In the extratropical stratosphere, winter and summer alternate every year with two relatively short transition periods in between. Compared to the summer-to-winter seasonal transition (ST), the winter-to-summer ST is much sharper and quicker ( Black and McDaniel, 2007), so we only discuss the winter-to-summer ST in this paper. The winter-to-summer ST witnesses the breakdown of the polar vortex and the buildup of summertime circumpolar easterlies. Because of the dynamic coupling between the stratosphere and the troposphere, the ST is dynamically linked to the mid-range weather prediction in the troposphere (e.g., Baldwin et al., 2007; Wang et al., 2012). Although many studies have examined stratospheric variations in winter and summer (e.g., Hess and Holton, 1985; Labitzke and Vanloon, 1988, 1992), fewer have focused on the ST process. An improved understanding of the ST and its controlling factors will definitely help to predict the general circulation adjustments and the variations of chemical species in both the stratosphere and the troposphere.

The basic features of stratospheric dynamics, such as the stratospheric structure and dynamic coupling with the troposphere, have been well-documented using several definitions of the stratospheric ST (e.g., Karpetchko et al., 2005). Most studies (e.g., Sherstyukov et al., 1997; Choi et al., 2008) have followed the traditional method that evenly divides a year into four seasons, as used in the tropospheric studies. Some recent studies (e.g., Waugh and Rong, 2002; Black and McDaniel, 2007) began to realize the limitation of the traditional definition and they defined the winter-to-summer ST as the date when the average wind velocity along the vortex edge falls below a threshold value. This is also known as stratospheric final warming (SFW). However, SFW strongly depends on the definition of the polar vortex edge and the threshold chosen.

Numerous studies have investigated the interannual variability of the stratospheric ST (e.g., Labitzke, 1982; Black and McDaniel, 2007). In early transition, once the vortex has broken down, the remnants of the vortex persist for longer than in late transition when the vortex disappears quickly ( Waugh and Rong, 2002). Studies on the long-term trend have shown that between the mid-1980s and the late 1990s, the springtime polar vortex was stronger and colder, and lasted for a longer time (e.g., Waugh et al., 1999; Zhou et al., 2000).

It is widely accepted that the activity of planetary waves (PW) plays a crucial role in modulating the occurrence of the ST (e.g., Newman et al., 2001; Polvani and Waugh, 2004). And PW activity is modulated by factors such as stratospheric sudden warming (SSW) (e.g., Liu et al., 2009) and the quasi-biennial oscillation (QBO) (e.g., Holton and Tan, 1982; Reid, 1994).

This article investigates the dynamic stratospheric ST and is organized as follows: Section 2 describes the data and methods. A definition of the ST can be found in section 3. The time and duration of the ST are presented in section 4. The interannual variability of the ST is presented in section 5, and its relationship with the SSW and the QBO are presented in sections 5.1 and 5.2, respectively. The conclusion is summarized in section 6.

The daily mean European Centre for Medium-Range Weather Forecasts (ECMWF) ReAnalysis Interim (ERA- Interim) dataset (1979-2011) ( Dee et al., 2011) was used with a horizontal resolution of 1.5°×1.5°. We identified the SSW (e.g., Andrews et al., 1987) following the World Meteorological Organization, which requires the reversal of the westerlies at 60°N and 10 hPa. As a quasi-periodic oscillation of the equatorial zonal wind between easterlies and westerlies in the tropical stratosphere (e.g., Baldwin et al., 2001), the QBO is defined by the average zonal wind at 30 hPa over the equator.

We modified the method of spatial similarity coefficient ( Zeng and Zhang, 1992; Xue et al., 2002) to define the ST. Essentially, this approach measures the similaritybetween a meteorological field at any time and a typical winter field, so we can judge how far this moment is from winter.

The zonal wind velocity, U (θ, λ, p, t), varies with longitude ( θ), latitude ( λ), pressure ( p), and time ( t). The stratospheric winter-to-summer ST is actually a change of zonal wind from strong westerly to easterly. Traditionally, the typical winter field, U_w, and summer field, U_s, are defined as the average U in January and July, respectively. But as shown in Fig. 1a, an example of zonal wind evolution at 70 hPa in 1989-1990, January is not always characterized by the strongest westerly wind which actually occurs in different times at different latitudes. So we selected 31 consecutive days in which the average U was maximum (period between two blue lines), then we defined the average U in these 31 days as the winter field at this level of this year. By calculating the average of the winter fields in 33 years, the typical winter field, U_w( θ, λ, p), was eventually found to be a variable of space. Using a similar method, we defined the typical summer field ( U_s) by looking for the minimum of the zonal wind.

To highlight the anomaly, the average of the typical winter and summer fields, U^* = (U_w+ U_s)/2, was subtracted. This gave

within a given latitudinal area A((θ) A), the similarity between U° and is

,

where the inner product and the norm between U° and are defined as follows:

Also, the similarity between and is

It is obvious that , and it can be proved that if the two fields, and , are exactly the same, then R_w= +1; if the fields are similar in reverse, and if they are not relevant.

Therefore, we can use R_w only to define the seasons as follows:

Figure 1

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	Figure 1 (a) The evolution of zonal-mean zonal wind (contour) at 70 hPa (units: m s-1), 1989-1990. The period between the two blue (red) lines is a month (31 days) with the strongest westerly (easterly) wind. (b) The evolution of similarity between daily zonal wind and winter zonal wind field ( Rw) at 70 hPa and 51°N in 1990.

In this paper, we calculated R_w ( λ, p, t) for each latitude belt (1.5° of latitude). For example, Fig. 1b shows the evolution of R_w at 70 hPa and 51°N in 1990 in which R_w decreases from about 1.0 in January to about -1.0 in July. However, the fluctuating variation of the ST shows up in the evolution of R_w, which does not decrease monotonically. Actually, R_w exceeds the transition value (-0.5 or 0.5) multiple times. Here, we defined the last time it was smaller than 0.5 (-0.5) (red dots) as the start (end) of the ST (red lines). So, the time of the ST depends on time, latitude, and pressure.

The climatological mean (1979-2011) time and duration of the ST (Fig. 2) change with year, pressure level and latitude. The start of the ST (Fig. 2a) occurs first in February in the region of 50-60°N at about 10 hPa. This is because of the strong PW activity in this region which accelerates the decay of the westerly wind. The farther away from this region, the later the ST occurs. The latest ST occurs below 30 hPa south of 30°N, and a large horizontal gradient appears in the latitudes around 40°N. The end of the ST has a dominant horizontal difference (Fig. 2b) with the largest gradient between 40°N and 50°N. The ST ends earlier at higher latitudes in the upper stratosphere and later at around 30°N in the middle and lower stratosphere. We obtained the duration of the ST (Fig. 2c) by subtracting the start date of the ST from the end date. The ST has a long duration of more than 75 days in the region of 40-50°N between 10 and 30 hPa, but in most areas it is less than 60 days.

Figure 2

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	Figure 2 The climatological mean (1979-2011) (a) start dates, (b) end dates, and (c) duration of the stratospheric winter-to-summer seasonal transition (ST) period in the Northern Hemisphere defined by ERA-Interim zonal wind velocity ( U) (units: (a, b) day of year; (c) day).

Compared to the traditional method that uses a fixed time (March-April-May) and duration (three months) for the ST, our method shows the spatial differences. These differences reveal the non-uniform evolutions of zonal wind in different areas of the stratosphere during the ST period.

An example (see Fig. 3) of the 10-hPa time and duration of the ST at 70.5°N (the core latitude of the stratospheric polar vortex) shows a pronounced interannual variability which is similar to the trend of the SFW. The SFW event is taken as a sign that the polar vortex has finally broken down and the zonal wind transition has changed from westerlies to easterlies. These are identified as the final time that the 10-hPa zonal-mean zonal wind at 70.5°N drops below zero without returning to the threshold value (10 m s^-1). As one of the definitions of the ST, the SFW successfully marks the time that the vortex breaks down and the wind reverses; however, it ignores the duration of the ST. Take 2009 for example: the 10-hPa zonal wind in the polar region (70.5-90°N) began to reverse with the onset of the SSW event in late January. From then, the zonal wind remained either easterly or as a weak westerly, which is exactly a characteristic of the ST, but the SFW event of this year happened in early May (close to the end of the ST). So, the long duration of this ST (nearly 100 days) had not been found by the SFW, but it had been seen clearly between the start and end of the ST.

Figure 3

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Figure 3 The evolution of polar (70.5-90°N) zonal-mean zonal wind (contours) at 10 hPa (units: m s-1) in 32 years: the start (black solid line) and end (black dash line) dates of the ST at 70.5°N, 10 hPa; and the stratospheric final warming (SFW) date (red solid line) and the date of vortex displacement stratospheric sudden warming (SSW) events (black circles) and vortex split SSW events (black dots). All the variables correspond to the left coordinate. The duration of the ST (white dashed line) corresponds to the right coordinate (units: day).

On the basis of the modified spatial similarity coefficient, the stratospheric winter-to-summer ST in the Northern Hemisphere was analyzed using ERA-Interim reanalysis data. Affected by PW activity, the ST occurs as early as February in the 50-60°N with the longest duration in the midlatitudes. Compared to the traditional definition, our definition focuses more precisely on the spatial difference of the stratospheric dynamic evolution. Based on this definition, the dynamic and chemical processes that occur in different locations during the ST period will be studied in the future.

Figure 4

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Figure 4 The composite zonal-wind-based ST start date anomaly in the Northern Hemisphere in (a) westerly QBO winters and (b) easterly QBO winters, and end date anomalies in the Northern Hemisphere in (c) westerly QBO winters and (d) easterly QBO winters (units: day). The zonal-mean zonal wind anomalies at 30 hPa in the Northern Hemisphere in (e) westerly QBO winters and (f) easterly QBO winters (units: m s-1); the white lines are the start and end date of the ST. The anomaly contours statistically significant at the 0.05 level (based on the Student’s t-test) are shown as shadow regions.

The time and duration of the ST display pronounced interannual variability. Compared to SFW, our ST can show the duration of the transition period, and we find it is strongly affected by SSW and the QBO. The late SSW events (occurring after 22 January) are strongly correlated to the start of the ST. The QBO plays a regionally different role in the ST, which can be explained by the Holton-Tan oscillation. The easterly winter QBO strengthens the zonal wind in midlatitudes and weakens it in the high latitudes. Therefore, an easterly QBO delays the transition in midlatitudes and hastens the onset of the ST in high and low latitudes, while the westerly QBO produces exactly the opposite effect.

As a dramatic event in the middle and high latitudes of stratospheric winter, the onset of SSW significantly determines the start of the ST in high and middle latitudes. And as a tropical phenomenon, the influence of the QBO on the ST in midlatitudes is stronger than in high latitudes. These influencers adjust the stratospheric dynamic through PW activity, and these adjustments will further influence the troposphere and the chemical field which will be studied in the future.