Influence of time step on flood design using the instantaneous unit hydrograph method in Shandong Province

The instantaneous unit hydrograph (IUH) method is one of the primary recommended methods for flood design in small and medium-sized catchments in Shandong Province, China. The selection of the calculation time step (Δt) directly affects the shape of the flood hydrograph and the peak discharge. Based on the fundamental principles of the IUH method, combined with the Shandong Provincial Hydrological Manual and engineering practices, influences of time step design on flood design is analysed. The study shows that an overly large time step leads to excessive smoothing of the unit hydrograph, resulting in underestimated peak discharge and a lag in time of peak discharge. Conversely, an excessively small time step can improve calculation accuracy but increases computational effort and is constrained by the division of net rainfall time steps. Shandong Province has established differentiated recommended ranges for the time step based on catchment’s concentration characteristics: 0.2–6.0 h for hilly areas and 2.0–6.0 h for plain areas. For engineering designs with high peak discharge accuracy requirements, it is recommended to adopt a refined time-step method near the flood peak, ensuring that the time step is less than 1/3-1/4 of the lag time of flood peak, which can effectively control peak discharge calculation errors. This study provides a reference for the rational selection of the time step in flood design using the IUH method in Shandong Province.