Quantifying the causal relationship between sea ice thickness and sea surface height (SSH) is essential for understanding the mechanisms driving polar climate dynamics. Conventional deep learning models often struggle with treatment effect estimation in climate settings due to time-varying confounding and the lack of physical constraints. To address these challenges, we propose the Knowledge-Guided Causal Model Variational Autoencoder (KGCM-VAE) to quantify the effect of SSH on sea ice thickness. The framework leverages established physical relationships between SSH and surface velocity to generate physically grounded, time-varying continuous treatments, where each treatment value can change at every time step within a sequence. The model also incorporates Maximum Mean Discrepancy (MMD) to balance treated and control distributions in the latent space, mitigating observed confounding bias. Using synthetic data, we evaluated the model's ability to predict sea ice thickness responses under hypothetical SSH forcing scenarios, demonstrating that KGCM-VAE achieves lower PEHE compared to state-of-the-art baselines. Ablation studies further confirm that MMD consistently enhances treatment effect estimation over the base model. Additionally, we conducted a real-world case study to examine the sensitivity of sea ice thickness to SSH forcing and validate our findings against existing physical modeling results.

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