Posted on February 28th, 2012 in Isaac Held's Blog
This post is concerned with arbitrariness in the terminology we use when discussing climate feedbacks. The choice of terminology has no affect on the underlying physics, but it can, I think, affect the picture we keep in our minds as to what is going on, and can potentially affect the confidence we have in this picture.
In feedback analyses of a climate response to some radiative forcing, we start with a reference response, the response “in the absence of feedbacks”, and then we look at how this reference response is modified by feedbacks. An electrical circuit analogy often comes to mind, with the reference response analogous to the unambiguous input into a circuit. But the choice of reference response in our problem is ultimately arbitrary. The following is closely based on the introductory section of Held and Shell 2012.
My starting point is the same as that for several other posts: an expression for the net incoming flux of energy at the top of the atmosphere. Here I am just going to think of the incoming energy flux as a function of three numbers, , where is the forcing agent and where and are two other things that depends on. Perturbing our forcing agent we define the radiative forcing as . I’ll assume that is positive. To establish a new equilibrium we need or
We could stop here, treating and on an equal footing. But suppose that we are mostly interested in . (In fact, let’s suppose that is the global mean surface temperature.) We no longer treat and in the same way but instead write the surface temperature response as
where and is a measure of B-feedback. (In using this terminology, we are presuming that can be thought of as proportional to — see post #22). The reference response in the absence of B-feedback is just . We can then write
where is a non-dimensional measure of the -feedback.
Now I am going to make a choice for that may seem a little odd — I’ll choose to be the tropospheric temperature. Most infrared photons escaping to space are emitted from the troposphere rather than the surface. If the troposphere does not warm, then to regain energy balance the surface has to warm by an order of magnitude more than if the tropospheric warming were comparable to that of the surface. If the surface and tropospheric responses are, in fact, comparable, this would be described as a large negative tropospheric feedback drastically reducing the magnitude of the reference response (the response at fixed tropospheric temperature).
This is clearly not the traditional formulation! The standard choice would be to set equal to the surface temperature minus the tropospheric temperature, so that -feedback would become lapse rate feedback. The reference response is now the response you get in the absence of lapse-rate feedback and is now much smaller — and the feedback relatively modest.
But what is wrong with this tropospheric feedback picture? It doesn’t change the final answer — it just makes for a different decomposition between reference response and feedback. The main problem is that the no feedback limit, in this tropospheric feedback perspective, is not physically plausible. Warming the surface without warming the troposphere would destabilize the atmosphere, and atmospheric circulations would develop to transfer energy from the surface to the troposphere to fight off this destabilization. Atmospheric models of all kinds as well as observations (especially on interannual time scales) are consistent with this picture. By choosing an unphysical reference response, we end up with a framework in which the total response is a small difference between two large terms. It’s not that it’s wrong; it’s just not natural.
The picture becomes even more problematic if we add another effect to the mix, for example a positive surface albedo feedback that we would typically think of as modest. For a given size of the radiative effect of the albedo change per unit surface warming, , in (W/m2)/K, the non-dimensional measure of the strength of the feedback, will be very large because the reference response, , is very large if one uses the tropospheric feedback framework. One is effectively evaluating the importance of albedo feedback by estimating how much it would increase temperatures while thinking that temperature perturbations are only damped by those infrared photons emitted by the surface. But this albedo feedback would never, in reality, operate in the absence of the strong negative “tropospheric feedback.” So one gets a very skewed picture of the underlying dynamics, despite the fact that this is simply making a particular, unconventional, choice of reference response.
Those of you who have glanced at the paper linked to above will realize that by introducing the idea of the arbitrariness of the reference response, what I am really trying to do here is soften you up to the idea of redefining how we talk about water vapor feedback — by using a fixed tropospheric relative humidity, rather than fixed specific humidity, as the reference response. More about this in another post.
[The views expressed on this blog are in no sense official positions of the Geophysical Fluid Dynamics Laboratory, the National Oceanic and Atmospheric Administration, or the Department of Commerce.]