Coupling stochastic models of different timescales

By Demetris Koutsoyiannis. 2001

108 citations recorded by the source corpus.

A methodology is proposed for coupling stochastic models of hydrologic processes applying to different timescales so that time series generated by the different models be consistent. Given two multivariate time series, generated by two separate (unrelated) stochastic models of the same hydrologic process, each applying to a different timescale, a transformation is developed (referred to as a coupling transformation) that appropriately modifies the time series of the lower‐level (finer) timescale so that this series becomes consistent with the time series of the higher‐level (coarser) timescale without affecting the second‐order stochastic structure of the former and also establishes appropriate correlations between the two time series. The coupling transformation is based on a developed generalized mathematical proposition, which ensures preservation of marginal and joint second‐order statistics and of linear relationships between lower‐ and higher‐level processes. Several specific forms of the coupling transformation are studied, from the simplest single variate to the full multivariate. In addition, techniques for evaluating parameters of the coupling transformation based on second‐order moments of the lower‐level process are studied. Furthermore, two methods are proposed to enable preservation of the skewness of the processes in addition to that of second‐order statistics. The overall methodology can be applied to problems involving disaggregation of annual to seasonal and seasonal to subseasonal timescales, as well as problems involving finer timescales (e.g., daily to hourly), with the only requirement that a specific stochastic model is available for each involved timescale. The performance of the methodology is demonstrated by means of a detailed numerical example.

Subfields: Environmental Engineering, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/51247eb8779b0425838b27050df6767b5b31daa5

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In Environmental Engineering

In Global and Planetary Change

Citations in the corpus

Generic and parsimonious stochastic modelling for hydrology and beyond (2016, background): “, monthly or daily) quantities (Koutsoyiannis 2001; Efstratiadis et al. 2014).”
Rainfall disaggregation using adjusting procedures on a Poisson cluster model (2001, background): “This problem may be remedied by introducing negative bias to the theoretical variation and skewness before simulation (see Koutsoyiannis, 2001).”
Rainfall downscaling in time: theoretical and empirical comparison between multifractal and Hurst-Kolmogorov discrete random cascades (2012, background): “Koutsoyiannis (2001) demonstrated that the vector θ which minimizes var[V] is of the form: [ ]{ } [ ]kjZ ,121 ~,cov,cov −−= YYYθ (30) Consequently, it can be shown that the least mean square prediction error of kjZ ,12 ~ − from Y is the following: [ ] [ ] [ ]θY,~cov~varvar ,12,12 kjkj ZZV −− −=…”
The Hurst phenomenon and fractional Gaussian noise made easy (2002, methodology): “It is based on a disaggregation technique introduced by Koutsoyiannis (2001).”
Modeling irregularly spaced residual series as a continuous stochastic process (2005, background): “…years, there has been a lot of effort in solving this problem, in the time series literature [Jones, 1980; Harvey and Pierse, 1984; Little and Rubin, 1987] but more recently also focused on hydrologic problems [Bierkens et al., 1999; Koutsoyiannis, 2001; Berendrecht et al., 2003; Yi and Lee, 2004].”
An entropic‐stochastic representation of rainfall intermittency: The origin of clustering and persistence (2006, methodology): “For the latter, an adaptation of the ideas studied by Koutsoyiannis [2001, 2002] related to the linking of the current period with previous and next periods and in Glasbey et al. [1995] and Koutsoyiannis and Onof [2001] related to the adjusting of some initially generated values will be helpful.”