Unknowable and knowable moments: are they relevant to hydrofractals? (Plenary talk)

Classical statistical moments, sometimes of high order, have been a customary diagnostic tool in fractal analyses of hydroclimatic processes. However, it has been articulated that they cannot be estimated from typical samples for order beyond two. In other words, high-order moments, albeit useful in characterizing certain properties of processes, are mostly unknowable. A class of knowable moments (K-moments) is introduced which virtually contains the classical moments as well as the L-moments. The latter are better estimated form samples, but they all are expectations of linear expressions of the process of interest and thus they cannot characterize even second-order dependence of processes. The K-moments overcome this deficiency of L-moments and are readily expanded to multi-scale analyses of processes. thus providing stochastic tools, such as the K-climacogram and K-climacospectrum, which can potentially be relevant to hydrofractal analyses.