Fitting satellite data with the 3 box model

Here is a fit of the average of UAH and RSS satellite temperature data using my 3 box model:

The light blue line is the average of UAH and RSS LT data with very light smoothing (over 3 months) to make comparison easier with the heavy blue line representing temperature of the atmosphere box in the 3 box model described previously.
I get the best match to the recent plateau in atmosphere temperature with climate sensitivity parameter set at just 1.2 K (per equivalent CO2 doubling). Most other parameters are the same that fit GISS data (plotted as red yearly values) since 1880. The fit for the model global average (orange) is not as good for recent GISS data now, which is not surprising since they are different data sets representing different aspects of the climate.
The main reason the model is able to reproduce the recent plateau is the reduction in solar forcing balances the forcing increase from GHG for the atmosphere box. Well mixed ocean temperature is still increasing slowly. The projected portion of the plot assumes GHG forcing continues to increase and solar stays at its current low level.

Fitting GISS temperatures with a warmer deep ocean

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:
http://spreadsheets.google.com/ccc?key=0Als9xXZMCAXsdDlQZzItRW5FWndCN2J0ODRzR0RZT3c&hl=en

Long term data for 3 box model

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:
http://www.climateaudit.org/?p=7054

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.

3 box model

I have extended my 2 box model to 3 boxes:

http://spreadsheets.google.com/ccc?key=0Als9xXZMCAXsdENKbUc1UnVtaVluNXJEYjNMNlZvd0E&hl=en


There is not much change in deep ocean temperature (about 0.05K from 1880 to now). However, it changes another 0.05K in just ten more years if forcing stays at the last (2003) value provided by GISS.

2 box model

Yet another 2 box climate model. Excel file model available here:
http://spreadsheets.google.com/ccc?key=0Als9xXZMCAXsdHlZSkI1UWhuZVJZUmFhUVNBLUtxc0E&hl=en

Click the image to see graph detail.



Since my model uses a different technique than some recently discussed fitting models, not all parameters may correspond, but this is what I use for heat capacities:
Co=400 MJ/(K-m^2) Heat capacity of ocean box (~100m well mixed depth)
Ca= 50 MJ/(K-m^2) (Comparable to Cs?) Heat capacity of atmosphere box (~3x higher than dry air, due to heat required to maintain constant RH?).

Most of the other fitting parameters are the heat conductivities between the boxes and outside (in W/(K-m^2)):
Gao = 3.0 atmosphere to ocean
Godo=0.22 ocean to deep ocean
Gsa =1.78 space to atmosphere (this corresponds to 2.25K climate sensitivity if CO2 doubling causes 4 W/m^2 forcing).

Other assumptions are:
Both space and deep ocean are heat sinks at -0.1 K from the GISS baseline
All forcing is applied to the atmosphere box.
The temperature to compare to GISS land-ocean data is a weighted average (Ta+2To)/3 based on area.

There are some additional comments in the spreadsheet itself.