A recursive multivariate principal‐monotonicity inferential downscaling approach (ReMPMID) is proposed for climate downscaling under complexities of data uncertainties, nonlinear predictor–predictand correspondences, predictand dependencies, non‐normal distributions, spatial homogeneities, and temporal non‐stationarities. This approach is applied to the Athabasca River Basin (ARB) to verify methodological effectiveness. Many findings are revealed. For instance, ReMPMID may enable improvement of statistical downscaling reliability in comparison with selected existing approaches under these complexities at least for the ARB. The overall accuracies of ReMPMID are relatively high for temperature, while being acceptable for precipitation at the multi‐year scale. This approach may overestimate temperature in spring and winter and precipitation in summer and autumn while underestimating temperature in summer and autumn and precipitation in spring and winter to a relatively small extent. The modelling accuracies are not sensitive to one parameter (i.e. the statistical significance level) and significantly vary with another parameter (i.e. the minimum partition row number, Nmin). The calibration accuracies decrease with the climbing of Nmin and there is not a significant monotonic relationship between Nmin and the verification accuracies. The optimal value of Nmin varies with grids and predictands and shows higher uncertainty for temperature compared with precipitation. The uncertainties in ReMPMID simulations increase from summer, autumn, spring to winter for temperature and from winter, spring, autumn to summer for precipitation. These findings are helpful for gaining insights into ReMPMID and the regional climate in the ARB or neighbouring regions.
