The shallow water equations are a set of hyperbolic partial differential equations that describe the flow below a pressure surface in a fluid, crucial for modeling weather events, ocean currents, and inundation due to tsunamis. These equations assume the horizontal length scale is much larger than the vertical scale, allowing for simplifications that make them essential in geophysical fluid dynamics applications.
Watershed modelling is the process of using mathematical simulations to represent and analyze the physical processes occurring in a watershed. This tool helps in understanding hydrological dynamics, predicting water flow, and managing water resources effectively.