Volume 127, Issue 2 e2021JE007112
Research Article

Natural Orthogonal Component Analysis of Daily Magnetic Variations at the Martian Surface: InSight Observations

H. Luo

Corresponding Author

H. Luo

Key Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China

College of Earth Science, University of Chinese Academy of Sciences, Beijing, China

Correspondence to:

H. Luo and Y. S. Ge,

[email protected];

[email protected]

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A. M. Du

A. M. Du

Key Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China

College of Earth Science, University of Chinese Academy of Sciences, Beijing, China

Contribution: Conceptualization, Project administration

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Y. S. Ge

Corresponding Author

Y. S. Ge

Key Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China

College of Earth Science, University of Chinese Academy of Sciences, Beijing, China

Correspondence to:

H. Luo and Y. S. Ge,

[email protected];

[email protected]

Contribution: Validation, Writing - review & editing

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C. L. Johnson

C. L. Johnson

Department of Earth, Ocean and Atmospheric Sciences, University of British Columbia, Vancouver, BC, Canada

Planetary Science Institute, Tucson, AZ, USA

Contribution: Methodology, Validation, Writing - review & editing

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A. Mittelholz

A. Mittelholz

Department of Earth Sciences, ETH Zürich, Zürich, Switzerland

Contribution: Validation, Writing - review & editing

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Y. Zhang

Y. Zhang

Key Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China

College of Earth Science, University of Chinese Academy of Sciences, Beijing, China

Contribution: Validation, Writing - review & editing

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S. Q. Sun

S. Q. Sun

Key Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China

Contribution: Validation

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L. Zhao

L. Zhao

Key Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China

Contribution: Writing - review & editing

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Y. Yu

Y. Yu

Key Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China

College of Earth Science, University of Chinese Academy of Sciences, Beijing, China

Contribution: Methodology, Writing - review & editing

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L. Tian

L. Tian

Key Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China

College of Earth Science, University of Chinese Academy of Sciences, Beijing, China

Contribution: Validation, Data curation

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S. Y. Li

S. Y. Li

Key Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China

College of Earth Science, University of Chinese Academy of Sciences, Beijing, China

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W. Y. Xu

W. Y. Xu

Key Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China

Contribution: Methodology

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First published: 26 January 2022
Citations: 1

Abstract

Distinguishing different sources of magnetic field variations at InSight is important to understand dynamic processes in the Martian ionosphere as well as the coupling between the solar wind and the Martian induced magnetosphere. Recent studies based on magnetic field measurements from InSight have suggested that the daily and seasonal variations in the magnetic field at the Martian surface are at least partially the result of neutral wind-driven ionospheric dynamo currents and their seasonal variations. However, the sources of the daily variations with different time scales need be further investigated. In this paper, magnetic field variations in a sol as well as during nearly a whole Martian year from InSight observations were decomposed into their natural orthogonal components. We found that the first eigenmode shows the previously identified early to midmorning peak, and varies with season. This corresponds to the solar quiet variations. The second and higher eigenmodes manifest the quasi-Carrington and sub-Carrington rotation periodicity represent disturbed components that may be stimulated by variations in the draped interplanetary magnetic field and/or the Martian ionospheric electron density. Different from their counterparts at the Earth, the amplitude of the first eigenmode is comparable with the sum of second to fifth ones, showing that the quiet and disturbed diurnal variations contribute similarly to the total diurnal variation. Decomposition of Martian surface magnetic field variations could provide monitoring of the Martian ionospheric current system as well as the solar wind conditions in the near-Mars space, which will be greatly enhanced when combined with Zhurong Martian surface field measurements in the future.

Key Points

  • The daily magnetic fields at Martian surface from InSight are investigated by natural orthogonal component analysis

  • The first eigenmode is consistent with representing the contribution to those variations from averaged ionospheric dynamo current

  • The disturbed variations with diurnal, quasi-Carrington, and sub-Carrington rotation time scales, are reflected in the higher eigenmodes

Plain Language Summary

The InSight flux magnetometer has made the first magnetic field measurements on the surface of Mars. The daily variations in the magnetic field have also been reported by previous studies. In this study, we investigate daily variations over nearly a whole Martian year by performing a natural orthogonal component analysis, which has been proven to be a valid method to decompose magnetic field signals into different parts. We conclude that the first part represents the quiet daily variations under lower solar wind dynamic pressure and magnetic field strength as measured by MAVEN satellite. The seasonal variations are also reflected in the first part. The disturbed variations with sol, time scales of one solar rotation and shorter, however, are reflected in the second-fifth parts, which may indicate the stronger solar wind dynamic pressure and magnetic field strength and/or the Martian ionospheric electron density.

1 Introduction

Recent studies from the Interior Exploration Using Seismic Investigations, Geodesy and Heat Transport (InSight; Banerdt et al., 2020) FluxGate (IFG) measurements (Banfield et al., 2019) have greatly enhanced our understanding of the magnetic field at the Martian surface from both internal and external sources. The magnetic field amplitude at InSight landing site was found to be about 2,000 nT, that is, ∼10 times stronger than previously predicted by satellite-based models (Johnson et al., 2020). The time-varying magnetic field reported at InSight landing site has provided further information about external magnetic field sources such as the ionospheric dynamo process and the electric current sheet (Chi et al., 2019; Johnson et al., 2020; Mittelholz et al., 2020).

Surface magnetic measurements from a fixed ground station are advantageous for the analysis of the dynamic ionospheric current system and/or the magnetic pileup region compared with measurements from a single moving satellite. Magnetic field measurements from InSight have shown clear diurnal as well as seasonal variations on the Martian surface (Johnson et al., 2020; Mittelholz et al., 2020). In particular, the peak amplitude of diurnal variations in the morning hours and their overall trend during the first 294 sols recorded by InSight IFG are consistent with the local time and seasonal dependences predicted by neutral wind—driven ionospheric dynamo models (Johnson et al., 2020; Lillis et al., 2019). The daily period and its harmonics of the magnetic field at InSight have also been clearly identified (Johnson et al., 2020; Mittelholz et al., 2020). Their results indicate that the diurnal and sol-to-sol variations are driven by ionospheric currents between ∼120 and ∼180 km altitude. For the time span up to sol 389, Mittelholz et al. (2020) found that the amplitude and seasonal variability of the surface magnetic fields are generally consistent with those predicted from wind-driven currents. In addition, they also found a regional dust storm could be responsible for the increased magnetic field amplitudes at around sol 100 and 550 (Mittelholz et al., 2021).

The dynamo region in the Martian ionosphere is an important region where electric currents are generated, that in turn produce a magnetic field. The plasma content in that region is one of the critical factors affecting the dynamo current intensities since it determines the conductivities. Both temporal and spatial variations of the permanent and transient layers, which is linked not only to the photoionization but also to the solar energetic particles (e.g., Sánchez-Cano et al., 2021), may contribute to the magnetic field variations on the Martian surface. Investigating the surface magnetic variations in response to the ionospheric variations is essential to understanding the solar wind-induced magnetosphere-ionosphere coupling.

Several studies have tried to predict the diurnal as well as seasonal variations of the surface magnetic field by modeling the wind-driven dynamo current at Martian ionosphere (Fillingim et al., 2012; Lillis et al., 2019; Mittelholz et al., 20202021). In particular, Fillingim et al. (2012) estimated surface magnetic perturbations about 1% of the surface magnetic intensity due to ionospheric primary and secondary currents. Lillis et al. (2019) modeled wind-driven ionospheric dynamo currents and predicted the resulting Martian surface field to be tens and up to 100 nT, with the strongest amplitudes occurring in the late morning and at times close to the solstices and perihelion. They also noted that the dynamic dayside magnetic draping field would lead to substantial variability in both the strength and direction of the surface field. It is well known that there are prominent changes in the solar irradiance between perihelion and aphelion due to the orbital eccentricity of Mars. As a consequence, the annual variations of the ionospheric density, as well as electron and neutral temperatures, due to variations in heliocentric distance are also very pronounced at Mars (e.g., Bergeot et al., 2019; Sánchez-Cano et al., 2016). These ionospheric variations could in turn also influence the surface magnetic fields.

Although some features of the time-varying surface magnetic field have been reported on or modeled, the behavior of its daily variations are still not fully understood due to the complex Martian space environment. It is still unclear what aspects of daily magnetic variations at InSight stem from ionospheric wind-driven fields as opposed to currents at the induced magnetosphere boundary and the bow shock (e.g., Boscoboinik et al., 2020; Ramstad et al., 2020). It is well known that the geometry of the ambient magnetic field and the neutral wind circulation determine the pattern of ionospheric dynamo currents. Compared with the non-intrinsic component of the Earth, the magnetic field in the Martian ionosphere is more dynamic because the interplanetary magnetic field (IMF) directly interacts with the ionosphere (e.g. Brain et al., 2010). Moreover, the local/regional rather than global structure of the crustal field leads to more complex dynamo currents within the Martian ionosphere (e.g. Withers et al., 2005). These complex dynamic variations can be studied using surface magnetic field measurements.

Different sources contributing to the daily variations in the Martian surface field may have the same contributing frequencies. Take for example, the daily variation on Earth, where the tidal wind and the ionospheric conductivities have periods of 1 day and its harmonics, affect the ionospheric dynamo process. Because the solar wind constantly impinges on the dayside induced magnetosphere boundary, currents flowing at the boundary, produce a magnetic field variation also with 1-day period. Those variations with the same period from different sources cannot be distinguished only by spectral analysis. The natural orthogonal components (NOCs) method (also known as Empirical Orthogonal Function [EOF] analysis), was successfully applied to decompose the daily geomagnetic variations with a single station on the Earth's surface (De Michelis et al., 2010; Xu & Kamide, 2004). This analysis enables investigations of whether the observed variables can be represented by a small number of eigenmodes, which may be identifiable with different physical sources. This method has previously been applied to decompose the ingredients of the main geomagnetic field and its time variations (Golovkov et al., 1978; Langel, 1987; Rotanova et al., 1982; Xu, 1998), and to characterize the sunspot number cycle, allowing future predictions to be made (Xu, 2002).

In this paper, for the first time, the NOC method is used to decompose the daily magnetic variations at the Martian surface into several eigenmodes. In Section 2 and Section 3 we describe the data sets and the methodology, respectively. In Section 4 we present results. Section 5 presents discussion and interpretation, with Section 8 providing conclusions.

2 Data Sets

The calibrated 0.2 Hz InSight IFG magnetic field data (Russell & Joy, 2021) from sol 15 to sol 668 are used to construct the NOC matrix. The effect of temperature and solar array currents, as well as transient signals of the lander origin, affect IFG measurements (Lander transitions, RISE communications, lander communications and arm operations, etc.) (Johnson et al., 2020; Joy et al., 2020), but recent studies have shown that those interferences had minimal effects on the magnetic variations observed in the final calibrated IFG data (Mittelholz et al., 2020). Figure 1 shows InSight magnetic field measurements from sol 15 to sol 668. The sol-to-sol as well as the seasonal variations are clearly demonstrated in all the components. It is evident that the diurnal amplitudes in autumn and winter are stronger than those in spring and summer (the seasons here after we refer to correspond to the northern hemisphere). The seasonal-averaged magnetic field components during a sol are shown in Figure 2, in which the diurnal amplitudes differences are clearly seen in the four seasons. The mechanisms for the differences will be investigated in Sections 3 and 4.

Details are in the caption following the image

The 10-min-averaged of the magnetic field from InSight measurements in the local INSIGHT_LL frame. (a–c) The north, east, and down components; (d and e) the horizontal component and the magnetic field strength. Four vertical blue dashed lines indicate the boundary lines of the four seasons. The data gaps are due to the Payload Auxiliary Electronics anomalies or an anomaly that could not be diagnosed and fixed until after communication with the spacecraft resumed following the end of solar conjunction (Mittelholz et al., 2020).

Details are in the caption following the image

Average diurnal variations of the magnetic field components in four seasons. The north component (a), the east component (b), the down component (c), and the total magnetic field (d). Different colored lines refer to different seasons.

3 Methodology

Here we briefly introduce the NOC method used in this study. The daily variations of any magnetic field component of InSight observations can be expressed by a summation of several EOFs as follows:
urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0001(1)
where urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0002 with its elements urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0003 is an urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0004 matrix with rows corresponding to sols (sol = 1, 2…, m) and columns corresponding to the true local solar time (TLST) in a sol day (LT = 1, 2, 3…, n), N is the number of the components chosen for the decomposition. urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0005 is the normalized mode of the kth component, and is a vector with n elements urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0006 (j = 1, 2…, n) describing the daily variation in each sol, and the urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0007 is the amplitude of the corresponding mode urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0008 (also named the principal components, PCs) for each sol and is a vector with m elements urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0009, i = 1, 2…, m.
To evaluate the EOFs urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0010 and the corresponding PCs urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0011 for a given data set, one can minimize the total squared difference between the observation and the expansion from Equation 1:
urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0012(2)
According to urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0013 one can construct the covariance matrix:
urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0014(3)
We solve for the eigenvalues urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0015 and the corresponding eigenvectors urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0016 for k = 1, 2…, N that satisfy the following equation:
urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0017(4)
The amplitudes urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0018 and the eigenmodes (or composition) urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0019 are then given by:
urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0020(5)
urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0021(6)

Data used in this study are 0.2 Hz resolution. To prepare data for the NOC analysis, the daily mean values were subtracted for each sol. The hourly averaged values of the three components are used to construct the matrix X (sol, LT). The rows and columns correspond to sols and TLST, respectively. In addition to the missing sols, we also discarded the sols in which at least 1 hr of successive data were missing. This resulted in 546 valid sols for each magnetic field component used in the NOC analysis.

4 Results

Figure 3 shows the eigenvalues of three magnetic field components, respectively. The eigenvalues represent the contributions of the corresponding eigenmodes to the total diurnal variations. In particular, the first five eigenvalues contribute up to 80%, 88%, and 79% of the total sol variability of the north, east, and down magnetic field components, respectively. This indicates that the first five eigenmodes could represent most of the contributions of the total magnetic field variations in a specific sol.

Details are in the caption following the image

The natural orthogonal component eigenvalues of the north (in read), east (in blue), and down component (in green).

Since the north and east components contribute most to the diurnal variations, we only present the NOC results of the H component (where urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0022) in the following. The first five eigenvectors and the associated amplitude of the H component are shown in Figures 4 and 5, respectively. The sol variation pattern of the first eigenvector (urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0023) is quite similar to that of the average variation during a sol as presented in Figure 4a, in which the sol variation pattern is characterized by a morning maximum at about 06 TLST and minimum (at about 08 TLST). The NOC amplitude (A1), associated with the first eigenvector, exhibits the previously explored characteristics of seasonal solar variations with stronger amplitudes in Autumn and Winter (Mittelholz et al., 2020). The second and third eigenvectors (urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0024 and urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0025), however, exhibit quite different patterns compared with that of the first one. There are no clear peaks during a sol, which may indicate that the scale of the source current systems that drive urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0026 and urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0027 are larger than that driving urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0028. From the amplitudes (A2 and A3) associated with the second and third eigenvectors we can see that remarkable amplitudes only appear at about sol 185.

Details are in the caption following the image

The averaged diurnal variations of the horizontal component (a) and the NOC eigenvectors urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0029 = 1, 2, 3, 4, and 5) of the first five eigenmodes of H component (b–f).

Details are in the caption following the image

(a–e) The natural orthogonal component amplitudes Ak ([k] = 1, 2, 3, 4, and 5) of the first five eigenmodes of horizontal magnetic field (H) component. The thick solid lines represent the 10-sol running average values. The day on Mars (sol), universal time (UT), solar longitude (Ls), and the heliocentric distance (RM) are labeled at the bottom of panel (e).

As for the fourth and fifth eigenvectors (urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0030 and urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0031), there are peaks at 07 and 12 TLST, respectively and their corresponding amplitudes (Figures 5d and 5e) also exhibit sol-to-sol variations with stronger amplitudes in Autumn and Winter. At the current stage, we can give no definite physical interpretation based on the NOC analysis alone. It is possible that the fourth and fifth eigenmodes are contributed by ionospheric currents resulting from the disturbed neutral wind.

Figure 6 shows the decomposition of the observed H component into two parts. As expected for the first eigenmode, there is a clear negative peak at about 6 TLST followed by a positive peak at ∼8 TLST. Two further negative peaks appear at 11 and 15 TLST, respectively. In addition, the diurnal variation amplitude shows clear seasonal changes with stronger amplitude in autumn and winter, which is consistent with the observations in Figure 1. More dynamic changes of the diurnal as well as sol-to-sol variations, however, are well reproduced by the modes 2–5 (Figure 6c). In addition, the diurnal amplitude captured by eigenmodes 2–5 shows little dependence on season compared with that captured by eigenmode 1. Some severely disturbed sols (e.g., sols ∼185) are also captured by modes 2–5.

Details are in the caption following the image

The observed horizontal (H) magnetic component (a), the first eigenmodes (b), and the sum of eigenmodes 2–5 (c) as a function of true local solar time over the first Martian year.

The contributions of different eigenmodes to the diurnal variations for two representatives are shown in Figures 7 and 8 together with the dynamic pressure and the magnetic field intensity from MAVEN observations. We use magnetic field data at 1 Hz from MAG instrument (Connerney et al., 2015; Jakosky et al., 2015). The dynamic pressure are calculated using urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0032 where N and V are the number density (1/cm3) and bulk velocity (km/s) at 0.125 Hz respectively, both acquired from the 3D moments of SWICA (Halekas et al., 2017). The dynamic pressure and magnetic intensity are demonstrated in the time period during which the MAVEN spacecraft was in the solar wind by visual inspection. For SOL0322, though measurements in the solar wind from MAVEN are sparse, the dynamic pressure and the IMF strength are quite steady and weak. During five MAVEN orbits, the average dynamic pressure and IMF intensity are about 0.34 nPa and 2.9 nT, respectively. Therefore, SOL0322 is thought to be a quiet sol. As one can see in Figure 7, the observed diurnal variation (black lines) can be expressed very well by the first eigenmode (red lines), while the sum of eigenmodes 2–5 (blue lines) only contributes little to the diurnal amplitude variation. For SOL0017 (Figure 8), both the dynamic pressure and the IMF intensity are obviously stronger than those in SOL0322, especially for the dynamic pressure (nearly three times stronger than on SOL0322) and this sol can be thought as a disturbed one. In contrast to SOL0322, the sum of eigenmodes 2–5 is dominant and contributes most to the diurnal variation especially for the north and down components. The first eigenmode shows smaller variations and amplitude and hardly contributes to the observed diurnal pattern. We simply calculated the correlation of two time series between the diurnal variations in each sol and SOL 0322 (quiet sol) as well as SOL0017 (disturbed sol). If the correlation coefficient between a diurnal variation in a sol and SOL 0322 is larger than 0.6, we believe this sol is a quiet sol. On the contrast, if the correlation coefficient between the diurnal variation in a sol and SOL0017 is larger than 0.6, we believe this sol is a disturbed sol. In addition, we also calculated the correlation between SOL0322 and SOL0017 and found the correlation coefficient is 0.10 (H component), which indicated they were not correlated. After inspecting all cases, we found that the H component daily variation pattern of 70% of the total sols are similar with that of the SOL0322 while ∼10% of the total sols are similar with that of the SOL0017 (correlation coefficient larger than 0.6).

Details are in the caption following the image

MAVEN observations of (a) dynamic pressure and (b) the magnetic field intensity in the solar wind. (c–e) The three components of InSight observations (black), the corresponding first eigenmode (F1, red), and the sum of eigenmodes 2–5 (F2 + 3 + 4 + 5, blue) of the natural orthogonal component fitting results for SOL0032.

Details are in the caption following the image

The format is identical to Figure 7, but for SOL0017.

Different eigenmodes and the corresponding variance reduction as a function of sols are shown in Figure 9. The product of peak plasma density above the InSight landing site and mean neutral wind velocity at 130 km altitude between 6 and 12 a.m. (Figure 9c), where the peak dynamo currents usually occur (Mittelholz et al., 2020), was obtained from the data sets from the Supporting Information of Lillis et al. (2019), which were taken from the Mars Climate Database v5.3 (Millour et al., 2017) with averaged EUV level and without dust storm scenario. This database is predicted using a Mars Global Circulation model coupled with an ionospheric module (Forget et al., 1999; Gonzalez-Galindo et al., 2013). It is shown that the trend of the diurnal amplitude of eigenmode 1 is somewhat consistent with that of the F(N, V), with a peak near perihelion at ∼sol 540. This is possibly due to both stronger neutral winds and higher plasma densities as a results of higher solar EUV photoionization (e.g., Lillis et al., 2019).

Details are in the caption following the image

(a) The sum of eigenmodes 2–5 amplitude, (b) the variance reduction captured by eigenmodes 2–5, (c) the eigenmode 1 amplitude of H component (black) and the product of neutral wind velocities at 130 km and mean peak plasma densities from 6 to 12 a.m. above the InSight landing site (blue), and (d) the variance reduction captured by eigenmode 1. Black thick lines in each panel indicate the 10-sols running-averaged values.

The variance reduction (vr) is defined to indicate the capability of a model to reconstruct the observed data. In order to investigate how much of the variance on each sol is captured by different eigenmodes, we calculated the vr by using the equations:
urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0033(7)
urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0034(8)
urn:x-wiley:21699097:media:jgre21819:jgre21819-math-0035(9)

It is shown that vr provided by eigenmode 1 exceeds 20% for nearly all the sols. Especially for sols around sol 60 and after sol 500, the vr exceeds 60% (Figure 9d). The vr provided by eigenmodes 2–5 exceeds 40% between sols 140 and 240 and it falls below 20% after sol 500 (Figure 9b). For both eigenmode 1 and eigenmodes 2–5, the vr exhibits strong fluctuations before sol 500 and after that it becomes quite steady.

We can notice that quasi-Carrington and sub-Carrington rotation period fluctuations appear in the diurnal peak amplitude of the sum of eigenmodes 2–5 (the black thick line in Figure 9a). This is confirmed by a spectral analysis based on the Welch method (Figure 10a). The power spectrum of eigenmodes 2–5 amplitude exhibits the characteristic periodicity at ∼27 days, which may correspond to the well-known Carrington periodicity (26.35 days). The first eigenmode, however, does not show a clear peak at this periodicity (Figure 10b).

Details are in the caption following the image

Spectral properties of the eigenmode 1 (b) and sum of eigenmodes 2–5 (a) of the diurnal amplitude of the H component. 10-sol running averaged diurnal amplitudes of corresponding eigenmodes from sol 15 to 600 are used to compute the spectra based on the Welch method, with 200 sols of the Hamming window of each segment length and 80 sols of the overlap length from segment to segment, respectively. Data gaps after the 10-sol running average are filled with a linear interpolation. Both of the spectra are normalized by the maximum value of the spectrum of F2 + 3 + 4 + 5. The 95% confidence intervals are indicated by the thin dashed lines.

5 Discussions

5.1 The Sources of Diurnal and SOL-to-SOL Variations at Martian Surface

Distinguishing different sources of the magnetic field variations at InSight is important to understand dynamic processes in the Martian ionosphere as well as the coupling between the solar wind and the Mars induced magnetosphere. The fixed magnetic field observations at the Martian surface from InSight facilitate investigating the diurnal variation as well as their SOL-to-SOL variability because temporal variations are not mixed with spatial ones as is the case for a moving spacecraft. Magnetic field variations at InSight originate from current systems in the Martian ionosphere and/or induced magnetosphere. The NOC analysis in this study provides important information regarding the origin of those current sources. The first eigenmode, exhibits clear seasonal changes, and represents the averaged ionospheric dynamo current. This part of the current varies with both neutral wind velocities and the peak plasma densities in the ionosphere and is not directly related to solar wind conditions. In contrast, the second and higher eigenmodes may be associated with current systems directly driven by the solar wind variations. However, which current (e.g., ionospheric or magnetospheric) contributes to the second and higher eigenmodes is difficult to assess because we know little about the current pattern in the near-Mars environments. We speculate that both ionospheric and induced magnetospheric currents contribute to the diurnal variation. The averaged H component contributed by eigenmodes 2–5 is about 15 nT (Figure 9a), which is about half of the contribution by the first eigenmode (Figure 9b). Since the ionospheric current pattern and strength respond to the draped magnetic field (direction and strength), we propose that the varying parts of the ionospheric dynamo currents information is also contained in the second and higher eigenmodes. Further understanding of those current systems would greatly benefit from observations at different locations on the Martian surface. The Chinese Mars Rover, equipped with two IFG magnetometers (Du et al., 2020), has successfully landed at the surface at 25.1°N, 109.9°E on 14 May 2021. Magnetic field variations due to distant sources such as the induced magnetospheric currents will be very similar at two stations but the effects produced by overhead ionospheric currents will be more different (Briggs, 1984; Xu, 1992). The magnetic field differences between the two points may allow identification of distinct contributions from the sources from ionospheric or induced magnetospheric current systems. In addition, spatial variations in the diurnal variations in the surface magnetic field can provide more information on the geometry and strength of the ionospheric currents.

It also should be noted that the EOFs used in NOC analysis are assumed to be orthogonal to each other. Actually, the magnetic fields generated by different current systems in the ionosphere and/or induced magnetosphere are not strictly orthogonal to each other. We did not separate the higher eigenmodes with one-to-one correspondence between the eigenmodes and the source currents because the current systems in the Mars' environment are still unknown. Nevertheless, current system contributions from different sources (ionospheric and/or magnetospheric) could be described by linear combinations of these eigenmodes.

5.2 The Role of Crustal Field and IMF on Variations of the Surface Magnetic Field

The absence of a global intrinsic magnetic field leads to substantial differences in the magnetic environment on Mars compared to that of planets with a core field such as the Earth. The magnetic field strength at Martian ionospheric altitude is about three orders smaller than that at the Earth's ionospheric altitude. According to studies of the daily variations on the Earth (e.g. Yamazaki & Maute, 2017) and on Mars (Johnson et al., 2020; Mittelholz et al., 20202021), diurnal amplitudes on the surface of the two planets are of the same order. The main reason is that the lower boundary of the dynamo region, which is defined by the altitude where the electron gyrofrequency is equal to the electron-neutral collision frequency, is much higher at Mars than at Earth. At a given altitude above the surface of Mars, both ion-neutral collision frequency (νin) and electron-neutral collision frequency (νen), as well as magnetic field strength, are lower than on the Earth, because of the thinner atmosphere and the absence of a global magnetic field (Mittelholz et al., 2020; Opgenoorth et al., 2010). Although the terrestrial collision frequency in the ionosphere is larger than on the Mars, the effects at dynamo region altitudes cannot cancel out the more substantial difference in the magnetic fields between the Earth and Mars. The dynamo region is about tens of kilometers higher at Mars than at Earth (Opgenoorth et al., 2010). Therefore, the dynamo region on Mars covers an area with higher plasma density than that on the Earth's dynamo region. The dynamo region at Mars above strong crustal field area will be also higher than that with weak crustal fields. We speculate that the diurnal variation amplitude at the surface in a region with strong crustal magnetic anomalies will become smaller because both Pedersen and Hall conductivities are 1–2 orders of magnitude smaller than the ionosphere above only weakly magnetized crustal regions on the dayside (Opgenoorth et al., 2010). The magnetic field measurements at InSight and the Chinese Mars Rover (Du et al., 2020) landing site enable comparison among surface magnetic field variations in regions with different crustal magnetic field.

Another significant difference between the two planets is that the ionospheric dynamo current at Mars is more dynamic compared to that at the Earth. Compared to the Earth, the magnetic field in the Martian ionosphere is greatly affected by the draped IMF as well as the solar wind dynamic pressure (Brain et al., 20032010). Using magnetic field measurements from the Mars Global Surveyor satellite, Mittelholz et al. (2017) investigated the external magnetic fields on Mars and found clear Carrington rotation period signals at 400 km altitude. The periodic variations (i.e., Carrington rotation periodicity) in the solar wind are more easily reflected in the Martian ionosphere than in the Earth's ionosphere due to the increased interaction between solar wind and Martian ionosphere because of the absence of the global dipole magnetic field at Mars (Brain et al., 20032010). Therefore, if only the magnetic field effect on the ionospheric dynamo processes is considered, the Carrington rotation period signal in the magnetic field could also be more easily reflected in the Martian ionospheric dynamo region and thus appear in the ionospheric currents and surface magnetic field. In Figures 7 and 8, we only compared solar wind dynamic pressure and magnetic field strength with different eigenmodes because we believe the surface magnetic field variations in the diurnal time scale were most probably related to the draped IMF in the Martian ionosphere. The draping effect on the diurnal time scale mainly resulted from the solar wind dynamic pressure and magnetic field strength rather the IMF sector. The IMF sector effect may affect the surface magnetic field in a longer time scale, that is, the Carrington rotation and/or sub-Carrington rotation time scales (e.g., Choi & Lee, 2019). The spectral properties of eigenmodes 2–5 in Figure 10a confirm this as there are quasi-Carrington and sub-Carrington rotation signatures. In addition, the electron densities in the ionosphere may also vary with Carrington rotations due to periodic solar radiation. The Martian ionospheric peak electron density is strongly correlated with solar radiation which can be represented by F10.7 (e.g. Tapping, 2013). Therefore the peak electron density at the dynamo region should also have the same solar rotation period as the solar radiation. Based on observations from the Mars Express, Nielsen et al. (2006) found that the maximum electron density at the sub-solar point varies in time with the solar rotation period, which indicates contribution of the solar ionizing radiation. By analyzing radio occultation-derived profiles electron density from the MGS satellite, Venkateswara Rao et al. (2014) statistically studied the variation of electron density at high latitude. They found that variation of the electron density with solar rotation period appear independent of the altitudes. This may also result in the Carrington rotation periodicity of the ionospheric dynamo current and hence the surface magnetic field. The quasi Carrington rotation period signals appear in the eigenmodes 2–5 of the H component (Figure 10a) confirm that ionospheric currents also vary with similar periods as those of the solar wind parameters. The relative importance of contribution between the solar wind and the electron density to the quasi Carrington rotation period fluctuation in the surface magnetic field amplitude is unknown and expected to be investigated by using surface magnetic field measurements with a longer time interval.

6 Conclusions

In this study, the NOC method is used to decompose the daily magnetic field variation at the Martian surface into several eigenmodes. Ionospheric dynamo currents as well as IMF induced variations are identified in different eigenmodes. The main results can be summarized as follows:
  1. The dependence on Martian season of the first eigenmode is similar to that of the peak plasma density and neutral wind. This is consistent with this part of the observed magnetic field resulting from variations from averaged ionospheric dynamo currents.

  2. The disturbed variations with diurnal, quasi-Carrington and sub-Carrington rotation time scales are reflected in eigenmodes 2–5. These may be related to variations of ionospheric dynamo with the same periods, which may be controlled by variations in the draped IMF and/or electron density in the Martian ionosphere.

Acknowledgments

This work was supported by the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB41010304), the Beijing Municipal Science and Technology Commission (Grant No. Z191100004319001), the pre-research Project on Civil Aerospace Technologies No. D020103 funded by the CNSA, and the National Natural Science Foundation of China (41874080, 41674168, and 41874197). A. Mittelholz acknowledges support from ETH 19-2 FEL-34.

    Data Availability Statement

    All MAVEN and InSight data used in this study are publicly available in the Planetary Data System: InSight IFG calibrated data (Russell & Joy, 2021), MAVEN calibrated SWIA data (Halekas, 2021), and MAVEN calibrated MAG data (https://doi.org/10.17189/1414178). The plasma density and neutral wind velocity above the InSight landing site used in this study are from Supporting Information Data Sets S1 of Lillis et al. (2019). The all derived data products are available and hosted online (Luo, 2022).