Modelling the extreme joint hazard risks of compound wind gusts and precipitation during the summer and winter periods for major cities in Canada

Compound extremes of wind-gust speed (WGS) and 24-h total precipitation amount (TPA) in summer and winter pose substantial risks for Canadian communities. Two bivariate samples were constructed at each station: annual-maximum WGS (or AMWGS) or AMTPA with corresponding TPA (or WGS), evaluated at lags 0 and 1 day. Extreme-value copulas with one- and two-component mixture margins were fitted to estimate joint and conditional probabilities and return periods (RPs), assessing how season and timing shape co-occurrence. Across stations, OR RPs are consistently shortest, Kendall RPs intermediate, and AND RPs longest. As paired design quantiles rise, AND and Kendall RPs shorten, revealing significant compound risk even when individual variables are only moderate. Toronto shows the most frequent summer co-occurrence; Halifax is similar and sensitive to 1-day offsets. Vancouver co-occurs mainly in summer, rarely in winter. Montreal and Quebec City show longer summer recurrence but notable winter stress. Calgary has high WGS but weaker WGS-TPA coupling. Regina is intermediate, with lags that weaken coupling for WGS-led pairs and can strengthen TPA-led ones. Conditional analysis at the 75th and 95th percentiles shows that modest increases in WGS or TPA shortened joint RPs. Effects are asymmetric: in summer, high WGS reduces AMTPA conditional RPs more than high TPA reduces AMWGS (strongest in Halifax, Vancouver, and Quebec City with 1-day offsets). In winter, risk is mainly WGS-led. Parametric-bootstrap uncertainty (95% ribbons for univariate return levels; 95% ellipses for bivariate AND/OR loci) widens with RP and heavier tails yet closely tracks the fits, supporting robustness. At Québec City, seasonal time-varying analysis shows two regimes. Summer (AMTPA–WGS, ±1 day): dependence strengthens (late-1970s to early-1990s), pushing design points higher; AND RPs at fixed thresholds shorten ), OR RPs lengthen, and AMTPA conditional RPs given high WGS decline. Winter (AMWGS-TPA, 0 lag): changes are mainly higher AMWGS with largely stable dependence. These findings inform hazard-reduction planning and support sustainable environmental management under compound climate extremes.