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. In this work, we present a
parametrization for a dry convective boundary layer based on a generative
adversarial network. The model incorporates the physics of self-similar layer
growth following from the classical mixed layer theory by Deardorff. 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. The
algorithm training is based on fully three-dimensional direct numerical
simulation data. Differently to stochastic parametrizations, our model is able
to predict the highly non-Gaussian 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 or
multi-plume stochastic 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
work paves the way to efficient data-driven convective parametrizations in
other natural flows, such as moist convection, upper ocean mixing, or
convection in stellar interiors.

基于生成对抗网络的对流参数化研究，能够预测对流边界层内不同高度处的合成湍流场的统计学特征，包括热浮力波动、垂直速度和浮力通量，同时捕捉最快的热气团穿过稳定顶部区域，为其他自然流动的高效数据驱动对流参数化研究铺平了道路。