scholarly journals Stratospheric gravity-waves over the mountainous island of South Georgia: testing a high-resolution dynamical model with 3-D satellite observations and radiosondes

2020 ◽  
Author(s):  
Neil P. Hindley ◽  
Corwin J. Wright ◽  
Alan M. Gadian ◽  
Lars Hoffmann ◽  
John K. Hughes ◽  
...  
Keyword(s):  
High Resolution ◽  
Southern Ocean ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Wave Activity ◽  
Satellite Observations ◽  
Total Flux ◽  
Mean Flow ◽  
South Georgia ◽  
Momentum Fluxes

Abstract. Atmospheric gravity waves are key drivers of the transfer of energy and momentum between the layers of the Earth’s atmosphere. The accurate representation of these waves in General Circulation Models (GCMs) however has proved very challenging. This is because large parts of the gravity wave spectrum are at scales that are near or below the resolution of global GCMs. This is especially relevant for small isolated mountainous islands such as South Georgia (54° S, 36° W) in the Southern Ocean. Observations reveal the island to be an intense source of stratospheric gravity waves, but their momentum fluxes can be under-represented in global models due to its small size. This is a crucial limitation, since the inadequate representation of gravity waves near 60° S during winter has been linked to the long-standing "cold-pole problem", where the southern stratospheric polar vortex breaks up too late in spring by several weeks. Here we address a fundamental question: when a model is allowed to run at very high spatial resolution over South Georgia, how realistic are the simulated gravity waves compared to observations? To answer this question, we present a 3-D comparison between satellite gravity wave observations and a high resolution model over South Georgia. We use a dedicated high-resolution run (1.5 km horizontal grid, 118 vertical levels) of the Met Office Unified Model over South Georgia and coincident 3-D satellite observations from NASA AIRS/Aqua during July 2013 and June–July 2015. First, model winds are validated with coincident radiosonde observations. The AIRS observational filter is then applied to the model output to make the two data sets comparable. A 3-D S-transform method is used to measure gravity-wave amplitudes, wavelengths, directional momentum fluxes and intermittency in the model and observations. Our results show that although the timing of gravity wave activity in the model closely matches observations, area-averaged momentum fluxes are generally up to around 25 % lower than observed. Further, we find that 72 % of the total flux in the model region is located downwind of the island, compared to only 57 % in the AIRS measurements. Directly over the island, the model exhibits higher individual flux measurements but these fluxes are more intermittent than in observations, with 90 % of the total flux carried by just 22 % of wave events, compared to 32 % for AIRS. Observed gravity wave fluxes also appear to dissipate more quickly with increasing height than in the model, suggesting a greater role for wave-mean flow interactions in reality. Finally, spectral analysis of the wave fields suggests that the model over-estimates gravity wave fluxes at short horizontal scales directly over the island, but under-estimates fluxes from larger horizontal scale non-orographic waves in the region, leading to a lower average value overall. Our results indicate that, although increasing model resolution is important, it is also important to ensure that variability in the background wind vector and role of non-orographic waves are accurately simulated in order to achieve realistic gravity wave activity over the Southern Ocean in future GCMs.

scholarly journals Intercomparison of AIRS and HIRDLS stratospheric gravity wave observations

2018 ◽  
Vol 11 (1) ◽  
pp. 215-232 ◽  
Author(s):  
Catrin I. Meyer ◽  
Manfred Ern ◽  
Lars Hoffmann ◽  
Quang Thai Trinh ◽  
M. Joan Alexander
Keyword(s):  
High Resolution ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Momentum Flux ◽  
Wave Spectrum ◽  
Horizontal Resolution ◽  
Wave Activity ◽  
Large Variability ◽  
Wave Event ◽  
The Waves

Abstract. We investigate stratospheric gravity wave observations by the Atmospheric InfraRed Sounder (AIRS) aboard NASA's Aqua satellite and the High Resolution Dynamics Limb Sounder (HIRDLS) aboard NASA's Aura satellite. AIRS operational temperature retrievals are typically not used for studies of gravity waves, because their vertical and horizontal resolution is rather limited. This study uses data of a high-resolution retrieval which provides stratospheric temperature profiles for each individual satellite footprint. Therefore the horizontal sampling of the high-resolution retrieval is 9 times better than that of the operational retrieval. HIRDLS provides 2-D spectral information of observed gravity waves in terms of along-track and vertical wavelengths. AIRS as a nadir sounder is more sensitive to short-horizontal-wavelength gravity waves, and HIRDLS as a limb sounder is more sensitive to short-vertical-wavelength gravity waves. Therefore HIRDLS is ideally suited to complement AIRS observations. A calculated momentum flux factor indicates that the waves seen by AIRS contribute significantly to momentum flux, even if the AIRS temperature variance may be small compared to HIRDLS. The stratospheric wave structures observed by AIRS and HIRDLS often agree very well. Case studies of a mountain wave event and a non-orographic wave event demonstrate that the observed phase structures of AIRS and HIRDLS are also similar. AIRS has a coarser vertical resolution, which results in an attenuation of the amplitude and coarser vertical wavelengths than for HIRDLS. However, AIRS has a much higher horizontal resolution, and the propagation direction of the waves can be clearly identified in geographical maps. The horizontal orientation of the phase fronts can be deduced from AIRS 3-D temperature fields. This is a restricting factor for gravity wave analyses of limb measurements. Additionally, temperature variances with respect to stratospheric gravity wave activity are compared on a statistical basis. The complete HIRDLS measurement period from January 2005 to March 2008 is covered. The seasonal and latitudinal distributions of gravity wave activity as observed by AIRS and HIRDLS agree well. A strong annual cycle at mid- and high latitudes is found in time series of gravity wave variances at 42 km, which has its maxima during wintertime and its minima during summertime. The variability is largest during austral wintertime at 60∘ S. Variations in the zonal winds at 2.5 hPa are associated with large variability in gravity wave variances. Altogether, gravity wave variances of AIRS and HIRDLS are complementary to each other. Large parts of the gravity wave spectrum are covered by joint observations. This opens up fascinating vistas for future gravity wave research.

scholarly journals Propagation paths and source distributions of resolved gravity waves in ECMWF-IFS analysis fields around the southern polar night jet

2021 ◽  
Vol 21 (24) ◽  
pp. 18641-18668
Author(s):  
Cornelia Strube ◽  
Peter Preusse ◽  
Manfred Ern ◽  
Martin Riese
Keyword(s):  
Southern Ocean ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Lower Stratosphere ◽  
Wave Activity ◽  
Lateral Shift ◽  
Apparent Lack ◽  
Wave Ray ◽  
Propagation Paths ◽  
Wave Momentum

Abstract. In the southern winter polar stratosphere, the distribution of gravity wave momentum flux in many state-of-the-art climate simulations is inconsistent with long-time satellite and superpressure balloon observations around 60∘ S. Recent studies hint that a lateral shift between prominent gravity wave sources in the tropospheric mid-latitudes and the location where gravity wave activity is present in the stratosphere causes at least part of the discrepancy. This lateral shift cannot be represented by the column-based gravity wave drag parameterisations used in most general circulation models. However, recent high-resolution analysis and re-analysis products of the European Centre for Medium-Range Weather Forecasts Integrated Forecast System (ECMWF-IFS) show good agreement with the observations and allow for a detailed investigation of resolved gravity waves, their sources, and propagation paths. In this paper, we identify resolved gravity waves in the ECMWF-IFS analyses for a case of high gravity wave activity in the lower stratosphere using small-volume sinusoidal fits to characterise these gravity waves. The 3D wave vector together with perturbation amplitudes, wave frequency, and a fully described background atmosphere are then used to initialise the Gravity Wave Regional or Global Ray Tracer (GROGRAT) gravity wave ray tracer and follow the gravity waves backwards from the stratosphere. Finally, we check for the indication of source processes on the path of each ray and, thus, quantitatively attribute gravity waves to sources that are represented within the model. We find that stratospheric gravity waves are indeed subject to far (>1000 km) lateral displacement from their sources, which already take place at low altitudes (<20 km). Various source processes can be linked to waves within stratospheric gravity wave (GW) patterns, such as the orography equatorward of 50∘ S and non-orographic sources above the Southern Ocean. These findings may explain why superpressure balloons observe enhanced gravity wave momentum fluxes in the lower stratosphere over the Southern Ocean despite an apparent lack of sources at this latitude. Our results also support the need to improve gravity wave parameterisations to account for meridional propagation.

scholarly journals Gravity waves in the winter stratosphere over the Southern Ocean: high-resolution satellite observations and 3-D spectral analysis

2019 ◽  
Author(s):  
Neil P. Hindley ◽  
Corwin J. Wright ◽  
Nathan D. Smith ◽  
Lars Hoffmann ◽  
Laura A. Holt ◽  
...  
Keyword(s):  
Southern Ocean ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Large Scale ◽  
Southern Andes ◽  
Global Circulation Models ◽  
The North ◽  
Short Timescale ◽  
Momentum Fluxes ◽  
Energy And Momentum

Abstract. Atmospheric gravity waves play a key role in the transfer of energy and momentum between layers of the Earth's atmosphere. However, nearly all Global Circulation Models (GCMs) seriously under-represent the momentum fluxes of gravity waves at latitudes near 60° S. This can result in modelled winter stratospheres that are unrealistically cold – a significant bias known as the "cold-pole problem". There is thus a need for measurements of gravity-wave fluxes near 60S to test and constrain GCMs. Such measurements are notoriously difficult, because they require 3-D observations of wave properties if the fluxes are to be estimated without using significant limiting assumptions. Here we use 3-D satellite measurements of stratospheric gravity waves from NASA's AIRS/Aqua instrument. We present the first extended application of a 3-D Stockwell transform (3DST) method to determine localised gravity-wave amplitudes, wavelengths and directions of propagation around the entire region of the Southern Ocean near 60° S during austral winter 2010. We first validate our method using a synthetic wave field and two case studies of real gravity waves over the Southern Andes and the island of South Georgia. A new technique to overcome wave amplitude attenuation problems in previous methods is also presented. We then characterise large-scale gravity-wave occurrence frequencies, directional momentum fluxes and short-timescale intermittency over the entire Southern Ocean. Our results show that highest wave-occurrence frequencies, amplitudes and momentum fluxes are observed in the stratosphere over the mountains of the Southern Andes and Antarctic Peninsula. However, we find that around 60–80 % of total zonal-mean momentum flux is located over the open Southern Ocean during June–August, where a large "belt" of increased wave-occurrence frequencies, amplitudes and fluxes is observed. Our results also suggest significant short-timescale variability of fluxes from both orographic and non-orographic sources in the region. A particularly striking result is a widespread convergence of gravity-wave momentum fluxes towards latitudes around 60° S from the north and south. We propose that this convergence, which is observed at nearly all longitudes during winter, accounts for a significant part of the under-represented flux in GCMs at these latitudes.

scholarly journals A Comparison between Gravity Wave Momentum Fluxes in Observations and Climate Models

2013 ◽  
Vol 26 (17) ◽  
pp. 6383-6405 ◽  
Author(s):  
Marvin A. Geller ◽  
M. Joan Alexander ◽  
Peter T. Love ◽  
Julio Bacmeister ◽  
Manfred Ern ◽  
...  
Keyword(s):  
High Resolution ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Climate Models ◽  
Radiosonde Data ◽  
Wave Source ◽  
Wide Range ◽  
Momentum Fluxes ◽  
High Resolution Models ◽  
Wave Momentum

Abstract For the first time, a formal comparison is made between gravity wave momentum fluxes in models and those derived from observations. Although gravity waves occur over a wide range of spatial and temporal scales, the focus of this paper is on scales that are being parameterized in present climate models, sub-1000-km scales. Only observational methods that permit derivation of gravity wave momentum fluxes over large geographical areas are discussed, and these are from satellite temperature measurements, constant-density long-duration balloons, and high-vertical-resolution radiosonde data. The models discussed include two high-resolution models in which gravity waves are explicitly modeled, Kanto and the Community Atmosphere Model, version 5 (CAM5), and three climate models containing gravity wave parameterizations, MAECHAM5, Hadley Centre Global Environmental Model 3 (HadGEM3), and the Goddard Institute for Space Studies (GISS) model. Measurements generally show similar flux magnitudes as in models, except that the fluxes derived from satellite measurements fall off more rapidly with height. This is likely due to limitations on the observable range of wavelengths, although other factors may contribute. When one accounts for this more rapid fall off, the geographical distribution of the fluxes from observations and models compare reasonably well, except for certain features that depend on the specification of the nonorographic gravity wave source functions in the climate models. For instance, both the observed fluxes and those in the high-resolution models are very small at summer high latitudes, but this is not the case for some of the climate models. This comparison between gravity wave fluxes from climate models, high-resolution models, and fluxes derived from observations indicates that such efforts offer a promising path toward improving specifications of gravity wave sources in climate models.

scholarly journals Intercomparison of AIRS and HIRDLS stratospheric gravity wave observations

2017 ◽  
Author(s):  
Catrin I. Meyer ◽  
Manfred Ern ◽  
Lars Hoffmann ◽  
Quang Thai Trinh ◽  
M. Joan Alexander
Keyword(s):  
High Resolution ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Momentum Flux ◽  
Wave Spectrum ◽  
Horizontal Resolution ◽  
Wave Activity ◽  
Large Variability ◽  
Wave Event ◽  
The Waves

Abstract. We investigate stratospheric gravity wave observations by the Atmospheric InfraRed Sounder (AIRS) aboard NASA's Aqua satellite and the High Resolution Dynamics Limb Sounder (HIRDLS) aboard NASA's Aura satellite. AIRS operational temperature retrievals are typically not used for studies of gravity waves, because their horizontal resolution is rather limited. This study uses data of a high-resolution retrieval which provides stratospheric temperature profiles for each individual satellite footprint. Therefore the horizontal sampling of the high-resolution retrieval is nine times better than that of the operational retrieval. HIRDLS provides 2D spectral formation of observed gravity waves in terms of along-track and vertical wavelengths. AIRS as a nadir sounder is more sensitive to short horizontal wavelength gravity waves and HIRDLS as a limb sounder is more sensitive to short vertical wavelength gravity waves. Therefore HIRDLS is ideally suited to complement AIRS observations. A calculated momentum flux factor indicates that the waves seen by AIRS contribute significantly to momentum flux, even if the AIRS temperature variance may be small compared to HIRDLS. The stratospheric wave structures observed by AIRS and HIRDLS agree often very well. Case studies of a mountain wave event and a non-orographic wave event demonstrate that the observed phase structures of AIRS and HIRDLS are conform. AIRS has a coarser vertical resolution, which results in an attenuation of the amplitude and coarser vertical wavelengths compared to HIRDLS. However, AIRS has a much higher horizontal resolution and the propagation direction of the waves can be clearly identified in geographical maps. The horizontal orientation of the phase fronts can be deduced from AIRS 3D temperature fields. This is a restricting factor for gravity wave analyses of limb measurements. Additionally, temperature variances with respect to stratospheric gravity wave activity are compared on a statistical basis. The complete HIRDLS measurement period from January 2005 to March 2008 is covered. The seasonal and latitudinal distributions of gravity wave activity as observed by AIRS and HIRDLS fit well. A strong annual cycle at mid and high latitudes is found in time series of gravity wave variances at 42 km, which has during wintertime its maxima and during summertime its minima. During austral wintertime at 60° S the variability is largest. Variations in the zonal winds at 2.5 hPa are associated with large variability in gravity wave variances. Altogether, gravity wave variances of AIRS and HIRDLS are conform and complementary to each other. Thereby large parts of the gravity wave spectrum are covered by joint observations. This opens up fascinating vistas for future gravity wave research.

scholarly journals Stratospheric gravity waves over the mountainous island of South Georgia: testing a high-resolution dynamical model with 3-D satellite observations and radiosondes

2021 ◽  
Vol 21 (10) ◽  
pp. 7695-7722
Author(s):  
Neil P. Hindley ◽  
Corwin J. Wright ◽  
Alan M. Gadian ◽  
Lars Hoffmann ◽  
John K. Hughes ◽  
...  
Keyword(s):  
High Resolution ◽  
Gravity Waves ◽  
General Circulation ◽  
General Circulation Models ◽  
Local Area ◽  
Satellite Observations ◽  
Small Island ◽  
Grey Zone ◽  
Transform Method ◽  
South Georgia

Abstract. Atmospheric gravity waves (GWs) play an important role in atmospheric dynamics but accurately representing them in general circulation models (GCMs) is challenging. This is especially true for orographic GWs generated by wind flow over small mountainous islands in the Southern Ocean. Currently, these islands lie in the “grey zone” of global model resolution, where they are neither fully resolved nor fully parameterised. It is expected that as GCMs approach the spatial resolution of current high-resolution local-area models, small-island GW sources may be resolved without the need for parameterisations. But how realistic are the resolved GWs in these high-resolution simulations compared to observations? Here, we test a high-resolution (1.5 km horizontal grid, 118 vertical levels) local-area configuration of the Met Office Unified Model over the mountainous island of South Georgia (54∘ S, 36∘ W), running without GW parameterisations. The island's orography is well resolved in the model, and real-time boundary conditions are used for two time periods during July 2013 and June–July 2015. We compare simulated GWs in the model to coincident 3-D satellite observations from the Atmospheric Infrared Sounder (AIRS) on board Aqua. By carefully sampling the model using the AIRS resolution and measurement footprints (denoted as model sampled as AIRS hereafter), we present the first like-for-like comparison of simulated and observed 3-D GW amplitudes, wavelengths and directional GW momentum flux (GWMF) over the island using a 3-D S-transform method. We find that the timing, magnitude and direction of simulated GWMF over South Georgia are in good general agreement with observations, once the AIRS sampling and resolution are applied to the model. Area-averaged zonal GWMF during these 2 months is westward at around 5.3 and 5.6 mPa in AIRS and model sampled as AIRS datasets respectively, but values directly over the island can exceed 50 mPa. However, up to 35 % of the total GWMF in AIRS is actually found upwind of the island compared to only 17 % in the model sampled as AIRS, suggesting that non-orographic GWs observed by AIRS may be underestimated in our model configuration. Meridional GWMF results show a small northward bias (∼20 %) in the model sampled as AIRS that may correspond to a southward wind bias compared to coincident radiosonde measurements. Finally, we present one example of large-amplitude (T′≈15–20 K at 45 km altitude) GWs at short horizontal wavelengths (λH≈30–40 km) directly over the island in AIRS measurements that show excellent agreement with the model sampled as AIRS. This suggests that orographic GWs in the full-resolution model with T′≈45 K and λH≈30–40 km can occur in reality. Our study demonstrates that not only can high-resolution local-area models simulate realistic stratospheric GWs over small mountainous islands but the application of satellite sampling and resolution to these models can also be a highly effective method for their validation.

scholarly journals Numerical simulation of mountain waves over the southern Andes, Part 2: Momentum fluxes and wave/mean-flow interactions

2021 ◽  
Author(s):  
David C. Fritts ◽  
Thomas S. Lund ◽  
Kam Wan ◽  
Han-Li Liu
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Acoustic Waves ◽  
Large Scale ◽  
Mean Flow ◽  
Mountain Wave ◽  
Southern Andes ◽  
Mountain Waves ◽  
Momentum Fluxes ◽  
Flow Interactions

AbstractA companion paper by Lund et al. (2020) employed a compressible model to describe the evolution of mountain waves arising due to increasing flow with time over the Southern Andes, their breaking, secondary gravity waves and acoustic waves arising from these dynamics, and their local responses. This paper describes the mountain wave, secondary gravity wave, and acoustic wave vertical fluxes of horizontal momentum, and the local and large-scale three-dimensional responses to gravity breaking and wave/mean-flow interactions accompanying this event. Mountain wave and secondary gravity wave momentum fluxes and deposition vary strongly in space and time due to variable large-scale winds and spatially-localized mountain wave and secondary gravity wave responses. Mountain wave instabilities accompanying breaking induce strong, local, largely-zonal forcing. Secondary gravity waves arising from mountain wave breaking also interact strongly with large-scale winds at altitudes above ~80km. Together, these mountain wave and secondary gravity wave interactions reveal systematic gravity-wave/mean-flow interactions having implications for both mean and tidal forcing and feedbacks. Acoustic waves likewise achieve large momentum fluxes, but typically imply significant responses only at much higher altitudes.

scholarly journals Gravity waves in the winter stratosphere over the Southern Ocean: high-resolution satellite observations and 3-D spectral analysis

2019 ◽  
Vol 19 (24) ◽  
pp. 15377-15414 ◽  
Author(s):  
Neil P. Hindley ◽  
Corwin J. Wright ◽  
Nathan D. Smith ◽  
Lars Hoffmann ◽  
Laura A. Holt ◽  
...  
Keyword(s):  
Southern Ocean ◽  
Gravity Wave ◽  
Gravity Waves ◽  
General Circulation ◽  
Large Scale ◽  
General Circulation Models ◽  
Southern Andes ◽  
The North ◽  
Short Timescale ◽  
Momentum Fluxes

Abstract. Atmospheric gravity waves play a key role in the transfer of energy and momentum between layers of the Earth's atmosphere. However, nearly all general circulation models (GCMs) seriously under-represent the momentum fluxes of gravity waves at latitudes near 60∘ S, which can lead to significant biases. A prominent example of this is the “cold pole problem”, where modelled winter stratospheres are unrealistically cold. There is thus a need for large-scale measurements of gravity wave fluxes near 60∘ S, and indeed globally, to test and constrain GCMs. Such measurements are notoriously difficult, because they require 3-D observations of wave properties if the fluxes are to be estimated without using significant limiting assumptions. Here we use 3-D satellite measurements of stratospheric gravity waves from NASA's Atmospheric Infrared Sounder (AIRS) Aqua instrument. We present the first extended application of a 3-D Stockwell transform (3DST) method to determine localised gravity wave amplitudes, wavelengths and directions of propagation around the entire region of the Southern Ocean near 60∘ S during austral winter 2010. We first validate our method using a synthetic wavefield and two case studies of real gravity waves over the southern Andes and the island of South Georgia. A new technique to overcome wave amplitude attenuation problems in previous methods is also presented. We then characterise large-scale gravity wave occurrence frequencies, directional momentum fluxes and short-timescale intermittency over the entire Southern Ocean. Our results show that highest wave occurrence frequencies, amplitudes and momentum fluxes are observed in the stratosphere over the mountains of the southern Andes and Antarctic Peninsula. However, we find that around 60 %–80 % of total zonal-mean momentum flux is located over the open Southern Ocean during June–August, where a large “belt” of increased wave occurrence frequencies, amplitudes and fluxes is observed. Our results also suggest significant short-timescale variability of fluxes from both orographic and non-orographic sources in the region. A particularly striking result is a widespread convergence of gravity wave momentum fluxes towards latitudes around 60∘ S from the north and south. We propose that this convergence, which is observed at nearly all longitudes during winter, could account for a significant part of the under-represented flux in GCMs at these latitudes.

scholarly journals Influence of the cloud-level neutral layer on the vertical propagation of topographically generated gravity waves on Venus

2019 ◽  
Vol 71 (1) ◽  
Author(s):  
Takeru Yamada ◽  
Takeshi Imamura ◽  
Tetsuya Fukuhara ◽  
Makoto Taguchi
Keyword(s):  
Layer Thickness ◽  
Gravity Wave ◽  
Local Time ◽  
Gravity Waves ◽  
Analytical Approach ◽  
Wave Activity ◽  
Neutral Layer ◽  
Low Latitudes ◽  
Vertical Propagation ◽  
The Waves

AbstractThe reason for stationary gravity waves at Venus’ cloud top to appear mostly at low latitudes in the afternoon is not understood. Since a neutral layer exists in the lower part of the cloud layer, the waves should be affected by the neutral layer before reaching the cloud top. To what extent gravity waves can propagate vertically through the neutral layer has been unclear. To examine the possibility that the variation of the neutral layer thickness is responsible for the dependence of the gravity wave activity on the latitude and the local time, we investigated the sensitivity of the vertical propagation of gravity waves on the neutral layer thickness using a numerical model. The results showed that stationary gravity waves with zonal wavelengths longer than 1000 km can propagate to the cloud-top level without notable attenuation in the neutral layer with realistic thicknesses of 5–15 km. This suggests that the observed latitudinal and local time variation of the gravity wave activity should be attributed to processes below the cloud. An analytical approach also showed that gravity waves with horizontal wavelengths shorter than tens of kilometers would be strongly attenuated in the neutral layer; such waves should originate in the altitude region above the neutral layer.

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