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.