EnKF and EM based parameter estimation of a convective gravity wave parameterization using Strateole 2 constant level balloon data

An offline methodology is applied to estimate parameters of a subgrid-scale non-orographic gravity-wave scheme using observations from constant-level balloons. The approach integrates the Ensemble Kalman Filter (EnKF) with an iterative parameter estimation method based on the expectationmaximization (EM) algorithm. The meteorological fields required for the parameterization offline are taken from the ERA5 reanalysis, corresponding to the instantaneous meteorological conditions found underneath the Strateole-2 balloon observations made in the lower tropical stratosphere from November 2019 to February 2021 and October 2021 to January 2022. Compared to a direct approach that minimizes a cost function and uses Bayesian inference of parameters, our analysis demonstrates that the EnKF/EM method effectively characterizes the launching amplitudes and altitudes of the parameterized gravity waves and while quantifying their associated uncertainties. Furthermore, we illustrate how the method can help improving a scheme, specifically the results indicate that introducing a background wave activity renders the convective wave parameterization more realistic.