As Earth orbits around the Sun, the duration of the four seasons is well defined at ground level at middle latitudes. Higher up between 50 and 100 km in the mesosphere and lower thermosphere (MLT), the separation is not well defined. Earth's atmosphere is a complex system governed by several processes that are continuously evolving (e.g., radiative heating, coupling, mixing processes). The dynamics of the MLT are forced mainly by solar radiation and the wave activities arising in the lower atmosphere, such as planetary waves, gravity waves, and tides e.g.,. Circulation patterns such as the stratospheric quasi-biennial oscillation QBO, and El Niño–Southern Oscillation ENSO, also influence the MLT dynamics at middle latitudes. During winter conditions strong planetary wave activity is present and, later on, in the transition from winter to summer, a reduction of the planetary activity occurs . With the transition, every year the zonal wind circulation in the MLT displays the final reversal of the wind direction from eastward to westward, in part produced by the wave dissipation generated by gravity wave activity see. In connection with this wind reversal, the mesopause experiences a decrease in temperature resulting in the appearance of ice particles, due to the water vapor present in the atmosphere. The presence of charged ice particles is observed through radar echoes known as polar mesospheric summer echoes PMSE; see, e.g.,. Between 80 and 90 km and on nanometer scales, a congregation of ice particles is called noctilucent clouds or polar mesospheric clouds e.g.,.

The above-mentioned summer characteristics exhibit interannual variabilities and interactions with adjacent layers, highlighting the importance of studying this season as well as its long-term behavior. Previous works, like , used the mean zonal wind reversal at around 25 km altitude to study long-term behavior between 1958 and 1982, obtaining an increase in the summer duration of 0.52 days per year (d yr-1). Nevertheless, the authors suggested a possible change in the trends after 1980 and reported a connection between the QBO and the wind reversal dates during 1958–1967 and again after 1977. Under the name of equivalent summer duration, defined by a threshold of 198 K at 87 km at middle latitudes, the temperature variations during summer were investigated by . This study covered the years 1988 to 2008, obtaining a change rate of 1.21 d yr-1. The authors also compared the obtained values with the zonal wind reversal in the stratosphere (20 hPa) that showed a decrease in the summer duration of 0.99 d yr-1. Later on, studied the hydroxyl nightglow rotational temperatures in the Antarctic region and compared them with satellite winds and temperatures at 86 km. The authors found a correlation between temperature and meridional winds but no significant correlation with the mean zonal winds. characterized the summer duration, referring to the stratospheric zonal wind reversal in broad ranges of latitude and altitude between 1948 and 2003. They found a dependency on latitude and altitude, with longer summer duration at higher altitudes and high latitudes for the Northern Hemisphere. However, in all the cases they detected a breakpoint around 1978–1980, obtaining an increase in summer duration before the breakpoint and negative trends after 1978/1980.

For several years, long-term studies aimed to investigate the anthropogenic influence in the atmosphere. Having in mind the atmosphere as a whole and considering that the temperature changes affect life at ground level, we can compare the summer length with the vegetation growing season. The normalized difference vegetation index (NDVI) is obtained from CO2 satellite measurements e.g.,. During the vegetation growing season there is an exchange of CO2 between the plants and the soil due to the process of photosynthesis and decomposition . In these studies the summer season starts around April/May and ends in September/October at middle latitudes, which appears to be comparable with the time interval for the mean zonal wind reversal investigated in this paper.

The middle-atmosphere studies, mentioned above, were made before 2010. Since the beginning of the 21st century, new radar systems have been deployed in Germany and Norway. After more than one solar cycle of system operations, we are able to look into the long-term trends. In this study, we aim to analyze the long-term variability of the mean zonal wind reversal, which occurs around March and in September by implementing two different definitions of summer length. Both definitions applied to radar wind measurements are related to different processes and regions in MLT and incorporate altitude and latitude features. With these definitions we search for possible correlations with known forcing events from above or below the MLT, like, e.g., solar activity measured by the Lyman α line, major sudden stratospheric warming MSSW,, and strong polar-night jet oscillations sPJO,. The Lyman α line is a good representation of the solar activity in the MLT, as a consequence of the hydrogen absorption that occurred by the Sun's ultraviolet light, maximizing at around 90 km .

To study the MLT summer length, we combine MLT winds from specular meteor radars (SMRs) and mesospheric winds from partial reflection radars PRR,. These systems are located in Germany and northern Norway. Our ground-based observations are complemented with similar years of satellite observations, specifically from the Microwave Limb Sounder (MLS) on board the Earth Observing System Aura satellite e.g.,.

The paper is organized as follows. Section  contains the description of the database and instruments used as well as a brief description of the applied data-processing methods for the individual systems. Section  gives a description of the climatology and the applied summer length definitions. The final time series and a brief description of the results are given in Sect. . This is followed by the discussion for the individual latitudes and a comparison between the definitions in Sect.  and, finally, a summary and conclusions are found in Sect. .

Considering the difficulties in obtaining a homogeneous data set, which are well known in long-term studies e.g.,, we used a combination of closely located SMRs at two selected latitudes. This combination allows us to reduce the number of data gaps and provides a highly reliable wind estimation for the regions under investigation. To study the mean zonal wind reversal at lower altitudes, namely below 80 km, we have included data from PRRs and the MLS on board the Aura Earth Observing System (Aura EOS). Both types of radars, SMRs and PRRs, have a good agreement between 80 and 90 km e.g.,. In the next subsections we briefly describe each of these systems and the methodology of the processed radar data.

A mean zonal wind climatology for both latitudes and combinations of stations is shown in Fig. . The high-latitude climatology (Fig. a) is generated from the combination of Andenes and Tromsø SMRs above 81 km and below from the Saura PRR. An equivalent approach is used for the middle latitudes (Fig. b), where between 81 and 100 km observations from Juliusruh and Collm SMRs are used and, for altitudes below 81 km, from the Juliusruh PRR wind climatology (years 2004–2020). During summer months, the mean zonal wind over these sites is expected to be equivalent to the zonal mean zonal wind e.g.,.

Both climatologies depict a reversal of the wind (grey line) around March–April, when the wind reverses from eastward (red) to westward (blue) at all altitudes. Between April and May at high altitudes, the wind changes from westward to eastward (grey line), and the temporal evolution of this reversal occurs rapidly from 100 km down to around 90 km (86 km for middle latitudes). From early June, the mean zonal wind reverses slowly with decreasing altitude until 85 km (78 km at middle latitudes) until middle September. Later on, the wind direction reverses rapidly from westward to eastward from these altitudes downwards, indicating the end of the summer in the MLT in middle September, around 1 week before the autumnal equinox. The dynamics of the mean zonal wind displays a clear dependence of altitude with respect to latitude e.g.,. Given this latitudinal dependence, we adjust the selected altitudes in the summer length definitions (described below) accordingly.

Figure  displays a climatological mean of the mean zonal wind reversal for all data sets. We are indicating the altitudes used in this work for the different summer definitions (see below). At 69∘ N, the mean zonal wind reversal from the combination of SMRs is depicted in purple and from PRR in orange lines, while for 54∘ N the combination of SMRs is shown in red and the PRR in green lines. The climatological zonal mean geostrophic zonal wind value is also represented at 82 km for 70∘ N (solid blue lines) and at 74 km height for 55∘ N (dash-dotted blue lines).

Here we briefly describe how the radar data have been processed and the results are obtained. We first calculate the daily mean of hourly winds for each altitude and site. Then the mean is smoothed by a 16 d running window, shifted by 1 d. In order to compress the data and to further reduce its variability and to be able to focus on the long-term changes, we implemented a principal component analysis (see details in Sect. ). With the first two components of principal component analysis, we are able to reconstruct the mean zonal winds year by year and, considering only the altitudes of interest, we extract the day of the year (DOY) on which the reversal occurs. Following this analysis, we obtain three different time series for each latitude and definition (summer beginning, summer end, and summer length). Each time series is treated with a default standard deviation error from the size of the smoothing window plus an extra consideration for the years where the mean zonal wind reversal is particularly difficult to assess due to an unclear transition. In these cases, the sum of days during the unclear reversal period is divided by 2 and manually implemented as an error for the particular value.

Figure  presents the detected wind reversal dates at high latitudes, i.e., MLT-SL (left column, purple lines) and M-SL (right column) for the previously introduced altitude definitions. Note that for M-SL, both MLS (blue lines) and PRR (red lines) results are included. The first three panels for both definitions (Fig. a, b, c and e, f, g) depict the DOY (ordinate) when the mean zonal wind reversal occurs for every year (abscissa) for summer beginning, summer end, and summer length, respectively.

To explore the long-term behavior, we fit a linear function and apply the Student's t test (with null hypothesis being the slope equal to zero) to investigate whether there is a significant slope incorporating the standard deviation error propagation e.g.,. The linear regression (solid line in the same color) is only shown for the summer beginning and summer length (first and third panels, respectively), and enclosed in dashed lines (same color) is shown the expected variability. In the case of summer end for both definitions, the linear regression is not shown since we were not able to reject the null hypothesis.

The M-SL (Fig. g) for the high latitudes is found to be 170±11 d long using PRR measurements (173±12 d for the MLS) with a tendency of 0.46±0.52 d yr-1 (1.23±0.62 d for the MLS). Most of the variability and trend is introduced by the summer beginning (Fig. a) occurring at DOY 93±10 d for PRR (3 April) and DOY 88±12 d for the MLS (29 March), with a tendency to start earlier, -0.62±0.48 and -1.26±0.62 d, respectively. For the MLT-SL (Fig. c) we found 136±8 d but with no significant trend starting around 7 May (see Table  for more details).

The last row for both definitions (Fig. d, h) represents proxies of possible forcing in the MLT region that occurred during the corresponding previous winter (for MSSW and strong polar-night jet oscillations) or centered in the mean value for the summer beginning (March, April, and May) for Lyman α line (black line), QBO and ENSO. ENSO is represented by the Oceanic Niño Index (ONI), where the values over 1 ∘C are considered an El Niño phase (orange) and under -1 ∘C a La Niña (green) see, e.g.,. The QBO is represented by the winds at 10 hPa from Singapore (scaled by 10 m s-1). QBO eastward (QBOe) is shown in red, and QBO westward (QBOw) is blue. The MSSWs are represented (in purple) as follows: when a displacement of the polar vortex occurred is indicated by a “D”, and in case of a split it is indicated by the bow tide symbol. The pink “sPJO” shows the year when strong polar-night jet oscillations occurred.

The middle-latitude results are shown in Fig.  in a similar format. The main difference is that the altitude for the summer end in both definitions is 74 km. There, the M-SL (Fig. g) is found to be 162±7 d long using PRR measurements (160±6 d for the MLS), with an almost identical tendency of 0.55±0.3 d yr-1 for the PRR and MLS. Equivalently to the high latitudes, this mostly corresponds to the summer beginning (Fig. a) occurring at DOY 95±5 d for PRR and DOY 97±7 d for the MLS (between 5 and 7 April) with tendencies of -0.49±0.25 and -0.72±0.32 d, respectively. For the MLT-SL (Fig. c) we found 141±4 d, but again with no significant trend, starting on 29 April.

The mean values, with the standard deviations from Figs.  and , are summarized in Table , as well as the slopes for the summer beginning and summer length with their standard deviations. The slopes are classified from the result of the Student's t-test, as follows. The slopes with less than 80 % of confidence have no stars, more than 90 % have one star, and more than 95 % have two stars.

As mentioned previously, in the case of middle latitudes one can extend the study of the M-SL using the Juliusruh PRR to 31 years by combining zonal winds obtained at the same place but with different partial reflection radar systems and measuring techniques. Figure  depicts the M-SL values from this combined data set covering the period 1990–2020. In this case, we show a linear function for the entire time series in black. Due to an apparent breakpoint around 2008, we include two linear regressions according to this breakpoint, i.e., 1990–2008 in dashed red line and 2008–2020 in dashed blue line. The breakpoint was obtained by a second-degree polynomial fitted by the least square method.

In this section we discuss the obtained result. Noteworthy, for both latitudes and definitions, is that the variability of the summer lengths is dominated by the summer beginning and, thus, by the winter conditions. Since our results display a latitudinal dependency, we also divided our discussion by latitude. In addition, we discuss the results of our summer definitions with respect to other definitions used in earlier studies. The long-term behavior of our results, including the 31-year analysis, is discussed separately.

Smoothed mean zonal winds between 2004/2005 and 2020 from different radars located at high and middle latitudes (Andenes SMR–Tromsø SMR, Saura PRR, Juliusruh SMR–Collm SMR and Juliusruh PRR), as well as MLS measurements, are used to study two different summer length definitions (see Sect. ). The MLT-SL definition is taken when the last wind reversal occurred from westward to eastward at 96 km (MLT-SB) and 82 km at high latitudes (74 km for middle latitudes) as MLT-SE. On the other hand, the M-SL definition is taken at the same altitude (M-SB and M-SE) but depending on the latitude (82 km at high latitudes and 74 km at middle latitudes), when the mean zonal wind reverses from eastward to westward (M-SB) and, again, from westward to eastward (M-SE).

With the obtained time series, we analyzed the summer length and studied the variability and the linear tendency. We looked into the dates and the different events occurring in the upper and lower atmosphere to understand the events modifying the summer length. Furthermore, we compared the summer length to the growing season length. The results are summarized as follows.

The summer length is determined by the mean zonal wind reversal, which depends on the actual latitude and altitude. High latitudes showed more variability than middle latitudes for both definitions. The summer beginning presents most of the variability that is transferred to the summer length. The summer end occurs for all latitudes in the same week before the autumn equinox and presents no significant linear trend.