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Positive Feedback in Climate: Stabilization Or Runaway, Illustrated by a Simple Experiment Jean-Louis Dufresne, Marion Saint-Lu

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Positive Feedback in Climate: Stabilization Or Runaway, Illustrated by a Simple Experiment Jean-Louis Dufresne, Marion Saint-Lu Positive feedback in climate: stabilization or runaway, illustrated by a simple experiment Jean-Louis Dufresne, Marion Saint-Lu To cite this version: Jean-Louis Dufresne, Marion Saint-Lu. Positive feedback in climate: stabilization or runaway, illus- trated by a simple experiment. Bulletin of the American Meteorological Society, American Meteoro- logical Society, 2016, 97 (5), pp.755-765. 10.1175/BAMS-D-14-00022.1. hal-01384430 HAL Id: hal-01384430 https://hal.archives-ouvertes.fr/hal-01384430 Submitted on 26 Oct 2016 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Generated using the official AMS LATEX template—two-column layout. B ULLETINOFTHE A MERICAN M ETEOROLOGICAL S OCIETY Positive feedback in climate: stabilization or runaway, illustrated by a simple experiment. JEAN-LOUIS DUFRESNE ∗ Laboratoire de Météorologie Dynamique (LMD/IPSL), Centre National de la Recherche Scientifique (CNRS), Université Pierre et Marie Curie (UPMC), Ecole Normale Supérieure (ENS), Ecole Polytechnique (EP), Paris, France MARION SAINT-LU Laboratoire des Sciences du Climat et de l’Environnement (LSCE/IPSL), Centre National de la Recherche Scientifique (CNRS), Commissariat à l’Energie Atomique (CEA), Université de Versailles Saint-Quentin (UVSQ), Gif-sur-Yvette, France ABSTRACT The response of the various climatic processes to climate change can amplify (positive feedback) or damp (negative feedback) the initial temperature perturbation. An example of a positive feedback is the surface albedo feedback: when the surface temperature rises, part of the ice and snow melts leading to an increase in the solar radiation absorbed by the surface and to an enhanced surface warming. Positive feedbacks can lead to instability. On Venus for example, a positive feedback is thought to have evolved into a runway greenhouse effect. However, positive feedbacks can exist in stable systems. This paper presents a simple representation of a positive feedback in both a stable and an unstable system. A simple experimental device based on a scale principle is introduced to illustrate the positive feedback and its stabilization or runaway regimes. Stabilization can be achieved whether the amplitude of the positive feedback declines (e.g. "saturation" of the feedback) or remains constant. The device can also be used to illustrate the existence of tipping points, which are threshold values beyond which the amplification due to feedbacks or the stability of the system suddenly changes. The physical equations of the device are established in the framework of the feedback analysis. Key features to understand why a positive feedback does not necessarily lead to a runaway effect are described. The analogy between the different components of the device and those of the climate system is established. Finally, the contribution of individual feedbacks to the total climate response is addressed. (Capsule Summary)To illustrate the concepts of positive feedback, stability, instability, tipping point and saturated feedback we conceive a very simple device based on a scale with two water reservoirs. 1. Introduction vapor, clouds and snow may vary with the surface temper- ature and may impact the energy budget. These estimates At the end of the 19th century, Joseph Fourier estab- were very crude and a major improvement was achieved lished that the Earth’s surface temperature is primarily 70 years later when Manabe and Wetherald (1967) esti- driven by a fundamental law, the law of conservation of mated the temperature response to an atmospheric CO in- energy (Fourier 1824, 1837; Pierrehumbert 2004). More 2 crease using a single-column radiative-convective model. specifically, he established that the surface temperature ad- These studies and many following ones emphasize the im- justs until the energy budget at the surface reaches equi- portance of changes in water vapor, clouds, snow and ice librium. He also established that any change of the energy extent to estimate the surface temperature change. budget at the surface has a direct impact on the surface The atmospheric water vapor amount, for exam- temperature. A few decades later, Svante Arrhenius used ple, increases with temperature following the Clausius- the single-layer model framework suggested by Fourier to Clapeyron law assuming fixed relative humidity. As wa- quantify each term of the energy budget at the surface and to estimate the energy imbalance due to a change in the at- ter vapor is a powerful greenhouse gas, such an increase contributes to a further warming of the climate. This pos- mospheric CO2 concentration (Arrhenius 1896). He also identified that the major physical phenomenon driving the itive ’feedback’ loop amplifies a given perturbation of the energy budget adjustment was the Stefan-Boltzmann ra- surface temperature by about a factor two (Manabe and diation emission law. Arrhenius also analyzed how water Wetherald 1967; Dufresne and Bony 2008). This feedback is amplified as the climate warms due to the increase in the tropopause height (Meraner et al. 2013). Depending on the ∗Corresponding author address: Jean-Louis Dufresne, LMD/IPSL, conditions, this feedback amplification can eventually turn UPMC boÃote˝ 99, 4 place Jussieu, 75272 Paris, France into a runaway greenhouse effect (Kasting 1988; Gold- E-mail: [email protected] Generated using v4.3.2 of the AMS LATEX template 1 2 B ULLETINOFTHE A MERICAN M ETEOROLOGICAL S OCIETY blatt et al. 2013): as the temperature rises, the moist con- 2. The mechanical device and the experiment vective layer becomes optically thicker and absorbs more a. Description of the device and more infrared radiation. A tipping point is reached when the layer becomes fully opaque and the tropopause The device is shown in Fig.1 and Fig.2 gives a simpli- acquires a fixed temperature (Goldblatt et al. 2013). The fied schematic of it. The simplifications of the schematic surface temperature then increases without modifying the aim at facilitating the mathematical expressions to model outgoing radiative flux until the planet is so warm that it the device. The device is a cross attached to a fixed pil- emits near-visible radiations. A runaway greenhouse ef- lar through its intersection O, so that the cross can rotate fect is thought to have happened on Venus, explaining around this fixed axis. Initially, the cross is vertical with a long vertical bar and a shorter horizontal bar. One cylin- its current atmospheric composition and its high density drical water container is hung on each side of the horizon- (Kasting 1988). tal bar, equidistant from O and separated by the distance Another climate feedback is due to surface albedo: l2 (note that the containers stay vertical in this simplified a surface cooling, for example, increases ice and snow schematic whereas in reality they rotate with the device). cover, which leads to an increased surface albedo and to The containers are about half filled with water and have the a further cooling of the surface (Budyko 1969; Sellers same mass. They can communicate through a pipe with a 1969). For a very cold Earth, an extra cooling perturbation tap at their bottom and another pipe at their top, so that the can trigger a runaway regime and the Earth can eventually circulation system is closed. A mass m3 is at the bottom be totally covered by snow: this is the so-called snowball of the vertical bar, at the distance l3 from O. Earth hypothesis (Stern et al. 2006; Kopp et al. 2005). The tilt Dq of the cross is driven by the sum of the mo- It could be intuitively stated that a positive feedback ments of force, which are given here by the product be- "never stops" and is necessarily associated with a runaway tween the mass weight and the horizontal projection of the regime. This actually may happen in some cases defined pivot-mass vector. as unstable, but this is not necessarily the case. The aim The construction of the device is of no practical diffi- of this paper is to illustrate how systems (e.g. the climate) culty and very common materials may be used. Feeders with positive feedbacks can be stable. When a system is for small rodents have been used for the reservoirs and the stable, the positive feedback simply amplifies a given per- pipe and tap have been found in aquarium stores. turbation without triggering a runaway regime. The sys- tem then stabilizes and reaches a new equilibrium. The b. The experiment physical environment of the system in each of its equilib- Initially, the system is vertically straight as illustrated in ria is similar. This paper also illustrates how systems with Figs.1a and 2a and the tap between the two containers is positive feedbacks can be or can become unstable. In this closed. At equilibrium, the sum of the moments of force is case the positive feedback triggers a runaway regime and null. A small mass m1 is added to one extremity of the hor- the system evolves and reaches a very different state. To izontal bar, and this leads to a tilt of the device by a small investigate positive feedbacks in both a stable and an un- angle Dqi (subscript i stands for initial change) (Figs.1b stable system, a simple mechanical device is used. This and 2b). The angle is small because of the counterweight device is based on a scale where a positive feedback can of the mass m3, which generates a return moment.
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