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Abstract We present estimates of gravity wave momentum fluxes calculated from Project Loon superpressure balloon data collected between 2013 and 2021. In total, we analyzed more than 5,000 days of data from balloon flights in the lower stratosphere, flights often over regions or during times of the year without any previous in‐situ observations of gravity waves. Maps of mean momentum fluxes show significant regional variability; we analyze that variability using the statistics of the momentum flux probability distributions for six regions: the Southern Ocean, the Indian Ocean, and the tropical and extratropical Pacific and Atlantic Oceans. The probability distributions are all approximately log‐normal, and using their geometric means and geometric standard deviations we statistically explain the sign and magnitude of regional mean and 99th percentile zonal momentum fluxes and regional momentum flux intermittencies. We study the dependence of the zonal momentum flux on the background zonal wind and argue that the increase of the momentum flux with the wind speed over the Southern Ocean is likely due to a varying combination of both wave sources and filtering. Finally, we show that as the magnitude of the momentum flux increases, the fractional contributions by high‐frequency waves increases, waves which need to be parameterized in large‐scale models of the atmosphere. In particular, the near‐universality of the log‐normal momentum flux probability distribution, and the relation of its statistical moments to the mean momentum flux and intermittency, offer useful checks when evaluating parameterized or resolved gravity waves in models. 

Abstract There are different strategies for training neural networks (NNs) as subgrid‐scale parameterizations. Here, we use a 1D model of the quasi‐biennial oscillation (QBO) and gravity wave (GW) parameterizations as testbeds. A 12‐layer convolutional NN that predicts GW forcings for given wind profiles, when trained offline in abig‐dataregime (100‐year), produces realistic QBOs once coupled to the 1D model. In contrast, offline training of this NN in asmall‐dataregime (18‐month) yields unrealistic QBOs. However, online re‐training of just two layers of this NN using ensemble Kalman inversion and only time‐averaged QBO statistics leads to parameterizations that yield realistic QBOs. Fourier analysis of these three NNs' kernels suggests why/how re‐training works and reveals that these NNs primarily learn low‐pass, high‐pass, and a combination of band‐pass filters, potentially related to the local and non‐local dynamics in GW propagation and dissipation. These findings/strategies generally apply to data‐driven parameterizations of other climate processes. 

Abstract Atmospheric gravity waves (GWs) span a broad range of length scales. As a result, the un‐resolved and under‐resolved GWs have to be represented using a sub‐grid scale (SGS) parameterization in general circulation models (GCMs). In recent years, machine learning (ML) techniques have emerged as novel methods for SGS modeling of climate processes. In the widely used approach of supervised (offline) learning, the true representation of the SGS terms have to be properly extracted from high‐fidelity data (e.g., GW‐resolving simulations). However, this is a non‐trivial task, and the quality of the ML‐based parameterization significantly hinges on the quality of these SGS terms. Here, we compare three methods to extract 3D GW fluxes and the resulting drag (Gravity Wave Drag [GWD]) from high‐resolution simulations: Helmholtz decomposition, and spatial filtering to compute the Reynolds stress and the full SGS stress. In addition to previous studies that focused only on vertical fluxes by GWs, we also quantify the SGS GWD due to lateral momentum fluxes. We build and utilize a library of tropical high‐resolution (Δx = 3 km) simulations using weather research and forecasting model. Results show that the SGS lateral momentum fluxes could have a significant contribution to the total GWD. Moreover, when estimating GWD due to lateral effects, interactions between the SGS and the resolved large‐scale flow need to be considered. The sensitivity of the results to different filter type and length scale (dependent on GCM resolution) is also explored to inform the scale‐awareness in the development of data‐driven parameterizations. 

Abstract. A novel fiber-optic distributed temperature sensing instrument, the Fiber-optic Laser Operated Atmospheric Temperature Sensor (FLOATS), was developed for continuous in situ profiling of the atmosphere up to 2 km below constant-altitude scientific balloons. The temperature-sensingsystem uses a suspended fiber-optic cable and temperature-dependent scattering of pulsed laser light in the Raman regime to retrieve continuous3 m vertical-resolution profiles at a minimum sampling period of 20 s.FLOATS was designed for operation aboard drifting super-pressure balloons inthe tropical tropopause layer at altitudes around 18 km as part of theStratéole 2 campaign. A short test flight of the system was conductedfrom Laramie, Wyoming, in January 2021 to check the optical, electrical, andmechanical systems at altitude and to validate a four-reference temperaturecalibration procedure with a fiber-optic deployment length of 1170 m. During the 4 h flight aboard a vented balloon, FLOATS retrieved temperatureprofiles during ascent and while at a float altitude of about 19 km. TheFLOATS retrievals provided differences of less than 1.0 ∘Ccompared to a commercial radiosonde aboard the flight payload during ascent.At float altitude, a comparison of optical length and GPS position at thebottom of the fiber-optic revealed little to no curvature in the fiber-opticcable, suggesting that the position of any distributed temperaturemeasurement can be effectively modeled. Comparisons of the distributed temperature retrievals to the reference temperature sensors show strongagreement with root-mean-square-error values less than 0.4 ∘C. Theinstrument also demonstrated good agreement with nearby meteorologicalobservations and COSMIC-2 satellite profiles. Observations of temperatureand wind perturbations compared to the nearby radiosounding profiles provide evidence of inertial gravity wave activity during the test flight. Spectral analysis of the observed temperature perturbations shows that FLOATS is an effective and pioneering tool for the investigation of small-scale gravity waves in the upper troposphere and lower stratosphere. 

Abstract Based on 20-day control forecasts by the 9-km Integrated Forecasting System (IFS) at the European Centre for Medium-Range Weather Forecasts (ECMWF) for selected periods of summer and winter events, this study investigates global distributions of gravity wave momentum fluxes resolved by the highest-resolution-ever global operational numerical weather prediction model. Two supplementary datasets, including 18-km ECMWF IFS experiments and the 30-km ERA5, are included for comparison. In the stratosphere, there is a clear dominance of westward momentum fluxes over the winter extratropics with strong baroclinic instability, while eastward momentum fluxes are found in the summer tropics. However, meridional momentum fluxes, locally as important as the above zonal counterpart, show different behaviors of global distribution characteristics, with northward and southward momentum fluxes alternating with each other especially at lower altitudes. Both events illustrate conclusive evidence that stronger stratospheric fluxes are found in the ECMWF forecast with finer resolution, and that ERA5 datasets have the weakest signals in general, regardless of whether regridding is applied. In the troposphere, probability distributions of vertical motion perturbations are highly asymmetric with more strong positive signals especially over latitudes covering heavy rainfall, likely caused by convective forcing. With the aid of precipitation accumulation, a simple filtering method is proposed in an attempt to eliminate those tropospheric asymmetries by convective forcing, before calculating tropospheric wave-induced fluxes. Furthermore, this research demonstrates promising findings that the proposed filtering method could help in reducing the potential uncertainties with respect to estimating tropospheric wave-induced fluxes. Finally, absolute momentum flux distributions with proposed approaches are presented, for further assessment in the future. 

Abstract. Current climate models have difficulty representing realistic wave–mean flow interactions, partly because the contribution from waves with fine vertical scales is poorly known. There are few direct observations of these waves, and most models have difficulty resolving them. This observational challenge cannot be addressed by satellite or sparse ground-based methods. The Strateole-2 long-duration stratospheric superpressure balloons that float with the horizontal wind on constant-density surfaces provide a unique platform for wave observations across a broad range of spatial and temporal scales. For the first time, balloon-borne Global Navigation Satellite System (GNSS) radio occultation (RO) is used to provide high-vertical-resolution equatorial wave observations. By tracking navigation signal refractive delays from GPS satellites near the horizon, 40–50 temperature profiles were retrieved daily, from balloon flight altitude (∼20 km) down to 6–8 km altitude, forming an orthogonal pattern of observations over a broad area (±400–500 km) surrounding the flight track. The refractivity profiles show an excellent agreement of better than 0.2 % with co-located radiosonde, spaceborne COSMIC-2 RO, and reanalysis products. The 200–500 m vertical resolution and the spatial and temporal continuity of sampling make it possible to extract properties of Kelvin waves and gravity waves with vertical wavelengths as short as 2–3 km. The results illustrate the difference in the Kelvin wave period (20 vs. 16 d) in the Lagrangian versus ground-fixed reference and as much as a 20 % difference in amplitude compared to COSMIC-2, both of which impact estimates of momentum flux. A small dataset from the extra Galileo, GLONASS, and BeiDou constellations demonstrates the feasibility of nearly doubling the sampling density in planned follow-on campaigns when data with full equatorial coverage will contribute to a better estimate of wave forcing on the quasi-biennial oscillation (QBO) and improved QBO representation in models. 

Abstract Atmospheric predictability from subseasonal to seasonal time scales and climate variability are both influenced critically by gravity waves (GW). The quality of regional and global numerical models relies on thorough understanding of GW dynamics and its interplay with chemistry, precipitation, clouds, and climate across many scales. For the foreseeable future, GWs and many other relevant processes will remain partly unresolved, and models will continue to rely on parameterizations. Recent model intercomparisons and studies show that present-day GW parameterizations do not accurately represent GW processes. These shortcomings introduce uncertainties, among others, in predicting the effects of climate change on important modes of variability. However, the last decade has produced new data and advances in theoretical and numerical developments that promise to improve the situation. This review gives a survey of these developments, discusses the present status of GW parameterizations, and formulates recommendations on how to proceed from there. 

Abstract The quasi‐biennial oscillation (QBO), a ubiquitous feature of the zonal mean zonal winds in the equatorial lower stratosphere, is forced by selective dissipation of atmospheric waves that range in periods from days to hours. However, QBO circulations in numerical models tend to be weak compared with observations, probably because of limited vertical resolution that cannot adequately resolve gravity waves and the height range over which they dissipate. Observations are required to help quantify wave effects. The passage of a superpressure balloon (SPB) near a radiosonde launch site in the equatorial Western Pacific during the transition from the eastward to westward phase of the QBO at 20 km permits a coordinated study of the intrinsic frequencies and vertical structures of two inertia‐gravity wave packets with periods near 1 day and 3 days, respectively. Both waves have large horizontal wavelengths of about 970 and 5,500 km. The complementary nature of the observations provided information on their momentum fluxes and the evolution of the waves in the vertical. The near 1 day westward propagating wave has a critical level near 20 km, while the eastward propagating 3‐day wave is able to propagate through to heights near 30 km before dissipation. Estimates of the forcing provided by the momentum flux convergence, taking into account the duration and scale of the forcing, suggests zonal force of about 0.3–0.4 m s⁻¹ day⁻¹for the 1‐day wave and about 0.4–0.6 m s⁻¹ day⁻¹for the 3‐day wave, which acts for several days.