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Summary: The increasing frequency and severity of droughts present a significant risk to vulnerable regions of the globe, potentially leading to substantial human displacement in extreme situations. Drought-induced displacement is a complex and multifaceted issue that can perpetuate cycles of poverty, exacerbate food and water scarcity, and reinforce socio-economic inequalities. However, our understanding of human mobility in drought scenarios is currently limited, inhibiting accurate predictions and effective policy responses. Drought-induced displacement is driven by numerous factors and identifying its key drivers, causal-effect lags, and consequential effects is often challenging, typically relying on mechanistic models and qualitative assumptions. This paper presents a novel, data-driven methodology, grounded in causal discovery, to retrieve the drivers of drought-induced displacement within Somalia from 2016 to 2023. Our model exposes the intertwined vulnerabilities and the leading times that connect drought impacts, water and food security systems along with episodes of violent conflict, emphasizing that causal mechanisms change across districts. These findings pave the way for the development of algorithms with the ability to learn from human mobility data, enhancing anticipatory action, policy formulation, and humanitarian aid.