Publisher: Copernicus Publications
Subjects: T, G, GE1-350, Geography. Anthropology. Recreation, Environmental technology. Sanitary engineering, Environmental sciences, Technology, TD1-1066
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
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.
The results below are discovered through our pilot algorithms. Let us know how we are doing!
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