The previous post showed what I think is a plausible calculation of deep ocean temperature in 1880 that I will now use to initialize the 3 box model and fit the GISS temperature data. This model includes all the GISS forcings (http://data.giss.nasa.gov/modelforce/) which go from 1880 to 2003. These have been extrapolated to 2020 for the figure below, except for solar forcing, where the data at: http://www.pmodwrc.ch/pmod.php?topic=tsi/composite/SolarConstant
has been used from 1990 to 2009, and kept constant from 2009 to 2020. Keeping future solar forcing constant allows easier interpretation of model results.
Speculation on results:
I think the warmer deep ocean box allows a better fit (especially for 1930 to the present, where presumably the temperature and forcing data are more accurate). It appears much of the warming before 1960 might be attributed to 'recovery from the LIA' as the deep ocean pulls temperatures up (these temperatures are all anomalies, so an absolute cold deep ocean can cause a relative increase in a warmer surface).
A lower sensitivity to forcing is sufficient for recent GHG concentrations to cause a rapid temperature increase from about 1980 to 2001 without much heat sinking from the deep ocean. This lower forcing sensitivity (equivalent to CO2 doubling sensitivity of 1.8K) combined with negative solar forcing could be the cause of the recent temperature plateau.
This 3 box model excel file is available at: