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Long-term studies of MLT summer length definitions based on mean zonal wind features observed for more than one solar cycle at mid- and high-latitudes in the northern hemisphere

Specular meteor radars (SMRs) and partial reflection radars (PRRs) have been observing mesospheric winds for more than a solar cycle over Germany (∼54°N) and northern Norway (∼69°N). This work investigates the mesospheric mean zonal wind and the zonal mean geostrophic zonal wind from the Microwave Limb Sounder (MLS) over these two regions between 2004 and 2020. Our study focuses on the summer when strong planetary waves are absent and the stratospheric and tropospheric 5 conditions are relatively stable. We establish two definitions of the summer length according to the zonal wind reversals: (1) the mesosphere and lower thermosphere summer length (MLT-SL) using SMR and PRR winds, and (2) the mesosphere summer length (M-SL) using PRR and MLS. Under both definitions, the summer begins around April and ends around mid-September. The largest year to year variability is found in the summer beginning in both definitions, particularly at high-latitudes, possibly due to the influence of the polar vortex. At high-latitudes, the year 2004 has a longer summer length compared to the mean 10 value for MLT-SL, as well as 2012 for both definitions. The M-SL exhibits an increasing trend over the years, while MLTSL does not have a well-defined trend. We explore a possible influence of solar activity, as well as large-scale atmospheric influences (e.g. quasi-biennial oscillations (QBO), El Niño-southern oscillation (ENSO), major sudden stratospheric warming events). We complement our work with an extended time series of 31 years at mid-latitudes using only PRR winds. In this case, the summer length shows a breakpoint, suggesting a non-uniform trend, and periods similar to those known for ENSO 15


Specular meteor radars
SMRs detect meteor trails between mostly 75 and 110 km altitude, measuring their position in space and radial velocity to derive the mean background winds (e.g. Hocking et al., 2001). To generate a homogeneous time series without gaps, we use a combination of detections from two closely located SMRs, using quasi-simultaneous detections binned in the same way as 85 a single radar mode does to obtain the hourly winds (for details see Chau et al., 2017). This combination helps us to reduce the observation gaps for the high-and mid-latitude regions we have selected. At mid-latitudes (ML) we combine two SMRs located in Germany, specifically Juliusruh (54.6 • N, 13.4 • E) and Collm (51.3 • N, 13.0 • E) (e.g. Hoffmann et al., 2010;Jacobi et al., 2015). At high-latitudes (HL) we use two SMRs in northern Norway: Andenes (69.3 • N, 16.0 • E) and Tromsø (69.6 • N,19.2 • E) (e.g. Singer et al., 2004;Hall et al., 2005). The covered years at mid-and high-latitudes are 2005-2020 and 2004-2020, 90 respectively.
Given the inherent variability within the radar measurements the wind dataset of 1 h resolution was first smoothed by a 16day-width sliding window. The smoothing suppresses short term fluctuations, which are caused by e.g. gravity waves and tides as well as instrumental effects, which are not within the focus of this study. For this long-term study dealing with a length of up to 31 years, the principal components analysis (PCA, Jolliffe and Jackson, 1993;Jolliffe, 2002) proofed to be a useful tool to compress the data. At each station and for each year, the zonal wind between DOY 100-280 and 82-98 km in the time-altitude depiction is arranged into a 2-dimensional matrix and decomposed as a linear combination of principal components. The first two principal components capture 97.6-99.5% of the total variance and are used to reconstruct the 2-dimensional matrix used for this study and effectively reducing its short-term variability. The principal components representing the dataset are planned to be investigated in more detail in respect of their temporal evolution in a subsequent study.

Partial reflection radars
PRRs use the mechanism of partial reflection through the ionized component in the atmosphere as a tracer for the neutral motions in the MLT between 50 and 100 km altitude, depending on the instrument configuration and by means of the solar and geomagnetic conditions (see e.g. Fukao and Hamazu, 2014;Reid, 2015). The Saura PRR, located in Andøya (69.1 • N, 16.0 • E), has been in operation since 2004 (e.g. Singer et al., 2005;Renkwitz and Latteck, 2017). For the mid-latitudes, we use 105 measurements from Juliusruh PRR (54.6 • N, 13.4 • E) that were obtained between 2004 and 2020 with a comparable system and method (e.g. Hoffmann et al., 2010). To complement our work, we also include data from the Juliusruh PPR predecessor system, using a different configuration and technique between 1990 and 2003. More details on this dataset can be found in Keuer et al. (2007).
Equivalently to the descriptions given for the SMR data, we implemented a 16-day sliding window and the PCA capturing

Microwave limb sounder
Onboard the Aura EOS satellite is the microwave limb sounder (MLS) instrument, sensing atmospheric temperatures from the troposphere up to 90 km (e.g. Waters et al., 2006;Livesey et al., 2015). From these measurements one can calculate the zonal 115 mean geostrophic zonal winds and geopotential heights (e.g. Yamazaki and Matthias, 2019). In this work, we use MLS zonal mean zonal winds at mid and high-latitudes between 2005 and 2020. It is important to consider that the zonal mean geostrophic zonal wind is a longitude average, while the radars are located at a specific longitude. These time series are extracted with a 16-day sliding window at 74 km (55 • N) and at 82 km (70 • N).
3 MLT mean zonal wind climatologies and summer length definitions 120 A mean zonal wind climatology for both latitudes and combination of stations is shown in Fig. 1. The high-latitudes climatology ( Fig. 1a) is generated from the combination of Andenes and Tromsø SMRs above 81 km and below from Saura PRR. An equivalent approach is used for the mid-latitudes (Fig. 1b), where between 81 and 100 km observations from Juliusruh and Collm SMRs are used and for altitudes below 81km 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. Hoffmann et al., until mid-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 mid-September, around one week before the autumnal equinox. The dynamics of the mean zonal wind displays a clear dependence of altitude with respect to latitude (e.g. Laskar et al., 2017;Conte et al., 2018;Wilhelm et al., 2019). Given this latitudinal dependence, we adjust the selected altitudes in the summer length definitions (described below) accordingly.  line). At middle latitude, the MLT-SB altitude is the same as in high-latitudes (i.e., 96 km), but the MLT-SE was chosen at 74 km, using PRR data (see the combination of the red and green lines in Fig. 2). In both definitions, the summer length is the difference between the SE and SB.

Mesosphere -Summer Length
The M-SL is selected at the same altitude varying only by latitude. The summer beginning and summer ending are considered 150 when the final MZWR occurs from east to west, and later from west to east direction, for high-latitudes at 82 km and for mid-latitudes at 74 km (see Fig. 2, orange and green lines, respectively). The same altitudes are taken for MLS (see 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-day running window, shifted by one day. 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 160 PCA (see details in Sect. 2). With the first two components of PCA, 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) in which the reversal occurs. Following this analysis, we obtain three different time-series for each latitude and definition (SB, SE, and SL=SE-SB). 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 MZWR is particularly difficult to assess due to an unclear transition. In these cases, the sum of days during 165 the unclear reversal period is divided by two and manually implemented as an error for the particular value. when the MZWR occurs for every year (abscisa) for SB, SE and SL, respectively.

170
To explore the long-term behavior, we fit a linear function and apply the Student's t-test (with null hypothesis being slope equal to zero) to investigate if there is a significant slope incorporating the standard deviation error propagation (e.g. Santer et al., 2000). 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 SE for both definitions, the linear regression is not shown since we were not able to reject the null hypothesis.

175
The M-SL ( Fig. 3g) for the high-latitudes is found to be 170 ± 11 days long using PRR measurements (173 ± 12 days for MLS) with a tendency of 0.46 ± 0.52 days per year (1.23 ± 0.62 days for MLS). Most of the variability and trend is introduced by the SB (Fig. 3a)  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 is indicated by the symbol bow tide. In pink are shown the sPJOs.
The mid-latitude results are shown in Fig. 4 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. 4g)   mostly corresponds to the SB (Fig. 4a) occurring at DOY 95±5 days for PRR and DOY 97±7 days for MLS (between 5 and 7 April) with a tendency of −0.49 ± 0.25 days and −0.72 ± 0.32 days, respectively. For the MLT-SL (Fig. 4c) we found 141 ± 4 days, but again with no significant trend, starting on 29 April.
The mean values, with the standard deviations from Fig. 3 and 4 are summarized in Table 1, as well as the slopes for the summer beginning and summer length with their standard deviations. The slope are colored from the result of the Student's-t 195 test, as follows. The slopes with less than 80% of confidence are red, more than 90% is green and greater than 95% are blue.
As mentioned previously, in the case of mid-latitudes one can extend the study of the M-SL using the Juliusruh PPR to 31 years, by combining zonal winds obtained at the same place but with different MF radar systems and measuring techniques.

Discussion
In this section we discuss the obtained result. Noteworthy, for both latitudes and definitions, the variability of the summer lengths are dominated by the summer beginning and thus, by the winter conditions. Since our results display a latitudinal 205 dependency, we also divided our discussion by latitude. In addition, we discuss the results of our summer definitions in respect to other definitions used in earlier studies. The long-term behavior of our results, including the 31-year analysis, is discussed separately.

High-latitudes
As both definitions represent different processes from the different altitudes (in the summer beginning) and therefore times in  (∼ 6K below the mean) and a higher concentration of water vapor at 83 km. In their study, they found strongly enhanced planetary wave activity uncommon for the time of the year (see Fiedler et al., 2015, Fig. 5).
A similar period has been recently studied in the MLT northern hemisphere high-latitude by Hall and Tsutsumi (2020). In the time series we were not able to find a relation to Lyman−α. In the case of ENSO and QBO, we also do not find a clear connection with the MZWR dates. A similar result is obtained analyzing the MSSW, sPJO years and the SB time series.
We can only find two particular clear cases where the SB is affected by a final warming.

Mid-latitudes
As we move far away from the polar vortex and approach the mid-latitudes, the summer beginning displays less variability than at high-latitudes and there is a clear time-latitude difference in the time series (also indicated in Fig. 2). The MZWR occurs earlier at high-latitudes and later on at mid-latitudes. Towards the end of the summer, the westward wind velocity decreases and finally reverses again to eastward direction at mid-latitudes and later on at higher latitudes. Thus, the summer length 240 difference is dependent on the latitude, as a consequence on the residual mesospheric wind circulation (e.g., Andrews et al., 1987;Hoffmann et al., 2002). The MZWR for both latitudes exhibit a comparable profile, while the MZWR at high latitudes occurs at about 5 km higher altitudes (see Fig. 1 and Fig. 2). Thus, for the use of the same upper altitude (96 km), the MZWR occurs earlier in mid-latitudes. Furthermore small differences in the profile steepness are visible, i.e. the wind reversal doesn't occur simultaneously at several altitudes. However near and especially above 100 km altitude the meteor count rates decrease 245 substantially, introducing larger uncertainties, which restrain us from selecting a higher altitude (e.g. Younger et al., 2009), where we exactly want to observe the MZWR and MLT-SB.
Looking into the unusual years seen at high-latitudes, the reversal during 2012 (Fig. 4.a) occurs on the DOY=116, representing an earlier start but within the variability. However, the reversal occurs in the same day at both latitudes, raising the question to what kind of event might produce a reversal of the wind in the same day at 15 degrees latitude difference. The

Comparisons to other definitions
Comparing the definitions proposed in this work with the one made by Offermann et al. (2004), we can find a big difference for the summer end. While Offermann et al. (2010) showed opposite sign slopes retrieved from a threshold in temperature in the beginning and end, we have found a variability dependence on the summer beginning. This difference is attributed to the 260 rapid wind changes in September, meanwhile the temperature appears to change with a weaker gradient. The summer duration obtained in their works is comparable with the values obtained for M-SL at mid-latitudes, with a difference of around ten days.
Inspired by the comparison between the summer duration in the MLT and that at ground level made by Offermann et al.

Long-term analysis
A linear regression was implemented for all the time series and the result proved with a Student's t-test. Since, in all the summer ending times series we were not able to reject the null hypothesis, we only show the significance levels for the summer beginnings and summer lengths. However, the MLT-SL definition shows no significant linear change over the years and thus, we consider this definition is not sensible to a possible long-term change. On the other hand, the M-SL and M-SB shows linear 280 tendencies with confidence greater than 95% in most of the cases. The only exception is in M-SL at high-latitudes (Saura PRR), where the slope shows a confidence greater than 90% (see Table 1). In none of the time series, we applied a correction by QBO or solar activity as they were used in others works (e.g. Offermann et al., 2010;Keuer et al., 2007). In the case of QBO, the influence is not clear or seen in the MZWR dates, probably due to the short time series. Pursuing this concept, we extended M-SL at mid-latitudes with the available data, obtaining a 31-year time series (see Fig. 5a). The summer beginning With the obtained time series, we analyzed the summer length, 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 310 summer length. Furthermore, we compared the summer length to the ground level growing season. The results are summarized as follows: -The summer length is determined by the MZWR, which depends on the actual latitude and altitude. High-latitudes showed more variability than mid-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 315 equinox and presents no significant linear trend.
-MLT-SL definition: the summer starts around 7 May at high-latitudes (SL=136 days) and around 29 April at midlatitudes (SL=141 days), showing a shorter summer length at high-latitudes. This definition presents no significant trends