Study of seasonal trends in flood data with the partial duration series model
The partial duration series (pds) method for flood frequency estimation analyzes ail flood peaks above a certain base level, or truncation level, QB, along with the times of occurrence of these flood « exceedances ». It has been shown that seasonal trends in river-flow 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 time-dependent 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 New-Brunswick, Canada. Knowing the base level, QB, 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 QB. Regression equations, using one or more transformed or untransformed independent variables, are derived. Results for the province of Quebec show that the two-year flood estimate QDA explains 92.5 % of the variability of the base flow QB, and the drainage basin area SD explains 83 % of QB variability. The existence of a strong correlation between QB 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 New-Brunswick, 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. Both versions of the graphical procedure are based on the same idea, and call 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 New-Brunswick. 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 New-Brunswick. 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.