Temperature trend 1960–2012 versus latitude and pressure. The value for each latitude and pressure is the medians of the trends at individual stations in that (10°) latitude bin. Units are °C per decade. From Sherwood and Nishant (2015).

Temperature trend 1960–2012 versus latitude and pressure. The value for each latitude and pressure is the medians of the trends at individual stations in that (10°) latitude bin. Units are °C per decade. From Sherwood and Nishant (2015).

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In this post, I’ll revisit the simple two-layer column model described in the last post. This time we’ll use the model as a way to start thinking about the way we define “climate feedback.”

The top-of-the-atmosphere energy budget has been the vehicle we’ve employed in order to explore how planets come into equilibrium with radiation from their stellar host, and here we wish to further investigate how that equilibrium is obtained. It follows that we ought to be interested in how the outgoing longwave radiation (OLR) varies with surface temperature. By now, you are hopefully familiar with the fact that increasing emissivity (i.e., the greenhouse effect) in the atmospheric column will reduce OLR by shifting the mean emission height to higher, colder levels (keeping temperatures held fixed). We call this radiative forcing, or the instantaneous effect of the increase in column absorption on emission to space. Furthermore, we also know that the temperatures must then increase in order for the OLR to return to its original value. We’ll assume that shortwave absorption by the planet is unchanged, so the OLR (at equilibrium) in the “perturbed emissivity” climate is exactly identical to the value in the unperturbed climate. That zero anomaly in OLR can thus be decomposed into two parts- the radiative forcing that decreased OLR, and an equal but opposite flux that arises from all changes that occurred in the column to get back to equilibrium. It is the latter we’d like to further diagnose, and hopefully make contact with how scientists actually use models operationally in order to quantify feedbacks.

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I have been absent from writing this blog for nearly two years, which sometimes happens when one has an interest in starting a blog. This is a post I felt was worth writing down though. Some of the context might not be entirely clear to those who haven’t gone through an atmospheric science program or picked up some textbooks dealing with climate physics, so I will try to clear that up.

I will try to outline what I feel can be improved in practical instruction of the greenhouse effect, just based on some modification to a toy model that has already been employed in many classrooms and textbooks (some examples are Atmosphere, Ocean and, Climate Dynamics; Global Physical Climatology; Global Warming: Understanding the forecast, all great reads by the way). The framing here can be presented to an upper-undergraduate or graduate classroom, but the calculus can be stripped away for courses with minimal math requirements. Here, my focus is in making better contact with how the greenhouse effect actually works rather than going through algebraic exercises that yield numbers which don’t have any particular special meaning.
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For those interested, I have a blog posting on the new Kepler 69 planets making the news. Here

(comments enabled there)

In previous posts, I have outlined in a few steps the interplay between the radiation balance of a planet, its temperature structure, and the feedback mechanisms that gives freedom for the climate to depart from its reference norm. In the ice-albedo post for example, we have seen a bifurcation structure in which removing enough CO2 (or lowering the sunlight a planet receives) can plunge the planet into a runaway ice-covered state. In this post, I’ll consider the “hot end” of a similar type of bifurcation, although now we enter a regime in which no ice exists and a significant fraction of the atmosphere is composed of water vapor. This would be typical of any ocean planet that becomes sufficiently hot to make water vapor a dominant constituent of the air. More traditional applications of the “water vapor feedback” to the global warming issue will be discussed.

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In discussions of climate change, it is often useful to think about the transition of the climate from one state to another, and ask how the magnitude of the response is related to changes in a control parameter (such as the solar constant, or CO2 concentration). This is the classical problem of climate sensitivity, which is intimately connected with assessing the degree to which Earth has the capacity to change. In such an analysis, we typically begin by reducing the “climate” to a single variable, commonly global mean temperature (T), and gauge its evolution as a function of the control parameter. Of general interest to society, for example, is how the global mean temperature responds to changes in CO2 concentration. I will build up some theoretical background into climate sensitivity in this article, and move on to observations and modeling results in subsequent posts.

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In Part 1 a first, simple model of planetary temperature was discussed, all based on knowledge of how much starlight a planet receives (Q) and how “reflective” that planet is (i.e, its albedo, \alpha, an effect elaborated on in this post).

In the first post, an “effective temperature” was solved for of the form:

\displaystyle T_{e}= [\frac{Q (1- \alpha)} {\sigma \mu}]^{0.25}

where \mu is a geometrical redistribution term that accounts for how well the input of stellar energy is evened out across the planet by rotation/thermal inertia and planetary motions. For a sufficiently rotating planet with an advecting atmosphere, it takes the value of ~4, but it would be more appropriate to take on a different local value on an airless body incapable of transporting much heat around (concerning the question of habitability, this could set up a regime in which water could exist in liquid form over parts of a planet but not others).

We now introduce the effect of an atmosphere that can interact with the radiation entering or exiting the planet. On Earth, that interaction is predominately in the infrared (the outgoing energy) via absorption/emission processes and is accounted for by trace gases in the atmosphere, which we refer to as greenhouse gases (water vapor, carbon dioxide, methane, nitrous oxide, etc); the interaction can also occur with aerosol particles in the atmosphere and with clouds, though these latter two also tend to scatter shortwave solar energy and cause a net cooling effect on Earth (there are exceptions to this, such as black carbon). Ozone interacts in the infrared as a greenhouse gas, but also absorbs incoming UV radiation high in the stratosphere to set up a persistent thermal inversion where temperatures increase with height.

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