The Key Factors Controlling the Seasonality of Planetary Climate

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1. Introduction

The seasonal cycle that a planet experiences is a function of a large number of parameters. A necessary condition

for a planet to experience a seasonal cycle is to have either non-zero obliquity or non-zero eccentricity, such that

the incoming solar radiation will have a seasonal cycle. The degree of seasonality, however, depends on other

parameters (e.g., Guendelman & Kaspi,2019,2020). The solar system's terrestrial planetary bodies, Earth, Mars,

and Titan, are great examples of planets with a similar obliquity, having a similarseasonal pattern of the incoming

solar radiation at the top of their atmosphere. Still, each planet experiences a different temperature seasonal cycle

at its surface (Figure1). This is a result of the different characteristics of these planets, especially, their radiative

timescale. The atmospheric radiative timescale can be estimated by (Mitchell & Lora,2016)



R=IR











(1)

where ξIR is the infrared optical depth, Cp is the specific heat at constant pressure, P is pressure, g is surface

gravity(with P/g is the atmospheric mass per unit area), σ is the Stefan-Boltzmann constant, and Te is the equilib-

rium temperature. To leading order the ratio between the radiative timescale and the orbital period should dictate

the strength of the seasonality that a planet will experience. For example, a planet with an orbital period that is

significantly longer than its radiative timescale, will experience a strong seasonal cycle, and vice versa (e.g.,

Guendelman & Kaspi,2019).

Earth has an atmospheric radiative timescale of ∼30days (Wells,2011). Additionally Earth's surface is mostly

covered by deep oceans resulting in high surface thermal inertia. The combination of high surface thermal inertia

and long atmospheric radiative timescale contribute to the strong modulation of Earth's seasonal cycle. Mars, on

the other hand has a dry rocky surface with low thermal inertia and a thin atmosphere (e.g., Read etal.,2015).

Abstract Several different factors influence the seasonal cycle of a planet. This study uses a general

circulation model and an energy balance model (EBM) to assess the parameters that govern the seasonal cycle.

We define two metrics to describe the seasonal cycle, ϕs, the latitudinal shift of the maximum temperature,

and ΔT, the maximum seasonal temperature variation amplitude. We show that alongside the expected

dependence on the obliquity and orbital period, where seasonality generally strengthens with an increase in

these parameters, the seasonality depends in a nontrivial way on the rotation rate. While the seasonal amplitude

decreases as the rotation rate slows down, the latitudinal shift, ϕs, shifts poleward. A similar result occurs in a

diffusive EBM with increasing diffusivity. These results suggest that the influence of the rotation rate on the

seasonal cycle stemsfrom the effect of the rotation rate on the atmospheric heat transport.

Plain Language Summary The seasonal cycle that a planet undergoes can be described by its

amplitude, that is, the maximal temperature difference experienced across the year. In addition, it can be

characterized by the latitudinal shift of the maximum temperature during that annual cycle. This study explores

the role of obliquity, orbital period, and rotation rate on the seasonality. We find that, as expected, increasing

the obliquity and orbital period results in a stronger seasonal cycle. Surprisingly, decreasing the rotation rate

has a complex effect on the seasonal cycle. It reduces the seasonal cycle amplitude but increases the latitudinal

shift of the maximum temperature. We find that this is a result of the effect of the rotation rate on the way

heat is redistributed within the atmosphere. These results emphasize the importance of studying the climate's

dependence on planetary parameters, as for example, an Earth-like planet with a slower rotation rate will

experience a significantly different seasonal cycle.

GUENDELMAN AND KASPI

This is an open access article under

the terms of the Creative Commons

Attribution License, which permits use,

distribution and reproduction in any

medium, provided the original work is

properly cited.

The Key Factors Controlling the Seasonality of Planetary

Climate

Ilai Guendelman1 and Yohai Kaspi1

1Earth and Planetary Department, Weizmann Institute of Science, Rehovot, Israel

Key Points:

• The seasonal cycle temperature

dependence on atmospheric and

orbital parameters is studied in an

idealized general circulation model

(GCM)

• The majority of the GCM temperature

seasonal dependence on obliquity,

orbital period, and rotation rate is

captured in a diffusive energy balance

model

• The maximum surface temperature

drifts poleward with decreasing

rotation rate due to a more efficient

atmospheric heat transport

Supporting Information:

Supporting Information may be found in

the online version of this article.

Correspondence to:

I. Guendelman,

ilai.guendelman@weizmann.ac.il

Citation:

Guendelman, I., & Kaspi, Y. (2022). The

key factors controlling the seasonality

of planetary climate. AGU Advances,

3, e2022AV000684. https://doi.

org/10.1029/2022AV000684

Received 23 FEB 2022

Accepted 19 AUG 2022

Peer Review The peer review history for

this article is available as a PDF in the

Supporting Information.

Author Contributions:

Conceptualization: Ilai Guendelman,

Yohai Kaspi

Formal analysis: Ilai Guendelman

Methodology: Ilai Guendelman

Supervision: Yohai Kaspi

Writing – original draft: Ilai

Guendelman

Writing – review & editing: Yohai Kaspi

10.1029/2022AV000684

RESEARCH ARTICLE

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AGU Advances

GUENDELMAN AND KASPI

10.1029/2022AV000684

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With an atmospheric radiative timescale of ∼1day (Wells,2011), it features the strongest seasonal cycle among

the three. In addition, Mars's eccentric orbit results in an hemispheric asymmetry between the southern and north-

ern summer solstices (Figure1). Titan, conversely, has a thick, cold atmosphere, that is, a long radiative timescale

(∼200years, Mitchell & Lora,2016), that also absorbs significant amounts of the shortwave radiation. All these

factors modulate its seasonal cycle. However, it has a very low surface thermal inertia, which acts to increase

the seasonal cycle. The competition between these two effects results in Titan having a moderate seasonal cycle.

Another importantparameter that differs among the three planets is the rotation rate, with Earth and Mars being

fast rotating planets and Titan being a slowly rotating planet (with a rotation period of ∼16 Earth days). Previ-

ous studies have shown that the atmospheric heat transport (AHT) on slowly rotating planets is more efficient,

resulting in flatter temperature gradients (Edson etal.,2011; Kaspi & Showman,2015; Liu etal.,2017; Merlis &

Schneider,2010; Noda etal.,2017; Pierrehumbert & Hammond,2019). This in turn has the potential to change

the seasonal cycle that a planet experiences (Tan,2022).

The obliquity of the giant planets, Saturn, Neptune, and Uranus, too, is significantly larger than zero. When

considering their long atmospheric radiative timescale, most studies agree that these planets should experience

weak-to-no seasonal cycle (e.g., Conrath etal.,1990). However, Li etal.(2018) have estimated a shorter radia-

tive timescale for the ice giants, suggesting that both Uranus and Neptune should experience some seasonality.

At least for Uranus, where the dynamics extends deep (Kaspi etal., 2013) this is in contrast to what current

observations suggest (Orton etal.,2015; Roman etal.,2020). An opposite example of a mismatch between the

observed and expected seasonality is Titan. The cold conditions and massive atmosphere of Titan result in an

atmospheric radiative timescale that is much longer than its orbital period (Mitchell & Lora,2016). However,

the seasonal cycle on Titan is not negligible, and in some aspects stronger than that of Earth (Figure1). Mitchell

and Lora(2016) have suggested that the strength of the seasonal cycle is forced from Titan's low surface thermal

inertia. Shortwave radiation warms the surface, which in turn radiates back to the atmospheric boundary layer

that has a shorter radiative timescale compared to the entire atmosphere, allowing the seasonal cycle to become

significant. Although this can explain the seasonality on Titan, in this study,we also explore the role of the rota-

tion rate and AHT on the seasonal cycle.

This diversity in the seasonality of the solar system planets is tiny compared to the potential variety among

planets outside the solar system. Even if remainingrestricted to terrestrial planets within the habitable zone of

their host star, the possible diversity is immense. For example, differences between ocean and rocky worlds,

planets with different obliquities, eccentricities, or atmospheric compositions that would affect both the short-and

long-wave optical depths, all these have an effect on the climate seasonality that a planet will experience (e.g.,

Armstrong etal.,2014; Colose etal.,2019; Guendelman etal.,2021,2022; Linsenmeier etal.,2015; Lobo &

Bordoni,2020). In addition to all these, recent studies have also shown that the planetary rotation rate has an

effect on the surface temperature latitudinal distribution and seasonal cycle (e.g., Edson etal.,2011; Guendelman

& Kaspi,2019; Kaspi & Showman,2015; Liu etal.,2017).

This study explores the seasonality dependence on different planetary parameters in an idealized setting, connect-

ing results from a simplified general circulation model (GCM) and a diffusive energy balance model (EBM). In

the idealized GCM we vary the obliquity, orbital period, and rotation rate. The obliquity represents the role of

the solar forcing, the orbital period represents the role of the atmospheric radiative response, and the rotation rate

Figure 1. The seasonal cycle of the zonally averaged surface temperature on Earth (climatology from 1980 to 2019,

reanalysis data from ERA5), Mars (climatology from reanalysis data from Greybush etal.,2019) and Titan (from a Titan

atmospheric model used in Faulk etal.(2020)).

AGU Advances

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represents the role of the dynamics. Although, as mentioned, numerous other parameters can also influence the

temperature, we consider these three as each represents a different part of the radiative and dynamical response

of the climate system. Similarly, in the EBM we explore the roles of obliquity and of a non-dimensional radia-

tive timescale and diffusion. As in the parameters studied in the GCM, these parameters have similar significance,

with the non-dimensional radiative timescale representing the ratio between the orbital period and radiative

timescale and the diffusion reflecting the role of the dynamics and AHT.

Note that in this study we explore the climate of planets in a circular orbit, that is, planets with zero eccentricity.

Planets in an eccentric orbit will experience a more complex seasonal cycle, which can include hemispheric

asymmetry, with different hemispheres experiencing different seasonal intensity (Guendelman & Kaspi,2020;

Ohno & Zhang,2019) and is outside the scope of this study. This manuscript is arranged as follows, in Section2,

we describe the GCM and EBM used in this study. Section3 describes the results, and we conclude and discuss

the significance of this study in Section4.

2. Methods

2.1. General Circulation Model

In this study, we use an idealized GCM with a seasonal cycle (Guendelman & Kaspi,2019). The top of the atmos-

phere is forced by diurnal mean insulation, given by:

𝑄

𝑆

𝜋

(ℎsin 𝜙sin 𝛿+ cos 𝜙cos 𝛿sin ℎ)

(2)

where S0 is the solar constant, h is the hour angle of the sun at sunrise and sunset, ϕ is for latitude and δ is the

declination angle (Hartmann,2016). The model is an aquaplanet model with a 10m depth mixed layer as the

lower boundary. The model solves the primitive equations in a T42 horizontal resolution and 25 vertical layers.

The radiation in the model is represented by a two-stream gray radiation scheme. The model utilizes a simplified

parameterization for moist convection processes (Frierson etal.,2006).

We vary the parameters as follows:

• Obliquity (γ): 10, 20, 30, 40, 50, 60, 70, 80, 90.

• Orbital period (ω):

1

,1,2,

• Rotation rate (Ω):

1

,1,

The values are normalized such that ω=1 is an orbital period of 360 Earth days, and Ω=1 is Earth's rotation

rate. We vary two parameters at a time while keeping the third constant, with Earth-like values, except for the

obliquity, which is 30°. This results in a total of ∼142 simulations. The Earth-like simulation (top right corner

in Figure2) has a stronger seasonal cycle compared to observations as it has a higher obliquity, a relatively low

mixed layer depth, and due to the model's simplicity. Although planets in a short orbital period can become tidally

locked, we do not consider this configuration in this study.

2.2. Energy Balance Model

A more simplified way to study the temperature response to the different parameters is a diffusive EBM, given by:

𝐶

𝜕𝑇

𝜕𝑡

=𝑄(1−𝑎)−𝜎𝑇 4+𝜕

𝜕𝜙 (

𝐷cos 𝜙𝜕𝑇

𝜕𝜙 ),

(3)

where C is the effective heat capacity, with the value of C for a 10m mixed layer depth being ∼4×10

7Jm

−2K

−1,

T is the temperature, Q is the diurnal mean insolation, a is the albedo, σ is the Stefan-Boltzmann constant, D is the

diffusion coefficient, taken to be constant (an appropriate value for Earth is ∼0.6Wm

−2K

−1, North & Kim,2017),

and ϕ is latitude. The diurnal mean insolation, Q, is calculated using Equation2. Although it is conventional to

use a linear form for the outgoing longwave radiation (OLR, e.g., Budyko,1969; North & Coakley,1979; Rose

etal.,2017), and is even found to be more accurate for Earth (Koll & Cronin,2018), it involves some assumptions

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摘要：

1.IntroductionTheseasonalcyclethataplanetexperiencesisafunctionofalargenumberofparameters.Anecessaryconditionforaplanettoexperienceaseasonalcycleistohaveeithernon-zeroobliquityornon-zeroeccentricity,suchthattheincomingsolarradiationwillhaveaseasonalcycle.Thedegreeofseasonality,however,dependsonother...

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