# Discontinuities in the Ozone Concentration Time Series from MERRA 2 Reanalysis

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Data and Method

_{t}(t = 1..T) and x

_{t}(t = T + 1,.. N). Thus, probability distribution functions F

_{1}(X) and F

_{2}(X) can be associated with the two subsequences. In practice, the null hypothesis H

_{0}is F

_{1}(X) is equal to F

_{2}(X), and the alternative hypothesis H

_{1}is F

_{1}(X) is not equal to F

_{2}(X). This method also involves a comparison of the observations so that:

_{i,j}= sgn(x

_{i}− x

_{j}),

_{i, j}= 1 if x

_{i}> x

_{j},

_{i, j}= 0 if x

_{i}= x

_{j},

_{i, j}= −1 if x

_{i}< x

_{j}.

_{T}, N = ∑

_{t = 1..T}∑

_{t = T, N}Di,j, t = 1..N

_{N}variable is derived from U

_{T, N}This new variable is defined:

_{N}max abs(U

_{T,N}) T = 1..N − 1.

_{N>K}) ≅ 6exp(−6k

^{2})/(N

^{3}+ N

^{2}).

_{0}is rejected if the probability of exceedance given in P is less than the significance level α for a one-sided statistic test.

## 3. Results

#### 3.1. Patterns of Ozone Concentration

#### 3.2. Temporal Occurrence of Discontinuities

^{93}Figure 5—upper panel for January). Going down this unimodal distribution change, the bimodal one with the main maximum was observed in 1993, and the secondary maximum was observed in 2004(B

^{93}^{,04}). In lower layers, the bimodal distribution with the main maximum in 2004 and the secondary one in 1993 (B

^{93,04}) could be seen. This transformation ended at 1 hPa (Figure 5 lower panel for January), where we observed unimodal distribution again, but the maximum occurred in 2004 in each month. Below 2 hPa down to 200 hPa, we observed flat temporal distribution of discontinuities (F) with no sharp maximum (Figure 6 upper panel for January) in each month. In January, the upper distribution border lay in 5 hPa. Below 200 hPa, we again observed unimodal temporal distribution with a maximum about the early 1990s (U

^{93T}, Figure 6—lower panel for January), but this distribution was broader than distribution U

^{93}in the upper model layers. When we observed the unimodal distribution of all discontinuities, the distribution of the significant ones must be similar. In the case of bimodal distribution, the situation was different. We could observe the bimodal distribution of all discontinuities, but the distribution of their significant counterparts can be unimodal. This was the case of bimodal distributions from 0.4 hPa and 0.5 hPa when we observed the bimodal distribution of all discontinuities, but the 1993 maximum was formed predominantly by the insignificant ones, and the 2004 maximum consisted predominantly of the significant discontinuities (Figure 7). Thus the distribution of the significant discontinuities in these cases was bimodal, but the maximum in 2004 was much stronger than that in 1993. Similarly, in the troposphere, the distribution U

^{93T}was seen only for all discontinuities, but for the significant ones, we observed nearly flat distribution due to the fact the 1993 maximum consisted predominantly of the insignificant discontinuities (Figure 8).

#### 3.3. Vertical Profile of the Discontinuities Occurrence

#### 3.4. Spatial Occurrence of Discontinuities

## 4. Discussion

_{2}. Sudden water vapour drops in the stratosphere around 2000. In ref [30] can also be the manifestation of the changes in the atmospheric behaviour.

## 5. Conclusions

- The data above 4 hPa are not suitable for the trend analyses due to occurrence of patterns of the average ozone concentration which cannot be explained by theory and due to the frequent occurrence of the significant discontinuities
- Below 4 hPa, the number of discontinuities is smaller, and they are mostly insignificant.
- In the troposphere, the number of discontinuities is higher than in the stratosphere, but they are mostly insignificant.
- The transition from SBUV to EOS Aura data in 2004 does not have a strong influence on discontinuities occurrence below 4 hPa.
- According to our results, the MERRA 2 ozone concentration data are suitable for trend analyses below 4 hPa with caution.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Average ozone concentration (kg/kg) in January at 0.1 hPa (

**upper panel**) and at 0.5 hPa (

**lower panel**).

**Figure 2.**The same as Figure 1, but for January at 1 hPa (

**upper panel**) and for July at 1 hPa (

**lower panel**).

**Figure 3.**Average ozone concentration (kg/kg) in January at 10 hPa (

**upper panel**) and at 50 hPa (

**lower panel**).

**Figure 4.**Average ozone concentration (kg/kg) in January at 300 hPa (

**upper panel**) and at 500 hPa (

**lower panel**).

**Figure 5.**Temporal distribution of all discontinuities in January at 0.1 hPa (

**upper panel**) and at 1 hPa (

**lower panel**).

**Figure 7.**Temporal distribution at 0.5 hPa of all (

**upper panel**) and significant (

**lower panel**) discontinuities.

**Figure 8.**The same as Figure 7, but for 300 hPa.

**Figure 9.**Vertical profiles of percentage occurrence of all (

**upper panel**) and significant discontinuities (

**lower panel**) in all months.

**Figure 10.**Geographical distribution of all (

**upper panel**) and the significant (

**lower panel**) discontinuities for January at 0.1 hPa (red—discontinuities, yellow—no discontinuities; upper panel all points have discontinuities.).

**Figure 11.**The same as Figure 10, but for 3 hPa.

**Figure 12.**Geographical distribution of all (

**upper panel**) and the significant (

**lower panel**) discontinuities for January at 10 hPa.

**Figure 13.**The same as Figure 12, but for 250 hPa.

**Figure 14.**Geographical distribution of all (

**upper panel**) and the significant (

**lower panel**) discontinuities for January at 500 hPa.

**Figure 15.**Geographical distribution of all (

**upper panel**) and the significant (

**lower panel**) discontinuities over the globe at 0.3 hPa.

**Figure 16.**The same as Figure 15, but for 0.4 hPa.

**Figure 17.**Geographical distribution of all (

**upper panel**) and the significant (

**lower panel**) discontinuities over the globe at 1 hPa.

**Figure 18.**The same as Figure 17, but for 5 hPa.

**Figure 19.**Geographical distribution of all (

**upper panel**) and the significant (

**lower panel**) discontinuities over the globe at 30 hPa.

**Figure 20.**The same as Figure 19, but for 300 hPa.

**Figure 21.**Geographical distribution of all (

**upper panel**) and the significant (

**lower panel**) discontinuities over the globe at 500 hPa.

**Table 1.**The vertical extent of ozone concentration pattern in a certain month (satellite—satellite-like pattern), max—the pattern with maximum over the Aleutian Islands (Al) or over Antarctica (An), UST—upper stratospheric pattern (maximum over equator and minimum over polar latitudes), LST—lower stratospheric pattern (maximum over the polar latitudes and minimum over equator), SH max—another maximum over the subpolar latitudes of the Southern Hemisphere.

January | February | March | April | May | June | |

Satellite | 0.1–0.5 | 0.1–0.5 | 0.1–0.5 | 0.1–0.5 | 0.1–0.5 | 0.1–0.5 |

max | 0.7–2 / Al | 0.7–2 / Al | 2–3 / Al | 0.7–2 / An | 0.7–2 / An | 0.7–3 / An |

UST | 3–10 | 3–10 | 5–10 | 7–20 | 7–20 | 7–20 |

LST | >30 | >30 | >30 | >40 | >40 | >40 |

SH max | No | No | No | No | No | No |

July | August | September | October | November | December | |

Satellite | 0.1–0.5 | 0.1–0.5 | 0.1–0.5 | 0.1–0.5 | 0.1–0.5 | 0.1–0.5 |

max | 0.7–3 / An | 0.7–3 / An | 0.7–3 / An | 0.7–2 / An,Al | 0.7–2 / Al | 0.7–2 /Al |

UST | 4–20 | 4–20 | 4–20 | 4–20 | 3–20 | 3–20 |

LST | >40 | >40 | >40 | >40 | >40 | >40 |

SH max | 30–250 | 30–250 | 30–250 | 30–300 | 30–300 | No |

**Table 2.**Temporal distribution of discontinuities at certain layers and certain months (U

^{93}—unimodal distribution with maximum in 1993, B

^{93,04}—bimodal distribution with two maxima in 1993 and 2004, the height of maxima was comparable, B

^{93}^{,04}—bimodal distribution, maximum in 1993 was higher than that in 2004, B

^{93,04}—bimodal distribution, maximum in 1993 was lower than that in 2004, U

^{04}—unimodal distribution with maximum in 2004, F—flat distribution with no maxima, U

^{93T}—unimodal distribution with wide maximum in 1993 which occurred in the troposphere).

[hPa] | January | February | March | April | May | June | |

0.1 | U^{93} | U^{93} | U^{93} | U^{93} | U^{93} | U^{93} | |

0.3 | B^{93}^{,04} | B^{93}^{,04} | B^{93}^{,04} | B^{93}^{,04} | U^{93} | U^{93} | |

0.4 | B^{93,04} | B^{93,04} | B^{93,04} | B^{93,04} | B^{93}^{,04} | B^{93,04} | |

0.5 | B^{93,04} | B^{93,04} | U^{04} | U^{04} | B^{93,04} | B^{93,04} | |

0.7 | B^{93,04} | U^{04} | U^{04} | U^{04} | U^{04} | U^{04} | |

1 | U^{04} | U^{04} | U^{04} | U^{04} | U^{04} | U^{04} | |

2 | U^{04} | U^{04} | U^{04} | U^{04} | F | F | |

3 | U^{04} | F | F | F | F | F | |

4 | U^{04} | F | F | F | F | F | |

5 | U^{04} | F | F | F | F | F | |

7–200 | F | F | F | F | F | F | |

250–500 | U^{93T} | U^{93T} | U^{93T} | U^{93T} | U^{93T} | U^{93T} | |

July | August | September | October | November | December | ||

0.1 | U^{93} | U^{93} | U^{93} | U^{93} | U^{93} | U^{93} | |

0.3 | U^{93} | U^{93} | B^{93}^{,04} | U^{93} | U^{93} | U^{93} | |

0.4 | B^{93,04} | B^{93,04} | B^{93,04} | B^{93,04} | B^{93}^{,04} | B^{93}^{,04} | |

0.5 | B^{93,04} | B^{93,04} | B^{93,04} | B^{93,04} | B^{93,04} | B^{93,04} | |

0.7 | B^{93,04} | B^{93,04} | U^{04} | U^{04} | U^{04} | B^{93,04} | |

1 | U^{04} | U^{04} | U^{04} | U^{04} | U^{04} | U^{04} | |

2 | U^{04} | U^{04} | U^{04} | U^{04} | F | F | |

3 | F | F | F | F | F | F | |

4 | F | F | F | F | F | F | |

5 | F | F | F | F | F | F | |

7–200 | F | F | F | F | F | F | |

250–500 | U^{93T} | U^{93T} | U^{93T} | U^{93T} | U^{93T} | U^{93T} |

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**MDPI and ACS Style**

Krizan, P.; Kozubek, M.; Lastovicka, J.
Discontinuities in the Ozone Concentration Time Series from MERRA 2 Reanalysis. *Atmosphere* **2019**, *10*, 812.
https://doi.org/10.3390/atmos10120812

**AMA Style**

Krizan P, Kozubek M, Lastovicka J.
Discontinuities in the Ozone Concentration Time Series from MERRA 2 Reanalysis. *Atmosphere*. 2019; 10(12):812.
https://doi.org/10.3390/atmos10120812

**Chicago/Turabian Style**

Krizan, Peter, Michal Kozubek, and Jan Lastovicka.
2019. "Discontinuities in the Ozone Concentration Time Series from MERRA 2 Reanalysis" *Atmosphere* 10, no. 12: 812.
https://doi.org/10.3390/atmos10120812