# Assessment of middle atmosphere climatology using lidar for aerospace applications

Nicolas Gilbert Tufel<sup>a,c,*</sup>, Philippe Keckhut<sup>a</sup>, Laurent Dumas<sup>b</sup>, Alexis Mariaccia<sup>a</sup>, Mustapha Meftah<sup>a</sup>, Yann Courcoux<sup>c</sup>, Marie Vicomte<sup>c</sup>, Alain Hauchecorne<sup>a</sup>

Received 18 November 2024; received in revised form 30 May 2025; accepted 2 June 2025

Available online 6 June 2025

## Abstract

This study evaluates temperature and density variations in the upper stratosphere and in the mesosphere using ERA-5 and NRLMSISE-2.0 models, by comparing them with our forty-years long temperature lidar observations. NRLMSISE-2.0, while reliable in terms of seasonal trends, is less accurate daily: it shows high biases with the lidar at high altitudes (globally less than 4 K below 50 km, up to 14 K at 80 km). The European Climate and Weather Forecast reanalysis model ERA-5 shows a bias to the lidar of –5 K the upper stratosphere but shows a larger difference reaching +20 K in the mesosphere. Lidar observations can reveal non-Gaussian distributions because of extreme events, such as Mesospheric Inversion Layers (MILs), minor and Major Sudden Stratospheric Warming (m- and M-SSWs) or Double Stratopauses (DSs). These events are atmospheric particularities which should not be mixed with steady-state profiles to compute a mean climatology if the aim is to create a reference. To address this issue, a new methodology was developed to remove those events, resulting in what we called "Steady-State" climatology. Our method based on lidar observation in four sites (Observatory of Haute-Provence, Reunion Island, Table Mountain and Mauna Loa) allowed us to give statistical information about these extreme phenomena. Furthermore, our findings show that when m-SSWs and MILs occur, the density profile deviates strongly from the NRLMSISE-2.0 density, which highlights the need for refined atmospheric models for aerospace applications. Corresponding density differences between NRLMSISE and lidar can reach –15% and +25% at most for MILs and m-SSWs, respectively.
© 2025 The Author(s). Published by Elsevier B.V. on behalf of COSPAR. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

**Keywords:** Lidar; Mesosphere; Mesospheric Inversion Layer (MIL); Sudden Stratospheric Warming (SSW); Re-entry; Density and temperature of the middle atmosphere

## 1. Introduction

The atmospheric state is only one of several sources of uncertainty in re-entry analysis, but it remains essential to evaluate and improve atmospheric knowledge and models, especially because data with good resolution are scarce for temperature and density. Although advances in atmospheric modelling have improved the general understanding of the mesosphere, some aspects in the middle

<footnote><sup>a</sup> Université de Versailles Saint-Quentin-en-Yvelines (UVSQ), Université Paris-Saclay, Sorbonne Université (SU), CNRS, Laboratoire Atmosphères, Observations Spatiales (LATMOS), 11 Boulevard d'Alembert, Guyancourt 78280, Île-de-France, France</footnote>

<footnote><sup>b</sup> Unité de formation et de recherche (UFR) de Versailles-Saint-Quentin, 45 Av. des États Unis, Versailles 78000, Île-de-France, France</footnote>

<footnote><sup>c</sup> Direction Générale de l'Armement, 60 Boulevard du Maréchal Martial Valin, Paris XV 75015, Île-de-France, France</footnote>

<footnote><sup>a</sup> Corresponding author at: Université de Versailles Saint-Quentin-en-Yvelines (UVSQ), Université Paris-Saclay, Sorbonne Université (SU), CNRS, Laboratoire Atmosphères, Observations Spatiales (LATMOS), 11 Boulevard d'Alembert, Guyancourt 78280, Île-de-France, France.

**E-mail address:** nicolas.tufel@latmos.ipsl.fr (N.G. Tufel).</footnote>
atmosphere remain insufficiently characterised, introducing potential risks for re-entry operations: for instance, long-term mesospheric trends, the influence of solar activity on mesospheric conditions through atmospheric tides, the formation and spatial extent of Mesospheric Inversion Layers (MILs) the triggering conditions of polar vortex breaking, or the general dynamics and variability of gravity waves in the mesosphere are still actively researched (Sheppard, 1959; Cnossen et al., 2024; Lastovicka, 2006; Hoffmann et al., 2011; Butler et al., 2015; Fritts et al., 2018). Research on such topics can only advance thanks to sufficiently vertically-resolute measurements, which current satellite data do not provide, or with large biases due to the average over the line of sight of limb sounders like SABER (Funatsu et al., 2016; Wing et al., 2018). A more precise understanding of atmospheric parameters at these altitudes would benefit re-entry models. Middle atmosphere variability is primarily driven by waves inducing continuous small-scale fluctuations (≈ 1K) around the mean, such as gravity waves propagating vertically (Wilson et al., 1990; Wilson et al., 1991; Hauchecorne et al., 1994). Some of them can reach up to 1 K, or 2 K in the stratopause, and even more while propagating in the higher-mesosphere, but this is especially the case for waves close to the polar night jet circulation (Kogure et al., 2017; Duck et al., 2001; Kogure et al., 2018; Ehard et al., 2015). Some gravity waves in extreme and very specific situations can due to orographic phenomena and without breaking reach +8 K under 80 km and up to +35 K in the high-mesosphere (85-100 km) (Taylor et al., 2019). However, their mean impact can be estimated to be less than 1-2 K as stated by Mzé et al. (2014). These fluctuations contribute to geophysical noise without altering mean climatology, unless they break, in which case they introduce a lasting effect (Sheppard, 1982; Holton, 1983; Fritts and Alexander, 2003). However, other long-lasting temperature deviations —spanning several days to weeks — can generate vertical profiles that diverge significantly from climatological expectations (10–50 K) (Angot et al., 2012). Such systematic deviations create bimodal distributions. Ground-based measurements help mitigate observational satellite limitations, which can miss some extreme phenomena occurring because of their coarser resolution.

Until recent times, atmosphere modelling for object re-entry focused mainly on the notion of standard atmosphere, i.e. an idealised representation of various parameters (temperature, pressure, density), rather than on a full time-dependent numerical model of the atmosphere (Regan and Anandakrishnan, 1993). One of the first of such climatologies was proposed by Penndorf (1946). It was based principally on physical models and not on observations (Atmospheric Standard Conditions). Backed by falling sphere probe experiments, the US Standard Atmosphere published in 1976 then became the reference for re-entry (Johnson, 1976). After this model, the COSPAR International Reference Atmosphere, CIRA-86 was devised. It integrated radar as well as stratospheric balloon

measurements, and allowed users to account for both seasonality and latitude parameters (Fleming et al., 1986). In parallel of the development of those standard atmospheres, NASA perfected a mean-climatology model which served first the purpose of describing satellite environments, MSIS (Mass Spectrometer Incoherent Scatter, which later expanded to lower layers and thus described more accurately the thermosphere and mesosphere (Hedin, 1987)). Through the 90s, it became the reference for those layers, and was refined with other experimental data to become first MSIS-90 and then NRLMSIS00, 2.0, and finally 2.1 (Picone et al., 2002; Guo et al., 2024). NRLMSISE-2.0 was validated by multiple satellite data and Na-Doppler lidar, but not with Rayleigh lidar (Emmert et al., 2020). Recently, these models were incorporated in re-entry modelling, for instance in the last version of the satellite re-entry model of the French Spatial Agency, DEBRISK v3 (Annaloro et al., 2024).

In 'standard atmospheres' and early climatology models, the range of possible temperature could amount up to 50 K around the highest altitudes, providing little information on the reality of conditions that take place daily in those environments (Meriwether and Gardner, 2000; Johnson et al., 2002). An interesting alternative to study the middle-atmosphere parameters is the Rayleigh-scattering lidar. This laser-based instrument, which can be set up on a ground station or embarked on a ship, measures the density and temperature from 30 and up to 85 km. It is thus one of the only means to obtain almost continuous upper-stratospheric and mesospheric data points. Around the globe, few lidars have been able to acquire enough temperature and density data to compute an accurate climatology: the Observatory de Haute-Provence (South of France, OHP), Maido (La Reunion Island, Indian Ocean), Mauna Loa (Hawaii) and Table Mountain (California) stations are among them (De Mazière et al., 2018). Of course, this climatology retrieved from lidar fails to capture any spatial dependency of observed profiles. However, it has proven useful for the description of both the general state of the middle atmosphere, in particular the polar vortex formation, the mesospheric winter circulation, and annual and semi-annual cycles going through the atmosphere layers in low and high-latitude regions (Hauchecorne et al., 1991; She et al., 1995; Leblanc et al., 1998). In addition, such direct observational data have allowed the validation of models, in particular CIRA-86 (Chanin et al., 1990). New instrumentation such as the Doppler-Rayleigh wind-Lidar located at the same place in OHP and Reunion provides new insights on the atmosphere composition and chemical transport, but they only work simultaneously during measurement campaigns (Ratynski et al., YYYY).

Nonetheless, few analyses of the accuracy of temperature climatology and models in the middle-atmosphere has been done, by lack of vertically-resolute instruments. Indeed, the previously designed climatology computed as a pure mean of all retrieved temperature profiles does not
represent an accurate view. Instead, it integrates extreme events that introduce a bias both in the mean temperature and the standard deviation. This bias is problematic because the distribution of those events could skew the climatology. In fact, some of them contribute almost exclusively to increasing and others to decreasing the average temperature, such as major and minor Sudden Stratospheric Warming (M-SSWs and m-SSWs), Mesospheric Inversion Layers (MILs) and Double Stratopauses (DS) (Hitchman et al., 1988; Meriwether and Gardner, 2000; Charlton and Polvani, 2007). This can cause the distribution of temperature at some given altitudes to divert from the Gaussian distribution. Major and minor SSWs are known to contribute to warming the stratopause but cooling down higher altitudes, while MILs are thought to contribute to warm layers above 70 km. The breaking and damping of gravity waves, as discussed above, also adds an additional degree of uncertainty to this layer (Holton, 1983; Hauchecorne et al., 1987; Fritts and Alexander, 2003). Unfortunately, the contribution of those events is barely known or quantified, because it occurs above 40 km and falls out of model validated ranges. The European Center for Meteorological and Weather Forecast (ECMWF) ERA-5 re-analyses was evaluated by Mariaccia et al. (2022): in winter, the variability observed by lidar, even during sudden stratospheric warming (SSWs) events, was reproduced accurately by the model in the upper stratosphere, but not higher, which means that the events occurring over this altitude are limitedly accounted for.

Our study wishes to take a first step in the quantification of the error on the atmospheric density. Atmospheric density and temperature biases are rarely assessed for re-entry purposes, for two reasons: the lack of resolute density data, and the hypothesis it is negligible for operational purposes. Let us mention only that upper atmosphere density variations are sometimes considered in order to monitor drag and re-entry of low orbits satellites (Yurasov et al., 2008; Leonard et al., 2012). Therefore, we advocate that a new methodology to provide accurate information of the middle and upper-atmosphere should be computed. It should take into account separately random geophysical variability and extreme phenomena like m-SSWs, MILs and DSs. Comparing the result of this "Steady State" profile selection to the classical climatology method or reanalysis models could prove interesting, given that they often fail to take into account these extreme events (Mariaccia et al., 2022).

This article aims at calling into question current climatology methods and models and developing a new lidar temperature climatology by accounting for extreme events like DSs, MILs and m-SSWs in the upper-stratosphere and the mesosphere. To do so, this study will first describe the dataset we used (Section 2), then the methods (Section 3). It will endeavour to demonstrate how models (ERA-5 and MSIS 2.0) deviate from Rayleigh lidar observations and cannot detect some extreme phenomena to justify

our use of this instrument in the rest of the study (Section 4). The large amount of profiles acquired by the lidar in four sites will help us discriminate profiles based on their nature (steady state profiles or extreme phenomena) in order to account for their impact on temperature (Section 5) and density for aerospace application (Section 6), thus demonstrating the possible challenge represented by the limited representation of the middle atmosphere for vehicle re-entry. The last section (Section 7) will discuss perspectives and lay out possible work ahead.

## 2. Data description

### 2.1. LIDAR

The temperature and density profiles in this study are obtained from Rayleigh lidar observations from different sites throughout the world. Using the beam of a monochromatic laser pointed at the sky, this instrument measures the back-scatter of light pulse along a vertical air column. Using a photomultiplier, the detector samples the echo, counting the pulses of photons travelling back, and this quantity is proportional to the air density. An assumption made on the state of the atmosphere as a perfect gas at hydrostatic equilibrium makes it possible to retrieve the absolute temperature of different layers. The hydrostatic equilibrium is supposed to be established given that the integration time of the lidar is about an hour or more as described by Hauchecorne et al. (1991). The method uses the pure molecular back-scatter, which means that the minimal observed altitudes are above the domain of aerosol scattering, around 25 km. To avoid saturation of the photomultiplier, the stronger scattering under 30 km is cut. Finally, the main error made on density and temperature measurements is due to the number of photons collected, and is expected to follow a Poisson-law. Due to the atmospheric density decreasing exponentially with altitude, the instrument is vertically limited to typically 85–90 km depending on the specific design of each instrument, including the laser power and the size of the receiver. Multiple references already describe in details the principle, the functioning and the abilities of this instrument. Temperature is retrieved absolutely with an approximation of ideal gas law, but density data have to be normalized by a reference value because absolute density cannot be measured (here, MSIS-90 absolute density at 40 km altitude is used) (Hauchecorne and Chanin, 1980).

Lidar was historically used for stratospheric ozone monitoring from the 1990s within the dedicated network called the Network for the Detection of Stratospheric Changes (NDSC), later within the Network for the Detection of Atmospheric Composition Changes (NDACC) with a wider scope (Kurylo, 1991; De Mazière et al., 2018). Thanks to this worldwide network, many additional Rayleigh-lidar observations have been made available freely, from sites including Ny Alesund and Andøya in Scandinavia, Hohenpeissenberg in Germany, Dome C
and Dumont d'Urville in Antarctica, Mauna Loa and Table Mountain in the US, Lauder in New-Zeland, Rio Gallegos in Argentina and the Observatory of Haute Provence and Maido in France. Ballistic missile re-entry uses data of the middle atmosphere, and as a result France has developed lidar observation capacity at the launch site called Centre d'Éssai des Landes (CEL) close to Bordeaux for 8 years (1984–1992) and the military ship Monge sailing in the Atlantic Ocean (Wing et al., 2021; Keckhut et al., 1993). Even if they can prove useful as a comparison to existing atmospheric models or for case studies, military observations cannot be used for climatology like ground-based stations because of the large and incoherent area covered by the ship, and of the relative short time-span during which the CEL operated.

**NDACC Lidar.** Historically, this network was formed around concern-driven scientists willing to target the hazardous ozone layer depletion, as well as a way to coordinate the validation of the Upper Atmosphere Research Satellite (UARS) instruments launched by NASA (Dessler et al., 1998). This network proved useful to the co-development of various breakthrough technologies and the coordination around prototypes of lidar. As such, many instruments have been operated routinely since 1991 from sites located from the poles to the tropics. Temperature had then appeared to be a critical parameter because ozone balance is strongly correlated with temperature through UV absorption and ozone dissociation effects (Brasseur and Solomon, 2005). These data, though owned on every site, are made available by a common database by the NDACC. Such data is then interpolated to a one-kilometre scale with a Hann filter and then uploaded to an open access dataset online that regroups most of stratospheric lidars around the world (De Mazière et al., 2018).

The uncertainty of measurement is dependant exponentially on the altitude and it varies from 1 K at the lowest boundary (30 km) to 3 K at the highest boundary (90 km). The observation also includes an error due to the initialisation, where a "seeding" value of pressure at the top of the profile (90–100 km depending on the lidar) is given by CIRA-86 or MSIS-90: the initialisation error is assessed to be 15% at initialisation level (Hauchecorne and Chanin, 1980). The bias then reduces when the altitude is decreasing, and it eventually amounts to only less than 2 K at 15 km below the initial height (that is around 70–80 km) (Keckhut et al., 1993). At that point the lidar measurement error is then greater in magnitude (She et al., 1995; Picone et al., 2002). Even with these uncertainties and biases, lidar data are deemed to accurately reflect the state of both density and temperature in its range owing to validation campaigns and cross-instrument exercises and satellite observations (Kurylo, 1991; Wing et al., 2020; Singh et al., 1996). The quality of lidar NDACC data is ensured by regular exercises (Keckhut et al., 2004), including software comparisons and sensitivity tests (Leblanc et al., 1998), satellite comparisons such as geographical transfers (Wild et al., 1995; Keckhut et al.,

2011) as well as inter-comparisons on site with a mobile lidar or other lidar sites (Margitan et al., 1995; Singh et al., 1996; MacPeters et al., 1999; Wing et al., 2020).

One of the longest lidar temperature series was obtained at the Observatory of Haute-Provence (OHP) registering systematic observations continuously since 1979. Laser pointing is typically performed there 20–25 days a month, because it can only operate with clear weather. They are acquired for a couple of hours around the same time of night, depending on the season, around 8 pm for OHP. The time span of this acquisition and the consistent time at which measurements are made with the lidar are such that the tidal effects are deemed negligible(Lindzen and Chapman, 1969; Keckhut et al., 2014; Keckhut et al., 1996; Jaya Prakash Raju, 2010). ERA-5 analyses chosen at the same hour as the lidar would thus not show too much of bias to the lidar due to atmospheric tide, but NRLMSISE-2.0 used satellite data which were not always at the same time of day, making it more subject to the tide. As a consequence of the acquisition time, only one profile is obtained every measurement night. Table 1 presents specifications of all four lidars used in this study (Keckhut et al., 2011).

## 2.2. Data from models

**Historic.** Middle Atmosphere models used as a reference were known as the US Standard atmosphere (1962 and 1972) (Johnson, 1976). They were based on rocket observations (Keckhut et al., 1999), leading to vertical temperature distribution using analytical functions for different latitudes. The 1972 version also included some information about the daily atmospheric variability. With the first space observations providing a global coverage (Gille et al., 2024) an atmospheric model has been developed under the framework of the COSPAR consortium based on data interpolation (Fleming et al., 1986). In addition to the new data from space, it included vertical fluctuations with latitude, longitude and season. Later, an improved version called MSIS was developed by Hedin (1991) using a thermosphere model and analytic functions. These models are statistical models providing the mean state of the atmosphere. This means they cannot reproduce the daily random variability.

To access knowledge on the daily variability in the middle and upper atmosphere (Charlton-Perez et al., 2013), chemistry-climate atmospheric models were developed with an altitude grid spanning up to the upper mesosphere. However, while these models exhibit a realistic variability, temperature evolutions above 50 km remain statistical in nature because they do not integrate data above the stratosphere. This is for instance the case for the model developed by the European Centre of Meteorology and Weather Forecast (ECMWF).

**NRLMSISE-2.0.** NRLMSISE-2.0 data is the latest product of NASA's model for upper-atmosphere and thermosphere. It consists primarily in a semi-statistical model that incorporates rocket, satellite, balloons, reanalysis data, NA-
<table><caption>Table 1
Characteristics of the lidars used in this study.</caption><thead><tr><th>Category</th><th>OHP</th><th>Table Mountain</th><th>Reunion Island</th><th>Mauna Loa</th></tr></thead><tbody><tr><td>Coordinates</td><td>44°N,6°E</td><td>34°N,111°W</td><td>21°S,55°E</td><td>19°N,155°W</td></tr><tr><td>Activity</td><td>1984–2023</td><td>1986–2013</td><td>1992–2023</td><td>1993–2013</td></tr><tr><td>Total Number of Profiles</td><td>4379</td><td>2441</td><td>1766</td><td>2504</td></tr><tr><td>Altitudes (km)</td><td>(30–90)</td><td>(25–90)</td><td>(30–75)</td><td>(25–90)</td></tr><tr><td>Typical integration time (hours)</td><td>4</td><td>Unspecified (≥1)</td><td>1–4</td><td>Unspecified (≥1)</td></tr><tr><td>Vertical resolution (km)</td><td>0.5</td><td>0.3</td><td>0.5</td><td>0.3</td></tr><tr><td>Temporal resolution (minutes)</td><td>5</td><td>5–120</td><td>5</td><td>5–120</td></tr></tbody></table>

lidar data and interpolates/extrapolates these data on other time and locations (Emmert et al., 2020). The principal measurements done to develop this model were acquired between 1965–1983 with various instruments ranging from incoherent scatter radar (ISR) to mass spectrometer and solar ultraviolet (UV) occultation, along with pressure gauge or falling sphere (Emmert et al., 2020). The latest additions to the 2.0 version include among others, a better modelling of the solar flux (Hedin, 1987; Picone et al., 2002; Emmert et al., 2020). As an input to the model, an approximation of the geomagnetic potential and a value of the solar flux are needed, and they are available on the NOAA website (NOAA, 2024). Comparison with a consistent long series of lidar measurements throughout the year in the upper-stratosphere and mesosphere has not been published yet with this new iteration of the model, even though temperature comparison were done with both satellite observations and NA-lidar in the mesosphere (Emmert et al., 2020).

ECMWF reanalysis product (ERA-5). ERA-5.0 Reanalysis dataset is the latest product of the ECMWF and consists in numerical modelling of past atmospheric states from the last 80 years. Using data throughout the world and at most altitudes, up to 40–45 km, the reanalyses use a numerical hydrostatic model incorporating observation data to obtain a continuous dataset on 137 levels above ground throughout the world, with a grid of 0.25° of latitude and longitude (Hersbach et al., 2020). For our case and like Gisinger et al. (2022), we downloaded the reanalysis at the same time as the beginning of the lidar measurement. We chose to average the nine grid points spatially closest to each Lidar. For the temperature profiles in particular, it had been shown in previous articles that ERA-5 simulations reproduced rather well the profile behaviour in terms of variation to the daily mean temperature under 45 km for sites at mid-latitudes (Mariaccia et al., 2022). However, the difference between ERA-5 and the lidar in terms of amplitude throughout the year and the whole mesosphere had not been shown.

# 3. Methods

## 3.1. Definition and detection algorithms of tackled middle atmosphere phenomena

Sudden Stratospheric Warming (SSW). Definition: SSWs are recurring phenomena that occur mostly during

winter in the Northern Hemisphere. During winter, a northern polar vortex of eastward jet-stream wind forms above the Arctic Sea at stratospheric altitudes. Through a process that is not completely understood, but believed to be caused by wave-mean flow interactions which interact with this wind and slow it down, the polar vortex can be shifted outwards from the centre (the pole) or broken, sometime into two or more pieces, which results in large increases in temperature (10–60 K) over a long time-scale as shown in Fig. 1a (Von Zahn et al., 1998). SSWs appear to have happened over many winters ever since this event could be recorded (SSWC, 2024). The definition of SSWs by the Weather Meteorological Office (WMO) is the inversion of the mean zonal wind at 60 degrees North at 10 hPa (Butler et al., 2015). However, this definition does not account for all phenomena inducing a warming at the mid-latitude stratopause during winter. Indeed, the polar vortex can be shifted outwards the pole, without breaking, and still inducing a warming of the stratopause altitude (Maury et al., 2016). The WMO had issued a purely local definition of +25 K of warming in a week or less at any latitude in the winter stratosphere in McInturff (1978). However, ever since, some proposals of definitions have been made using the slowing of the polar vortex wind, along with local definitions: there is overall no clear and accepted consensus (Butler et al., 2015). In this article we shall then discuss the denominations Major SSW (M-SSW), as the SSWs registered by the WMO, and the minor SSWs (m-SSWs), which we define as local winter warming of the stratopause that exceed a standard deviation of the mean temperature.

Detection: However, SSWs do not impact the winter climatology the same way at all sites. The OHP might be too far to use a detection method based on the zonal wind mean. As a result, to detect m-SSWs, we followed a method inspired from Angot et al. (2012) and which consider only the anomaly in warmth at the stratopause. In Angot’s paper, temperature extremes outside one standard-deviation around the average profile were studied: authors concluded that this fraction of extreme warm profiles were not linked to radiative processes and standard dynamical activity. Therefore, to detect the m-SSWs, the temperature profiles are averaged to obtain a climatology (as explained below), and a sinusoidal fit is applied to determine and remove the annual component linked to the seasonal cycle.
<figure><img src="image_1.png" /><figcaption>Fig. 1. Representation of events tackled in this article. Example of (a) the shape of a m-SSW from a profile at OHP on 1st January 1987 at 7 PM and well reproduced by ERA5 (as suggested by Mariaccia et al. (2022)) but not by NRLMMSISE-2.0 (at that time of year, a M-SSW was registered by SSWC (2024). Example of (b) a DS from a profile at OHP on 16th February 1988 at 6PM. Example of (c) the shape of a MIL from a profile at OHP on 26th December 1989 at 5PM, maybe coupled to a SSW (Note how ERA-5 reanalysis fails both to reproduce the stratopause point and to place correctly the temperature enhancement).</figcaption></figure>

Following Angot's study, we then study temperature anomalies on a 2D histogram for the temperature values between 30 and 50 km on a sliding window of 30 days. A 2D Gaussian function of the following form is then fitted to the histogram for each altitude level:

$$P(x, y) = \|A\| \exp \frac{(x - \mu_0)^2}{\sigma} \quad (1)$$

The standard deviation is then used to select each profile: if any of the values between 30 and 50 km are found outside one standard deviation of the Gaussian parametrisation, it is selected as a m-SSW.

**Double Stratopause (DS).** **Definition:** DSs are a phenomenon during which the stratopause structure appears to exhibit two maxima as shown in the example in Fig. 1b. In such cases, the two different stratopauses are separated in average by 10 km (Sivakumar et al., 2006). Only a few papers in the literature address this subject because it is generally deemed to be caused only by the passage of planetary or gravity waves (Hitchman et al., 1988). Some authors suggested it might be linked to the state of the atmosphere after a SSW (Okui et al., 2021). This theory is challenged by reports of frequent detections of DSs in low-latitudes regions far from the poles.

**Detection:** In this study, we scanned the temperature profile, detecting the first temperature peak, and registering temperature points higher in altitude while staying above 90% of the first peak, until finding a second maximum or reaching 60 km.

**Mesosphere Inversion Layers (MIL).** **Definition:** MILs are defined as layers of increasing temperature in the mesosphere, which divert from the expected negative temperature gradient, as seen in Fig. 1c (Fritts et al., 2018). Those structures were first detected during atmospheric study using rockets by Schmidlin (1976). They are often observed at night and at all latitudes, from the near equatorial Reunion Island to the mid-latitude OHP. Because lidar detects vertical variations but not horizontal or temporal variations, little is known about the time-span and the space extent of this phenomenon, but they have been detected in multiple sites and during many measurement nights (Meriwether and Gardner, 2000; Salby et al., 2002; Chane-Ming et al.,

2023). MILs could be formed through various dynamical processes, which include planetary wave breaking, turbulent mixing, interactions between gravity waves and tidal forces (Meriwether and Gerrard, 2004). Last, strong wind shear and wind inversion caused by turbulent heating when gravity waves break is also a hypothesis put forward (Meriwether and Gerrard, 2004; Szewczyk et al., 2013).

**Detection:** In this study, we scanned the temperature profile, detecting the stratopause and then detecting the presence of a gradient inversion. The algorithm has some restrictions, which reflects our understanding of what a MIL is. For instance, it should be at least 5 km above the stratopause, and the peak should exceed the lidar's error. It should also exceed 3 K, which is our way to account for atmospheric random variability (Mzé et al., 2014).

## 3.2. Climatology

To obtain a daily mean of the temperature profile over the year between 30–80 km, we used a method already presented in various papers that use the preliminary lidar temperature profiles (Hauchecorne et al., 1991; Leblanc et al., 1998; Keckhut et al., 2012; Ardalan et al., 2022). First, temperature profiles are interpolated on levels between 30 and 80 km at half-kilometre intervals. Profiles spanning all the lidar observation years (1984–2024 for OHP for instance) are collected into a table with a value per day. We interpolate if we lack a value for a day, but not for values which are more than 15 days away from any other measurement (to prevent us from using interpolated and smoothed profiles generated with the interpolation of a single point). A Hann filter with a window of 33 days is applied to smooth the product, using the following formula:

$$\bar{T}_{Hann}(d, z) = \sum_{i=d-15}^{d+16} T(i, z) \sin\left(\frac{i\pi}{33}\right)^2 \quad (2)$$

During this process, the result of this step is a matrix $(T(d, z))_{d,z}$ containing for each day $d$ in the 1984–2024 span one Hann-filtered temperature profile. Some days might be missing if, as said above, 15 days were done without a measurement. As a consequence, we introduce:
* D is the set of days where the Hann filtered value, T was computed;

* $\tilde{d} \in [0, 365]$ is the corresponding day as a calendar day of $d \in D$ (day number during leap years are normalised by 365/366);

* $n(\tilde{d})$ is the number of days $d \in D$ whose calendar day is $\tilde{d}$.

Previous papers only averaged monthly or weekly, but the large volume of profiles provided by the NDACC dataset of the four stations of interest allowed us to consider daily variation: from the matrix $(T(d, z))_{d,z}$, we sum on in 365-days matrix all the profiles of the corresponding day, and we normalise them:

$$ \hat{T}(\tilde{d}, z) = \frac{1}{n(\tilde{d})} \sum_{d \in D} T(d, z) \quad (3) $$

Daily variations (standard deviation). Once the mean daily temperature is computed, we assess the standard deviation. To do so, we used the previously computed climatology as $\hat{T}(\tilde{d})$, and the matrix $(T(d, z))_{d,z}$ containing for each day of the 1984–2024 period the temperature profiles. The daily standard deviation is then computed as stated hereafter:

$$ STD(\tilde{d}, z) = \frac{1}{n(\tilde{d})} \sqrt{\sum_{d \in D} (\hat{T}(\tilde{d}, z) - T(d, z))^2} \quad (4) $$

An additional step was required to remove the error linked to the Lidar observations. Because this error is related to photon-counting, whose uncertainty follows a Poisson distribution, it increases exponentially with the rising altitude and decreasing density (Hauchecorne et al., 1991). Traditionally, it is assumed that this instrument error is independent of the variability of the air, and that therefore, the assessed atmospheric variability can be expressed:

$$ \sigma_{T,variability}^2 = \sigma_{T,total}^2 - \sigma_{lidar}^2 \quad (5) $$

When we compute the standard deviation, the squared lidar measurement error is thus removed. This way we assume that the resulting standard deviation is solely caused by atmospheric variability.

Density Standard Deviation. The density profiles obtained in the OHP contain both a density profile as a function of altitude and an assessed error related to photo-counting. From the set of density and errors $(\text{dens}(z, d), \epsilon(z, d))$, we compute the pure mean and standard deviation on the time variable:

$$ \rho(\hat{z}) = \frac{1}{|D|} \sum_{d \in D} \rho(z, d) \quad (6) $$

$$ \sigma_{\rho,total}^2(z) = \frac{1}{|D|^2} \sum_{d \in D} (\rho(z) - \rho(z, d))^2 \quad (7) $$

$$ \sigma_{\epsilon}^2(z) = \frac{1}{|D|^2} \sum_{d \in D} \epsilon^2(z, d) \quad (8) $$

We then assume again that the atmospheric variability and the lidar measurement error are independent variables, which allows us to obtain the assessed atmospheric variability as:

$$ \sigma_{\rho,variability}^2(z) = \sigma_{\text{dens}}^2(z) - \sigma_{\epsilon}^2(z) \quad (9) $$

Model Climatology. To obtain a similar climatology, we downloaded (for ERA-5) or produced (with MSIS-2.0) the profiles corresponding to each day and hour of the lidar dataset, in order to remove any effect due to the atmospheric tide. With this method, we ensure that the sampling for the Lidar profile does not play a role in the difference of profiles between the model and the observations.

* For MSIS, we used the exact longitude and latitude along with the exact time and date of the lidar measurement;

* For the ERA-5 reanalysis, which is resolved worldwide on a 0.25°× 0.25°grid and has a temporal resolution of an hour, we downloaded the profiles from the 3×3 grid points closest to the lidar coordinates and at the lidar acquisition hour.

The model profiles are then processed using the exact same method as the lidar profiles, with the only difference that they have no measurement error like the lidar.

Mean profiles. To create mean profiles of each phenomenon seen by the lidar, we created a dictionary of each detected event with its registered date, and parameters (altitude and amplitude). With those parameters, we take the mean of amplitude of each phenomenon. We preferred to use a geometric mean profile for the MILs rather than a arithmetic mean profile because the distribution of their amplitude at a given altitude is log-normal. For MIL profiles we chose to represent the geometric mean of the profiles presenting a MIL at the most-common altitude they occur (that is to say, 71 km for the OHP and 68 km for Table Mountain). We present on each mean profile a box-plot of the typical amplitude of the MIL, m-SSW and DS. These statistics are computed on all detected events. Box-plots we present show the mean in red, the standard deviation as the box, and whiskers span to 1.5 * IQD, where the Inter Quartile Difference is the difference between the 75th and the 25th quartiles. They allow to represent better the possible span of register events, by removing anomalies.

# 4. Climatologies retrieved from Lidar observation

## 4.1. Mid-latitude observations

The mean temperature climatology obtained at OHP can be seen in Fig. 2a. A semi-annual almost sinusoidal variation can be seen throughout the year, reaching a peak at the stratopause in June at about 275 K. The cold Stratosphere - warm Mesosphere anti-correlation is visible, with the mesosphere being coldest during summer, around
<figure><img src="image_2.png" /><figcaption>Fig. 2. Climatology of temperature from the measurements of the OHP lidar showing the (a) mean and (b) standard deviation, Table Mountain lidar showing the (c) mean and (d) standard-deviation, Reunion Island lidar showing the (e) mean and (f) standard-deviation, Mauna Loa lidar showing the (g) mean and (h) standard-deviation.</figcaption></figure>
190 K in July, and warmest during winter, sometimes reaching 240 K. The transition between late summer and winter is characterised by a much wider stratopause that creates a general increase of warmth around October.

In terms of variability, as shown in the Fig. 2b, the mid-
dle atmosphere of the OHP is characterised by an impor-
tant variability above 75 km, reaching a peak in the
summer at almost 10 K. In the lower parts of the atmo-
sphere, the temperature is mostly stable in summer and
autumn, showing a minimum of variability at 50 km in
October, with as little as 1 K. The upper stratosphere
appears to show a peak of variability during winter, espe-
cially in February and March, almost reaching 8 K; this
is thought to be the consequence of SSW. Another peak
of variability at 60 km during winter could indicate cooling
of those altitudes due to either MIL or SSW.

Results in Table Mountain are fairly similar, showing an anti-correlation of the middle atmosphere (Fig. 2c) and high values of standard deviation in high altitudes in summer (Fig. 2d), reaching about 6–7 K. The increased standard deviation occurs slightly lower in altitude in winter, around 65 km (about 8–10 K), in the beginning of winter, and could be due to the influence of MILs. However, they display a lower variability around 35 km in winter, certainly due to its lower latitude, as we thought the m-SSWs were the reason for this effect at OHP.

4.2. *Tropical sites*

The mean value of the climatology for Reunion Island is shown in Fig. 2e. It exhibits a smaller annual variation, with a slight decrease of temperature in the austral winter, around July. Variability maps (in Fig. 2f) prove more interesting, revealing a band of high standard deviation at 40–50 km with a maximum in July, which we suppose represents the influence of the DS phenomenon. At altitudes around 60–70 km, we also register an area of strong standard deviation during the end of austral winter (September-October) with a peak at 8 K, the rest being capped under 7 K.

Mauna Loa's site presents a fairly similar climatology,
shifted by half a year because it is in the Northern Hemi-

sphere. It shows a maximum temperature around April (Fig. 2g). It also exhibits a seasonal variation, with the Northern Hemisphere pattern of warm stratosphere and cold mesosphere, even though it is weaker than the high latitude observations The standard deviation (Fig. 2h) is way smaller, but closer in shape to the one observed in the other non sub-tropical locations in the Northern Hemisphere, and there is no band around 45–50 km as seen at Reunion Island.

4.3. Evaluation of the daily bias of the climatological model MSIS 2.0

To obtain the mean bias between NRLMSISE-2.0 and the lidar climatology, we removed the value of the model to the lidar. Like other papers before us comparing model to the lidar, the NRLMSISE-2.0. profile was computed the same days and at the same full hour times as the lidar. Because NRLMSISE-2.0 is a climatological model, it is not pertinent to assess the difference in terms of variability between the instrument and the model: the only parameters from measured data which are added to NRLMSISE-2.0 are the values of the magnetic field and of the solar flux, and the standard deviation associated is very small.

*Mid-latitudes sites.* The OHP LIDAR minus NRLMSISE-2.0 comparison reveals differences of climatology in Fig. 3a. The temperatures measured by the lidar seem to be generally colder than NRLMSISE-2.0 for low altitudes (around 30 to 45 km), reaching a maximum difference of –4 K in November-December. Two areas of warmer lidar data are found between 50 and 70 km in both March-April and November, reaching up to +6 K. Above 75 km, the lidar seems generally warmer, varying between +6 and +12 K.

*Tropical sites.* In Fig. 3b, the temperature data of the lidar in Reunion Island show a cooler layer than NRLMSISE-2.0 between 30 and 35 km, increasing at the end of the austral summer. The lidar temperature then reaches a maximum difference of –4 to –6 K to the NRLMSISE-2.0 model. At higher altitudes (50–75 km), lidar temperature is warmer from April to November by up to +12 K: the bias increases with altitude and proximity

<figure><img src="image_3.png" /><figcaption>Fig. 3. Comparison between the lidar and NRLMSISE-2.0 (lidar minus NRLMSISE-2.0) at (a) OHP and b Reunion Island.</figcaption></figure>
<table><caption>Table 2
Standard deviation of NRLMSISE-2.0 compared to lidar.</caption><thead><tr><th>Altitude range<br>Altitude (km)</th><th>OHP<br>Temperature (K)</th><th>Reunion Island<br>Temperature (K)</th><th>ALOMAR lidar (Emmert et al., 2020)<br>Temperature (K)</th><th>SABER (Emmert et al., 2020)<br>Temperature (K)</th></tr></thead><tbody><tr><td>30–50</td><td>3.6</td><td>3.2</td><td>Not Specified</td><td>5.7</td></tr><tr><td>50–75</td><td>4.0</td><td>6.9</td><td>10.0</td><td>8.1</td></tr><tr><td>75–100</td><td>7.6</td><td>11.8</td><td>14.2</td><td>15.4</td></tr></tbody></table>

to the austral winter. In general, the amplitude of the difference between NRLMSISE-2.0 and the lidar we computed is higher at low-latitude than at mid-latitude sites.

We compare our results with the findings of NRLMSISE-2.0 presentation paper (Emmert et al., 2020), by computing as shown in Table 2 for the OHP and Reunion Island the standard deviation of the difference between the lidar data and NRLMSISE-2.0 data. As expected, the order of magnitude is the same, with a tendency of increasing difference with height. However, we note that our agreement with the NRLMSISE-2.0 model is better than shown in Emmert et al. (2020) for Na-lidar and SABER.

## 4.4. Evaluation of the meteorological re-analyses model ERA5

As stated in the previous section, ERA-5 reanalyses are widely used for climate analysis. Because this European model assimilates data up to the upper stratosphere at approximately 1 hPa (from microwave sounding, infrared sounder, ...), ERA-5 is supposed to take into account real-time atmospheric variability at least up to those altitudes (50 km). OHP and Reunion Island were selected to evaluate the ERA-5 reanalysis outputs because of their long series of measurements. Both the mean bias computed by averaging daily the differences of profiles the difference of the standard deviation profiles (representing daily variance) are shown.

OHP. The difference in mean between lidar and ERA-5 is shown in Fig. 4a. OHP lidar temperatures are systematically colder in the 35–45 km band than ERA-5, with some slight differences in height and amplitude, but typically shifting from –2 to –4 K. Above 50 km and during summer, the lidar data prove warmer than ERA-5, with differences reaching +5 K to +6 K at 55 km then to +12 K at 70 km and +20 at 80 km. In the winter months, ERA-5 modelling is a little better, with an difference staying between +4 K and +6 K up to 70 km, where it reaches +12 K, then +20 K at 80 km like the rest of the year. As shown in Fig. 4b and as expected, the lidar variability is greater than ERA-5’s all year, with the retrieved variability lower than 1 K in Winter, as we expected from the study of Mariaccia et al. (2022). However, the difference in standard deviation show a more variable lidar in summer (≈ 1 K), and a variability to ERA-5 diverging above 65 K, reaching +2 to +5 K at 80 km.

Reunion Island. Mean results are shown in Fig. 4c. The temperature observed by the lidar is also colder up to 45 km (about –3 to –5 K), with an exception during the austral winter, but the quality of representation decreases quickly with altitude, reaching +5 to +10 K between 45–55 km and +12 K at 55 km and up to +26 K in March to December above 60 km. Standard deviation in Fig. 4d of the Reunion Island lidar is typically greater. It is below +3 K from 35 up to 45 km all year and up to 55 km during the austral winter, but higher differences reach +4 to +8 K.

# 5. Impact of extreme events and steady-state climatology

## 5.1. Extreme event characterisation

We found that existing models deviate from the lidar measurements. Thus, knowing extreme events can have a lasting effect on the temperature profile and which are not taken into account by the models, we assume that these events could participate in this discrepancy at high altitudes. We therefore aim here to evaluate the contribution of the extreme phenomena in the climatology we computed, and typical profiles of those events. For each phenomenon described above, (the m-SSWs, the DSs and the MILs) we removed the profiles according to the detection methods described in Section 2. The climatology is then computed again without these profiles, and will be later referred to as Steady-State Climatology (StS-Climatology). In Reunion Island and Mauna Loa, m-SSWs, which are mid- to high-latitude phenomena, are not considered.

In Table 3 we summarise the number of profiles removed for each lidar site and phenomenon. The sum of the removed profile may not equal the removed profiles because some of them might be detected as two different phenomena.

## 5.2. Climatology difference

Removing the extreme event profiles from the classic dataset and computing a Steady-State climatology provide interesting insights into the sources of atmospheric variability linked to lasting events like m-SSWs, MILs or DSs. They represent an additional source of variability which is distinct - by their impact on the mean temperature and their duration - to the general atmospheric variability linked to the atmospheric turbulence, gravity waves (if they
<figure><img src="image_4.png" /><figcaption>Fig. 4. Difference between OHP lidar climatology and ERA-5 (OHP minus ERA-5), showing the systemic bias (a) and the standard deviation difference (b). Difference between Reunion Island lidar climatology and ERA-5 (Reunion Island minus ERA-5), showing the systemic bias (c) and the standard deviation difference (d).</figcaption></figure>

<table><caption>Table 3
Number of detected phenomena profiles in each lidar site.</caption><thead><tr><th>Category</th><th>OHP</th><th>Table Mountain</th><th>Reunion Island</th><th>Mauna Loa</th></tr></thead><tbody><tr><td>Coordinates</td><td>44°N,6°E</td><td>34°N,111°W</td><td>21°S,55°E</td><td>19°N,155°W</td></tr><tr><td>Total Profiles</td><td>4379</td><td>2441</td><td>1766</td><td>2504</td></tr><tr><td>MILs</td><td>1084 (24.8%)</td><td>732 (30.0%)</td><td>234 (13.3%)</td><td>1211 (48.4%)</td></tr><tr><td>DSs</td><td>526 (12.0%)</td><td>867 (35.5%)</td><td>235 (13.3%)</td><td>623 (24.9%)</td></tr><tr><td>m-SSWs</td><td>771 (31.6%)</td><td>1084 (24.8%)</td><td>N.C.<sup>1</sup></td><td>N.C<sup>1</sup></td></tr><tr><td>StS Profiles</td><td>2242 (51.2%)</td><td>720 (29.5%)</td><td>1333 (75.5%)</td><td>964 (38.5%)</td></tr></tbody></table>

don't break) and planetary waves. At OHP for instance, almost half the profiles were removed. Fortunately, the size of the dataset still allowed us to obtain enough profiles to compute a climatology.

We can see in Fig. 5a that the classic climatology in OHP is warmer in the region between 30 and 40–45 km, especially in December and March-April where this difference amounts to 2–3 K. Moreover, removing the 30–40 km variability also creates a much cooler area between 55 and 65–70 km during winter, with a peak at about 65 km, reaching –4 to –6 K in December and January. The m-SSWs removed from our algorithm which only targets the 30–40 km layer cause thus in the results a warmer stratopause and a cooler middle mesosphere. As for the upper

mesosphere, the difference in OHP between the classic and the StS climatology shows a warmer area of about 2–3 K in mean at 70 km in winter and at 75–80 km in summer, which is due to the removal of MILs. m-SSWs are not considered for the Fig. 5b presenting results for Reunion Island. For that site, the classic climatology appears consistently cooler from 30 to 60 km throughout the year. Differences can reach from –1 to –3 K at 45–50 km which corresponds to the altitude of the stratopause. We infer this cooler area might be linked to the DSs cases in the analysis. Above 60 km, the classic climatology appears to be warmer throughout the year but particularly in the Austral summer by +2 to +5 K, and which could be due to the removal of MILs.

<footnote n="1">¹ Not Computed</footnote>
<figure><img src="image_5.png" /><figcaption>Fig. 5. Climatology of the difference between StS and Classic climatology with (a) the OHP lidar and (b) Reunion Island lidar (Classic minus StS).</figcaption></figure>

## 5.3. Mean profiles and tables

We quantify the impact of these events by comparing a typical profile during those events to the mean profile in Steady-State Climatology. For some events like DSs and m-SSWs we present a mean profile, and for MILs we use a geometric mean profile on MILs which occur at the most common altitude (that is to say 71 km for OHP and 68 km for Table Mountain). We do not use the overall geometric mean profile of MILs at all altitudes because averaging profiles containing different altitude MILs would result in averaging both the amplitude and altitude distribution, showing a profile which does not represent a typical temperature profile of MILs. For MILs and m-SSWs, we present a box-plot at the mean altitude of the event showing their statistical impact, one standard-deviation around it, and whiskers reaching 1.5 * IQR = 1.5 * (Q75th - Q25th). In addition to the visual help provided by those figures, Table 4 gives a quantification of such events' impact.

MILs. MILs' detected geometric mean profiles at both OHP and Table Mountain in Fig. 6a and Fig. 6b show a steeper gradient from the stratopause in winter (45 to 65 km) before showing an inversion of the gradient and a second peak of temperature at 70 km of about 8–10 K above the mean winter profile. The box plot represent the possible statistical amplitude range of the inversion, please note that the altitude of the MIL can change.

DSs. In Reunion Island, as shown in Fig. 6c, the double stratopause mean profile globally shows a cooling of the stratopause and two distinct peaks around the stratopause altitude compared to the mean stratopause overall, which explains the 45 km structure seen in the Fig. 5b.

m-SSWs. In Fig. 6d at OHP, the mean m-SSW profile in winter follows a rather classic pattern that resembles the composition of an SSWs, with a typical temperature increase about +12.5 K above the mean profile in winter at the stratopause (40–45 km) and a cooling of about 8 K around the altitude of 70 km.

Tables of variability. In Table 4, we present key numbers on extreme events. One takeaway from this chart is the impact of m-SSWs on the OHP winter stratopause and 70 km temperature, which shows that the detected m-

<table><caption>Table 4
Quantification of the detected events.</caption><thead><tr><th></th><th>OHP</th><th>TM</th><th>Reunion</th><th>ML</th></tr></thead><tbody><tr><td>Stratopause<sup>3</sup></td><td></td><td></td><td></td><td></td></tr><tr><td>Alt<sub>Strato</sub> (km)</td><td>48.1 ± 2.6</td><td>47.6 ± 2.1</td><td>48.0 ± 2.4</td><td>47.5 ± 1.9</td></tr><tr><td>T<sub>Strato</sub> (K)</td><td>266.5 ± 6.9</td><td>267.4 ± 5.4</td><td>269.7 ± 7.5</td><td>268.9 ± 2.9</td></tr><tr><td>MIL data</td><td></td><td></td><td></td><td></td></tr><tr><td>All Year</td><td></td><td></td><td></td><td></td></tr><tr><td>ΔT<sub>MILs</sub> (K)</td><td>14.5 ± 10.2</td><td>10.1 ± 6.6</td><td>17.7 ± 16.3</td><td>9.3 ± 6.3</td></tr><tr><td>Alt<sub>MILs</sub> (km)</td><td>71.2 ± 3.7</td><td>68.4 ± 2.9</td><td>68.4 ± 2.7</td><td>72.9 ± 5.2</td></tr><tr><td>Summer</td><td></td><td></td><td></td><td></td></tr><tr><td>ΔT<sub>MILs</sub> (K)</td><td>13.5 ± 9.3</td><td>8.2 ± 4.6</td><td>17.5 ± 17.0</td><td>9.3 ± 6.3</td></tr><tr><td>Alt<sub>MILs</sub> (km)</td><td>74.1 ± 2.5</td><td>68.8 ± 2.9</td><td>68.2 ± 2.6</td><td>71.9 ± 5.1</td></tr><tr><td>Winter</td><td></td><td></td><td></td><td></td></tr><tr><td>ΔT<sub>MILs</sub>(K)</td><td>16.3 ± 10.4</td><td>13.4 ± 8.5</td><td>17.5 ± 15.9</td><td>9.1 ± 6.3</td></tr><tr><td>Alt<sub>MILs</sub>(km)</td><td>70.6 ± 3.3</td><td>68.4 ± 2.6</td><td>68.0 ± 2.8</td><td>72.7 ± 5.4</td></tr><tr><td>DS data</td><td></td><td></td><td></td><td></td></tr><tr><td>T<sub>US</sub> (K)</td><td>262.2 ± 8.3</td><td>264.2 ± 5.2</td><td>264.5 ± 5.4</td><td>265.1 ± 3.2</td></tr><tr><td>T<sub>LS</sub> (K)</td><td>262.3 ± 8.5</td><td>263.9 ± 5.2</td><td>264.5 ± 5.0</td><td>265.0 ± 3.2</td></tr><tr><td>Alt<sub>US</sub>(km)</td><td>51.6 ± 4.5</td><td>50.5 ± 2.7</td><td>51.7 ± 2.6</td><td>50.5 ± 2.1</td></tr><tr><td>Alt<sub>LS</sub>(km)</td><td>44.7 ± 3.7</td><td>45.1 ± 2.2</td><td>45.5 ± 2.0</td><td>45.4 ± 1.8</td></tr><tr><td>m-SSW data</td><td></td><td></td><td></td><td></td></tr><tr><td>ΔT<sub>40km</sub> (K)</td><td>9.1 ± 9.7</td><td>1.5 ± 7.1</td><td>N.C.<sup>2</sup></td><td>N.C.<sup>2</sup></td></tr><tr><td>ΔT<sub>70km</sub> (K)</td><td>-7.2 ± 12.5</td><td>0.8 ± 11.3</td><td>N.C.<sup>2</sup></td><td>N.C.<sup>2</sup></td></tr></tbody></table>

Uncertainty given at one standard deviation

² Not Computed (N.C.)

³ Stratopause statistics on all profiles including MILs, DSs and SSWs

SSWs profiles at the stratopause specifically warm the stratopause (about +9 K). However they are also associated with a cooling of -7 K at 70 km. DSs at both low-latitude sites have both peaks separated by at least two standard deviations, while at both high-latitudes sites their peaks seem relatively closer. This table also shows that MILs have a greater amplitude at Reunion Island and OHP throughout the year than at other sites. We also note how consistently MILs' amplitudes decrease in summer and increase in winter at the mid-latitude sites, while their altitude lowers during winter. MILs observed at low-latitudes seem, however, not to fluctuate much in either amplitude or altitude throughout the year.
<figure><img src="image_6.png" /><figcaption>Fig. 6. Geometric mean of temperature profiles showing MIL at the most common altitude in (a) OHP and (b) Table Mountain Lidar, showing the winter temperatures of all detected MILs at the site as a boxplot. Mean profiles of (c) DSs at Reunion Island during summer. (d) Mean winter m-SSW OHP temperature profiles (profiles detected out of one standard-deviation).</figcaption></figure>

**6. Application for aerospace: density difference**

The previous analysis was performed on temperature instead of density because temperature profiles are retrieved with absolute value and without external calibration. However, density is much more relevant to the field of aerodynamics. Density anomalies are directly related to temperature anomalies with the ideal gas law. We present in this paragraph consequences of those extreme phenomena on the density profile. Below we present in Fig. 7 a comparison between a retrieved lidar temperature and density profile and the values given by NRLMSISE-2.0. Both temperature profiles are shown in Fig. 7a and Fig. 7c: as expected, NRLMSISE-2.0 is unable, as a climatology model, to give a representation of either a m-SSW and a MIL. When tackling the impact on the density profile, we see in Fig. 7b and Fig. 7d that compared to the NRLMSISE-2.0 density profile, the m-SSW are associated to an increase to about 25% at 60 km and the MILs with a decrease of 15% in density at 70 km.

The Fig. 8 tackles the effect of extreme events on the density profile. We computed this table with the selection of events presented above for the OHP. There is a density profile for each temperature profile from 1992 to 2024 at the OHP. As stated in the introduction, the density profiles

have to be normalised by a reference density at a given altitude (in our case MSIS-90 at 40 km) because its absolute value cannot be measured. In the Fig. 8 and Table 5, we only considered the winter density profile, because in this season we can compare the influence of all events (the m-SSWs occur only at this period.).

We present result in Fig. 8 with respect to NRLMSISE-2.0. The winter density decreases up to -4% at the stratosphere during a m-SSW, but increases up to +5% in the higher mesosphere. During a MIL, the density decreases by -9% above 70 km. The DS case does not seem to be linked to a significant variation to the classic profile. The mean classic climatology is -5% less dense at 55 km and above and +2.5% denser at 30 km. While showing approximately the same pattern, the StS profiles seem to agree slightly better with NRLMSISE-2.0, and this especially at 70 km, when the error with the model reaches down to -2%.

However, to compare those results with the standard deviation of the density at that period, we computed the climatology of the density profiles, and retrieved the overall variance. We present the different values of standard deviation in the Table 5. Above 55 km, this assessed standard deviation of the atmosphere density stays below 10%.

Only the result in Fig. 8 for the m-SSWs appears to have an effect which overcomes the assessed atmospheric stan-
<figure><img src="image_7.png" /><figcaption>Fig. 7. Example profiles of (a) a m-SSW and (c) a MIL with the NRLMSISE-2.0 profile associated. Ratio between the NRLMSISE-2.0 density profile and the (b) m-SSW density profile of the temperature event shown in (a) and (d) the MIL density profile of the temperature event shown in (c) (lidar/NRLMSISE-2.0).</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 8. Relative density difference in % between the mean density of different events and climatology during winter and the density retrieved from NRLMSISE-2.0.</figcaption></figure>

dard deviation of the density profile. It appears thus the rest of the phenomena do not stand out of the random atmospheric variability.

## 7. Discussion - conclusion

Our study demonstrates that ERA-5 shows a relatively high bias in the middle-atmosphere temperature, though ERA-5 follows more accurately lidar trends. The NRLMSISE-2.0. model, while reliable in general trends, does not capture daily variability and still includes a high bias in the middle and high mesosphere. We found that extreme events such as m-SSW, MIL and DS had an impact on the climatology especially in mid-latitude sites, introducing a bias in the mean temperature. We then presented a statistical and visual representation of those phenomena on the temperature profile, and established a Steady-State Climatology. Finally, we opened the discussion towards the impact on aerospace by showing at least m-SSWs had a significant impact on the density profile. These findings are relevant for the community working in the field of atmospheric re-entry because they establish that both climatological models and numerical models are imperfect proxies for the atmospheric state and could be improved in this region. Quantitative results include:

* For mid-latitude sites, NRLMSISE-2.0 is about 2 K colder up to 40 km, 4 to 8 K warmer between 50 and 70 km and 12 K warmer between 70 and 80 km throughout the year. For low-latitude sites, NRLMSISE-2.0 is about 2 K colder up to 35 km, consistently warmer on
<table><caption>Table 5
Mean density at different altitude levels with the variability.</caption><thead><tr><th>Altitude</th><th>Mean value</th><th>Instrument Noise</th><th>Assessed variability</th><th>Total Variability</th></tr><tr><th>h<br>km</th><th>ρ<br>kg.m<sup>-3</sup></th><th>σ<sub>ρ,lidar</sub><br>%</th><th>σ<sub>ρ,variability</sub><br>%</th><th>σ<sub>ρ,total</sub><br>%</th></tr></thead><tbody><tr><td>30 – 35</td><td>1.8.10<sup>-2</sup></td><td>0.12</td><td>5.42</td><td>5.42</td></tr><tr><td>35 – 40</td><td>8.0.10<sup>-3</sup></td><td>0.12</td><td>3.70</td><td>3.70</td></tr><tr><td>40 – 45</td><td>3.6.10<sup>-3</sup></td><td>0.12</td><td>1.04<sup>1</sup></td><td>1.05<sup>1</sup></td></tr><tr><td>45 – 50</td><td>1.8.10<sup>-3</sup></td><td>0.19</td><td>4.39</td><td>4.39</td></tr><tr><td>50 – 55</td><td>9.3.10<sup>-4</sup></td><td>0.29</td><td>7.43</td><td>7.44</td></tr><tr><td>55 – 60</td><td>5.0.10<sup>-4</sup></td><td>0.43</td><td>9.32</td><td>9.34</td></tr><tr><td>60 – 65</td><td>2.6.10<sup>-4</sup></td><td>0.68</td><td>10.5</td><td>10.6</td></tr><tr><td>65 – 70</td><td>1.3.10<sup>-4</sup></td><td>1.1</td><td>11.1</td><td>11.1</td></tr><tr><td>70 – 75</td><td>6.5.10<sup>-5</sup></td><td>1.9</td><td>10.8</td><td>10.9</td></tr><tr><td>75 – 80</td><td>3.0.10<sup>-5</sup></td><td>3.5</td><td>12.1</td><td>12.6</td></tr></tbody></table>

1: The low value of variability around 40 km is due to the normalisation of our density profile by MSIS-90. at that precise altitude (Hauchecorne and Chanin, 1980).

higher altitudes, ranging from 2 K at 40 km to 12 K at 70 km. Mean standard deviation stays below 4.0 K under 75 km in the OHP, and under 50 km in Reunion Island; Because of the relatively recent development of NRLMSISE-2.0, few studies have compared it with existing lidar.

* For both mid- and low-latitude sites, lidar data is -2 K colder all year between 35 and 45 km than ERA-5, with a bias inverting and reaching from +4 to +15 K between 50 and 70 km. Close values of standard deviation is shown for mid-latitude sites, with relatively good following of lidar fluctuations to the mean throughout the year, below 3 K over the all year when under 60 km, with an exception in December.

* We detect about 25–30% MIL profiles at mid-latitude sites. MILs mostly occur around 70 km and increase the temperature by about +10 K at all four sites. MILs induce a variation of the climatology by consistently making it warmer by +2 to +4 K above 65 km at all four sites. Specific MIL events can respectively decrease down to 15% the density.

* At mid-latitude sites, we detect about 25% winter profiles as m-SSWs. These winterly events increase locally the temperature at 40 km by 10 K (and decrease it in the OHP by -8 K at 70 km.) m-SSWs therefore induce a warming of the climatology from +4 to +6 K at the stratopause and a cooling of -6 to -8 K in the region 55–65 km. Specific m-SSWs events can increase up to 25% the density, over a spatial extent of 15 km or more. Compared to the overall winter density mean, when a m-SSW occurs, the air density can decrease in mean by 3% at 35 km and increase by 5% at 60 km compared to NRLMSISE-2.0.

* DSs seem to cool the low-latitude climatology at least by -2 to -3 K at 50 km during the all year.

* StS-climatology is closer to NRLMSISE-2.0 than the classic climatology in density, especially around 65–70 km.

Our study is supported on the comparison of climatological models by other results with the predecessor of

NRLMSISE-2.0, mainly Hauchecorne et al. (1991). Because NRLMSISE-2.0 uses as a base the MSIS-90 Model and incorporates some of the data which helped devising it (CIRA-86), we can compare our results to those found previously when comparing CIRA-86 to the OHP and Reunion Island lidars by Leblanc et al. (1998). When comparing the OHP lidar to CIRA-86, similar conclusions were reached regarding the difference between the lidar and the climatological model above 50 km, but the new version of NRLMSISE seemingly improves the discrepancy with the lidar on the upper stratosphere. We can draw similar conclusions for the Table Mountain site, noting in addition that there is spot where the lidar data is +6 K warmer than the model in February-March in our study at about 70 km, which was also found in Leblanc’s study. Our conclusions are also close the ones found by the latest evaluation of the model by their developing team: Emmert et al. (2020). In terms of climatology, it is close to former studies lead by our team on the same altitudes (She et al., 1995).

The discrepancy that we found between lidar and NRLMSISE-2.0 could also be explained further by long atmospheric trends, such as mesosphere cooling caused by global warming, as described by Garcia (2021). Indeed, while ERA-5 and the lidar take this trend into account, because they use in situ and up to date data, NRLMSISE-2.0 use a fixed database and thus cannot take those trends into account.

We based our method to remove m-SSWs on our understanding of Angot et al. (2012), and our results seem to show that the structure of the removed profiles agree with this determination. Even if we acknowledge that our detected m-SSWs are not all corresponding to the definition of the WMO and thus part of the NOAA registered M-SSWs, we still decided to assess which profiles were removed by comparing them to the findings of another method. Therefore, we conducted a SSW detection algorithm based on Bancala et al. (2012). Their team’s method averages the mean zonal wind at 60°N, 10 hPa and register
SSWs by its inversion. With this method, which follows closely the WMO's, we found that for each of the OHP and Table Mountain lidars, our detection method encompassed 55% of the registered SSWs Bancala's algorithm. Even if this result can seem underwhelming, Bancala's method principally targets the 60°N and look for the breaking of the polar vortex in terms of wind speed. As a result, it is possible that some M-SSWs do not have an impact to such lower latitudes (43–44°). The longitude where the M-SSWs happen is also another parameter taken into account by Bancala but that might not reflect in both lidar sites: it could thus explain this relatively low percentage.

While this study provides valuable insights, several limitations must be acknowledged.

The medium percentage (55%) of M-SSW out of our retrieved m-SSWs in mid-latitude regions indicates a need for further refinement of the detection method. Additionally, the arbitrary thresholds set for MILs (3 K) and DSs (90% of the stratopause) require more investigation, as we may have inadvertently included other phenomena such as extreme gravity waves. Future research should explore alternative detection methods and validate them against more comprehensive datasets. Alternatives to this detection could have been to fix an increasing threshold with altitude to separate them as suggested by Mzé et al. (2014), but there is no consensus regarding the method to use. Another limitation we can highlight is the remaining overall standard deviation. The Steady-State Climatology does not show an overall decrease of the total standard deviation when compared to the classic way to produce it. Indeed, only the OHP standard deviation decreases (4.3 to 4.0 K), while Table mountain stays constant (3.4 K) and Reunion Island and Mauna Loa increase slightly. Removing profiles may have increased the deviation to temperature means, potentially due to errors and anomalies in the remaining data. It might have caused increased periods without lidar measurements in our dataset, making the climatology mean less accurate, which would thus influence the standard deviation. Last, even if the density shown in this paper indicates that these events have an impact on the density profile compared to NRLMSISE 2.0, it is difficult to conclude on the impact of extreme phenomena on the density profile, except for m-SSWs. The considered density change compared to the classic ratio with the model for MILs at high altitudes occurs in areas where the assessed overall standard deviation of the density (11 %) is higher than the value we find (-9 %). It also happens to be a region where the density itself is very low (under $3.10^{-2}g.m^{-3}$). Finally, the extent to which the density at those latitude is important is unknown. Now that the uncertainty over the density profile is assessed, further study should focus on taking density and temperature as an input and assess the impact of such uncertainties on re-entry models.

In conclusion, our study provides new insights into middle atmospheric variability. It offers a first glance which

calls for future refinement of middle atmosphere models and extreme phenomenon detection algorithms. Continued research in this area in addition of re-entry models taking this uncertainty into account will help bridge the current gaps in understanding and improve atmospheric predictions which are crucial for satellite and aerospace operations. Often neglected compared to other error factors in atmospheric re-entry, the density and temperature knowledge in the middle atmosphere still need to be directly measured by lidar instruments to acquire an accurate atmospheric state above 1 hPa. This calls for the installation of more lidars throughout the world close to re-entry sites to diminish possible risks linked to extreme events and atmosphere variability. Complementing instruments like probe balloons could help obtain both an absolute temperature and density at those key places, as seen with the French Navy ship le Monge with Wing et al. (2020), campaign.

It is possible that thanks to the result we present, future model designers choose to incorporate middle-atmosphere data from lidars or satellite. It could also into global models the way to discriminate between "standard" atmospheric state and atmospheric state disturbed by lasting and wide events like MILs or SSWs (Blanc et al., 2018).

## Declaration of Competing Interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Nicolas Gilbert Tufel reports financial support was provided by General Directorate of Armaments. Nicolas Gilbert Tufel reports a relationship with German Aerospace Center DLR that includes: employment. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgments

This study was performed with the support of the Direction Générale de l'Armement. Lidar operations are supported by CNRS, NASA, CNES, La Réunion and Versailles Saint-Quentin en Yvelines universities. Some lidar data used in this publication are publicly available obtained as part of the Network for the Detection of Atmospheric Composition Change (NDACC) and are available through the NDACC international website: "www.ndacc.org" and through the French National Centre for Atmospheric Data and Services AERIS: "www.aeris-data.fr/projects/ndacc-france". We would like to thank in addition the Project Investigator (PI) of the 4 lidar instruments used in this study, not only for the available access to data, but also for the exceptionally long series provided: Pr. Thierry Leblanc for Mauna Loa and Table Mountain and Prs. Keckhut and Hauchecorne for the OHP and the
Reunion Island. This research was funded by the Délégu-
tion Générale pour l'Armement (DGA) from the French
Ministry of Armed Forces under the contract 202395002.

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