The instantaneous unit hydrograph (IUH) is a limiting theoretical construct in surface-water hydrology: the direct-runoff response of a catchment to a unit depth of rainfall applied over an infinitesimally short duration, obtained either as the time-derivative of the S-curve or, in the Nash conceptual model, as the outflow from a cascade of linear reservoirs to an instantaneous unit inflow. Because it is duration-independent, the IUH allows direct-runoff hydrographs to be computed for arbitrarily non-uniform rainfall intensity distributions via a convolution (superposition) integral, extending the unit hydrograph method beyond its core assumptions of uniform-intensity rainfall and small catchment area. This belongs to hydrology, specifically the theory of catchment response (rainfall-runoff transformation) and its parent discipline of surface-water hydrology/hydraulic engineering.
The instantaneous unit hydrograph (IUH) is a limiting theoretical construct in surface-water hydrology: the direct-runoff response of a catchment to a unit depth of rainfall applied over an infinites…