Describing the interannual variability of precipitation with the derived distribution approach: effects of record length and resolution

Abstract

Interannual variability of precipitation is traditionally described by fitting a probability model to yearly precipitation totals. There are three potential problems with this approach: a long record (at least 25–30 years) is required in order to fit the model, years with missing rainfall data cannot be used, and the data need to be homogeneous, i.e., one has to assume stationarity. To overcome some of these limitations, we test an alternative methodology proposed by Eagleson (1978), based on the derived distribution (DD) approach. It allows estimation of the probability density function (pdf) of annual rainfall without requiring long records, provided that continuously gauged precipitation data are available to derive external storm properties. The DD approach combines marginal pdfs for storm depths and inter-arrival times to obtain an analytical formulation of the distribution of annual precipitation, under the simplifying assumptions of independence between events and independence between storm depth and time to the next storm. Because it is based on information about storms and not on annual totals, the DD can make use of information from years with incomplete data; more importantly, only a few years of rainfall measurements should suffice to estimate the parameters of the marginal pdfs, at least at locations where it rains with some regularity. For two temperate locations in different climates (Concepción, Chile, and Lugano, Switzerland), we randomly resample shortened time series to evaluate in detail the effects of record length on the DD, comparing the results with the traditional approach of fitting a normal (or lognormal) distribution. Then, at the same two stations, we assess the biases introduced in the DD when using daily totalized rainfall, instead of continuously gauged data. Finally, for randomly selected periods between 3 and 15 years in length, we conduct full blind tests at 52 high-quality gauging stations in Switzerland, analyzing the ability of the DD to estimate the long-term standard deviation of annual rainfall, as compared to direct computation from the sample of annual totals. Our results show that, as compared to the fitting of a normal or lognormal distribution (or equivalently, direct estimation of the sample moments), the DD approach reduces the uncertainty in annual precipitation estimates (especially interannual variability) when only short records (below 6–8 years) are available. In such cases, it also reduces the bias in annual precipitation quantiles with high return periods. We demonstrate that using precipitation data aggregated every 24 h, as commonly available at most weather stations, introduces a noticeable bias in the DD. These results point to the tangible benefits of installing high-resolution (hourly, at least) precipitation gauges, next to the customary, manual rain-measuring instrument, at previously ungauged locations. We propose that the DD approach is a suitable tool for the statistical description and study of annual rainfall, not only when short records are available, but also when dealing with nonstationary time series of precipitation. Finally, to avert any misinterpretation of the presented method, we should like to emphasize that it only applies for climatic analyses of annual precipitation totals; even though storm data are used, there is no relation to the study of extreme rainfall intensities needed for engineering design.