Machine Learning (ML) provides a powerful tool for investigating the relationship between the large-scale flow and unresolved processes which, in climate models, need to be parameterized. The current work explores the performance of the Random Forest Regressor (RF) as a non-parametric model in the reconstruction of non-orographic gravity waves (GWs) over midlatitude oceanic areas. The ERA5 dataset from the European Center for Medium-range Weather Forecasts (ECMWF) model outputs is employed in its full resolution to derive GW variations in the lower stratosphere. Coarse-grained variables in a column-based configuration of the atmosphere are used to reconstruct the GWs variability at the target level. The first important outcome is the relative success in reconstructing the GW signal (coefficient of determination R2 ≈ 0.85 for “E3” combination). The second outcome is that the most informative explanatory variable is the local background wind speed. This questions the traditional framework of gravity wave parameterizations, for which, at these heights, one would expect more sensitivity to sources below than to local flow. Finally, to test the efficiency of a relatively simple, parametric statistical model, the efficiency of Linear Regression was compared to that of Random Forests with a restricted set of only five explanatory variables. Results were poor. Increasing the number of input variables to 15 hardly changes the performance of the linear regression (R2 changes slightly from 0.18 to 0.21), while it leads to better results with the random forests (R2 increases from 0.29 to 0.37).

The way the large-scale flow determines the energy of the nonorographic mesoscale inertia–gravity waves (IGWs) is theoretically significant and practically useful for source parameterization of IGWs. The relations previously developed on the f plane for tropospheric sources of IGWs including jets, fronts and convection in terms of associated secondary circulations strength are generalized for application over the globe. A lowpass spatial filter with a cut-off zonal wavenumber of 22 is applied to separate the large-scale flow from the IGWs using the ERA5 data of ECMWF for the period 2016–2019. A comparison with GRACILE data based on satellite observations of the middle stratosphere shows reasonable representation of IGWs in the ERA5 data despite underestimates by a factor of smaller than three. The sum of the energies, which are mass-weighted integrals in the troposphere from the surface to 100 hPa, as given by the generalized relations is termed initial parameterized energy. The corresponding energy integral for the IGWs is termed the diagnosed energy. The connection between the parameterized and diagnosed IGW energies is explored with regression analysis for each season and six oceanic domains distributed over the globe covering the Northern and Southern Hemispheres and the Tropics. While capturing the seasonal cycle, the domain area-average seasonal mean initial parameterized energy is weaker than the diagnosed energy by a factor of three. The best performance in regression analysis is obtained by using a combination of power and exponential functions which suggests evidence of exponential weakness.

<p>The variability of the upper atmosphere is largely influenced by dynamical forcing from the lower and middle atmosphere. The Mesosphere and Lower Thermosphere (MLT) is the transition region between the middle atmosphere and the upper atmosphere, and it determines dynamical forcing to the upper atmosphere from below. It is thus of high importance to know, describe, and understand the dynamical processes within the MLT to quantify dynamics. Therein, General Circulation Models (GCMs) have been a significant tool to explain MLT processes.</p><p>However, developing the right parameterizations that allow to accurately model near-to-realistic states of the MLT by GCMs is challenging, which is reflected in a large diversity of results from different models in comparison to observations, e.g., of winds and temperatures at the MLT.</p><p>In recent years, the community model ICON (Icosahedral Nonhydrostatic Weather and Climate Model) has been expanded into altitudes up to 150 km, named the UA (Upper Atmosphere) branch. UA-ICON is increasingly being applied to model and to understand MLT processes and how they are controlled by the lower and middle atmosphere.</p><p>We present newly developed capabilities of UA-ICON. Examples are mesospheric cooling during stratospheric warming events, low summer mesopause temperatures through appropriate specification of gravity wave parameterizations and runs of high spatial resolution. Results are discussed in comparison with observations and with predictions by other GCMs.</p>

<p>One of the remaining issues in the parameterization of inertia-gravity waves is the estimation of wave characteristics such as wavenumber and intrinsic frequency. In this survey, we explore a new way to estimate the wave characteristics at the launch level. To this end, we retrieve the wavenumber using the Riesz Transform which is the generalized form of the Hilbert Transform applicable in the multi-dimensional analysis. For this purpose, the high-resolution horizontal divergence field has been employed since it filters the background flow and thus provides a reasonable representation of the inertia-gravity wave signal. This is followed by the application of machine learning to reconstruct the retrieved wavenumber using the coarse-grained resolvable variables including the horizontal wind speed, the large scale vertical velocity, the cross-stream ageostrophic wind speed, the frontogenesis function and the latent heat released during condensation as explanatory variables at the launch level.<br>We have employed the ERA5 dataset in this survey, having observed that the dataset can directly resolve the inertia-gravity waves at its full resolution. In order to avoid mountain waves and focus on non-orographic inertia-gravity waves, two areas far from the significant obstacles over the midlatitude of the Atlantic Ocean and Northern Pacific Ocean are considered from December 2018 to February 2019. The results show a reasonable correlation between the reconstructed wavenumber using low-resolution explanatory variables and the retrieved one using the Riesz Transform so that this method can be utilized to estimate the inertia-gravity wave number at the launch level.</p>