Climate change is a pressing global challenge, and X (Twitter) has become an important arena where disasters and policy events shape public sentiment. Natural language processing has been widely applied to climate-related social media discourse, but sentiment classification, event detection, and event-specific topic modeling have typically been used separately rather than connected within a single reproducible workflow. This study addresses this gap with a transparent sentiment-to-topic pipeline. A tweet corpus from April 2015 to March 2026 was assembled from three datasets. Valence Aware Dictionary and sEntiment Reasoner (VADER) and Twitter-RoBERTa (Robustly Optimized BERT Pretraining Approach) were benchmarked against a manually annotated subset, and the better performer built the daily sentiment time series. A rolling-threshold procedure flagged candidate peaks, the days on which average sentiment deviated sharply from its recent baseline. These were cross-checked against records of disasters from the Emergency Events Database (EM-DAT) and Conference of the Parties events under the United Nations Framework Convention on Climate Change (UNFCCC), then filtered with Tukey's interquartile-range criterion to retain the strongest as high-impact events. Pre- and post-event sentiment around these events was analyzed across multiple windows, and Latent Dirichlet Allocation (LDA) was applied to selected event windows using coherence-based screening, robustness checks, and manual inspection. Twitter-RoBERTa outperformed VADER, and Tukey filtering retained 10 high-impact events. Most showed pre-event turbulence followed by sustained week-long shifts or sharp, short-lived responses. LDA topics revealed three categories: political figures and policy speeches, climate skepticism and denial, and physical climate impacts. Cross-checking these events produced one clear match and two loose ones, indicating that several peaks aligned with political or media events not captured by either database. The study contributes a data-driven workflow that links sentiment shifts on X to event detection and topic modeling, identifying high-impact events through a fixed statistical procedure.