Multivariate non-normally distributed random variables in climate research - introduction to the copula approach

By C. Schölzel, Petra Friederichs. 2008

319 citations recorded by the source corpus.

Abstract. Probability distributions of multivariate random variables are generally more complex compared to their univariate counterparts which is due to a possible nonlinear dependence between the random variables. One approach to this problem is the use of copulas, which have become popular over recent years, especially in fields like econometrics, finance, risk management, or insurance. Since this newly emerging field includes various practices, a controversial discussion, and vast field of literature, it is difficult to get an overview. The aim of this paper is therefore to provide an brief overview of copulas for application in meteorology and climate research. We examine the advantages and disadvantages compared to alternative approaches like e.g. mixture models, summarize the current problem of goodness-of-fit (GOF) tests for copulas, and discuss the connection with multivariate extremes. An application to station data shows the simplicity and the capabilities as well as the limitations of this approach. Observations of daily precipitation and temperature are fitted to a bivariate model and demonstrate, that copulas are valuable complement to the commonly used methods.

Subfields: Finance, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/8b76a8777c69e67edcf10864f783297a99157995

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Citations in the corpus

Ensemble Model Output Statistics for Wind Vectors (2012, background): “Schefzik (2011) provides a detailed discussion of the ECC technique and exposes its ties to copulas (Schölzel and Friederichs 2008).”
Selecting and estimating regular vine copulae and application to financial returns (2012, background): “However there is a growing demand for non-Gaussian models especially in ﬁnance (Cherubini et al., 2004) but also in climate research (e.g., Sch¨olzel and Friederichs (2008)), environmental sciences (Salvadori et al. (2007) and Kazianka and Pilz (2011)), medicine (e.g., Beaudoin and Lakhal-Chaieb…”
Copula-based statistical refinement of precipitation in RCM simulations over complex terrain (2011, unknown): “…frequency analysis, risk assessment, geostatistical interpolation and multivariate extreme value analyses (e.g.De Michele and Salvadori, 2003; Bárdossy, 2006; Genest and Favre, 2007; Renard and Lang, 2007; Scḧolzel and Friederichs, 2008; Bárdossy and Li , 2008; Zhang and Singh, 2008).”
The distribution of Kendall's tau for testing the significance of cross-correlation in persistent data (2011, methodology): “It has been recently shown that many natural data do not follow the MVG temporal dependence model (e.g. Grimaldi and Serinaldi 2006, Salvadori et al. 2007, Schölzel and Friederichs 2008).”
Data assimilation in the geosciences: An overview of methods, issues, and perspectives (2017, methodology): “The anamorphosis framework can, however, be further extended by the use of copulas (Schölzel & Friederichs, 2008).”
Review of probabilistic pollen-climate transfer methods (2012, methodology): “In the latter case, [CjVj,Q] is described by a Gaussian mixture model (Kühl et al., 2002) or by a copula model (Kühl et al., 2007; Litt et al., 2009; Schölzel and Friederichs, 2008) in order to allow for nonGaussian marginal distributions, e.g., precipitation values.”
Copula-based assimilation of radar and gauge information to derive bias-corrected precipitation fields (2012, methodology): “…frequency analysis, geostatistical interpolation and multivariate extreme value analyses (e.g. De Michele and Salvadori, 2003; Dupois, 2007; Bárdossy, 2006; Genest and Favre, 2007; Renard and Lang, 2007; Schölzel and Friederichs, 2008;15 Bárdossy and Li, 2008; Zhang and Singh, 2008).”
Is southwestern China experiencing more frequent precipitation extremes? (2014, methodology): “In recent years, copulas have been used for analyzing hydro-meteorological extremes widely (Madadgar and Moradkhani 2013, Renard and Lang 2007, Scholzel and Friederichs 2008, Zhang and Singh 2007, Zhang et al 2012b, 2013b).”
Multivariate—Intervariable, Spatial, and Temporal—Bias Correction* (2015, methodology): “The ensemble copula coupling (ECC) is an adaptation thereof to multivariate ensemble post-processing (Schefzik et al. 2013; M öller et al. 2012 ; Schuhen et al. 2012; Thorarinsdottir et al. 2015).”