K-moments and their application to ombrian modelling

K-moments, or knowable moments, provide a robust framework for high-order statistical characterization of stochastic variables. They are defined through expectations of order statistics (maxima or minima) that remain reliably estimable even from limited samples. Unlike conventional moments or L-moments, they effectively mitigate tail sensitivity, sampling variability, and the influence of long-range dependence. This presentation explores their theoretical foundations and practical advantages in ombrian modelling — the stochastic representation of rainfall intensity across multiple timescales through ombrian curves (previously and erroneously termed intensity-duration-frequency or IDF relationships). Applications demonstrate improved fitting of local and regional rainfall data, more accurate design storm estimation, and superior handling of extremes in hydrological practice.