Greater Climate Sensitivity and Variability on TRAPPIST-1e than Earth

To study the climate extremes and dynamics of TRAPPIST-1e and compare them to those of an Earth-analog planet, we utilize the ExoCAM GCM (publicly available at https://github.com/storyofthewolf/ExoCAM; Wolf et al. 2022). ExoCAM is a well-established model that has been previously utilized to study the atmospheric circulation of a broad range of exoplanets (Kopparapu et al. 2017; Wolf 2017; Haqq-Misra et al. 2018; Komacek & Abbot 2019; Yang et al. 2019; Suissa et al. 2020; May et al. 2021). The model is built from the Community Atmosphere Model (CAM) version 4 (Neale et al. 2012), and includes routines to consider planetary properties and orbital configurations of a range of exoplanets, along with the novel nongray correlated-k radiative transfer scheme ExoRT (https://github.com/storyofthewolf/ExoRT).

In this work, we conduct a suite of atmospheric model simulations of both TRAPPIST-1e and an Earth-analog planet. To simulate the atmosphere of TRAPPIST-1e, we initialize the atmosphere from the end state of previous simulations of TRAPPIST-1e (May et al. 2021). Specifically, we conduct a set of three simulations with 1 bar of N₂ and varying pCO₂ from 10⁻² to 1 bar with intervals of an order of magnitude between each level of pCO₂ (referred to from this point on as "Low," "Mid," and "High" pCO₂ scenarios, respectively). This sweep of pCO₂ was chosen to cover the range of possible climate states for TRAPPIST-1e (Wolf 2017). In all three simulations, we use a radius of TRAPPIST-1e of 0.92 Earth radii, a surface gravity of 9.12 m s⁻², and an incident stellar flux of 900.85 W m⁻² with an incident stellar spectrum corresponding to an M dwarf with effective temperature of 2600 K (Allard et al. 2007). We assume that TRAPPIST-1e is tidally locked with an orbital and rotation period of 6.10 Earth days, that its orbit has zero eccentricity, and that TRAPPIST-1e has zero obliquity. We consider the surface of the planet to be a global ocean (i.e., an aqua-planet) with a depth of 50 m. We include a thermodynamic sea-ice scheme (Bitz et al. 2012) but do not include ocean heat transport. From the initial condition of May et al. (2021), we then continue each simulation for 80 yr to obtain a daily mean output that we use to analyze climate extremes and dynamics.

To compare with the TRAPPIST-1e simulations described above, we conduct a similar suite of model simulations with planetary properties comparable to that of Earth. We likewise conduct three simulations covering pCO₂ ranging from 10⁻² to 1 bar, assuming 1 bar of background N₂. To enable direct comparison with the simulations of TRAPPIST-1e, these simulations also assume an aqua-planet surface with a 50 m deep slab ocean and zero ocean heat transport, along with zero orbital eccentricity and zero planetary obliquity. These Earth-analog simulations use a planetary radius of 6.37122 × 10⁶ m, a surface gravity of 9.80616 m s⁻², a rotation period of 8.64 × 10⁴ s, and an incident stellar flux of 1360 W m⁻² with an incident stellar spectrum corresponding to our Sun.

All simulations presented in this work, both for the TRAPPIST-1e and Earth-analog cases, have 40 vertical levels and a horizontal grid spacing of 4° × 5° (or longitude–latitude 72 × 46). The dynamical time step of the simulations was set to 30 minutes, and the radiative time step to 90 minutes. Though each ExoCAM simulation includes ∼45 yr of initial spin-up, we only analyze the final 80 yr of daily output from all cases.

TRAPPIST-1e T_max and precipitation mean climatology for each pCO₂ scenario (Figure 1) are computed by averaging over their entire period (i.e., 80 yr). We define extremes at the grid-box level, by retaining daily atmospheric values that exceed the 95th percentile of their distribution. We further consider six subregions, namely mid-latitude antistellar (30-60N, 345-15E), mid-latitude substellar (30-60N, 165-195E), equatorial antistellar (−15-15N, 345-15E), equatorial substellar (−15-15N, 165-195E), equatorial west-terminator (−15-15N, 75-105E), and equatorial east-terminator (−15-15N, 255-285E; Figure 1(a)). We choose these subregions since they separate the dayside and nightside hemispheres along with the terminator regions in order to distinguish the impacts of tidal locking on climate variability.

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The spatial patterns of TRAPPIST-1e and the Earth-analog extremes are computed as follows: (i) for each pCO₂ simulation and grid box take the extremes (i.e., values >95th percentile), and (ii) for each grid box take the mean of extremes. For ERA5 we use the same procedure. Then, the spatial differences (Δ) between Earth and TRAPPIST-1e, ERA5 and TRAPPIST-1e, and ERA5 and Earth are computed by subtracting the medians of the extremes. We further compute, at the grid-box level, the mean anomalies of climate extremes for TRAPPIST-1e, Earth, and ERA5. The mean anomalies of extremes for TRAPPIST-1e, Earth, and ERA5 are computed based on ERA5 (1979–2020) daily climatology and are displayed in box plots.

To characterize the climate dynamics of TRAPPIST-1e, the Earth-analog, and ERA5 reanalysis data sets we use a recently developed approach, which combines Poincaré recurrences with extreme value theory (Lucarini et al. 2012). This dynamical systems point of view has been fruitfully utilized in the Earth climate literature for various climate variables and data sets (Rodrigues et al. 2018; Faranda et al. 2019b, 2019; De Luca et al. 2020a, 2020b; Hochman et al. 2021a). This perspective permits the computation of instantaneous characteristics of chaotic dynamical systems. Hence, it is suitable to investigate the time-series dynamics of exoplanet atmospheres. The temporal sequence of two-dimensional atmospheric variables, in our case T_max (see main text) or T_min (see Appendix), are used as samples from a long trajectory in the atmosphere's phase space. For each daily longitude–latitude map, we compute instantaneous dynamical properties. The analysis concentrates on two metrics: persistence (θ⁻¹) and local dimension (d) (Faranda et al. 2017). The persistence (θ⁻¹) of a specific atmospheric state would approximate for how long the T_max maps in the ERA5 reanalysis or ExoCAM model simulations resemble the chosen atmospheric state every time the trajectory arrives near that state. The local dimension (d) is an estimate for the number of options that the atmospheric state can transition from and to (see Figure 2 for some intuition on the dynamical systems metrics meaning).

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In practical terms, we consider an atmospheric variable x (i.e., T_max or T_min) over a given domain (e.g., one of the regions in Figure 1(a)) and a state of interest ζ. Then, we compute a value of θ⁻¹ and d for each time step of x (i.e., each day). Recurrences of ζ are states that are close to ζ in phase space, and thus have spatial configurations that are very similar to ζ in physical space. We define recurrences using the Euclidean distance (dist). To compute recurrences, one has to first define an observable via logarithmic returns as follows:

$$\begin{eqnarray*}&&g\left(x\left(t\right),\zeta \right)=-\mathrm{log}\left[\mathrm{dist}\left(x\left(t\right),\zeta \right)\right],\end{eqnarray*}$$

where x(t) represents the complete time series of the variable x. Then, a sufficiently high quantile threshold s(q, ζ) (in our case the 98th percentile) is defined for the time series g(x(t), ζ), so that for g(x(t), ζ) > s(q, ζ) (i.e., a recurrence) it is possible to define u(ζ) = g(x(t), ζ) − s(q, ζ). The cumulative distribution function F(u, ζ) converges to the exponential member of the generalized Pareto distribution, which is relevant for modeling the tails of physical distributions (Freitas et al. 2010):

$$\begin{eqnarray*}&&F(u,\zeta )\simeq {\text{}}{\exp }\left[-\vartheta (\zeta )\displaystyle \frac{u(\zeta )}{\sigma (\zeta )}\right],\end{eqnarray*}$$

where the parameters ϑ and σ are functions of the chosen state ζ. The local dimension (d) is then computed as d = 1/σ. The parameter ϑ is the extremal index and is here estimated using the approach in Süveges (2007). While the persistence is given by

$$\begin{eqnarray*}&&{\theta }^{-1}\left(\zeta \right)=\displaystyle \frac{{\rm{\Delta }}t}{\vartheta \left(\zeta \right)},\end{eqnarray*}$$

where Δt is the time interval between T_max or T_min maps. In practice, we obtain a value of θ⁻¹ and d for each output time step in our data set. From this point on we use the inverse persistence metric (θ) for illustration purposes only, so that when both θ and d are low there is less change with time of the atmosphere, and vice versa.

The statistical significance for the median spatial differences of climate extremes has been assessed for each grid box with a two-tailed Wilcoxon rank-sum test (Mann & Whitney 1947). In addition to the Wilcoxon rank-sum test, we also implemented the Bonferroni correction to the p-values obtained (Bonferroni 1936; Sedgwick 2014). The Bonferroni correction considers Type I errors (or false positives) that can occur when performing a large number of statistical tests. Lastly, we tested the significance at the 5% level (p-value <0.05) of the differences between medians and standard deviations for extreme anomalies and dynamical systems properties. For the medians, we perform a two-tailed Wilcoxon rank-sum test for Earth and TRAPPIST-1e between "Low" and "Mid," and "Low" and "High" pCO₂. The same applies when testing the standard deviations, but here we used a bootstrap test with 10,000 realizations (Markowski & Markovski 1990). The statistical tests we used throughout this study have been used previously in many Earth climate studies (e.g., De Luca et al. 2020a, 2020b; Hochman et al. 2021a, 2022).

We first analyze the spatial differences between TRAPPIST-1e and Earth climate extremes. To do so, we start by comparing the TRAPPIST-1e mean climatology to its extremes (Figure 1 with respect to Figures 3(a), (c), (e) and 4(a), (c), (e), respectively). For T_max, the highest mean temperature (∼20°C–30°C in the "Low" and "Mid" pCO₂ scenarios, and ∼60°C in the "High" scenario) is located around the substellar region at the planet's dayside. The minimum values (∼−60°C in the "Low," ∼−35°C in the "Mid," and ∼45°C in the "High" scenarios) are found at mid-latitude antistellar regions (Figures 1(a), (c), (e)). The peak extremes for T_max are located at the equatorial substellar region (∼−3°C in the "Low," ∼2°C in the "Mid," and ∼35°C in the "High" pCO₂ scenarios; Figures 3(a), (c), (e)). For precipitation, the highest mean (∼12 mm d⁻¹ in the "Low" and "Mid" pCO₂ scenarios, and ∼10 mm d⁻¹ in the "High" scenario) and extreme (∼30 mm d⁻¹ in the "Low," ∼45 mm d⁻¹ in the "Mid," and ∼55 mm d⁻¹ in the "High" scenarios) values are located at the substellar equatorial region (Figures 1(b), (d), (f) and 4(a), (c), (e)). Note, however, that for the "High" pCO₂ scenario another maximum emerges at the polar regions (Figures 1(f) and 4(e)). Indeed, the higher pCO₂, and consequently the higher temperatures, allow precipitation to develop at the poles.

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Next, we compare the climate extremes of the Earth-analog simulations to ERA5 reanalysis (T_max in Figures 3(b), (d), (f) with Figure 3(g) and precipitation in Figures 4(b), (d), (f) with Figure 4(g)). Both the Earth-analog and ERA5 show the maxima for extremes of T_max and precipitation at equatorial regions. However, the Earth analog shows higher absolute values, particularly for T_max (∼60°C in the "Mid" pCO2 scenario and ∼70°C in the "High" scenario compared to ∼30°C in ERA5). This is due to the higher pCO₂ we consider, as compared to the observed values on present-day Earth (see Section 3.1). In addition, the spatial variability in ERA5 is larger than the Earth analog, in which T_max ranges from −50°C to 55°C in ERA5 as compared to just ∼25°C to 45°C in the Earth analog (see the "Low" pCO₂ scenario in Figures 3(b)–(g)). The reason is that in the Earth-analog simulation, we consider an aqua-planet with zero obliquity and hence no seasonality (see Section 3.1), whereas this is not the case in the representation of Earth in ERA5. Indeed, when considering T_max in ERA5, "hot spots" are located over land, e.g., over Australia and the mid-latitude desert strip, whereas for the Earth-analog the "hot spot" is uniformly distributed around the equator (Figures 3, (b), (d), (f), and (g)). The highest precipitation values in ERA5 are situated over the oceans particularly close to the continents and at equatorial regions; however, in the Earth-analog simulations a very clear inter-tropical convergence zone (ITCZ) and precipitation patterns resembling the Hadley, mid-latitude, and polar cells are revealed (Figures 4(b), (d), (f), and (g)). Note that for the "Mid" pCO₂ scenario a double ITCZ emerges, which is not apparent in the other two scenarios. Such a feature may be linked to differences in the atmospheric energy transport in the "Mid" scenario (e.g., Adam et al. 2018; see Figures 4(d) to (b) and (f)).

Finally, we quantitatively compare the differences in climate extremes between TRAPPIST-1e, the Earth-analog simulation, and ERA5 (Figures 5 and 6). In these Figures, red (blue) refers to warmer/drier (colder/wetter) extreme conditions on Earth relative to TRAPPIST-1e. Generally, both the Earth analog and ERA5 display warmer extremes as compared to TRAPPIST-1e, except for the "High" scenario, in which TRAPPIST-1e displays warmer extremes (Figures 5(a), (b), (d), (e), (g), (h)). Indeed, the largest differences in T_max are situated at the mid-latitude antistellar regions for the "Low" and "Mid" scenarios (Figures 5(a), (b), (d), (e); ∼45°C–75°C). This is the coldest region in the TRAPPIST-1e simulation due to cold-core Rossby gyres formed because of the planetary Matsuno–Gill wave pattern induced by the contrast in irradiation from dayside to nightside (Pierrehumbert & Hammond 2019). However, in the "High" scenario, particularly for the difference between ERA5 and TRAPPIST-1e, the largest differences are located at the southern pole (Figure 5(h)). Regarding precipitation, the Earth analog is significantly wetter at equatorial regions, but rather drier at relatively small regions north and south of the substellar point, especially in the "Low" and "High" scenarios (Figures 6(a), (g)). In the "High" pCO₂ scenario, the Earth analog is also drier at the polar regions (Figure 6(h)).

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Shifting the focus to the difference between ERA5 and TRAPPIST-1e climate extremes, the general spatial difference patterns are kept, but the location, sign, and numerical values vary (see Figures 6(b), (e), (h) with Figure 6(a), (d), (g)). As also mentioned above, we relate this to TRAPPIST-1e, assumed to be a tidally locked aqua-planet with higher pCO₂ and slower rotation rate as observed on Earth (see Section 2). Indeed, ERA5 has significantly larger T_max extremes over the continents, whereas significantly lower T_max extremes at its substellar regions as compared to TRAPPIST-1e (Figures 5(b), (e), (h)). ERA5 displays wetter (drier) extremes at equatorial regions and at mid-latitude coastal regions (mid-latitude substellar and polar regions; Figures 6(b), (e), (h)). As a reference, we further provide the differences in climate extremes between ERA5 and the Earth analog (Figures 5(c), (f), (i) and Figures 6(c), (f), (i)).

The climate sensitivity of TRAPPIST-1e and the Earth analog to pCO₂ show some significant differences (Tables 1–2 and Figures 7–10). In these figures, red (blue) refers to TRAPPIST-1e (Earth) and black/gray refers to the ERA5 reanalysis values. Starting from T_max, both TRAPPIST-1e and the Earth analog show a significant increase in both the extremes and median values related to an increase in pCO₂ (Figures 7 and 8; Tables 1 and 2). Globally, the increase in T_max extremes and medians for TRAPPIST-1e is ∼1.5 times larger than the increase for the Earth analog; indeed, the Earth case exhibits a greater increase in values from "Low" to "Mid" pCO₂ compared to TRAPPIST-1e. Yet, TRAPPIST-1e exhibits a greater increase in values from "Mid" to "High" pCO₂ (Figures 7(a) and 8(a)). However, observing in more detail, we find that the larger sensitivity is particularly located at the antistellar and terminator regions rather than at the substellar ones (Figures 7(b)–(g) and 8(b)–(g)). The differences between the regions are most probably related to the fact that the more sensitive regions in TRAPPIST-1e are areas transitioning between temperatures that are well below zero degrees to above zero degrees as a function of the increase in pCO₂. Moreover, these regions do not receive irradiation, thus the day-to-night temperature contrast decreases with increasing pCO₂.

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Next, we describe the influence changes in pCO₂ have on precipitation in both planets (Tables 1 and 2; Figures 9 and 10). Globally, there are some differences between TRAPPIST-1e and the Earth analog. Indeed, the TRAPPIST-1e simulations provide evidence for an increase in both the extremes, the median and variability with an increase in pCO₂ (Figures 9(a) and 10(a); Tables 1 and 2). However, the Earth analog displays a somewhat different picture. The extremes do show a significant increase with pCO₂ increase (Figure 9(a); Table 1), but the median values show a general decrease and an increase in variability (Figure 10(a); Table 2). This paradoxical relation is also projected for some regions on Earth, i.e., an overall decrease in precipitation but with an increase in the extremes (IPCC 2021).

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The detailed regional analysis provides further insights into precipitation variability as a function of an increase in pCO₂. The increase in extremes for TRAPPIST-1e as pCO₂ increases are particularly evident at the equatorial substellar and east-terminator regions (Figures 9(e), (g); Table 1). The asymmetry between the east- and west-terminator regions is due to the superrotating eastward equatorial jet that preferentially transports water vapor lofted upward at the substellar regions to the eastern terminator. The Earth analog shows the largest variations in extremes at all equatorial regions, i.e., ITCZ regions (Figures 9(c)–(f); Table 1). Indeed, the extremes are particularly influenced where the highest amounts of precipitation are located in each planet (Figure 4).

Figure 10 shows that the median precipitation values of TRAPPIST-1e significantly decrease and variability increases at the mid-latitude substellar, equatorial substellar, and equatorial antistellar regions due to an increase in pCO₂ (Figures 10(c), (d), (e); Table 2). Indeed, in these regions TRAPPIST-1e displays a ∼2 times stronger sensitivity of precipitation to changes in pCO₂. However, the Earth analog shows significant decreases in median precipitation and an increase in variability in all regions (Figures 10(b)–(g); Table 2). The time series for both the annual climate means and extremes are displayed in Figure 11. Generally, the time-series variability in both mean and extreme precipitation is larger than in temperature and increases with increasing mean precipitation.

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Changes in the climate dynamics of TRAPPIST-1e and the Earth analog due to an increase in pCO₂ are examined using a dynamical systems point of view computed for the T_max variable (Figure 12; Table 3). The first evident result is that an increase in pCO₂ increases the persistence of the atmospheric circulation (lowering of θ). This effect is much larger in the TRAPPIST-1e simulations as compared to the Earth-analog simulations, except for the equatorial substellar region. Indeed, in that region of highest solar incoming radiation the persistence is much higher (low θ) as compared to other regions on TRAPPIST-1e (see Figure 12, left column; Table 3).

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The second key finding is that for the Earth-analog simulations we see a uniform increase in persistence (lowering of θ) both globally and in all regions (Figure 12, middle column; Table 3). This result has important implications as to the changes in the climate dynamics on Earth due to climate change. Indeed, we show here that an increase in pCO₂ may result in an increase in persistent atmospheric configurations, including their extremes, and therefore a direct change in their possible impacts. In addition, some regions both in TRAPPIST-1e and in the Earth analog show a decrease in d with increasing pCO₂. Taking the changes in both θ and d together suggests a tendency toward an atmosphere that changes less with time. This is particularly prominent for equatorial regions in the Earth analog and for all regions in TRAPPIST-1e except for the equatorial substellar region (Figure 12; Table 3).

Finally, when comparing the Earth-analog simulations (Figure 12, middle column; Table 3) to ERA5 reanalysis (Figure 12, right column; Table 3) we find that the time-series dynamics in the "real" Earth tends to change more with time (higher θ and d) as compared to the Earth analog (note the different ranges of the y-axis in Figure 12). We relate this to the fact that in the Earth simulation we consider an aqua-planet with zero obliquity and thus no seasonality (see Section 2), whereas this is not the case as Earth is represented in ERA5.