Compound flooding, characterized by the co-occurrence of multiple flood mechanisms, is a major threat to coastlines across the globe. Tropical cyclones (TCs) are responsible for many compound floods due to their storm surge and intense rainfall. Previous efforts to quantify compound flood hazard have typically adopted statistical approaches that may be unable to fully capture spatio-temporal dynamics between rainfall-runoff and storm surge, which ultimately impact total water levels. In contrast, we pose a physics driven approach that utilizes a large set of realistic TC events and a simplified physical rainfall model and simulates each event within a hydrodynamic model framework. We apply our approach to investigate TC flooding in the Cape Fear River, NC. We find TC approach angle, forward speed, and intensity are relevant for compound flood potential, but rainfall rate and time lag between centroid of rainfall and peak storm tide are the strongest predictors of compounding magnitude. Neglecting rainfall underestimates 100-yr flood depths across 28% of the floodplain, and taking the max of each hazard modeled separately still underestimates 16% of the floodplain. We find the main stem of the river is surge-dominated, upstream portions of small streams and pluvial areas are rainfall-dominated, but midstream portions of streams are compounding zones, and areas close to the coastline are surge-dominated for lower return periods but compounding zones for high return periods (100-yrs). Our method links joint rainfall-surge occurrence to actual flood impacts and demonstrates how compound flooding is distributed across coastal catchments.