# Dynamic Analysis of Meteorological Parameters in Košice Climatic Station in Slovakia

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Data

#### 2.2. Decriptive and Chaotic Analysis

_{i}. The m dimensional phase space is searched for its nearest neighbours (Y

_{j}). The Euclidean distance is calculated between each Y

_{m}(i) and Y

_{m}(j). Then, the same is calculated in the (m + 1)

^{th}dimension. The ratio of both distances is taken as R

_{i}, which is given in Equation (1). The value will be more than one as the distance in the higher dimension cannot be less than that in the lower dimension. Therefore, in order to distinguish between true and false neighbours, a threshold value is fixed for the ratio (R

_{t}) in a way that the Euclidean distance measured between the neighbours in the (m + 1)th dimension should be comparable to that in mth dimension. From the literature, it is found that the threshold can be fixed around 10 [28].

_{t}), then the neighbours are considered to be false, or vice versa [29].

_{t}is the value of variable x at any time t; and $\overline{x}$ is the mean of all of the values of x.

## 3. Results

#### 3.1. Statistical Analysis

_{max}values at the station at 100% and 27.3%, respectively. The value of wind speed shows high variation, with the maximum and minimum values at Kosice being 54 and 0 kmph, respectively. The value of sunshine hours shows high variation, with the maximum and minimum values at Kosice being 15.2 h and 0.1 h, respectively. The maximum value for the dew point temperature at Kosice is 29.1 degrees. Evaporation values show high variation due to climatic conditions. The maximum value of evaporation measured at Kosice is 12.1 mm/day.

#### 3.2. Trend Analysis

#### 3.3. Nonlinear Dynamic Analysis of Meteorological Parameters

## 4. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

- Hipel, K.W.; McLeod, A.I. Time Series Modelling of Water Resources and Environmental Systems; Elsevier: Amsterdam, The Netherlands, 1994. [Google Scholar]
- Kantz, H.; Schreiber, T. Nonlinear Time Series Analysis; Cambridge University Press: Cambridge, UK, 1997. [Google Scholar]
- Williams, P. Chaos Theory; Tamed, Joseph Henry Press: Washington, DC, USA, 1997. [Google Scholar]
- Sivakumar, B. Chaos in Hydrology; Springer Science + Business Media: Dordrecht, The Netherlands, 2017. [Google Scholar]
- Sivakumar, B. Rainfall Dynamics at Different Temporal Scales: A Chaotic Perspective. Hydrol. Earth Syst. Sci.
**2001**, 5, 645–651. [Google Scholar] [CrossRef] - Sivakumar, B.; Jayawardena, A.W.; Li, W.K. Hydrologic complexity and classification: A simple data reconstruction approach. Hydrol. Process.
**2007**, 21, 2713–2728. [Google Scholar] [CrossRef] - Lorenz, E.N. Deterministic nonperiodic flow. J. Atmos. Sci.
**1963**, 20, 130–141. [Google Scholar] [CrossRef] - Buizza, R. Chaos and weather prediction January 2000. Analysis
**1996**, 12, 1–28. [Google Scholar] - Das, P. Nonlinear Analysis of Daily Temperature Data. In Proceedings of the 2009 ETP International Conference on Future Computer and Communication, Wuhan, China, 6–7 June 2009; pp. 273–277. [Google Scholar]
- Millan, H.; Ghanbarian-Alavijeh, B.; Garcia-Fornaris, I. Nonlinear dynamics of mean daily temperature and dewpoint time series at Balolsar, Iran, 1961–2005. Atmos. Res.
**2010**, 98, 89–101. [Google Scholar] [CrossRef] - Farzin, S.; Ifaei, P.; Farzin, N.; Hassanzadeh, Y.; Aalami, M.T. An Investigation on Changes and Prediction of Urmia Lake water Surface Evaporation by Chaos Theory. Int. J. Environ. Res.
**2012**, 6, 815–824. [Google Scholar] - Guo, Z.; Chi, D.; Wu, J.; Zhang, W. A new Wind speed forecasting strategy based on the chaotic time series modelling technique and the Apriori algorithm. Energy Convers. Manag.
**2014**, 84, 140–151. [Google Scholar] [CrossRef] - Snyder, W.M. Some Possibilities for Multivariate Analysis in Hydrologic Studies. J. Geophys. Res.
**1962**, 67, 721–729. [Google Scholar] [CrossRef] - Schiff, S.; So, P.; Chang, T.; Burke, R.; Sauer, T. Detecting dynamical interdependence and generalized synchrony through mutual prediction in a neural ensemble. Phys. Rev. E
**1996**, 54, 6708–6724. [Google Scholar] [CrossRef] - Quyen, M.L.; van Martinerie, J.; Adam, C.; Varela, F.J. Nonlinear analyses of interictal EEG map the brain interdependences in human focal epilepsy. Phys. D Nonlinear Phenom.
**1999**, 127, 250–266. [Google Scholar] [CrossRef] - Cao, L.; Mees, A.; Judd, K. Dynamics from multivariate time series. Phys. D Nonlinear Phenom.
**1998**, 121, 75–88. [Google Scholar] [CrossRef] - Sfetsos, A.; Coonick, A.H. Univariate and multivariate forecasting of hourly solar radiation with artificial intelligence techniques. Sol. Energy
**2000**, 68, 169–178. [Google Scholar] [CrossRef] - Porporato, A.; Ridolfi, L. Multivariate nonlinear prediction of river flows. J. Hydrol.
**2001**, 248, 109–122. [Google Scholar] [CrossRef] - Jin, Y.H.; Kawamura, A.; Jinn, K.; Berndtsson, R. Nonlinear multivariable analysis of SOI and local precipitation and temperature. Nonlinear Process. Geophys.
**2005**, 12, 67–74. [Google Scholar] [CrossRef] - Han, M.; Wang, Y. Analysis and modeling of multivariate chaotic time series based on neural network. Expert Syst. Appl.
**2009**, 36, 1280–1290. [Google Scholar] [CrossRef] - Dhanya, C.T.; Nagesh Kumar, D. Multivariate nonlinear ensemble prediction of daily chaotic rainfall with climate inputs. J. Hydrol.
**2011**, 403, 292–306. [Google Scholar] [CrossRef] - Jothiprakash, V.; Kirty, S.; Tara, M.S. Prediction of meteorological variables using artificial neural networks. Int. J. Hydrol. Sci. Technol.
**2011**, 1, 192–206. [Google Scholar] [CrossRef] - SHMI: Climate Atlas of Slovakia. Banská Bystrica; Slovak Hydrometeorologic Institute (SHMI): Bratislava, Slovakia, 2015; 228p. [Google Scholar]
- Zeleňáková, M.; Vido, J.; Portela, M.M.; Purcz, P.; Blišťan, P.; Hlavatá, H.; Hluštík, P. Precipitation Trends over Slovakia in the Period 1981–2013. Water
**2017**, 9, 922. [Google Scholar] [CrossRef] - Zeleňáková, M.; Purcz, P.; Blišťan, P.; Alkhalaf, I.; Hlavatá, H.; Portela, M.M.; Silva, A.T. Precipitation trends detection as a tool for integrated water resources management in Slovakia. Desalination Water Treat.
**2017**, 99, 83–90. [Google Scholar] [CrossRef] - Sivakumar, B.; Liong, S.Y.; Liaw, C.Y. Evidence of chaotic behavior in Singapore rainfall. J. Am. Water Resour. Assoc.
**1998**, 34, 301–310. [Google Scholar] [CrossRef] - Jayawardena, A.W.; Lai, F. Analysis and prediction of chaos in rainfall and stream flow time series. J. Hydrol.
**1994**, 153, 23–52. [Google Scholar] [CrossRef] - Kennel, M.B.; Brown, R.; Abarbanel, H.D.I. Determining embedding dimension for phase space reconstruction using a geometric method. Phys. Rev. A
**1992**, 45, 3403–3411. [Google Scholar] [CrossRef] [PubMed] - Vignesh, R.; Jothiprakash, V.; Sivakumar, B. Streamflow variability and classification using false nearest neighbor method. J. Hydrol.
**2015**, 531, 706–715. [Google Scholar] [CrossRef]

Statistics | Average Temperature (°C) | Relative Humidity (%) | Wind Speed (kmph) | Sunshine Hours (h/Day) | Dew Point Temperature (°C) | Pan Evaporation (mm/Day) |
---|---|---|---|---|---|---|

Mean | 9.92 | 73.47 | 3.00 | 6.12 | 14.60 | 2.31 |

Stand Deviation | 8.93 | 13.95 | 1.94 | 4.09 | 5.61 | 1.44 |

Skewness | −0.19 | −0.19 | 1.55 | 0.276 | 0.30 | 0.93 |

Kurtosis | −0.96 | −0.64 | 3.24 | −1.037 | −0.96 | 1.08 |

Maximum | 29.75 | 100 | 15.66 | 15.20 | 29.10 | 12.10 |

Minimum | −14.50 | 27.33 | 0 | 0.10 | 2.50 | 0 |

Statistics | Average Temperature (°C) | Relative Humidity (%) | Wind Speed (kmph) | Sunshine Hours (h/Day) | Dew Point Temperature (°C) | Pan Evaporation (mm/Day) |
---|---|---|---|---|---|---|

tau | 0.034 | −0.017 | −0.024 | 0.006 | 0.033 | 0.024 |

P | <0.0001 | 0.032 | 0.002 | 0.474 | <0.0001 | 0.004 |

Z | 4.369 | −2.153 | −3.166 | 0.729 | 4.267 | 3.074 |

Trend | P | N | N | No trend | P | P |

**Table 3.**Autocorrelation function (ACF) and average mutual information (AMI) values for all of the parameters at Kosice station.

Parameters | ACF | AMI |
---|---|---|

Average temperature | 91 | 16 |

Relative humidity | 80 | 10 |

Wind speed | 72 | 3 |

Sunshine hours | 92 | 12 |

Dew point temperature | 88 | 12 |

Pan evaporation | 126 | 12 |

False Nearest Neighbour Analyses | Average Temperature | Relative Humidity | Wind Speed | Sunshine Hours | Dew Point Temperature | Pan Evaporation |
---|---|---|---|---|---|---|

FNN | 6 | 5 | 6 | 6 | 5 | 5 |

FNN (ACF) | 6 | 6 | 5 | 6 | 13 | 10 |

FNN (AMI) | 6 | 5 | 7 | 6 | 6 | 4 |

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**MDPI and ACS Style**

Zeleňáková, M.; Jothiprakash, V.; Arjun, S.; Káposztásová, D.; Hlavatá, H.
Dynamic Analysis of Meteorological Parameters in Košice Climatic Station in Slovakia. *Water* **2018**, *10*, 702.
https://doi.org/10.3390/w10060702

**AMA Style**

Zeleňáková M, Jothiprakash V, Arjun S, Káposztásová D, Hlavatá H.
Dynamic Analysis of Meteorological Parameters in Košice Climatic Station in Slovakia. *Water*. 2018; 10(6):702.
https://doi.org/10.3390/w10060702

**Chicago/Turabian Style**

Zeleňáková, Martina, Vinayakam Jothiprakash, Sasi Arjun, Daniela Káposztásová, and Helena Hlavatá.
2018. "Dynamic Analysis of Meteorological Parameters in Košice Climatic Station in Slovakia" *Water* 10, no. 6: 702.
https://doi.org/10.3390/w10060702