# Traveling planetary-scale waves cause cloud variability on tidally locked
aquaplanets

Maureen Cohen School of GeoSciences, The University of Edinburgh
Edinburgh, EH9 3FF, UK  Centre for Exoplanet Science, The University of
Edinburgh, UK  Massimo A. Bollasina School of GeoSciences, The University of
Edinburgh
Edinburgh, EH9 3FF, UK  Denis E. Sergeev Department of Mathematics
College of Engineering, Mathematics, and Physical Sciences, University of
Exeter
Exeter, EX4 4QF, UK  Paul I. Palmer School of GeoSciences, The University of
Edinburgh
Edinburgh, EH9 3FF, UK  Centre for Exoplanet Science, The University of
Edinburgh, UK  Nathan J. Mayne Department of Astrophysics
College of Engineering, Mathematics, and Physical Sciences, University of
Exeter
Exeter, EX4 4QF, UK Maureen Cohen<EMAIL_ADDRESS>
###### Abstract

Cloud cover at the planetary limb of water-rich Earth-like planets is likely
to weaken chemical signatures in transmission spectra, impeding attempts to
characterize these atmospheres. However, based on observations of Earth and
solar system worlds, exoplanets with atmospheres should have both short-term
weather and long-term climate variability, implying that cloud cover may be
less during some observing periods. We identify and describe a mechanism
driving periodic clear sky events at the terminators in simulations of tidally
locked Earth-like planets. A feedback between dayside cloud radiative effects,
incoming stellar radiation and heating, and the dynamical state of the
atmosphere, especially the zonal wavenumber-1 Rossby wave identified in past
work on tidally locked planets, leads to oscillations in Rossby wave phase
speeds and in the position of Rossby gyres and results in advection of clouds
to or away from the planet’s eastern terminator. We study this oscillation in
simulations of Proxima Centauri b, TRAPPIST 1-e, and rapidly rotating versions
of these worlds located at the extreme inner edge of their stars’ habitable
zones. We simulate time series of the transit depths of the 1.4 $\mu$m water
feature and 2.7 $\mu$m carbon dioxide feature. The impact of atmospheric
variability on the transmission spectra is sensitive to the structure of the
dayside cloud cover and the location of the Rossby gyres, but none of our
simulations have variability significant enough to be detectable with current
methods.

Exoplanets (498) — Exoplanet atmospheres (487)

††software: We used the Iris python package to manage and analyse model output
data (MetOffice, 2010). We used the windspharm python library to perform
Helmholtz decompositions to characterise the mean circulation (Dawson, 2016)
and NASA’s Planetary Spectrum Generator to simulate transit spectra
(Villanueva et al., 2018)

##  1 Introduction

The capabilities of the James Webb Space Telescope (JWST) have raised the
prospect of characterizing the atmospheres of transiting exoplanets through
transmission spectroscopy (Mollière et al., 2017; Greene et al., 2016;
Beichman et al., 2014). Particular interest has focused on the
characterization of rocky and temperate planets orbiting at distances from
their host stars that would allow liquid water to exist on their surfaces
(Gialluca et al., 2021; Morley et al., 2017). A number of terrestrial planets
have been found in this range of orbital distances, known as the habitable
zone (Kasting et al., 1993), including the non-transiting Proxima Centauri b
(Anglada-Escudé et al., 2016) in orbit around the closest star to Earth,
Proxima Centauri, and three transiting planets in orbit around the star
TRAPPIST-1 (Gillon et al., 2017). These planets are thought to be tidally
locked to their host stars as a result of their close-in orbits (Barnes,
2017), and indeed tidally locked planets around M-dwarf stars may be the most
common type of potentially habitable planet (Dressing & Charbonneau, 2015;
Kopparapu, 2013).

A challenge for transmission spectroscopy of transiting exoplanets is the
presence of clouds, which mute spectroscopic features by scattering light
isotropically at the level of the cloud deck (Barstow, 2021; Helling, 2019).
Clouds are believed to exist on multiple known exoplanets (Burningham et al.,
2021; Helling et al., 2021; Kreidberg et al., 2014). Modelling studies of the
impact of clouds on the transmission spectra of water-rich rocky planets have
indicated that in most cases it would take anywhere from ten to hundreds of
transits to detect atmospheric absorption features using the JWST (Komacek et
al., 2020; Suissa et al., 2020; Fauchez et al., 2019). Available observations
of the planets in the TRAPPIST-1 system have ruled out hydrogen-rich
primordial atmospheres for these planets Garcia et al. (2022); Moran (2018);
de Wit et al. (2016), but are unable to break the degeneracy between a cloud-
or aerosol-heavy atmosphere, a high molecular mean weight atmosphere, or the
absence of an atmosphere, although the JWST may be able to do so in future
(Lustig-Yaeger et al., 2019). Some work has offered brighter prospects of the
detection of water vapor on arid (icy) planets (Ding & Wordsworth, 2022) and
found that stratospheric (as opposed to tropospheric) clouds would not
necessarily affect observations by the JWST (Doshi et al., 2022). As water-
rich planets are expected to form substantial cloud decks, this limitation is
a significant obstacle to the detection of atmospheric chemistry and potential
biosignatures on water-rich habitable worlds.

One possible avenue for characterizing water-rich planets is temporal
variability in cloud cover. Studies of exoplanet variability are extremely
limited so far, but variable wind speeds may have been detected on KELT-9b
(Asnodkar et al., 2022) and variation in the offset of the peak of the phase
curve of HAT-P-7b was reported by Armstrong et al. (2016) and later disputed
by Lally & Vanderburg (2022). Some theoretical (Welbanks & Madhusudhan, 2022;
Powell et al., 2019; Line & Parmentier, 2016) and observational (Mikal-Evans
et al., 2022; Ehrenreich et al., 2020) studies have found that it may be
possible to detect spatial variability in cloud cover at the planetary
terminators of large exoplanets. In a one-dimensional model, Tan & Showman
(2019) found that cloud radiative feedback can drive atmospheric variability
on brown dwarfs and giant planets. Most relevantly, Fauchez et al. (2021) and
May et al. (2021) simulated the effect of cloud variability on transmission
spectra and atmospheric retrievals of TRAPPIST-1e. In the latter study,
general circulation model simulations exhibited cloud cover variability at the
planetary limb. The authors combined ten synthetic spectra randomly chosen
from a time series of 365 days of the planet’s climate and used the resulting
composite spectrum to retrieve atmospheric chemical abundances, finding that
this did not result in a difference compared to the use of non-variable
spectra. However, May et al. (2021) did not study the cause of the cloud
variability in their simulations. An understanding of the physics of cloud and
climate variability is necessary to confirm that this variability is not noise
and to explain why different models predict vastly different degrees of
variability.

In this work, we describe a dynamical mechanism driving cloud and climate
variability in the atmospheres of moist tidally locked terrestrial exoplanets
and investigate its impact on time series of transmission spectra. In Section
2, we describe our general circulation model, simulation parameter space, and
radiative transfer scheme for simulating transmission spectra. In Section 3,
we outline a feedback loop between cloud radiative effects, incoming stellar
radiation, and the dynamical state of the atmosphere that causes back-and-
forth propagation of planetary-scale (Rossby) waves and regular variations in
cloud cover at the planetary limb. We further discuss the interaction between
the propagating Rossby gyres and the dayside cloud structure and simulate time
series for the water absorption feature at 1.4 $\mu$m and the carbon dioxide
feature at 2.7 $\mu$m. Our results support the findings of May et al. (2021)
and Fauchez et al. (2021) that cloud variability is unlikely to affect JWST
observations, except in specific cases where the cloud structure and wave
propagation may interact in a fortuitous way. In Section 4, we discuss our
results in the context of previous work on Rossby wave structures on tidally
locked planets, as well as implications of dynamical variability for the
planetary climate and for observational practices. We conclude in Section 5.

##  2 Methods

###  2.1 Model description

Our simulations are based on the Global Atmosphere 7.0 (GA7) configuration of
the Met Office Unified Model (UM). Idealized versions of the UM have
previously been used to simulate hot Jupiters (Christie et al., 2021; Mayne et
al., 2017, 2014) and terrestrial planets (Braam et al., 2022; Sergeev et al.,
2022a; Eager et al., 2020; Boutle et al., 2017). The model uses the ENDGame
(Even Newer Dynamics for General atmospheric modelling of the environment)
dynamical core to solve the non-hydrostatic, fully compressible, deep-
atmosphere Navier-Stokes equations (Wood et al., 2014). GA7 contains
parameterizations for sub-grid scale turbulence, convection, non-orographic
gravity wave drag, boundary layer processes, precipitation, and clouds.
Radiative transfer is simulated using the SOCRATES (Suite Of Community
RAdiative Transfer codes based on Edwards and Slingo) community radiative
transfer code. All simulations are run at a resolution of $2^{\circ}$ latitude
by $2.5^{\circ}$ longitude. The substellar point is defined to be at
$0^{\circ}$ longitude and latitude, while the antistellar point is located at
$180^{\circ}$ longitude and the eastern and western terminators at
$90^{\circ}$E and $90^{\circ}$W, respectively. “Days” refers to Earth days
throughout this work.

The UM has a fully prognostic cloud scheme, the Prognostic Cloud fraction and
Prognostic Condensate (PC2) scheme (Wilson et al., 2008). The scheme has three
prognostic cloud fractions (liquid, ice, and mixed-phase), as well as water
vapor and liquid and frozen condensate. These prognostic variables are updated
in increments by processes in the model, including advection, convection, and
precipitation. The column cloud fraction is determined by exponential random
overlap. The moist atmosphere configuration includes water vapor with
evaporation and precipitation and an otherwise 100 % nitrogen atmosphere with
fixed trace CO2. In the TRAPPIST-1 Habitable Atmosphere Intercomparison (THAI)
(Sergeev et al., 2022b), the UM’s cloud scheme produced a mean cloud fraction
in the middle of the comparison (60 %), compared to the extremes of the
Laboratoire de Météorologie Dynamique - Generic model (LMD-G, at 28 %) and the
Resolving Orbital and Climate Keys of Earth and Extraterrestrial Environments
with Dynamics model (ROCKE-3D, at 77 %).

Parameter | Control ProxB | Warm ProxB | Control TRAP-1e | Warm TRAP-1e | Dry TRAP-1e
---|---|---|---|---|---
Semi-major axis (AU) | 0.0485 | 0.0423 | 0.029 | 0.025 | 0.029
Stellar irradiance (W m-2) | 881.7 | 1100.2 | 837.7 | 1392.9 | 837.7
Orbital period (Earth days) | 11.2 | 9.2 | 6.1 | 4.2 | 6.1
Rotation speed (rad s-1) | 6.501$\times$10-6 | 7.933$\times$10-6 | 1.192$\times$10-5 | 1.746$\times$10-5 | 1.192$\times$10-5
Eccentricity ($\cdot$) | 0 | 0 | 0 | 0 | 0
Obliquity ($\cdot$) | 0 | 0 | 0 | 0 | 0
Radius (km) | 7160 | 7160 | 5797 | 5797 | 5797
Acceleration due to gravity (m s-2) | 10.9 | 10.9 | 9.1 | 9.1 | 9.1
CO2 (ppm) | 378 | 378 | 400 | 400 | 400
Number of levels ($\cdot$) | 60 | 60 | 39 | 39 | 39
Model top (km) | 85 | 85 | 80 | 80 | 80
Table 1: Model parameters for all simulations

###  2.2 Simulation parameters

We performed five simulations:

  1. 1.

A “control” moist Proxima Centauri b with planetary and orbital parameters as
described in Anglada-Escudé et al. (2016) (Control ProxB)

  2. 2.

A “warm” moist Proxima Centauri b with planetary orbital parameters
corresponding to the inner edge of Proxima Centauri’s habitable zone (Warm
ProxB)

  3. 3.

A “control” moist TRAPPIST-1e with planetary and orbital parameters as
described in Gillon et al. (2017) (Control TRAP-1e)

  4. 4.

A “warm” moist TRAPPIST-1e with planetary and orbital parameters corresponding
to the inner edge of TRAPPIST-1’s habitable zone (Warm TRAP-1e)

  5. 5.

A “dry” TRAPPIST-1e atmosphere identical to the control case aside from the
dry atmosphere (Dry TRAP-1e)

Table 1 lists the values of the parameters varied between each simulation.
These parameters were chosen to facilitate comparison with previous UM studies
of the two planets. The simulation set-up for Proxima Centauri b is based on
Boutle et al. (2017) and Cohen et al. (2022), using a model top of 85 km with
60 vertical levels, quadratically spread to give greater resolution near the
surface. The planet is simulated with a slab ocean (Frierson et al., 2006)
which has a mixing depth of 2.4 m, representing a heat capacity of $10^{7}$ J
K-1 m-2. The stellar spectrum for Proxima Centauri, modelled as a quiescent
M-dwarf, was taken from BT-Settl (Rajpurohit et al., 2013) with $T_{eff}=3000$
K, g= $1000\mathrm{ms^{-2}}$, and metallicity $=0.3$ dex. The Proxima Centauri
b simulations were spun up from an equilibrium state of a previous simulation
performed using the UM with the same configuration.

For TRAPPIST-1e, we use the simulation parameters of the TRAPPIST-1 Habitable
Atmosphere Intercomparison for both the dry and the moist atmosphere cases
(Fauchez et al., 2021; Turbet et al., 2022; Sergeev et al., 2022b; Fauchez et
al., 2022). In this instance, the models use 39 vertical levels with a top of
80 km. The planet’s surface in the moist case is a slab ocean with a mixing
layer of 1 m, representing a heat capacity of $4\times 10^{6}$ J K-1 m-2. The
spectrum is taken from BT-Settl (Rajpurohit et al., 2013) with $T_{eff}=2600$
K and Fe/H=0. The TRAPPIST-1e simulations were spun up from an initial state
of an isothermal (300K) dry atmosphere at rest with zero winds, following the
THAI protocol (Fauchez et al., 2020). Unlike in the THAI project, our
simulations were run with the UM’s gravity wave drag scheme switched on,
resulting in some differences in the wind structure.

All the simulations correspond to tidally locked planets. The Control ProxB,
Warm ProxB, Control TRAP-1e, and Dry TRAP-1e simulations were run until a
balance between incoming and outgoing radiation at top-of-atmosphere was
achieved. Control ProxB, Warm ProxB, and Control TRAP-1e ran for 6,000 days
and the period from day 5,000 to 6,000 was sampled for analysis. The Warm
TRAP-1e simulation underwent a runaway greenhouse effect, with convection
reaching the model top after approximately 4,000 days. We sampled a 990-day
period (day 3,000 to the crash just before day 4,000) and include the results
here to study the extreme limit of the habitable zone and in particular the
potential effect of cloud variability on observations of close-in rocky
planets (Venus analogues). As the Dry TRAP-1e simulation achieved radiative
balance faster than the moist atmospheres, we ran the simulation for 4,000
days and used the period from day 3,000 to 4,000 for analysis. In the results
reported below,“day 10” and similar formulations refer to the day of the
sample period, not the day of the simulation.

###  2.3 NASA Planetary Spectrum Generator

We use the NASA Planetary Spectrum Generator (Villanueva et al., 2018),
publicly available at https://psg.gsfc.nasa.gov/ (PSG), to simulate time
series of water vapor and carbon dioxide features of the four moist atmosphere
simulations as observed by the James Webb Space Telescope’s NIRSpec (Near
Infrared Spectrograph) instrument. We omit the dry case as it has no time-
varying atmospheric chemistry or clouds. The NIRSpec instrument’s range covers
water vapor features in the infrared at 1.4, 1.8, and 2.7 $\mathrm{\mu m}$, as
well as CO2 features at 2.1, 2.7, and 4.3 $\mathrm{\mu m}$ (Team et al.,
2022). For each simulated atmosphere, we prescribe the orbital, planetary, and
stellar parameters shown in Table 1, together with the pressure, temperature,
altitude, H2O, N2, and CO2 data from the UM. For the Proxima Centauri b
simulations, the 85 km model top was sufficient for the PSG to calculate a
spectrum, and we use only the model output data. For the TRAPPIST-1e
simulations, however, the 80 km model top was slightly too low to enable the
PSG to model the spectrum. We used the Met Office’s _iris_ package’s built-in
linear extrapolation method to extend the temperature, H2O, ice cloud, liquid
cloud, N2 and CO2 profiles to one extra atmospheric level with an altitude of
85 km and half the pressure of the layer immediately below (MetOffice, 2010).
Previous works have used the PSG to generate a spectrum for each grid box and
averaged the spectra for a final output representing the signal during transit
(May et al., 2021; Suissa et al., 2020; Komacek et al., 2020). To reduce the
computational expense of simulating long time series for multiple simulations
and absorption features, we instead average the atmospheric values for each
day around the limb first, generate a transit spectrum for each day, and
extract and plot the absorption features against time.

##  3 Results

###  3.1 Climatology

Figure 1: Comparative climatology of the five simulations, showing (from left to right) the vertical temperature profile at the substellar and antistellar point, the zonal mean zonal wind, the vertical water vapor profile at the substellar and antistellar point, and the surface temperature. From top row to bottom row: Control ProxB, Warm ProxB, Control TRAP-1e, Warm TRAP-1e, Dry TRAP-1e. All values are 300-day means.  Quantity | Control ProxB | Warm ProxB | Control TRAP-1e | Warm TRAP-1e | Dry TRAP-1e
---|---|---|---|---|---
Mean air temperature (sub) (K) | 211.4 | 229.9 | 217.9 | 250.7 | 240.3
Max air temperature (sub) (K) | 285.1 | 300.6 | 278.0 | 310.5 | 331.6
Min air temperature (sub) (K) | 167.8 | 180.6 | 179.2 | 178.2 | 181.4
Mean air temperature (anti) (K) | 201.6 | 220.6 | 210.4 | 246.3 | 222.1
Max air temperature (anti) (K) | 259.7 | 274.7 | 260.6 | 295.8 | 284.7
Min air temperature (anti) (K) | 167.9 | 180.4 | 179.0 | 179.4 | 181.4
Mean zonal mean zonal wind (m/s) | 17.1 | 18.4 | 15\. 6 | 25.2 | -1.2
Max zonal mean zonal wind (m/s) | 59.0 | 73.5 | 69.6 | 113.9 | 24.8
Min zonal mean zonal wind (m/s) | -35.4 | -24.3 | -6.4 | -17.4 | -20.1
Mean specific humidity (sub) (kg/kg) | 1.5$\times$10-3 | 4.9$\times$10-3 | 1.0$\times$10-3 | 10.5$\times$10-3 | 0
Max specific humidity (sub) (kg/kg) | 8.2$\times$10-3 | 21.0$\times$10-3 | 5.0$\times$10-3 | 34.5$\times$10-3 | 0
Min specific humidity (sub) (kg/kg) | 0.5$\times$10-7 | 4.8$\times$10-7 | 0.1$\times$10-7 | 2.5$\times$10-7 | 0
Mean specific humidity (anti) (kg/kg) | 0.4$\times$10-4 | 6.2$\times$10-4 | 0.6$\times$10-4 | 52.9$\times$10-4 | 0
Max specific humidity (anti) (kg/kg) | 3.0$\times$10-4 | 33.9$\times$10-4 | 3.5$\times$10-4 | 171.8$\times$10-4 | 0
Min specific humidity (anti) (kg/kg) | 0.5$\times$10-7 | 5.3$\times$10-7 | 0.1$\times$10-7 | 2.4$\times$10-7 | 0
Mean surface temperature (K) | 219.1 | 243.4 | 231.0 | 276.2 | 212.9
Max surface temperature (K) | 286.3 | 301.8 | 281.6 | 312.3 | 342.5
Min surface temperature (K) | 149.5 | 196.5 | 205.2 | 250.4 | 157.3
Table 2: Mean, maximum, and minimum values for each plot shown in Figure 1.
Values are given separately for the substellar and antistellar profiles of
temperature and specific humidity.

Boutle et al. (2017) present a detailed climatology of Proxima Centauri b as
simulated by the UM. Similarly, a full description of the climatology of
TRAPPIST-1e as simulated by the UM with a dry and moist atmosphere is given in
Turbet et al. (2022) and Sergeev et al. (2022b), respectively. We give a brief
overview of the equilibrium climates of all five simulations here.

Figure 1 shows the vertical temperature structure, zonal mean zonal wind,
vertical humidity profile, and the spatial distribution of surface temperature
of each simulation. All simulations display a nightside temperature inversion,
although in the Warm TRAP-1e case it is very small and the temperature profile
is nearly identical on the dayside and nightside. The specific humidity
profiles are likewise consistent for Control ProxB, Warm ProxB, and Control
TRAP-1e, with much greater humidity on the dayside and an arid nightside. Only
the Warm TRAP-1e (incipient runaway) simulation has substantial humidity on
the nightside. A comparison of the zonal mean zonal wind of the Control vs.
Warm ProxB and Control vs. Warm TRAP-1e cases supports an increase in zonal
wind speeds for planets orbiting closer in. The Proxima Centauri b simulations
have a broad equatorial jet in the troposphere and a series of vertically
stacked opposing jets in the stratosphere in a longitudinally asymmetric
stratospheric oscillation (LASO) as described in Cohen et al. (2022). In
contrast, the Control and Warm TRAPPIST-1e simulations form a mid-latitude
tropospheric jet in each hemisphere. In these simulations, unlike in the THAI
project, the planet also generates a LASO in the equatorial region due to the
acceleration of the flow contributed by the gravity wave drag scheme.

The zonal mean zonal wind for the Dry TRAP-1e case differs from that reported
in THAI (Turbet et al., 2022) for the equivalent N2-dominated atmosphere case.
Turbet et al. (2022) reported a stable state with two mid-latitude jets, while
our result is a broad equatorial jet more similar to that of Proxima Centauri
b or the CO2-dominated atmosphere case in Turbet et al. (2022). Recent work
has shown that UM simulations of TRAPPIST1-e exhibit climate bistability, with
one stable dynamical state corresponding to an equatorial jet and the other to
two mid-latitude jets (Sergeev et al., 2022a). It may be that the inclusion of
gravity waves, which affect the dynamical structure of the atmosphere and heat
transport between dayside and nightside, tipped this simulation into the
equatorial jet state. The zonal wind magnitude is in line with that shown in
Turbet et al. (2022) and considerably less than that in the moist atmosphere
cases. The tropospheric jet structure influences the location and propagation
of Rossby wave structures discussed below, as the zonal wind magnitude is a
component of the Rossby wave phase speed and Rossby waves can be advected by
the flow.

###  3.2 Mechanism of oscillation

Figure 2: Time-longitude diagrams of the mid-latitude (55 to 85N) averaged
meridional wind at an altitude of 2.96 km above the surface. Positive values
correspond to northward flow, while negative values represent southward flow.

All five simulations exhibit the presence of Rossby waves which propagate
westwards in the dry case and alternatingly eastwards and westwards in all the
moist cases. Figure 2 represents these waves as fluctuations in the mean mid-
latitude meridional wind at a height of 2.96 km. Investigation of the vertical
vorticity profile and inspection of the eddy rotational component at different
atmospheric levels showed that the Rossby wave-associated vorticity and wind
speeds in the vertical region where clouds form are greatest at this height.
Accordingly, single-level plots in our results are shown at 2.96 km. Results
for other levels are qualitatively similar but typically of smaller magnitude.
In Figure 2, the longitudes at which the mean meridional wind alternates
between northward and southward represent the longitudinal range of the
oscillation in the moist atmosphere cases. This back-and-forth propagation in
the moist atmospheres is regular and associated with periodic climate
variability on a planetary scale. To understand the mechanism driving this
oscillation, we analyzed and compared the Control and Dry TRAP-1e simulations.

Figure 3: Wind vectors for Control TRAP-1e simulation on days 0, 10, and 20
and Dry TRAP-1e simulation on days 0, 30, and 60.

Figure 3 shows the wind pattern at 2.96 km for Control TRAP-1e and Dry TRAP-1e
at three different simulation times, chosen to correspond to the easternmost,
westernmost, and again easternmost location of the gyres in the Control
TRAP-1e simulation, covering a full cycle of motion. In the control
simulation, Rossby gyres are clearly visible in the northern and southern
polar regions of the eastern hemisphere, for example at 60N and 60-90E in
Figure 3 a). These gyres propagate eastwards and westwards such that the
centers of the gyres shift from between 30-60E to 120-150E on an approximately
20-day cycle. A matching western pair is less apparent due to interactions
with other elements of the flow. In the dry simulation, gyres form at lower
latitudes, are irregular in shape, and propagate at slow speeds exclusively
westwards.

We explain the motion of the gyres using the theory of Rossby waves. Following
e.g., Holton & Hakim (2013) or Vallis (2017), the phase speed of Rossby waves
is given by:

$c_{p}=\bar{U}-\frac{\beta}{k^{2}+l^{2}},$ (1)

where _$\bar{U}$_ is the zonal mean zonal wind speed, $\beta$ is the Rossby
parameter $frac{2\Omega cos\phi}{r}$ (with $\Omega$ the planet’s rotation rate
in radians/second, $\phi$ the latitude in radians, and r the planet’s radius),
and _k_ and _l_ are the zonal and meridional wavenumbers in units of m-1. To
determine why the Rossby gyres oscillate in the moist atmosphere cases only,
we compared the Rossby wave phase velocity for Control TRAP-1e and Dry
TRAP-1e. Figure 4 shows time series of the phase velocity of the Rossby wave
with the highest power spectral density (PSD) in the flow for these two
simulations. To extract the wavenumbers of the highest powered waves in the
flow, we first performed a Helmholtz decomposition of the wind field at 2.96
km to calculate the eddy rotational component as in (Hammond & Lewis, 2021).
We then input the magnitude of the eddy rotational component, which we equate
to the Rossby waves, into a 2-D Fourier transform and extracted the zonal (k)
and meridional (l) wavenumbers of the wave with the maximum PSD on each
simulation day. Finally, we calculated a day-specific Rossby wave phase
velocity as per Equation 1 (i.e. the phase velocity varies by day depending on
both the zonal wind and the predominant Rossby wave). In this calculation, we
used the time-varying daily value of the zonal mean zonal wind U.

Figure 4 shows that, in the moist simulation, the Rossby wave phase velocity
oscillates between positive (eastward) and negative (westward) values on an
approximately 20-day cycle, while it remains negative in the dry case over the
same time period. Note that this method only takes into account the phase
velocity contribution from the wave with the highest PSD; however, our
analysis showed multiple waves present in the flow, occasionally with similar
PSDs. This reduces the accuracy of the magnitude of the calculated phase
velocity, but does not undermine the qualitative finding that the velocity
oscillates in only the moist atmosphere.

For the Control TRAP-1e simulation, the Rossby wave phase velocity oscillates
in a band of latitudes between 50-70N/S, with a tendency toward increasingly
eastward flow further polewards. A similar analysis for the Control ProxB and
Warm ProxB simulations found that the oscillatory latitude band starts at
55N/S and extends to the poles. This is attributable to the larger size of
Proxima Centauri b, as the wavenumbers in m-1 vary by latitude and the degrees
of latitude for each planet correspond to different distances. The eastern
gyres in the Control TRAP-1e simulation are centered around 60-70N/S, while
those in the ProxB simulation are centered further equatorwards at 55-60N/S.
The latitudinal position may be influenced by the position of the zonal jets
on the two planets. On Earth, Rossby waves are associated with the mid-
latitude jet stream (Vallis, 2017). As seen in Figure 1, Proxima Centauri b’s
equatorial jet extends to about 55N/S, while the mid-latitude jets on
TRAPPIST-1e extend further polewards to approximately the latitude of the
Rossby vortices. Previous work simulating TRAPPIST-1e with the UM has also
shown that the circulation can take on one of two regimes: a single equatorial
jet or two mid-latitude jets (Sergeev et al., 2022a). In the single equatorial
jet regime, as in our Proxima Centauri b simulations, the gyres form further
equatorwards than in the double mid-latitude jet regime.

Figure 4: Time series of Rossby wave phase velocity of the primary wave in the
flow at 56N for Control and Dry TRAP-1e simulations.

The formation of Rossby gyres in simulations of tidally locked planets is
believed to be related to the spatially periodic thermal forcing (Showman &
Polvani, 2011, 2010; Gill, 1980; Matsuno, 1966). As our model’s stellar
spectra do not vary with time and the planet is tidally locked with zero
eccentricity or obliquity, atmospheric processes must be responsible for the
temporal variability in our simulations. To determine why the constituent
Rossby waves in the wind field (and hence the Rossby wave phase velocity) vary
periodically with time, we searched for correlations between quantities
thought to play a role in the Matsuno-Gill response to periodic forcing.
Figure 5 compares the variations over time of the vertical cross sections of
dayside mean air temperature, vertical wind, zonal wind, net surface shortwave
flux, and the PSD of the zonal wavenumber 1 Rossby wave (identified as the 1-0
wave) and, separately, the sum of the PSDs of the Rossby waves identified as
1-1, 2-1, 2-2, and 3-2 waves, where the first digit refers to the zonal
wavenumber and the second digit refers to the meridional wavenumber. Regular
20-day cycles are visible in all quantities in the moist atmosphere case, but
are absent in the dry atmosphere. The air temperature, vertical wind, and
shortwave surface heating increases precede the increase in the Rossby wave
power. For example, Figure 5 a), c), and g) show a peak in these three
quantities at around 10 days, while the spike in the 1-0 Rossby wave (red line
in Figure 5 g)) occurs at 18-20 days. This pattern repeats five times over the
period displayed in the plots. Figure 6 further shows variability in the
dayside mean total (ice and liquid) cloud cover on the same 20-day cycle. The
cloud mass fraction grows during the heating/rising and drops during the
cooling/subsiding part of the cycle.

We posit an internal feedback between the dayside cloud cover and the
intensity of the Matsuno-Gill response. A decrease in cloud cover allows more
shortwave radiation to reach the surface, leading to atmospheric heating and
subsequent ascending motion of the air mass. The 1-0 Rossby wave responds to
the increase in forcing, boosting its power spectral density relative to the
other constituent Rossby waves in the wind field. To support this
interpretation, we show in Figure 5 g) and h) both the PSD of the 1-0 wave and
the summed PSD of a number of other large-scale waves, namely the 1-1, 2-1,
2-2, and 3-2 waves. At the troughs of the cycle, the PSD of the 1-0 wave is
roughly equal to that of the other waves combined, and occasionally even drops
below it. At the peaks, however, the PSD of the 1-0 wave increases
substantially more than that of the sum of the remaining waves, indicating
that this wave disproportionately receives energy during the cycle, as would
be expected from its direct relationship to the Matsuno-Gill periodic forcing
pattern. (Note that in the dry atmosphere case, the PSD of all waves is an
order of magnitude smaller than in the moist case despite the larger shortwave
flux and atmospheric temperature anomalies, highlighting the important role of
moisture.) As longer wavelength Rossby waves have higher westward phase
speeds, this shift towards the 1-0 wave contributes to the westward
propagation of the gyres. When cloud cover increases again, less radiation
reaches the surface, the air mass cools and subsides, and the 1-0 Rossby wave
becomes weaker relative to other waves, shifting the Rossby wave phase
velocity eastwards. It is possible that the location of the Rossby gyres in
turn affects the cloud cover, closing the causal loop, but we believe it is
unlikely that the Rossby waves are the only or main factor in the density of
the clouds. The zonal wind speed, which influences both the Rossby wave phase
velocity and the stability of the dayside cloud cover, is also affected by the
changes in the thermodynamic properties of the dayside atmosphere shown above
(Figure 5 e)). Untangling these intricate relationships requires a better
understanding of the factors controlling the zonal wind speed on tidally
locked planets than is currently available. In addition, the cloud layer is
likely to be sensitive to multiple processes in the atmosphere in addition to
the zonal wind variation, including the intensity of convection, specific
humidity, and the advective and radiative time scales.

Figure 5: Top three rows: Vertical profiles of dayside mean air temperature, vertical wind, and zonal wind over time for the moist atmosphere Control TRAP-1e and the dry atmosphere Dry TRAP-1e (left and right, respectively). The vertical range of a) and b) is 0 to 5 km to better show the temperature oscillation near the surface. Due to the relatively low resolution of our simulations, this close-in view results in discontinuities between vertical levels. The discontinuities are not visible in c)-f) because the vertical range shown in 0 to 35 km. Bottom row: Time series of the dayside mean net downward shortwave flux close to the planet’s surface (black), shown with the power spectral density of the zonal wavenumber 1 Rossby wave (red) and the sum of the power spectral density of the waves with zonal and meridional wavenumbers 1-1, 2-1, 2-2, and 3-2 (blue). Note the different limits of the y-axis. Figure 6: Vertical profile of dayside mean total cloud cover (ice and liquid) over time for the Control TRAP-1e simulation. As in Figure 5 a) and b), the short vertical range of 0 to 5 km results in discontinuities between vertical levels due to the low resolution of the simulation. Quantity | Control ProxB | Warm ProxB | Control TRAP-1e | Warm TRAP-1e
---|---|---|---|---
Rotation period (days) | 11.2 | 9.2 | 6.1 | 4.2
Oscillation period (days) | 157.5 | 120 | 19.4 | 16.2
Mean global zonal mean zonal wind (m/s) | 5.3 | 4.1 | 17.8 | 15.1
Mean equator-pole temperature gradient (K/m) | -1.45$\times$10-6 | -1.41$\times$10-6 | -2.70$\times$10-6 | -2.62$\times$10-6
Mean n. hemisphere thermal wind, h=2.96 km (m/s) | 1.80 | 1.34 | 3.11 | 1.78
Table 3: Rotation period, period of Rossby gyre oscillation, mean zonal mean
zonal wind, mean meridional temperature gradient, and mean northern hemisphere
thermal wind for each of the four moist atmosphere cases. The periodicity was
determined from the cloud cover oscillation shown in Figure 8. The meaning
period for the bottom three quantities was chosen to be the same as in Figure
1, the first 300 days of the sampling period for each simulation.

The period of the oscillation, given in Table 3, varies substantially between
the four moist atmosphere cases. Understanding why the period is longer in
some simulations is important because a slower oscillation implies the planet
will have a longer period of clear skies at the limb, potentially allowing for
repeat observations when conditions are favorable. We find that the
oscillation period monotonically decreases in parallel with the rotation
period, but the relationship is not linear. We expect the rotation period to
influence the Rossby wave phase velocity directly through $\beta$. However,
other factors are clearly in play. While the rotation period decreases by
similar amounts (2-3 days) between each simulation, there is a
disproportionately large difference between the oscillation periods of the
Proxima Centauri b and TRAPPIST-1e simulations. We believe the non-linearity
can be explained by the additional influence of the zonal wind on the Rossby
wave phase velocity as defined in Equation 1. Figure 7 shows latitude-time
diagrams of the Rossby wave phase velocity for each simulation. Both the
eastward and westward phase of the oscillation display higher phase velocities
in the TRAPPIST-1e simulations as compared to Proxima Centauri b, accounting
for the much shorter oscillation periods of the former. The phase velocities
differ because the zonal mean wind, reported in Table 3, jumps significantly
between the the Proxima Centauri b (4-5 m/s) and Trappist-1e (15-18 m/s)
simulations. The higher zonal mean wind in the TRAPPIST-1e cases may in turn
be explained by a larger meridional temperature gradient via the thermal wind
balance.

The Rossby number for all four moist simulations is small, on the order of
$10^{-2}$, as the characteristic length scale of the phenomenon (the zonal
wavenumber 1 Rossby wave) is approximately half the circumference of the
planet, while the characteristic zonal wind is on the order of tens of meters
per second. This means the geostrophic approximation can be applied and the
thermal wind balance equation holds true:

$u_{t}=-\frac{R_{d}}{f}\frac{\partial{\bar{T}_{v}}}{\partial{y}}\frac{\partial{p}}{p},$
(2)

where $u_{t}$ is the vertical gradient of the zonal wind, $R_{d}$ is the gas
constant for dry air, f is the Coriolis parameter $2\Omega sin\phi$,
$\frac{\partial{\bar{T}_{v}}}{\partial{y}}$ is the mean meridional temperature
gradient of a layer, and p is the pressure (Vallis, 2017). According to the
weak temperature gradient theory applicable to slowly rotating tidally locked
planets (Pierrehumbert & Hammond, 2019), the equator-pole temperature gradient
should increase with increasing rotation rate, which is consistent with the
values in Table 3. We used the mean equator-pole temperature gradient to
calculate the mean northern hemisphere thermal wind in the final row of Table
3. As predicted, Control TRAP-1e (3.11 m/s) has a higher thermal wind than
Control ProxB and Warm ProxB (1.80 and 1.34 m/s). In contrast, Warm TRAP-1e
has a weaker thermal wind, even though its meridional temperature gradient is
similar to that of Control TRAP-1e (and different from that of both Proxima
Centauri b cases). We believe this is due to greater pressure variation within
the same vertical range for this near-runaway simulation, combined with the
effect of the larger Coriolis parameter in the denominator of 2. These
patterns broadly suggest that more slowly rotating planets with weaker
equator-pole temperature gradients are likely to have longer oscillation
periods and longer windows of cloudless sky at the terminators.

Figure 7: Latitude-time diagrams of Rossby wave phase velocity for each
simulation at h=2.96 km height. Positive values correspond to eastward flow,
while negative values represent westward flow.

###  3.3 Cloud variability and observables

The migration of Rossby gyres impacts the amount of moisture transport and
thus cloud condensate at the planetary terminators. All four of the moist
atmosphere simulations display cloud cover variability at the terminators,
shown in Figure 8. The Control and Warm ProxB runs in Figure 8 a) and b),
respectively, exhibit large fluctuations in cloud condensate in the observable
regions of the planet, ranging from near 0 to $7\times 10^{-7}$ kg/kg and
$2.5\times 10^{-6}$ kg/kg, respectively, on a time scale matching the
migratory cycle of the Rossby gyres (120 days/160 days). The TRAPPIST 1-e
simulations do not undergo these long-period cycles, but show regular smaller
magnitude fluctuations on an approximately 20-day time scale.

Figure 8: Mean cloud condensate (mixing ratio, kg/kg) over time at the
planetary limb for each of the four moist atmosphere simulations. Liquid and
ice cloud are shown separately. Each type of cloud is averaged over all
latitudes and all heights on the eastern and western terminator. The data has
been filtered to remove cycles with periods shorter than 10 days. Note the
different limits of the y-axis.

Figure 9 depicts the interaction between the wind field and the dayside
clouds. Figure 9 a) and b) are two stages in the Rossby gyre migratory cycle
for the Warm ProxB simulation, corresponding to a cloud condensate maximum and
minimum. During the maximum, the eastern pair of Rossby gyres is at the
extreme western part of its propagation path, where it intersects with the
region of heavy cloud cover around the substellar point. During the minimum,
the gyres are at the extreme eastern part of the propagation path and do not
interact with the dayside clouds. In the TRAPPIST-1e case, shown in Figure 9
c) and d), the Rossby gyres are too far polewards to interact with the dayside
cloud cover. The short-period cycles shown in Figure 8 c) are likely a direct
reflection of the fluctuation in cloud condensate and moisture described in
3.2 and shown in Figures 5 and 6, on which the longer-period effect from the
traveling wave structures is overlaid.

Figure 9: Wind vectors overlaid on the total cloud condensate (ice and liquid)
at the given height for Warm ProxB and Control TRAP-1e simulations. The images
are daily snapshots chosen to illustrate the eastmost and westmost phases of
the Rossby gyre migration for each planet.

The magnitude and periodicity of the variation in cloud cover at the planetary
limb is highly sensitive to not only the Rossby wave propagation, but also the
dayside cloud structure. As demonstrated by the TRAPPIST-1e cases, the amount
of cloud at the terminator will not be affected by the Rossby wave oscillation
unless the Rossby gyres form at low or mid-latitudes where they can advect
cloud from the substellar region. Figure 10 shows cross-sections of the
dayside cloud layer at the equator and at longitude 0 for the four moist
atmosphere simulations. The extent of the cloud cover in longitude, latitude,
and altitude depends on the temperature and moisture profile of each simulated
planet, but as the longitude, latitude, and even peak altitude of the Rossby
waves also vary in different simulations, the parameter space of the resulting
wave-cloud interaction is complex.

Figure 10: Longitudinal and latitudinal cross-sections of the dayside cloud
layer for the four moist atmosphere simulations. The total cloud is the sum of
ice and liquid cloud condensate. The images depict 120-day means.

To explore the potential impact of wave-cloud interactions on observations, we
simulated transit spectra for the Control ProxB, Warm ProxB, Control TRAP-1e,
and Warm TRAP-1e simulations, excluding the Dry TRAP-1e simulation as it does
not form clouds. We constructed time series of two absorption features, shown
in Figure 11. We chose the water line at 1.4 $\mu$m because it does not
overlap with any CO2 features and the CO2 feature at 2.7 $\mu$m because it is
a strong line in the available NIRSpec spectrum and does not overlap with the
N2-N2 collision-induced absorption line at 4.3 $\mu$m. As the CO2 abundance in
the simulations is fixed, variability in the transit depth of this feature can
only be due to differences in the muting effect of cloud cover or due to
temperature fluctuations and not due to variations in CO2 content. For the
water feature, variations in transit depth may also be due to differences in
water vapor content on different days, caused by other factors such as the
LASO and random fluctuation (model noise). However, the time series for the
H2O and CO2 are well-correlated, supporting clouds as a factor in the
variability. In the Control and Warm ProxB simulations in Figure 11 a)-d), the
time series show clear long-period variation in addition to small continuous
fluctuations, but the relative difference in the transit depths for these
simulations is only 4-5 %. The percentage variation for the Warm TRAP-1e
simulation is the largest in the comparison at 18-20 %, but the transit depths
are profoundly muted compared to Control TRAP-1e because of the high cloud
deck visible in Figure 10 d) and h). In addition, while the Control and Warm
ProxB time series have extended periods of larger transit depths,
corresponding to the longer period of the cloud cover oscillation for this
planet, the TRAP-1e runs lack these multi-week periods of stronger transit
signals due to their shorter Rossby wave cycle as described in Section 3.2.

Figure 11: Time series of the 1.4 $\mu$m water absorption feature and 2.7
$\mu$m CO2 absorption feature for the Control ProxB, Warm ProxB, Warm TRAP-1e,
and Control TRAP-1e simulations. In a)-d), a sample of 300 days is taken to
cover the 157.5 and 120 day oscillation periods in the Control and Warm
Proxima Centauri b simulations, respectively. In e)-h), a sample of 100 days
is taken to cover the 19.4 and 16.2 day periods in the Control and Warm
TRAPPIST-1e simulations.

##  4 Discussion

Our results support the existence of internal atmospheric variability on
tidally locked aquaplanets even in the absence of a varying stellar spectrum
or stellar activity, rotation with respect to the host star, obliquity, and
eccentricity. The stabilizing feedback between the dayside cloud cover and
atmospheric temperature, identified in previous work on the inner edge of the
habitable zone for tidally locked Earth-like planets (Kopparapu et al., 2016;
Yang et al., 2014), induces periodicity in the atmospheric dynamics. Edson et
al. (2011) postulated that the large amplitude of the zonal wavenumber 1
Rossby wave on slowly rotating planets with superrotating atmospheres is
caused by resonance between this wave and the spatially periodic heating. Our
finding of a disproportionate increase in the power spectral density of the
$1-0$ wave directly after an increase in net surface shortwave flux supports
their hypothesis.

The increase in surface heating is caused by a drop in total cloud cover in
the dayside, reducing the cloud albedo. This periodic reduction in cloud cover
may be affected by the propagation of the Rossby gyres in a closed feedback
loop, but it is likely that other aspects of the circulation, especially the
magnitude of the zonal and vertical winds and intensity of convection in the
substellar region also play a role. The potential relationship between
atmospheric moisture and cloud-radiative feedback is reminiscent of theories
of the Madden-Julian Oscillation (MJO) (Zhang et al., 2020; Zhang, 2005),
particularly the moisture-mode hypothesis, which also posits a planetary wave
response. As there is no consensus about the mechanism of the MJO and the
complexity of the factors influencing the cloud cover on the dayside is high,
we limit our analysis to identifying the immediate cause of the Rossby gyre
oscillation and its effects on observables, and defer detailed analysis of the
moist atmosphere feedbacks between clouds, convection, specific humidity, and
the zonal wind to future studies.

Our simulations of transit spectra show that the variable cloud cover caused
by traveling Rossby waves could affect transit depths, though for our chosen
planets the effect is too small to be observable with current instruments. May
et al. (2021) reported a transit depth variation due to cloud cover on the
order of 10 ppm for their 10-4 bars of CO2 TRAPPIST-1e simulation with ExoCAM
(Wolf et al., 2022), which is comparable to the THAI Hab 1 set-up (Sergeev et
al., 2022b) and to our Control TRAP-1e experiment. THAI Part III (Fauchez et
al., 2021) found the standard deviation of the variation of the continuum
level for Hab 1 to be 3 ppm for ExoCAM and 1 ppm for the UM, compared to our
min-max difference of 1.26 ppm for for the 2.7 $\mu$m feature. The slightly
smaller degree of variation in our results compared to May et al. (2021) is in
line with the finding in Sergeev et al. (2022b) and Fauchez et al. (2021) that
ExoCAM displays the greatest degree of cloud variability out of the four
models included in the comparison. Our quantitative findings agree with the
results of these previous works and support the conclusion that atmospheric
variability due to clouds will be below the noise floor of JWST.

From a qualitative perspective, the impact of Rossby waves on observations is
highly sensitive to the location of both the Rossby gyres and the cloud deck.
If clouds form on or extend to the planetary terminators, migrations by Rossby
gyres could regularly clear this region for periods of time as long as the
planet’s transit. Without prior knowledge of the cloud structure, cycle
duration, and cycle phase, it is impossible to predict when such clearing
events might occur and to time observations to avoid flattened, featureless
spectra due to clouds (Garcia et al., 2022; Diamond-Lowe et al., 2018; de Wit
et al., 2016; Kreidberg et al., 2014; Knutson et al., 2014). However, as the
body of data from transit spectroscopy grows, atmospheric and climate
variability should be considered when combining or interpreting data from
different observing periods. In addition, as our theoretical understanding of
climate variability on exoplanets improves, it may be beneficial to obtain
data from consecutive transits instead of randomly chosen ones, as consecutive
observations are more likely to represent a real atmospheric state rather than
an averaged, composite one.

Traveling Rossby waves could also affect the chemical composition of the
planet’s atmosphere. Several studies using chemistry-climate models have found
that different chemical environments form on the dayside and nightside of
tidally locked planets due to the presence or absence of photochemistry (Braam
et al., 2022; Yates et al., 2020; Chen et al., 2018). In particular, the
nightside gyres can build up high concentrations of species that are destroyed
on the irradiated dayside. In our simulations of TRAPPIST-1e, however, the
nightside gyres frequently travel back and forth over the eastern terminator,
exposing chemically enriched nightside air to radiation. This process may
reduce chemical differences between the dayside and nightside, leading to a
more homogeneous planetary climate.

The specific features of this atmospheric oscillation, including the period,
the latitudes and longitudes of the Rossby gyres, their size, the distance
they travel, and how much cloud (if any) they advect are dependent on model
set-up, especially the cloud parameterization. The THAI project found
significant differences in the cloud water paths predicted by the four models
included in the intercomparison, with the UM in the middle of the pack
(Sergeev et al., 2022b). The location of the Rossby gyres also differs between
models and between simulations with varying parameters. To date, only Skinner
& Cho (2022) have studied the Rossby wave lifecycle in a tidally locked planet
simulation. In their high-resolution, hot gas giant simulations, Rossby gyres
(or “modons”) fully circumnavigate the planet in the westward direction,
periodically dissipate, and then reform and begin circulating again. We did
not observe circumnavigation even in a matching high-resolution simulation
performed with our control Proxima Centauri b model. Numerous factors such as
the temperature structure of the atmosphere and the presence of clouds may
influence the motion of Rossby waves in simulations of tidally locked planets.
A better understanding of the sensitivity and evolution of these waves in
atmospheric models of tidally locked planets is key to understanding climate
variability and a fruitful avenue for future work.

##  5 Conclusion

We describe a mechanism in the atmosphere of tidally locked terrestrial
exoplanets in which feedbacks between clouds and incoming stellar radiation
influence the dynamical state of the atmosphere, especially the zonal
wavenumber-1 Rossby response to the thermal forcing, leading to alternating
eastward and westward propagation of the Rossby gyres previously characterized
as largely stationary. The oscillation in the location of the Rossby gyres can
affect the distribution of clouds if the path of the Rossby gyre migration
intersects with the dayside cloud cover. In our simulations of Proxima
Centauri b, this interaction results in periodic clear and cloudy days at the
planet’s eastern terminator, while in our simulations of TRAPPIST-1e, the
Rossby gyres are located too far polewards to interact with the dayside
clouds. Time series of synthetic spectra generated for a 300-day sample of the
climate oscillation confirmed that the variation in cloud cover and
atmospheric humidity associated with the feedback mechanism results in a time-
varying transmission spectrum, but the magnitude of the variation in transit
depths is too small to be detectable for our simulated planets.

This study and our previous work in Cohen et al. (2022) identify physical
mechanisms of variability which cause cycles in the planetary climate even in
idealised exoplanet models without eccentricity, obliquity, or changes in the
stellar spectrum. More complex environments on real planets are no doubt
subject to additional sources of variability. As the body of exoplanet
observations grows in the age of JWST and other upcoming telescopes,
consideration of long-term climate variability and of weather on other planets
can help interpret observations taken at different times, construct time
series, and inform observing and data processing practices.

We acknowledge the funding and support provided by the Edinburgh Earth,
Ecology, and Environmental Doctoral Training Partnership and the Natural
Environment Research Council [grant number NE/S007407/1]. We also kindly
acknowledge our use of the Monsoon2 system, a collaborative facility supplied
under the Joint Weather and Climate Research Programme, a strategic
partnership between the Met Office and the Natural Environment Research
Council. Our research was performed as part of the project ‘Using UKCA to
investigate atmospheric composition on extra-solar planets’ (ExoChem). This
work was supported by a UKRI Future Leaders Fellowship [grant number
MR/T040866/1], Science and Technology Facilities Council Consolidated Grant
[ST/R000395/1] and the Leverhulme Trust through a research project grant
[RPG-2020-82].’

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