AirSea Interactions on Titan Effect of Radiative Transfer on the Lake Evaporation and Atmospheric Circulation_2

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Air–Sea Interactions on Titan: Effect of Radiative Transfer on the Lake Evaporation and

Atmospheric Circulation

Audrey Chatain

1,2

, Scot C. R. Rafkin

, Alejandro Soto

, Ricardo Hueso

, and Aymeric Spiga

Department of Space Studies, Southwest Research Institute (SwRI), 1050 Walnut Street, Suite 300, Boulder, CO 80302, USA; audrey.chatain@boulder.swri.edu

Departamento de Física Aplicada, Escuela de Ingeniería de Bilbao, Universidad del País Vasco/Euskal Herriko Unibertsitatea (UPV/EHU), Plaza Ingeniero Torres

Quevedo 1, E-48013 Bilbao, Spain

Laboratoire de Météorologie Dynamique/Institut Pierre-Simon Laplace (LMD/IPSL), Centre National de la Recherche Scientiﬁque (CNRS), Sorbonne Université, 4

place Jussieu, Tour 45-55 3

étage, F-75252 Paris, France

Received 2022 June 27; revised 2022 August 21; accepted 2022 August 24; published 2022 October 13

Abstract

Titan’s northern high latitudes host many large hydrocarbon lakes. Like water lakes on Earth, Titan’s lakes are

constantly subject to evaporation. This process strongly affects the atmospheric methane abundance, the

atmospheric temperature, the lake mixed layer temperature, and the local wind circulation. In this work we use a

2D atmospheric mesoscale model coupled to a slab lake model to investigate the effect of solar and infrared

radiation on the exchange of energy and methane between Titan’s lakes and atmosphere. The magnitude of solar

radiation reaching the surface of Titan through its thick atmosphere is only a few watts per square meter. However,

we ﬁnd that this small energy input is important and is comparable in absolute magnitude to the latent and sensible

heat ﬂuxes, as suggested in a study by Rafkin & Soto (2020). The implementation of a gray radiative scheme in the

model conﬁrms the importance of radiation when studying lakes at the surface of Titan. Solar and infrared radiation

change the energy balance of the system leading to an enhancement of the methane evaporation rate, an increase of

the equilibrium lake temperature almost completely determined by its environment (humidity, insolation, and

background wind), and a strengthening of the local sea breeze, which undergoes diurnal variations. The sea breeze

efﬁciently transports methane vapor horizontally, from the lake to the land, and vertically due to rising motion

along the sea breeze front and due to radiation-induced turbulence over the land.

Uniﬁed Astronomy Thesaurus concepts: Titan (2186);Natural satellite atmospheres (2214);Radiative transfer

(1335);Planetary climates (2184);Planetary atmospheres (1244)

1. Introduction

Titan is the only place beyond the Earth known to have

lakes and seas (Stofan et al. 2007; Hayes 2016).AsonEarth

where the evaporation of water from oceans, seas, and lakes

drives the planet water cycle, the evaporation of methane

from lakes and seas on Titan is an important element for the

atmospheric circulation (Tokano 2009a)and the most

probable source of methane to the atmosphere of Titan

(Lunine & Lorenz 2009).

Prior studies have investigated the magnitude of the

evaporative processes on Titan through relatively simple

analytical models (e.g., Mitri et al. 2007)and more complex

mesoscale modeling (e.g., Rafkin & Soto 2020). All of these

studies assumed that radiative forcing was unimportant. Indeed,

due to its farther distance to the Sun, and its thick and aerosol

covered atmosphere, only a few watts per square meter reach

the surface of Titan at maximum, compared to several hundreds

of watts per square meter in the case of the Earth. Mitri et al.

(2007)predicted turbulent sensible and latent heat ﬂuxes at the

surface much larger in magnitude than the radiative ﬂuxes.

However, Rafkin & Soto (2020)showed that the results from

Mitri et al. (2007)were driven by the assumption of a constant

air temperature. The lack of atmospheric cooling resulted in

large sensible heat ﬂuxes as the lake temperature dropped

through evaporative cooling. Thus, the surface ﬂuxes in

Mitri et al. (2007)were overestimated compared to a scenario

where a cold and moist marine layer could develop over the

lake. Rather than having large turbulent ﬂuxes, Rafkin & Soto

(2020)indicated that the ﬂuxes trended toward small values,

which often approach values close in magnitude to the

insolation. Rafkin & Soto (2020)thus concluded that

neglecting radiative forcing may not be a good assumption.

In the absence of radiative forcing, both Mitri et al. (2007)and

Rafkin & Soto (2020)independently found that a local balance

of energy was achieved whereby the sensible heat ﬂux—driven

by the temperature difference between the lake and atmosphere

—was opposite and equal in magnitude to the latent heat ﬂux—

driven by the difference between the saturation vapor pressure

over the lake and the relative humidity of the atmosphere.

The objective of this study is to investigate whether the

addition of radiative forcing upsets the ﬂux balance between

lakes and the overlying atmosphere found in prior studies, and

if so, in what way. The study uses the same mesoscale model

used in Rafkin & Soto (2020)and incorporates a gray radiative

transfer scheme (Section 2). A reference simulation with

radiation is compared to the case without radiation to identify

the mechanisms by which radiative forcing affects the

mesoscale circulation over lakes on Titan (Section 3).A

sensitivity study is then performed on other parameters of the

model to understand how they are affected by radiative forcing

(Section 4). The effect of seasonal and latitudinal insolation

variations is also quantiﬁed (Section 5).Weﬁnally discuss the

consequences of these new results relatively to current research

questions on Titan (Section 6).

The Planetary Science Journal, 3:232 (26pp), 2022 October https://doi.org/10.3847/PSJ/ac8d0b

Original content from this work may be used under the terms

of the Creative Commons Attribution 4.0 licence. Any further

distribution of this work must maintain attribution to the author(s)and the title

of the work, journal citation and DOI.

2. Model Description

2.1. Settings and Improvements of the Model

We use in this study the Titan mesoscale model mtWRF

previously described in Rafkin & Soto (2020), and conﬁgured

almost identically. This model is based on the Weather

Research and Forecasting (WRF)model and uses the

Advanced Research WRF (ARW-WRF)dynamical core

(Skamarock et al. 2008). We run 2D simulations because they

allow faster performance and more numerous testing of the

relevant parameters that we explore here. Limitations include

the absence of topography, the impossibility to deﬁne complex

lake shorelines, and the removal of vorticity-induced effects.

Therefore, the results quantify the relative importance of the

different phenomena and processes around lakes on Titan under

idealized conditions.

The simulation domain is 3200 km wide with 2 km

horizontal resolution and 59 atmospheric vertical levels

stretched from 3 m at the lowest level to 20 km at the top of

the domain. Simulation time is given in Titan days (tsols), with

one tsol corresponding to ∼15.9 days on Earth. The center of

the domain is occupied by a 300 km-wide lake that is

represented by a slab lake model. The slab consists of a single

layer of liquid methane with a temperature that instantaneously

responds to a net change in energy. The depth of this layer

represents the mixing depth of the lake, which is not

necessarily the depth of the lake. Mixing depths of 1 m,

10 m, and 100 m are investigated in this paper, as there is

evidence of lakes exceeding 100 m depth on Titan from Cassini

radar measurements (Mastrogiuseppe et al. 2019). The width of

the model lake is comparable to the size of large lakes on Titan:

the six largest have a length of 1170 km (Kraken Mare),

500 km (Ligeia Mare), 380 km (Punga Mare), 240 ×90 km

(Jingpo Lacus), 220 ×60 km (Ontario Lacus), and 200 km

(Hammar Lacus). In addition, Titan also hosts at least 45 lakes

with sizes between 30 and 200 km. These smaller lakes should

also show similar evaporation processes scaled down to their

sizes as explored in Rafkin & Soto (2020). Although the

simulation domain length is nonnegligible compared to Titan’s

circumference of 16,179 km, the size of the domain is mainly

chosen to avoid numerical edge effects on the lake-induced

circulation. For simplicity, we therefore use a spatially uniform

insolation over the domain.

In the simulations presented by Rafkin & Soto (2020), the

land surrounding the lake was at a ﬁxed temperature (93.47 K),

which was dictated by the Huygens atmospheric temperature

proﬁle. Instead of a ﬁxed temperature, we used the WRF soil-

slab model described in the appendix of Blackadar (1979),

modiﬁed for use on Titan, including using a thermal inertia of

600 J m

−2

−1

−0.5

typical of plains and lakes (MacKenzie

et al. 2019b). We highlight that, in this model, the subsurface

conduction ﬂux is proportional to the soil thermal inertia. The

soil-slab model implements basic physics with a minimum of

empirical tuning, and the fundamental physics are captured

with sufﬁcient ﬁdelity to match our very limited knowledge of

Titan’s subsurface. Thus, the surface temperature is free to vary

through subsurface conduction, through radiative ﬂuxes, and

through sensible heat exchange with the overlying atmosphere.

The subsurface soil temperature at an inﬁnitely deep lower

boundary is set to a constant. There is currently no

measurement of the subsurface temperature, but its value has

a signiﬁcant inﬂuence on the surface temperature. Therefore,

we also investigate the sensitivity to this parameter in this

work. No evaporation, condensation, or adsorption of methane

is allowed on the land. The land is dry and the latent heat ﬂux

is zero.

The numerical accumulation of errors in the evaluation of

prognostic variables (i.e., tendencies)was also improved

compared to Rafkin & Soto (2020). Wind, temperature, and

methane vapor tendencies are small under Titan’s conditions,

and their values after one time step were often at or below the

numerical precision of an 8 byte ﬂoat. The addition of an

accumulator for the surface temperature tendency in Rafkin &

Soto (2020)ameliorated much of this problem. Here, we

further improve this technique by increasing the dynamical

time step from 15.9 to 159 s to further compensate for small

tendencies and to better correct the numerical precision without

having to invoke the multi-time-step accumulator as frequently

as in Rafkin & Soto (2020). The larger time step produces

small, inconsequential changes in the output, mainly during the

short spin-up of the simulation. Results with dynamical time

steps of 79.5 s and 190.8 s effectively give the same results as

159 s, demonstrating that the numerical precision problem is

ameliorated for this range of values.

Finally, a gray radiation scheme based on Schneider at al.

(2012)was incorporated. The description of solar scattering in

the atmosphere was modiﬁed and the short wave radiative

transfer parameters were adjusted to better ﬁt the net solar ﬂux

proﬁle at the Huygens landing site (Tomasko et al. 2008a).

Details on the description, implementation, and tuning of the

gray radiative scheme are given in the Appendix. The gray

scheme treats broadband solar and broadband infrared energy

separately (Weaver & Ramanathan 1995). The solar ﬂux enters

the top of the atmosphere, is absorbed and scattered in the

atmosphere, and is reﬂected at the surface. The thermal

(infrared)ﬂux is emitted and absorbed by the surface and the

atmosphere. All of these computations are done at each

dynamical time step. All simulations presented here are started

at 00:00 local time (midnight). Initializing the model at

different local times has almost no effect on the evolution of

the stabilized, diurnally repeatable solution.

Due to all of the above improvements and modiﬁcations, the

new results should be taken as more realistic and accurate

results that supersede the results of Rafkin & Soto (2020).

While the general evolution of the system found by Rafkin &

Soto (2020)is mirrored in this study, there are important details

and new behaviors that arise with the inclusion of radiation and

the land surface model.

2.2. Initialization

To investigate the sensitivity of the model to various parameters

and to explore the effects of diurnal, seasonal, and geographical

variations of the solar insolation, several sets of simulations listed

in Table 1were performed. The studied parameters were the initial

relative humidity of the lowest atmospheric layer, the subsurface

temperature boundary condition, the initial lake surface temper-

ature, the lake mixed layer depth, the background wind speed, the

solar longitude (season), and the latitude. Seas and lakes on Titan

are mostly found at high latitudes (Punga Mare at 85°N, Ligeia

Mare at 79°N, Jingpo Lacus at 73°N, Ontario Lacus at 72°S, and

Kraken Mare at 68°N), although some are observed at mid-

latitudes (Hammar Lacus at 49°N, Sionascaig Lacus at 42°S, and

Urmia Lacus at 39°S; Grifﬁth et al. 2012; Vixie et al. 2015;

Tokano 2020). As the scope of this paper is to study the effect of

The Planetary Science Journal, 3:232 (26pp), 2022 October Chatain et al.

radiation on the evaporation of lakes, and as the solar radiative

forcing is higher at lower latitudes, we performed most

simulations at the lowest latitude at which lakes are found: 42°.

A comparison to higher latitudes is given in Section 5.

The Huygens/HASI temperature proﬁle (Fulchignoni et al.

2005)is used in all of the simulations. The initial land surface

temperature was set to the air temperature measured by Huygens

at 3 m, and ﬁxed to 93.47 K. This initial condition minimized an

initial sensible heat ﬂux due to thermal imbalance between the

surface and the atmosphere. We note that on Titan this thermal

proﬁle will, in reality, vary with latitude and seasons. But these are

only minor variations (Schinder et al. 2012;Newmanetal.2016)

that are not expected to greatly affect our investigation, which is

focused on the direct effect of radiation on the evaporation of

lakes. These are idealized experiments that aim to understand the

physical processes at stake and are not intended to exactly

reproduce the seasonal and latitudinal thermal conditions for all

simulations. All of the results must be interpreted within the

context of the idealized experiment assumptions and simpliﬁed

physics.

Initial methane vapor proﬁles were computed similarly to the

stably stratiﬁed proﬁles described in Rafkin & Soto (2020),

taking into account the virtual buoyancy of methane vapor. The

methane mixing ratio was kept constant from the surface up to

the saturation point, then the saturation curve was followed up

to 30 km, and ﬁnally the methane mixing ratio remains constant

to the model top (see Figure 1). The mixing ratio at the surface

is determined by specifying the relative humidity. The

deﬁnition of the saturation vapor pressure was modiﬁed to

use a larger range in temperatures compared to Rafkin & Soto

(2020), as described in the appendix of Moses et al. (1992).

3. The Reference Simulation

In this section, we investigate the effect of radiation on a

baseline, reference conﬁguration. Since there are currently little

or no measurements of the lake mixed layer depth, the lake

temperature or the subsurface temperature, we selected values

that are reasonable as a reference case. The sensitivity of the

results to other parametric values is discussed in the next

Table 1

Parameter Settings for All of the Simulations

Simulation

Name

Initial Surface Rela-

tive Humidity (%)

Deep Subsurface

Temperature (K)

Initial Lake Surface

Temperature (K)

Lake Mixed

Layer

Depth (m)

Background Wind

(ms

−1

)Ls (°)Latitude (°)

S-A

45 93.47 90.5 1 0 0 42

S-B 45 93.21 90.5 1 0 0 42

S-C 093.47 86.5 10042

S-D 0 93.21 86.5 10042

S-E 20 93.47 88 10042

S-F 70 93.47 92 10042

S-G 45 93.47 93.47 10042

S-H 45 93.21 93.47 10042

S-I 45 93.47 88 10042

S-J 45 93.47 90.5 10 0042

S-K 45 93.47 90.5 100 0042

S-L 45 93.47 90.5 1 1042

S-M 45 93.47 90.5 1 3042

S-N 45 93.47 90.5 1 0 90 −85

S-O 45 93.47 90.5 1 0 270 −42

S-P 45 93.47 90.5 1 0 270 −85

S-Q

093.47 93.47 10042

S-R 45 93.47 90.5 1 0 90 85

S-S 45 93.47 90.5 1 0 90 −42

S-T

20 93.47 88 30 1 270 −72

S-U 45 93.47 90.5 1 0 0 70

S-V 45 93.47 90.5 1 0 0 85

Note. Bold values highlight the differences with the reference simulation S-A.

These simulations have been run twice, one with the radiative transfer scheme on, and

one with the radiative transfer scheme off. In the text, an “0”is added at the end of the simulation name to signal simulations when the radiation scheme is turned off,

e.g., S-A has radiation, and S-A0 does not.

S-T is done to be close to Ontario Lacus summer conditions, and it is the only simulation done on a 100 km large lake.

The Planetary Science Journal, 3:232 (26pp), 2022 October Chatain et al.

section by comparison to the reference case. The lake mixed

layer depth is set to 1 m, the initial lake temperature to 90.5 K,

and the land underground temperature to 93.47 K (the same as

the initial surface temperature in this case). The lake extends

150 km in both directions from the center of the domain, and

there is no background wind. The initial relative humidity is set

to 45% at the surface. We ran this conﬁguration with the

radiative scheme on (simulation S-A, the reference simulation)

and with the radiative scheme off (simulation S-A0).

The general solution of the reference simulation is similar to

that found by Rafkin & Soto (2020). The diurnally stable

solution is a sea breeze driven by the temperature difference

between the cold air above the lake and the warmer air above

the land. However, in our reference simulation, the addition of

radiation repartitions the energy budget, and this, in turn,

affects the circulation.

3.1. Diurnal Variations

The ﬁrst new result is the appearance of diurnal variation in

S-A, which is not present in S-A0 due to its lack of radiative

forcing (Figure 2). The diurnal variations in most of the model

ﬁelds conﬁrm that radiative processes are large enough

compared to other energy budget terms to have an impact.

In both S-A and S-A0, a sea breeze, where winds blow from

the lake toward the land, forms (Figures 2(a)–(d)). The lake is

cooled by evaporation (Figures 2(g)and (h)), and the air above

the lake is then cooled by sensible heat ﬂux transfer from the

air to the colder underlying lake (Figures 2(i)and (j); processes

are detailed in Section 3.2). The temperature difference

between the cold dense air above the lake and the warmer air

over land drives the sea breeze. Indeed, with the warm air being

more buoyant, it creates a low pressure zone that draws in cold

air from over the lake onto the land. Without radiation, in S-A0,

the sea breeze front continuously extends over land, and a

stabilized state (i.e., when variables do not substantially change

in time)is reached above the lake in 1–2 tsols.

The situation is different in S-A. The diurnally varying

insolation heats the land during the day (see more details in

Section 3.2). This leads to a relatively large sensible heat ﬂux

exchange between the hot land and the colder air above,

especially when cold marine air moves inland (Figures 2(i)and

(j)). The sensible heating of the atmosphere leads to dry

convective overturning and instability. Convection is clearly

visible in the surface wind during daytime as seen in the dark

bands of the horizontal and vertical winds in Figures 2(a)and

(e). Even though some convection is required over land to close

the sea breeze circulation, the rigorous daytime turbulent

episodes mix and diffuse the marine air mass over the land such

that the sea breeze over the land largely collapses during the

day (except at the shore). A new sea breeze forms at the lake

shore on the following night and propagates inland until

heating and mixing destroy most of the circulation on the next

tsol. Because of the daytime attenuation of the sea breeze over

land, the maximal sea breeze extension over land is limited to

700 km from the lake center (with a remnant, previous tsol

front up to 1000 km). A similar turbulent convective phenom-

enon also occurs on Earth when cold sea breeze air masses

propagate over heated surfaces (Crosman & Horel 2010).

When the diurnal variation of variables repeats itself every

day, then the simulation has reached a stable, diurnally

oscillating model state. For this reference simulation, this

stable model state is reached after 1–2 tsols, as seen in Figure 2.

Though diurnally varying, the intensity of the sea breeze wind

is, on average, strongly increased in the case with radiation S-A

(especially at night over land)compared to S-A0 without

radiation (Figure 2). The addition of radiation increases the

temperature difference between the air above the lake and

above the land (explained in detail in Section 3.2), which leads

to stronger winds toward the land, especially at night.

There is weak nocturnal turbulence over land in the case

with radiation (Figures 2(a)and (e)). This turbulent convection

is due to two processes. First, the marine air is substantially

colder than the surface, even at night. Second, the land tends to

be kept warm because the downward IR ﬂux from the

atmosphere is slightly higher than the upward IR ﬂux emitted

by the surface (Figure A1(b)in the Appendix). As is the case

during the day, the temperature contrast between the surface

and air above drives a sensible heat ﬂux (Figures 2(i)and (j))

that destabilizes the lowest atmospheric layers (see more details

in Section 3.2). This is different from what typically occurs on

Earth, where the ground cools down very quickly by IR

emission at night and other energy budget terms are unable to

keep the land warmer than the air. Thus, the sign of the

nocturnal sensible heat ﬂux on Earth is usually opposite to that

of Titan, which leads to a nocturnal radiation inversion on

Earth and not on Titan. However, above the shallow unstable

nocturnal layer on Titan, the marine layer is stable with a well-

deﬁned marine inversion, just like Earth.

3.2. Energy Budget

To investigate in greater detail the processes that drive the

observed changes in structure, characteristics, and evolution

between the radiative and nonradiative solutions, the evolution

of key variables is compared to the evolution of energy ﬂuxes

in Figures 3and 4. We identiﬁed wind, air temperature, land/

lake temperature, and methane mixing ratio as key variables

that affect the atmospheric circulation and energy transport,

since these are variables that we initialize at the beginning of

the simulation. The energy ﬂuxes of sensible heat, latent heat,

solar radiation, infrared radiation, and soil conduction then

evolve as a response to both the initial state and the evolution

of the key variables.

Figure 1. Methane mixing ratio proﬁles used in this work, compared to the

Huygens/GCMS measurements (Niemann et al. 2010). Relative humidity (RH

in the subpanel)indications are surface values.

The Planetary Science Journal, 3:232 (26pp), 2022 October Chatain et al.

Figure 2. Evolution with time of the horizontal wind at 3 m (panels (a)and (b)) and 230 m (panels (c)and (d)) in altitude, the vertical wind at 200 m (panels (e)and

(f)), the latent heat ﬂux to the surface (panels (g)and (h)), and the sensible heat ﬂux to the surface (panels (i)and (j)). Results obtained in the reference simulation with

radiative transfer S-A (left column)are compared to results in the same conditions without radiative transfer S-A0 (right column). The dark blue line indicates the lake

position. Simulations are started at midnight.

The Planetary Science Journal, 3:232 (26pp), 2022 October Chatain et al.

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Air–SeaInteractionsonTitan:EffectofRadiativeTransferontheLakeEvaporationandAtmosphericCirculationAudreyChatain1,2,ScotC.R.Rafkin1,AlejandroSoto1,RicardoHueso2,andAymericSpiga31DepartmentofSpaceStudies,SouthwestResearchInstitute(SwRI),1050WalnutStreet,Suite300,Boulder,CO80302,USA;audrey.chatain@bould...

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AirSea Interactions on Titan Effect of Radiative Transfer on the Lake Evaporation and Atmospheric Circulation_2

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