Bogardii, J.J. and L. Duckstein (1993). Event-based analysis
of the dry spell phenomenon. Rev. Sci. Eau,
6 (1) : 23-46. [article in french]
Original title : Evénements de période sèche
en pays semi-aride.
One form of drought is the interruption of the rainy season
by a sa called dry spell. Dry spell can be defined as a sequence of dry days
including days with less than a threshold value of rainfall.
A dry spell, defined a on daily scale, becomes untraceable by statistics
using longer than one-day-long equidistant time intervals. If the daily
discretization of the rainy season is te be avoided, an intermediate technique
Event-based analysis of the rainfall and dry spell provides This approach.
The method is demonstrated with data from the Dodoma Region, situated in the
semiarid highlands of Tanzania. The climate is characterized by one rainy tesson
from the and of November until the end of April. The occurrence of rainfall
The average seasonal precipitation is about 600 mm with variations between
450 and over 800 mm. Rainy seasons are separated by an almosl 7 month long
During the rainy season convective type storms prevail. Single storms lasi
a few hours, but their occurrence is clearly grouped within the timespan of
a few days, separated by the dry spells which are usually much longer.
Conventional statistics of dry spells are summarized in tables 1 and 2 using
1.0 mm daily precipitation as the threshold.
It is shown that dry spells occur
randomly during the rainy season. For the event-based analysis dry spell is
detined as a dry event. Dry events are considered as a sequence of dry days
separated by rainfall events from each other. Thus the rainy season is detined
as a series of rainfall and subsequent dry events. Rainfall events are defined
as the uninterupted sequence of rainy days, when at least on one day more
than a threshold amount of rainfall has been observed- Rainy days with less
Man the threshold depth of precipitation are accounted for the rainfall event
if they occur in an uninterrupted sequence. Only isolated subthreshold rainfall
will be discarded, and considered as part of a dry event (fig. 2). ln this
analysis the threshold value of 5.0 mm/day was seiected.
The comparison of tables 1 and 4 shows that the length of the mean maximum
dry spell doubles by replacing the 1.0 mm/day threshold by 5.0 mm/day. The
sequence of rainfall and dry events is characterized by Dn, m, duration
of the mth rainfall of the nth rainy season, and by the inter-event time Zn,
m (duration of the dry event) between the end at the preceding and the
start of the succeeding rainfall event.
In case of convective type storms the series of the subsequent events (either
dry or rainfall) could be considered independent, thus their number/season
should follow the Poisson distribution.
In case of independence of subsequent events, the waiting lime for a new event
must follow the exponential pdf.
By measuring the waiting time in days the discrets equivalent of the
exponential pdf can be used.
Since the sequences of convective type storms de not contain purely independent
events, the waiting time t follows instead the discrete counterpart of the
2 parameter gamma pdf, the negative binomial pdf. This modified Poisson-modal,
Poisson pdf for the number of rainfall events and the negative binomial pdf
for the length of the inter-event lime has been applied to describe the rainy
season. Table 3 summanzes the parameters r and p for different rein gangas.
By focusing on the dry spell event, the duration of the rainfall events Dn,
in fact be identified as inter-event time. This change of rotes fils the
original Poisson model better. Since rainfall events are shorter, their duration
the geometrical pdf, as theoretically required.
The Poisson pdf seems to fit slightly better the number of dry events than
the rainfall ones (fig. 5). If has to be pointed out that the event-based
definition of the rainy season dues not exactly fit the theoretical precondition,
to have a certain fixed period. Rainy seasons have variable longths, as they
are a stochastic fonction of the events themselves. For "modal fitting" the
consideration of the core of the rainy season, from January to April would
be a better choice. However it would truncate the physical phenomenon wilh
the potentiel omission of extrema long dry events. Therefore, in spite of mediocre
fitting, the Poisson modal will be used ln analysis.
Tables 4 and 5 summarize the statistical characteristics of the dry events
for the selected rain gouges for bath the whole, and for the core of the rainy
Dry events accurring in the core of the rainy season were identified as those
ending within the timespan of January -April.
The mean lengths of the longest dry spells in the core are less than the corresponding
value for the whole season. However, at two stations, Kondoa and Gwandi, in
more han 70 % of the season the longest dry spell did occur during the core.
This coincidence was only 40 % for the Farkwa rain gauge.
For planning purposes,
the longest dry spells associated with the varions statistical recurrence
periods are derived on the basis of the fitted Pearson III type probability
functions (fig. 6, table 6).
The event-based analysis, relying on the expected number ot events/season
and the negative binomial pdf for the length of the dry events, can also be
to approximate the distribution of the extreme long dry spells. Contrary to
the Pearson III distribution fitted to the seasonal extreme values, the negative
binomial pdf f (n) determines the probability that a random dry event would
last n days.
Consequently, the exceedence probability Pe (N), that an extreme
long dry event would occur at least once within a given statistical recurrence
period of T
years must be equal to the reciprocal value of the product •T,
where R denotes the expected number of dry eventslyear (season). •T
specifies the expected number of "trials" needed to observe at least
once the extreme duration of N days associated with the return period of T
The length of this
extreme dry spell can then be obtained from the cumulative negative binomial
pdf (table 6). The deviations observed for low number of "trials" between
the event-based and the extreme seasonal value approach are due to the conceptual
Table 7 displays the simultaneous occurrence of dry events at several rain
gauges. By using Farkwa as the reference station, table 7 does not account
for dry events that might have occurred simultaneously at Gwandi and Kandoa
without having been recorded at Farkwa.
Except for the very short (1 or 2 days) and the very long dry events (over
30 days), the overwhelming majority of the dry events occurred at least at
two stations simultaneously. Furthermore, excluding the 1, 2 or more than
30 day - long events, more than 63 % of the dry events have been observed at
Two (or three) dry events were only classified as simultaneous if more than
hall of the duration of the reference event at Fartwa was overlapped by an
uninterrupted dry event at the other station (s).
Event-based analysis, even if it is carried out on the bases of a few years
of observation, can rely on large number of data points (table 3).
While the expected
number of events/season is still derived from very few data, this estimate
is more reliable than the approximative expected length of the longest seasonal
dry spell, since the variability of the former is usually less than that of
the latter, for the same data sets (table 8).
Event-based analysis, semi-arid countries, dry period, rainy
season, Poisson distribution, dry events, negative binomial distribution, geomefric
distribution, Pearson III distribution, generation of synthetic events.
Bogardii, J.J., Department of Water Resources, Wageningen
Agncultural University, 6709 PA Wageningen, The Netiierlands