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I have read about the Fixed Anvil Temperature (FAT) hypothesis and wonder why radiative cooling decreases with decreasing water vapor mixing ratio. Doesn't this stand in contrast with the fact, that water vapor acts as a greenhous gas since it absorbs LW radiation? How can it then cool the atmosphere?

Best regards Jan

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Let's for a moment think about the troposphere consisting of stacked layers. The anvil clouds can only be found in the upper layer of the troposphere, since this is where they have to extend horizontally due to the tropopause acting as a natural barrier (see Figure 1. in Hartmann, Larson linked below). Let's assume that moisture does not penetrate the tropopause or stratosphere and that layers containing moisture fully absorb long wave radiation (this is obviously not true but it helps here to get to the point). This means that the outgoing long wave radiation from this upper layer can not be absorbed by water vapor by layers above them.

Since the layer containing the anvil clouds will absorb all outgoing long wave radiation from the layers below (by our hypothesis stated above), we can conclude that this layer is the single most important layer that determines how much radiation is going to space and thus, cools the atmosphere.

This explains how an atmospheric layer can contribute to cooling but does not explain why cooling decreases with decreasing water vapor mixing ratio. The answer can be explained in terms of the atmospheric lapse rate. The dry adiabatic lapse rate in the atmosphere is about $\Gamma_d = 10$ K/km. The moist adiabatic lapse rate is about $\Gamma_w = 6$ K/km. The more the water vapor mixing ratio decreases, the closer the lapse rate will be to $\Gamma_d$. And thus the upper most layer of the troposphere will be colder compared to a situation where the water vapor mixing ratio is high. A colder top layer will radiate less and therefore cooling decreases, since there is less outgoing long wave radiation.

The FAT assumes that the temperature of this upper atmospheric layer is independent of surface temperature and thus, would amplify warming. What changes is the height of the upper layer - the troposphere has a larger vertical extent in a warming climate.

Hartmann, Larson - An important constraint on tropical cloud - climate feedback

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Evapotranspiration cools the surface of the Earth. Under the right circumstances, the moisture-laden air can rise higher into the troposphere, where it cools and eventually condenses into a mist in clouds. This helps cool the troposphere as condensation is an exothermic process. Cumulonimbus clouds can reach the very top of the troposphere. Greenhouse backradiation is greatly reduced at this high of an altitude, enabling the tops of those very tall clouds to radiate into space.

This is of course countered by the fact that water vapor is a greenhouse gas. It is a very short-lived greenhouse gas. On average, water molecules stay in the atmosphere about 8 to 9 days between evapotranspiration and rain. The combination of the short-lived nature of water vapor, the interaction of the surface with clouds, and the different effects of high versus low clouds remain one of the key stumbling blocks in attaining a better understanding the sensitivity of the climate to rising $\ce{CO2}$ levels.

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Don`t forget the clouds !
The cloud radiative effect (CRE) is cooling ~ -19W/m² according to IPCC AR6 WG1 chapter 7.2.1
and is a net value of -47W/m² reflected solar radiation by clouds and +28W/m² absorbed thermal radiation. Not to be confused with the warming positive cloud feedback (αC = +0.42 W m–2 °C–1) in a warmer climate due to higher clouds and decreasing low cloud cover. https://www.ipcc.ch/report/ar6/wg1/downloads/report/IPCC_AR6_WGI_Chapter07.pdf (page 935)
You can read here how mankind could also cool the earth through higher evaporation and cloud cover and at the same time lower the rise in sea level.

https://climate-protecion-hardware.webnode.page/english/

@David " This helps cool the troposphere as condensation is an exothermic process. " Condensation as an exothermic process warms the troposphere and does not cool it - as you claim. The atmophere cools by outgoing thermal radiation at TOA and precipitation.

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  • $\begingroup$ Hi, thank you for your comment. But I'm not sure if it answers the question. To be more precisely, I don't get how water vapor can cool the troposphere. In several papers (e.g., Hartmann & Larson 2002; doi.org/10.1029/2002GL015835), the cooling effect is attributeted to the LW emission, but how can the LW emission offset the warming through absorption of LW radiation (H2O as a greenhous gas)? $\endgroup$
    – Jan
    Jun 23, 2022 at 14:34
  • $\begingroup$ Water vapor warms and cools the atmosphere. As a GHG, it has 3-4 times the potential of CO2. Look (again) at the graphs of the clear sky and all sky energy balances: link.springer.com/article/10.1007/s00382-018-4413-y/figures/14 Here you can see the LW & SW amounts of energy flowing in and out of the atmosphere. Note the statement by the IPCC (see link above) that an atmosphere completely without clouds would increase the earth's temperature considerably (~+4-5°C). H2O of clouds reflect SW radiation into space (-47W/m2) - LW absorption by water vapor (+28W/m²) = -19W/m² cooling. $\endgroup$
    – Rammstein
    Jun 25, 2022 at 17:21

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