Characteristics of the Underestimation Error of Annual Maximum Rainfall Depth Due to Coarse Temporal Aggregation

This study analyzed all characteristics of the error committed in evaluating annual maximum rainfall depth, H-d, associated with a given duration, d, when data with coarse temporal aggregation, t(a), were used. It is well known that when t(a) = 1 min, this error is practically negligible while coarser temporal aggregations can determine underestimation for a single H-d up to 50% and for the average value of sufficiently numerous series of H-d up to 16.67%. By using a mathematical relation between average underestimation error and the ratio t(a)/d, each H-d value belonging to a specific series could be corrected through deterministic or stochastic approaches. With a deterministic approach, an average correction was identically applied to all H-d values with the same t(a) and d while, for a stochastic correction, a thorough knowledge of the statistical characteristics of the underestimation error was required. Accordingly, in this work, rainfall data derived from many stations in central Italy were analyzed and it was assessed that single and average errors, which were both assumed as random variables, followed exponential and normal distributions, respectively. Furthermore, the single underestimation error was also found inversely correlated to the corresponding annual maximum rainfall depth.