Spatial R-vine copula for streamflow scenario simulation

As there are spatial and temporal dependencies of streamflow at hydroelectric power plants (HPPs), we develop a high dimensional statistical model for streamflow scenario simulation which considers both. We use a pair-copula-based model reparametrized in terms of spatial variables derived from the river network, the distance between HPPs and precipitation measurements. This approach reduces the complexity of the model by reducing the number of parameters, preserves however the flexibility introduced by the pair-copulas. Based on simulations, we demonstrate that our model can capture spatial and temporal dependence between HPPs and thus, generate multivariate scenarios that reproduce historical features as shown in an empirical exercise with 39 HPPs.

[1]  Using Copulas for Stochastic Streamflow Generation , 2008 .

[2]  Pair-copula decomposition constructions for multivariate hydrological drought frequency analysis , 2011, 2011 International Symposium on Water Resource and Environmental Protection.

[3]  A. Frigessi,et al.  Pair-copula constructions of multiple dependence , 2009 .

[4]  Claudia Czado,et al.  Selecting and estimating regular vine copulae and application to financial returns , 2012, Comput. Stat. Data Anal..

[5]  Christine M. Anderson-Cook,et al.  Book review: quantitative risk management: concepts, techniques and tools, revised edition, by A.F. McNeil, R. Frey and P. Embrechts. Princeton University Press, 2015, ISBN 978-0-691-16627-8, xix + 700 pp. , 2017, Extremes.

[6]  H. Joe Families of $m$-variate distributions with given margins and $m(m-1)/2$ bivariate dependence parameters , 1996 .

[7]  T. Bedford,et al.  Vines: A new graphical model for dependent random variables , 2002 .

[8]  Roger M. Cooke,et al.  Uncertainty Analysis with High Dimensional Dependence Modelling , 2006 .

[9]  Claudia Czado,et al.  Pair-Copula Constructions of Multivariate Copulas , 2010 .

[10]  Roger M. Cooke,et al.  Uncertainty Analysis with High Dimensional Dependence Modelling: Kurowicka/Uncertainty Analysis with High Dimensional Dependence Modelling , 2006 .

[11]  Roger M. Cooke,et al.  Probability Density Decomposition for Conditionally Dependent Random Variables Modeled by Vines , 2001, Annals of Mathematics and Artificial Intelligence.

[12]  M. Sklar Fonctions de repartition a n dimensions et leurs marges , 1959 .

[13]  Claudia Czado,et al.  R‐vine models for spatial time series with an application to daily mean temperature , 2014, Biometrics.

[14]  Joaquim Dias Garcia,et al.  A high-dimensional VARX model to simulate monthly renewable energy supply , 2014, 2014 Power Systems Computation Conference.

[15]  Goran Andersson,et al.  Probabilistic N−1 security assessment incorporating dynamic line ratings , 2013, 2013 IEEE Power & Energy Society General Meeting.

[16]  K. Hipel,et al.  Time series modelling of water resources and environmental systems , 1994 .

[17]  G. Papaefthymiou,et al.  Using Copulas for Modeling Stochastic Dependence in Power System Uncertainty Analysis , 2009, IEEE Transactions on Power Systems.

[18]  C. Czado,et al.  Truncated regular vines in high dimensions with application to financial data , 2012 .