LARGE NEGATIVE BIASES IN DESIGN RAINFALL CAUSED BY TEMPORAL AGGREGATION OF PRECIPITATION DATA AND BY EXTRACTING MAXIMA FROM A SUBSET OF ALL STORMS

摘要

In previous work, we derived Depth-Duration-Frequency (DDF) values at a research weather station in Concepcion, Chile. When comparing with the officially-recommended values, used for engineering design, we found severe underestimation in the latter, particularly for shorter durations. We hypothesised that there could be methodological causes behind this large bias, potentially implying a nation-wide problem, which could very well explain the perennial failure of urban storm water systems in Chile. In this work, we analyse two alternative explanations for the observed underestimation: (i) the use of temporally-aggregated instead of continuous rainfall data, and (ii) considering only the four largest storms per year when extracting the rainfall maxima, instead of sampling all independent storm events. Similar procedures have been traditionally used in Chile and other countries to obtain DDF values. In order to obtain both the mean and variability in the bias, for each one of the two studied effects, we did our analyses with precipitation data from 52 different weather stations in Switzerland. Each location had the same brand and model of instrument, and the same gauging protocols, over a concurrent, continuous 32 year-long (1982-2013) record consisting of accumulated rainfall over 10 min-long aggregation periods. We first obtained the "correct" DDF values at each station, for rainfall durations of 1, 2, 3, 4, and 5 h, considering the full-resolution data and all storms in the record. We then generated alternative DDF values, first by aggregating the original 10-min data over increasing time windows (20, 30, and 60 min), and then by extracting the rainfall maxima from only the four largest storms for every year in the record. In order to avoid estimation problems, we only worked with frequent, 1 to 5 year return periods, and the DDF values were obtained directly from ranked partial duration series. Biases introduced by (i) temporal aggregation, (ii) considering only a subset of storms, and (iii) using both procedures simultaneously, were then computed and analysed. Even though there are differences between locations, results were quite similar overall, and actually quite surprising: Two accepted practices, the aggregation of rainfall data over even "reasonably short" periods and not considering all storms when searching for the maxima, result in large underestimation of design precipitation. For example, in the case of the 1-hr rainfall with return periods T between 1 and 5 yr, aggregating rainfall data over 60 min-long periods causes a mean bias of -10.4% (averaging over all locations and return periods), which can go up to -22.6% for T=5 yr, at some locations. In turn, and again for the 1-hour rainfall, extracting the maxima from only the four largest storms per year instead of considering all storms, introduces a mean (averaging across all locations) bias of -35.5% for T=1 yr, which monotonically decreases to -14.9% for T=5 yr. The maximum underestimation due to this effect can reach up to 57%. As should be theoretically expected, both effects decrease sharply for increasing rainfall durations. Still, their combination (i.e., as is done in Chile: aggregating data over fixed 60 min intervals and simultaneously considering only the four largest storms when extracting the maxima) results in mean biases of -24.9%, -12.9%, -7.4%, -5.0% and -3.3%, for durations of 1, 2, 3, 4, and 5 h, respectively, for T=5 yr, which increase for more frequent return periods. In the mean, these two methodological effects do indeed cause severe negative biases in DDF values, when averaging over 52 Swiss stations. For individual stations though, the underestimation can be up to 5.1 times as high as the average, depending on rainfall duration, for T=5 yr. It must also be remembered that the original data used in these analyses are not continuous but were already aggregated over 10-min periods, so that the actual biases should be even higher than what we