Misinformation about climate change poses a significant threat to societal well-being, prompting the urgent need for effective mitigation strategies. However, the rapid proliferation of online misinformation on social media platforms outpaces the ability of fact-checkers to debunk false claims. Automated detection of climate change misinformation offers a promising solution. In this study, we address this gap by developing a two-step hierarchical model, the Augmented CARDS model, specifically designed for detecting contrarian climate claims on Twitter. Furthermore, we apply the Augmented CARDS model to five million climate-themed tweets over a six-month period in 2022. We find that over half of contrarian climate claims on Twitter involve attacks on climate actors or conspiracy theories. Spikes in climate contrarianism coincide with one of four stimuli: political events, natural events, contrarian influencers, or convinced influencers. Implications for automated responses to climate misinformation are discussed.