Influence of Rainfall Patterns on Rainfall–Runoff Processes: Indices for the Quantification of Temporal Distribution of Rainfall

To understand the influence of rainfall patterns on rainfall–runoff processes, we propose two indices: skewnessPEAK (skewp), representing the relative timing of peak rainfall, and the normalized root-mean-square error peak (NRMSEp), which quantifies the concentration of rainfall near the peak. By analyzing approximately 25,000 rainfall scenarios, we examined the relationship between these indices and peak flood discharge in the rainfall–runoff process. The analysis revealed that peak flood discharge positively correlates with the NRMSEp, indicating that concentrated rainfall near the peak substantially increases discharge. Conversely, a negative correlation with skewp suggests that earlier peak rainfall reduces discharge. These insights were synthesized into a three-dimensional solution space providing a comprehensive framework for predicting how variations in rainfall distribution affect flood discharge. The findings underscore the importance of incorporating these indices into real-time flood forecasting models and urban flood risk management strategies.