EnKF and expectation‐maximization 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 convective gravity‐wave scheme using observations from constant‐level balloons. The approach integrates the ensemble Kalman filter (EnKF) with an iterative method based on the expectation‐maximization (EM) algorithm. The meteorological fields required for the parameterization are taken from the European Centre for Medium‐Range Weather Forecasts (ECMWF) Reanalysis Version 5 (ERA5) reanalysis, corresponding to the instantaneous meteorological conditions found underneath the Strateole‐2 balloon observations made in the lower tropical stratosphere. Compared with optimizations with fixed parameters with an uncertainty quantification using Bayesian inference from an ensemble of simulations, our analysis demonstrates that the EnKF/EM method characterizes the launching amplitudes and altitudes of the parameterized gravity waves effectively and quantifies their uncertainties. We also show that the method can help improve the realism of the scheme: for example, by incorporating background‐wave activity. By allowing parameters to vary in time, the ENKF/EM approach also makes it possible to pinpoint processes that the scheme under‐represents.