When I first joined the small but intrepid band of Length-of-Day (LOD) enthusiasts in mid-2012, heat fluctuations in the Earth's inviscid outer core was my first thought. This was motivated by some remarks in Munk and McDonald's monograph "The Rotation of the Earth" (CUP 1960) about slabs being pushed down and interfering with irregularities at the surface of the inner core. This is what's behind column 4 of my AGU FM2012 poster.
One problem with that source of thermal fluctuations is the immense time required for them to reach the surface. So subsequently, following recent suggestions in the literature, I looked to mechanical effects in the lithosphere resulting from fluctuations in the Earth's oblateness, as per section 6 (p.7) of my AGUFM2014 poster. But then part way through a discussion of Ekman transport (relevant to my poster) with Scripp's Lynne Talley after her talk on the last day of AGUFM2014, the chance arrival of Columbia's Ryan Abernathey changed my thinking yet again. When we told Ryan what we were talking about, he immediately suggested fluctuations in upward flow of lava.
While the logic of that mechanism was clear, I realized that I had overlooked it because I had been analyzing oblateness as though the Earth were a drop of a suitably viscous but homogeneous fluid. Nothing in that model gets preferential treatment. Ryan's suggestion turned my attention to the inhomogeneities in the lithosphere, in particular the difference in hardness between magma and its containing chambers (which need not be as great as that between a bottle and its contents because both are very hot). The heat difference makes the magma less dense than the chamber and therefore buoyant, whence, like a bubble, it flows upwards wherever possible until reaching the surface as lava. Fluctuations in LOD will be felt as variations in g and hence in buoyancy: the shorter the LOD the greater the buoyancy.
The question then arises as to how LOD might influence surface temperature. I decided to model pressure of lava in chambers, which I assumed increases with increasing buoyancy. The pressure is relieved in three ways: leakage (dominantly upwards as expected of buoyancy), decrease in g (from increasing LOD), and relaxation of the (hot but not molten) chamber (if LOD does not change over a long period the magma and its somewhat harder chamber settle down together into a new equilibrium that leaks at the same rate as at any other sustained LOD).
This model suggests a simple filter whose transfer function converts LOD into thermal flux. LOD and hence g are given directly and hence don't need a parameter, and the other two influences on pressure are modeled with one parameter each. However analysis of the filter's impulse response shows that the effect of faster leakage on heat arriving at the ocean floor is indistinguishable from faster relaxation, whence as far as thermal release is concerned there is no loss in modeling precision when they are combined into a single parameter. If the two parameters are of separate interest they will need to be estimated from other data than thermal flux.
1. This transfer function applied to LOD, in combination with the expected contribution of CO2 to warming, tracks 20-year-smoothed HadCRUT4 (what the IPCC uses in its definition of TCR) for 15 of the 16 decades from 1855-2015 very well. The only serious discrepancy is 1940-1950, which this model undershoots by 0.05 to 0.1 °C.
Possible explanations.
(a) My heating model is too simple.
(b) The transition from canvas buckets to engine coolant as the source of SST measurements around that time has introduced additional uncertainty into that period. Decreasing that decade by 0.05 °C greatly improves the fit, to the extent that Arrhenius even in his lifetime (he died in 1927) with access to the same CO2 and LOD data could have foreseen the current temperature to within 0.2 °C.
(c) Some other phenomenon, either not taken into account (such as WW2) or unrecognized altogether, raised the temperature of that decade.
2. The current hiatus does not exist in 20-year HadCRUT4, though it can be seen in 10- and especially 5-year smoothings. The additional wiggles in this less-aggressive smoothing reduce the R2 of the fit. Incorporating the Hale cycle, modeled as a 20.5 year sinusoid, brings the R2 back up, with the additional benefit of the modeled temperature being essentially flat during the observed hiatus. The Hale cycle is clearly visible in SST and hence in both PDO and AMO indexes, whence attributions of the hiatus to the PDO or any other "oscillation" might more appropriately be attributed to the Hale cycle. Arrhenius could have forecast the hiatus very precisely in time though a tad low in temperature.
The Hale cycle is clearly visible also in Central England Temperature, not only after the Maunder Minimum (MM) but even during its last half century, right at the start of CET. As the sunspots resume at the end of the MM the atmospheric Hale cycle is 180 degrees out of phase but within a cycle or so locks into the solar cycle with the same phase as we observe today, peaking shortly after the transition from north to south Bz (the component of the Interplanetary Magnetic Field normal to the Sun's equatorial plane) in the heliomagnetosphere, namely when the Earth's and Sun's magneitc fields link up to form a loop. It's a nice question what phase the heliomagnetosphere was in towards the end of the MM.