A NEW METHOD FOR CALCULATING SOLAR IRRADIANCE AT MARS.
I. de Oliveira, Max Planck Institute for Solar System Research, Göttingen, Germany (oliveira@mps.mpg.de),
Institut für Astrophysik, Georg-August-Universität Göttingen, Göttingen, Germany, A. I. Shapiro, K. Sowmya,
A. Medvedev, Max Planck Institute for Solar System Research, Göttingen, Germany, N.-E. Nèmec, Institut für
Astrophysik, Georg-August-Universität Göttingen, Göttingen, Germany, L. Gizon, Max Planck Institute for Solar
System Research, Göttingen, Germany, Institut für Astrophysik, Georg-August-Universität Göttingen, Göttingen,
Germany, Center for Space Science, New York University Abu Dhabi, Abu Dhabi, UAE.

Introduction
Solar irradiance is an important source of energy for
planetary atmospheres. This quantity is, however, mainly
measured from the vantage point of Earth. Recently,
we have been provided with measurements of extreme
ultraviolet solar radiation at Mars, determined by the
Extreme UltraViolet Monitor (EUVM, Eparvier et al.
2015), onboard the Mars Atmosphere and Volatile EvolutioN (MAVEN) mission, which is in orbit of Mars
since September, 2014.
Several studies used measurements of irradiance from
Earth to estimate the irradiance at Mars (e.g. Peter et al.
2014; Ramstad et al. 2015). This estimation can be
done by applying an extrapolation method, described
by Thiemann et al. [2017]. The method assumes that
the irradiance source regions on the surface of the Sun
simply rotate with a Carrington sidereal period of 25.38
days, i.e., that changes of the solar irradiance are only
caused by the rotation of the Sun, ignoring the evolution
of active regions on the solar surface. Measurements
of irradiance at Earth made before and after the visible
solar disk rotates past Mars at a specific day are linearly
interpolated. This gives us, in principle, the irradiance
at Mars on that day.
In this work, we test the accuracy of the interpolation
method and develop a new method for calculating the
irradiance at Mars, as well as at any other body in the
Solar System.

Data and Methods
To obtain the solar irradiance, we need to first calculate
the distribution of magnetic features (faculae and spots)
on the surface of the Sun. We utilize the Surface Flux
Transport Model (SFTM, Cameron et al. 2010), which is
an advective-diffusive model that describes the transport
of radial magnetic field on the surface of the Sun. It
is, on average, a reliable statistical representation of
the distribution of faculae and spots on the Sun. We
use full-surface magnetic field maps obtained using the
SFTM model. We follow an approach of Nèmec et al.
[2020] and Sowmya et al. [2021] and use these fullsurface maps for calculating solar irradiance as a sum of
contributions from the quiet Sun (i.e. regions without

magnetic activity), faculae, and spots.
For this study, we calculate the irradiance at 200.5
nm as it would be observed at four different longitudes
within the ecliptic: 0°, 90°, 180°, and 270°. For the
purpose of this work, we assume that the Earth is always
located at 0° longitude and the location of Mars varies
between 90°, 180°, and 270° (i.e., the Mars-Sun-Earth
angle). Figure 1 shows an example of faculae and spots
on the visible solar disks at the four longitudes.
Our method directly calculates the irradiance at a
given position within the ecliptic. We apply the extrapolation method (Thiemann et al. 2017), i.e., we extrapolate the measurements obtained at 0° to the other three
longitudes, in order to compare the two methods and
assess how well the results correlate.
As for the time series, we choose two periods of
one year each, corresponding to a period of high solar
activity (from September 15th, 1989) and a period of
low solar activity (from August 7th, 1995).

Results
Figures 2 and 3 show the irradiance at 200.5 nm calculated with our method at 90° longitude (red) and extrapolated to 90° (blue), for periods of low and high
solar activity, respectively. The irradiance values are
normalized to 1 AU, for the purpose of comparison.
We perform a Pearson correlation of the calculated
and extrapolated curves. The correlation coefficient is
denoted as “r” in the Figures, and it is 0.97 for a period
of low solar activity and 0.92 for a period of high solar
activity.
The correlation between our method and the extrapolation method is the largest for time ranges of lower
solar activity, i.e., when there are less faculae and spots
on the Sun. However, the correlation is still large for
periods of high solar activity. This pattern extends to
the results of Mars-Sun-Earth angles of 180° and 270°
as well.
The correlation coefficients at 180° are the smallest
among all Mars-Sun-Earth angles analyzed (r = 0.89
for the period of high solar activity). This is expected,
since the extrapolation method only averages irradiance
at Earth before and after the visible solar disk rotates
past the point of interest, and this point is the furthest to

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Figure 2: Time series of the S-index, calculated at a Mars-SunEarth angle of 90°(red) and extrapolated from Earth position
(blue), for a year of low solar activity.

Figure 1: Synthetic maps of the distribution of faculae (blue
shades) and spots (red) on the surface of the Sun on December
22nd, 1989. The visible disk (bright area) is centered at the
longitude indicated in the top left corner of each panel.

Earth at an angle of 180°. The accuracy of our method
is higher, because it calculates irradiance at the point of
interest.

Conclusions
We propose a simple method for estimating irradiance
at Mars, based on a statistically correct solar model
(SFTM). We calculate the irradiance at 200.5 nm at
three Mars-Sun-Earth angles, and compare our results
with the extrapolation method, described by Thiemann
et al. [2017].
The results of our method correlate well with the
extrapolation method. However, our method has greater

Figure 3: The same as in Figure 2, but for a year of high solar
activity.

accuracy, once it is based on the distribution of magnetic
features on the whole surface of the Sun, while the extrapolation method only takes into account the the solar
disk which is visible from Earth.
As a future work, we will estimate the irradiance at
Mars in real-time, making use of methods of far-side
imaging of the Sun. Then, our method will not only be
statistically correct, but also realistic.

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