Greenland iceberg discharge exhibits complex nonlinear dynamics with limited observability, challenging traditional predictive models. We present a Hybrid NARX-LLM framework that combines a nonlinear autoregressive model with exogenous inputs (NARX) and a large language model (LLM) for residual correction. We further propose a Physics-Informed Prompt (PIP) method that transforms unstructured physical knowledge into structured prompts for zero-shot in-context reasoning. The primary objective is to explore the corrective potential of this framework for modeling Greenland iceberg discharge, rather than merely optimizing predictive accuracy. The NARX component captures intrinsic temporal dependencies, while the LLM, guided by PIP, encodes glacier dynamics and environmental drivers and perceives key trend patterns to correct systematic prediction errors. This integration allows the model to reason about unmodeled factors and produce interpretable residuals, enhancing overall predictive accuracy. Applied to Greenland iceberg discharge time series, our approach addresses extreme events that are difficult to predict due to rare variations and nonstationary trends, a limitation often overlooked by traditional methods. By fusing structured time-series modeling with knowledge-driven foundation AI, the framework offers a scalable and interpretable pathway to bridge data-limited climate forecasting with physics-informed LLM reasoning. The code is available.

翻译：格陵兰冰山排放表现出复杂的非线性动力学特征且可观测性有限，对传统预测模型构成挑战。我们提出了一种混合NARX-LLM框架，该框架结合了非线性自回归模型（NARX）与大型语言模型（LLM）进行残差校正。进一步提出物理信息提示（PIP）方法，将非结构化的物理知识转化为结构化提示以实现零样本上下文推理。本研究的核心目标在于探索该框架在格陵兰冰山排放建模中的校正潜力，而非单纯优化预测精度。NARX组件捕获内在时间依赖性，而由PIP引导的LLM编码冰川动力学与环境驱动因子，并感知关键趋势模式以修正系统性预测误差。这种集成使模型能够推理未建模因素并生成可解释残差，从而提升整体预测精度。将该方法应用于格陵兰冰山排放时间序列，我们成功处理了因罕见变异和非平稳趋势而难以预测的极端事件——这一局限性常被传统方法忽视。通过融合结构化时间序列建模与知识驱动的基础AI，该框架为数据有限的气候预测与物理信息LLM推理的结合提供了可扩展且可解释的路径。代码已开源。