Editing Cloud feedback (section)

==== Cloud Altitude ====
The longwave feedback is dominated by the positive cloud altitude feedback<ref name="Zelinka-2010" /> which is mainly found in the tropics with the mechanisms being identical in the extra tropics.<ref name="Ceppi-2017" /> The LW radiation emitted by the high cloud tops is proportional to the temperature at the cloud top.<ref name="Ceppi-2017" /> The altitude of the high clouds changes with rising temperatures, due to the following mechanisms:<ref name="Ceppi-2017" /> Higher temperatures on the surface force the moisture to rise, which is fundamentally described by the [[Clausius–Clapeyron relation|Clausius Clapeyron]] equation.<ref name="Ceppi-2017" /><ref name="Zelinka-2010" /> The altitude at which the radiative cooling is still effective is closely tied to the humidity and rises equally.<ref name="Ceppi-2017" /><ref name="Zelinka-2010" /> The altitude, at which the [[radiative cooling]] becomes inefficient due to a lack of moisture, then determines the detrainment height of [[Atmospheric convection|deep convection]] due to the [[Conservation of mass|mass conservation]].<ref name="Ceppi-2017" /><ref name="Zelinka-2010" /> The could top height therefore strongly depends on the surface temperature.<ref name="Ceppi-2017" />

There are three theories on how the altitude and thus temperature depends on surface warming.<ref name="Ceppi-2017" /> The [[Fixed anvil temperature hypothesis|FAT]] (Fixed Anvil Temperature) hypothesis argues, that the isotherms shift upwards with [[Climate change|global warming]] and the temperature at the cloud top stays therefore constant.<ref name="Hartmann-2002">{{Cite journal |last1=Hartmann |first1=Dennis L. |last2=Larson |first2=Kristin |date=2002 |title=An important constraint on tropical cloud - climate feedback |url=https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2002GL015835 |journal=Geophysical Research Letters |language=en |volume=29 |issue=20 |page=1951 |doi=10.1029/2002GL015835 |bibcode=2002GeoRL..29.1951H |issn=0094-8276}}</ref> This results in a positive feedback, since no more radiation is emitted while the surface temperature is rising.<ref name="Hartmann-2002" />  According to the FAT hypothesis this leads to a feedback of  0,27 W m<math>^{-2}</math> K<math>^{-1}</math><ref name="Zelinka-2010">{{Cite journal |last1=Zelinka |first1=Mark D. |last2=Hartmann |first2=Dennis L. |date=2010-08-27 |title=Why is longwave cloud feedback positive? |url=https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2010JD013817 |journal=Journal of Geophysical Research: Atmospheres |language=en |volume=115 |issue=D16 |doi=10.1029/2010JD013817 |bibcode=2010JGRD..11516117Z |issn=0148-0227}}</ref>. The second hypothesis called PHAT (Proportionally Higher Anvil Temperature) claims a smaller cloud feedback of 0.20 W m<math>^{-2}</math> K<math>^{-1}</math><ref name="Zelinka-2010" />, due to a slight warming of the cloud tops which agrees better with observations.<ref name="Zelinka-2010" /> The static stability increases with higher surface temperatures in the upper troposphere and lets the clouds shift slightly to warmer temperatures.<ref name="Ceppi-2017" /> The third hypothesis is FAP (Fixed Anvil Pressure) which assumes a constant cloud top pressure with a warming climate, as if the cloud top does not move upwards.<ref name="Zelinka-2010" /> This results in a negative LW feedback, which does not agree with observations.<ref name="Zelinka-2010" /> It can be used to calculate the impact of the cloud height change on the LW feedback.<ref name="Zelinka-2010" /> Most models agree with the PHAT hypothesis which also agrees the most with observations.<ref name="Zelinka-2010" />