Introduction of the neural framework for stationary and nonstationary probability distribution modelling of hydroclimatological extremes in Canada, and performance comparison with classical models

Canada. We analyze annual maximum 24-hour precipitation (AMTPA) during summer and winter for Montreal, Quebec City, and Toronto, and annual peak discharge (Qmax) for the Fraser and Saint John Rivers. Classical parametric frequency analysis (FA) remains standard for design rainfall and flood estimation but can be sensitive to rigid distributional/tail assumptions, leading to biased high-return-period (RP) quantiles, especially for short records and under time-varying (TV). We introduce a neural network (NN) framework that learns the full marginal distribution by training on empirical targets based on Gringorten plotting positions. Building on this, we extend the model to nonstationarity NN-TV, by incorporating a time covariate to learn evolving conditional distributions and nonstationarity return levels (RLs) and RPs. NN/NN-TV models are benchmarked against parametric, kernel density, extreme-value mixture, and parametric-TV (via generalized additive model for location, scale, and shape (GAMLSS)) baselines. Bootstrap resampling and deep ensembles quantify aleatoric and epistemic uncertainty in uncertainty in nonstationary design curves. Under stationarity, compact NN architectures selected via cross-validation outperform classical baselines, especially in the upper tail. NN-based design quantities remain tightly constrained within 90 % bootstrap intervals. Under diagnosed nonstationarity, NN-TV reconstructs evolving extremes more accurately and stably than parametric-TV models, reducing RMSE by roughly half for Quebec City winter AMTPA compared with the best parametric-TV baseline. Deep ensembles and bootstrap refits decompose uncertainty in nonstationary RLs into epistemic and sampling components. Also, translate nonstationary design curves into explicit probabilities of trend direction, revealing declining summer AMTPA in Toronto, episodic winter AMTPA variability in Quebec City, and increasing Qmax in Saint John River. Combined with trend-slope diagnostics, they turn NN-TV design curves into explicit probabilities of rising and falling risk, strengthening climate-adaptive and risk-informed planning. • Neural network (NN) framework developed for stationary and time-varying (TV) hydrologic extremes. • NN provides a superior alternative to classical frequency‑analysis models. • Stationary NN return levels and return periods remain well constrained for long horizons. • NN-TV yields smooth, stable nonstationary design curves within bootstrap limits. • Deep ensembles show lower Toronto summer risk, episodic Quebec winters, and rising Saint John flood hazard. • The framework offers a flexible, distribution‑focused tool for climate‑adaptive design.