Development of a macroscale distributed hydro-modeling method: Bayesian principal-monotonicity inference

•Innovate a BaPMI method for macro-scale distributed hydrologic modeling.•Apply it to a typical large cold-region watershed, Athabasca River Basin in Canada.•Verify feasibility & advantages in characterizing macro-scale cold-region hydrology.•Quantify parametric & hyperparametric sensitivities for facilitating its applications.•Reveal variabilities of climate-driven cross-scale uppermost hydro-variational effects.