Comparison of methods for analysis of extremes when records are fragmented: A case study using Amazon basin rainfall data

摘要

The analysis of annual extremes of hydrological and meteorological variables is frequently complicated by the presence of gaps in record, and when records are not only fragmented but also short, it is necessary to utilize to the full the information contained in them. One method is to abstract for statistical analysis all extreme events whose peaks exceed a pre-selected threshold value, but the threshold must be carefully chosen if "clumps" of peaks are to be avoided. A common alternative is a statistical analysis of maxima in years that are complete, possibly including in the analysis values from incomplete years according to some empirical rule. A plausible probability distribution has been proposed by [Jones, DA, 1997. Plotting positions via maximum likelihood for a non-standard situation. Hydrol. Earth Syst. Sci. 1, 357-366] for the extremes observed in incomplete years, which takes into account not only the proportion of record that is missing within an incomplete year, but also the effect of seasonality. As part of a larger study on the hydrology of the Amazon basin, this paper uses 484 records with length not less than 12 years from an extensive network of 750 rain gauges, to compare the method proposed by Jones (termed the DAJ method) with the following alternative procedures: (i) using only complete years of record and (ii) including years with less than 20% missing record, as if they were complete. Using the large-sample variance calculated for the annual maximum one-day rainfall with 100-year return period (P_100), the method proposed by Jones is shown to give smaller standard errors than either of the alternatives. Using the number of years in each record to calculate weighted mean variances over the 484 records, the mean standard errors of P_100 obtained by methods (i) and (ii) were 1.25 and 1.06 times the mean standard error given by the DAJ method. The precision of estimates obtained by the latter method was therefore better than either alternative.