Atmospheric Convection Plays a Key Role in the Climate of Tidally Locked Terrestrial Exoplanets: Insights from High-resolution Simulations

In the control (MassFlux) simulation of the Trappist-1e and Proxima b cases, the spatial distribution of the time-mean surface temperature (T_s) has a maximum at the substellar point and a minimum over the nightside mid-latitudes (Figures 2(a), (b)), typical for quickly rotating tidally locked planets with zero obliquity (e.g., Hammond & Pierrehumbert 2018; Komacek & Abbot 2019). In terms of absolute values, Proxima b has a larger T_s contrast of $138\,{\rm{K}}$ compared to $111\,{\rm{K}}$ for Trappist-1e, due to a much lower T_s in the nightside cold traps: $177\,{\rm{K}}$ for Trappist-1e versus $149\,{\rm{K}}$ for Proxima b (Table 3). The day side, on the other hand, has a maximum of $\approx 288\,{\rm{K}}$ on both planets. Previous 3D GCM studies of these planets report higher T_s, especially on the night side of the planet (e.g., Turbet et al. 2016; Wolf 2017; Fauchez et al. 2020). As discussed by Boutle et al. (2017), the differences stem from different representations of various parameterized processes in GCMs, such as the radiative effects of nightside clouds, subgrid-scale mixing in the boundary layer, and water vapor export from the day side. The latter is investigated below in detail with respect to the dayside convection.

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Table 3.  Mean Global, Mean Dayside, Mean Nightside, Maximum, and Minimum Surface Temperature (${\rm{K}}$) in the Control and Sensitivity Simulations of Trappist-1e and Proxima b

	Trappist-1e					Proxima b
Simulation	$\overline{{T}_{s}}$	$\overline{{T}_{s,d}}$	$\overline{{T}_{s,n}}$	${T}_{s,\max }$	${T}_{s,\min }$	$\overline{{T}_{s}}$	$\overline{{T}_{s,d}}$	$\overline{{T}_{s,n}}$	${T}_{s,\max }$	${T}_{s,\min }$
MassFlux	231.8	260.0	202.7	288.3	177.1	226.6	261.7	190.5	287.3	148.7
Adjust	249.3	268.3	229.3	294.3	214.1	241.0	272.0	209.0	299.3	166.0
NoCnvPm	234.4	256.6	211.1	284.1	193.2	220.4	258.8	180.7	290.9	138.3

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The dayside vertical stratification of the troposphere is defined by the irradiated surface beneath it and the emerging convective motions that redistribute the energy upward. The temperature profile is quite steep near the surface and closely follows the dry adiabatic lapse rate (Figures 3(a), (b)). Above the boundary layer ($\approx 850\,\mathrm{hPa}$), the air temperature is closer to a moist adiabat, demonstrating the importance of moist convection, i.e., that the fall of temperature with height is offset by the release of latent heat of condensation.

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The surface on the night side of both planets is extremely cold. This is explained by both the absence of incoming solar radiation and small optical thickness because of low water vapor concentration. In our simulations, the only source of energy for the night side is the atmospheric heat transport from the day side. This idea is conceptually encapsulated in a two-column model of Yang & Abbot (2014), who note that the free troposphere should have a weak horizontal temperature gradient—the dayside and nightside vertical profiles in Figures 3(a), (b) indeed are the same above $\approx 700\,\mathrm{hPa}$. While the free tropospheric gradients are damped, the near-surface air cools radiatively, and then the boundary layer mixing cools the atmosphere above. As a result, the night side is characterized by a very steep near-surface temperature inversion (e.g., Wordsworth 2015; Joshi et al. 2020). In such a stably stratified atmosphere, vertical turbulent mixing of energy is suppressed, reinforcing the cold traps at the surface. Note that the nightside surface temperature, through the day–night heat transport, is very sensitive to changes in the dayside surface temperature, which is, in turn, set by a combination of processes. In simulations with a dynamic ocean (e.g., Del Genio et al. 2019), the response of the nightside temperature to the choice of the convection parameterization is likely to be different but is out of scope of the present study.

Using the Adjust setup has broadly the same impact on both planets' mean T_s: it increases globally ($18\,{\rm{K}}$ for Trappist-1e and $14\,{\rm{K}}$ for Proxima b, see Table 3). As is visible in Figures 2(c) and (d), the greatest warming happens in the nightside cold traps, increasing T_s to $214\,{\rm{K}}$ for Trappist-1e and $166\,{\rm{K}}$ for Proxima b. On the day side, the change in T_s is smaller—only about $10\,{\rm{K}}$ for both planets. It is still positive everywhere for Proxima b (Figure 2(d)), while for Trappist-1e, it is positive in the tropics and negative in the mid-latitudes (Figure 2(c)). As a result, the mean temperature difference between the substellar and the anti-stellar hemisphere (Δ T_dn) is reduced from 57 to $39\,{\rm{K}}$ for Trappist-1e and from 71 to $63\,{\rm{K}}$ for Proxima b (Table 3).

Temperature profiles in the Adjust simulation largely follow those in the MassFlux case, albeit with some deviations (Figure 3, orange curves). For Trappist-1e, using the adjustment scheme warms and moistens the low troposphere but cools and dries the upper troposphere (Figures 3(a), (c)). For Proxima b, it makes the air even warmer and moister throughout the entire troposphere (Figures 3(b), (d)). Altering the convection scheme in our model affects the temperature profile on the night side indirectly via a change in the global wave pattern (see Section 3.1.2). In the Adjust simulation of Trappist-1e (Figure 3(a)), the nightside boundary layer is profoundly warmer, while in its lowest part, the inversion is stronger, despite the surface also being warmer.

One unexpected result of our experiments is that changing the convection parameterization in the model alters the temperature not only on the day side but also, and even more so, on the night side (where there is no convection). In addition, the disparity between the global climate of Proxima b in our model and that simulated by Turbet et al. (2016) appears to be due to the difference in the convection scheme, as posited by Boutle et al. (2017). For example, the temperature profile in the Adjust case (Figure 3(b)) agrees better with the profile of Turbet et al. (2016), who also used a convection adjustment scheme in their simulations. The same argument can be made when comparing the nightside surface temperature minimum in the Trappist-1e case (Figure 2) to that found using other GCMs (e.g., Fauchez et al. 2020).

When we turn off the convection parameterization (the NoCnvPm simulation) and let the UM remove thermal instability via large-scale dynamics, the resulting global climate settles on a state different to that of the MassFlux and Adjust cases. The globally averaged T_s is about $3\,{\rm{K}}$ higher for Trappist-1e but $6\,{\rm{K}}$ lower for Proxima b than in MassFlux (Table 3). The higher T_s of Trappist-1e is mostly due to the warming of the coldest nightside regions (Figure 2(e)), similar to the Adjust simulation. Along the equator at almost all longitudes, but especially in the dayside mid-latitudes, T_s is a few degrees lower compared to the control simulation. In the NoCnvPm simulation of Proxima b, surface cooling happens everywhere, except for the small region at the substellar point (Figure 2(f)). Meanwhile, its coldest regions become even colder: the temperature minimum drops to $138\,{\rm{K}}$

The temperature change in the substellar hemisphere suggests that in the NoCnvPm simulation, the UM is less efficient in exporting energy from the hottest region of the planet. One might indeed expect this outcome from a 3D Earthlike GCM. However, in the Trappist-1e case, the atmospheric circulation seems to mask this tendency by sufficiently warming the coldest regions, as discussed in Section 3.1.2.

The atmospheric stratification at the substellar point and its antipode in NoCnvPm is overall close to that in Adjust for Trappist-1e and to that in MassFlux for Proxima b (Figure 3, green curves). The NoCnvPm simulation is noticeably colder and drier than MassFlux for Trappist-1e, and especially dry in the upper atmosphere (Figure 3(c)). This cannot be explained by only invoking the Clausius-Clapeyron equation: while the temperature above $200\,\mathrm{hPa}$ is almost the same in all three sensitivity experiments, the water vapor content is lower by two or more orders of magnitude. Instead, it is likely due to the less efficient moisture upwelling on the day side and, thus, weaker moisture transport between hemispheres. Consequently, the magnitude of clear-sky longwave cooling on the night side is diminished (not shown).

In all simulations, strong heating from the constantly irradiated surface on the dayside results in a pressure minimum and a lower-level wind convergence. This region is associated with strong upward motions that transport heat and moisture to the upper atmosphere, reducing convective instability. In the upper troposphere above the substellar point, the wind field is divergent (Figure 2). The main feature of the global wind field at this level is the eastward (prograde) jets, emerging in the atmosphere of many synchronously rotating planets (e.g., Showman & Polvani 2011; Carone et al. 2015).

The global circulation can be interpreted with the help of the eddy geopotential field (shown by shading in Figure 4). In the MassFlux experiment, the quadrupole geopotential height distribution comprises two anticyclones to the east of the substellar point symmetric around the equator and two symmetric cyclones near the anti-stellar point (Figures 4(a), (b)). Accordingly, the horizontal eddy wind field is characterized by alternating regions of divergence and convergence between the gyres in mid-latitudes. This pattern corresponds to a particular wave solution in the shallow water equations, namely the westward propagating equatorial Rossby wave (see Figure 3(e) in Kiladis et al. 2009). These planetary waves have a barotropic structure, as confirmed by analyzing the eddy geopotential field at different levels: cyclonic and anticyclonic gyres are aligned in height (not shown). This is also indicated by the free tropospheric temperature contours in Figures 4(a), (b), largely aligning with the isolines of eddy geopotential.

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The planetary-scale equatorial Rossby wave pattern dominates the atmospheric circulation both in the Trappist-1e and Proxima b MassFlux cases. However, there are subtle differences in their dynamical regimes, which can be expressed in terms of the ratio of the Rossby deformation radius and the Rhines length scale to the planet's radius (Haqq-Misra et al. 2017). Following Leconte et al. (2013) and Haqq-Misra et al. (2017), we estimate the nondimensional Rossby radius of deformation, λ_Ro, and the nondimensional Rhines length, λ_Rh, as

$$\begin{eqnarray}&&{\lambda }_{\mathrm{Ro}}=\displaystyle \frac{{L}_{d}}{{r}_{p}}=\sqrt{\displaystyle \frac{{NH}}{2{\rm{\Omega }}{r}_{p}}},\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{\lambda }_{\mathrm{Rh}}=\displaystyle \frac{{L}_{\mathrm{Rh}}}{{r}_{p}}=\pi \sqrt{\displaystyle \frac{U}{2{\rm{\Omega }}{r}_{p}}},\end{eqnarray} \tag{ 2 }$$

where L_d is the equatorial radius of deformation, L_Rh is the Rhines length, r_p is the planet radius, Ω is the planetary rotation rate, $N=\sqrt{g/\theta \partial \theta /\partial z}$ is the Brunt-Väisälä frequency, θ is the potential temperature, $H={R}_{d}T/g$ is the atmospheric scale height, R_d is the dry air specific gas constant, T is the air temperature, and U is the zonal component of the wind vector. Note the equatorial Rossby radius of deformation for continuously stratified fluids L_d is used in the derivation above, and $\beta =2{\rm{\Omega }}/{r}_{p}$. Thermodynamic variables and the wind speed are calculated here as mass-weighted tropospheric averages (within 0–15 km in height).

Estimates of λ_Ro and λ_Rh reveal that the planets' global circulation is close to the boundary between different rotation regimes (Figure 5). The atmosphere of Trappist-1e is in an especially delicate position, with the planetary Rossby wavelength almost exactly matching the planet's radius (λ_Ro ≈ 1). For Proxima b, the Rossby deformation radius does not fit within the confines of the spherical geometry of the planet, as λ_Ro ≈ 1.25. Adding the Rhines length to the picture, we expect that zonal turbulence-driven jets can form and cause a departure from symmetry in the thermally direct circulation in the Trappist-1e case, because the length scale for the turbulent energy cascade is smaller, albeit not by much, than the planetary radius, i.e., λ_Rh ≲ 1. Proxima b is farther away from the transitional boundary with λ_Rh > 1, indicating that its atmosphere is more dominated by thermally direct circulation (Haqq-Misra et al. 2017).

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In the Adjust simulation of Trappist-1e, the change in the atmospheric circulation regime explains the remarkable recession of cold spots on the night side. To first order, it is already hinted at by λ_Ro crossing the boundary in Figure 5, thus, indicating that the circulation regime is closer to the rapid rotation than to the Rhines rotation (as defined in Haqq-Misra et al. 2017). The distribution of the eddy geopotential height is dominated by a pair of cyclonic gyres to the east of the substellar point and a pair of anticyclonic gyres to the west of it (Figure 4(c)). This pattern is almost a mirror-opposite of the distribution in the MassFlux simulation (Figure 4(a)), plus the gyres are shifted poleward and are more zonally elongated. Furthermore, the cyclone-anticyclone pairs have baroclinic structure, as illustrated by the large temperature gradient within their cores. This structure corresponds to the extratropical Rossby wave pattern (e.g., Carone et al. 2015).

Why is the atmospheric circulation in the Trappist-1e case defined by extratropical, rather than equatorial, Rossby waves? We speculate that this is caused by the change in the zonal temperature gradient on the day side, which in turn is due to a different convection regime at the substellar point. Comparing Figures 2(c) to 2(a), we see that in the Adjust simulation the day side, the tropics become warmer, while the substellar mid-latitudes become colder, thus enhancing baroclinicity toward the poles. Larger baroclinicity enhances the extratropical Rossby waves, which then propagate meridionally and break in lower latitudes, decelerating the equatorial super-rotating jet (Mitchell & Vallis 2010). Since the equatorial jet weakens, while the mid-latitude jets strengthen due to larger baroclinicity (via the thermal wind balance), the heat redistribution to the extratropics of the night side becomes more effective, thus causing the cold traps to warm.

In NoCnvPm, the mechanism of the nightside warming for Trappist-1e appears to be similar to that in Adjust, confirmed by λ_Ro < 1 (Figure 5). Even though the substellar point does not warm as in Adjust, the dayside mid-latitude regions become substantially colder, so the baroclinicity increases, resulting in the extratropical Rossby wavelike response (Figure 4(e)).

Due to deep convection, most of the day side of Trappist-1e and Proxima b is covered with multiple layers of clouds (shading in Figure 6). The water vapor carried upwards by convective updrafts eventually precipitates out, mostly in the form of rain (green contours in Figure 6). Snowfall forms a ring of weaker precipitation around the substellar region, coincident with lower temperatures (blue contours in Figure 6).

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While the day sides of both planets in the MassFlux simulations are comparable in terms of the cloud cover and precipitation, the night sides are different. Compared to the mostly cloudless Proxima b case, the night side of in the Trappist-1e case is almost completely covered by low- and mid-level clouds and has more snowfall. This disparity between the two simulated climates is associated with different energy balances: the longwave radiation cooling of Trappist-1e is partly due to the presence of clouds, while in the Proxima b case, it is entirely due to clear-sky radiation (not shown). Note the clouds also act as a greenhouse agent and emit radiation back to the surface.

In Adjust (Figures 6(c), (d)), the day sides of both planets experience a severe reduction in low clouds with respect to MassFlux: the substellar region is now shielded from the incessant stellar radiation only by mid- and high-level clouds. For Trappist-1e, the high cloud layer is smaller and confined to the tropical latitudes, exposing large areas of the planet's surface to space. For Proxima b, high-level clouds are broadly the same, but a large swath of day side is cloudless. Consequently, the Bond albedo of both planets drops to ≈0.14.

On the night side, using the Adjust setup results in different cloud responses for Trappist-1e and Proxima b, as a consequence of the differences in the circulation regime. The polar regions of Trappist-1e become completely enveloped with thick clouds in the Adjust simulation, whereas the tropical regions are only covered with a thin veil of low clouds (and a high-level anvil at the eastern terminator, Figure 6(c)). The increase in extratropical clouds is associated with the increased role of baroclinic instabilities. Meanwhile, the cloud layer on the night side of Proxima b is only slightly thicker and does not extend higher than $2\,\mathrm{km}$ (Figure 6(d)). In the end, the changes in cloudiness and precipitation result in a slightly more positive nightside water balance (i.e., positive precipitation minus evaporation) on both planets compared to that of the MassFlux experiment, with potential ramifications for the global water supply being permanently trapped on the night side as ice over geologic timescales.

Due to the different treatment of condensed water in the convection parameterization (see Section 2.3) and overall atmospheric warming, the total precipitation rate increases more than two-fold in the Adjust experiments over the control. The balance between the "convective" and the "large-scale" precipitation is tipped in favor of the former: from only 20%–25% of total precipitation being convective in MassFlux to 90%–95% in Adjust. Note that while this separation between convective and large-scale precipitation is artificial from the physical point of view, it is a necessary component of most GCMs. More importantly, an incorrect balance between them can result in a different climate state as demonstrated here for tidally locked Earthlike planets.

In NoCnvPm, the dayside cloud pattern is close to that in MassFlux, while the nightside pattern in the Trappist-1e case is close to that in Adjust, in accordance with the global circulation response (see Section 3.1.2). These changes are accompanied by more concentrated precipitation over the substellar point. As the blue isolines in Figures 6(e), (f) demonstrate, the dayside rainfall field is much noisier, which is a manifestation of the grid-scale motions removing instability without the smoothing effect of the convection parameterization. While the substellar region experiences a surge in precipitation, it declines significantly over the rest of the planet both in the Trappist-1e and Proxima b simulations, resulting in less water being deposited on the night side.

Cloud distribution affects the fluxes of energy at the top of the atmosphere (TOA). We use the TOA radiation fluxes to calculate the global cloud radiative effect (CRE) for each simulation (Table 4). CRE is derived as the difference between the clear-sky and all-sky radiative flux (Ceppi et al. 2017). The day sides of tidally locked terrestrial planets are mostly affected by their shortwave component (CRE_SW), which is negative, because H₂O clouds generally reflect solar radiation stronger than the planet's surface. Both for Trappist-1e and Proxima b in the MassFlux simulations, the magnitude of CRE_SW is quite large ($-52.5\,{\rm{W}}\,{{\rm{m}}}^{-2}$ and $-58.3\,{\rm{W}}\,{{\rm{m}}}^{-2}$, respectively) because of the high amount of thick clouds on the day side. Clouds usually reduce outgoing terrestrial radiation, so the longwave CRE (CRE_LW) is globally positive. CRE_LW is half as big for the planets in our study, compared to the present-day Earth. To explain this, we recall that unlike its shortwave counterpart, CRE_LW depends primarily on the emission temperature, which is a function of cloud altitude. While the night sides of the planets are characterized by the strong near-surface temperature inversion, the low-level and, especially, mid-level clouds are suspended in the warmest layer (Figures 3(a), (b)). Consequently, the emission temperature of clouds is higher than that of the clear sky, resulting in a negative nightside (and lower globally) CRE_LW, notably in the case of Trappist-1e (see Figure 6(a) and Table 4).

In the Adjust experiment, CRE is dramatically reduced with respect to the control—mostly due to the smaller magnitude of its shortwave component to $\approx -20\,{\rm{W}}\,{{\rm{m}}}^{-2}$ (Table 4, middle row). This is because the convection adjustment scheme used here immediately precipitates the available condensate, which results in fewer low- and mid-level clouds and, thus, lower CRE_SW. Without the convection scheme (NoCnvPm), the day side is enshrouded in thick clouds with a high-altitude anvil extending to the east (Figures 6(e), (f)), increasing the magnitude of CRE_SW and making the total CRE more negative (Table 4, bottom row). This effect is also evident in the increase of the dayside albedo.

A useful estimate of the horizontal energy transport in planetary atmospheres is the mass-weighted vertical integral of the horizontal divergence of the moist static energy (MSE) flux, ${\int }_{0}^{{z}_{\mathrm{top}}}\rho {\rm{\nabla }}\cdot \left({\boldsymbol{u}}h\right){dz}$, where $h={c}_{p}T+{gz}+{L}_{v}q$ and ${\boldsymbol{u}}$ is the horizontal wind vector. Its average profile is presented in Figure 7 as a function of longitude. Principally, we see the MSE flux diverging in the substellar hemisphere and converging in the anti-stellar hemisphere in all of our simulations. The divergence of dry static energy (DSE, ${c}_{p}T+{gz}$) flux dominates over the latent component (LSE, ${L}_{v}q$), especially on the dry night side of the planet. At the substellar point, the DSE flux divergence in the upper troposphere is substantially compensated for by the convergence of LSE flux in the lower troposphere, reminiscent of the Hadley circulation on Earth. A similar structure of the MSE transport divergence was also found in simulations of a slowly rotating Earthlike aquaplanet (Merlis & Schneider 2010), albeit with higher amplitude due to the higher insolation received from the Sun. Both in Figures 7(a) and (b) it is evident that the longitudinal profiles are not perfectly symmetric around the prime meridian and instead have peaks shifted east by a few degrees. This is related to the eastward shift of the hottest part of the atmosphere due to the upper-level jets (e.g., Showman & Guillot 2002; Penn & Vallis 2018); it also justifies the positioning of the high-resolution domain (see Section 3.2).

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To first order, profiles of MSE flux divergence are similar in the Trappist-1e case compared to those in the Proxima b case. The largest difference is in the profiles of the latent component of MSE: the LSE flux convergence at the substellar point is much stronger in the Proxima b case (Figure 7(b)) in all three simulations, while in the Trappist-1e case, it is quite weak in the MassFlux simulation and almost negligible in the sensitivity simulations (Figure 7(a)). At the same time, there is a larger contribution of the latent component to the MSE flux divergence on the night side of Trappist-1e compared to that of Proxima b, which is in accordance with the higher nightside column-integrated water vapor content in the Trappist-1e case (though the LSE component is still smaller than the DSE component). In both cases, using the Adjust setup results in a more intense energy transport and, in particular, a larger share of the LSE flux divergence in the global energy transport.

To investigate the structure of this inter-hemispheric energy transport, we turn our attention to the zonal transport of sensible (${c}_{p}T$) and latent (${L}_{v}q$) heat through the plane of the eastern terminator (Figure 8), where the change in MSE flux divergence is the steepest (Figure 7). The sensible heat transport clearly dominates the total heat transport, while its latent counterpart is ≈2 orders of magnitude smaller. Their structure in the vertical and horizontal is dictated by the wind field but depends on the temperature and water vapor distribution too. The day-to-night energy transport is the strongest at $\approx 5\,\mathrm{km}$ above the surface ($\approx 500\,\mathrm{hPa}$), i.e., slightly lower than the jet stream maxima and coinciding with the altitude of the weak horizontal temperature gradient (Figures 3(a), (b)). Close to the surface in the tropics, the heat transport is negative, partly canceling the net dayside divergence of the MSE flux (Figure 7). The intensity of water vapor transport is largely correlated with the intensity of dry heat transport (see contours and shading in Figure 8). Consequently, there are differences in the water vapor path on the night side, as mentioned above.

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The heat flux cross sections in Figures 8(c)–(f) elucidate the response to different convection parameterizations and how it differs between the two planets. Consistent with the changes in the circulation regime, the dry heat transport maxima is almost doubled in the Adjust experiment for Trappist-1e, while the water vapor transport substantially intensifies too and is more concentrated in the tropical region (Figure 8(c)). With no convection parameterization (NoCnvPm, Figure 8(e)), the dry heat transport is also greater than that in the MassFlux simulation, but the water vapor transport is substantially weaker. Both in the Adjust and NoCnvPm cases, the day side to night side heat transport is closer to the equator, while the opposite flow emerges in the polar regions (Figures 8(c), (e)). The Proxima b case generally responds in a similar way, but the response is much more muted, especially in terms of the sensible heat transport cross sections (Figures 8(d), (f)). Most importantly, the overall structure of the heat transport in the sensitivity experiments remains the same as in the MassFlux experiment.

The global heat transport efficiency can be also expressed via the TOA energy fluxes. Following Leconte et al. (2013), we compare the ratio of the mean nightside TOA OLR over the mean dayside TOA OLR, referred to as the global heat redistribution parameter (η). This parameter reaches its maximum when the horizontal transport is the largest, i.e., in the Adjust experiments: 0.81 for Trappist-1e and 0.67 for Proxima b. For Trappist-1e, η is the lowest in MassFlux (0.70) and for Proxima b in NoCnvPm (0.53). Thus, selecting one convection parameterization or another for a terrestrial exoplanet can induce a difference of ≈10% in its thermal emission footprint. Note that the amount of water vapor on the night side of the planet affects the heat redistribution too by changing the emissivity of atmosphere (Lewis et al. 2018).

To sum up, the choice of convection parameterization is important for the global circulation and thermodynamic regime of tidally locked planets. By modulating the heat redistribution, they alter the thermal contrast between the day and night hemispheres. The change in the thermal contrast is not likely to be observable by modern telescopes, implying that GCMs can rely on current convection parameterizations without affecting their synthetic phase curves too much. Nevertheless, the change in the surface temperature, especially on the night side, is substantial (see Table 3) and comparable to the impact of large variations in the incident stellar flux (e.g., Komacek & Abbot 2019). Furthermore, by looking at two slightly different planetary configurations, we show that the impact of convection on the global climate is sensitive to the planetary circulation regime in general and, thus, depends on external parameters such as the stellar irradiance, gravity, radius, and the rotation rate of the planet. It should be noted that none of the existing parameterizations of convection are perfect, but most exoplanetary GCMs rely on them. The results of this study demonstrate that caution should be taken when interpreting results of GCM simulations with one parameterization or another. In the absence of observations, our best alternative to parameterized convection is a high-resolution convection-permitting model, used in the next section.

Figures 9 and 10 present instantaneous TOA OLR in the (parent) global and HighRes model simulations over the substellar region. Besides reproducing individual convective plumes, shown by low values of OLR (i.e., high clouds), HighRes also simulates cloud-free areas of subsidence more clearly than the coarse-resolution model (cf. middle and right panels in Figures 9 and 10). As a result, there is a clear separation between the two models in the TOA OLR histogram (Figures 11(a), (b)). In the global model, TOA OLR tends to be higher and has a peak at $\approx 220\,{\mathrm{Wm}}^{-2}$, corresponding to warmer and, hence, lower cloud tops ($250\,{\rm{K}}$, ≲$5\,\mathrm{km}$). The HighRes histogram has only a minor secondary peak at this TOA OLR value (Figure 11(a)), while the absolute maximum is at $\approx 120\,{\mathrm{Wm}}^{-2}$, corresponding to colder and higher clouds ($214\,{\rm{K}}$, ≳$10\,\mathrm{km}$). The decrease of OLR (≈15%–20%) at the top of the atmosphere in HighRes is compensated by the increase of the outgoing shortwave radiation. In other words, the average Bond albedo of the substellar region increases by about 3% both for Trappist-1e and Proxima b. It is important to note that the TOA OLR histograms are sensitive to the sampling region and time. Using data from a central part of the domain and only over the last 10 days of the HighRes simulation results in more similarity between the global and HighRes data, especially for the Proxima b case (Figure 11(d)). The remaining positive OLR bias of the global model in the Trappist-1e case (Figure 11(c)) can be attributed to the maximum in the liquid cloud condensate mixing ratio (see Section 3.2.2). We aim to conduct more convection-permitting simulations with various grid configurations and nested domain placements in the future to explore the robustness of these results.

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Grid cells with clouds and intense precipitation (Figure 12(a)) correspond to the most intense convective updrafts, represented by positive vertical wind values, while dry patches are associated with downdrafts (Figure 12(b)). In the global model, the vertical wind field is mostly positive but has much lower absolute values in each grid cell. Concomitantly, the precipitation rate in the global model is significantly weaker and spread over the whole region more evenly (not shown). This results in the precipitation rate being capped at $\approx 40\,{\mathrm{mmd}}^{-1}$ in the global model, while the maximum precipitation rate in the HighRes model exceeds $100\,{\mathrm{mmd}}^{-1}$ (Figure 12(a)). There are >40% more cells with low precipitation rate ($\leqslant 1\,{\mathrm{mmd}}^{-1}$) in the HighRes model than in the global simulation, reminiscent of the change in rainfall on Earth with and without parameterized convection (Maher et al. 2018). Qualitatively speaking, the HighRes simulation is able to reproduce a wider spectrum of atmospheric circulations, including individual convective cells, mesoscale frontal structures, and cyclonic vortices.

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Despite the spatial variability of convective activity and TOA energy fluxes, the average atmospheric stratification in the substellar region is rather similar between the global simulation and the HighRes simulation. The temperature and water vapor in the HighRes simulation essentially follow the MassFlux lapse rates shown in Figure 3, though there is some minor deviation: the lower troposphere is slightly colder and drier in the Trappist-1e case and slightly warmer and moister in the Proxima b case—resembling the effect of the NoCnvPm simulation. Note that the vertical profiles represent 10 day averages, and instantaneous profiles differ more.

More prominent differences between the global and HighRes experiments appear in the vertical profiles of cloud liquid and frozen water content (Figure 13). In general, these profiles show a transition between liquid-phase clouds at lower model levels to mixed-phase clouds within ≈1.7–3.5 km, to ice-phase clouds aloft. Parameterized convection in the global simulation, interacting with the cloud scheme, tends to underproduce clouds in the boundary layer (2–3 times less liquid water) when compared to the HighRes model. However, in the mixed-phase cloud layer above, the liquid water content is overestimated by the global model, resulting in an overall higher liquid water content within the substellar region. The concentration of ice crystals in the global model, on the other hand, has a smaller bias relative to the HighRes model, though it is positive in the Trappist-1e case and negative in the Proxima b case. With regards to the mixed phase (where ice crystals comprise between 20% and 80% of the total cloud condensate, Sergeev et al. 2017), the global simulation makes this type of cloud thicker by several hundred meters than that in HighRes. This has an impact on the formation of precipitation, as well as graupel-type hydrometeors and, hence, the generation of lightning (Tost et al. 2007). The latter may then alter the atmospheric composition, potentially detectable by future telescopes (Ardaseva et al. 2017).

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The TOA energy balance over the substellar point is predominantly affected by the upper layers of convective clouds; therefore, the disparity in frozen cloud condensate between coarse- and high-resolution simulations could be crucial. As Figure 13 shows, the cloud ice profiles at the very top of the domain are congruent in both models, which is an unexpected result given the noticeable differences in TOA fluxes mentioned above. A deeper investigation of the model's microphysics scheme and its interaction with the convection parameterization is required to reveal the answer to this.

Within the lower-to-mid troposphere, radiation heating is much weaker than the temperature changes due to the latent heating or cooling (not shown). Differences in cloud structure between the global and HighRes model affect this heating profile. The HighRes model, having more low-level liquid-phase clouds (Figure 13), tends to have a strong negative latent cooling due to the evaporation of cloud condensate (Figure 14). In the global simulation, on the other hand, the cloud-related temperature change is smaller, hovering around zero at these vertical levels. At approximately $800\,\mathrm{hPa}$ ($\approx 2\,\mathrm{km}$) we see a local cooling peak, which is especially prominent in the Proxima b case (Figure 14(b)). Above this level, the latent heating starts to dominate both in the global and HighRes simulations, with shortwave heating overtaking in the upper troposphere (not shown). The rate of the latent heat release is stronger in the global model, though the difference is obscured by internal variability (see, e.g., Figure 14(a)). Nevertheless this contrast in heating rates results in the different upper-level flow divergence, as we discuss in the next section (Section 3.3).

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