The ionosphere is an important part of the near-Earth space environment, and the mesosphere is the coldest region in the Earth's atmosphere. Polar mesosphere summer echoes (PMSEs) are strong echoes detected by radars from medium-frequency (MF) to ultra-high-frequency (UHF) bands in the polar summer mesopause, and PMSEs have been considered to be possible indicators of global climate change (Thomas and Olivero, 2001). The observation range is from 75 to 100 km, where the strongest echo occurs at the altitude of about 86 km on average (Czechowsky et al., 1979). Radar waves in the very-high-frequency (VHF) band are backscattered due to the irregularities of electron density with spatial scales of about half the wavelength of the radar. This has been confirmed by Blix et al. (2003) from simultaneous rocket and radar observations. The most extensively accepted theory is that the irregularities of electron density are sustained due to the reduction in electron diffusion characterized by the slowest ambipolar diffusion mode associated with the charged ice grains (Cho et al., 1992). Varney et al. (2011) scrutinized one particular aspect of the turbulent theory of PMSEs: the electron density dependence of the echo strength. One remarkable feature of all PMSEs is the fact that the radar echoes often occur in the form of two or more distinct layers which can persist for periods of up to several hours. Until now, the layering mechanism leading to these multiple structures has only been poorly understood in spite of some previous attempts involving gravity waves, the general thermal structure, and Kelvin–Helmholtz instabilities (Röttger, 1994; Klostermeyer, 1997; Hill et al., 1999; Hoffmann, 2005).

Palmer et al. (1996) statistically analyzed the PMSEs in the Northern Hemisphere observed by the EISCAT VHF radar during 1988–1993. They suggested that (1) PMSEs are summer phenomena, lasting from June to August; (2) PMSEs occur mostly around noon and midnight, following a semidiurnal pattern; and (3) the echoing structures move bodily, perhaps in response to gravity waves. Based on measurements at Andenes, Norway, observed by the 53.5 MHz ALOMAR SOUSY radar during 1994–1997 and the ALWIN radar during 1999–2001, Bremer et al. (2003) found that the variation of PMSEs is markedly controlled by solar cycle variations and precipitating high energetic particle fluxes. Bremer et al. (2006) discussed how the strength of PMSEs depends on the level of ionization because of the long-term changes in mesospheric summer echoes caused by the incident solar wave radiation and precipitating high energetic particle fluxes from about 20 May to the end of August during 1998–2006. Smirnova et al. (2010) used the ESRAD MST (Esrange Mesosphere–Stratosphere–Troposphere) radar's measurements and found that the inter-annual variations of the PMSE OR (occurrence ratio) and length of the season anticorrelated with solar activity (F10.7 index, the daily solar activity proxy) but not significantly, and that the PMSE OR correlates with geomagnetic activity (AP index). However, no statistically significant trends in PMSE yearly strengths were found in their work. Smirnova et al. (2011) concentrated on the accurate calculation of PMSE absolute strength as expressed by radar volume reflectivity and found that the inter-annual variations of PMSE volume reflectivity strongly correlate with the local geomagnetic K index and anticorrelate with solar 10.7 cm flux. However, they did not find any statistically significant trend in PMSE volume reflectivity during 1997–2009. Li and Rapp (2011) reported that the PMSE OR at 224 MHz shows a positive correlation with both the solar and geomagnetic activities. PMSEs have been detected and widely studied based on long-term observations of many different MST radars (Reid et al., 1989; Thomas et al., 1992; Smirnova et al., 2011). Since the first observation of PMSEs in 1979, it has been well known that the PMSE observations are different when observed by different-frequency radar even at the same sites, and PMSEs often show obvious layered events.

Many studies have widely reported that there is a significant correlation between the ionization level and PMSEs observed by 53.5 MHz radar (Inhester et al., 1990; Belova et al., 2007; Latteck et al., 2008). The correlation of the ionization level with PMSEs at 224 MHz is as significant as that of the correlation of the ionization level with PMSEs at 53.5 MHz; previous studies provide the research basis and ideas for the PMSE study detected by 224 MHz radar. There are still a few significant problems that must be solved with the characteristics of the layered PMSE OR. Hence, it is necessary to analyze the layered PMSE OR and study layered PMSE characteristics deeply with data measured by 224 MHz EISCAT VHF radar under different observation conditions. The statistical results of the layered PMSE OR with the same radar at the same site over the period 2004–2015 are given in this paper, which was based on the experimental data detected by 224 MHz EISCAT VHF radar. In addition, the correlation of the PMSE OR with the geomagnetic K index and F10.7 is analyzed and discussed. The method of the correlation analysis between the layered PMSE OR and solar activity and between the layered PMSE OR and geomagnetic activity is given in this paper without being affected by the defect of discontinuous PMSE measurements of EISCAT radar. It is helpful for describing the characterization of the layered PMSE OR. The aim of the current work is to provide a definitive data foundation for further analysis of layered PMSEs, and we try to identify important open issues for future investigations.

The PMSE observations used here were obtained with 224 MHz EISCAT VHF radar from 2004 to 2015. The EISCAT VHF radar is located at Tromsø, Norway (69.35∘ N, 19.14∘ E), using a parabolic cylindrical 120 m × 40 m antenna. It is a powerful tool to study the lower ionosphere. Detailed descriptions of the radar can be found in Baron (1986). The measurements by EISCAT radar are very well suited for investigating the characteristics of PMSEs (for previous work, see, e.g., Li et al., 2010, and references therein). It has frequency and phase modulation capability with a pulse length of 1 µs to 2 ms. The parameters are shown in Table 1 for accuracy control of EISCAT VHF radar.

EISCAT VHF radar ran several standard experimental modes: manda, beata, bella, tau7, arcd (arc_dlayer), and tau1. The main differences between these experimental modes are illustrated in Table 2. The manda and arcd modes are mainly used for low-altitude detection and provide spectral measurements at mesospheric altitude. Therefore, the accurate data used in this study are mainly provided by manda and arcd modes.

In this study, we use the EISCAT VHF radar data from 2004 to 2015. The GUISDAP software package (Grand Unified Incoherent Scatter Design and Analysis Program) (see Lehtinen and Huuskonen, 1996, and visit http://www.eiscat.se, last access: 27 May 2019, for details) was used to analyze the radar data. The electron density Ne analyzed by the GUISDAP software was obtained between 106 and 1014 m-3. The level of electron density represents the intensity of echoes.

First of all, the heating parts were removed from the data set to avoid the heating effect. After that, the presence of PMSEs was defined as the threshold of electron density (Ne>2.6×1011 m-3). We have used the PMSE threshold given by Hocking and Röttger (1997) and Appendix A Table A2 of Li and Rapp (2011). In addition, some abnormal echoes are related to meteors. It is not considered to be a PMSE and is neglected in later discussion. PMSEs are not continuous in time. If the electron density satisfies the threshold (Ne>2.6×1011 m-3), we considered it to be a PMSE event. We have considered only those events whose PMSEs are continuous for time (t≥1 min).

The layered PMSE OR was calculated and the relations among PMSE mono-, double-, and tri-layer ORs were analyzed statistically. At the same time, the mean seasonal variations of the layered PMSE OR and PMSE total OR have been presented. Hoffmann (2005) shows that the layering occurs because of subsequent nucleation cycles of ice particles in the uppermost (and coldest) gravity-wave-induced temperature minimum (see Hoffmann, 2005, Fig. 3a). Subsequently, these newly created ice particles grow and sediment down and lead to the distinct layering. In addition, Rapp and Lübken (2004) found that charged ice particles and atmospheric turbulence play major roles in the change in the electron number density that leads to PMSEs in the mesopause region. We know that solar and geomagnetic activities have a certain degree of influence on the occurrence of PMSEs; however, the effects of solar and geomagnetic activities on layered PMSEs are not understood well. Therefore, it is necessary to study the effects of solar and geomagnetic activities on layered PMSEs. The occurrence ratio obtained by the ratio of the occurrence time of PMSEs to the total observation time is the calculation method in the traditional sense. It is easy to understand and accurately analyze the short-term variations, such as diurnal variation and seasonal variation of PMSEs. However, the long-term trend is subject to error and dispute by this calculation method. Furthermore, it is difficult to discuss and analyze the correlation of the layered PMSE OR with solar and geomagnetic activities. Therefore, we have presented a new calculation method for calculating the layered PMSE occurrence ratio, which is different from the method given in Sect. 4.2, so that the layered PMSE OR is relatively accurate. The correlation of PMSEs with solar and geomagnetic activities is not expected to be affected by discontinuous PMSEs. The study of relations between PMSEs and solar activities and between PMSEs and geomagnetic activities is significant.

In this paper, the PMSE occurrence ratios with monolayers, double layers and tri layers detected by EISCAT VHF radar during a solar cycle have been presented. The daily and seasonal variation of the layered PMSEs was analyzed. We implemented a method to provide more accurate conclusions about the study of the long-term variation of PMSEs with different thresholds. The correlation between layered PMSEs and solar radiation flux (F10.7) and between layered PMSEs and geomagnetic activity (K index) was given. The following conclusions were reached.

Mono-, double-, and tri-layer PMSEs have different seasonal behaviors. Monolayer PMSEs often begin in late May, reach their maximum in early June or mid-June, keep this level until the end of July or beginning of August, and gradually decrease or vanish when they are close to the end of August or the beginning of September in general, which is in agreement with the earlier report (Smirnova et al., 2011). The double-layer PMSE OR reaches its maximum in mid-July and simply fades away in early August. The tri-layer PMSE appears later and disappears earlier in comparison with mono- and double-layer PMSEs, and it is large at the end of June and in early July.