1 has produced a long-lurking side discovery: the detrended AMO model output correlates with -LOD (negative Length-of-Day, i.e., Earth’s rotational acceleration) at r = +0.70 on decadal timescales, across a 140-year span from 1880 to 2020. The LOD is shown to the right2
This wasn’t an engineered result but a side-effect. The AMO model was fit independently against sea-surface temperature data using only tidal forcing as input — none of the long-term (multidecadal) wandering LOD data was ever used in the fitting procedure, only the shorter tidal factors that contribute to the fast LOD cycles were calibrated to over a short range after 1962. You can see those fast cycles in the above chart. The correlation emerged after the model was fitted to AMO, just by comparing the model’s decadal envelope against the historical LOD record — note that this pure correlation between AMO and LOD is not new as it has been observed previously3. What is new however is this round-trip connection between AMO and LOD via tidal forcing — the fact that lunisolar tides were involved has not really been considered.
That’s the ansatz — although the faster LOD cycling comes about directly from lunisolar torquing4, the longer-range wander doesn’t derive from standard tidal factor bookkeeping. This is described below:
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