### Abstract

This chapter reviews two examples of applied mathematics techniques for data analysis in dynamical systems. The two examples are: (1) Methods for quantifying predictability and model error based on data clustering and information theory and (2) nonlinear Laplacian spectral analysis (NLSA) algorithms for extracting spatiotemporal patterns from high-dimensional data. The chapter highlights these techniques with applications to climate atmosphere ocean science (CAOS), in particular, predictability assessment and Markov modeling of circulation regimes in a simple ocean model and extraction of modes of organized convection in the tropics from infrared brightness temperature satellite data. A common theme in these methods has been the coarse-grained geometry of the data. The machinery of discrete exterior calculus and spectral graph theory was combined with delay-coordinate mappings of dynamical systems to extract spatiotemporal modes of variability which are describable in terms of low-dimensional sets of diffusion eigenfunctions.

Original language | English (US) |
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Title of host publication | Mathematical and Computational Modeling |

Subtitle of host publication | With Applications in Natural and Social Sciences, Engineering, and the Arts |

Publisher | Wiley |

Pages | 137-191 |

Number of pages | 55 |

ISBN (Electronic) | 9781118853986 |

ISBN (Print) | 9781118853887 |

DOIs | |

State | Published - May 8 2015 |

### Keywords

- Climate atmosphere ocean science
- Data clustering
- Information theory
- Markov modeling
- Nonlinear Laplacian spectral analysis algorithms
- Spatiotemporal patterns

### ASJC Scopus subject areas

- Mathematics(all)
- Physics and Astronomy(all)
- Chemistry(all)
- Computer Science(all)

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## Cite this

*Mathematical and Computational Modeling: With Applications in Natural and Social Sciences, Engineering, and the Arts*(pp. 137-191). Wiley. https://doi.org/10.1002/9781118853887.ch7