Machine Tuning of Entrainment Rates in an Extended EDMF Scheme: Toward a Unified Parameterization of Shallow and Deep Convection

The eddy diffusivity/mass flux (EDMF) parameterization offers a framework for a unified parameterization of sub-grid scale turbulence and convection by decomposing subgrid motions into (possibly multiple) updrafts and an environment. The recently developed extended EDMF framework (Tan et al., 2017, JAMES) has prognostic equations for updrafts and environmental turbulent kinetic energy (TKE), with a consistent (conservative) decomposition of energies between updrafts and the environment. This prognostic modification to the steady EDMF parameterization is essential as model resolutions increase, which renders the assumption of quasi-equilibrium between the large scale and deep convection invalid. However, the adequacy of the EDMF framework depends on a correct representation of the interaction between updrafts and the environment through entrainment and detrainment.

In this work, entrainment and detrainment rates are tuned using a Markov chain Monte-Carlo (MCMC) algorithm to learn these parameters from large eddy simulations (LES) of a large number of test cases. We investigate the identifiability of the parameters first in a perfect-model setting and then show how LES can be used to tune them.