
Citation
Ashkar, F., ElJabi, N. and T.B.M.J. Ouarda (1993). Study
of seasonal trends in flood data with the partial duration series model. Rev.
Sci. Eau, 6 (2) : 131152. [article in french]
Original title : Etude
des variations saisonnières des crues par le modèle de dépassement.
Full
text (PDF)

Abstracts
The partial duration series (pds) method for flood frequency
estimation analyzes ail flood peaks above a certain base level, or truncation
level, Q_{B}, along
with the times of occurrence of these flood « exceedances ».
It has been shown that seasonal trends in riverflow processes have a significant
effect on the distribution of flood exceedances. Two pds models have been
presented in the literature for studying these seasonal variations in flood
magnitude. The first, which can be called the « discrete seasonal pds
mode) », divides the year into n seasons and determines n different
distribution functions to fit the exceedances in each of these n seasons.
The second, which can be called the « continuous seasonal pds model »,
accounts for seasonal flood variations by modeling flood magnitude as a continuous
timedependent random variable. The discrete seasonal model makes a few assumptions
concerning flood characteristics, but the statistical estimation of its
parameters is considerably less complex than in the case of the continuous
seasonal
model. Results of a study using the discrete seasonal pds modal are presented
in this paper, along with two important applications of this modal in hydrology.
The model is applied to 34 gaging stations in the province of Quebec
and 28 stations in the province of NewBrunswick, Canada. Knowing the base
level, Q_{B}, is essential for applying this model, but there is no
universal technique for determining this truncation level. In this study, a
technique
is proposed that uses multiple regression for estimating Q_{B}. Regression
equations, using one or more transformed or untransformed independent variables,
are derived.
Results for the province of Quebec show that the twoyear flood estimate
QDA explains 92.5 % of the variability of the base flow Q_{B}, and
the drainage basin area SD explains 83 % of Q_{B} variability. The
existence of a strong correlation between Q_{B} and SD suggests that
it is possible to determine the base flow at sites where no historical record
is available, by using the physical characteristics
of the basin.
A graphical procedure associated with the partial duration series model is
proposed to study the seasonal trends in flood data at the selected gaging
stations. The study deals specifically with the choice of seasons to be entered
into the pds model. It is particularly emphasized that the seasons should be
determined on the basis of the data on band, instead of taking the four usual
seasons (winter, spring, summer, and fall). Two different forms of the graphical
procedure are applied to the gaging stations in the provinces of Quebec
and New Brunswick. The first, applied to the province of Quebec, consists
of plotting the mean number of exceedances A (t) in a lime interval (0, 1•]
equal 1a one year, against the lime t, for each station, and for a number of
increasing base levels. The behavior of these A (1) plots (change at slope,
piecewise linearity, etc.) indicates the significant seasons for each station.
The second form of the graphical procedure, applied to stations in the province
of NewBrunswick, is slightly different front the procedure mentioned above.
For each station of the province, a relatively high base level is selected,
corresponding to a mean number of exceedances per year in the order of 0.3
to 1.0. The Limes of occurrence of these exceedances are used to define the
significant hydrological seasons in the year, which are then presented in graphical
form. Varying the base level gives a fine seasonal partitioning of the year
for each station, and allows grouping the stations into geographical regions
that are homogeneous In seasonal flood distribution. Bath versions of the graphical
procedure are based on the same idea, and cal! far careful graphical examination
of the seasonal behavior of floods at different gaging stations.
An appropriate partitioning of the year into seasons is obtained for different
parts of the two provinces. For bath provinces, and for al' the stations that
were investigated, no more than two significant seasons were found necessary
for modeling seasonal flood variations. Based on the seasons determined for
each station, and the geographical distribution of these stations, a geographical
regionalization of seasonality Is obtained for the provinces of Quebec
and NewBrunswick. Each province is divided into tour homogeneous regions,
and appropriate seasons for each region are proposed.
The discrete seasonal model was found adequate and sufficient for the study
of the seasonal behavior of floods in the provinces of Quebec and NewBrunswick.
However, more detailed studios would be necessary to determine with more certitude
if the continuous seasonal model is more appropriate in some cases. In all
cases, a graphical examination of the empirical distribution function of
flood magnitudes occurring in various periods of the year may help either in
identifying
homogeneous periods within which flood magnitudes may be considered as identically
distributed, or In indicating a need for modeling flood magnitude as a random
variable whose distribution varies continuously with time.
Keywords
Flood, partial duration series model, stochastic mode!, base flow,
regionalization, seasonal model.
Corresponding author
Ashkar, F.,Prof., Dépt. de Mathématiques, Univ. de Moncton,
Moncton, NB EIA 3E9, Canada
Telephone : (506) 8584312
 