# Impacts of Quasi-Biennial Oscillation and El Niño–Southern Oscillation on Stratospheric Isentropic Mixing Process

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Data and Methods

#### 2.1. Data

#### 2.2. Methods

#### 2.2.1. Calculation of the Equivalent Length

**u**is the horizontal wind vector and k is the constant parameter of the diffusion coefficient. By defining a coordinate based on the tracer concentration, the equivalent latitude ${\varphi}_{e}$, the equation (R-4) can be transformed into a pure diffusion equation:

_{e}is defined such that

#### 2.2.2. Multiple Linear Regression Model

_{1}is the amplitude, and lag τ

_{1}is the lag related to QBO. b

_{2}is the amplitude, d τ

_{2}is the lag related to ENSO, and ϵ(t,ϕ,z) is the residual.

#### 2.2.3. Eliassen–Palm Flux

^{2}/s

^{2}) can be calculated by [44,45]:

^{8}m

^{3}/s

^{2}), and vortex heat transport per unit mass of air in the north–south direction (magnitude is 10

^{6}Pa∙m

^{2}/s

^{2}), respectively. In Equation (R-2) and Equation (R-3), ${r}_{0}$ is the radius of the Earth, $f$ is the Coriolis force parameter, $\phi $ is the latitude, $\theta $ is the potential temperature, and u′ and v′ are the latitudinal and meridional wind disturbances, respectively. The superscripts “-” and “′” indicate the latitudinal mean and latitudinal deviation; the subscript “p” indicates the deviation from the barometric pressure.

#### 2.2.4. Selection of MEI Index and QBO Index

#### 2.2.5. Composite Analysis

## 3. Results and Analysis

#### 3.1. Interannual Variability of Isentropic Mixing Intensity

#### 3.2. Multiple Regression Model

#### 3.3. Composite Analysis of Modulation of Stratospheric Mixing by QBO and ENSO

## 4. Summary and Discussion

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Time series of QBO index at 50 hPa (

**a**) and MEI index (

**b**) averaged in the winters from 1980 to 2010.

**Figure 2.**Interannual variabilities of the equivalent length at 480 K and 880 K in the tropics (

**a**,

**b**) and their winter averages (

**c**,

**d**) during 1980–2010 in ERA-Interim (seasonality in the data is removed).

**Figure 3.**Frequency power spectra of the (

**a**) equivalent lengths calculated from the ERA-Interim and (

**b**) MERRA-2 data.

**Figure 4.**Sequences of the QBO index (solid red line) and MEI index (solid blue line) defined by the 50 hPa zonal mean wind in the Northern Hemisphere winter from 1980 to 2010. The vertical axis represents the value of the two indexes, and the number in the lower left corner is the correlation coefficient between the two indexes.

**Figure 5.**Time series of original value (red) and simulated value (blue) of the equivalent length calculated from ERA-Interim on the 480 K and 880 K isentropic surfaces. The two panels are regional averages for the equatorial region (0–30°N), the middle two panels are regional averages for the mid-latitude region (30–60°N), and the bottom two panels are for the polar region (60–90°N).

**Figure 6.**Distribution of long-term linear trends (a(ϕ,z)) in multiple regression results for ERA-Interim and MERRA-2 data.

**Figure 7.**Time-latitude cross-sections at 480 K and 880 K based on ERA-Interim (

**left**) and MERRA2 (

**right**) from 1980 to 2010 for calculation using the basis function in the multiple regression model (∆1 = b1 × p1).

**Figure 8.**Time-latitude cross-sections at 480 K and 880 K based on ERA-Interim (

**left**) and MERRA2 (

**right**) from 1980 to 2010 for calculation using the basis function in the multiple regression model (∆2 = b2 × p2).

**Figure 9.**Composite latitude-height cross-sections of zonal mean equivalent length and E–P flux (vectors) and E–P flux divergence (color shadings) in the Northern and Southern Hemispheres in winter in the WQBO and EQBO phases based on the ERA-Interim reanalysis product and corresponding zonal wind anomalies. Black dotted areas are for values significant at the 90% confidence level by t-test. Cases used for composite analysis are listed in Table 1. The contours show zonal mean wind at 10 m/s intervals (solid gray lines are for westerly winds, dashed gray lines are for easterly winds, and the white lines indicate zero wind speed).

**Figure 10.**Composite latitude-height cross-sections of zonal mean equivalent lengths and E–P flux (vectors) and E–P flux divergence (color shadings) in the El Niño and La Niña years and corresponding zonal wind anomalies based on ERA-Interim reanalysis data for the period 1980–2010. The black dotted area represents values passing the 90% confidence level test (by t-test). The cases used for composite analysis are shown in Table 2. The contours show mean zonal winds at intervals of 10 m/s (solid gray lines for westerly winds, dashed gray lines for easterly winds, and white lines for zero winds).

Event | Year |
---|---|

EQBO | 1981, 1984, 1989, 1996, 1998, 2001, 2003, 2005, 2007 |

WQBO | 1980, 1982, 1985, 1987, 1988, 1990, 1992, 1993, 1995, 1997, 1999, 2002, 2004, 2006, 2008 |

Event | Year |
---|---|

El Niño | 1980, 1983, 1987, 1988, 1990, 1992, 1993, 1995, 1998, 2003, 2005 |

La Niña | 1982, 1984, 1985, 1986, 1989, 1996, 1997, 1999, 2000, 2001, 2006, 2008, 2009 |

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**MDPI and ACS Style**

Liang, J.; Wang, Z.; Zhang, Z.; Luo, J.
Impacts of Quasi-Biennial Oscillation and El Niño–Southern Oscillation on Stratospheric Isentropic Mixing Process. *Remote Sens.* **2023**, *15*, 2715.
https://doi.org/10.3390/rs15112715

**AMA Style**

Liang J, Wang Z, Zhang Z, Luo J.
Impacts of Quasi-Biennial Oscillation and El Niño–Southern Oscillation on Stratospheric Isentropic Mixing Process. *Remote Sensing*. 2023; 15(11):2715.
https://doi.org/10.3390/rs15112715

**Chicago/Turabian Style**

Liang, Jing, Zhiting Wang, Zhiyi Zhang, and Jiali Luo.
2023. "Impacts of Quasi-Biennial Oscillation and El Niño–Southern Oscillation on Stratospheric Isentropic Mixing Process" *Remote Sensing* 15, no. 11: 2715.
https://doi.org/10.3390/rs15112715