D. Koutsoyiannis, Knowable moments for high-order characterization and modelling of hydrological processes for sustainable management of water resources, Invited Lecture, Bologna, Italy, doi:10.13140/RG.2.2.35109.86248, University of Bologna, 2019.
Stochastic modelling is an essential tool for planning water resources management and sustainable development. Setting up stochastic models requires the estimation of the moments of the underlying probability distribution. Classical moments, raw or central, express important theoretical properties of probability distributions but cannot be estimated from typical hydrological samples for order beyond 2. L-moments are better estimated but they all are of first order in terms of the process of interest; while they are effective in inferring the marginal distribution of stochastic processes, they cannot characterize even second order dependence of processes (and hence change) and thus they cannot help in stochastic modelling. Picking from both categories, we introduce knowable (K-) moments, which combine advantages of both classical and L-moments, and enable reliable estimation from samples and effective description of high order statistics, useful for marginal and joint distributions of stochastic processes. Further, by extending the notion of climacogram and climacospectrum we introduce the K-climacogram and the K-climacospectrum, which enable characterization, in terms of univariate functions, of high-order properties of stochastic processes, as well as preservation thereof in simulations.
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