dataesr/scientific-paragraphs-categorization huggingface dataset:
, 2008; Gruesbeck et al. , 2018)  and is considered through either a local impact  (Nemec et al. , 2020)  or a global influence  (Fang et al. , 2015 (Fang et al. , , 2017)). Garnier et al. (2022)  -hereafter referred to G22 -analyzed in detail the influence of the crustal fields on the Martian BS location by combining datasets from MAVEN and MEX. They showed the influence of the crustal field is significant (with several hundreds of km of induced variation) with a primary influence of the strongest crustal field source region in the southern hemisphere, seen first through a clear dependence on the angular distance to this region. The BS location also varies with the crustal field pressure integrated over large areas, or with the planetary longitude when focusing around southern latitudes instead of considering all latitudes as in previous studies.
Wang, Xie, et al. (2020)  recently proposed a 3D parametric model of the In this study, we investigate the possible drivers of the BS location based on both MAVEN and MEX BS crossings datasets. Instead of focusing on only few drivers (and independently from each other) as most authors, we compare and rank the relative importance of the drivers of the Martian BS based on several methods, including a partial correlation approach to take into account possible biases due to mutual correlation, and the Akaike Information Criterion (AIC) and Lasso regularization model selection methods to compare the relative importance of the drivers. This allows providing a comprehensive view of the Martian BS dynamics with respect to internal and external drivers. Figure  1  shows a sketch of the Martian interaction, with the possible drivers of the BS investigated in this work and detailed later: crustal fields parameters (angular distance from the strongest crustal field region center, crustal field pressure, longitude vs.
Sun of the strongest crustal field region), solar Extreme Ultra-Violet fluxes, SW magnetosonic Mach number, SW dynamic pressure, IMF intensity and orientation (θ bn angle between the normal of the BS and the IMF vector; θ vn angle between the normal of the BS and the SW velocity vector; θ bv angle between the SW velocity vector and the IMF vector, also called cone angle). The paper is organized as follows: in Section 2 we first describe the MAVEN and MEX datasets used (2. 1) as well as the methods considered in this study (2. 2). Then, in Section 3, we first show the results of the direct analysis of the possible drivers of the Martian BS location (3. 1) and then we show how cross-correlations are considered to appropriately interpret the influence of minor drivers (3. 2). A focus is then made on the influence of parallel versus perpendicular BS (3.
Description of the Datasets We use in this study the same datasets as G22, which we refer to for a more detailed description of the lists of MAVEN and MEX crossings considered. Here we provide a brief description. B IMF refers to the interplanetary magnetic field (IMF) intensity, θ bn to the angle between the normal of the bow shock (BS) and the IMF vector, θ vn between the normal of the BS and the SW velocity vector, θ bv between the solar wind (SW) velocity vector and the IMF vector. The signs + (with red color) and -(blue color) refer to the known or expected impact of the driver, with increased crustal fields and Extreme UltraViolet fluxes pushing the BS further from the planet, while increased SW dynamic pressure and magnetosonic mach number push it closer to the planet. The background figure is a drawing by Anastasia Grigoryeva.
The MEX BS crossings dataset was derived by BH16 from the MEX ASPERA-3 ELS data  Barabash et al. (2006) , including 11,820 crossings from January 2004 to May 2015. The MAVEN BS crossings dataset is a combination of the lists of crossings published by  Fang et al. (2017)  and  Gruesbeck et al. (2018) , derived from the analysis of the MAVEN magnetic field MAG data  (Connerney et al. , 2015) , electron SWEA data  (Mitchell et al. , 2016) , and ion SWIA data  (Halekas et al. , 2015). The MAVEN dataset comprises 3837 BS crossings from November 2014 to April 2017. A large number of BS crossings for MEX and MAVEN -due to their respective orbital periods of 6. 7 and 4. 5 hrallows for a large spatial and temporal coverage that enables statistical analyses. Significant differences between both datasets need to be considered.
First, MEX covers a large period through a whole solar cycle, while the MAVEN dataset corresponds to a shorter period where the mean EUV level (given by the solar 10. 7 cm radio flux) was larger by ∼14% compared with the MEX dataset. We thus focus on the dynamics rather than on absolute BS location due to the different solar conditions encountered. Second, the MEX spacecraft is not equipped with a magnetic field instrument, which prevents us from using MEX data to investigate the influence of IMF related parameters (such as IMF intensity and orientation, magnetosonic Mach number). We derive and analyze the extrapolated terminator altitude already used by previous authors  (Edberg et al. , 2008; Fang et al. , 2017; Hall, Lester, Sánchez-Cano, et al. , 2016). It allows to represent the variability of the BS location by removing the strong solar zenith angle influence, assuming an axisymmetric symmetry.
G22 successfully used this technique to disentangle the influence of the crustal fields on the Martian BS location despite a significant cross correlation with EUV in the MAVEN data. It was also used by several authors for the solar wind Earth interaction  (Simms et al. , 2021) , solar physics  (Le & Zhang, 2017) , or galaxies and compact objects  (Ni et al. , 2020; Yesuf & Ho, 2019). This method allows investigating cross correlations in a rigorous manner, without using sub-selections of the dataset to control specific parameters, which reduces the number of samples in each dataset by a factor 2 n (n number of variables) which becomes critical in the case of the Martian BS that may be influenced by a number of parameters. The correlations are considered linear (y = a + ∑ i x i ⋅ b i with a constant and b i slopes), but can alternatively correspond to power laws 𝐴𝐴 ( 𝑦𝑦 = 𝑎𝑎 ∏ 𝑖𝑖 𝑥𝑥 𝑏𝑏 𝑖𝑖 𝑖𝑖 ) then linearized by a logarithm.
Direct Analysis of the Drivers Influence In this section, we study the influence of the following possible drivers for the BS location, previously mentioned in Section 1 and derived as detailed below: 1. Solar Extreme UltraViolet fluxes (EUV) for MAVEN and MEX: the EUV values were determined for MAVEN from the FISM model  (Chamberlin et al. [2007] ; available for MAVEN but not MEX on the CDPP/AMDA database -http://amda. cdpp. eu/) for 10-120 nm wavelengths, and for MEX from the solar 10. 7 cm radio flux index extrapolated to Mars assuming a  1∕ 2   law; using solar radio flux values for MAVEN leads to almost identical results since both parameters are strongly correlated (with a correlation factor of 0. 98 (n)); however, we choose the FISM model for MAVEN since it is available and slightly more precise than the radio flux proxy, and the absolute values of EUV are of no interest in our study where we focus on methods which are unit independent 2.
As shown by previous authors, the BS is located at higher altitudes in response to stronger EUV fluxes or lower Mms values, as well as under weaker SW dynamic pressures or spacecraft locations closer to the strongest crustal source region in the southern hemisphere. The MAVEN panels (upper panels) clearly show that larger Mms values lead to smaller R TD values. Enhanced EUV leads to higher BS altitudes for both MAVEN and MEX datasets. The influence of SW dynamic pressure and angular distance to the strongest crustal source region is also visible in the observations by both missions: the mean profile (black dashed line) shows that despite very strong data scattering (due to the presence of other significant drivers at the same time and possibly spatial asymmetry of the boundary) the MAVEN and MEX BS R TD values decrease with increasing SW dynamic pressure by hundreds of km; the panels b and f show the same results as G22, with decreasing R TD values (by several hundreds of km) from the region around the strongest crustal fields -with an angular extent of 40/50° corresponding to the size of the strongest crustal source regionto regions away from the strongest crustal source region, with slight peaks around angular distances of 120-150° that may correspond to the influence of localized crustal sources indeed present at such angular distances.
The upper panel uses the following approach: each set of parameters (EUV, Mms, etc. ) was separated into low (=below the median value of the parameter) and high (=above the median value of the parameter) subsets; the median terminator altitudes of the "low" (blue) and "high" (red) subsets are then determined for each parameter to show how low/high regimes of each driver influences the terminator altitude of the BS. The main differences between both missions are the smaller changes observed (in both altitude variations and correlations) for MEX compared to MAVEN, and lower terminator altitudes for MEX. Regarding the first difference, the much larger dataset for MEX (11,820 crossings compared to 1,760) induces a stronger mixing of different influences and a greater difficulty to distinguish one driver from another.
Systematic differences may also exist between MAVEN and MEX due to different instruments and methods for determining the BS locations. The second difference most probably originates from the EUV levels encountered at the MAVEN and MEX crossings. The large MEX dataset allows for a wide range of EUV conditions, with a full solar cycle (including the lower and extended ever recorded solar minimum), while the MAVEN dataset corresponds to a  period with an active Sun in 2014 and 2015 (where most of our MAVEN crossings occurred) below a declining activity in 2016-2017. The mean EUV level of the MAVEN crossings (given by the solar 10. 7 cm radio flux: 49 ⋅ 10 -22 W/m 2 /Hz) was thus larger by ∼14% compared with the MEX dataset (43 ⋅ 10 -22 W/m 2 /Hz). Given the major influence of EUV on the BS location (see below), the larger EUV conditions associated with the MAVEN dataset certainly contribute to the slightly larger BS distances observed (by ∼5%) for MAVEN than for MEX.
Note that using the averaged crustal field intensity instead of the averaged crustal field pressure, or an even smaller power law index of the pressure such as 𝐴𝐴 ( 𝐵𝐵 2 ∕ (2𝜇𝜇0) ) 1∕6 as used by XF17, also leads to similar results with close correlation factor values or absolute variations that may vary by ±10% maximum with no change of the above ranking conclusions. An illustration of the complex dynamics of the Martian BS that involves a combination of various physical drivers is the comparison between the extreme BS locations observed and the extreme solar events encountered by the MAVEN and MEX missions, which shows a variety of situations. The maximum R TD value (7,913 km altitude) for the MEX dataset was reached on 22 October 2014 and was induced by a combination of large crustal fields, a relatively low SW dynamic pressure, and most importantly one of the largest EUV conditions encountered.
These extreme EUV conditions were related to the event consisting of M and X type solar flares originating from the same active region 12,192 from 19th to 22 October 2014, surprisingly not accompanied with coronal mass ejections  (Sun et al. , 2015; Thalmann et al. , 2015). Over the 3 days of the solar flares event, all BS crossings R TD values were among the 7% largest of the MEX dataset. The smallest R TD value (1614 km altitude) for the MEX dataset was reached on 25 June 2010, at a period with very low EUV (but not among the extreme low values), relatively strong SW dynamic pressure, and over the strongest crustal source region. No extreme solar CME-type event happened closely before this crossing to our knowledge, except for the slow CME mentioned by  Manchester et al. (2017)  but which happened probably too early (on 16 June 2010) to be related to the extreme low Martian BS crossing location.
Regarding the MAVEN BS dataset, neither the extreme low (on 4 March 2016; R TD = 2016 km altitude) nor the extreme high (on 31 January 2015; R TD = 9243 km altitude) BS terminator distances correspond to extreme solar events as listed by  Lee et al. (2017)  who provided a comprehensive overview of the space weather events during the first 2 years of the MAVEN mission. These two extreme BS locations were due to a combination of both strong/low EUV and magnetosonic Mach number, but not among the most extreme values. Another typical example of the complex influence of solar events on the BS is the early March 2015 period where MAVEN encountered one of the stormiest space weather conditions, with a series of a solar flare and CME activity (including a strong ICME impact on 8 March 2015). Despite extreme external conditions (in EUV, SW dynamic pressure) leading to strong consequences  (Jakosky et al.
The figure shows the same figure as Figure  1  where we superimposed the direct linear Pearson correlation factors between the BS terminator altitude and the possible drivers of the BS location, as well as The schematics show, beyond the statistically significant correlation (p-values below 5%) between a number of drivers and the BS location (with in particular the major influence of EUV and Mms), cross correlations between most of the drivers themselves. One notes that the direct correlations between the major drivers and the BS R TD are stronger than the cross correlations, which increases the confidence in their direct influence on the BS location. For example, the EUV correlation with R TD is stronger than the correlation of EUV with other possible drivers. This is the case for EUV (with both MEX and MAVEN datasets), Mms (MAVEN dataset), and crustal fields (with the MEX dataset, see below for the MAVEN dataset).
The cross correlations among the drivers must be considered to avoid biased interpretations, particularly when they are comparable or even greater than the direct zero-order correlation with R TD. In the case of the MAVEN dataset, the cross correlations between the crustal field parameters considered and the BS location is for example, smaller than the cross correlations between the crustal field parameters and the EUV. At least a part of the influence of the crustal fields in the MAVEN dataset shows up through the cross influence of EUV which is a major driver of the BS location. G22 investigated this issue and used the partial correlation approach to investigate whether the crustal fields had a significant influence not only in the MEX dataset (where no such bias exists) but also in the MAVEN dataset.
However, these direct correlations of the SW dynamic pressure previously mentioned in Section 3. 1 may be slightly underestimated in both MAVEN and -to a lesser extent -MEX datasets due to a small positive cross correlation between SW dynamic pressure and EUV fluxes (correlations of respectively 0. 12 (n) and 0. 09 (n) for MAVEN and MEX datasets): the solar wind dynamic pressure was for example, for MAVEN on average of ∼0. 8 nPa during the low EUV periods, and of ∼1 nPa during the high EUV periods. Enhanced EUV fluxes push the BS to higher altitudes, so that enhanced EUV fluxes occurring at the same time as slightly enhanced solar wind dynamic pressure may partially hide the compression of the BS due to small solar wind dynamic pressure pulses. With a partial correlation analysis assuming a linear regression (or power law with similar results) and control over the EUV fluxes and -for MAVEN only -magnetosonic Mach number, the partial correlations between the solar wind dynamic pressure and the BS R TD altitude become larger at -0.
The Influence of the Interplanetary Magnetic Field We focus on the MAVEN dataset in this section to analyze the influence of the IMF (intensity and orientation) on the Martian BS location. We discuss in more detail the impact of the IMF, whose characteristics include complex cross correlations beyond those with the major drivers. We also compare with results obtained in the literature at planets where the IMF influence was more widely investigated. The specific influence of the θ bn angle is discussed in Section 3. 4. The IMF intensity is apparently significantly positively correlated with the R TD altitudes (Pearson correlation factor of 0. 26 (n)), in contradiction with the simple effect of an increased external magnetic pressure. A positive correlation could be due to the fact that an enhanced IMF induces a stronger draping around the planet, which could consequently push the BS further.
Wang, Xie, et al. (2020)  recently proposed a 3D parametric model of the Martian BS based on a MHD model, including solar wind parameters (dynamic pressure, IMF intensity, and orientation, Mms) but not EUV or crustal fields. Beyond the strong influence of Mms (and of SW dynamic pressure according to the authors), they suggested that the IMF components have differential effects, with the BS expanding along the MSO Y/Z axis for respectively increasing B Z /B Y IMF components and a stronger influence of B X in the tail. However, the analysis of our dataset does not show such differential influence on the BS R TD altitudes: the IMF components have little influence compared to the total IMF on R TD , with for example, a partial correlation significance of B Z with R TD below the null H 0 assumption when focusing on BS crossings around the MSO Y axis sector.
No significant cone angle dependence can thus be seen as was observed at Venus by  Alexander et al. (1986) , where the authors interpreted BS variations as possibly due to a more efficient mass loading through GARNIER ET AL. 10. 1029/2021JA030147 14 of 29 an enhanced conventional electric field  ⃖⃖ ⃗  = -⃖⃖ ⃗   ⃖⃖ ⃗  cross product for incident flows perpendicular to the IMF. At Earth,  Wang, Lu, et al. (2020)  showed that the flaring of the Earth's BS increases at low cone angles, leading to further shocks in the tail and closer shocks near the nose, which is not observed with our martian dataset based on partial correlations and direct plotting of the location of the crossing. The clock angle of the IMF appeared as a significant driver in the previous analysis based on direct correlations, with BS located farther in response to low clock angles, that is, for an IMF along the MSO Y axis, thus corresponding to an electric field along the Z axis.
Moreover, the unpaired student t-test mentioned above confirming an a priori shifted pole versus equator asymmetry becomes poorly significant (the p-value rises up to 2%) as soon as we remove the EUV and Mms influence by considering residuals. A close to equator versus pole asymmetry is thus suggested by the MAVEN direct data analysis. Chai et al. (2014)  mentioned that the Venusian BS equator versus pole asymmetry was stronger at the terminator or beyond for large IMF B Y intensities, which is not observed with our dataset, but our tail coverage is poor. Overall, it is very difficult to conclude on the influence of a specific minor driver such as the "clock angle" of the crossings based solely on a direct analysis such as provided in Figure  6 , due to the combined influence of other important parameters (EUV, Mms…).
Quasi-Perpendicular Versus Quasi-Parallel Shocks Another parameter suggested as significant in Section 3. 1 is θ bn the angle between the BS normal and the IMF direction, available for the MAVEN dataset. This angle is a distinguishing indicator between quasi-parallel (low θ bn values) and quasi-perpendicular (large θ bn values) BS. Our correlation analysis revealed a rather strong correlation (0. 19 (n)) between the MAVEN BS R TD altitude and the sine of θ bn (or 0. 22 (n) with θ bn itself). Figure  7  shows the MAVEN BS altitude dataset organized as a function of the sine of θ bn (θ bn is considered positive). This profile suggests indeed that perpendicular BS happens on average at higher altitudes than parallel BS, which is also observed in the residuals of Figure  7  after removing the linear dependence with respect to EUV and Mms.
Based on this equation, it appears that perpendicular BS (θ bn close to 90°) leads to larger velocity values of the magnetosonic wave (the wave velocity being thus anisotropic), which could induce a further location of the BS. In the literature,  Alexander et al. (1986)  or  Russell et al. (1988)  suggested at Venus that the asymmetries observed could be a consequence of an anisotropic magnetosonic wave velocity, instead of an increased mass loading effect. Khurana and Kivelson (1994)  modeled this anisotropic velocity at Venus to account for an elliptic cross section of the BS in the tail. At Earth,  Peredo et al. (1995)  confirmed, based on a more than 1,000 BS crossings dataset issued from 17 spacecraft, previous analysis suggesting a north-south versus east-west asymmetry in the Mach cone.
They suggested that the differential Mach cone extension was a consequence of the anisotropy of the magnetosonic wave velocity depending on the IMF orientation (through θ bn ), with an influence mostly expected in the tail and for low Mach values (where the anisotropy has more time to develop). Dmitriev et al. (2003)  then compared several BS models with Geotail and Wind crossings datasets (with >4000 crossings) and mentioned the important role of the dawn-dusk asymmetry of the BS tail region that was mostly controlled by a faster magnetosonic wave due to a perpendicular configuration. Chapman et al. (2004)  confirmed with MHD modeling the significant influence of the θ bn angle due to enhanced wave velocity on the Earth's BS asymmetries, in particular at low Mach numbers. Later,  Chai et al.
At Mars, a few early works also mentioned the influence of θ bn. Zhang et al. (1991)  first used Phobos magnetometer data from 27 BS crossings to investigate the IMF control of the BS. They concluded that the Martian BS exhibited asymmetries similar to the Venus case in a magnetic frame (MSE equivalent), that is, North versus South, pole versus equator, and perpendicular versus parallel with respect to the IMF, the latter being presumably the consequence of an anisotropic wave velocity. Later,  Vignes et al. (2002)  mentioned a possible difference between perpendicular and parallel BS crossings (with perpendicular BS at R TD values ∼3% above) but could not explain it. Overall, a number of Earth and Venus studies, as well as few Mars studies, thus mentioned a possible influence of the anisotropic wave velocity on the BS, essentially based on geometrical arguments rather than based on quantitative arguments.
[2015] ). However, if the direct correlation of this tangential component with the BS location also appears strong in our dataset (correlation factor of 0. 30 (n)), it is due to the cross-correlation with Mms that is a major driver of the BS location: the partial correlation of the IMF tangential component with R TD becomes very small (-0. 03, with a p-value of 2. 3% only) after controlling over Mms and EUV, while the θ bn influence does not reduce after controlling for a linear influence of Mms or other variables. Apart from the anisotropy of the wave speed explanation, several authors linked the perpendicular versus parallel BS differences to dawn versus dusk asymmetries observed at planetary BS, in particular since the Parker spiral average configuration implies (depending on the IMF B X component) that parallel/perpendicular BS correspond to respectively dawn/dusk sectors (see expectations at Earth by  Walters [1964]  and  Dmitriev et al.