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Extreme rainfall events in hyper-arid regions are rare but can trigger disproportionally large hydrological and geomorphological responses. On 24–26 March 2015, an unprecedented precipitation event struck the Atacama Desert in northern Chile, producing destructive floods in normally dry basins, including the Salado River Basin. This study investigates the hydrological response of this hyper-arid catchment using the fully coupled Atmospheric and Hydrological Modeling System (AHMS), which integrates the Weather Research and Forecasting (WRF) model with the distributed Hydrological Modeling System (HMS) through the Noah-MP land surface model. A 13-day online simulation is performed to reproduce the extreme event, while an 8-year offline simulation driven by ERA5 reanalysis data is conducted to place the 2015 flood within a longer-term hydrological context. The online simulation reproduces intense precipitation over the high-elevation Precordillera, with accumulated rainfall exceeding 120 mm, and generates peak discharges of approximately 1000 m3 s−1 at El Salado and about 930 m3 s−1 at Chañaral, consistent with previous independent estimates. The offline simulation indicates that such discharges are far outside typical basin conditions, with probability density functions of daily streamflow showing that the 2015 event exceeds the 99.9th percentile of the modeled distribution. Despite severe data limitations, this study provides a process-based numerical reconstruction of runoff generation in one of the driest environments on Earth, highlighting both the potential and the limitations of fully coupled atmospheric–hydrological modeling for extreme flood analysis in data-sparse hyper-arid basins.