In a warming planet, the thermodynamic and dynamic environments of climate system have been altered, affecting the biogeochemical processes between the geosphere and atmosphere, which has substantial impacts on hydrological extremes and the terrestrial carbon budget. It was traditionally expected that the precipitation extremes should non-monotonically intensify with atmospheric warming. However, the reduced or hook-like sensitivity of extreme precipitation to temperatures have been pervasively reported, which seems counterintuitively contract the increases in precipitation extremes. How to physically explain the hook structure remains highly controversial in the hydrological and climate communities. I will reveal the physical mechanism of extreme precipitation trajectories by combining atmospheric physics and climate models, and then understand their complicated effects on hydrological extremes (e.g., heatwaves, storms, floods, droughts, and compound hazards). Moreover, I will present how to constrain the water-carbon cycle by machine learning and atmospheric dynamics, and finally quantify their feedbacks on socio-economic productivity and terrestrial carbon sink.