Hydrogen distribution is key to understanding the chemistry and dynamics of the middle and upper atmosphere (Bishop, 2001). Atomic hydrogen in the mesosphere is a byproduct of photolysis reactions of H 2 O, CH 4 , and H 2 and plays an important role in O 3 chemistry in the middle atmosphere (Brasseur and Solomon, 2005). Furthermore, as a minor species in the lower thermosphere, atomic hydrogen becomes increasingly important in the upper thermosphere, where hydrogen charge exchange reactions contribute to hydrogen kinetics and escape (Chamberlain and Hunten, 1987). In the exosphere, neutral hydrogen becomes the dominant species and resonantly scatters sunlight at Lyman- α (1,216 Å; hereafter referred to as Ly- α ) to produce the diffuse geocorona around the Earth. Increased exospheric hydrogen contributes to the recovery of the plasmasphere after geomagnetic storms as well as ring current decay during geomagnetic storms (Krall et al., 2018). Additionally, hydrogen charge exchange reactions between hydrogen and hydrogen ions result in energetic neutral atoms (ENAs). Therefore, reliable measurements of the geocoronal density are essential for techniques such as ENA imaging to determine the ion distributions of the inner magnetosphere (Ilie et al., 2013).

Multiple studies have analyzed geocoronal hydrogen ground- and space-based measurements and how they compare to the NRLMSISE-00 [(Picone et al., 2002); hereafter referred to as MSIS-00] empirical model. Gallant et al. (2019) compared ground-based geocoronal hydrogen Balmer- α (6,563 Å; hereafter referred to as H α ) observations from a Fabry-Perot interferometer (FPI) located at Pine Bluff Observatory (PBO) in 2000–2001 (Mierkiewicz et al., 2012) to MSIS-00 forward modeled H α intensities. The results indicate a seasonal trend in the observed dusk-to-dawn intensity variation consistent with a diurnal variation in the underlying thermospheric hydrogen density distribution. Furthermore, they found that the observed H α emission intensities are higher than the MSIS-00 forward modeled intensities by 1.5–2.5 rayleighs indicating a discrepancy in the underlying MSIS-00 hydrogen distribution (Gallant et al., 2019). Nossal et al. (2012) compared ground-based H α observations from the Wisconsin H-Alpha Mapper (WHAM) FPI to MSIS-00 forward modeled H α intensities over an entire solar cycle. The MSIS-00 forward modeled intensities show a greater solar cycle variation than the observed emission intensities and, therefore, indicate possible discrepancies in the underlying hydrogen distribution for solar minimum and maximum during nighttime conditions (Nossal et al., 2012). Moreover, Waldrop and Paxton (2013) analyzed Ly- α measurements from the Global Ultraviolet Imager (GUVI) instrument aboard NASA’s Thermosphere Ionosphere Mesosphere Energetics and Dynamics (TIMED) spacecraft and found that MSIS-00 overestimates GUVI upper thermospheric hydrogen density by 36%–67% at solar minimum and 42%–74% at solar maximum during dayside conditions. Wan et al. (2022) demonstrated that exobase hydrogen densities derived from GUVI Ly- α observations exhibit solar cycle, seasonal, and local time variability not captured by MSIS-00 or NRLMSIS 2.0 (Emmert et al., 2021), including a weakening dawn-dusk asymmetry towards solar minimum. In contrast, Joshi et al. (2019) used MSIS-00 to prescribe the background thermosphere within a radiative transfer model inversion of Ly- α emission measured by GUVI. They found that the vertical flux of thermospheric hydrogen is nearly constant over a large range of solar activity and typically exceeds the calculated thermal evaporative flux. These studies emphasize the need for improved representations of upper thermospheric hydrogen transport and coupling in empirical models across various temporal scales.

WACCM-X (Whole Atmosphere Community Climate Model-eXtended) is a comprehensive numerical model that simulates the entire atmosphere and ionosphere from the Earth’s surface to ∼ 700 km (Liu et al., 2018). Previous work by Qian et al. (2018) compared WACCM-X simulations of atomic hydrogen for different temporal and spatial scales to observations from TIMED’s Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) instrument as well as abundances specified by MSIS-00. They found that in the upper thermosphere, hydrogen density is predicted to be higher in the winter than summer, higher at solar minimum than solar maximum, and higher during the night than day.

We forward model WACCM-X hydrogen density and temperature profiles using the radiative transport code, lyao_rt (Bishop, 1999) to obtain H α column emission intensities. Intensities are reported in rayleighs (R), where 1 R is defined as an apparent column emission rate of 10 6 ph s − 1 cm − 2 (Chamberlain, 1961), which has been shown (Baker and Romick, 1976) to be numerically equivalent to a specific intensity (or surface brightness) of 10 6 /4 π ph s − 1 cm − 2 sr − 1 . WHAM observations are calibrated against the North American Nebula (NGC 7000) using the 850 R absolute intensity standard (Scherb, 1981). Additionally, the WACCM-X simulations used in this study are from Solomon et al. (2019) for the years 2001–2005 run for perpetual solar maximum conditions and were selected to be compared qualitatively to the Mierkiewicz et al. (2012) ground-based H α observations from 2000 to 2001. Here, we compare these WACCM-X model runs for the March equinox with observations from March 2000. Although these simulations do not reproduce the observational conditions for March 2000, they are appropriate for a qualitative seasonal comparison. WACCM-X is chosen over other models like the Thermosphere Ionosphere Electrodynamics-General Circulation Model (TIE-GCM), Whole Atmosphere Model (WAM), and Ground-to-topside model of Atmosphere and Ionosphere for Aeronomy (GAIA) for simulating upper atmosphere temperature, winds, and neutral species densities, including hydrogen density, because of its vertical coverage from the surface to the exobase ( ∼ 700 km depending on solar activity), advanced chemistry modules, including multi-species hydrogen chemistry, and self-consistent neutral and ionized species coupling. It captures key processes such as hydrogen transport, ion-neutral interactions, and variability driven by tides and planetary waves more holistically than models with limited altitude ranges (TIE-GCM) or simpler chemistry and ion-neutral coupling (WAM and GAIA). Additionally, this work aims to build off the previous work of Gallant et al. (2019) that compared the 2000–2001 PBO observations to forward modeled MSIS-00 results. The broader significance of this work lies in establishing a framework for examining geocoronal hydrogen variability over a wide range of temporal scales, including during geomagnetic storm conditions.

The 2000–2001 ground-based H α observations from Mierkiewicz et al. (2012) are described in Section 2.1, the WACCM-X simulations used in this study are described in Section 2.2, and the forward modeling technique to produce WACCM-X and MSIS-00 H α emission intensity is described in Section 2.3. Results are presented in Section 3 and discussed in Section 4.

In order to investigate variations of upper thermospheric hydrogen, WACCM-X thermospheric temperature and density profiles for the conditions outlined in Table 1 are used as inputs to lyao_rt. MSIS-00 forward modeled simulations are also conducted for the conditions in Table 2. For the MSIS-00 case, lyao_rt uses the Ap index as opposed to the Kp index used by WACCM-X. Therefore, to be consistent with WACCM-X, Kp = 3 is converted to Ap = 15 using NOAA’s Geomagnetic Kp and Ap Indices. Furthermore, the solar Ly- β line center flux for high solar activity is estimated to be 14.0 × 1 0 9 ph cm − 2 s − 1 ̊A − 1 . This value was calculated by deriving the scaling needed to match the forward modeled H α column emission intensity with the full set of March 2000 PBO observations (Myers et al., 2024) and is within range of the values reported in Bishop et al. (2004). Lastly, observational uncertainty in the geocoronal signal arises from tropospheric scattering by molecules and aerosols in the lower atmosphere (Bishop et al., 2004) as well as cascade enhancements of the Balmer- α line profile (Roesler et al., 2014; Mierkiewicz et al., 2012). The March 2000 observations are not adjusted to account for estimates of tropospheric scattering and the model runs do not account for cascade enhancements. These effects will be carefully considered in future work.

In this work, we use WACCM-X simulations as inputs to the radiative transport code, lyao_rt (Bishop, 1999), facilitating a comparison between modeled H α column emission intensities and ground-based geocoronal H α observations. March equinox WACCM-X simulations characterized for perpetual solar maximum conditions from 2001 to 2005 are compared to ground-based observations from March 2000 taken at Pine Bluff Observatory in Wisconsin. Both the WACCM-X simulations and the Fabry-Perot observations were performed during periods of similar geophysical conditions. Although the WACCM-X runs were for perpetual solar maximum conditions and not specifically for the conditions of the observations, we can obtain qualitative information regarding the model’s ability to simulate the underlying thermospheric [H] distribution. The MSIS-00 empirical model is also coupled to lyao_rt to perform a model-model-data comparison for the March equinox case. Several points of discussion are presented below:

The modified MSIS-00 H α emission intensity profile, or the reference profile, offers better agreement with the March 2000 observations than WACCM-X and MSIS-00 (see Figures 1a,b). This is expected because, in the modified case, lyao_rt uses inputs of exobase density n exo , photochemical upward flux ϕ , and mesospheric peak density n max that are consistent with Bishop et al. (2004) to substitute the MSIS-00 [H] profile with a user-specified [H] profile that best fits the March 2000 PBO observations. Lyao_rt then calculates the H α emission intensity using this user-specified [H] profile. For model-data comparisons, the modified MSIS-00 intensity profile is treated as a proxy to the observations.

We present an early application of forward modeling WACCM-X simulations to compute H α emission intensities. Here, we also include a comparative analysis with MSIS-00 and its “modified version.” The PBO WACCM-X simulations used in this work were run for March equinox (day of year 79 or 80) during the years 2001–2005, perpetual solar maximum conditions, and UT = 0. In the present work, the lyao_rt simulations assume a spherically symmetric hydrogen density, which represents a first-order approximation intended to isolate the primary dependencies of the H α signal on the global hydrogen density structure. While this assumption enables efficient forward modeling and comparison with observations, it may introduce systematic biases in the modeled H α intensities if strong asymmetries are present (e.g., along the Sun-Earth line). As an intermediate approximation, some effects of time-dependent asymmetry could be explored through a sequence of lyao_rt simulations that each assume spherical symmetry but allow the hydrogen density to evolve in time, with the resulting H α intensities interpreted in an averaged sense. Such an approach may capture aspects of the net variability in global hydrogen abundance while avoiding the computational complexity of fully asymmetric radiative transfer. However, this approximation would still be unable to reproduce directional scattering effects explicitly tied to the Sun-Earth geometry. Addressing these effects more rigorously would require extending lyao_rt to incorporate asymmetric hydrogen distributions, for example, through parameterized day-night density contrasts or coupling to two- or three-dimensional exospheric models along the Sun-Earth direction. Such developments are beyond the scope of the current study but represent an important avenue for future work aimed at improving the physical realism of H α modeling and reducing potential biases associated with symmetry assumptions. In future work, we plan to increase the accuracy of these model-model-data comparisons by comparing the 2000–2001 PBO observations to WACCM-X simulations that are representative of observational conditions, including correct dates, solar conditions, and nudged with meteorology analysis fields in the troposphere-stratosphere so the model atmosphere remains close to observed meteorological conditions. Model uncertainties and observational errors will also be explored more in depth. We will also run lyao_rt with line-of-sight viewing geometries consistent with the observations as opposed to the synthetic viewing geometry used in this work. Other future work includes producing line widths for WACCM-X simulations as well as coupling NRLMSIS 2.0 (Emmert et al., 2021) with lyao_rt to conduct further comparisons with this new MSIS model version.

Radiative transfer processes, such as the resonant scattering of solar Ly- α by atomic hydrogen and multiple scattering, rely on an accurate representation of hydrogen thermospheric density and temperature where these profiles directly control the populations of energetic states and the resulting exospheric hydrogen intensity. As a result, comparisons between forward modeled WACCM-X H α intensities and ground-based observations contribute to validating thermospheric hydrogen variability within the WACCM-X numerical model.