### Abstract

Eigen techniques such as empirical orthogonal function (EOF) or coupled pattern (CP)/maximum covariance analysis have been frequently used for detecting patterns in multivariate climatological data sets. Recently, statistical methods originating from the theory of complex networks have been employed for the very same purpose of spatio-temporal analysis. This climate network (CN) analysis is usually based on the same set of similarity matrices as is used in classical EOF or CP analysis, e.g., the correlation matrix of a single climatological field or the cross-correlation matrix between two distinct climatological fields. In this study, formal relationships as well as conceptual differences between both eigen and network approaches are derived and illustrated using global precipitation, evaporation and surface air temperature data sets. These results allow us to pinpoint that CN analysis can complement classical eigen techniques and provides additional information on the higher-order structure of statistical interrelationships in climatological data. Hence, CNs are a valuable supplement to the statistical toolbox of the climatologist, particularly for making sense out of very large data sets such as those generated by satellite observations and climate model intercomparison exercises.

Original language | English |
---|---|

Pages (from-to) | 2407-2424 |

Number of pages | 18 |

Journal | Climate dynamics |

Volume | 45 |

Issue number | 9 |

Early online date | 28 Jan 2015 |

DOIs | |

Publication status | Published - Nov 2015 |

### Keywords

- Climate networks
- Empirical orthogonal functions
- Coupled patterns
- Maximum covariance analysis
- Climate data analysis
- Nonlinear dimensionality reduction
- El-Nino
- Time-Series
- Atmospheric teleconnections
- Southern-oscillation
- Surface-temperature
- Visibility graph
- Cautionary note
- Prediction

### Cite this

*Climate dynamics*,

*45*(9), 2407-2424. https://doi.org/10.1007/s00382-015-2479-3

**How complex climate networks complement eigen techniques for the statistical analysis of climatological data.** / Donges, Jonathan F.; Petrova, Irina; Loew, Alexander; Marwan, Norbert; Kurths, Juergen.

Research output: Contribution to journal › Article

*Climate dynamics*, vol. 45, no. 9, pp. 2407-2424. https://doi.org/10.1007/s00382-015-2479-3

}

TY - JOUR

T1 - How complex climate networks complement eigen techniques for the statistical analysis of climatological data

AU - Donges, Jonathan F.

AU - Petrova, Irina

AU - Loew, Alexander

AU - Marwan, Norbert

AU - Kurths, Juergen

N1 - Acknowledgments: This work has been financially supported by the Leibniz association (Project ECONS), the German National Academic Foundation, the Potsdam Institute for Climate Impact Research, the Stordalen Foundation, BMBF (Project GLUES), the Max Planck Society, and DFG Grants KU34-1 and MA 4759/4-1. For climate network analysis, the software package pyunicorn was used that is available at http://tocsy.pik-potsdam.de/pyunicorn.php (Donges et al. 2013). We thank Reik V. Donner and Doerthe Handorf for discussions and comments on an earlier version of the manuscript

PY - 2015/11

Y1 - 2015/11

N2 - Eigen techniques such as empirical orthogonal function (EOF) or coupled pattern (CP)/maximum covariance analysis have been frequently used for detecting patterns in multivariate climatological data sets. Recently, statistical methods originating from the theory of complex networks have been employed for the very same purpose of spatio-temporal analysis. This climate network (CN) analysis is usually based on the same set of similarity matrices as is used in classical EOF or CP analysis, e.g., the correlation matrix of a single climatological field or the cross-correlation matrix between two distinct climatological fields. In this study, formal relationships as well as conceptual differences between both eigen and network approaches are derived and illustrated using global precipitation, evaporation and surface air temperature data sets. These results allow us to pinpoint that CN analysis can complement classical eigen techniques and provides additional information on the higher-order structure of statistical interrelationships in climatological data. Hence, CNs are a valuable supplement to the statistical toolbox of the climatologist, particularly for making sense out of very large data sets such as those generated by satellite observations and climate model intercomparison exercises.

AB - Eigen techniques such as empirical orthogonal function (EOF) or coupled pattern (CP)/maximum covariance analysis have been frequently used for detecting patterns in multivariate climatological data sets. Recently, statistical methods originating from the theory of complex networks have been employed for the very same purpose of spatio-temporal analysis. This climate network (CN) analysis is usually based on the same set of similarity matrices as is used in classical EOF or CP analysis, e.g., the correlation matrix of a single climatological field or the cross-correlation matrix between two distinct climatological fields. In this study, formal relationships as well as conceptual differences between both eigen and network approaches are derived and illustrated using global precipitation, evaporation and surface air temperature data sets. These results allow us to pinpoint that CN analysis can complement classical eigen techniques and provides additional information on the higher-order structure of statistical interrelationships in climatological data. Hence, CNs are a valuable supplement to the statistical toolbox of the climatologist, particularly for making sense out of very large data sets such as those generated by satellite observations and climate model intercomparison exercises.

KW - Climate networks

KW - Empirical orthogonal functions

KW - Coupled patterns

KW - Maximum covariance analysis

KW - Climate data analysis

KW - Nonlinear dimensionality reduction

KW - El-Nino

KW - Time-Series

KW - Atmospheric teleconnections

KW - Southern-oscillation

KW - Surface-temperature

KW - Visibility graph

KW - Cautionary note

KW - Prediction

U2 - 10.1007/s00382-015-2479-3

DO - 10.1007/s00382-015-2479-3

M3 - Article

VL - 45

SP - 2407

EP - 2424

JO - Climate dynamics

JF - Climate dynamics

SN - 0930-7575

IS - 9

ER -