A recent article by Lord Christopher Monckton over at WUWT argues that there has been an “elementary error of physics” that has led to climate sensitivity being overestimated by about a factor of 2.

I agree with the conclusion but not the reason why. It is already known from the work of Otto et al. (2013), Lewis & Curry (2015) and others that the climate system (including the deep oceans) has warmed by an amount that suggests a climate sensitivity only about half of what the models produce (AR5 models warm by an average of 3.4 deg. C in response to a doubling of CO2).

But the potential reasons why are many, and as far as I can tell not dependent upon Christopher’s arguments. For those who don’t know, Lord Monckton is a pretty talented mathematician. However, like others I have encountered over the years, I believe he errs in his assumptions about how the climate research community uses — and does or does not depend upon — the concept of feedback in climate modeling.

You Don’t Have to Use F-Words

I’ve been told that the feedback concept used by climate researchers is a very poor analog for feedbacks in electrical circuit design. Fine. It doesn’t matter. How modern 3D coupled ocean-atmosphere climate models work does not depend upon the feedback concept.

What they DO depend upon is energy conservation: If the system is in energy equilibrium, its average temperature will not change (that’s not precisely true, because it makes little sense energetically to average the temperature of all ocean water with the atmosphere, and there can be energy exchanges between these two reservoirs which have vastly different heat capacities. Chris Essex has written on this). The point is that the total heat content of the system in Joules stays the same unless an energy imbalance occurs. (Temperature is focussed on so intensely because it determines the rate at which the Earth sheds energy to outer space. Temperature stabilizes the climate system.)

The amount of surface temperature change in response to that energy imbalance is, by definition, the climate sensitivity, which in turn depends upon feedback components. You can call the feedbacks anything… maybe “temperature sensitivity parameters” if you wish. Feedback is just a convenient term that quantifies the proportionality between an imposed energy imbalance and the resulting temperature change response, whether it’s for a pot of water on the stove, the climate system, or anything that is initially at a constant temperature but then is forced to change its temperature. Christopher’s claim that the Earth’s effective radiating temperature (ERT) to outer space (around 255 K) itself causes a “feedback” makes no sense to me, because it isn’t (nor does it represent) a “forcing”. Feedbacks, by the climate definition, are only in response to forced departures from energy equilibrium.

The proportionality factor between a forcing (another f-word) and temperature response in climate parlance is called the net feedback parameter, and has units of Watts per sq. meter per deg. C, usually referenced to a surface temperature change. You could come up with a sensitivity parameter for a pot of water on the stove, too. In the climate system the net feedback parameter has components from temperature-dependent changes in clouds, water vapor, etc., as well as the Sigma-T^^4 “Planck” effect that ultimately stabilizes the climate system from experiencing large temperature fluctuations.

Now, in the process of describing climate change in simple terms with such proportionalities between imposed energy imbalance and temperature response, various feedback equations have been published. But NONE of the IPCC models depend upon any formulation of any feedback equation you wish to devise. Neither do they depend upon whether the Earth’s natural greenhouse effect on surface temperature is estimated to be 33 deg. C, or 75 deg. C (Manabe & Strickler, 1964), or any other value. Nor do they depend upon how that 33 deg or 75 deg is apportioned from different components. These are all conceptual constructs which help us understand and discuss the climate system, but the climate models do not depend upon them.

Modern 3D climate models are basically weather forecast models (with an ocean model added) that are run for a hundred years or more of model run time (rather than 3-14 days, which is pretty common for weather forecast models). One of the biggest differences is that climate models have been tuned so that they keep a relatively constant temperature over a long integration, which also means their rates of energy gain (from the sun) and energy loss to outer space are, in the long term, equal. (I question whether they actually conserve energy, but that’s a different discussion).

Once you have a model whose temperature does not drift over time, then you can impose a forcing upon it. All that means is impose an energy imbalance. Once again, it doesn’t matter to the physics what you call it. To change the energy balance, you could increase the solar input. Or, you could reduce the rate of radiative cooling to outer space, e.g. from increasing atmospheric CO2. The point is that forcing is just an imposed energy imbalance, while feedback quantifies how much of a temperature response you will get for a given amount of forcing.

As the climate system warms from an energy imbalance, a wide variety of changes can take place (clouds, water vapor, etc.) which affect how much warming will occur before energy balance is once again restored, and the system stops warming. Those component changes, for better or worse, are called “feedbacks” (e.g. cloud feedback, water vapor feedback). Again, you don’t have to use the f-word. Call it anything you want. Its just a proportionality constant (or not a constant?) that quantitatively relates an energy imbalance to a temperature response.

Nowhere do the IPCC models invoke, use, assume, or otherwise depend upon any feedback equations. Those equations are just greatly simplified approximations that allow us to discuss how the climate system responds to an imposed energy imbalance. If somebody has published a paper that incorrectly explains the climate system with a feedback equation, that does not invalidate the models. There might be many errors in models that cause them to be too sensitive, but how someone misrepresents the model behavior with their favorite feedback equation is that person’s problem… not the model’s problem.

Feedbacks in the IPCC models are diagnosed after the model is run; they are not specified before it is run. Now, it IS true that how some uncertain model processes such as cloud parameterizations are specified will affect the feedbacks, and therefore affect the climate sensitivity of the model. So, I suppose you can say that feedbacks are indirectly imposed upon the models. But there isn’t a feedback factor or feedback equation input into the model.

The ultimate climate sensitivity of the models to an energy imbalance (say, increasing CO2) depends upon how clouds, water vapor, etc., all change with warming in the model in such a way to make the warming either large or small. The equations in the models governing this involve energy and mass conservation, moisture, thermodynamics, dynamics, radiation, etc., along with some crucial approximations for processes which the models cannot resolve (e.g. cloud parameterizations, which will affect cloud feedback) or which we do not even understand well enough to put in the models (e.g. temperature-dependent changes in precipitation efficiency, which will affect water vapor feedback).

But nowhere does the sensitivity of modern 3D climate models depend upon any feedback equations.

Now, if I have misrepresented Lord Monckton’s argument, I apologize. But I am having difficulty determining exactly what his argument is, and how it affects the processes specified in climate models. Maybe someone can help me. We can agree that the models are too sensitive, but we must make sure our arguments for their excessive sensitivity make sense, or we will continue to be dismissed out of hand by the mainstream climate community.