Two-Dimensional Convective Boundary Layer: Numerical Analysis and Echo State Network model

The numerical study of global atmospheric circulation processes requires the parametrization of turbulent buoyancy fluxes in the lower convective boundary layer which typically cannot be resolved by the coarse-scale computational grids. We investigate a two-dimensional model of a shallow convective boundary layer in the Boussinesq limit by direct numerical simulations. A series of simulation runs evaluates the turbulent transport properties as a function of the flux ratio at the top and bottom. Furthermore, the resulting simulation data records are used to train and test a recurrent neural network realized in this work by an echo state network. We show that an echo state network, which was trained with simulation data at two different top fluxes, can approximate an unseen third data record with a different top flux. We find, amongst others, that the statistical properties of the buoyancy flux across the layer are reproduced by our model without solving the underlying highly nonlinear equations of motion.