Hurricanes on tidally locked terrestrial planets: Fixed surface temperature experiments

Hurricanes (also known as tropical cyclones or typhoons) are low-pressure weather systems with well-organized convection, which are among some of the most destructive disasters on Earth because they can induce strong winds, a rapid rise in local sea level, and heavy precipitation (Anthes Anthes (1982), Emanuel Emanuelb (2018)). Hurricanes can also enhance the vertical mixing of heat and nutrients in the ocean, increase horizontal oceanic heat transport, and, subsequently, influence global climate (Emanuel Emanuela (2001), Jansen & Ferrari Jansen (2009), Li & Sriver LiH (2018)). For instance, the curl of strong hurricane winds can cause divergence and convergence in the upper ocean, producing regions of up-welling and down-welling, enhancing the exchanges between surface and subsurface oceans. Therefore, it is an important and interesting issue to consider whether hurricanes can form on other potentially habitable planets beyond Earth.

In this study, we focus on tidally locked terrestrial planets around M dwarfs due to their relatively large planet-to-star ratios and frequent transits based on observations. These planets differ from Earth in three major aspects: the uneven distribution of stellar energy between the permanent day and night sides, the slow rotation rate due to strong tidal force, and the redder stellar spectrum than the Sun. Several atmospheric general circulation models (AGCMs) have been employed and modified to simulate and understand the atmospheric and climatic dynamics of the planets (Joshi et al. Joshi (1997), Merlis & Schneider Merlis (2010), Edson et al. Edson (2011), Pierrehumbert Pierrehumberta (2011), Wordsworth et al. Wordsworthetal (2011), Leconte et al. Lecontea (2013), Menou Menou (2013), Showman et al. Showmanb (2013), Carone et al. Carone (2015), Wordsworth Wordsworth (2015), Shields et al. Shields (2016), Turbet et al. Turbetetal (2016), Boutle et al. Boutle (2017), Checlair et al. Checlair (2017), Haqq-Misra et al. Haqq-Misra (2017), Kopparapu et al. Kopparapu (2017), Noda et al. Noda (2017), Wolf Wolf2017 (2017), Turbet et al. Turbet (2018), Del Genio et al. Del Genio (2019), Pierrehumbert & Hammond Pierrehumbertb (2019), Yang et al. Yang (2019)).

These AGCMs have horizontal resolutions that are always equal to or larger than 300 km, so that most of their studies focus on planetary-scale phenomena, such as global-scale Walker circulation, equatorial superrotation, and forced Rossby and Kelvin waves, and their models are not able to properly simulate the characteristic features of hurricanes, such as the warm core, the eye-eyewall structure, and the spiral rain bands. No work has investigated synoptic phenomena apart from Bin et al. (Bin (2017)). Based on the output data of an AGCM, the authors estimated genesis potential index of hurricanes and showed that the probability of hurricane formation is low for planets in the middle range of the habitable zone of M dwarfs. However, the model resolution they used was not directly capable of simulating hurricanes and the question of whether the empirical index could be applied to exoplanets could not be answered. Moreover, they considered planets in the middle range of the habitable zone only. Here, we show that the possibility of hurricane formation increases with temperature and for planets with higher temperatures (closer to the inner edge of the habitable zone), the possibility is greater.

In this study, we explicitly simulate hurricane formation on tidally locked terrestrial planets with a high-resolution ($\approx$50 km) AGCM. The structure of the paper is as follows. Section 2 describes our methods, Section 3 presents our results, and Section 4 gives our conclusions.

For our model, we used the global Community Atmosphere Model version 4 (CAM4) with a dynamical core of finite volume (Neale et al. Neale (2010)). Deep convection was parameterized using the updated mass flux scheme of Zhang and McFarlane (ZhangG (1995)). Subgrid-scale momentum transport associated with convection was included (Richter & Rasch Richter (2008)). The parameterization of shallow moist convection is based on Hack (Hack (1994)). Condensation, evaporation, and precipitation parameterization is based on Zhang et al. (ZhangM (2003)) and Rasch and Kristjansson (Rasch (1998)). Cloud fraction is diagnosed from atmospheric stratification, convective mass flux, and relative humidity (Slingo Slingo (1987), Hack et al. Hack1993 (1993), Kiehl et al. Kiehl (1998), Rasch & Kristjansson Rasch (1998)). The realistic radiative transfer of water vapor, clouds, greenhouse gases, and aerosols are included as well (Ramanathan & Downey Ramanathan (1986), Briegleb Briegleb (1992), Collins et al. Collins (2002), Neale et al. Neale (2010) ).

The horizontal resolution we employed is 0.47^∘ $\times$ 0.63^∘ in latitude and longitude, respectively. The number of vertical levels is 26. The planetary surface is covered by seawater throughout (namley, an aquaplanet). Because of the high resolution and limited computational power, we specify surface temperature (T_S) in the simulations. With a fixed T_S, the atmosphere reaches an equilibrium state within several years. If the model were coupled to a 50-m slab ocean, the surface and atmosphere would require tens of years to reach the equilibrium state, which is about one order of magnitude longer than that in the simulations with fixed T_S. The thermal inertia of the slab ocean is much larger than that of the atmosphere. If the model were coupled to a fully dynamical ocean with a depth of, for example, 3000 m, the model will require thousands of years to reach the equilibrium state due to the high thermal inertia and the slow motion of the deep ocean. For simulating hurricanes, a fixed surface temperature experiment is a good start and a useful method for understanding the formation and the properties of hurricanes, as found in hurricane simulations on Earth, carried out, for example, in the studies of Held and Zhao (Held (2008)) and Khairoutdinov and Emanuel (Khairoutdinov (2013)) and the recent review papers of Emanuel (Emanuelb (2018)) and Merlis and Held (Merlis19 (2019)). The fixed-temperature surface acts as a boundary condition for the atmosphere system. Under a fixed T_S, the surface and the top of the atmosphere are not in energy balance, but the atmosphere itself is in energy balance; this is because the energy deficit or excess at the surface is approximately equal to that at the top of the atmosphere. In the coupled slab ocean experiment (shown in Sect. 4 below), the surface, the top of the atmosphere, and the atmosphere are all in energy balance.

The surface temperature is set according to previous simulations of lower resolution AGCMs coupled to a 50-m slab ocean (Yang et al. Yang13 (2013), Wolf et al. Wolf (2019)). On the day side, the surface temperature is a function of latitude and longitude: $(T_{max}-T_{min})cos(\varphi)cos(\lambda)+T_{min}$, or $(T_{max}-T_{min}){cos}^{1/4}(\varphi){cos}^{1/4}(\lambda)+T_{min}$, where $T_{max}$ is the maximum surface temperature, $T_{min}$ is the minimum surface temperature, $\varphi$ is the latitude, and $\lambda$ is the longitude. On the night side, the surface temperature is uniform with a value of $T_{min}$. Three groups of $T_{max}$ and $T_{min}$ are used. One is for planets near the inner edge of the habitable zone, 315 K & 310 K. The other two are for planets in the middle range of the habitable zone, 308 K & 275 K and 301 K & 268 K; the power of 1/4 is used due to the very weak temperature gradients in the substellar region and strong temperature gradients near the terminators.

The planetary rotation period is set equal to the orbital period. Four rotation periods are examined: 6, 10, 20, and 40 Earth days. For other types of spin-orbit resonance, such as 3:2 as in the case of Mercury, the climate lies between the synchronous rotation and the rapid rotation of Earth (Yang et al. Yang14 (2014)) and we have not carried out these kinds of experiments to date. Planetary radius and gravity are set to be the same as Earth, but both obliquity and eccentricity are set to zero. Stellar temperature is set to 2,600 or 3,700 K. The stellar radiation at the substellar point is set to 1,300 or 1,800 W m^-2. By default, the mean surface pressure is 1.0 bar with $\approx$79% N₂ and $\approx$21% O₂. For greenhouse gases, we set the CO₂ concentration to 367 parts per million by volume (ppmv), N₂O to 316 parts per billion by volume (ppbv), and CH₄ to 1760 ppbv. The ozone concentration is set to be the same as present-day Earth, which may influence the outflow temperature of hurricanes and the overshooting of extremely strong convection.

In order to briefly test the effect of atmospheric composition on hurricane formation, we did several ideal experiments in which the background gas is set to H₂, He, N₂, O₂, and CO₂, respectively. The corresponding mean molecular weights are 2.02, 4.00, 28.01, 31.99, and 44.00 g mole^-1 and the corresponding specific heats (Zhang & Showman ZhangX (2017)) are 28.9, 20.8, 29.1, 29.5, and 37.2 J mole^-1 K^-1. We modify these two constants only. The model we employed is incapable of calculating the radiative transfer of dense H₂, He, O₂, or CO${}_{2};$ meanwhile, surface temperatures under background gases that differ from Earth have not been seriously examined. Thus, we chose to use the globally uniform surface temperature (301 K) and stellar radiation (340 W m^-2) with neither a seasonal nor diurnal cycle. This idealized thermal boundary condition is unrealistic, but it is capable of avoiding the effects of any strong wind shear, the baroclinic zone, or other features that may inhibit hurricane formation or propagation (Merlis & Held Merlis19 (2019)). We used two planetary rotation periods: of one and of three Earth days.

The initial states of the experiments were based on long-term (of 40 Earth years) simulations using a lower resolution of 4^∘$\times$5^∘ or 1.9^∘$\times$2.5^∘ under the same experimental designs and parameterization schemes. Then each experiment was run for five Earth years under high resolution and the last four years were used to carry out the analysis, presented below.

Hurricane formation and tracking is based on six hourly model output variables using the Geophysical Fluid Dynamics Laboratory tracking algorithm (Zhao et al. Zhao (2009)). Candidate hurricanes are identified by finding regions that satisfy the following criteria: 1) the local 850-hPa relative vorticity maximum exceeds 3.5$\times$10^-5 s^-1; 2) the 850-hPa warm-core temperature must be at least 0.5 K warmer than the surrounding local mean; 3) the distance between the local sea level pressure minimum and the vorticity maximum should be within a distance of 2^∘ latitude or longitude and so, this should also be the distance between the local sea level pressure minimum and the warm-core center; 4) the maximum 850-hPa wind speed exceeds $\approx$33 m s^-1 at some point. These values for the thresholds impact the exact number of detected hurricanes but they do not affect the main conclusions of this study.

For Earth, a useful method for estimating the possibility of hurricane formation is the genesis potential index (GPI; Emanuel & Nolan Emanuelc (2004)), which is written as:

where $\zeta$ is the vertical component of relative vorticity, $f$ is the planetary vorticity, $RH$ is the relative humidity at the middle troposphere (600 hPa), $V_{shear}$ is the wind shear of horizontal winds between the upper and lower troposphere (300 minus 850 hPa; or called vertical wind shear), and $V_{pot}$ is potential intensity. The $V_{pot}$ is a measure of the maximum near-surface wind that can be maintained by hurricane under given environmental conditions. We note that these parameters are not entirely independent; for instance, vertical wind shear can influence relative humidity. The value of $V_{pot}$ is calculated based on a local balance between thermal energy import and mechanical energy dissipation (Emanuel Emanuel (1988), Bister & Emanuel Bister (2002)), written as

where $C_{k}$ is the exchange coefficient for enthalpy, $C_{D}$ is the drag coefficient, $T_{s}$ is the surface temperature, $T_{o}$ is the mean outflow temperature, ${CAPE}^{\ast}$ is the convective available potential energy of air lifted from saturation at sea surface, and ${CAPE}^{b}$ is that of the boundary layer air. Both ${CAPE}^{\ast}$ and ${CAPE}^{b}$ are computed at the radius of maximum surface wind.

In the discussion of the size of hurricanes, the Rossby deformation radius ($L_{R}$) is used, as described in Section 3.3 below. Here, $L_{R}$ is the length scale at which rotational effects become as important as the effects of gravity waves or buoyancy in the evolution of the flow in a disturbance. The $L_{R}$ is equal to $\frac{NH\ }{f}$, where $N$ is the Brunt-Vaisala frequency, and $f$ is the Coriolis parameter. Furthermore, $H$ is the scale height, equaling to $\frac{R^{\ast}\bar{T}}{M_{d}g}$, where $R^{\ast}$ is the universal gas constant, $\bar{T}$ is the mean air temperature, $M_{d}$ is the molar weight of the atmosphere, and $g$ is the gravity (Wallace & Hobbs Wallace (2006)). The $L_{R}$ decreases as $M_{d}$ increases due to the reduction of $H$. In idealized experiments with uniform surface temperature or uniform rotation, it is one of the rough scales that can be used for understanding hurricane size (Held & Zhao Held (2008)); however, in more realistic conditions such as on Earth, $L_{R}$ is not a good scaling (Chavas et al. Chavas16 (2016), Chavas & Reed Chavas19 (2019)).

We find that hurricanes can form on tidally locked planets especially for those orbiting near the inner edge of the habitable zone of late M dwarfs. For planets in the middle range of the habitable zone, hurricanes are relatively fewer. Storm theories of Earth and Saturn can be used to understand the hurricane formation on tidally locked planets. Hurricanes can enhance the ocean mixing and oceanic heat transport from warmer to cooler regions in both horizontal and vertical directions. Hurricanes can also influence the transmission spectra of tidally locked planets. For instance, if a hurricane moves to the terminator, water vapor concentration would increase (Fig. S4), which can influence the transmission signals. Unfortunately, present-day telescopes are not capable of observing this feature (Morley et al. Morley (2017), de Wit et al. de Wit (2018)) mainly due to the small-scale height of the atmosphere and the relatively small size of the hurricane compared to the planetary radius. Differentiating them requires the large space telescopes or ground-based extremely large telescopes of the future.

Furthermore, future studies require the use of AGCMs coupled to a slab ocean or fully coupled atmosphere–ocean models. The result of a test of the atmosphere coupled to a slab ocean is shown in Fig. 9. We can still find hurricanes in the experiment, whereas more results for different rotation periods, different stellar fluxes, and different CO₂ concentrations will be presented in a separate paper in the near future. Moreover, future works are required to examine how continents influence the results of such studies. Hurricanes always decay quickly when they move over land because of the dramatic reduction in evaporation and the increase in surface roughness. Global climate models with more realistic cloud schemes and regional cloud-resolving models with more accurate radiation transfer are required to simulate the hurricane genesis, especially for those who have quite different atmospheric compositions or air masses from Earth. One another weakness in this study is the convection scheme that was developed based on the knowledge of convection on Earth. Future studies using high-resolution models with explicit convection (e.g., Sergeev et al. Sergeev (2020)) are required. Moreover, convective self-aggregation (such as Bony et al. Bony (2016), Pendergrass et al. Pendergrass (2016), Wing et al. Wing (2017)) may have occurred in our simulations, particularly in the 310–315 K experiment. A future work is required to analyze this feature.

Recently, using Earth-based metrics for hurricane genesis, Komacek et al. (Komacek (2020)) found that hurricane genesis is most favorable on tidally locked terrestrial exoplanets with intermediate rotation periods of about 8–10 days in the habitable zones of late-type M dwarf stars, and that on slowly rotating planets hurricane generis is unfavorable. The latter is consistent with Bin et al. (Bin (2017)) and our results. Future simulations using hurricane-resolved models are required to verify the intermediate rotation periods conclusion shown in Komacek et al. (Komacek (2020)).