[论文解读] Parameter sensitivity analysis of a sea ice melt pond parametrisation and its emulation using neural networks

Simon Driscoll, Alberto Carrassi+4 more|arXiv (Cornell University)|Apr 11, 2023

Arctic and Antarctic ice dynamicsEarth and Planetary Sciences被引用 3

一句话总结

本研究采用Sobol敏感性分析方法，探究Icepack模型中海冰融池参数化（MPP）的参数敏感性，发现对不确定参数具有高度敏感性。研究提出并验证了一种数据驱动的神经网络模拟器，可准确替代基于物理的MPP，实现输入复杂度降低的同时保持长期行为一致性，展示了在气候模型中实现更优、可解释且高效的亚网格参数化的新路径。

ABSTRACT

Accurate simulation of sea ice is critical for predictions of future Arctic sea ice loss, looming climate change impacts, and more. A key feature in Arctic sea ice is the formation of melt ponds. Each year melt ponds develop on the surface of the ice and primarily via affecting the albedo, they have an enormous effect on the energy budget and climate of the Arctic. As melt ponds are subgrid scale and their evolution occurs due to a number of competing, poorly understood factors, their representation in models is parametrised. Sobol sensitivity analysis, a form of variance based global sensitivity analysis is performed on an advanced melt pond parametrisation (MPP), in Icepack, a state-of-the-art thermodynamic column sea ice model. Results show that the model is very sensitive to changing its uncertain MPP parameter values, and that these have varying influences over model predictions both spatially and temporally. Such extreme sensitivity to parameters makes MPPs a potential source of prediction error in sea-ice model, given that the (often many) parameters in MPPs are usually poorly known. Machine learning (ML) techniques have shown great potential in learning and replacing subgrid scale processes in models. Given the complexity of melt pond physics and the need for accurate parameter values in MPPs, we propose an alternative data-driven MPPs that would prioritise the accuracy of albedo predictions. In particular, we constructed MPPs based either on linear regression or on nonlinear neural networks, and investigate if they could substitute the original physics-based MPP in Icepack. Our results shown that linear regression are insufficient as emulators, whilst neural networks can learn and emulate the MPP in Icepack very reliably. Icepack with the MPPs based on neural networks only slightly deviates from the original Icepack and overall offers the same long term model behaviour.

研究动机与目标

• 通过全局方差敏感性分析，评估海冰模型输出对融池参数化（MPP）中不确定参数的敏感性。
• 评估机器学习，特别是神经网络，是否能有效模拟Icepack模型中基于物理的MPP行为。
• 通过特征选择，识别数据驱动MPP模拟器中最小但足够准确的输入变量集合。
• 探索用数据驱动模拟器替代传统基于物理的MPP的可行性，以提升计算效率和可解释性。

提出的方法

• 对Icepack中的层状冰MPP执行Sobol敏感性分析，量化参数在时空维度上对模型输出的影响。
• 利用基于物理的MPP生成的合成训练数据，训练线性回归与非线性神经网络模型，以模拟MPP的输入-输出行为。
• 采用互信息方法进行特征选择，识别最具信息量的输入变量，降低模拟器输入的维度。
• 通过将模拟器在线集成到完整Icepack模型中，验证其长期模拟保真度。
• 从模型输出精度与计算效率两方面，对比神经网络模拟器与原始MPP及线性回归模拟器的性能。
• 探讨未来工作中使用观测数据的潜力，预见到数据稀疏性与噪声带来的挑战，并提出结合数据同化与机器学习技术的策略。

Figure 1: Schematic overview of the Icepack model. Panel a: the columnar model set-up, with 4 tiles representing land, open water, slab ice (without snow) and a full ice-thickness distribution (ITD). Panel b: the most important vertical processes represented in Icepack when using the ITD. Courtesy o

实验结果

研究问题

• RQ1 Icepack模型对其中融池参数化（MPP）参数的变化有多敏感？
• RQ2 机器学习模型，特别是神经网络，能否准确模拟海冰模型中基于物理的MPP行为？
• RQ3 对于数据驱动的MPP模拟器，哪些输入变量对保持高预测精度最为关键？
• RQ4 能否通过使用少于原始MPP的输入变量，构建一个简化但性能相当的模拟器？
• RQ5 与传统参数化方法相比，数据驱动的MPP模拟器在计算效率和可解释性方面能提升多少？

主要发现

• Icepack模型对融池参数化中参数的变化表现出高度敏感性，且空间分布不均，表明微小的参数不确定性可能引发显著的预测误差。
• 线性回归模型在在线模式下无法有效模拟MPP，未能复现原始Icepack的行为，凸显了线性近似在复杂非线性过程中的局限性。
• 神经网络模拟器成功替代了Icepack中的基于物理的MPP，仅与原始模型存在微小偏差，且长期行为保持一致。
• 基于互信息的特征选择识别出一组精简的输入变量——包括上一时间步的融池面积占比、融池高度、冻结盖高度、近地表温度与空气温度、以及积雪融化速率——足以实现高性能模拟。
• 由此生成的更小规模神经网络模拟器，使用更少的输入变量，性能优异，显著提升了计算效率并增强了物理可解释性。
• 本研究展示了可行的数据驱动路径，可替代传统过参数化的MPP，实现更精确、高效且可解释的气候模型亚网格参数化。

Figure 2: Probability distribution functions we sample from using the SALib library for sensitivity analysis, for the 5 parameters invoked in the level-ice melt pond parametrisation with the mushy thermodynamics scheme (triangular and uniform). Red lines indicate default parameter values in the mode