### Abstract

A very fine temporal and volumetric resolution precipitation time series is modeled using Markov models. Both 1st and 2nd order Markov models as well as seasonal and diurnal models are investigated and evaluated using likelihood based techniques. The 2nd order Markov model is found to be insignificant. The 1st order Markov model seems to be the most important, followed by the seasonal and diurnal ones. The final model is a continuous state-space 1st order Markov process with seasonal variation. Inclusion of seasonality in the continuous Markov chain model proved difficult, and with respect to likelihood it actually makes the model fit decrease.

Original language | English |
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Title of host publication | Proceedings of the 12th International Conference on Urban Drainage |

Publication date | 2011 |

Publication status | Published - 2011 |

Event | 12th International Conference on Urban Drainage - Porto Alegre, Brazil Duration: 11 Sep 2011 → 16 Sep 2011 Conference number: 12 http://www.acquacon.com.br/icud2011/en/ |

### Conference

Conference | 12th International Conference on Urban Drainage |
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Number | 12 |

Country | Brazil |

City | Porto Alegre |

Period | 11/09/2011 → 16/09/2011 |

Internet address |

### Keywords

- Markov chain modeling
- Continuous state-space Markov chain modeling
- Seasonal precipitation modeling
- Precipitation modeling
- Tipping bucket rain gauges
- Waiting times

## Cite this

Sørup, H. J. D., Madsen, H., & Arnbjerg-Nielsen, K. (2011). Markov chain modeling of precipitation time series: Modeling waiting times between tipping bucket rain gauge tips. In

*Proceedings of the 12th International Conference on Urban Drainage*http://www.acquacon.com.br/icud2011/en/