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The Dynamic Impacts of COVID-19 Pandemic Lockdown on the Multifractal Cross-Correlations between PM_{2.5} and O_{3} Concentrations in and around Shanghai, China

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## Abstract

**:**

## 1. Introduction

## 2. Data Description and Preprocessing Method

## 3. Methodology

#### 3.1. Mf-Dcca Method

#### 3.2. Multifractal Cause Analysis

- Step 1
- The original series is shuffled to remove any potential correlations. The MF-DCCA analysis is conducted on the shuffled series and the multifractal characteristic ${H}_{x/y}^{shuf}\left(q\right),\Delta {\alpha}_{x/y}^{shuf}$ is determined.
- Step 2
- The surrogate series are constructed by phase-randomizing the original series using the IAAFT algorithm. The MF-DCCA analysis is carried out on the surrogate series and ${H}_{x/y}^{surr}\left(q\right),\Delta {\alpha}_{x/y}^{surr}$ are calculated;
- Step 3
- Steps 1–2 are repeated until 80,000 sets of {${H}_{x/y}^{shuf}\left(q\right),{H}_{x/y}^{surr}\left(q\right),\Delta {\alpha}_{x/y}^{shuf}$, $\Delta {\alpha}_{x/y}^{surr}$} of the hourly PM${}_{2.5}$ and O${}_{3}$ series in and around Shanghai, China, before and during the COVID-19 partial lockdown are accumulated.
- Step 4
- The differences between ${H}_{x/y}^{shuf}\left(q\right),{H}_{x/y}^{surr}\left(q\right),\Delta {\alpha}_{x/y}^{shuf},\Delta {\alpha}_{x/y}^{surr}$ are checked to determine the components of the multifractality and intrinsic multifractality of the hourly PM${}_{2.5}$ and O${}_{3}$ series in four cities before and during the COVID-19 partial lockdown, respectively.
- Step 5
- Finally, the comparisons between the above multifractality parameters are applied to determine the dynamic impacts of the COVID-19 pandemic on the intrinsic multifractality hourly PM${}_{2.5}$ and O${}_{3}$ series in and around Shanghai, China.

#### 3.3. Formation of a New Index $\zeta $

## 4. Results and Discussion

#### 4.1. Multifractal Cross-Correlations of PM${}_{2.5}$-O${}_{3}$

#### 4.2. Causes of Cross-Correlations between PM${}_{2.5}$ and O${}_{3}$

#### 4.3. The Coordinated Control Degree of PM${}_{2.5}$-O${}_{3}$

#### 4.4. Disscussion

## 5. Conclusions

- (1)
- The cross-correlations between PM${}_{2.5}$ and O${}_{3}$ in and around Shanghai both before and during the COVID-19 partial lockdown have multifractal characteristics. Moreover, there are weaker multifractal cross-correlation degrees of PM${}_{2.5}$-O${}_{3}$ in four cities during the COVID-19 partial lockdown.
- (2)
- The impacts of multifractality due to the nonlinear correlation part in and around Shanghai are greater than the linear correlation part and the fat-tailed probability distribution part. The intrinsic multifractal cross-correlations between PM${}_{2.5}$ and O${}_{3}$ decreased in all cities during the COVID-19 partial lockdown.
- (3)
- Although the COVID-19 lockdown contributes to the improvement of multifractal cross-correlations between PM${}_{2.5}$ and O${}_{3}$, their effects are limited from the perspective of intrinsic multifractality.
- (4)
- The mean values of $\zeta $ in and around Shanghai all increased during the COVID-19 partial lockdown. This indicates that the PM${}_{2.5}$-O${}_{3}$ coordinated control degrees in all four cities become weaker. Among these four cities, the added value of $\zeta $ in Shanghai is the maximum.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The hourly PM${}_{2.5}$ and O${}_{3}$ series in Shanghai, Jiaxing, Nantong and Suzhou before and during the COVID-19 partial lockdown, the blue line is the mean value of PM${}_{2.5}$ and O${}_{3}$ in different period in four cities.

**Figure 4.**The q dependences of the generalized Hurst exponents ${H}_{x/y}\left(q\right)$ between the shuffled and surrogate hourly PM${}_{2.5}$ and O${}_{3}$ series in and around Shanghai before and during the COVID-19 partial lockdown. The error bars are the standard deviations for the 10,000 shuffled and surrogate series, respectively. “Original” is the MF-DCCA analysis result of the original PM${}_{2.5}$ and O${}_{3}$ series, “Shuffle” and “Surrogate” represent the MCASS analysis results of specified series obtained from shuffling and phase-randomizing the original series.

**Figure 5.**The multifractal spectra (${\alpha}_{x/y},{f}_{x/y}\left({\alpha}_{x/y}\right)$) calculated from MCASS method between the shuffled and surrogate PM${}_{2.5}$ and O${}_{3}$ series in and around Shanghai before and during the COVID-19 partial lockdown. The error bars are the standard deviations for the 10,000 shuffled and surrogate series, respectively. “Original” is the MFDCCA analysis result of the original PM${}_{2.5}$ and O${}_{3}$ series, “Shuffle” and “Surrogate” represent the MCASS analysis results of specified series obtained from shuffling and phase-randomizing the original series.

**Figure 6.**The mean values of $\zeta $ of PM${}_{2.5}$-O${}_{3}$ in Shanghai, Jiaxing, Nantong and Suzhou before and during the COVID-19 partial lockdown.

**Table 1.**Descriptive statistics of the hourly PM${}_{2.5}$ and O${}_{3}$ series in Shanghai, Jiaxing, Nantong and Suzhou before and during the COVID-19 partial lockdown.

City | Pollutant | Mean | Std. | Median | Skewness | Kurtosis | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Period | Period | Ratio | Period | Period | Period | Period | Period | Period | Period | Period | ||

I(A) | II(B) | (B−A)/A | I | II | I | II | I | II | I | II | ||

Shanghai | PM${}_{2.5}$ (μg/m${}^{3}$) | 49.26 | 32.89 | −33.2% | 34.75 | 21.07 | 39.75 | 27.15 | 1.19 | 1.18 | 1.28 | 0.76 |

O${}_{3}$ (μg/m${}^{3}$) | 39.26 | 72.33 | 84.2% | 22.73 | 24.07 | 38.37 | 73.58 | 0.52 | 0.23 | 0.16 | 0.98 | |

Jiaxing | PM${}_{2.5}$ (μg/m${}^{3}$) | 42.99 | 42.87 | −0.3% | 30.75 | 35.99 | 37.19 | 32.7 | 1.62 | 1.51 | 3.92 | 2.24 |

O${}_{3}$ (μg/m${}^{3}$) | 33.58 | 59.34 | 76.7% | 22.04 | 25.73 | 31 | 58.22 | 0.87 | 0.45 | 0.43 | 0.25 | |

Nantong | PM${}_{2.5}$ (μg/m${}^{3}$) | 49.62 | 43.2 | −12.9% | 34.92 | 35.81 | 43.12 | 33.6 | 1.26 | 1.51 | 2.02 | 2.29 |

O${}_{3}$ (μg/m${}^{3}$) | 34.93 | 58.99 | 68.9% | 21.24 | 25.3 | 32.66 | 57.59 | 0.72 | 0.46 | 0.13 | 0.25 | |

Suzhou | PM${}_{2.5}$ (μg/m${}^{3}$) | 51.49 | 33.99 | −34.0% | 33.86 | 21.31 | 42.62 | 28.85 | 1.1 | 1.11 | 1.25 | 1.23 |

O${}_{3}$ (μg/m${}^{3}$) | 29.42 | 67.9 | 130.8% | 21.95 | 26.19 | 26.06 | 67.12 | 0.92 | 0.38 | 0.58 | 0.4 |

**Table 2.**Comparison of the width of multifractal spectrums of original, shuffled, surrogate PM${}_{2.5}$ and O${}_{3}$ series in Shanghai, Jiaxing, Nantong and Suzhou before and during the COVID-19 partial lockdown. The numbers in parentheses are the standard deviations. Period I: before the COVID-19 lockdown, Period II: during the COVID-19 lockdown.

City | Pollutant | $\Delta {\alpha}_{\mathit{x}/\mathit{y}}$ | $\Delta {\alpha}_{\mathit{x}/\mathit{y}}^{\mathit{shuf}}$ | $\Delta {\alpha}_{\mathit{x}/\mathit{y}}^{\mathit{surr}}$ | |||
---|---|---|---|---|---|---|---|

Period I | Period II | Period I | Period II | Period I | Period II | ||

Shanghai | PM${}_{2.5}$-O${}_{3}$ | 1.321 | 0.843 | 0.112 | 0.115 | 0.349 | 0.292 |

(0.062) | (0.064) | (0.132) | (0.122) | ||||

Jiaxing | PM${}_{2.5}$-O${}_{3}$ | 0.741 | 0.454 | 0.125 | 0.119 | 0.218 | 0.145 |

(0.071) | (0.067) | (0.112) | (0.084) | ||||

Nantong | PM${}_{2.5}$-O${}_{3}$ | 0.556 | 0.389 | 0.116 | 0.120 | 0.189 | 0.142 |

(0.066) | (0.082) | (0.103) | (0.082) | ||||

Suzhou | PM${}_{2.5}$-O${}_{3}$ | 1.146 | 0.583 | 0.113 | 0.113 | 0.292 | 0.269 |

(0.066) | (0.123) | (0.135) | (0.123) |

**Table 3.**Comparison of the components of the width of multifractal spectrums of original, shuffled, surrogate PM${}_{2.5}$ and O${}_{3}$ series in and around Shanghai before and during the COVID-19 partial lockdown. The numbers in parentheses are the standard deviations. Period I: before the COVID-19 lockdown, Period II: during the COVID-19 lockdown.

City | Pollutant | $\Delta {\alpha}_{\mathit{x}/\mathit{y}}^{\mathit{LM}}$ | $\Delta {\alpha}_{\mathit{x}/\mathit{y}}^{\mathit{NL}}$ | $\Delta {\alpha}_{\mathit{x}/\mathit{y}}^{\mathit{PDF}}$ | $\Delta {\alpha}_{\mathit{x}/\mathit{y}}^{\mathit{INTR}}$ | INTR Ratio${}_{\mathit{x}/\mathit{y}}$ | |||||
---|---|---|---|---|---|---|---|---|---|---|---|

Period I | Period II | Period I | Period II | Period I | Period II | Period I | Period II | Period I | Period II | ||

Shanghai | PM${}_{2.5}$-O${}_{3}$ | 0.237 | 0.177 | 0.972 | 0.550 | 0.112 | 0.115 | 0.972 | 0.550 | 73.59% | 65.32% |

(0.146) | (0.138) | (0.132) | (0.122) | (0.062) | (0.064) | (0.132) | (0.122) | (9.98%) | (14.46%) | ||

Jiaxing | PM${}_{2.5}$-O${}_{3}$ | 0.093 | 0.026 | 0.523 | 0.309 | 0.125 | 0.119 | 0.523 | 0.309 | 70.58% | 68.16% |

(0.132) | (0.108) | (0.112) | (0.084) | (0.071) | (0.067) | (0.112) | (0.084) | (15.10%) | (18.60%) | ||

Nantong | PM${}_{2.5}$-O${}_{3}$ | 0.073 | 0.023 | 0.368 | 0.247 | 0.116 | 0.120 | 0.368 | 0.247 | 66.10% | 63.41% |

(0.122) | (0.106) | (0.103) | (0.082) | (0.066) | (0.082) | (0.103) | (0.082) | (18.49%) | (20.94%) | ||

Suzhou | PM${}_{2.5}$-O${}_{3}$ | 0.179 | 0.156 | 0.854 | 0.314 | 0.113 | 0.113 | 0.854 | 0.314 | 74.53% | 53.86% |

(0.149) | (0.138) | (0.135) | (0.123) | (0.066) | (0.123) | (0.135) | (0.123) | (11.74%) | (21.01%) |

**Table 4.**Comparison of the apparent ($\Delta {\alpha}_{x/y}$) and intrinsic ($\mathbb{E}$(INTR ratio)${}_{x/y}$) multifractal cross-correlation in and around Shanghai.

City | Pollutant | $\Delta {\alpha}_{\mathit{x}/\mathit{y}}$ | $\mathbb{E}$(INTR ratio)${}_{\mathit{x}/\mathit{y}}$ | ||||
---|---|---|---|---|---|---|---|

Period I(A) | Period II(B) | Change(B−A)/A | Period I(C) | Period II(D) | Change(D-C) | ||

Shanghai | PM${}_{2.5}$-O${}_{3}$ | 1.321 | 0.843 | −36.2% | 73.59% | 65.32% | −8.3% |

Jiaxing | PM${}_{2.5}$-O${}_{3}$ | 0.741 | 0.454 | −38.8% | 70.58%) | 68.16% | −2.4% |

Nantong | PM${}_{2.5}$-O${}_{3}$ | 0.556 | 0.389 | −30.0% | 66.10% | 63.41% | −2.7% |

Suzhou | PM${}_{2.5}$-O${}_{3}$ | 1.146 | 0.583 | −49.1% | 74.53% | 53.86% | −20.7% |

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**MDPI and ACS Style**

Li, X.; Su, F. The Dynamic Impacts of COVID-19 Pandemic Lockdown on the Multifractal Cross-Correlations between PM_{2.5} and O_{3} Concentrations in and around Shanghai, China. *Atmosphere* **2022**, *13*, 1964.
https://doi.org/10.3390/atmos13121964

**AMA Style**

Li X, Su F. The Dynamic Impacts of COVID-19 Pandemic Lockdown on the Multifractal Cross-Correlations between PM_{2.5} and O_{3} Concentrations in and around Shanghai, China. *Atmosphere*. 2022; 13(12):1964.
https://doi.org/10.3390/atmos13121964

**Chicago/Turabian Style**

Li, Xing, and Fang Su. 2022. "The Dynamic Impacts of COVID-19 Pandemic Lockdown on the Multifractal Cross-Correlations between PM_{2.5} and O_{3} Concentrations in and around Shanghai, China" *Atmosphere* 13, no. 12: 1964.
https://doi.org/10.3390/atmos13121964