Methods
Spring flood
identification
Two spring streamflow characteristics, the magnitude
(Qmax) and timing of specific peak flow
(QmaxT, in day of year or DOY) were selected to
characterize the spring freshet, and their interannual variability
calculated from the daily flow historical records. A sufficiently large
spring window of four months, from March 1st to June 30th, was selected
based on the observed seasonal cycle of the streamflow records and
considering the inter-annual and spatial variability of the spring
freshet of all basins. The observed Qmax and
QmaxT values within this time window were identified for
every year. Then, the pre-flood period was defined to extend between the
flood onset point, defined here as the point that marks the beginning of
the rise in streamflow, and the peak flow date (Fig. 2). The onset point
was identified as the first date having a flow value above the 30%
percentile of the annual flow distribution and followed by a continuous
increase in flow over a minimum of three consecutive days, before the
peakflow date. This automatic procedure worked well for most years and
basins, but exceptions were noted upon visual inspection. Intermittent
snowmelt occurred during some years due to low air temperatures
associated with the advection of cold polar air masses, which interrupts
snowmelt for several days and causes separate floods according to
melting events (Mazouz et al., 2012). This makes it difficult in some
years to precisely pinpoint a general flood onset date and this decision
may subsequently influence the relation between the peak flow magnitude
and the pre-event hydroclimate conditions. Hence for some years the
percentile threshold was either adjusted, or the point was chosen
manually when the automatic algorithm failed.
Antecedent factors and statistical analysis of spring
freshet
peak
In total, six antecedent factors related to snowmelt, rainfall and soil
moisture were selected and calculated during the pre-flood period as
defined in section 3.1., except for the maximum (peak) SWE, which was
calculated between the beginnings of spring (March 1) and the peak flow
date. The Cemaneige model simulates snow accumulation and melt in five
equal-area altitudinal bands based on the air temperature and
precipitation interpolated to the median altitude of each band. A
basin-wide SWE value was derived by averaging the SWE from all bands.
The contribution of snowpack conditions to the variations in spring peak
flow characteristics (Qmax and QmaxT)
was assessed by three variables. The maximum SWE, SWEmax(mm), simulated by the model before the melt, represents the amount of
snow accumulated and to be released during the spring freshet. The
cumulated amount of pre-flood snowmelt, there after ‘cumulative
snowmelt’ (Meltsum, mm), and the snowmelt intensity, or
average melting rate (Meltint, mm/d), were also
calculated over the pre-flood period to evaluate their contribution to
interannual variability in peak flow characteristics.
Rainfall is used as another antecedent condition that can affect spring
floods by changing snowpack characteristics or directly contributing to
runoff. The sum of daily rainfall, Rainsum (mm),
accumulated during the pre-flood period, was calculated after separating
the solid and liquid fraction in the snow model. The mean rainfall
intensity, Rainint (mm/d), was also calculated during
the pre-flood period. The mean soil moisture saturation level during the
pre-flood period, Smean (unitless), was simulated by the
model and used as another antecedent factor. The selected antecedent
factors are summarized in Table 3.
The time of transfer of the basin must be considered when deriving
pre-flood hydroclimatic drivers. In the GR4J, this is represented by the
calibrated base time of the unit hydrograph, which varied between 2 and
4 days (see Table 2). However, this parameter (x4) was calibrated over
the entire year and is likely to overestimate the faster time of
transfer in spring, when rainfall events falling on snow or frozen
ground cause rapid runoff. For this reason, a common value of one day
was used instead for all basins, i.e., preconditioning variables were
calculated from the flood onset date up to 1 day before the flood peak
date.
Multivariate linear regression analysis was first used to identify the
relative contribution of rainfall and snowmelt volumes to the
interannual variability in flood volumes. The relative contributions
were derived from the standardized coefficients of the multivariate
regression model. The relationship between the antecedent hydroclimatic
factors and peak streamflow characteristics was first assessed by linear
univariate correlation analysis using the Pearson correlation
coefficient. Then, a stepwise multivariate regression analysis was
performed to identify the best predictors of peak flow
(Qmax) (Equation 1).
Y = β0 + β\(1X1\) +
β\(2X2+\ldots+\beta n\text{Xn}\ +\epsilon\ \) (1)
where β0 is the intercept, β1…n are the regression slope
coefficients and \(\epsilon\) is a random error term (Draper and Smith,
1998). The stepwise method consists in choosing the combination of
pre-flood predictor variables (X ) which together best explain the
interannual variability of flood characteristics
(response variable Y ) using
an iterative procedure. The stepwise procedure requires two significance
levels for adding and removing predictors based on a variance ratio (F)
test, for the improvement of the model. Starting with the initial model,
a p- value for the F-statistic is calculated at each step of
adding or removing a variable in the model (Draper and Smith, 1998). An
entrance tolerance p- value of < 0.05 and an exit
tolerance p- value < 0.10 were used.