User:Katharina Franziska Schmitt/sandbox

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Radiative Convective Equilibrium

The radiative-convective equilibrium (RCE) is a concept for the radiative balance of the atmosphere. It describes the balance between the net radiative longwave cooling and the heating due to convection and surface fluxes[1] The main difference to the pure Radiative equilibrium is that the lapse rate in the troposphere is adjusted to a more realistic one [2].

In climate models, the concept is used to simulate the globally averaged thermal structure of the atmosphere and offers the opportunity to analyse the sensitivity of this structure to CO2 [3]. Syukuro Manabe won the Physics Nobel Prize for his RCE model as it was the first to produce a realistic estimate of the Earth's Climate sensitivity (ECS)[4]. On Earth, the tropical atmosphere is on many scales close to RCE [5]. Therefore, the concept has also been used for studying tropical circulation and different aspects of moist convection [1].

The concept has its limititations in cases of a very stable atmosphere which nearly eliminates convection[6].

Concept

Most of the atmospheric heating is done by the surface as the atmosphere is transparent to solar radiation in most parts of the spectrum [6]. Considering only pure radiative equilibrium, the layer close to the surface heats strongly and becomes unstable. To balance this instability, atmospheric motions like updrafts transport the heat upward in the atmosphere creating a new equilibrium that can be seen in Figure 1[6][7]. Therefore, the surface and troposphere are strongly coupled and must be considered as a unit[6]. This strong coupling is taken into account in the RCE with a „convective adjustment“. This is done by adjusting the lapse rate to the moist adiabatic one (Γ = 6.5 K km -1 ) as soon as the layer becomes more unstable than this value[6]. This adjustment eliminates some of the unrealistic features of a pure radiative equilibrium atmosphere like a very warm earth’s surface (332.3 K) to a more realistic value (300.3 K)[3]. The strong coupling between the surface and the troposphere implies that the energy balance at the top of the atmosphere rather than the balance at the surface is critical for the analysis of climate sensitivity [6].

Equations for a single-layer atmosphere[7]

According to Figure 1, the energy budget at the top of the atmosphere reads

⁠S0 (1-α)/4⁠ = σTa4

and at the surface

⁠S0 (1-α)/4⁠ + σTa4 = σTs4 + Fc

  • S0: Solar constant
  • α: Albedo
  • σ: Stefan-Boltzmann constant
  • Ta: Atmospheric temperature
  • Ts: Surface temperature
  • Fc: Convective flux

At the top of the atmosphere, the equations depict the balance between incoming solar radiation that is not reflected and outgoing longwave radiation, which depends on the atmosphere's temperature. At the surface, in addition to incoming solar radiation, there is also radiation received from the atmosphere above. These components of the equations align with those of pure radiative equilibrium. However, the current equations now incorporate a convective flux that partially balances the surface fluxes. This flux represents the "convective adjustment" described earlier.

Usage

The RCE is the simplest yet valid description of the climate system [8]. From observations, it is known that especially the tropical atmosphere is close to RCE on larger scales but also on a daily time scale [1]. Due to these prerequisites, RCE is widely used for modeling. The most famous usage of RCE was done by Manabe and Wetherland in 1967 in their paper "Thermal Equilibrium of the Atmosphere with a Given Distribution of Relative Humidity" where they first provided a realistic estimate of the ECS (2.3 °C) [9]. Syukuro Manabe was awarded with the Nobel Prize in Physics in 2021 for this key finding.

As greater computational resources became available, the application of the RCE concept evolved from the one-dimensional models of Manabe and Wetherland to cloud-resolving and general circulation models[5]. Today, the concept is used to investigate various aspects, including the predictability of mesoscale rainfall, tropical anvil clouds, precipitation extremes, aerosol-cloud interactions, factors controlling convective organization as well as how the land surface influences the climate state[5][8]. Cloud feedbacks are also examined using RCE, and it has been found that in particular tropical cloud feedbacks are well-captured[10]. Moreover, RCE has also been used as a background state for e.g tropical cyclone studies as well as for simulating the globally averaged thermal structure of the atmosphere in climate models[3][8].

Limitations

The concept has its limitations in cases of a very stable atmosphere which nearly eliminates convection. In this case, the surface is decoupled from the region of atmospheric absorption [11]. Examples of this are high-latitude winters and tropical ocean regions with upwelling of cold waters[6].

  1. ^ a b c Jakob, Singh and Jungandreas (2019). "Radiative Convective Equilibrium and Organized Convection: An Observational Perspective". Journal of Geophysical Research: Atmospheres.
  2. ^ Manabe and Strickler (1964). "Thermal Equilibrium of the Atmosphere with a Convective Adjustment". Journal of the Atmospheric Sciences.
  3. ^ a b c Manabe and Wetherland (1967). "Thermal Equilibrium of the Atmosphere with a Given Distribution of Relative Humidity". Cover Journal of the Atmospheric Sciences Journal of the Atmospheric Sciences.
  4. ^ Press release: The Nobel Prize in Physics 2021: https://www.nobelprize.org/prizes/physics/2021/press-release/
  5. ^ a b c Popke, Stevens and Voigt (2013). "Climate and climate change in a radiative-convective equilibrium version of ECHAM6". Journal of Advances in Modeling Earth Systems.
  6. ^ a b c d e f g Jeevanjee, Held and Ramaswamy (2022). "Manabe's Radiative–Convective Equilibrium". Cover Bulletin of the American Meteorological Society Bulletin of the American Meteorological Society.
  7. ^ a b Jeevanjee (2023). "Climate sensitivity from radiative-convective equilibrium: A chalkboard approach". American Journal of Physics.
  8. ^ a b c Wing; et al. (2018). "Radiative–convective equilibrium model intercomparison project". Geoscientific Model Development. {{cite journal}}: Explicit use of et al. in: |last1= (help)
  9. ^ Manabe and Wetherland (1975). "The Effects of Doubling the CO2 Concentration on the climate of a General Circulation Model". Cover Journal of the Atmospheric Sciences Journal of the Atmospheric Sciences.
  10. ^ Stauffer and Wing (2023). "Explicitly Resolved Cloud Feedbacks in the Radiative-Convective Equilibrium Model Intercomparison Project". Journal of Advances in Modeling Earth Systems.
  11. ^ Ramaswamy and Kiehl (1985). "Sensitivities of the radiative forcing due to large loadings of smoke and dust aerosols". Journal of Geophysical Research: Atmospheres.
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