# Investigation and Analysis of Sea Surface Temperature and Precipitation of the Southern Caspian Sea Using Wavelet Analysis

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Methods

## 3. Wavelet

#### 3.1. Wavelet Discrete Transformation

#### 3.2. Multistage Decomposition

#### 3.3. Choosing the Proposed Filter Using the Wavelet Function

## 4. Wave Reconstruction

## 5. Results

#### 5.1. Decomposition of Climate Data Time Series

#### 5.1.1. Decomposition of SST Data

#### 5.1.2. Decomposition of Precipitation Data

#### 5.2. Wavelet Function Selection for Use with the Suggested Filter

#### 5.3. Wavelet Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**General map of the Caspian Sea and its location (the inset). SC: south Caspian Sea, MC: Middle Caspian Sea, and NC: North Caspian Sea domains.

**Figure 14.**Yearly time series of SST and related trends in (

**a**) JJA and (

**c**) DJF and Morlet wavelet power spectrum of the SST in (

**b**) JJA and (

**d**) DJF.

**Figure 15.**Wavelet coherence and the phase difference between the yearly SST data and precipitation, (

**a**) in JJA, and (

**b**) DJF.

Reconstruction Maximum Error | SST JJA | SST DJF | Prec JJA | Prec DJF |
---|---|---|---|---|

Level 1 | $2.7978\times {10}^{-14}$ | $2.7200\times {10}^{-14}$ | $1.1369\times {10}^{-13}$ | $2.2737\times {10}^{-13}$ |

Level 2 | $9.1815\times {10}^{-14}$ | $1.2790\times {10}^{-13}$ | $4.5475\times {10}^{-13}$ | $9.0949\times {10}^{-13}$ |

Level 3 | $1.8296\times {10}^{-13}$ | $1.2523\times {10}^{-13}$ | $1.0396\times {10}^{-13}$ | $9.3792\times {10}^{-13}$ |

**Table 2.**Visualization of the seven wavelet functions with the highest energy values and their respective number of coefficients for the epileptiform events used.

Wavelet Function | Coefficients | Energy (%) | |||
---|---|---|---|---|---|

SST (JJA) | SST (DJF) | Prec (JJA) | Prec (DJF) | ||

sym3 | 6 | 96.22 | 91.34 | 95.23 | 90.59 |

sym4 | 8 | 95.31 | 92.29 | 94.76 | 91.50 |

sym5 | 10 | 96.45 | 93.31 | 95.46 | 92.00 |

sym6 | 12 | 96.37 | 93.49 | 95.76 | 92.43 |

coif1 | 6 | 95.72 | 90.52 | 94.85 | 89.85 |

coif2 | 12 | 97.81 | 93.72 | 95.44 | 92.65 |

coif3 | 18 | 97.92 | 95.43 | 96.01 | 93.71 |

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**MDPI and ACS Style**

Molavi-Arabshahi, M.; Azizpour, J.; Nikan, O.; Naderi Beni, A.; Lopes, A.M.
Investigation and Analysis of Sea Surface Temperature and Precipitation of the Southern Caspian Sea Using Wavelet Analysis. *Axioms* **2023**, *12*, 10.
https://doi.org/10.3390/axioms12010010

**AMA Style**

Molavi-Arabshahi M, Azizpour J, Nikan O, Naderi Beni A, Lopes AM.
Investigation and Analysis of Sea Surface Temperature and Precipitation of the Southern Caspian Sea Using Wavelet Analysis. *Axioms*. 2023; 12(1):10.
https://doi.org/10.3390/axioms12010010

**Chicago/Turabian Style**

Molavi-Arabshahi, Mahboubeh, Jafar Azizpour, Omid Nikan, Abdolmajid Naderi Beni, and António M. Lopes.
2023. "Investigation and Analysis of Sea Surface Temperature and Precipitation of the Southern Caspian Sea Using Wavelet Analysis" *Axioms* 12, no. 1: 10.
https://doi.org/10.3390/axioms12010010