The 3 box model I posted last month would be much more interesting if the deep ocean box had more impact. Especially needed is long term data to get something other than a guess for the deep ocean box temperature. Note that what I intend to do here is to make the parameters used in my model more plausible; I'm not claiming any of this is 'the right answer'.
Recently, Hu McCulloch reviewed a new paper by Kaufman et. al. at Climate Audit: http://www.climateaudit.org/?p=7005
"Darrell S. Kaufman, David P. Schneider, Nicholas P. McKay, Caspar M. Ammann, Raymond S. Bradley, Keith R. Briffa, Gifford H. Miller, Bette L. Otto-Bliesner, Jonthan T. Overpeck, and Bo M. Vinther (Science 9/4/2009) propose a reconstruction of Arctic summer land temperatures for the last 2000 years, using 23 diverse proxies."
This time frame of 2000 years is interesting compared to deep ocean response times, and the Arctic temperature may correlate well with sinking ocean currents. Both McCulloch and McIntyre find significant issues with Kaufman. McIntyre proposes a sensitivity variation on the base Kaufman proxies:
What I have done is to average these two variations for ModerateClimate input. This at least adds diversity to the proxies and removes the effect of the proxies used in disputed polarity:
Click on image for better resolution.
This shows a Roman warm period higher than the Medieval warm period and comparable to the modern warm period. Thanks to McIntyre for turnkey R code to produce the input data. A spreadsheet for the above is at: http://spreadsheets.google.com/ccc?key=0Als9xXZMCAXsdGlRMThhTjdGOWFEZ3VaWWtGZWVRNEE&hl=en
The units used here are not calibrated to temperature, so I converted to temperature by multiplying by 0.7, which very roughly agrees with the modern instrumental record. These values were then used to force the shallow ocean temperature in my previously described timestep simple climate model. The specific spreadsheet used here is the lngmod tab of the above link.
The result is a deep ocean (orange line in the figure) retaining a temperature from the Roman and Medieval warm periods that is much above the more recent pre-industrial level.