The subgrid technique provides an efficient way to model coastal hydrodynamics using a relatively coarse grid, but incorporating small-scale geometrical details into the coarse grid model. A typical subgrid model based on the nonlinear shallow water equations applies a certain subgrid algorithm, which is based on either deterministic representation of the mass balance, or stochastically simplified momentum balance applied in the subgrid scale. In this study, we developed a data-driven subgrid approach which extracts the flow characteristics in the subgrid scale from the data pre-calculated from a full grid model. The machine learning algorithm, Random Forest method, was used in the data training process. Compared to the stochastic-based subgrid model, which has the assumption of the isotropic flow field at the subgrid scale, the data-driven subgrid approach takes into account more appropriate upscaling factors representing anisotropic subgrid effects. Test results showed that the model can provide accurate solutions even with a large subgrid ratio.

子网格技术提供了一种使用相对粗糙的网格对沿海水动力进行建模的有效方法，但是将小规模的几何细节纳入了粗糙网格模型中。基于非线性浅水方程的典型子网格模型采用某种子网格算法，该算法基于质量平衡的确定性表示，或基于子网格规模的随机简化动量平衡。在这项研究中，我们开发了一种数据驱动的子网格方法，该方法从完整网格模型预先计算的数据中提取子网格规模的流量特征。在数据训练过程中使用了机器学习算法，即随机森林方法。与基于随机的子网格模型相比，该模型具有在子网格规模上各向同性的流场的假设，数据驱动的子网格方法考虑了代表各向异性子网格效应的更合适的放大因子。测试结果表明，即使在较大的子网格比率下，该模型也可以提供准确的解决方案。