We present a comprehensive inter-comparison of linear regression (LR), stochastic, and deep-learning approaches for reduced-order statistical emulation of ocean circulation. The reference data set is provided by an idealized, eddy-resolving, double-gyre ocean circulation model. Our goal is to conduct a systematic and comprehensive assessment and comparison of skill, cost, and complexity of statistical models from the three methodological classes. The model based on LR is considered as a baseline. Additionally, we investigate its additive white noise augmentation and a multi-level stochastic approach, deep-learning methods, hybrid frameworks (LR plus deep-learning), and simple stochastic extensions of deep-learning and hybrid methods. The assessment metrics considered are: root mean squared error, anomaly cross-correlation, climatology, variance, frequency map, forecast horizon, and computational cost. We found that the multi-level linear stochastic approach performs the best for both short- and long-timescale forecasts. The deep-learning hybrid models augmented by additive state-dependent white noise came second, while their deterministic counterparts failed to reproduce the characteristic frequencies in climate-range forecasts. Pure deep learning implementations performed worse than LR and its simple white noise augmentation. Skills of LR and its white noise extension were similar on short timescales, but the latter performed better on long timescales, while LR-only outputs decay to zero for long simulations. Overall, our analysis promotes multi-level LR stochastic models with memory effects, and hybrid models with linear dynamical core augmented by additive stochastic terms learned via deep learning, as a more practical, accurate, and cost-effective option for ocean emulation than pure deep-learning solutions.

中文翻译：

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构建低维海洋模型的数据驱动方法比较

我们提出了线性回归 (LR)、随机和深度学习方法的综合比较，用于海洋环流的降阶统计模拟。参考数据集由理想化的涡旋双环流海洋环流模型提供。我们的目标是对三种方法学类别的统计模型的技能、成本和复杂性进行系统和全面的评估和比较。基于LR的模型被认为是基线。此外，我们研究了其加性白噪声增强和多级随机方法、深度学习方法、混合框架（LR 加深度学习）以及深度学习和混合方法的简单随机扩展。考虑的评估指标是：均方根误差、异常互相关、气候学、方差、频率图、预测范围和计算成本。我们发现多级线性随机方法在短期和长期预测中表现最佳。由附加状态相关白噪声增强的深度学习混合模型排在第二位，而它们的确定性对应模型未能重现气候范围预测中的特征频率。纯深度学习实现的性能比 LR 及其简单的白噪声增强更差。LR 的技能及其白噪声扩展在短时间尺度上相似，但后者在长时间尺度上表现更好，而 LR-only 输出在长时间模拟中衰减为零。总体而言，我们的分析促进了具有记忆效应的多级 LR 随机模型，