Simple equations clarify cloud climate conundrum

Tight physical and observational constraints suggest the anvil cloud area feedback is weak, but the anvil cloud albedo feedback remains highly uncertain.
Published in Earth & Environment and Physics
Simple equations clarify cloud climate conundrum

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The problem

According to the Intergovernmental Panel on Climate Change (IPCC), clouds are the largest source of uncertainty in predicting future global warming. Tropical anvil clouds are particularly hard to constrain because, unlike most other clouds, they are effective at both reflecting sunlight and trapping heat. They start as towering clouds of deep convection, which mainly reflect sunlight that would otherwise heat the surface. As they age, the air in their cores flows out from their tops, around twelve kilometers high, to produce wispy cirrus which mainly insulate Earth’s heat from escaping to space. 

Anvil clouds can span up to hundreds of kilometers in length and can number in the hundreds to thousands across the tropics. With such a large collective area, they have a large impact on Earth’s radiation balance, and potentially on global warming. A few years ago, it was hypothesized that anvil clouds should shrink as temperatures rise. According to this “stability iris hypothesis”, when the atmosphere warms, it moistens and becomes more convectively stable. This enhanced stability inhibits the convective towers and outflows that form anvil clouds, leading to a reduction in their area.

This hypothesis has been verified in tropical-wide satellite observations of year-to-year anvil cloud variability; and it can explain the response of anvil cloudiness to warming across diverse climate simulation configurations. The problem is whether this reduction in area will lead to a positive, negative, or neutral feedback on global warming; and whether other changes in anvil clouds, such as their optical thickness, might also contribute to the uncertainty.

The findings

For many years, qualitative arguments have suggested that an anvil cloud area feedback should be small because anvils, in fact, reflect as much sunlight as they insulate heat over the course of their lifetime. All else being equal, changing their area shouldn’t have much effect on global warming. But this insight is qualitative (as opposed to quantitative) and thus does not really say how small it should be. It also neglects the potential influence of low clouds beneath anvils. In more quantitative assessments such as the IPCC report, the area feedback is often lumped together with the anvil cloud optical depth feedback, which relates to how opaque and reflective the cloud is, so its magnitude and uncertainty are still obscured.

To better separate these distinct feedbacks, and to bridge the gap between qualitative intuition and quantitative results, we (me and my coauthors Sandrine Bony and Jean-Louis Dufresne) devised a way to calculate feedbacks with simple equations. It was an approach that harkened back to our days studying physics in university. As soon as these equations were derived, we knew we could use them to constrain the anvil cloud area feedback. We did a rough calculation on a piece of paper to sketch out how the radiative neutrality of anvil clouds should lead to a small area feedback (about -0.02 Wm-2K-1, which is many times smaller than the feedback from stratocumulus clouds for example).

Equations we derived to study the anvil cloud area feedback. This was the first time we realized our equation could help refute a large anvil cloud area feedback.
Equations we derived to study cloud feedbacks. Here, we realized for the first time that we could use these equations to refute a strong anvil cloud area feedback.

In the published paper, we refine the equations to account for the impact of low clouds beneath anvils, and we quantify the feedback more precisely by inputting satellite observations of cloud area and radiation into our equations. It turns out that the radiative neutrality of anvil clouds implies they must change in area by about 50% for every degree of warming to make a modest feedback (0.2 Wm-2K-1). We looked at observations of year-to-year variability in anvil clouds across the tropics and found they only change at about 9% K-1. The stability iris hypothesis suggests they should only change at about 2-3% K-1. Both of these estimates are far less than what is required for a large feedback, so we can, for the first time, confidently rule out a strong area feedback.


We then tried to apply this method to constrain part of the optical depth feedback. However, it was much less successful because there is no theory for how optical depth should change, and our observational analysis suggests anvil clouds thicken with warming, whereas other analyses suggest they thin. For these reasons, we conclude the anvil cloud optical depth feedback to be a major source of uncertainty that should be addressed in future studies.

To solve this problem, a good place to start might be coming up with a hypothesis for why anvil cloud optical depth should change, and then using it to help interpret simulations and observations. Such an approach would help the more sophisticated methods of feedback analysis found across the scientific literature, because our ability to predict climate change has always been rooted in physical understanding. 

We think our work could help the research community by making it easier to link observations and physical understanding to predictions of cloud feedbacks and climate change.

This work is published in Nature Geoscience as Weak anvil cloud area feedback suggested by physical and observational constraints. See the press release from the University of Exeter for additional context. 

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Climate Sciences
Physical Sciences > Earth and Environmental Sciences > Earth Sciences > Climate Sciences
Classical and Continuum Physics
Physical Sciences > Physics and Astronomy > Classical and Continuum Physics

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