More Musings about Schmith et al.

I got an e-mail from Søren Johansen about my post about the Schmith et al. paper that he coauthored. In response I thought a bit more about whether there could be a long run relationship between atmospheric temperature, sea level, and radiative forcing. I had said that that didn't make much physical sense to me and proposed a statistical explanation for what they found. But the fact is that atmospheric temperature is in equilibrium with the temperature of the ocean surface or the mixed layer (generally the top few tens of metres of the ocean). But heat is being slowly transmitted to the deep ocean and ocean height reflects the temperature of the entire ocean. So the relation between ocean height and atmospheric temperature might need the forcing variable to complete it over the length of the annual time series available. Also of course the oceans are not simply rising from thermal expansion but due to meltwater from glaciers and ice sheets.