To make weather and climate models computationally affordable, small‐scale processes are usually represented in terms of the large‐scale, explicitly resolved processes using physics‐based/semi‐empirical parameterization schemes. Another approach, computationally more demanding but often more accurate, is super‐parameterization (SP). SP involves integrating the equations of small‐scale processes on high‐resolution grids embedded within the low‐resolution grid of large‐scale processes. Recently, studies have used machine learning (ML) to develop data‐driven parameterization (DD‐P) schemes. Here, we propose a new approach, data‐driven SP (DD‐SP), in which the equations of the small‐scale processes are integrated data‐drivenly (thus inexpensively) using ML methods such as recurrent neural networks. Employing multiscale Lorenz 96 systems as the testbed, we compare the cost and accuracy (in terms of both short‐term prediction and long‐term statistics) of parameterized low‐resolution (PLR) SP, DD‐P, and DD‐SP models. We show that with the same computational cost, DD‐SP substantially outperforms PLR and is more accurate than DD‐P, particularly when scale separation is lacking. DD‐SP is much cheaper than SP, yet its accuracy is the same in reproducing long‐term statistics (climate prediction) and often comparable in short‐term forecasting (weather prediction). We also investigate generalization: when models trained on data from one system are applied to a more chaotic system, we find that models often do not generalize, particularly when short‐term prediction accuracies are examined. However, we show that transfer learning, which involves re‐training the data‐driven model with a small amount of data from the new system, significantly improves generalization. Potential applications of DD‐SP and transfer learning in climate/weather modeling are discussed.

中文翻译：

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使用深度学习进行数据驱动的超参数化：使用多尺度Lorenz 96系统进行实验和转移学习

为了使天气和气候模型的计算负担得起，通常使用基于物理/半经验参数化方案的大规模，明确解决的过程来表示小规模的过程。在计算上要求更高但通常更准确的另一种方法是超级参数化（SP）。SP涉及将小规模过程的方程式集成到嵌入在大规模过程的低分辨率网格中的高分辨率网格上。最近，研究已使用机器学习（ML）来开发数据驱动的参数化（DD-P）方案。在这里，我们提出了一种新的方法，即数据驱动的SP（DD-SP），其中使用递归神经网络等ML方法将小规模过程的方程式以数据驱动的方式集成（因此价格便宜）。采用多尺度Lorenz 96系统作为测试平台，我们比较了参数化低分辨率（PLR）SP，DD-P和DD-SP模型的成本和准确性（就短期预测和长期统计而言）。我们证明，在相同的计算成本下，DD‐SP的性能明显优于PLR，并且比DD‐P更准确，尤其是在缺乏规模分离的情况下。DD-SP比SP便宜得多，但其准确性在复制长期统计信息（气候预测）时是相同的，在短期预测（天气预测）中通常可比。我们还研究泛化：将基于一个系统的数据训练的模型应用于更混乱的系统时，我们发现模型通常无法泛化，尤其是在检查了短期预测准确性时。但是，我们表明转学，这涉及用新系统中的少量数据重新训练数据驱动的模型，从而显着提高了泛化能力。讨论了DD-SP和转移学习在气候/天气模型中的潜在应用。