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.

翻译：湍流参数化仍将是千米尺度地球系统模型中不可或缺的组成部分。在对流边界层中，当位温、湿度等守恒属性的平均垂直梯度近似为零时，标准方法（通过涡扩散系数将湍流通量与平均垂直梯度相关联）必须通过针对大气边界层中典型非对称上升气流和下沉气流的质量通量参数化进行扩展。本研究提出了一种基于生成对抗网络的干对流边界层参数化方案。该模型融入了Deardorff经典混合层理论中自相似层增长的物理机制，从而增强了生成式机器学习算法的训练数据库，显著提升了边界层内不同高度处合成湍流场统计特性的预测效果。算法训练基于全三维直接数值模拟数据。与随机参数化方案不同，本模型能够预测不同高度处浮力波动、垂直速度及浮力通量的高度非高斯瞬态统计特征，从而捕捉到进入稳定顶层区域的最强热羽流。我们的生成式算法结果与标准双方程或多羽流随机质量通量方案相吻合。此外，本参数化方案还能提供湍流对流的颗粒状水平组织特征——这是其他任何闭合模型都无法获得的。本研究为在其他自然流场（如湿对流、上层海洋混合或恒星内部对流）中实现高效数据驱动型对流参数化奠定了基础。