An Empirical Predictive Model for Atmospheric H Lyman-α Emission Brightness at Mars

Abstract

Characterizing the abundance of atmospheric hydrogen (H) at Mars is critical for determining the current and, subsequently, the primordial water content on the planet. At present, the atmospheric abundance of Martian H is not directly measured but is simulated using proprietary models that are constrained with observations of H Lyman-α emission brightness, as well as with observations of other atmospheric parameters, such as temperature and Solar UV irradiance. Publicly available brightness measurements require further processing to have scientific utility. To make the data needed to model H abundances and escape rates more accessible to the community, we use H Lyman-α emissions made with the Mars Atmosphere and Volatile Evolution (MAVEN) mission. The near decade-spanning data set is reduced to obtain disk-pointed averages of the H brightness in the upper atmosphere of Mars and then analyzed for statistical trends across multiple variables. The H Lyman-α emission brightness is found to be dependent on Solar illumination, Solar cycle, and season. The resulting data trends are used to derive empirical fits to build a predictive framework for future observations or an extrapolative tool for estimates of water content at previous epochs. Data that was intentionally not included in the empirical derivations are used to validate the predictions successfully to within 18% accuracy, on average. This first-of-its kind predictive model for H brightness is presented to the community and can be used with atmospheric models to further derive and interpret the abundances and escape rate of H atoms at Mars.

Introduction

Estimating the primordial water content at Mars is an involved undertaking that requires a comprehensive understanding of water variability in the present epoch using multiple synergistic observations and analyses (e.g., Jakosky, 2021). The reservoir of escaping atmospheric species lies in the upper atmosphere of Mars. As water molecules propagate from the surface to space, Solar photons and chemical reactions dissociate the molecules into their atomic constituents, providing additional species to observe, such as atomic hydrogen, deuterium, and oxygen (e.g., Clarke et al., 2014; Fedorova et al., 2021; Heavens et al., 2018; Krasnopolsky, 2019; Stone et al., 2020). The water cycle, and subsequently the abundance of H atoms in the atmosphere, is affected by multiple drivers, such as: surface and cloud dynamics, circulation patterns, seasonal variations, dust activity, atmospheric tides and waves, atmospheric chemistry, illumination conditions, and Solar activity (e.g., Heavens et al., 2018; Montmessin et al., 2022). These drivers can cause atmospheric properties to vary at timescales that range from days to many years. To determine water loss at Mars requires quantifying how the upper atmospheric H atoms are expected to vary across these various timescales.

Atmospheric loss is determined by deriving the escape rates of species from the upper atmosphere. The water escape rate at Mars is derived from the abundance of H atoms in the atmosphere (Clarke et al., 2024). The abundance of H atoms at Mars is derived from upper atmospheric UV emission measurements (Mayyasi et al., 2022). Hydrogen atoms produce UV emissions at Lyman-α (1215.67 Å) when Solar photons resonantly scatter off the atoms. These H emissions can be observed and used to derive a line-of-sight brightness value when compared with a calibrated source (e.g., Mayyasi et al., 2017, 2023). The H Lyman-α emission at Mars is optically thick and can be interpreted by using radiative transfer models to derive the abundance of H atoms from an estimated column of atoms along the line-of-sight (e.g., Anderson & Hord, 1977; Bhattacharyya et al., 2020; Chaffin et al., 2018; Chaufray, Gonzalez-Galindo, et al., 2021; Chaufray, Mayyasi, et al., 2021; Chaufray et al., 2008; Gladstone, 1982). Once H abundances are derived, the present day escape rate and content of water in the upper atmosphere of Mars can be estimated and then extrapolated to primordial conditions (Jakosky, 2018).

Using atmospheric H Lyman-α brightness measurements with radiative transfer techniques is one of the most prevalent ways to estimate atmospheric H abundances (e.g., Bhattacharyya et al., 2015, 2020; Chaufray, Gonzalez-Galindo, et al., 2021; Chaufray, Mayyasi, et al., 2021; Chaufray et al., 2008; Mayyasi et al., 2018, 2022). The motivation for this work is to provide an empirical predictive model for H brightness in the upper atmosphere of Mars obtained of the disk of the planet from an orbiting spacecraft. Applying radiative transfer techniques with this predictive model to further derive H abundances is beyond the scope of this work. The focus here is to describe, validate, and disseminate the H brightness predictive model for further interpretation within the scientific community.

The analysis in this study is Mars-specific; however, the empirical and predictive framework developed and presented in this work can be exported to other planetary and exoplanetary systems with optically thick H Lyman-α atmospheres when making appropriate assumptions (e.g., scaling solar irradiances). These results can therefore further support independent derivations of the atomic H content in the upper atmosphere of Mars and other Mars-like bodies.

Data and Methods

Deriving the predictive model begins with ingesting a large data set obtained over 9 years of in-orbit upper atmospheric disk-pointed observations of the Martian upper atmosphere. The MAVEN mission carries a remote sensing Imaging Ultraviolet Spectrograph (IUVS) instrument (Jakosky et al., 2015). The IUVS instrument measures H Lyman-α brightness in low spectral resolution (FUV) mode, and measures H and D Lyman-α brightness in high spectral resolution echelle (ECH) mode (McClintock et al., 2014). In this study, the ECH mode data are used since they can separate the H from D Lyman-α emissions and provide an analysis of pure H variability. IUVS ECH data cover disk, limb, and coronal observations of the planet. Since the H Lyman-α observations made of the Martian limb and corona can include non-negligible contributions from Interplanetary Hydrogen (IPH) emissions, this study only utilizes disk-pointed observations where the IPH emissions along the line-of-sight are negligible (Mayyasi et al., 2023).

As seen from the surface of Mars, the MAVEN/IUVS line-of-sight to the disk can vary between being directly overhead to being close to the horizon. The atmosphere of Mars is not symmetric along the line of sight and can vary on multiple timescales as short as minutes due to solar activity and illumination (as shown in the next section). Therefore, disk observations that were made when the instrument line-of-sight was closest to nadir, and that were taken over a duration of 29 s each, are used for this study to minimize the contributions of atmospheric variability along the observational line-of-sight.

The Martian H corona spans several planetary radii that extend beyond the orbital altitude of the MAVEN spacecraft (Anderson & Hord, 1971; Bhattacharyya et al., 2023; Chaufray et al., 2008; Nagy et al., 1990). Subsequently, the IUVS ECH disk-pointed observations include a significant amount of illuminated H atoms that are resonantly scattering Solar photons, even when the line-of-sight is pointed at the night-side of the planet. The resulting data set of H Lyman-α emission brightness spans a comprehensive range of illumination conditions and spans the last third of Mars Year (MY) 32 through the first third of MY37. During the MAVEN observational timeline, the Solar cycle ranged from maximum to minimum of Solar Cycle 24 and continued through the increasing activity phase of Solar Cycle 25. The data set used here therefore also represents a range of Solar activities.

The IUVS ECH mode observations are optimized for orders of H and D Lyman-α that reflect off an echelle grating onto a 1,024 × 1,024 pixel detector (McClintock et al., 2014). The observed photon counts are reduced and integrated across the aperture and spectral range to obtain a brightness in kilo-Rayleigh (kR) (e.g., Mayyasi et al., 2017). Earlier in the mission lifetime, the detector-binning schemes, voltage gain setting, and exposure time were varied to maximize data yield for the optical configuration. Here we use data from when these settings settled to their optimal values: a 332 × 74 spectral × spatial binning scheme, a voltage gain of 796.29 V, and an exposure time of 29.0 s. Two disk-pointed echelle observations are typically obtained for each orbit: one on the inbound segment of the orbit (leading up to spacecraft periapsis) and one on the outbound leg of the orbit (following spacecraft periapsis). The data from each orbit include between 8 and 20 exposures. For H observations, the data from each exposure in a single orbital segment are averaged to obtain one data point. This averaging maintains the integrity of the observation geometry while optimizing the signal-to-noise (e.g., Mayyasi et al., 2017, 2022, 2023).

MAVEN has been in orbit around Mars since September 2014. This work utilizes observations made between November 2014 and May 2023. The data set used to obtain empirical trends spans 12 November 2014 (orbit 240), through 14 February 2023 (orbit 18,202), and includes 6529 data points. The data set used exclusively to compare with predictions span 15 February 2023 (orbit 18,210), through 14 May 2023 (orbit 18,794) and included 185 data points.

Once the publicly accessible data are reduced to derive a representative average across the integrations for multiple observing geometries (e.g., illumination along the line-of-sight, latitude, and longitude), the resulting averages are then used to characterize the variability in H Lyman-α brightness measurements. The variation in the data is analyzed across time and observational conditions to develop statistical trends with empirical fits. The empirical fits, developed where data exist, are interpolated to fill in observational gaps to produce a predictive model of H brightness in the upper atmosphere of Mars. Predictions are made and then compared with new data to assess reproducibility.

A statistical approach was used to derive H brightness trends. The H brightness is the dependent variable (labeled as Y). The H brightness values, derived across the mission timeline, were examined for dependance on several observable variables, listed in Table 1 as X1, X2, X3, etc. Variables that showed no obvious trends in Y were ruled out. Variables that did show obvious trends with Y were then further investigated for inter-dependance. A functional form was used to fit the empirical trends to the resulting sub-set of variables with first-order estimates that was then optimized using minimum square variance to produce a best-fit. The resulting best-fit functional form was then used to predict values of H brightness. A subset of data (last 3 months) was intentionally excluded from the empirical analysis so that it could be used exclusively to test the predictive capabilities of the model.

Table 1 Variables Used to Examine (Inter)Dependency on H Lyman-α Brightness

Variable	Observable	Definition
X1	SZA	Solar Zenith Angle
X2	Ls	Solar Longitude
X3	LT	Local Time
X4	SI	Solar Irradiance
X5	EA	Emission Angle
X6	Lat	Latitude
X7	Lon	Longitude
X8	SC	Spacecraft Altitude

The variables in Table 1 were chosen based on their potential to directly impact the variability of H brightness along the observational line-of-sight. Solar zenith angle and local time are expected to impact the illumination along the column of H atoms as these represent how much overhead illumination the atmosphere is subjected to. Solar longitude and Solar irradiance (also used to account for Solar cycle) are expected to affect the incident upper atmospheric Lyman-α photon flux that can interact with H atoms and so are also considered as candidate variables to analyze.

Observations were filtered for a low emission angle (deviation of the line-of-sight from nadir) of <40° to minimize longer path lengths across a non-uniform atmosphere, and so, the deviation from strictly nadir observing (EA of 0°) up to 40° was examined as a potential impactor of H brightness. Latitude and Longitude were also evaluated for potential topographical effects on upper atmospheric H brightness. The altitude of the MAVEN spacecraft in its orbit during the observations was also examined to account for any biases in the observing conditions. Other variables such as: integration time of the observations and observational segment (e.g., inbound vs. outbound), were investigated for completeness but had no effects on H brightness trends.

Results and Discussion

The H emission brightness from the co-added MAVEN IUVS ECH mode disk observations are shown in Figure 1. The brightness varies between 0.18 and 12.79 kR throughout the mission timeline and can change with multiple timescales. The observations were made during both inbound and outbound segments of the orbit, where illumination conditions are different, resulting in two data points from the same orbit having different brightness values. Furthermore, a Mars year spans 687 days, where the planetary distance from the Sun varies, resulting in variations in the Solar irradiation-sensitive H brightness values. Added to these drivers, the Solar cycle transitioned from maximum to minimum to another maximum across the timeline, providing an additional timescale for the variability in the observed atmospheric H brightness.

Figure 1. H Lyman-α emission brightness in kR (black circles), averaged over each orbital segment, plotted as a function of mission timeline. Measurement uncertainties are shown as gray error bars and are negligible for the H Lyman-α emissions in this data set.

Mars encounters regional and global dust storms during its perihelion season (Ls ∼180°–360°, the latter half of each MY). Studies have shown effects of dust-storms that increase H atomic abundances and emission brightness in the lower atmosphere, at ∼80 km (e.g., Holmes et al., 2022). Planetary dust storms and Solar weather events can heat up and inflate the dominant and heavier species in the atmosphere (namely, CO₂). This atmospheric expansion leads to higher collision frequencies within atmospheric constituents and subsequently more suppression of H atoms that would otherwise have diffused more freely to altitudes of ∼250 km and higher (e.g., Mayyasi et al., 2018). This seasonal heating could affect the observed upper atmospheric H brightness from year to year (Chaffin et al., 2018, 2021; Mayyasi et al., 2023).

H Brightness Dependencies

To understand, quantify, and predict the H brightness as a function of time (through the MAVEN mission timeline and beyond), the H brightness was examined against the observational variables listed in Table 1 to isolate the most dominant drivers of variability and to derive a functional form for the trends in the data. The first four variables, X1 through X4, resulted in the clearest trends, as shown in Figure 2.

Figure 2. Nine + years of H Lyman-α emission brightness collected by MAVEN and examined for dependencies on observational variables. (a) H brightness as a function of Solar zenith angle (black circles) is shown with averages and standard deviations (red vertical lines) for 18 × 10° bins with a fit to the average (red trendline). (b) H brightness as a function of Solar longitude (black circles) is shown with averages and standard deviations (red vertical lines) for 36 × 10° bins with a fit to the average (red trendline). (c) H brightness as a function of Solar irradiance (black circles) is shown with averages and standard deviations (red vertical lines) for 20 × 6.7 × 10−4 W/m2 bins with a fit to the average (red trendline). (d) H brightness as a function of Local Time (black circles) is shown with averages and standard deviations (red vertical lines) for 24 × 1-hr bins with a fit to the average (red trendline).

SZA measures the angle between a vector normal to the surface from the observational point along the instrument line-of-sight, and a vector from that observation point on the surface to the Sun. In this data set, the SZA ranges between 10.18° and 167.8°. H Lyman-α emissions are therefore brightest when the Sun is nearest to being overhead at low SZA and become faintest on the nightside at higher SZA when much of the line of sight within the atmosphere is in the shadow of the planet. This trend of decreasing brightness with increasing SZA is evident in the data (Figure 2a). At high SZA, the brightness decreases to low values with lower scatter about the mean, and at low SZA, the brightness increases with larger scatter about the mean. In binning the H brightness by 10° in SZA, averages with standard deviations from the mean showed the variance to range from a maximum of ±2.5 kR at SZA < 40° to a minimum of ±0.3 kR at SZA > 140°. This scatter in brightness at low SZA is likely due to variations in other parameters such as season and Solar cycle in each 10° SZA bin, as is described next.

The Solar longitude in the observations varies between 0.0634° and 359.96°, effectively covering the full seasonal range at Mars. Aphelion at Mars is when the planet is farther from the Sun in its orbit; between 0° and 180° Ls. Perihelion at Mars is when the planet is closer to the Sun in its orbit; between 180° and 360° Ls. The trend in the data of Figure 2b shows a significant amount of smaller scale variability that is attributed to SZA, and shows fainter H emissions at aphelion than at perihelion, due to the proximity of the planet to the Sun. Binning the H brightness by 10° bins in Ls and taking the average and standard deviation in brightness for each bin showed a variance that ranged from a minimum of ±0.8 kR at Ls < 180° and a maximum of ±5.5 kR at Ls > 180°. The large spread in the data is attributed to the varying SZA as well as the timing of perihelion's onset of dust storms that can begin between 165° and 210° Ls and can end between 280° and 310° Ls (Kass et al., 2016, 2019).

Solar irradiance at Mars is measured in situ using the MAVEN Extreme Ultraviolet Monitor (EUVM) instrument (Eparvier et al., 2015; Eparvier, 2022). For these observations, the values obtained from the Lyman-α channel of the EUVM instrument range between 1.866 × 10⁻² W/m² and 3.202 × 10⁻² W/m². The plot in Figure 2c shows a trend of increasing H Lyman-α brightness as Solar irradiance increases, as expected. H brightness values were binned by 6.7 × 10⁻⁴ W/m² to obtain the average and variance in SI within each bin and the latter was found to range between ±0.75 kR and ±3.5 kR. This trend compounds the effects of a changing Solar cycle throughout the timeline of MAVEN observations with the effects of changing orbital location. The next section addresses the interdependencies of these two effects.

The local time in the observations combines the effects of SZA, location on the surface, and declination of Mars as measured along the line-of-sight. In these observations, the local time ranged between 0.33 and 23.65 hr, effectively covering the full range of local times. The trends shown in Figure 2d show an increasing H brightness at local noon that tapers off to lower values during local nighttime. Binning the H brightness values into 1-hr bins in LT and taking the average and variance in each bin showed a spread ranging from a minimum of ±1 kR at nighttime to a maximum of ±2.5 kR during local noon. The effects of local time are compounded with SZA and will be addressed in the next section on interdependencies.

H brightness variations against the remaining variables in Table 1 (X5–X9) are shown in the Supporting Information S1 (Figure S1) for completeness. The data showed significant scatter with these variables. While the values for H brightness did not change based on what variable they were examined against, the spread in the data indicated no obvious trendlines when compared with changing emission angle, latitude, longitude, and spacecraft altitude.

Interdependencies

To derive a functional form that can be used to represent (and predict) H brightness, the leading variables (SZA, LT, Ls, and SI) are first investigated to account for potential interdependencies. SZA and LT are interdependent as the former is derived from a combination of the latter, declination of the Sun, and latitude. For this data set, the SZA is smallest at local noon conditions and increases closest to local midnight, as shown in Figure 3a. To account for this, we opt for using the SZA over LT as the preferred independent variable.

Figure 3. Interdependencies in the H brightness drivers show a (a) SZA dependence on LT, and a (b) Solar irradiance dependence on Ls. The colors represent data collected in different Mars Years with MY32 data shown in red, MY33 data shown in green, MY34 data shown in blue, MY35 data shown in gray, MY36 data shown in purple, and MY37 data shown in black.

Due to Mars' elliptical orbit, there is a dependence expected for Solar irradiance with Solar longitude. As shown in Figure 3b, the Solar irradiance observed at Mars depicts a few trends with Solar longitude. The small scale sinusoidal variability in SI that spans ∼20° in Ls throughout the Mars Year is due to the Solar rotation period. The larger scale sinusoidal variability in SI is due to Mars' location in its elliptical orbit. The variability in SI from one MY to the next is due to varying Solar activity in Solar cycles 24 and 25.

No other interdependencies are expected in the remaining variables (SZA vs. Ls, SZA vs. SI, SI vs. LT, and Ls vs. LT), as verified in Figure S2 in Supporting Information S1.

Functional Representation

The distilled variables considered to drive H Lyman-α emission brightness are SZA, Ls, and Solar cycle. In this parameterization study, the SZA resolution is 1°, taken between 0° and 180°. The Ls resolution is 10°, between 0° and 360°. The two phases of the Solar cycle are designated as Solar minimum and Solar maximum, where observations considered for Solar minimum are those made between 30 June 2015, and 2 April 2022. Observations considered for Solar maximum are those bookending Solar minimum, made between the earliest MAVEN ECH data acquired on 12 November 2014, through 29 June 2015, and between 3 April 2022, through 15 February 2023. Of the total 6529 data points used in this analysis, 5508 are obtained during Solar minimum, and 1021 are obtained at Solar maximum. Figure 3b shows the Solar maximum observations as those made throughout MY32 (red circles), during the latter half of MY36 (vertically offset purple circles) and throughout MY37 (black circles).

MAVEN arrived at Mars in September 2014, during the end of Solar cycle 24. At this time, most of the MAVEN data has been collected at Solar minimum and the spacecraft is in extended mission to continue observations as Solar cycle 25 progresses to its maximum phase. To simplify the derivations, the ad hoc designation of Solar minimum and Solar maximum is made here to delineate when the Solar Lyman-α irradiance at Earth drops below a threshold of 2.15 W/m², as shown in Figure S3 in Supporting Information S1. When more Solar maximum observations of MAVEN/ECH H Lyman-α brightness are available, a more continuous designation can be made for Solar activity.

Solar longitude spans between 0° and 360° and is binned into 10° bins. In this binning scheme, all 36 × 10° Ls bins have Solar minimum data, with the number of datapoints ranging between 21 and 221. Not all Ls bins have Solar maximum data. The number of datapoints in populated bins range between 15 and 198. As MAVEN continues to make observations, these Solar activity data gaps will be filled in. The resulting data points for H brightness versus SZA for each bin and at each Solar activity are then fit to a curve. An S-curve was found to be representative of the empirical trends, and can be formulated as: [Image Omitted. See PDF]Where Y is the H brightness in kR, x is the SZA in degrees, and A, B and C are constants for each Ls bin and each Solar activity. These values that are given ad hoc initial estimates A_i, B_i, and C_i. The initial estimates are varied incrementally by stepping less than and greater than their initial values over a total set of A_n, B_n, and C_n values. An iteration algorithm steps through all the combination of values for A_n, B_n, and C_n to generate a curve and calculate its variance to the data, χ². The combination of A_n, B_n, and C_n values that produces the minimum variance are used as the optimal and final set of values (A_f, B_f, and C_f) that are then used to generate the best-fit curve to the data in each bin.

B_i was the least sensitive value to the curve fits and was taken to be 0.03 for all the bins. The initial values of A and C values, used as first estimates for each bin, are shown in Table 2. The A and C values were varied by 0.5 between ±4.0 of their initial estimates. The B value was varied by 0.005 between ±0.025 of its initial value.

Table 2 First Estimates of Fitting Values Used in the Iterative Fits to the Data

Solar activity	Ls bin	Ai	Ci
Minimum	<180°	4.5	6.0
	210°–230°	5.0	7.0
	270°–280°	10	7.0
	300°–310°	10	9.0
	All other bins	7.0	6.0
Maximum	<180°	6.0	9.5
	280°–290°, 300°–310°	14	10
	All other bins	8.0	14

The resulting best-fit curves and the data for all the bins are shown in Figure 4, normalized by the best fitting A_f value for visibility. The best fit curves generally did well to reproduce the H brightness trends with SZA. The individual binned data and their fits are shown in the Supporting Information S1 (Figure S4).

Figure 4. H brightness, normalized to the best fit Af value, as a function of SZA. The data are binned by Ls according to the legend in the center. Circles indicate the normalized H brightness measurements obtained at that Ls bin at Solar minimum in Panel (a) and at Solar maximum in Panel (b).

Data Parametrization and Interpolations

The best-fit values (A_f, B_f, and C_f) used to derive the optimal fitting curves are shown in Figure 5. During Solar minimum, the best fit A_f value varied throughout the Mars Year with a clear annual trend. The B_f value was generally the same as the initial estimate, with few deviations around its average of 0.03. The C_f value had significant scatter around its average value of 6.74. During Solar maximum, the best fit A_f value varied with Ls with a similar trend to its Solar minimum counterpart, where data existed. The B_f value averaged to 0.034. The C_f value had significant scatter around its average value of 12.6.

Figure 5. Final values (black circles) of the variables used to generate the optimal fits to the data. The top row shows Solar minimum A, B, and C values in unintentionally similarly named panels (a–c), respectively. The bottom row shows Solar maximum A, B, and C values in panels (d–f), respectively. The A values (Left Column), B values (Middle Column) and C values (Right Column) show the quantities used in Equation 1 for each Ls bin. The red lines in each panel are fits to the trends in A, B, and C values. Uncertainties (gray vertical lines) indicate the standard deviation in each set of values.

An empirical trend is fit to the A_f values that were derived for Solar minimum, where data is continuous. To account for Solar maximum data gaps, the A_f value curve from Solar minimum was used and scaled by a factor of 1.2. Values at low Ls were constrained to the Solar maximum data available (where A_f was 6). The average B and C values from each Solar activity case are used to extrapolate the curves into regions with data gaps. These extrapolated values are used to make predictions for the upper atmospheric H emission brightness at Mars.

The large scatter in C values for Solar minimum and maximum fits has the least effect on the S-curve shape and effectively dictates where (in SZA space) the downward inflection begins to deviate from the horizontal plateau at lower SZAs. The difference in brightness between curves fit with the extreme C values is <15% for all SZA.

Adopting the empirical and scaled fits to the A value and using the averages for the B and C value (i.e., the red curves in Figure 5) provided the range of values to use for predictive modeling of what the H emission brightness would be.

Validation and Predictions

The first step in validating the results was to compare the model predictions with the data that they were derived from. Using the observational conditions (SZA, Ls, and Solar cycle), the best-fit H brightness was calculated. A comparison of calculated and empirical data is shown in Figure 6a. The empirical fits reproduced the data well, as expected from the best-fit derivations for both Solar maximum and Solar minimum conditions. Deviations from the data were within ∼2 kR, and were largest during perihelion conditions, when variable dust storms impacted the atmosphere and likely affected the circulation patterns that propagate water molecules to the upper atmosphere where they break down to from atomic H.

Figure 6. Disk-pointed MAVEN ECH observations of H Lyman-α emission brightness across the mission timeline spanning MY32-MY37, averaged for each orbital segment (gray circles). (a) H brightness values derived using the empirical best-fits to the data for Solar minimum (light blue circles) and Solar maximum (yellow circles). (b) H brightness values derived using the interpolated best-fits for Solar minimum (blue circles) and for Solar maximum (red circles). New data (black circles) not used in the previous analysis collected by MAVEN ECH during Solar maximum conditions with the values predicted from the interpolated fits (green circles). In both panels, the difference between the observed and fit data (ΔH) are shown in violet circles, vertically offset by 16 kR for visibility. A horizontal dotted line at 0 kR denotes the zero-level for H brightness in the data. Horizontal lines at 14, 16, and 18 kR denote the −2, 0 and +2 kR levels for the difference (ΔH) as indicated on the offset right y-axis.

The second step in validating the results was to compare the model predictions with new data. Mariners 6, 7, 9, Mars Express, and the Emirates Mars Mission are among a few missions to obtain UV spectra of H Lyman-α from the Martian disk during flyby or orbit (e.g., Barth et al., 1971, 1973; Bertaux et al., 2004, 2006; Holesclaw et al., 2021). However, none of these data have the required spectral resolution to separate H from D Lyman-α. The 1215.34 Å emission from D atoms in the atmosphere of Mars can vary seasonally and can contribute up to 1 kR to the total Lyman-α emissions (Mayyasi et al., 2023). The Hubble Space Telescope (HST) has an observation mode with comparable spectral resolution to MAVEN/ECH, but contamination of the strong Geocoronal H emissions in those data are not conducive to a proper comparison. Therefore, we use data from MAVEN/ECH that was not used in the parent data set from which the empirical fits were derived.

The results of the comparison between the “old” and “new” data and the predictive model are shown in Figure 6b. The predictive model was able to reproduce the old data to within ∼2 kR, with the largest discrepancies occurring around perihelion season of each Mars Year. The new data was obtained at Solar maximum aphelion and was reproduced by the predictive model to within <0.5 kR. These comparisons demonstrate the accuracy of the predictive model in simulating the H Lyman-α emission brightness in the upper atmosphere of Mars for the present-day epoch.

Note that dust storm effects on H brightness are not analyzed in this work. Regional dust storms on the planet vary from Mars Year to Mars Year and the predictability of the start, peak, and end date of these events is currently unreliable (e.g., Pieris & Hayne, 2023). The variations in the trends and the parametrized projections found in this work would provide helpful predictions during Solar minimum and/or aphelion conditions with more certainty than during Solar maximum/perihelion conditions, due to the present dearth of empirical constraints in the latter scenario. With the availability of more MAVEN ECH data, the statistical trends would become more robust.

Summary and Conclusion

The H Lyman-α brightness values in the upper atmosphere of Mars, measured by the orbiting MAVEN mission, have been analyzed for trends that may indicate predictable patterns. The brightness values were found to be dependent, in part, on the Solar illumination that impinges on the upper atmosphere of the planet. The observational quantities that were considered in evaluating the trends in brightness are SZA, location of Mars in its orbit, and Solar activity. A functional form was derived to best fit binned subsets of the brightness data with SZA for each Solar activity and Ls bin. The resulting fits were used to predict what the future observations of H Lyman-α brightness, measured from the upper atmosphere of Mars, would be.

The empirically derived best-fit curves to the data reproduced the trends in H brightness to within 6%, on average, for Solar minimum, and to within 9%, on average, for Solar maximum. The discrepancies between the data and the empirical fits are relatively small at aphelion (6 ± 8%) as well as at perihelion (6 ± 10%) when the H brightness tends to be highest. These discrepancies may be due to the year-to-year variability in dust activity onset and severity that could explain the scatter in the data in dusty Ls seasons. The interpolated best-fit curves to the data reproduced the data to within 6%, on average, for Solar minimum, and to within 13%, on average, for Solar maximum. The interpolated best-fit curves were able to predict new data at aphelion to within 18% on average. This accuracy is expected to improve at Solar minimum conditions.

As additional MAVEN ECH data become available, the empirical derivations can continue to be supplemented (especially at Solar maximum perihelion, where there is a current absence of data) to provide a more comprehensive empirical baseline for predictions. Future iterations of this work could also include analysis of dust opacity measurements to account for dust activity.

The predictive tool presented here is the first step toward developing a consistent set of Martian “psychrometric” charts to evaluate the volatility of hydrogen content in the upper atmosphere (e.g., Mayyasi et al., 2022; Kleinböhl et al., 2024). Additional quantities to empirically constrain the upper atmosphere include temperature, Solar Lyman-α irradiance, and abundance of CO₂. The capabilities to make predictions of these additional quantities with the H Lyman-α emission brightness prediction tool would minimize the assumptions that are typically required in radiative transfer modeling and would facilitate empirically based predictions of H abundance and escape rates at Mars. The subsequent results of H abundance and escape rates provide an empirical baseline for present-day conditions at Mars that could be used to extrapolate to primordial conditions (e.g., Chassefiere et al., 2013; Jakosky, 2018). The methodology developed here can further be applied to other planetary systems with extended H atmospheres and/or Mars-like exoplanets orbiting Sun-like stars.

Acknowledgments

The authors thank the reviewers for their recommendations for improving the manuscript. MM thanks Professor Stephan Sturm for discussions of statistical approaches, and Ms. Assaf for her helpful proofreading.

Data Availability Statement

The MAVEN ECH data used in this study are available as fits files on the NASA PDS Atmospheres Node at: https://pds-atmospheres.nmsu.edu/data_and_services/atmospheres_data/MAVEN/maven_main.html. IUVS echelle level1a v13 data and EUVM level3 data were used. The methodology to reduce the data are described in detail in previous publications (Mayyasi et al., 2017, 2022) under https://doi.org/10.1002/2016JA023466, and https://doi.org/10.1029/2022EA002602, respectively. The methodology required to reproduce the results in this work are self-contained in this manuscript.