Climate change poses significant challenges for accurate climate modeling due to the complexity and variability of non-Gaussian climate systems. To address the complexities of non-Gaussian systems in climate modeling, this thesis proposes a Bayesian framework utilizing the Unscented Kalman Filter (UKF), Ensemble Kalman Filter (EnKF), and Unscented Particle Filter (UPF) for one-dimensional and two-dimensional stochastic climate models, evaluated with real-world temperature and sea level data. We study these methods under varying conditions, including measurement noise, sample sizes, and observed and hidden variables, to highlight their respective advantages and limitations. Our findings reveal that merely increasing data is insufficient for accurate predictions; instead, selecting appropriate methods is crucial. This research provides insights into issues related to information barrier, curse of dimensionality, prediction variability, and measurement noise quantification, thereby enhancing the application of these techniques in real-world climate scenarios.

翻译：气候变化因其非高斯气候系统的复杂性和多变性，对精确气候建模提出了重大挑战。为应对气候建模中非高斯系统的复杂性，本论文提出一种贝叶斯框架，利用无迹卡尔曼滤波器（UKF）、集合卡尔曼滤波器（EnKF）和无迹粒子滤波器（UPF）处理一维和二维随机气候模型，并使用真实世界温度与海平面数据进行评估。我们在不同条件下研究这些方法，包括测量噪声、样本量、观测变量与隐变量，以阐明各自的优势与局限。研究发现，仅增加数据不足以实现精确预测；选择合适的方法至关重要。本研究为信息障碍、维度灾难、预测变异性和测量噪声量化等问题提供了见解，从而增强了这些技术在实际气候场景中的应用能力。