Generative Convective Parametrization of a Dry Atmospheric Boundary Layer.

Turbulence parametrizations will remain a necessary building block in kilometer‐scale Earth system models. In convective boundary layers, where the mean vertical gradients of conserved properties such as potential temperature and moisture are approximately zero, the standard ansatz which relates turbulent fluxes to mean vertical gradients via an eddy diffusivity has to be extended by mass‐flux parametrizations for the typically asymmetric up‐ and downdrafts in the atmospheric boundary layer. We present a parametrization for a dry and transiently growing convective boundary layer based on a generative adversarial network. The training and test data are obtained from three‐dimensional high‐resolution direct numerical simulations. The model incorporates the physics of self‐similar layer growth following from the classical mixed layer theory of Deardorff by a renormalization. This enhances the training data base of the generative machine learning algorithm and thus significantly improves the predicted statistics of the synthetically generated turbulence fields at different heights inside the boundary layer, above the surface layer. Differently to stochastic parametrizations, our model is able to predict the highly non‐Gaussian and transient statistics of buoyancy fluctuations, vertical velocity, and buoyancy flux at different heights thus also capturing the fastest thermals penetrating into the stabilized top region. The results of our generative algorithm agree with standard two‐equation mass‐flux schemes. The present parametrization provides additionally the granule‐type horizontal organization of the turbulent convection which cannot be obtained in any of the other model closures. Our proof of concept‐study also paves the way to efficient data‐driven convective parametrizations in other natural flows. Plain Language Summary: Even though global simulations of the Earth system on monthly timescales reach now resolutions of 2.5 km, essential turbulent transport processes in the lowest part of the atmosphere still have to be modeled. Here, we implement a machine learning‐based mass‐flux parametrization of the subgrid‐scale heat flux for a shear‐free dry atmospheric boundary layer by a generative adversarial network. Training data and prediction capability of the algorithm are increased by incorporating the physics of boundary layer growth following from classical mixed layer similarity theory. Our model is compared successfully to standard mass‐flux parametrizations based on an equation model. It is additionally found to reproduce the intermittent fluctuations of the convective buoyancy flux and the horizontal organization of the transiently evolving turbulence correctly. Key Points: A generative adversarial network produces the subgrid‐scale buoyancy flux for a transiently growing dry convective boundary layerThe training data are enhanced by renormalizing simulation snapshots in correspondence with the self‐similar growth by mixed‐layer theoryThe algorithm generates data with the right spatial patterns and non‐Gaussian statistics, and agrees with standard parametrizations [ABSTRACT FROM AUTHOR]