###### Abstract  
A climatology of Mesospheric Inversion Layers (MIL) has been created using the Rayleigh lidar located in the south of France at L'Observatoire de Haute Provence (OHP). Using criteria based on lidar measurement uncertainties and climatological mean gravity wave amplitudes, we have selected significant large temperature anomalies that can be associated with MILs. We have tested a novel approach for classifying MILs based on a k-mean clustering technique. We supplied different parameters such as the MIL amplitudes, altitudes, vertical extension, and lapse rate and allowed the computer to classify each individual MIL into one of three clusters or classes. For this first proof of concept study, we selected k = 3 and arrived at three distinct MIL clusters, each of which can be associated with different processes generating MILs in different regimes. All clusters of MIL exhibit a strong seasonal cycle with the largest occurrence in winter. The four decades of measurements do not reveal any long-term changes that can be associated with climate changes and only show an inter-annual variability with a quasi-decadal oscillation. mesosphere inversion layer; clustering method; middle atmosphere; Rayleigh lidar +
Footnote †: journal: _arxiv.org_  
0000-0002-4000-0000-0000-0000-0000-00000-0000-0000-0000-0000-0000-0000-0000  
In a review article, [PERSON] and [PERSON] [6] described two broad classes of MILs. The first class is the lower MIL, occurring between 65 and 75 km with a summer amplitude of 5 to 10 K and a winter amplitude sometimes exceeding 20 K. It is generally considered that the lower MILs have two formation mechanisms: Firstly, when large, upward-propagating planetary waves reach an altitude where their phase speed matches the speed of the background horizontal wind, the waves break down, dissipate via turbulence, and begin to deposit momentum and energy into the atmosphere. This process acts to slow and potentially reversing the background wind and provide local heating, which reverses the local temperature lapse rate and creates the inversion layer [7]. Secondly, gravity waves can also saturate and interact with the mean horizontal wind in the same fashion as planetary waves. It was further shown by [PERSON] et al. [2], [PERSON], et al. [8] that GWs will preferentially break within a MIL, providing sufficient energy to sustain an inversion with amplitudes up to 40 K. This theory has the added appeal that it can explain seasonal variations in mid-latitude MIL frequencies by relating them directly to their analogues in GW seasonal cycles. Disentangling the relative contributions of PWs and GWs to lower MIL formation is still a relatively open question. The second class is the upper MIL, occurring in the upper mesosphere with typical amplitudes between 10 and 35 K. This class of MIL is thought to result from non-linear wave breaking and wind-wave interactions [2], as well as from tidal wave breakdown and GW-tidal interactions [9; 10]. A third class of MIL was also recently reported by [PERSON] et al. [11] in the mesopause region, driven by chemical heating of atomic oxygen. In this paper, we will restrict our analysis to the lower MILs occurring mainly in the lower-middle mesosphere between 60 and 80 km, which are regularly measured by the lidar with high accuracy and precision. Given that what we are presenting is a novel statistical technique for classifying MILs, we will demonstrate our method on the more robust dataset and defer the analysis of upper MILs for a future study. In general, understanding MIL phenomena and their driving mechanism is important as it can provide insight into the general stability and energy transfer of the middle-atmosphere. Such a large variability has a large impact on the mean temperature and could probably have a significant impact on decadal trends in the mesosphere. The mesosphere is expected to cool due to the increase in greenhouse gases.