But your papers claim of a «bias» in the surface temperature record * if * it is used as a linear predictor
of atmospheric heat content only makes sense * if * indeed people had used it in that sense.
If La Nina / El Nino can affect global air temperatures in a period of a few years, than other changes in ocean currents (driven by AGW) can affect
global atmospheric heat content in a few years.
As indicated above, TMin is a poor proxy
for atmospheric heat content, and it inflicts this problem on the popular TMean temperature record which is then a poor proxy for greenhouse warming too.
This is due to the unabated upward trends in human population growth (6),
atmospheric heat content, and OA (2).
We continue to «discover» vast, active volcanoes in the deep oceans, could they not have an impact on ocean heat content and via that
the atmospheric heat content?
As you said, the oceans count and
atmospheric heat content is negligible compared to OHC.
With respect to your statement that «No one calculates the surface temperature (which is well observed) using
the atmospheric heat content».
In fact, recent measurements are that
the atmospheric heat content is going down.
Not all at once of course, but as mentioned above, when the PDO goes positive, we can likely expect a significant change in
the atmospheric heat content as heat energy is transferred from the deep oceans back into the atmosphere.