Quantifying the causal relationship between ice melt and freshwater distribution is critical, as these complex interactions manifest as regional fluctuations in sea surface height (SSH). Leveraging SSH as a proxy for sea ice dynamics enables improved understanding of the feedback mechanisms driving polar climate change and global sea-level rise. However, conventional deep learning models often struggle with reliable treatment effect estimation in spatiotemporal settings due to unobserved confounders and the absence of physical constraints. To address these challenges, we propose the Knowledge-Guided Causal Model Variational Autoencoder (KGCM-VAE) to quantify causal mechanisms between sea ice thickness and SSH. The proposed framework integrates a velocity modulation scheme in which smoothed velocity signals are dynamically amplified via a sigmoid function governed by SSH transitions to generate physically grounded causal treatments. In addition, the model incorporates Maximum Mean Discrepancy (MMD) to balance treated and control covariate distributions in the latent space, along with a causal adjacency-constrained decoder to ensure alignment with established physical structures. Experimental results on both synthetic and real-world Arctic datasets demonstrate that KGCM-VAE achieves superior PEHE compared to state-of-the-art benchmarks. Ablation studies further confirm the effectiveness of the approach, showing that the joint application of MMD and causal adjacency constraints yields a 1.88\% reduction in estimation error.

翻译：量化冰融与淡水分布之间的因果关系至关重要，因为这些复杂的相互作用表现为海面高度（SSH）的区域性波动。利用SSH作为海冰动力学的代理变量，有助于深入理解驱动极地气候变化和全球海平面上升的反馈机制。然而，由于未观测到的混杂因素以及物理约束的缺失，传统的深度学习模型在时空场景中往往难以实现可靠的处理效应估计。为解决这些挑战，我们提出了知识引导因果模型变分自编码器（KGCM-VAE）来量化海冰厚度与SSH之间的因果机制。该框架集成了一个速度调制方案，其中平滑的速度信号通过由SSH跃迁控制的Sigmoid函数动态放大，以生成基于物理的因果处理。此外，模型结合了最大均值差异（MMD）在潜在空间中平衡处理组与对照组的协变量分布，并采用因果邻接约束解码器以确保与既定物理结构的一致性。在合成及真实北极数据集上的实验结果表明，KGCM-VAE相较于现有先进基准方法实现了更优的PEHE。消融研究进一步验证了该方法的有效性，表明联合应用MMD与因果邻接约束可使估计误差降低1.88%。