D. Koutsoyiannis, An advanced method for preserving skewness in single-variate, multivariate and disaggregation models in stochastic hydrology, 24th General Assembly of the European Geophysical Society, Geophysical Research Abstracts, Vol. 1, The Hague, 346, doi:10.13140/RG.2.1.1749.2725, European Geophysical Society, 1999.
Preservation of skewness in hydrological stochastic models is hard to accomplish, especially when the model structure involves a large number of noise (innovation) variables. This is the case in long memory single-variate ARMA models, in multivariate stochastic models, even with short-memory, and particularly in multivariate disaggregation models. The problem is in fact a consequence of the central limit theorem, because the linear combination of a large number of noise variables tends to have a symmetric distribution. However, it is well known that there exists an infinite number of coefficients of linear combinations of noise variables, all resulting in preservation of the first and second (marginal and joint) moments of the involved hydrological variables. Each of these infinite combinations results in different skewness coefficients of the noise variables. The smaller these skewness coefficients are, the more attainable their preservation is in a finite generated sample. Consequently, the problem may be formulated in an optimisation framework aiming at the minimisation of skewness coefficients of all noise variables. Analytical expressions of the derivatives of this objective function are derived, which allow the development of an effective nonlinear optimisation algorithm. The method is illustrated through real-world applications, which indicate a very satisfactory performance of the method.
Our works that reference this work:
|1.||D. Koutsoyiannis, A generalized mathematical framework for stochastic simulation and forecast of hydrologic time series, Water Resources Research, 36 (6), 1519–1533, doi:10.1029/2000WR900044, 2000.|