Stratospheric gravity wave momentum flux from limb and occultation observations
Atmospheric gravity waves carry momentum from weather systems into the stratosphere and mesosphere, yet most climate models cannot resolve them directly. Satellite limb and occultation observations now make their signatures measurable, if imperfectly.
Sensors
- COSMIC-2 / FORMOSAT-7: Six-satellite GNSS radio occultation constellation operated by NOAA and Taiwan's NSPO. Delivers roughly 5,000 occultation profiles per day, with vertical resolution of approximately 100 m in the stratosphere after Abel inversion. Horizontal resolution along the ray path is 200–300 km, which sets the hard lower bound on detectable horizontal wavelengths.
- Aura MLS (Microwave Limb Sounder): Limb emission sounder on NASA's Aura satellite, measuring temperature and composition from roughly 8 km to 90 km altitude. Vertical resolution near 3–4 km in the stratosphere; horizontal along-track resolution approximately 165–200 km. Used widely for gravity wave temperature variance studies between 20 and 60 km.
- AIRS on Aqua: Nadir-viewing infrared sounder with 2,378 channels across 3.7–15.4 µm. Horizontal footprint of 13.5 km at nadir, but stratospheric weighting functions broaden effective vertical resolution to 6–10 km, limiting sensitivity to longer vertical wavelengths (above roughly 15 km). Useful for mapping horizontal wave structure across wide swaths.
- ICON-MIGHTI: Michelson Interferometer for Global High-resolution Thermospheric Imaging on NASA's ICON satellite. Measures thermospheric winds and temperatures by limb emission at 90–300 km altitude. Provides an upper boundary reference for gravity wave momentum deposition well above the stratopause, complementing MLS and occultation records.
Why a wave that nobody can see controls the stratospheric circulation
The quasi-biennial oscillation, the roughly 28-month alternation of easterly and westerly winds in the tropical stratosphere, cannot be reproduced in general circulation models without parameterised gravity wave drag. The same applies to the sudden stratospheric warmings that periodically collapse the polar vortex and influence surface weather for weeks afterward. Gravity waves are the mechanism: they carry momentum deposited by convection, orography and jet streams upward until the atmosphere can no longer support them, at which point they break and deposit that momentum directly into the mean flow.
The problem is scale. Horizontally, the most dynamically active waves span 100 to 2,000 km. Vertically, their temperature perturbations are often 1–5 K superimposed on a background of 200 K or more. No single sensor captures the full spectrum. Occultation profiles resolve the vertical structure well but integrate over hundreds of kilometres horizontally. Limb sounders see horizontal structure more clearly but smear the vertical. Nadir sounders like AIRS see horizontal patterns across wide swaths but are nearly blind to short vertical wavelengths. Understanding what any given dataset actually shows requires being precise about its observational filter.
What a temperature perturbation profile actually contains
The standard approach to extracting gravity wave signals from an occultation profile is to fit and subtract a smooth background, typically a polynomial or a running mean over several kilometres, and treat the residual as the wave perturbation. COSMIC-2 profiles, after Abel inversion from excess phase, carry vertical resolution of roughly 100 m but horizontal averaging of 200–300 km along the ray. This means the dataset is sensitive to waves with vertical wavelengths above about 2 km and horizontal wavelengths above roughly 100–200 km. Shorter horizontal wavelengths are attenuated by the geometry of the occultation ray, not by any failure of the receiver.
From the perturbation profile, the vertical wavelength can be estimated by Fourier or wavelet analysis. The horizontal wavelength requires either a statistical assumption (isotropy, which is often wrong over mountains or in the tropics) or a multi-profile method using closely spaced occultations. COSMIC-2's constellation geometry occasionally provides pairs or clusters of profiles close enough in space and time to attempt direct horizontal wavelength estimation, but this is the exception rather than the rule.
Pseudo-momentum flux, the quantity that actually enters the momentum budget, is proportional to the square of the temperature perturbation divided by the background temperature, multiplied by a factor derived from the dispersion relation. Computing it requires knowing the intrinsic frequency of the wave, which in turn requires knowing the background wind. Radiosonde climatologies and reanalysis products are typically used for this, introducing uncertainty that is difficult to bound precisely.
Limb radiance as a complementary geometry
Aura MLS observes the atmosphere in emission rather than in transmission, scanning the limb ahead of the satellite. Its along-track horizontal resolution of roughly 165–200 km and vertical resolution of 3–4 km in the stratosphere make it sensitive to a different part of the wave spectrum than occultation. Specifically, MLS is better suited to waves with long vertical wavelengths and can detect temperature variances associated with gravity wave activity throughout the 20–60 km range. Published studies using MLS have mapped the global distribution of stratospheric gravity wave activity, showing the well-known hotspots over the Southern Andes, the Antarctic Peninsula and the Himalayas.
The horizontal structure of waves is more accessible from AIRS, which covers a 1,650 km swath in nadir mode. Horizontal wavelengths down to roughly 50–100 km are detectable in the 4.3 µm CO₂ band channels that peak near 40 km altitude, provided the vertical wavelength is long enough to survive the broad weighting function. The combination of AIRS horizontal mapping and MLS or occultation vertical profiling is a practical, if imperfect, way to constrain both dimensions simultaneously.
Honest limits: what the observational filter hides
Every method described here has a spectral blind spot. Occultation misses short horizontal wavelengths. Limb sounders miss short vertical wavelengths. Nadir sounders miss short vertical wavelengths even more severely. The consequence is that the total momentum flux inferred from any single observing system is an underestimate, and the underestimate is not uniform across latitude or season. Convectively generated waves in the tropics tend to have shorter horizontal wavelengths than orographic waves at high latitudes, so tropical flux estimates suffer disproportionately from the observational filter.
Cloud contamination is not a significant issue for microwave limb sounders or GNSS occultation in the stratosphere, but it does affect the lower stratosphere retrievals from AIRS. More important is the ambiguity in separating gravity waves from planetary (Rossby) waves in the long-wavelength part of the spectrum. The standard practice is to treat perturbations with zonal wavenumbers above roughly 6 as gravity waves and below as planetary waves, but this boundary is physically motivated rather than exact.
Latency is also a practical constraint. COSMIC-2 near-real-time profiles are available within roughly three hours of observation through NOAA's data portal, which is adequate for model assimilation but not for rapid event response. MLS and AIRS science products typically have latencies of one to several days for the fully processed versions.
From profiles to model validation
The primary scientific use of these observations is benchmarking the gravity wave drag parameterisation schemes in atmospheric models, including the non-orographic and orographic schemes in the ECMWF IFS, GFDL AM and UKESM families. The validation workflow compares simulated temperature variance profiles against observed profiles, after applying the model output to the same observational filter that the satellite would impose. Skipping the filter step produces spurious disagreements and is a common methodological error.
Satellize can ingest COSMIC-2 and MLS level-2 products, apply background subtraction and wavelet decomposition, and produce gridded pseudo-momentum flux climatologies or event-specific anomaly maps for clients running or evaluating middle-atmosphere models. The Tonga crop-estimation programme is a different domain, but the underlying workflow, ingesting open constellation data and producing quantitative geophysical outputs for a specific client question, is the same.
For operational forecast centres, the most useful deliverable is a bias map showing where a model's parameterised gravity wave drag systematically over- or under-predicts observed temperature variance, stratified by season and altitude band. That kind of targeted diagnostic is more actionable than a global root-mean-square score.
The near-future: better coverage, same physics
The European Space Agency's Aeolus mission demonstrated that direct wind measurement from orbit is feasible, and its successor concepts aim at stratospheric coverage. Several commercial radio occultation constellations, including Spire Global's LEMUR satellites, are now adding to the profile count available for gravity wave studies, with Spire publishing occultation rates exceeding 10,000 profiles per day across their constellation. More profiles mean better sampling of the wave field's spatial and temporal variability, though the horizontal resolution limit imposed by ray geometry does not improve with constellation size.
The outstanding problem is not data volume. It is the ambiguity between wave parameters that cannot be resolved from single-point or single-track observations. Stereo limb imaging, where two instruments view the same atmospheric volume from different angles simultaneously, could in principle resolve horizontal and vertical wavelengths independently. No operational mission currently does this in the stratosphere, though it has been proposed repeatedly in the literature.
Typical figures
| Vertical resolution (GNSS occultation) | ~100 m after Abel inversion; effective gravity wave sensitivity above ~2 km vertical wavelength |
| Horizontal resolution along ray (GNSS occultation) | 200–300 km; sets lower bound on detectable horizontal wavelength at ~100–200 km |
| Vertical resolution (Aura MLS) | 3–4 km in stratosphere; along-track horizontal ~165–200 km |
| AIRS horizontal footprint | 13.5 km at nadir; stratospheric weighting functions broaden effective vertical resolution to 6–10 km |
| Daily profile count (COSMIC-2) | ~5,000 occultation profiles per day globally |
| Altitude coverage | Occultation: ~5–50 km; MLS: ~8–90 km; AIRS stratospheric channels: ~20–45 km |
| Minimum detectable temperature perturbation | ~0.5–1 K for occultation; ~1–2 K for MLS at stratospheric altitudes (signal-to-noise dependent) |
| Near-real-time latency (COSMIC-2) | ~3 hours from observation to NOAA provisional product |
| Archive depth | COSMIC-1 from 2006; COSMIC-2 from 2019; Aura MLS from 2004; AIRS from 2002 |
| Data formats | NetCDF-4 (COSMIC-2 level-2, MLS level-2, AIRS level-3); HDF-EOS for AIRS level-2 |
Analytics Satellize can run
| Gravity wave temperature variance profiles | Background subtraction (polynomial or running-mean fit) followed by wavelet or Fourier decomposition of COSMIC-2 or MLS level-2 temperature profiles | Gridded NetCDF climatology or event profile set, stratified by altitude and season |
| Pseudo-momentum flux maps | Dispersion-relation inversion using observed perturbation amplitude and vertical wavelength, combined with reanalysis background wind fields; standard method from published literature | Latitude-longitude-altitude gridded flux fields in GeoTIFF or NetCDF, monthly or event-specific |
| Model parameterisation bias diagnostic | Observation-filter-corrected comparison of model temperature variance against satellite-derived variance; filter applied to model output before differencing | Bias map report by altitude band and season, in PDF with supporting data tables |
| Gravity wave hotspot anomaly alerts | Running climatology baseline subtracted from near-real-time COSMIC-2 profiles; threshold exceedance flagged over user-defined regions | Automated alert feed (JSON or email) with profile plots attached |
| Multi-sensor horizontal wavelength estimation | Cross-sensor synthesis of AIRS horizontal wave patterns and MLS or occultation vertical profiles to jointly constrain both wavelength dimensions | Case-study report with wave parameter tables and uncertainty ranges |
| Seasonal gravity wave drag climatology | Multi-year aggregation of pseudo-momentum flux estimates from COSMIC-2 and MLS, binned by latitude, altitude and month | Interactive dashboard or static GIS layers for model development teams |
Who does the work
We can get this done for you. Satellize runs its own analyst desk and a strong science team. You do not buy a data feed and work out what it means; our people source the imagery, run the analysis described on this page, and hand you the answer with its confidence limits stated. Discuss this requirement.