User:Katharina Franziska Schmitt/sandbox

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.

The main difference to the pure Radiative equilibrium is that the lapse rate in the troposphere is adjusted to a more realistic one.

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. 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). On Earth, the tropical atmosphere is on many scales close to RCE. Therefore, the concept has also been used for studying tropical circulation and different aspects of moist convection.

The concept has its limits in cases of a very stable atmosphere which nearly eliminates convection.

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. Considering only pure radiative equilibrium, the layer close to the surface heats strongly and becomes unstable. Atmospheric motions like updrafts transport the heat upward in the atmosphere to balance this instability. This new equilibrium can be seen in Figure 1. Therefore, the surface and troposphere are strongly coupled and must be considered as a unit. 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. 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). The strong coupling between the surface and the troposphere implies that the energy balance at the top of the atmosphere is critical for the analysis of climate sensitivity instead of the balance at the surface.

Equations for a single-layer atmosphere
According to Figure 1, the energy budget at the top of the atmosphere reads

$S_{0} (1-α)⁄4$ = σTa4

and at the surface

$S_{0} (1-α)⁄4$ + σTa4 = σTs4 + Fc


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

Usage
The RCE is the simplest but already valid description of the climate system. 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. The most famous usage of RCE was done by Manabe in 1967 in their paper "Thermal Equilibrium of the Atmosphere with a Given Distribution of Relative Humidity" where they first produced a realistic estimate of the ECS (2.3 °C). From observations, it is known that especially the tropical atmosphere is close to RCE on larger scales but also on a daily time scale. As greater computational resources became available, the application of the RCE concept evolved from the earliest one-dimensional models to cloud-resolving models. Nowadays, the concept has been used to study 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. RCE has also been used as a background state for tropical cyclone studies.

Limits
The concept has its limits in cases of a very stable atmosphere which nearly eliminates convection. Thus, the surface is decoupled from the region of atmospheric absorption. Examples of this are high-latitude winters and tropical ocean regions with upwelling of cold waters. The most extreme case is the „nuclear winter“ scenario.