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The Fixed Anvil Temperature (FAT) hypothesis proposes that upper tropospheric cloud fraction peaks at a special isotherm that is independent of surface temperature. It has been argued that a FAT should result from simple ingredients: Clausius-Clapeyron, longwave emission from water vapor, and tropospheric energy and mass balance. Here the first cloud-resolving simulations of radiative-convective equilibrium designed to contain only these basic ingredients are presented. This setup does not produce a FAT: the anvil temperature varies by about 40% of the surface temperature range. However, the tropopause temperature varies by only 4% of the surface temperature range, which supports the existence of a Fixed Tropopause Temperature (FiTT). In full-complexity radiative-convective equilibrium simulations, the spread in anvil temperature is smaller by about a factor of 2, but the tropopause temperature remains more invariant than the anvil temperature by an order of magnitude. In other words, our simulations have a FiTT, not a FAT.

Plain Language Summary Tropical anvil clouds play a large role in Earth's radiation balance, and their effect on anthropogenic global warming has been a point of contention. One popular school of thought is the Fixed Anvil Temperature (FAT) hypothesis, which argues that no matter how much the Earth warms, anvil clouds would continue to radiate to space at the same temperature. This behavior would amplify the warming caused by the addition of greenhouse gases to the atmosphere. In this paper, we show that the chain of logic underlying the FAT hypothesis-which attributes anvil cloud formation to a rapid decline of radiative cooling at the top of the troposphere-contains many weak and unsupported links. These weak links undermine the FAT hypothesis, which does not hold empirically in our simulations. However, the radiative tropopause does remain at a fixed temperature as the surface warms in our simulations. Therefore, we find evidence for a Fixed Tropopause Temperature (FiTT) rather than a FAT. There is currently no accepted theory for the tropopause temperature or why it appears to be independent of the surface temperature.