Characteristics of layered occurrence ratio of polar mesosphere summer echoes observed by EISCAT VHF 224 MHz Radar

Polar Mesosphere Summer Echoes (PMSE) are strong radar echoes observed in polar mesopause during local summer. Measurements of layered PMSE observed by the European Incoherent Scatter Scientific Association Very high frequency (EISCAT VHF) radar from 2004 to 2015 in the latest solar cycle, can be used to study the variations of PMSE occurrence ratio (OR). The seasonal variation 15 of PMSE mono-, doubleand tri-layer occurrence ratio was analyzed, and there is different seasonal behavior. A method was given to calculate the PMSE mono-, doubleand tri-layer occurrence ratio under different electron density threshold conditions. In addition, the correlation between PMSE layered occurrence ratios and solar 10.7 cm flux index (F10.7), and the correlation between PMSE layered occurrence ratios and geomagnetic K index were analyzed respectively in this study. It can be obtained 20 that PMSE mono-, doubleand tri-layer OR are positively correlated with the K index. The correlation coefficient between PMSE monoand double-layer OR and F10.7 is weak, and the PMSE tri-layer OR has a negative correlation with F10.7.


Introduction
The ionosphere is an important part of near the earth space environment and the mesosphere is the coldest region in the earth's atmosphere at local summer time.Polar Mesosphere Summer Echoes (PMSE) are strong echoes detected by radars from medium frequency (MF) to ultra-high frequency (UHF) bands in pattern; (3) the echoing structures move bodily, perhaps in response to gravity waves.Bremer et al. (2003) derived that the variation of PMSE is markedly controlled by solar cycle variations and precipitating high energetic particle fluxes based on measurements at 53.5 MHz in Andenes, Norway, with the ALOMAR SOUSY radar during 1994-1997and with the ALWIN radar during 1999-2001. Bremer et al. (2006) discussed that the strength of PMSE depends on the level of ionization because of the long-term changes 20 of 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); Yi et al.(2017) found that inter-annual variations of PMSE OR (occurrence ratio) and length of the season anticorrelate with solar activity represented by the solar 10.7 cm radio flux, and correlate with geomagnetic activity represented by AP index based on ESRAD MST radar measurements in Kiruna,

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Sweden.Nevertheless, no statistically significant trends in PMSE occurrence ratio or in the length of the PMSE season were found in the paper.Smirnova et al. (2011) concentrated on the accurate calculation of PMSE absolute strength as expressed by radar volume reflectivity and found that inter-annual variations of PMSE volume reflectivity strongly correlate with the local geomagnetic K-index and Ann.Geophys.Discuss., https://doi.org/10.5194/angeo-2019-13Manuscript under review for journal Ann.Geophys.Discussion started: 28 January 2019 c Author(s) 2019.CC BY 4.0 License.
anticorrelate with solar 10.7 cm flux but did not find any statistically significant trend in PMSE volume reflectivity during 1997-2009.Li and Rapp (2011) reported that the correlations of the occurrence ratio of PMSE at 224 MHz with the solar and geomagnetic activities both show positive correlations.PMSE have been detected and widely studied based on long-term observations of many different MST radars (Reid et al., 2013;Thomas et al., 1992;Smirnova et al., 2011) (Reid et al. 1989;Thomas et al. 1992;5 and Smirnova et al. 2011), since the first observation of PMSE in 1979, it is well-known that the observation results are different when PMSE are observed by different frequency radar even in the same sites, and PMSE often show obvious layered events.
Previous study by 53.5MHz radar has provided the basic characteristics, the short-term statistical variations of PMSE and the relation among the PMSE, solar activity and geomagnetic activity detected.

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The correlation of PMSE at 224 MHz to the ionization level, however, is as significant as that of PMSE at 53.5 MHz to the ionization level, then it provides the basis and ideas for the research of 224MHz radar.
There are still a few significant problems that must be solved with the characteristics of layered PMSE OR.Hence, it is necessary to analyze the PMSE layered OR and study layered PMSE characters deeply with data measured by 224 MHz EISCAT VHF radar under different observation conditions.The 15 statistical results of PMSE layered OR with the same radar at the same site over the period [2004][2005][2006][2007][2008][2009][2010][2011][2012][2013][2014][2015] are given in this paper, which was based on the experiment data detected by 224 MHz EISCAT VHF radar.In addition, the relationships of PMSE OR, geomagnetic K index and F10.7 are analyzed and discussed.The PMSE OR calculation method given in this paper solves the defect that the measurements of EISCAT radar is discontinuous, which makes a significant breakthrough in the calculation and 20 characterization of the PMSE layered OR detected by EISCAT radar and the results could provide definitive data foundation for further analysis and the investigation of the physical mechanism of PMSE.

radar and experiment data
The experiment data of PMSE was obtained by 224MHz EISCAT VHF radar from 2004 to 2015.The radar is located at Tromsø,Norway (69.35°N,19.14°E),and a cylindrical 120m×46m antenna, with 25 beam-widths of 1.8° north-south and 0.6° east-west was used on it.It has frequency and phase modulation capability with pulse length of 1 s  to 2 ms .Furthermore, reliable information of the raw electron density about PMSE, which is not derived by analysis of the incoherent scatter spectrum, but power profiles or near-zero-lag data can be obtained by EISCAT radar, and the level of electron density represents the intensity of echoes.The parameters described in Table 1for accuracy control of EISCAT VHF radar.
EISCAT VHF radar ran several standard experiment modes: "manda, beata, bella, tau7, arcd (arc_dlayer) and tau1".The main differences between the arcd and manda modes are illustrated in Table 2.The manda and arcd modes main used for low altitude detection, and provide spectral measurements at mesospheric altitude.Therefore, the data used in this study is mainly given by manda and arcd modes.
The Grand Unified Incoherent Scatter Design and Analysis Program (GUISDAP) software package have been used for analyzing the EISCAT VHF radar data.The electron density   analyzed by GUISDAP software is obtained between 10 6 and 10 14 m -3 .
.  and c) show the typical events of PMSE monolayer, double-layer and tri-layer, respectively.One remarkable feature of all PMSE is the fact that the radar echoes often occur in the form of two or more 5 distinct layers that can persist for periods of up to several hours.Until now, the layering-mechanism leading to these multiple structures is not well understood.Here we are studying the occurrence of these multiple layer events and its relationship with solar and geomagnetic activity.This content will be discussed in detail later in the article.

Calculation method
To find the characteristic of PMSE occurrence ratio (OR), a computing method and threshold must be defined.First of all, the data during radar heating experiments has been eliminated.After that, the number of data points satisfying the threshold of electron density (Ne >2.6×10 11 m -3 ) was calculated (Hocking and Röttger ,1997).PMSE is not continuous in time, so if the number of data points satisfying the electron 5 density threshold of PMSE were less than 8 data points in any time interval, these data points were replaced with the average of electron density (Ne) of 80-90 km regardless of the threshold (Rauf et al., 2018).It maintained the original electron density values at the corresponding time, so that the correlation is not influenced.The correlation coefficients have been calculated between PMSE OR and the 10.7cm of the solar flux index (F10.7),PMSE OR and geomagnetic events K indices, respectively.Because we 10 chose the integration time of manda and arcd models are 4.8s and 2s respectively, on the basis of the condition (t≥1 min), the PMSE is needed to be simultaneous for≥12 and 30 data points, respectively.
What's more, some abnormal echoes are related to the precipitation particle areas are not considered to be PMSE and is neglected in later discussion.
The emphasis of this paper is to present a hybrid algorithm based on grid partitioning.The calculation 15 method is based on time.Taking the calculation method of PMSE monolayer occurrence ratio as an example, the electron density detected by the EISCAT VHF radar are counted, and the electron density with the value larger than the threshold in this time period are taken out, and the ratio between the number of electron densities values during the monolayer PMSE sustained time and the number of electron densities values during total observation time is obtained.At different heights, when an electron density 20 value greater than the threshold and less than the threshold is continuously alternate observed in an observation region with altitude range from 3-4km, we believe that double-layer or multi-layer PMSE events occur.The PMSE double-layer OR is the ratio between the sustained time of PMSE double layer and the total observation time.The tri-layer OR is also calculated in this way.

The variations of PMSE layered occurrence ratios 25
For studying the PMSE layered OR, PMSE layered occurrence time (OT) and total observing time detected by EISCAT VHF radar from 2004 to 2015 were illustrated in Table 3. PMSE mono-doubletri-layer and total OR were presented in

Discussion
We have calculated the PMSE layered OR and the relations among PMSE mono-, double-and triplelayer OR were analyzed statistically.At the same time, the mean seasonal variations of the layered PMSE OR and PMSE total OR were given.It is now generally accepted that both charged ice particles and atmospheric turbulence play major roles in the change of the electron number density that lead to PMSE 5 in the mesopause region (Rapp and Lübken, 2004).We know that solar and geomagnetic activities have a certain degree of influence on the occurrence of PMSE, but the effects of solar and geomagnetic activities on layered PMSE are not clear.Therefore, it is necessary to study the effects of solar and geomagnetic activities on layered PMSE.The occurrence ratio obtained by the ratio of the occurrence time of PMSE to the total observation time is the calculation method in the traditional sense.It is easy to 10 understand and accurately analyze the short-term variations, such as diurnal variation and seasonal variation of PMSE.However, the long-term trend is inaccurate by this calculation method, because the radar measurement data is not continuous.And it is difficult to discuss and analyze the relations between PMSE and solar activities and between PMSE and geomagnetic activities.Therefore, we have designed a new calculation method for calculating the PMSE layered occurrence ratio, which is based on the height.
15 so that the occurrence of PMSE becomes continuous, and the long-term variations of PMSE becomes easy and relatively accurate.The relations between PMSE and solar activities and between PMSE and geomagnetic activities can be studied.

Calculation method
The calculation method is based on altitude.A large number of literatures and experimental observations 20 shown that the altitude range of PMSE is 80-90km (Li and Rapp, 2011;Smirnova et al., 2010;Latteck and Bremer, 2013).Among all the altitude and electron density observed by EISCAT VHF radar, we only take the apparent electron density in the altitude range of 80-90km, and then take out the electron density greater than the threshold in the period when the PMSE is known to be present.The ratio between the numbers of layered PMSE electron densities values greater than the threshold and the numbers of total 25 electron density in the range of 80-90 km was calculated respectively.The double-layer and tri-layer PMSE OR obtained by this method have a higher occurrence ratio than the first method.the results are shown in Fig. 5, 6, and 7.That is, Fig. 5, Fig. 6 and Fig. 7 show PMSE mono-double-and tri-layer OR under different electron density threshold conditions, respectively.In the calculation method 5 section we said that we defined the electron density threshold (Ne>2.6×10 11m -3 ).Here, we give the PMSE layered OR with threshold conditions of Ne >1×10 11 m -3 , Ne >1.5×10 11 m -3 , Ne >2.6×10 11 m -3 , Ne >3 × 10 11 m -3 and Ne >3.5 × 10 11 m -3 ,respectively.We can get their variation trends to be largely consistent, in addition, the larger the threshold, the smaller the ratio.Since these occurrence ratios are calculated in the case where the occurrence of PMSE is determined, there is no case of missing data, and it can be recognized that these occurrence rates are reliable.The legends on the figure is the average of PMSE mono-, double-and triple-layer OR with threshold conditions of Ne >1×10 11 m -3 , Ne >1.5×10 11 m - 3 , Ne>2.6×10 11 m -3 , Ne >3×10 11 m -3 and Ne>3.5×10 11 m -3 during the periods of 2004-2006, 2007-2011 and 2012-2015.It is well known that 2006 is solar minimum and 2012 is solar maximum, but the PMSE mono-and double-layer average OR is not consistent with solar activity.In other words, there has no 15 correlation between PMSE mono-and double-layer OR and solar activity.What's more, we found that PMSE triple-layer OR and solar activity in opposite directions.To prove the conclusion, we will calculate the correlation coefficient between PMSE layered OR and solar activity and between PMSE layered OR and geomagnetic activity in next section.Therefore, the relation between them can be judged directly.

Correlation coefficients
A correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables (Boddy and Smith, 2009).The Pearson correlation coefficient known as Pearson's r, is a measure of the strength and direction of the linear relationship between two variables that is defined as the covariance of the variables divided by the product of their standard deviations.This Spearman's rank correlation coefficient is a measure of how well the relationship between two variables can be described by a monotonic function.The Spearman correlation between two variables is equal to the Pearson correlation between the rank values of those two variables.While Pearson's correlation 20 assesses linear relationships, Spearman's correlation assesses monotonic relationships (whether linear or not) (Well and Myers, 2003).For a sample of size n, the n raw scores Xi, Yi are converted to ranks rgXi, rgYi, and rs is computed from:  the enhanced solar activity increases the electron density due to the increase of ionization, and with the increase of solar radiation, the photodissociation enhance and the water vapor content is reduced.On the other hand, the positive correlation between PMSE OR and K index may be apprehensible as because of the enhanced magnetic activity caused precipitating particles increase in the mesosphere, and lead to increase in electron densities.But I still can't explain why there is a negative correlation between tri-layer 10 PMSE OR and F10.7, or this may be our future research focus.

Conclusions
In the paper, we presented PMSE occurrence ratios with monolayer, double-and triple-layers that were detected by EISCAT VHF radar during a solar cycle.It was obtained that the daily variation and seasonal variation of the layered PMSE.We implemented a new method to provide more accurate conclusions on the study of the long-term variation of PMSE with different thresholds.Then the relationship between layered PMSE and solar radiation flux (F10.7) and between layered PMSE and geomagnetic activity (K index) were given.The following conclusions were reached: (1) Mono-, double-and tri-layer PMSE have different seasonal behavior.Monolayer PMSE events often begins in late May, reaches its maximum in early June or mid-June, keeps this level until the end 20 of July or beginning of August, and gradually decreases or vanishes when it is close to the end of August or the beginning of September in general, which was in agreement with references (Smirnova et al., 2011).The double-layer PMSE reaches its maximum appears in mid-July and simply fade away in early August.The triple-layer PMSE appears later and disappears earlier in comparison to mono-, doublelayer PMSE, and it is large in end of June and early July.

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(2) The variation trends of PMSE mono-double-and tri-layer OR under different electron density threshold conditions are largely consistent.It was got that the larger the threshold, the smaller the ratio.Beyond that, PMSE mono-and double-layer OR were not associated with solar activity.and PMSE triple-layer OR is inversely proportional to solar activity.
(3) PMSE layered OR is positively correlated with the K index.The correlation between PMSE monoand double-layer OR and F10.7 is relatively weak, and PMSE tri-layer OR has a negative correlation with F10.7.

Fig. 1
Fig. 1 The typical layered PMSE events observed by EISCAT 224MHz VHF radar.a) The observation on 19 July, 2007 (Upper panel); b) The observation on 9 July, 2005 (Middle panel); c) The observation on 7 July, 2004 (lower panel).The red circle marks the obvious layered phenomenon of PMSE events.

Fig. 2
Fig. 2 PMSE layered occurrence ratio.The OR of total (red dot line).The OR of monolayer (black solid 5

Fig. 2 10 3. 3
Fig.2shows that the mono-double-and triple-layer OR agrees with the total PMSE OR.We calculated the Spearman rank correlation coefficients between mono-layer OR and double-layer OR, mono-layer OR and tri-layer OR, mono-layer OR and Total OR, respectively.The correlation coefficients (rs) are 10

5 Fig. 5
Fig. 5 PMSE monolayer occurrence ratio under different electron density threshold conditions.Vertical is a measure of the solar radio flux per unit frequency at a wavelength of 10.7 cm, near the peak of the observed solar radio emission.F10.7 is often expressed in SFU or solar flux units (1 25 SFU = 10 −22 W•m −2 • Hz −1 ).It represents a measure of diffuse, nonradiative coronal plasma heating.It is an excellent indicator of overall solar activity levels and correlates well with solar UV emissions.The Kindex quantifies disturbances in the horizontal component of earth's magnetic field with an integer in the Ann.Geophys.Discuss., https://doi.org/10.5194/angeo-2019-13Manuscript under review for journal Ann.Geophys.Discussion started: 28 January 2019 c Author(s) 2019.CC BY 4.0 License.range 0-9 with 1 being calm and 5 or more indicating a geomagnetic storm.It is derived from the maximum fluctuations of horizontal components observed on a magnetometer during a three-hour interval.The K-index was introduced by Julius Bartels in 1938(Bartels et al., 1939).The K index values used in the paper is the median of the K index observed on a magnetometer during a day, which has removed the effects of the heating experiment.

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the best known and most commonly used type of correlation coefficient.Pearson's correlation coefficient Given a pair of random variables (X, Y), the formula for r is (Wilks, 1995Cov is the covariance.15 σX is the standard deviation of X σY is the standard deviation of Y.

Fig. 9
Fig. 8 (a) The variations of F10.7 values corresponding to the occurrence of PMSE.Upper panel: F10.7 values corresponding to the occurrence of mono-layer PMSE; Middle panel: F10.7 values corresponding to the occurrence of double-layer PMSE; lower panel: F10.7 values corresponding to the occurrence of triplelayer PMSE.(b) The variations of geomagnetic K index values corresponding to the occurrence of PMWE.Upper panel: K index values corresponding to the occurrence of mono-layer PMSE; Middle panel: K index

Table 1
Parameters of the radars. 3

Layered PMSE Occurrence ratios PMSE
occur in thin layers having thickness up to 3-4 kilometers, and the mean altitude distribution of PMSE events is 80-90km.It is considered to be the area of independent abnormal echoes.

Table 3
Statistical data from 2004 to 2015.