Forcings and feedbacks

After my lengthy exchange with Roger Pielke Sr, I thought I might write a quick post about forcings and feedbacks. I thought I might also comment on this tweet from Roger

“I also don’t think that the term forcing in climate science is quite equivalent to a force in physics.” Wow https://t.co/FiQVC0X2Re

— Roger A. Pielke Sr (@RogerAPielkeSr) May 21, 2015

I’m really not sure quite why this is a “Wow” thing to have said. The only thing I probably regret saying is “I don’t think” at the beginning. They very obviously are not the same thing. The units are different, and one is a vector (force), the other a scalar (radiative forcing). For clarity, a radiative forcing is

In climate science, radiative forcing or climate forcing, is defined as the difference of insolation (sunlight) absorbed by the Earth and energy radiated back to space.

In physics, a force is

a force is any interaction which tends to change the motion of an object.

Consider Newton’s laws of motion if you want a more extensive discussion of the concept of a force. I can see why climate science uses a forcing/feedback paradigm (a forcing pushes the system out of energy balance, and the feedbacks act to return it to energy balance) but that doesn’t mean that they’re exactly equivalent.

Okay, back to forcings and feebacks. A forcing is some external influence that causes, as pointed out above, a change in the energy balance of the system. For example, if we are in energy balance and there is then a change in forcing of Image may be NSFW.
Clik here to view., then if Image may be NSFW.
Clik here to view. is positive, it means – if nothing else changes – that we’ve moved into a state where we are now accruing energy at a rate of Image may be NSFW.
Clik here to view. Joules per square metre per second. If Image may be NSFW.
Clik here to view. is negative, then we will be losing energy. If the initial energy imbalance was not zero, then Image may be NSFW.
Clik here to view. tells us how much it has changed.

If we are out of energy balance, then that we are accruing – or losing – energy means that we will either warm, or cool. The change in temperature then causes a feedback response, and these are normally quantified with respect to the change in surface temperature (Image may be NSFW.
Clik here to view.). Examples of feedbacks are the Planck response (negative), water vapour (positive), lapse rate (negative), and clouds (probably positive). The units of feedbacks are Image may be NSFW.
Clik here to view., so it tells us what impact that feedback would have on our energy balance if the temperature changed by 1K. If a feedback is positive, it causes additional warming/cooling. If it is negative, it acts to drive us back to energy balance.

Given that our climate is long-term stable, overall feedbacks (including the Planck response) are clearly negative. If not, a small change in radiative forcing would cause runaway warming; it clearly does not. The more interesting question is whether or not the feedbacks other than the Planck response are positive or negative. Our current understanding is that these feedbacks (water vapour, lapse rate, clouds) are overall positive. This means that we expect a change in radiative forcing to be amplified by these feedbacks and for the overall warming to be larger (by a factor of 2 – 3) than would be the case in the absence of these feedbacks.

To put this into a slightly more formal context, consider a situation where – at time Image may be NSFW.
Clik here to view. – we have a planetary energy imbalance of Image may be NSFW.
Clik here to view.. Now consider a later time, Image may be NSFW.
Clik here to view., where there has been a change in forcing of Image may be NSFW.
Clik here to view., and a change in temperature of Image may be NSFW.
Clik here to view.. The planetary energy imbalance, Image may be NSFW.
Clik here to view., at Image may be NSFW.
Clik here to view., will be

Image may be NSFW.
Clik here to view.

where, the second term on the right-hand side is the Planck response (and includes the emissivity, Image may be NSFW.
Clik here to view., of the atmosphere), and the final term is all the other feedbacks. We can rewrite this as

Image may be NSFW.
Clik here to view.

So, the forcings and feedbacks are both determined as changes relative to some earlier time (Image may be NSFW.
Clik here to view., when the planetary energy imbalance was Image may be NSFW.
Clik here to view.) and they, together, tells us how the planetary energy imbalance has changed between time Image may be NSFW.
Clik here to view. and Image may be NSFW.
Clik here to view.. It is, however, a fairly simple formalism and the system is clearly much more complex than this simple formalism can – alone – indicate. However, it is still a useful way to quantify – in a globally averaged sense – how we might respond to changes in forcings, or – if we already have some information – how we have responded to known changes in forcings. We can, essentially, use it to estimate our climate’s sensitivity to changes in radiative forcings.

Anyway, I hope that roughly clarifies the situation with regards to forcings and feedbacks. If anyone has anything to add, or would like to correct something, feel free to do so; there are some complexities that I’ve ignored. I’ll also add that some may be aware – via Twitter – that I’m not very happy with the manner in which Roger has chosen to represent our discussion. However, since this is not WUWT, I’m not really interested in some kind of lengthy discussion about Roger’s behaviour. He can own it, as far as I’m concerned. The only reason I’m saying this is to simply warn commenters that I’ll aim to moderate anything that I regard as non-constructive.