Posted on March 1st, 2012 in Isaac Held's Blog
Some feedbacks in AR4 models, from Held and Shell 2012. The three red columns on the right provide the traditional perspective: the “Planck feedback”– the response to uniform warming of surface and troposphere with fixed specific humidity (), the lapse rate feedback at fixed specific humidity (), and the water vapor feedback (). The three blue columns on the left provide an alternative perspective — with the fixed relative humidity uniform warming feedback (), the fixed relative humidity lapse rate feedback, (), and the relative humidity feedback (). The sum of the three terms, shown in the middle black column, is the same from either perspective. Surface albedo and cloud feedbacks are omitted. Each model is a dot.
This is the continuation of the previous post, describing how we can try to simplify the analysis of climate feedbacks by taking advantage of the arbitrariness in the definition of our reference point, or equivalently, in the choice of variables that we use to describe the climate response. There is nothing fundamentally new here — it is just making explicit the way that many people in the field actually think, myself included. And if you don’t like this reformulation, that’s fine — it’s just an alternative language that you’re free to adopt or reject.
The simplest way to think about this reformulation it that it describes climate change in terms of changes in temperature and relative humidity rather than temperature and specific humidity (or water vapor concentration or vapor pressure). Consistently, the reference response is computed by assuming that the surface and troposphere warm uniformly while relative humidity within the troposphere remains unchanged.
The key is the claim that fixing the relative humidity is a much more natural starting point than fixing specific humidity. I am open to new observations or models that point in a different direction, but I don’t see anything on the horizon that looks like it will modify my personal expectation in this regard. I will try to explain why I feel this way in forthcoming posts. But here are a general comment to think about in the meantime:
We want to use a reference response that is physically meaningful in itself — ie, that doesn’t require “feedbacks” to be present to ensure that it remains physically meaningful as climate changes. But specific humidity can’t remain fixed as we cool the climate — the atmosphere would become supersaturated in a lot of places. And this would happen pretty quickly; the amount of cooling at the peak of the last glacial would be more than enough. Why should fixing specific humidity be a useful starting point as we warm but not as we cool the atmosphere? We would have to argue that there is something special about the position of the present climate in the space of climates with different temperatures.
Using the same notation as in the previous post, and ignoring clouds and surface albedos, in the traditional formulation we have
where the three terms on the right account respectively for the effect on the incoming top-of-atmosphere flux of a uniform increase in temperature of the surface and the troposphere, the effect of differences between the tropospheric and surface temperature responses, and the effects of the increase in water vapor. In equilibrium,
where the reference response with fixed specific humidity is and where and . Estimates from the AR4 models are shown in red in the figure above.
We now divide into three terms: the effect on the flux of the increase in vapor needed to maintain fixed relative humidity, assuming that the troposphere warms by the same amount as the surface (); the effect of the additional vapor needed to maintain relative humidity given that the tropospheric and surface warming differ (); and the effect of changes in relative humidity (). We can then define the effect of warming the troposphere equal to that of the surface, with fixed relative humidity, as , and the effect of the lapse rate change with fixed relative humidity .
The decomposition on the left side is shown for the same AR4 models in the blue columns in the figure. Corresponding to this reformulation, we can also define a new reference response, and non-dimensional feedback strengths, and .
So you can describe these model responses as starting with the fixed relative humidity-no lapse rate change reference (about 1.75 (W/m2)/K) with a bit of negative (I had written “positive” originally — IH–3/6) fixed relative humidity-lapse rate feedback (about 0.25 (W/m2)/K) and very small relative humidity feedback, leading to the 2 (W/m2)/K total in the absence of any surface albedo or cloud feedbacks. I think we can agree that this is a simpler picture of the model responses, avoiding the cancellation between the large positive water vapor and negative lapse rate feedbacks.
A key point is that the scatter among the models in the individual terms is now considerably smaller. The tendency for water and lapse rate feedbacks to be negatively correlated across models has been noted since these feedback analyses were first performed across multiple models (Zhang, et al, 1994) and has been discussed recently by Ingram, 2010. (I’ll like to return to Ingram’s paper in a future post — there is also the possibility of going a step further and distinguishing between holding tropospheric relative humidity unchanged at a fixed height and holding it unchanged at a fixed temperature.) At least from this perspective of the model responses, avoiding the negative correlation seems like a very helpful simplification.
Another interesting point is that the fixed relative humidity lapse rate feedback is negative, albeit small. This is the basis for my response to a question on post #20 regarding why I thought that negative lapse rate feedback wins out over increased water vapor feedback when a model’s tropical upper tropospheric warming is increased.
It is also interesting to add other sources of feedbacks, like clouds, into the mix. The cloud feedback as measured by is unchanged by anything said here. But the non-dimensional measure is changed, from to . In the traditional perspective, cloud feedback is effectively thought of as independent of water vapor feedback. But if cloud feedback is negative, say, then the resulting reduction in the temperature response will reduce the water vapor in the atmosphere, assuming fixed relative humidity, which makes the effect on temperature of this negative feedback stronger. I think this way of looking at things gives us a better picture of the net effect of cloud feedbacks.
It is also worth thinking about this reformulation from the perspective of the issue of skewness in our uncertainty in climate sensitivity (ie Roe and Baker, 2007). If we have a distribution of values of that is symmetric about its mean, then the distribution of will be skewed with a long tail towards higher values. But in this reformulation, we have increased the value of the reference response, the numerator in , and increased the denominator by the same ratio, so we have decreased the total . How does this square with the skewness argument, since I have repeatedly stressed that we’re not changing anything about the final result, just our interpretation of it? I’ll leave this for the reader to think about.
Note added March 5:
One e-mail has asked why there isn’t more spread in the “reference” responses, either with fixed specific or with fixed relative humidity. Another e-mail asks why there is any spread at all in these reference responses.
In this paper, we have used a single radiative code for all computations, and we also assume a single unperturbed climate state. We do not use the radiative algorithms or the unperturbed climate states from the individual models. So we are in that sense underestimating the intermodel spread in these reference responses. Differences in clouds in the unperturbed climate states simulated by the models are probably the biggest source of spread (the effects of an increase in temperature or water vapor on infrared emission to space depends especially on what the prescribed high cloud cover is.)
So why is there any spread at all in the and columns in the figure? Because the reference responses are computed by assuming that the troposphere warms by the same amount as the surface at each horizontal location, but without assuming that the warming is horizontally uniform. Alternatively one could define the reference response to be what one gets by assuming a uniform warming both horizontally and vertically. With the latter definition, there would be no spread at all in the reference responses, and the “lapse rate” feedback would account for all spatial inhomogeneity in the warming, both horizontal and vertical. The latter definition is simpler but the differences are quite small and we decided to retain consistency with some of our own earlier papers. So the spread that you do see is the very small effect of the differences among models in the horizontal non-uniformity of the warming at the surface.
[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.]