Temperatures of Anvil Clouds and Radiative Tropopause in a Wide Array of Cloud-

We present ninety-nine cloud-resolving simulations to study how temperatures of anvil clouds and radiative tropopause change with surface warming. Our simulation results show that the radiative tropopause warms at approximately the same rate as anvil clouds. This relationship persists across a variety of modeling choices, including surface temperature, greenhouse gas concentration, and the representation of radiative transfer. We further show that the shifting ozone profile associated with climate warming may give rise to a fixed tropopause temperature as well as a fixed anvil temperature. This result points to the importance of faithful treatment of ozone in simulating clouds and climate change; the robust anvil-tropopause relationship may also provide alternative ways to understand what controls anvil temperature.


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The tropical upper troposphere is home to extensive cirrus clouds detrained from thunderstorms. 20 As the surface warms, these clouds -known as anvil clouds -are robustly predicted to rise to 21 greater altitudes so that their mean temperature increases less than that of the surface. This holds surface warming, they will emit less longwave radiation to space than if they were to warm at the 27 same rate as the surface. This yields a positive climate feedback when our reference assumption is 28 that clouds should otherwise warm at the same rate as the surface. For this reason, the most recent 29 IPCC report expressed high confidence in a positive longwave cloud altitude feedback (Forster et   Since radiative tropopause may be simulated by 1-D models without clouds, a robust anvil-  their simulations the temperature of radiative tropopause varied by less than 2 K despite 50 K of 67 surface warming, yet the anvil warming was greater by an order of magnitude. They suggested 68 that not only is there a fixed tropopause temperature (FiTT) with respect to surface warming, but 69 tropopause temperature is unlikely to be related to the temperature of the anvil peak. That is, the 70 top of the troposphere should be disentangled from the anvil location. Given this disagreement and 71 the potential clarity provided by an anvil-tropopause relationship, it is worthwhile to investigate 72 more thoroughly whether the location and temperature anvil clouds are in fact related to the 73 location and temperature of tropopause.

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To test for an anvil-tropopause relationship, we conduct idealized experiments in a CRM   The model is run over a sea surface with a prescribed temperature until the atmosphere 104 approximately reaches radiative-convective equilibrium (RCE). RCE is an idealization of the 105 tropical atmosphere which states that the latent heating from convection is balanced by radiative 106 cooling in the free troposphere. Each simulation is integrated for 500 days, except for simulations 107 without ozone, which required 1000 days to equilibrate. The data reported are from the final 40% 108 of the model integration. We identify cloudy grid cells as those whose condensates exceed either 109 1 10 −5 / or 1% of the saturation specific humidity, whichever is smaller. This is consistent    Table 1.

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As the climate warms, anvil clouds rise in altitude so that their temperature increases less than the 122 air at any given level. Figure 1a shows profiles of cloud fraction from the Standard simulations 123 (see Table 1). The cloud fraction profile has a two-peaked structure. Following the convention of in cloud fraction as the anvil, which migrates upward as the surface warms. Figure 1b  anvil temperature increases with warming. 128 We require a precise and general definition of "anvil temperature" appropriate for the wide range coverage of at least 80% of that maximum value: where T is temperature, CF is cloud fraction, and 80%,↑ and 80%,↓ are the highest and lowest 142 pressure levels where the cloud fraction is at least 80% of its maximum value. This cutoff is 143 arbitrary choice, but in the supplemental material we show that Eq. (1) gives nearly the same 144 temperature as a strict "peak" definition except in a few cases where the shape of the cloud profile 145 changes abruptly with warming (Fig. S2). In those cases Eq. (1) retains monotonic behavior rather 146 than allowing an arbitrary jump in . Therefore, this method is more appropriate for this study.

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To reduce the imprecision introduced by a discrete model resolution, we linearly interpolate ( ) As the climate warms, the radiative tropopause becomes warmer as well. Figure 1c shows radiative 158 heating using temperature as a vertical coordinate. Considering the troposphere as the region of 159 the atmosphere in radiative-convective equilibrium, we identify radiative tropopause as the 160 temperature at which radiative heating changes sign. That is, tropopause is the y-intercept in Here, is a pressure velocity ( / ), is the radiative heating rate ( / ) and σ is the 243 static stability ( / ), given by: Where Γ is the lapse rate ( / ), Γ d is the dry-adiabatic lapse rate, is density, and is the

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The radiative heating rate from the Standard experiment is shown in Fig. 1c. Since radiation is  Figure 3b shows the relationship between this convergence-weighted 268 temperature and anvil temperature. As found by previous studies of CRMs, GCMs, and 269 observations, the temperature of cloud anvils is well-predicted by the convergence temperature.

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The empirical relationship between tropopause temperature, anvil temperature, and convergence surface. This is unrealistic. In the real tropical atmosphere, the ozone profile should evolve in 280 response to the changing location of tropopause as tropospheric mixing reduces ozone.

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Additionally, upward transport of ozone may increase as stratospheric upwelling intensifies with 282 surface warming (Lin et al. 2017). This will alter the equilibrium tropopause temperature, as ozone 283 is the main absorber responsible for radiative heating there (Thuburn and Craig 2002). As shown 284 in our simulations, surface warming leads to a warmer tropopause with a fixed O3 profile.

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However, lifting the O3 profile can lead to the local decline of ozone heating, which tends to reduce 286 temperature. Therefore, there is a "tug of war" between the two effects to determine how 287 tropopause temperature responds to climate warming in the real tropical atmosphere. Thus, we 288 cannot predict anvil or tropopause's temperature trend with warming using a fixed ozone profile.

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We use WACCM6 data from a pre-industrial control run in which the CO2 concentration is fixed  In that region, tropical sea surface temperature increases from 301.21 K at the end of the piControl 304 simulation to 306.65 K at the end of the abrupt-4xCO2 simulation. Figure 4a shows that the ozone 305 concentration decreases below the 20 hPa level and increases above. The ozone profile shifts   330 We have shown that the temperatures of cloud anvils and radiative tropopause strongly covary 331 across a wide range of model settings and surface temperatures in a 2D cloud-resolving model. simulations. This is most apparent in Fig. 2a. When CO2 is removed, the modeled tropopause 345 temperature declines more than anvil temperature. Even though anvil and tropopause appear to be 346 related phenomena, we should be cautious of conflating the two. 347 We also find that the anvil temperature closely matches the temperature of maximum radiatively  Finally, we mention several caveats to this study. To afford the computational expense of 371 conducting 99 five-hundred-day simulations, we use a small, two-dimensional domain. We 372 prescribe no mean ascent or descent, whereas real tropical anvil clouds form in the context of mean 373 ascent in both the troposphere and stratosphere. Our analysis relates cloud amount to the 374 radiatively driven convergence in clear skies. However, that is not a closed budget for cloud 375 amount. Other factors are known to cause detrainment from the convective core, and cloud amount 376 further depends on its lifetime after detrainment (Seeley et al. 2019a,b). As with other studies on 377 this topic, we only consider the temperature of the cloud near its peak amount, not its effective 378 radiating temperature, which may be different.  Model output used to achieve these results can be found at the UC Davis Box website. Additional 388 data related to this paper may be requested from the authors. (1), we show the anvil temperature as defined by (i) Eq. (1), (ii) the peak in CF (as in Fig. S1), (iii) Eq.

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(1), modified so that the "anvil" is declined to include all levels where cloud fraction as at least 70% of its is the temperature of maximum cloud fraction, 542 as marked in Fig. S1. The tropopause-anvil relationship still holds for most experiments even when the 543 anvil temperature is defined as . 544