## Abstract

As climate models can be used to reproduce historical climates, the outcomes can be used to put climate extremes in to a proper historical perspective. This also allows investigation of nonlinear properties of hydrologic processes (e.g. precipitation, runoff) to better understand regional hydrologic dynamics. To this end, the present study uses results from a so-called 'paleosimulation' (i.e. simulation of climate during periods prior to the development of measuring instruments, including historic and geologic time, for which only proxy climate records are available) covering the Baltic Sea drainage basin and the surrounding areas. Time series of annual temperature, precipitation, and runoff are simulated to study their dynamic characteristics. Three different simulation periods between years 1000 and 1929 are considered: 1000-1199, 1551-1749, and 1751-1929; these three periods represent a warm, a cool, and an intermediate climate episode, respectively. Both linear (autocorrelation function) and nonlinear (phase space reconstruction) methods are employed. The autocorrelation function is a normalized measure of the linear correlation among successive values in a time series, while the basic idea behind the phase space reconstruction is that the past history of a single variable contains important information about the dynamics of the multivariable system. The 30-year average for all the three variables seems to follow a quasi-periodic behavior. An increasing trend is noted for temperature and precipitation during the later periods, but no such pronounced trend is evident for runoff. There is a general linear correlation between annual temperature and precipitation equal to 0.53, and between precipitation and runoff equal to 0.77; however, the correlation between temperature and runoff is as low as 0.30. The annual temperature series has one significant autocorrelation coefficient (lag 1 year), but precipitation and runoff series have no significant coefficients. Significant and slowly decreasing autocorrelation may be an indication of chaotic dynamics and temporal persistence that could be related to fractals. Due to the small autocorrelation, further analyses are carried out using serial time series (i.e. the simulated data are assumed continuous in time). The 30-year moving average for these serial time series reveals linear correlations between the variables; the cross-correlation between temperature and precipitation is 0.88, between precipitation and runoff is 0.83, and between temperature and runoff is 0.52. For these serial time series, phase space reconstruction is carried out to investigate the possible presence of attractors. Univariate (temperature, precipitation and runoff, independently) as well as multivariate (temperature-precipitation, temperature-runoff, precipitation-runoff) reconstructions are performed. For reconstruction, a delay time value of 5 years is considered for the univariate cases, while two delay time values (0 and 5 years) are considered for the multivariate cases. The results generally indicate clear attractors for all the variables and combinations, suggesting nonlinear relationships between temperature, precipitation, and runoff. These relationships could be exploited in prediction schemes, in both univariate and multivariate senses. Such an analysis would contribute to a better understanding of regional runoff dynamics due to climate effects. This is especially important for the Baltic Basin, since transport of nutrients, for example, are strongly correlated to the runoff conditions.

Original language | English |
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Title of host publication | 18th World IMACS Congress and MODSIM 2009 - International Congress on Modelling and Simulation |

Subtitle of host publication | Interfacing Modelling and Simulation with Mathematical and Computational Sciences, Proceedings |

Editors | R.S. Anderssen, R.D. Braddock, L.T.H. Newham |

Publisher | Modelling and Simulation Society of Australia and New Zealand Inc. (MSSANZ) |

Pages | 3893-3899 |

Number of pages | 7 |

ISBN (Electronic) | 9780975840078 |

Publication status | Published - 2020 |

Event | 18th World IMACS Congress and International Congress on Modelling and Simulation: Interfacing Modelling and Simulation with Mathematical and Computational Sciences, MODSIM 2009 - Cairns, Australia Duration: 2009 Jul 13 → 2009 Jul 17 |

### Publication series

Name | 18th World IMACS Congress and MODSIM 2009 - International Congress on Modelling and Simulation: Interfacing Modelling and Simulation with Mathematical and Computational Sciences, Proceedings |
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### Conference

Conference | 18th World IMACS Congress and International Congress on Modelling and Simulation: Interfacing Modelling and Simulation with Mathematical and Computational Sciences, MODSIM 2009 |
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Country/Territory | Australia |

City | Cairns |

Period | 2009/07/13 → 2009/07/17 |

## Subject classification (UKÄ)

- Oceanography, Hydrology, Water Resources

## Free keywords

- Baltic sea
- Chaos
- Climate
- Nonlinearity
- Precipitation
- Regional hydrology
- Runoff
- Temperature