I have, incidentally, found using a multilayer diffusive ocean model that there is a near complete identity in the path of the model surface temperature response to a step forcing, for the better part of a century, over a wide range of equilibrium climate sensitivities if
effective ocean diffusivity is varied to compensate.
Using
an effective ocean diffusivity of 0.65 cm ^ 2 / s (which is the central estimate derived in the Forest 06 study), the surface temperature response to a step forcing increase reaches about 90 % of its ultimate level within 25 years, if I've got everythng right.
Effective ocean diffusivity, Kv, and total aerosol forcing, Faer, are estimated simultaneously with S.
NL: I note that the PDFs for
Effective Ocean Diffusivity from the 2008 and 2011 studies also differ substantially, with that from Libardoni and Forest 2011 being even further from the PDF in Forest 2006.
At least with a model like the MIT one used in Forest 2006 one can (if the descriptions of it are correct) set the key climate sensitivity,
effective ocean diffusivity and aerosol forcing levels independently and with some confidence (I'm not the person to ask how much) that the simulated results reflect those settings.
CEF Response:
The effective ocean diffusivity, Kv, is discussed in Sokolov & Stone (1998, Clim.
A detailed reanalysis is presented of a «Bayesian» climate parameter study (Forest et al., 2006) that estimates climate sensitivity (ECS) jointly with
effective ocean diffusivity and aerosol forcing, using optimal fingerprints to compare multi-decadal observations with simulations by the MIT 2D climate model at varying settings of the three climate parameters.
Not exact matches
The treatment of uncertainty in the
ocean's uptake of heat varies, from assuming a fixed value for a model's
ocean diffusivity (Andronova and Schlesinger, 2001) to trying to allow for a wide range of
ocean mixing parameters (Knutti et al., 2002, 2003) or systematically varying the
ocean's
effective diffusivity (e.g., Forest et al., 2002, 2006; Frame et al., 2005).
In particular, equilibrium climate sensitivity (S),
effective vertical deep
ocean diffusivity (Kv) and total aerosol forcing (Faer) have been estimated in this way.
The fact is that
effective diffusivities of the
ocean are higher than that of land.
If there's no mixing lower (
effective diffusivity = 0) that extra energy only has to warm up a volume of water 1/10 as large as the entire
ocean.
That will raise the temperature of the entire
ocean about 0.2 C with infinite
effective diffusivity in one century.
The larger the
effective diffusivity is, the more temperature changes will be masked by the heat sink that is the
ocean.
I tell you what I would do for temperature, which is to analyze the heat equation and evaluate how much the
ocean would uptake assuming there is an uncertainty in the
effective diffusivity and a smearing of the stimulating thermal interface.
For climate sensitivity the data are limited and have large errors, and are non-linearly related to sensitivity (and to
ocean effective diffusivity, often estimated alonside sensitivity).