Joint Dependence of Longwave Feedback on Surface Temperature and Relative Humidity

Various studies have suggested that Earth's clear‐sky outgoing longwave radiation (OLR) varies linearly with surface temperature, with a longwave clear‐sky feedback that is, independent of surface temperature and relative humidity. However, this uniformity conflicts with the notion that humidity controls tropical stability (e.g., the “furnace” and “radiator fins” of Pierrehumbert (1995, https://doi.org/10.1175/1520-0469(1995)052%3C1784:TRFATL%3E2.0.CO;2)). Here, we use a column model to explore the dependence of longwave clear‐sky feedback on both surface temperature and relative humidity. We find that a strong humidity dependence in the feedback emerges above 275 K, which stems from the closing of the H2 O window, and that the furnace and radiator fins are consequences of this dependence. We then clarify that radiator fins are better characterized by tropical variations in clear‐sky feedback than OLR. Finally, we construct a simple model for estimating the all‐sky feedback and find that although clouds lower the magnitude of longwave feedback, the humidity‐dependence persists.


Plain Language Summary
The dependence of outgoing longwave radiation radiation on surface temperature (i.e., the feedback) is a major determinant of the climate's stability. Various studies have suggested that the feedback is largely independent of both surface temperature and relative humidity, which implies that the climate stability is also independent of surface temperature and relative humidity. However, this uniformity seems to contradict other work which shows that the subtropics are relatively stable and the deep tropics are relatively unstable, implying the feedback must vary between the two regions. We resolve this apparent contradiction by systematically computing the feedback as a function of both surface temperature and relative humidity. Above 275 K, the feedback depends significantly on relative humidity. We then show the feedback does indeed vary in the tropics and that this difference arises from regional differences in relative humidity. Finally, we estimate the effects of clouds on the feedback with a simple model and find that although clouds have a destabilizing influence, the significant dependence on relative humidity persists. Our work gives a renewed appreciation for how the feedback can vary significantly with both surface temperature and relative humidity.

MCKIM ET AL.
 between the radiator fins and the furnace is due to the difference in humidity, as emphasized by Pierrehumbert (1995), or if the drop is due to the difference in temperature. If we look again at the phase space in Figure 1, we can take a path that goes from the subtropics to the deep tropics in two parts (the order does not matter): a first part with constant surface temperature, and a second part with constant relative humidity (see the dashed gray arrows). In this region of phase space, the doubling of relative humidity from 30% to 60% causes a much larger change in cs E  than the increase in surface temperature from 295 to 300 K does.
Our answer to the first part of Question 1 is then: zonal-mean cs E  exhibits local extrema, which may be usefully viewed as the "furnace" and "radiator fins" of the tropics. Furthermore, these extrema are indeed due to RH variations, consistent with Pierrehumbert (1995). cs E  exhibits a local maxima in the subtropics because they are hot and dry enough for the feedback to exhibit a Planck-dominated response, and cs E  exhibits a local minimum in the deep tropics because they are hot and moist enough for the feedback to exhibit a window-dominated response (Figure 1c).
To answer the second part of Question 1, that is, why radiator fins should not be regarded as a contrast in the zonal-mean OLR cs E , we plot the annual-and zonal-mean OLR cs E OLR as E does have more significant subtropical extrema, but these should not be interpreted as a furnace and radiator fins because the longwave warming effect of deep tropical clouds is balanced by their shortwave cooling effect (Hartmann & Berry, 2017;Pierrehumbert, 1995).

Incorporating the Effects of Cloudiness
In Question 3, we asked whether clouds affect the meridional structure in zonal-mean longwave feedback in the tropics. Rather than explicitly compute cloud feedbacks, which is beyond the scope of this study, we try to estimate them by constructing a simple model for how clouds modify longwave emission. is taken directly from ERA5 reanalysis. E f is diagnosed from ERA5 reanalysis as the local max of the zonal-mean cloud fraction profile above a 550 hPa threshold, which is used to avoid misidentifying cloud tops with boundary layer cloudiness. ct E T is the atmospheric temperature  that lie outside this range should be considered the "radiator fins" and "furnace," respectively, of the tropics. Note the equal-area scaling of the x-axis.
 and as E  ) but a large, global OLR increase (Dong et al., 2019). The discrepancy between the weak, local and the strong, global radiative response from warming the deep tropics arises from atmospheric temperature changes not associated with a local s E T change, that is, the remote warming of the free troposphere (Ceppi et al., 2017;Mauritsen, 2016). A local feedback analysis, by construction, cannot capture the effects of remote warming, which should be noted when comparing results across studies. The relative contributions of local surface warming versus non-local free-tropospheric warming to OLR change is relatively unexplored, so further study might alter our characterization of the tropical radiative response if one contribution can be shown to dominate over the other.
Our new understanding of the state dependence of cs E  gives context to previous results. For example, Bloch-Johnson et al. (2021) and Meraner et al. (2013) attributed an increase in equilibrium climate sensitivity to the decrease in cs E  with warming. We expect these variations in cs E  to be enhanced in climates