chapter - Atmospheric and Oceanic Science

Statistical analysis of extreme events in a non-stationary context
or three consecutive days on which rainfall exceeded this threshold; it would then
necessary to select, from this “cluster” of days, only the day on which the maximum
rainfall occurred. If all days in the cluster were included for analysis, the peaks
could not be considered as statistically independent. Independence between peaks
can be obtained by choosing the threshold to be very high, but if the threshold is
very high, the number of retained peaks will be small. The occurrence of “clumping”
is, of course, much more evident when the “peak” events are low discharges
below a threshold.
Independence between successive observations is also important when using
the Block method. It is almost always assumed that the events that occur in successive
years are statistically independent. This assumption is valid for the analysis of
rainfall intensities of short duration, but it may be less appropriate for the analysis
of droughts, which may extend from one hydrological year into the next. It may
also be invalid for the analysis of flood discharges in large drainage basins with
extensive storage in soils and aquifers, since above-average rainfall in one year will
fill storage, which may then contribute to the peak discharge of the following year.
Conversely, below-average rainfall in a given year will deplete the volume in storage,
so that the recharge of storage by rainfall in the following year may result in a
depletion of flood flow. This is a feature of flood peaks observed at Ladário on the
Upper Paraguay, where there is a highly significant serial correlation (0.48)
between peak flood levels in successive years. Thus, the assumptions commonly
made in the frequency analysis of flood records need to be carefully checked, in the
case of large drainage basins of South America. Serial correlation in hydrological
variables such as mean annual discharge is likely to be more important than the correlation
between annual maximum discharges, but since this report is concerned
with extremes rather than mean values, this problem is not considered further.
However it should be noted that there will be strong correlation between annual
maximum rainfall intensities of different durations (the rainfall event giving annual
maximum 5-minute and 10-minute intensities is likely to be the same); this will
be important where it is required to give confidence regions for curves that relate
rainfall intensity to rainfall duration, for different return periods.
15.2. Parametric and non-parametric methods for detecting trend in
hydrological variables
Where the Block approach is used, trends may be detected in records of
extreme rainfall, or in records of extreme discharges, by either parametric or nonparametric
methods. The Mann-Kendall test is perhaps the most well-known nonparametric
test for trend in annual values of a hydrological variable, when it can be
assumed to be independent from one year to the next; this and other non-parametric
tests have the advantage that nothing need be assumed about either the form of
probability distribution of the variable being analyzed, or the nature of the trend.
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