A wave-amplitude approximation adapted from inviscid WKB (Wentzel-Kramers-Brillouin) theory is tested for tsunami-generated gravity waves in the thermosphere up to 500 km altitude. The idea is to use a standard inviscid WKB wave-amplitude term m-1/2, where m(z) is the vertical wavenumber and z is the altitude, but to replace the inviscid m with an m obtained from a viscous and thermally diffusive dispersion relation. The m-1/2 approximation is implemented in an anelastic Fourier model for two-dimensional steady-state solutions in the tsunami reference frame. Comparisons are made with a more accurate numerical multilayer model giving solutions to a linearized system of anelastic governing equations. Though there is no perturbation analysis supporting the m-1/2 approximation for viscous m, the approximation compares well with numerical multilayer solutions except for overestimating wave amplitudes in very strong viscosity. The overestimate is due to the neglect by the m-1/2 approximation of a coupling between upgoing gravity-wave and dissipative modes.

This paper presents and tests a deep-atmosphere, nonhydrostatic dynamical core (DyCore) targeted towards ground-to-thermosphere atmospheric prediction using the spectral element method (SEM) with IMplicit-EXplicit (IMEX) and Horizontally Explicit Vertically Implicit (HEVI) time-integration. Two versions of the DyCore are discussed, each based on a different formulation of the specific internal energy and continuity equations, which, unlike the dynamical cores developed for low-altitude atmospheric applications, are valid for variable composition atmospheres. The first version, which uses a product-rule (PR) form of the continuity and specific internal energy equations, contains an additional pressure dilation term and does not conserve mass. The second version, which does not use the product-rule (no-PR) in the continuity and specific internal energy, contains two terms to represent pressure dilation in the energy equation and conserves mass to machine precision regardless of time truncation error. The pressure gradient and gravitational forces in the momentum balance equation are reformulated to reduce numerical errors at high altitudes. These new equation sets were implemented in two SEM-based atmospheric models: the Nonhydrostatic Unified Model of the Atmosphere (NUMA) and the Navy Environmental Prediction sysTem Utilizing a Nonhydrostatic Engine (NEPTUNE). Numerical results using both a deep-atmosphere and shallow-atmosphere baroclinic instability, a balanced zonal flow, and a high-altitude orographic gravity wave verify the fidelity of the dynamics at low and high altitudes and for constant and variable composition atmospheres. These results are compared to those from existing deep-atmosphere dynamical cores and a Fourier-ray code, indicating that the proposed discretized equation sets are viable DyCore candidates for next-generation ground-to-thermosphere atmospheric models.

While it is well known that exothermic chemistry and dissipating gravity waves provide the dominant energy inputs continuously driving the nighttime upper mesosphere and lower thermosphere (UMLT), possible effects of exothermic chemical heating on evolving UMLT gravity-wave dynamics remain largely unquantified. By deriving and combining analytical solutions of diabatic UMLT gravity-wave dynamics and of wave-perturbed heating rates for the seven exothermic chemical reactions most relevant to the heat budget of the nighttime UMLT, we show that an analytical thermal rate term captures the first-order diabatic feedback of wave-perturbed chemical heating on gravity-wave dynamics. Although complex in general, the rate coefficient is real to a very good approximation throughout the UMLT and thus acts primarily to either amplify or damp wave amplitudes. Evaluating this coefficient over all seven exothermic reactions reveals that wave-perturbed exothermic chemical heating amplifies gravity-wave amplitudes from 80 to 98 km at rates peaking near 1 near 90 km. These amplification rates vary substantially with local time due to strong tidal modifications of the background chemical heating rates. Largest amplification rates arise from monatomic oxygen recombination and from ozone destruction by atomic hydrogen, the latter producing excited hydroxyl emissions used to image UMLT gravity waves from the Atmospheric Waves Experiment (AWE). Accumulated chemical amplification is greatest for those waves with slower vertical group velocities and hence longer residence times in the 80-98 km height interval. Simplified approximations to the exact analytical rate expressions are provided for efficient numerical implementation in models and parameterizations.

Thermal infrared satellite radiances acquired from stratospheric channels during regular Aqua satellite overpasses of the Southern Ocean in July 2014 revealed unusual short-wavelength structure extending many hundreds of kilometers downstream of the Kerguelen and Heard Islands. Although near the limits of detection in nadir swath imagery, careful analysis and cross validation verify the structure to be geophysical. Theory, reanalysis, modeling, and available observations are combined to show that these features are resonant trapped island lee waves established by successive downstream vertical reflections from a strong stratopause jet and the ocean surface. This is the first definitive proof that resonant trapped lee-wave disturbances can extend to stratopause altitudes at around 40–50 km. Possible implications of this new form of stratospheric wave dynamics are discussed.

Mesopause‐region (87 km) gravity waves (GWs) generated by tropical convection are investigated within the four longitude sectors encompassing Africa, the Indian Ocean, the Intertropical Convergence Zone, and South America during the Dec 2023–Feb 2024 Southern Hemisphere monsoon season. Variances () in the OH Q‐line emission measured by the Atmospheric Waves Experiment (AWE) capture GW activity, and precipitation rates (PR) from the Global Precipitation Measurement (GPM) Mission identify regions of convective activity. The zonal component of GWs comprising the between 10S‐10N primarily propagate eastward. The distributions are latitudinally shifted and more confined in local solar time (LST) compared with those of PR. Mesospheric winds (including tides) appear to induce the latitude‐longitude‐LST variability seen in through critical‐level filtering and Doppler‐shifting of the GWs. These new insights into the variability of the GW spectrum entering the ionosphere‐thermosphere system further our understanding of the dynamical connections between tropospheric and space weather.

The U.S. Navy is building a coupled thermosphere-ionosphere prediction system. As part of this project, we are developing a new dynamical core (DyCore) extending from the ground to the exobase (~500 km). The DyCore must be able to handle large variations in both temperature and composition, which motivates a new Horizontally Explicit Vertically Implicit (HEVI) time integrator. Unlike traditional linear Implicit-EXplicit (IMEX) methods commonly used in numerical weather prediction (NWP), HEVI does not require a fixed reference state. Our DyCore combines HEVI with a Specific Internal Energy Equation (SIEE) and a Spectral Element Method (SEM) spatial discretization to form a robust, whole-atmosphere model for the neutral atmosphere. We present results for two test cases using the proposed DyCore: an idealized heating/cooling test extending into the middle thermosphere and a perturbation experiment yielding nonhydrostatic baroclinic instability. The idealized heating/cooling test, which is compared to corresponding results from the hydrostatic Navy Global Environmental Model (NAVGEM), demonstrates that HEVI is more robust than traditional linear IMEX methods. The baroclinic instability test shows that HEVI, when combined with a banded lower-upper (LU) direct solve, is efficient and allows a large timestep. These numerical results suggest that our HEVI-enabled DyCore is a good candidate for the proposed thermosphere-ionosphere prediction system.This work was funded by the Office of Naval Research Marine Meteorology and Space Weather program.

A previously developed numerical-multilayer modeling approach for systems of governing equationsis extended so that unwanted terms can be removed from the dispersion-relation polynomialassociated with the system. The new approach is applied to linearized anelastic and compressiblesystems of governing equations for gravity waves including molecular viscosity and thermaldiffusion. The ability to remove unwanted terms from the dispersion-relation polynomialis crucial for solving the governing equations when realistic background parameters, such as horizontal velocity and temperature, with strong vertical gradients, are included. With the unwanted terms removed, previously studied dispersion-relation polynomials, for which methods for defining upgoing and downgoing vertical wavenumber rootsalready exist, are obtained. The new methods are applied to a comprehensive set of medium-scale time-wavepacketexamples, with realistic background parameters, lower boundary conditions at 30 km altitude, and modeled wavefields extending up to 500 km altitude. Result from the compressibleand anelastic model versions are compared, with compressible governing-equation solutionsunderstood as the more physically accurate of the two. The new methods provide significantlyless computationally expensive alternatives to nonlinear time-step methods, which makesthem useful for comprehensive studies of the behavior of viscous/diffusive gravity wavesand also for large studies of cases based on observational data.Additionally, they generalize previously existing Fourier methods that have been applied to inviscidproblems while providing a theoretical framework for the study of viscous/diffusive gravity waves.

The foundational conservation equations of Eliassen and Palm (EP) and Bretherton and Garrett (BG) governing the pseudomomentum and action of waves in geophysical fluids are shown to be approximations that do not hold generally within atmospheres of varying mass composition, such as the Earth's thermosphere and other planetary atmospheres. Standard BG/EP conservation equations assume a fixed connection between mean-state entropy and pressure that breaks down when composition varies. New entropy-corrected (EC) forms of these equations are derived that conserve total energy and momentum in atmospheres where composition varies. Three separate and largely independent derivations are presented that all lead to the same EC forms of these equations and their associated diagnostics, such as nonacceleration conditions. Since EC forms present as corrective scaling factors to standard BG/EP equations, existing models and diagnostics are easily generalized. Representative thermospheric calculations reveal that the EC equations remove systematic energy and momentum biases of up to 40% that in turn lead steady conservative waves to grow more rapidly in amplitude with increasing altitude.

Equatorial Plasma Bubbles (EPBs) are a region of depleted ionospheric densities. EPBs are known to fluctuate both seasonally and day to day, and have been linked to changes in solar activity, geomagnetic activity, and seeding resulting from dynamics occurring at lower altitudes. Here, EPB activity is investigated over a 15-day period with overlapping coincident ground-based 630 nm oxygen airglow measurements, near-infrared hydroxyl mesospheric temperature mapper (MTM) measurements, and Rate Of change of Total Electron Content Index (ROTI) values. The data are compared with the Navy Global Environmental Model (NAVGEM) reanalysis over the same time period. It is found that several days with strong EPB activity coincided with the positive/northward meridional wind phase of the quasi-two-day wave (QTDW) in the mesosphere. These initial observations indicate correlations of the QTDW phase and the occurrence rates of EPBs, and suggest a need for further investigations to assess potential causal relationships that may affect the variability and prevalence of EPBs.

The in situ generation and characteristics of planetary waves (PWs) in the mesosphere and lower thermosphere (MLT) during the January 2021 sudden stratospheric warming (SSW) are investigated using the Navy Global Environmental Model. During SSW, upward-propagating PWs can be absorbed, refracted, or amplified, the latter implying in situ PW generation. Additionally, asymmetric dissipation of gravity wave (GW) drag in the MLT due to varying stratospheric winds may also seed PW generation. Ultimately, the interaction of waves with instability can enhance three components of PWs [westward-propagating PWs (WPWs), quasi-stationary PWs (QSPWs), and eastward-propagating PWs (EPWs)]. The propagation pathway of a wave is diagnosed by its refractive index and is dependent on factors such as the baroclinic/barotropic stability of the atmosphere, the wave's relative phase velocity, and the wavenumber. Through these pathways, waves are able to transfer heat and momentum throughout the atmosphere. Under particular conditions, the waves can amplify in situ by extracting energy from the background wind. Our study identifies two scenarios in which WPWs and EPWs were amplified successively. Amplified WPWs propagated upward and influenced the MLT, while amplified EPWs propagated downward and influenced the upper troposphere.

The virtual temperature used to model moisture-modified tropospheric dynamics is generalized to include a new thermospheric component. The resulting hybrid virtual potential temperature (HVPT) transitions seamlessly with height, from moist virtual potential temperature (MVPT) in the troposphere, to potential temperature in the stratosphere and mesosphere, to thermospheric virtual potential temperature thereafter. For numerical weather prediction (NWP) models looking to extend into the thermosphere, but still heavily invested in retaining MVPT-based dynamical cores for tropospheric prediction, upgrading to HVPT allows the core to capture critical new aspects of variable composition thermospheric dynamics, while leaving the original MVPT-based tropospheric equations and numerics essentially untouched. In this way, HVPT augmentation can both simplify and streamline extension into the thermosphere at little computational cost beyond the inevitable need for more vertical layers and somewhat smaller time steps. To demonstrate, we upgrade the MVPT-based dynamical core of the Navy global NWP model to HVPT, then test its performance in forecasting analytical globally balanced states containing hot or rapidly heated thermospheres and height-varying gas constants. These tests confirm that HVPT augmentation offers an efficient and effective means of extending MVPT-based NWP models into the thermosphere to accelerate development of future ground-to-space NWP models supporting space weather applications. The related issues of variable gravitational acceleration and shallow-atmosphere approximations are also briefly discussed.

The Atmospheric Waves Experiment (AWE) is a new NASA mission aimed at investigating the effects of tropospheric weather on space weather. An Advanced Mesospheric Temperature Mapper (AMTM) airglow imager will be deployed on the International Space Station (ISS) in December 2023. This proven instrument will map the nighttime mesospheric temperature at the altitude of the hydroxyl (OH) layer (~87 km) during two years, providing 2D gravity wave (GW) fields over a 600 km field-of-view, every second.Four state-of-the-art models will also help achieving the three science objectives:Quantify the seasonal and regional variabilities and influences of GWs near the mesopause, Identify the dominant dynamical processes controlling GWs observed near the mesopause, Estimate the wider role of GWs in the Ionosphere-Thermosphere-Mesosphere (ITM). This presentation will give an overview of the AWE mission and describe the future data levels using synthetic images.

The Hunga-Tonga Hunga-Ha'apai volcano underwent a series of large-magnitude eruptions that generated broad spectra of mechanical waves in the atmosphere. We investigate the spatial and temporal evolutions of fluctuations driven by atmospheric acoustic-gravity waves (AGWs) and, in particular, the Lamb wave modes in high spatial resolution data sets measured over the Continental United States (CONUS), complemented with data over the Americas and the Pacific. Along with >800 barometer sites, tropospheric observations, and Total Electron Content data from >3,000 receivers, we report detections of volcano-induced AGWs in mesopause and ionosphere-thermosphere airglow imagery and Fabry-Perot interferometry. We also report unique AGW signatures in the ionospheric D-region, measured using Long-Range Navigation pulsed low-frequency transmitter signals. Although we observed fluctuations over a wide range of periods and speeds, we identify Lamb wave modes exhibiting 295-345 m s(-1) phase front velocities with correlated spatial variability of their amplitudes from the Earth's surface to the ionosphere. Results suggest that the Lamb wave modes, tracked by our ray-tracing modeling results, were accompanied by deep fluctuation fields coupled throughout the atmosphere, and were all largely consistent in arrival times with the sequence of eruptions over 8 hr. The ray results also highlight the importance of winds in reducing wave amplitudes at CONUS midlatitudes. The ability to identify and interpret Lamb wave modes and accompanying fluctuations on the basis of arrival times and speeds, despite complexity in their spectra and modulations by the inhomogeneous atmosphere, suggests opportunities for analysis and modeling to understand their signals to constrain features of hazardous events.

Parameterizations of NO cooling rates in thermospheric models have not changed substantially since the work of Kockarts (1980, https://doi.org/10.1029/GL007i002p0013 ). We investigate three areas to augment the standard parameterization. The first focuses on cooling‐rate contributions from the first NO “hot band.” Arguments concerning the difficulty or irrelevance of parameterizing hot‐band rates are addressed and either refuted or clarified. Parameterized hot‐band cooling peaks during periods of high solar activity, contributing up to 10%–15% additional cooling, in agreement with published line‐by‐line calculations. The second focuses on collisional NO‐O quenching rates. Recent theoretical calculations predict temperature‐dependent rates similar to those seen in collisional CO 2 ‐O quenching rates. Yet available measurements of NO‐O quenching rates do not reveal clear temperature trends. Quenching rates parameterized with and without temperature dependence produce substantially different thermospheric cooling rates. Further research is needed to resolve these discrepancies. The third involves a linearization of parameterized NO cooling rates around a prescribed state, yielding thermal damping rates for use in parameterizations of subgrid‐scale dynamics. Thermal relaxation rates peak at up to 2 days −1 near 140 km, where they are competitive with corresponding rates due to viscous thermal conduction, consistent with the imputed role of NO in regulating thermospheric climate in response to extraterrestrial energy inputs.

The most common boundary condition (BC) imposed at the model top in many nonhydrostatic, height-based models is a rigid lid (no mass-flux) complemented by an absorbing sponge layer. This BC is unphysical and not appropriate for large-scale heating and cooling processes present in the upper atmosphere with a high model top. To address this problem, we have derived a physics-based open atmosphere BC from first principles that allows fluid to smoothly exit and enter the model domain during heating and cooling processes, respectively. The new BC is derived from both the compressible and hydrostatic continuity equation and accounts for bulk and surface heating as well as horizontal divergence by modeling the velocity normal to the model top (vertical velocity). This physics-based BC was implemented in two height-based, spectral element nonhydrostatic atmospheric models and tested on both 1D and 3D atmospheric test cases using two idealized heating tests targeted toward high altitude applications. The numerical results indicate that the BC is stable using explicit, fully implicit, and horizontally explicit, vertical implicit (HEVI) time integrators. Unlike the rigid BC, the proposed BC produces stable numerical results without producing spurious oscillations near the model top. Unlike sponge layers, the proposed BC does not require any tuning parameters since all parameters are consistent with the BCs used in many hydrostatic models.

A general method for computing solutions of systems of linear gravity-wave governing equations, allowing for vertically varying background parameters, is introduced and applied to two sets of governing equations for gravity waves in the thermosphere, both of which include molecular viscosity and thermal diffusion. The first set is fully compressible and the second set is anelastic. In the latter case, a new set of viscous and diffusive anelastic governing equations is given, and an anelastic dispersion relation, previously obtained only as a limiting case of a fully compressible dispersion relation, is shown to follow from the new anelastic governing equations. The new full-wave method is an extension of a numerical multilayer method described previously by Knight et al. (2019). Here, the term "numerical multilayer method"refers to a multilayer method that converges to a solution of an underlying vertical structure equation or system of equations in the limit of infinitesimal layer width. The previously described method was primarily suitable for dispersion-relation partial differential equations (PDEs), solutions of which only give approximate solutions of the underlying governing equations when the background parameters vary. Much of the theory developed for the previous method is still applicable to the new method, with some modifications, including the definition of upgoing and downgoing modes in terms of roots of the dispersion relation and the use of imaginary frequency shifts to make this classification of modes possible in all cases. The practical advantage of solving the anelastic equations instead of the compressible equations is that the needed imaginary frequency shifts are easier to determine in the anelastic case. To simplify the discussion, the application of the new full-wave method to the two sets of governing equations is only worked out for two-dimensional waves in the situation where kinematic viscosity varies but background temperature, scale height (for density), and horizontal wind are constant. Full-wave anelastic and compressible solutions are given for three idealized examples and compared with each other and with anelastic dispersion-relation PDE solutions. It is seen that full-wave anelastic solutions give good approximations of full-wave compressible solutions, while dispersion-relation PDE solutions become increasingly inaccurate with increasing kinematic viscosity for large horizontal wavelengths.(c) 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Recent studies suggest linkages between anomalously warm temperatures in the winter stratosphere, and the high-latitude summer mesopause. The summer temperature anomaly is manifested in the decline of polar mesospheric clouds. The 2-day wave is a strong-amplitude and transient summer feature that interacts with the background state so as to warm the high-latitude summer mesopause. This wave has been linked to a low-latitude phenomenon called inertial instability, which is organized by breaking planetary waves in the winter stratosphere. Hence, inertial instability has been identified as a possible nexus between the disturbed winter stratosphere, and summer mesopause warming. We investigate a sustained occurrence of inertial instability during 19 July–8 August 2014. During this period, stratospheric winter temperatures warmed by about 10 K, while a steep decline in polar mesospheric clouds was reported between 26 July and 6 August. We present, for the first time, wave driving associated with observed inertial instability. The effect of inertial instability is to export eastward momentum from the winter hemisphere across the equator into the summer hemisphere. Using a primitive equation model, we demonstrate that the wave stresses destabilize the stratopause summer easterly jet. The reconfigured wind profile excites the wavenumber-4 component of the 2-day wave, leading to enhanced warming of the summer mesopause. This work supports previous numerical investigations that identified planetary wave–driven inertial instability as a source of the 2-day wave.

Gravity wave (GW) momentum and energy deposition are large components of the momentum and heat budgets of the stratosphere and mesosphere, affecting predictability across scales. Since weather and climate models cannot resolve the entire GW spectrum, GW parameterizations are required. Tuning these parameterizations is time-consuming and must be repeated whenever model configurations are changed. We introduce a self-tuning approach, called GW parameter retrieval (GWPR), applied when the model is coupled to a data assimilation (DA) system. A key component of GWPR is a linearized model of the sensitivity of model wind and temperature to the GW parameters, which is calculated using an ensemble of nonlinear forecasts with perturbed parameters. GWPR calculates optimal parameters using an adaptive grid search that reduces DA analysis increments via a cost-function minimization. We test GWPR within the Navy Global Environmental Model (NAVGEM) using three latitude-dependent GW parameters: peak momentum flux, phase-speed width of the Gaussian source spectrum, and phase-speed weighting relative to the source-level wind. Compared to a baseline experiment with fixed parameters, GWPR reduces analysis increments and improves 5-day mesospheric forecasts. Relative to the baseline, retrieved parameters reveal enhanced source-level fluxes and westward shift of the wave spectrum in the winter extratropics, which we relate to seasonal variations in frontogenesis. The GWPR reduces stratospheric increments near 60°S during austral winter, compensating for excessive baseline non-orographic GW drag. Tropical sensitivity is weaker due to significant absorption of GW in the stratosphere, resulting in less confidence in tropical GWPR values.