There’s a 40-thousand mile long ridge of volcanic activity running under the world’s oceans. Both volcanos and hot smokers are transferring terawatts of heat to the oceans daily. This heat flow is assumed to be constant, so it’s not categorized as a ‘variable’ in climate and weather. But we really don’t have a way of measuring the heat transfer or charting it over time.
The core and mantle are heated by fission. Radioactive decay constantly heats the core and that heat drives columns of magma up through the crust. The heat flow and distribution are manifestly lumpy because there is significant variability in volcanic activity over both near-term and geologic time.
Most likely Earth’s core heat migrates towards the surface slowly in giant viscous clumps or bubbles of hotter and less dense material. Sort of like how the material behaves in a lava lamp except on a much longer time scale.
With all this bubbling going on I see no reason to assume the geothermal heat flow into the ocean is completely constant, absent scientific proof. I do see reason to assume the heat flow varies according to the number and intensity of undersea eruptions from one year to the next. The heat flow IS a ‘variable’.
In more general terms, it should be pointed out that before the AGW period there was no working theory of what caused the Pacific to undergo its periodic shifts from El Nino to La Nina states (several variants are recognized, it’s a little more complex than just either/or), and there was never any attempt made by AGW theorists (whether they are right or wrong) to explain the variations or to postulate whether AGW would change the balance.
So in other words, the Pacific variations remain separate from AGW theory and you could postulate that if AGW has some partial merit (humans are partly or even mostly responsible for the recent warming observed) that merit does not extend to any new or greater understanding of these Pacific variations. Pretty much the same can be said for other signals like the Atlantic Oscillation. The best AGW could claim is that they have introduced a theory that takes the old pre-AGW climate and warmed it up by about 1 C degree, without explaining any of the variations within the regional trends (other than some claims made that variability is increasing, itself a controversial claim).
Personally, I might expect in a generally warming climate that El Nino would lose frequency and La Nina would gain frequency; the reason for that is that stronger subtropical highs tend to promote La Nina (by driving more cold water north along the west coast of South America, it is when that process weakens that El Nino patterns develop, so they are correlated with weaker subtropical highs). Some of the observed northern hemisphere weather correlations with El Nino or La Nina may not be direct consequences but just similar responses if the two hemispheres see similar trends in the strength of subtropical highs. This could in theory not be linked either by hemispheres or by different ocean systems. So it’s all rather complex and as we have seen, the AGW approach is a simple one and does not handle complexity very well.