Abstract
This study analyzed all characteristics of the error committed in evaluating annual maximum rainfall depth, Hd, associated with a given duration, d, when data with coarse temporal aggregation, ta, were used. It is well known that when ta = 1 min, this error is practically negligible while coarser temporal aggregations can determine underestimation for a single Hd up to 50% and for the average value of sufficiently numerous series of Hd up to 16.67%. By using a mathematical relation between average underestimation error and the ratio ta/d, each Hd 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 Hd values with the same ta 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.
Highlights
Rainfall data may be available with temporal aggregation, ta, that varies depending on the technologies used and the procedures followed by the rain gauge station manager
An average correction is identically applied to all Hd values characterized by the same ta and d while, for a more realistic correction, a stochastic approach, which requires a thorough knowledge of the statistical characteristics of the underestimation error, should be used
With the main purpose to determine the best probability function representing the single underestimation error assumed as a random variable, all errors on the annual maximum rainfall depth due to the use of “generated” data characterized by temporal aggregation in the range of 10 to 1440 min were first grouped considering different ta /d ratios
Summary
Rainfall data may be available with temporal aggregation (or time resolution), ta , that varies depending on the technologies used (for example, a recording system with paper rolls, which was largely adopted in the past, allowed hourly or half hourly aggregations) and the procedures followed by the rain gauge station manager. The rainfall characteristics such as rain rates are obtained by aggregating the number of tips over selected ta , which is a variable between one minute and 24 h. When rainfall data are aggregated, their analyses at a time scale smaller than the adopted ta are not possible. The specific choice regarding ta could influence the results of the analyses involving time durations greater than or equal to ta itself [20]
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