Ou (J Clim 2001), " Possible Bounds on the Earth’s Surface Temperature" is an attempt to explain why a climate “not unlike the present-day one has prevailed on the earth since its early history when the sun was considerably dimmer”, a question that Lee was musing about and, IMHO, an interesting question. The tricky thing is how you get both ice age and hothouse periods not only without careening out of control, but going to the other side, again without careening out of control. Ou also has a more recent article on the same topic that I’ve noticed but haven’t read. I’m not vouching for anything here other than I found the article interesting and the question stimulating. Most climate models have very strong positive feedbacks and intuitively one feels that if they were applied to the history of the Earth, they would have projected the Earth turning into either Venus hothouse or Mars icehouse long ago. (I don’t "know" that they would do this, it’s just an impression.)
Ou poses the following question:
How the earth maintains this climate is a matter of speculation, and many possible scenarios have been suggested. The most widely circulated among them is a much higher concentration of carbon dioxide (CO2) in the atmosphere, which has been attributed to external factors, though poorly constrained by observational data. Also suggested but less explored is a reduced cloud albedo that may offset the solar effect. Since there are no proxy data for the cloud cover, which in addition is an internal variable, this possibility may be assessed only through a model that has included interactive cloud covers. Conversely, without a physical closure that contains variable clouds – which directly affect the energy flow into the system- one simply does not have an explanation of the earth’s temperature. It is the desire to formulate such a model to try to address this faint young sun” paradox that motivates the current study.
Ou noted that GCMs are not helpful for studying the effect of low clouds since, even if they have variable cloud formation, Ou says that the relevant parameters, such as threshold relative humidity for cloud formation are “tuned” by GCMs to yield the present observed cloud covers and therefore are of little use for modeling "fundamental changes". He noted that there have been few attempts to determine the earth’s temperature from first principles, mentioning Paltridge’s maximum entropy work as an exception. In this connection, he noted that Paltridge justified maximizing a thermodynamic quantity on the basis that the underlying system contained more degrees of freedom than could be practically constrained and followed this sort of strategy, in Ou’s case, by maximizing turbulent wind at the surface, said to correlate strongly to the kinetic energy dissipation (i.e. internal entropy formation) as follows:
Similarly, since a maximization of the internal entropy production implies a minimized entropy exchange with the surroundings (there could be no change of entropy in the steady state), Paltridge (1978) used the latter to determine the latitudinal distribution of surface temperature and cloud cover and met with considerable success, further underscoring the thermodynamic nature of the system. Since such extremization principles, if operative, are properties of a dissipative thermodynamic system, they should be equally applicable to vertical as to latitudinal models.In the view of the current theory, the cloud covers merely adjust to whatever is required by global balances, and their regulatory effects enter mainly through the internal degrees of freedom they endow upon the system. In other words, rather than a low cloud that cools the surface, it is the surface temperature- somewhat independently constrained by water properties- that determines the cloud covers through global heat balance.
Ou has separate degrees of freedom for high clouds (e.g. cirrus, storm tracks which are characterized as SW transparent and LW black) and for low clouds (stratus etc., characterized as black SW and LW). Here’s a diagram of the components in his system:
Original Caption: The surface, the top of the air-sea interfacial layer, the top of the low clouds, and the tropopause. Because of the shallowness of the low clouds, no distinction in height is made between level 2 and the LCL. Variables with a numerical subscript indicate global means at the respective level, which may differ from their values in the updrafts. The symbols A, N2, N3 indicate fractional areas occupied by the deep updrafts, the low, and high clouds, respectively; u9 is the turbulent wind velocity at level 1; and w and wi are the vertical velocities of the deep updrafts and the settling ice (both taken as positive), respectively.
Adding some piquancy to the low cloud issue is that these seem to be somewhat problematic in GCMs. It was my impression, although I hasten to say that it is merely an impression, that IPCC TAR GCMs tended to under-formation of stratiform clouds (and this was a systemic bias in the ensemble in the sense that none over-formed stratiform clouds.) I also noticed that, in the climateprediction.net model, one of the frequent causes of "bad runs" is the "cold equator problem" and I recall vaguely that this was connected to clouds and this might be connected (or might not be).
Ou’s most striking conclusion from his model is that a +-50% variation in solar constant results in only a 10K difference in surface temperature. (A 4 wm-2 variation, the standard 2xCO2 forcing, would proportionally yield a 0.11K change in surface temperature.) I don’t have strong views on this. If I’ve said something incorrect here, as I could easily have, it won’t disprove observations that I’ve made about Mann’s proxy methodologies, although I’m sure that some of the lurking trolls will try to use such an eventuality as fuel. In posting this, I’m simply trying to be constructive in response to an interest shown by a reader.
Reference: Ou (2001) Possible Bounds on the Earth’s Surface TemperatureJ Clim 2001, 2976) http://www.earthinstitute.columbia.edu/generalInfo/CEImembers/about/Ou_JournalClimate.pdf