Objective Duration-Class Partitioning and Block Discretisation for Method of Average Variability Design Hyetographs: A Bootstrap and Dynamic Programming Optimisation Framework

Design hyetographs derived with the Method of average variability (MAV) depend on two decisions usually made subjectively: the boundaries of the duration classes used to average rainfall events and the number of blocks into which the events are divided. This study proposes an objective framework for both decisions and applies it to 259 events lasting 10–120 minutes from 10 years of 5-minute rainfall data in Osijek, Croatia. The stability of each candidate MAV hyetograph was quantified by bootstrap subsampling. Admissibility required a sufficient number of rainfall events, stable peak characteristics and compliance with the prescribed discretisation constraints. Among admissible combinations, the partition of the duration range was found by exact dynamic programming (DP), implicitly considering approximately 2.1 million possible partitions. As peak dispersion increased with block count, stability was treated as a constraint, while the deviation of block durations from the recording interval was minimised. The data supported four to five classes; the selected partition, [10, 25], (25, 45], (45, 70] and (70, 120] min with 3, 7, 12 and 16 blocks, satisfied all criteria. Two subjectively defined partitions had almost three times poorer resolution and at least twice the peak dispersion, and only one of their nine classes was admissible.