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Remote Sens. 2022, 14, 3866. https://doi.org/10.3390/rs14163866 www.mdpi.com/journal/remotesensing
Article
Simplified Relations for the Martian Night-Time OH* Suitable
for the Interpretation of Observations
Mykhaylo Grygalashvyly 1,*, Dmitry S. Shaposhnikov 2, Alexander S. Medvedev 1, Gerd Reinhold Sonnemann 1
and Paul Hartogh 1
1 Max Planck Institute for Solar System Research, 37077 Goettingen, Germany
2 Moscow Institute of Physics and Technology, 141701 Moscow, Russia
* Correspondence: gryga@iap-kborn.de
Abstract: Observations of excited hydroxyl (OH*) emissions are broadly used for inferring infor-
mation about atmospheric dynamics and composition. We present several analytical approxima-
tions for characterizing the excited hydroxyl layer in the Martian atmosphere. They include the OH*
number density at the maximum and the height of the peak, along with the relations for assessing
different impacts on the OH* layer under night-time conditions. These characteristics are deter-
mined by the ambient temperature, atomic oxygen concentration, and their vertical gradients. The
derived relations can be used for the analysis of airglow measurements and the interpretation of
their variations.
Keywords: Mars; excited hydroxyl; Martian atmosphere; airglow; OH*; nightglow
1. Introduction
Hydroxyl molecules in excited states (OH*) produce airglow in visible and near-IR
bands. Excited hydroxyl in the vibrationally excited state originates from the reaction of
ozone with atomic hydrogen; then, it can be deactivated by collisions with other mole-
cules and atoms, chemically removed by reaction with atomic oxygen, or emit a photon
by spontaneous emission. The distribution and abundances of hydroxyl are very sensitive
to atmospheric dynamics, thermodynamics, and photochemistry. Therefore, airglow
measurements provide a useful tool for studying these processes. In the terrestrial atmos-
phere, observations of emissions of OH* are broadly used to obtain information about
tides [1,2], planetary waves [3,4], gravity waves [5–7], and quasi-biennial oscillation [8].
These emissions are also utilized for studying sudden stratospheric warming events
[9,10]. Observations of OH* emissions have been used for retrieving temperature trends
and variations induced by the solar cycle, e.g., [11–15], and chemical composition in the
mesopause region [16–18].
Recently, hydroxyl emissions were found in the atmosphere of Venus [19–23] and on
Mars [24]. Future observations open the possibility for similar applications of the emis-
sions at these planets (for example, investigations of waves and tides by airglow observa-
tions and measurements of atomic oxygen concentrations). Commonly, complex photo-
chemical and general circulation models (i.e., non-linear global with interactively coupled
dynamics, chemistry, and radiation) are required for reproducing the behavior of the OH*
layer, the main characteristics of which are the altitude, emission intensity, and the shape.
When interpretating measurements, it is desirable to establish straightforward relations
between these quantities and the ambient temperature, air density, and concentration of
minor species involved in photochemical reactions and induced emissions. Since full so-
lutions are complex, it is not easy to assess the impacts of individual processes and inter-
pret the variabilities. Since the conditions differ between planets, we focus on Mars in this
paper.
Citation:
Grygalashvyly, M.;
Shaposhnikov, D.S.; Medvedev, A.S.;
Sonnemann, G.R. Simplified
Relations for the Martian
Night
-Time OH* Suitable for the
Interpretation of Observations.
Remote Sens.
2022, 14, 3866.
https://doi.org/10.3390/rs14163866
Academ
ic Editors: Lin Li, Yuanzhi
Zhang and Shengbo Chen
Received:
1 July 2022
Accepted:
7 August 2022
Published:
9 August 2022
Publisher’s Note:
MDPI stays neu-
tral with regard to
jurisdictional
claims in published maps and institu-
tional affiliations.
Copyright:
© 2022 by the authors. Li-
censee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and con-
ditions of the Creative Commons At-
trib
ution (CC BY) license (https://cre-
ativecommons.org/licenses/by/4.0/).
Remote Sens. 2022, 14, 3866 2 of 12
Satellite airglow measurements are not sufficiently precise and result in typical errors
in the determination of the layer altitude ~2–3 km. Ground-based observations are re-
stricted to local points and integrated volume emission, which leads to even larger errors
in the determination of the altitude (on Earth, the OH* layer is commonly assumed at 87–
88 km). In order to study the morphology and variability of the layer, we select the con-
centration of OH* at the peak, which is directly proportional to the volume emission, and
the altitude of the maximum as the characteristics of interest. In the next section, we ana-
lytically derive several approximations for these parameters as well as for relative varia-
tions of the OH* layer. In Section 3, we present applications of the derived formulae based
on the input from the Mars Climate Database (MCD) and determine their validity. Con-
clusions are given in Section 4.
2. Analytical Formulae Derivation
The list of photochemical reactions pertinent to hydroxyl in the Martian atmosphere,
along with the corresponding rates, is given in Table 1.
Table 1. List of reactions, nomenclature of reaction rates, quenching coefficients, and spontaneous
emission coefficients used in the paper.
Reactions
Coefficients
References
R1
. H + O
OH,…,+ O = 1.4 10470
,…,= 0.47,0.34,0.15,0.03,0.01
[25,26]
R2
. O + O
+ CO
O
+ CO
= 6.1 10
(
298
).
[25]
R3
. O + O2O = 8 10
2060
[25]
R4
. O + OH,..,O+ H (= 9, … ,1)= (5.42,4.8,
4.42, 4, 3.77,4.43,3.74,3,3.15)10
[27]
R5
.OH+ CO, O, N, O
OH+ CO, O, N, O ,,
See text
[26–29]
R6
.OH
OH
+ h
[30]
The table includes the source reaction for vibrationally excited hydroxyl (R1), the re-
action of chemical removal (R4), the reactions for collisional deactivation (R5), and spon-
taneous emission (R6). Reactions R2 and R3 are related to the ozone balance equation,
which will be used below. This list omits the reaction of hydroperoxy radicals (HO2) with
atomic oxygen because they represent a negligible (or even non-existing) source for the
population of vibrationally excited hydroxyl [30–34]. Thus, the starting point of our con-
sideration is the almost complete set of equations for OH*.
Next, we assume that the excited hydroxyl is in a photochemical equilibrium at night
[31]; hence, we can write its concentration as a ratio of production to the loss term. This
allows us to explicitly express the concentration of excited hydroxyl at all excitation levels
(v = 1, …, 9) in the form
[][][]+[]
[]+[]
[]+
+[]
[]+[]
[]+
+[]
[]
+[]
+[]
+
+[]
+
+
+()[],<
< (1
)
Remote Sens. 2022, 14, 3866 3 of 12
where v is the vibrational number; fv are the nascent distributions; r1 and r4 are the reaction
rates; and Avv′, Bvv′, Gvv′, and Dvv′ are the quenching coefficients by carbon dioxide, molec-
ular oxygen, molecular nitrogen, and atomic oxygen, respectively. Hereafter, the square
brackets denote the number density of a particular chemical constituent. Relation (1) can
be simplified by only considering the main processes of production and relaxation,
namely, the reaction of ozone with atomic hydrogen, quenching by carbon dioxide, mo-
lecular oxygen, and molecular nitrogen:
[][][]+[]
[]+
+[]
[]+[]
[]
[]
+[]
+[]
,<
<. (2
)
In (2), we neglected a spontaneous emission and quenching by atomic oxygen be-
cause these processes are weak on Mars. For example, the total spontaneous emission co-
efficients for vibrational levels OHv = 9 and OHv = 1 are E9 = 199.2495 s−1 and E1 = 17.62 s−1,
respectively [30]. On the other hand, [CO2] ≥ 1015 cm−3 at 50 km, e.g., [35,36], the collisional
removal rates A9 = 9.1 × 10−11 cm3 s−1, and A1 = 2.9 × 10−13 cm3s−1 [29,31,37–39] yield the first
term in the denominator in (1) exceeding 9 × 104 s−1 and 2.9 × 102 s−1 for the corresponding
vibrational numbers. Atomic oxygen concentrations at 50–60 km are around 109–1011 cm−3,
e.g., [35,40,41]. Ref. [27] derived for reactive (O + OHv → O2 + H) and non-reactive (O +
OHv → OHv′<v + O) quenching rates by atomic oxygen (at T = 160 K) the values 7.7 × 10−11
cm3 s−1 and 6 × 10−11 cm3 s−1 for v = 9 and 1, respectively. Hence, the corresponding colli-
sional removal rate due to atomic oxygen is less than 8–6 s−1 for all the vibrational numbers
and can be neglected.
Following the work of [31], we assume that ozone is in a photochemical equilibrium
in the vicinity of the night-time OH* layer. Then, the balance equation for ozone can be
represented as [][][]=[][]+[][]. (3
)
The share of the reaction of ozone with atomic oxygen in total ozone loss is small
since, for typical temperatures at 50–60 km (~150 K), the reaction rate r3 (~8.7 × 10−18 cm3
s−1) is about 106 times smaller than r1 (~6.1 × 10−12 cm3 s−1), but the atomic hydrogen number
density is smaller than that of atomic oxygen by no more than ~102–103 times in this region
[31,35,36,40]. Therefore, the second term on the right-hand side of (3) can be neglected:
[][][][][]. (4
)
The substitution of (4) into the first term in the numerator in (2) gives
[][][][]+[]
[]+
+[]
[]+[]
[]
[]
+[]
+[]
,<
<. (5
)
Molecular oxygen and molecular nitrogen number densities are linearly proportional
to the concentration of carbon dioxide []=[]=,[]=[], where M is the
air number density, and α, β, and χ are the proportionality coefficients at the heights of
the OH* layer, e.g., [35,41]. In the current work, one will find such behavior below in Fig-
ure 1a. This allows us to exclude the dependencies on concentrations [O2] and [N2] and re-
arrange (5):
[][]+[]
,<
<, (6
)
where
=
++
and
=
+
+
.
Writing the numeric value of the reaction rate r2 explicitly and reorganizing (6), we
can obtain
Remote Sens. 2022, 14, 3866 4 of 12
[][]., (7
)
where = 6.1 10298. and =
, (= 0, <, <).
Note that the coefficient ε depends on r2 and, therefore, can vary. For example, refs.
[29,31] utilized r2 = 1.2 × 10−27 after the work in [42]. The other examples of r2 applied in
previous studies include 2.7 × 10−34∙3002.4 [40], 1.4 × 10−34∙3002.4 [35], and 1.5 × 10−34∙3002.4 [43].
Despite the differences, all the studies were in consensus that ~..
Figure 1. Night-time zonal mean quantities averaged between 70°N and 90°N and over the period
of solar longitudes Ls = 265°–320°: (a) O, O3, H, O2, CO2, N2, T from MCD; (b) OHv = 1,…,9, calculated
with (1) (solid lines) and estimated with (7) (dashed lines); (c) volume emissions from (1) and (7)
(solid and dashed lines, respectively) for vibrational transitions 1–0 (blue), 2–1 (green), and 2–0 (red).
2.1. Peak Concentration of the Excited Hydroxyl Layer and Its Altitude
We now can derive an expression for the peak concentration of the hydroxyl layer
OH* and its altitude. For that, we exclude air density M from (7) using the ideal gas law:
[].[], (8
)
where the notation =
is used, p is pressure, and is the Boltzmann constant.
Differentiating (8) by pressure and equating the result to zero gives the pressure at
the local maximum of OH* concentration:
1
3.4 ln
ln[]
1
ln .
[], (9
)
Substituting (9) into (8), we obtain the value of the maximum concentration of the
excited hydroxyl:
[].[]
3.4 ln
ln[]
.[]
ln .
[], (10
)
It is seen from (9) and (10) that the peak concentration of OH* and its height are ex-
plicitly determined by vertical profiles of temperature, the concentration of atomic oxy-
gen, and the coefficient , which encompasses photochemical parameters. Note that the
derivations above are valid only within a thin layer near the peak of the OH* layer because
several assumptions were utilized that are only valid in this region.
2.2. Variations of the Excited Hydroxyl Layer
The hydroxyl layer is extremely variable. Therefore, it is desirable to link its relative
variations to those of the observable background quantities. For that, we decompose the
atomic oxygen number density, temperature, and air number density into the mean
Remote Sens. 2022, 14, 3866 5 of 12
([]
,,
) and deviations ([],,), where the bar denotes an appropriate (spatial, tem-
poral, or both) averaging, and substitute them into (7):
[]=[]
+[](+).[]
+[]. (11
)
Temperature variations / are small, at least on Mars and other planets of the ter-
restrial group. This allows one to apply the Taylor series expansion to the term with tem-
perature in (11). Cross-multiplying all terms yields
[][]
.[]
+[]
.[]+[].[]
2.4[]
.[]
+[].[]
2.4[]
.[]2.4[].[]
2.4[].[].
(12
)
The excited hydroxyl concentration for a given vibrational number can be written in
a more compact form:
[][]
+[]+[]+[]+[]+[]
+[]+ , (13
)
where the following notations are used: []
=.[]
[]
,[]=
.[]
[],[]=.[][]
,[]=2.4.[]
[]
,[]=
.[][],[]=2.4.[]
[],[]=2.4.[][]
.
Hence, relative variations of OH* concentration due to linear parts (RV′) can be ex-
pressed in terms of the relative variations of temperature, atomic oxygen, and concentra-
tion of air: []
[]
=2.4
,
[]
[]
=[]
[]
,
[]
[]
=[]
[]
.
(14
)
The relative variations of the concentration due to second momenta (RV″) are
[]
[]
=2.4 []
[]
,
[]
[]
=[][]
[]
[]
,
[]
[]
=2.4 []
[]
.
(15
)
In the derivation of (14) and (15), namely, in handling the terms with air number
density, we assumed that variations of the height of the OH* layer do not exceed the air
density scale height. Therefore, the derived equations are only valid when the displace-
ments of the OH* layer from the average altitude do not exceed the air density scale
height. In the terrestrial atmosphere, this condition is fulfilled for day-to-day, intra-sea-
sonal, gravity wave-induced variations and for annual cycles at latitudes where height
deviations of the OH* layer are relatively small. Similar care should be taken when (14)
and (15) are applied on Mars.
3. Calculations and Discussion
In this section, we test the applicability of the derived formulae. They contain photo-
chemical parameters in the most general form. In particular, they assume multi-quantum
relaxation for quenching and spontaneous emission processes, where transitions occur
from all vibrational levels above to all levels below. To date, not all multi-quantum
quenching coefficients for carbon dioxide and molecular nitrogen are known. Only the
Remote Sens. 2022, 14, 3866 6 of 12
rates for the so-called collisional cascade quenching [33], where transitions take place to
one level below, have been provided in the literature. The most recent update for these
coefficients was presented by [28,29] for quenching by carbon dioxide and molecular ni-
trogen, respectively. We adopted these values in our calculations. Namely, we used the
diagonal matrix for Avv′ and Gvv′ for transitions v → v − 1 with values of [28,29] and as-
signed the non-diagonal terms for other transitions to zero.
The input profiles of O, O3, H, O2, CO2, and N2 concentrations, and temperature, were
taken from the Mars Climate Database (MCD), which is based on simulations with the
Laboratoire de Météorologie Dynamique General Circulation Model (LMD-GCM) [44,45].
The MCD contains distributions of minor gases in the Martian atmosphere, including
ozone [46], which is directly involved in OH* production; water vapor [47], which is the
principal source of odd-hydrogens (H, OH, HO2); and variations of other long-lived spe-
cies (carbon dioxide and molecular nitrogen) involved in quenching processes [48,49].
Figure 1a presents the input profiles of night-time O, O3, H, O2, CO2, and temperature
T from the MCD averaged zonally between 70°N and 90°N and over the interval of solar
longitudes Ls = 265°–320°. The averaging over this region and time period has been per-
formed in order to provide a colocation with the observations [24]. The results of calcula-
tions for [OH*] using the general Formula (1) and approximated by (7) for OHv = 1,…,9 are
shown in Figure 1b with solid and dashed lines, correspondingly.
The results illustrate good agreement between OH* concentrations and peak alti-
tudes calculated with the full model (1) and the simplified formula (7). The best agreement
occurs near the peaks at ~48–53 km. The differences below and above the maxima can be
partially explained by deviations of ozone from photochemical equilibrium in the polar
night region, where the ozone lifetime is prolonged under the condition of permanent
night and downward transport of atomic oxygen [50].
The vertical separation of the hydroxyl layer depending on vibrational numbers is
well-known in Earth’s atmosphere, e.g., [26,51]. It cannot be explained from (9) since v
does not depend on p. This is the result of omitting quenching by atomic oxygen in the
loss term for excited hydroxyl. The inclusion of this term produces a weak vertical sepa-
ration by vibrational numbers (solid lines). Vertical distances between layers correspond-
ing to different vibrational numbers are expected to be smaller on Mars than on Earth, as
was found by [24]. This is because the atomic oxygen quenching, which is responsible for
separation, is comparable with that of molecular oxygen near the Earth mesopause but is
negligible compared to the CO2 quenching in the Martian atmosphere.
The increase in excited hydroxyl concentration with decreasing vibrational number
was found from observations and modeling for the Earth's atmosphere [26,28,32,33,51]
and from modeling results for the Martian atmosphere [31]. To explain this fact, let us
consider Equation (6). Direct population from the reaction of ozone with atomic hydrogen
(first term in the numerator) is a slower process than population by quenching from the
upper vibrational levels (second term in the numerator). The second term in the numera-
tor (and therefore the whole numerator) increases with a decreasing vibrational number,
whereas the denominator can only decrease with a decline in the vibrational number.
Thus, the increase in the OH* concentration with a decreasing vibrational number be-
comes evident.
Volume emission is a measurable quantity that is proportional to the concentration
of OH*. We calculated it with the full formula (1) and approximated it by (7) (both assume
the photochemical equilibrium of excited hydroxyl) and plotted it in Figure 1c using solid
and dashed lines, respectively. The colors indicate the main vibrational transitions: 1–0
(blue), 2–1 (green), and 2–0 (red). The figure shows that the locations of peaks (at ~48–53
km) and the corresponding volume emissions are in good agreement with the observa-
tions of [24] in terms of shape and magnitude.
Equations derived in Section 2 provide some predictions and can be applied for anal-
ysis in the future, which we illustrate below. The terrestrial OH* airglow layer demon-
strates annual and semiannual variations [2,8,52,53]. Similar variations can be expected
Remote Sens. 2022, 14, 3866 7 of 12
from the Martian OH* due to seasonal changes in atomic oxygen, air number density, and
temperature.
Figure 2 shows time series of night-time one-month sliding averaged values at the
peak of the OHv = 2 layer calculated with (1) at middle (40° N) latitudes: (a) the concentra-
tion [OHv = 2], (b) the height of the peak, (c) the atomic oxygen concentration, and (d) tem-
perature. It is seen that the concentration and the height of the peak at the northern middle
latitude vary seasonally, with the maxim concentrations and lowest height occurring dur-
ing the first half of the year (Ls ≈ 0°–180°). The amplitude of the annual height variation
on Mars is more than 20 km (Figure 2b), which by several times exceeds that near the
Earth mesopause (~5–10 km). The figures show a clear anticorrelation between the OHv = 2
number density and the height of the peak, as also follows from (8). Since volume emission
is linearly proportional to the hydroxyl concentration, this points to an anticorrelation be-
tween the emission and the height of the layer. A similar anticorrelation has also been
observed on Earth, e.g., [8,54,55].
Figure 2. Night-time mean one-month sliding averaged values at the peak of the OHv = 2 layer calcu-
lated with (1) at middle (40° N) latitudes: (a) concentration [OHv = 2], (b) the height of the peak, (c)
atomic oxygen concentration, and (d) temperature.
Figure 2a,c demonstrates a correlation between the concentrations of atomic oxygen
and excited hydroxyl. This correlation happens between Ls~210° and 340°, where the mi-
nor maximum of [OH*] coincides with the maximum of [O]. The correlation between the
air number density and the peak altitude is even more robust because the magnitude of
seasonal variations of the air density is larger than that of atomic oxygen. The effects of
atomic oxygen and air number densities on the OH* layer oppose each other. When the
OH* layer is low in summer, the air density is large, while the atomic oxygen concentra-
tion is small. The OH* layer moves higher in winter, and the air density decreases, but the
Remote Sens. 2022, 14, 3866 8 of 12
atomic oxygen concentration rises. In the Earth’s mesosphere at high and middle lati-
tudes, the behavior of the OH* layer is opposite: high altitude and low emission in sum-
mer, but a lower altitude and stronger emission in winter. This is because the main driver
for the OH* layer on Earth is atomic oxygen, which is transported downward in winter
and upward in summer. On Mars, the layer behavior is additionally determined by air
density variations. Seasonal changes in temperature play a minor role in the annual cycle
of OH* since it only varies by about 15 K over the year (Figure 2d).
In order to assess the sensitivity of the OH* layer to input parameters, we separately
calculated the contributions of relative variations of atomic oxygen, temperature, and air
density to variations of [OH*] or to the volume emission rate. We only considered the first
half of the year (Ls = 0°–180°), during which displacements of the height of the layer did
not exceed the air density scale height (~10 km). Thus, the overbar in (14) and (15) denotes
a semiannual averaging, and primes are for deviations from the semiannual mean. As in
Figure 2, we only considered night-time values at 40° N, which were smoothed with the
one-month moving window averaging.
The results are plotted in Figure 3, with contributions from (14) and (15) shown by
solid and dashed lines, respectively. The figure illustrates our notion above that tempera-
ture (red lines) plays a minor role in the hydroxyl layer variability. The main contribution
comes from variations of atomic oxygen and the ambient air concentration acting in op-
posite phases. The first peak of [OH*] at Ls~40°–50° (Figure 2a) is primarily determined by
the growth of the air number density (blue line) and, to a much lesser degree, by the de-
clining temperature (red line, see also Figure 2d). The secondary peak of [OH*] around
Ls~150° is mainly caused by the increase in the atomic oxygen concentration (green line),
whereas the declining air density and rising temperature act in the opposite direction. The
variations due to second momenta (dashed lines) are much weaker (do not exceed 10%).
Figure 3. Relative variations calculated over the first half of the Martian year with (14) (solid lines)
and (15) (dashed lines) at 40°N.
4. Conclusions
We presented the derivation of the simplified formulae relating the height of the peak
of the excited hydroxyl layer, its displacements, and the strength of emission with values
Remote Sens. 2022, 14, 3866 9 of 12
that can be observed in the Martian atmosphere at night-time. The assumptions used in
the derivation and relevant for Mars conditions include (1) the photochemical equilibrium
of ozone near the peak of the layer and (2) that total quenching by carbon dioxide, molec-
ular oxygen, and molecular nitrogen is greater than quenching by atomic oxygen and
spontaneous emission.
Under these approximations, the night-time concentration of OH* near the peak is
directly proportional to the concentration of atomic oxygen and pressure and inversely to
the power of temperature. Since pressure drops with altitude, the hydroxyl emission, the
major part of which is produced in the vicinity of the peak, anticorrelates with the height
of the OH* layer.
Calculations using input parameters from the Mars Climate Database demonstrate
annual variations of the OH* layer at middle latitude (40°N) resulting from the seasonal
cycle of temperature, air number density, and atomic oxygen. We illustrated how relative
variations of each of these quantities directly impact the relative variations of the concen-
tration of the hydroxyl layer.
The presented approach and simplified formulae can be applied for the analysis and
interpretation of future observations of hydroxyl emission on Mars. Coupled with obser-
vations of temperature and atomic oxygen (or ozone), airglow measurements can reveal
additional information about the Martian atmosphere’s dynamics and composition.
Finally, we should note that Equations (9) and (10) introduce the possibility of infer-
ring the altitudes of the OH* peak, the concentration at peak, the atomic oxygen concen-
tration at peak, and the ground-state hydroxyl concentration (which is the key constituent
for resolving the problem of the Martian (CO2) atmosphere stability due to catalytic re-
combination [56–58]), by surface-based or nadir observations of emissions from two vi-
brational transitions, accompanied by temperature observations from vibro-rotational
transitions following [59].
The strength and advantage of full models are that they seek to most fully encompass
processes occurring in a photochemical system. The advantage of an analytical approach
is that it allows inferring, under certain conditions and assumptions, simple relations
within this system. In this work, we did exactly the latter: derived simplified relations
between OH* peak height and density and observable parameters of emission. They
can/should motivate the development of future observations and help with interpreta-
tions when such observations become available.
Author Contributions: Conceptualization, M.G., D.S.S., A.S.M., G.R.S. and P.H.; methodology,
M.G., D.S.S., A.S.M., G.R.S. and P.H.; software, M.G., D.S.S., A.S.M., G.R.S. and P.H.; validation,
M.G., D.S.S., A.S.M., G.R.S. and P.H.; formal analysis, M.G., D.S.S., A.S.M., G.R.S. and P.H.; investi-
gation, M.G., D.S.S., A.S.M., G.R.S. and P.H.; writing—original draft preparation, M.G., D.S.S.,
A.S.M., G.R.S. and P.H.; writing—review and editing, M.G., D.S.S., A.S.M., G.R.S. and P.H.; visual-
ization, M.G., D.S.S., A.S.M., G.R.S. and P.H. All authors have read and agreed to the published
version of the manuscript.
Funding: This research was partially funded by Russian Science Foundation grant 20-72-00110.
Data Availability Statement: The MCD data were obtained from the webpage (http://www-
mars.lmd.jussieu.fr/, accessed on 12 October 2021). The results of calculations are stored at
https://doi.org/10.5281/zenodo.5558814.
Acknowledgments: The authors are grateful to Francois Forget and Jean-Paul Huot for creating the
open access Mars Climate Database and to all collaborators of LMD who worked on the database.
Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the
design of the study; in the collection, analyses, or interpretation of data; in the writing of the manu-
script, or in the decision to publish the results.
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