Solar 27-day signatures in standard phase height measurements above central Europe

We report on the effect of solar variability at the 27-day and the 11-year time scale on standard phase height measurements carried out in central Europe. Standard phase height corresponds to the reflection height of radio waves in the ionosphere near 80 km altitude. Using the superposed epoch analysis (SEA) method, we extract statistically highly significant solar 27-day signatures in standard phase heights. The 27-day signatures are roughly anti-correlated to solar proxies, such as 5 the F10.7 cm radio flux or the Lyman-α flux. The sensitivity of standard phase height change to solar forcing at the 27-day time scale is found to be in good agreement with the sensitivity for the 11-year solar cycle, suggesting similar underlying mechanisms. The amplitude of the 27-day signature in standard phase height is larger during solar minimum than during solar maximum, indicating that the signature is not only driven by photo-ionisation of NO. We identified statistical evidence for an 10 influence of ultra-long planetary waves on the quasi 27-day signature of standard phase height in winters of solar minimum periods.


Introduction
The electromagnetic radiation emitted by the sun exhibits variability over a large range of different temporal scales.At time scales shorter than a century the most important solar variability cycles 15 are the 11-year Schwabe-cycle (Schwabe, 1843) -being part of the 22-year Hale-cycle (Hale et al., 1919) -as well as the quasi 27-day solar cycle, which is caused by the sun's differential rotation (presumably first observed by Galileo Galilei or Christoph Scheiner in the first half of the 17th century).Note that the differential rotation of the sun does not lead to variations in solar proxies with a period of exactly 27 days.However, the term "27-day cycle" will be used in the following.solar flux (bottom panel) for the period from 02/1959 to 02/2017 ("SC" refers to "solar cycle").The red line in the top panel corresponds to a 365-day running mean.The repeating pattern with a period of 1 year is the seasonal cycle in standard phase height data further discussed in Peters and Entzian (2015).An 11-year solar cycle signature is also discernible.

Superposed Epoch Analysis (SEA)
The analysis technique employed to extract solar-driven 27-day variations in standard phase height 90 data is the superposed epoch analysis (further on referred to as SEA) technique (e.g., Howard, 1833;Chree, 1912), also known as composite analysis.The F10.7 cm solar radio flux or LYA is used as a solar proxy in the current study.Panels b) and c) of Figure 1 show LYA and the F10.In a first step we determined anomaly time series by removing a 41-day running mean from both 95 the SPH and the F10.7 cm flux data.Using 41 days is arbitrary to a certain extent, but the results are only weakly dependent on the width of the smoothing window used, as will be discussed in more detail in section 4. Figure 2 shows the obtained anomaly time series for SPH (top panel) and the F10.7 cm solar flux (bottom panel).In order to quantify the variability of the two anomalies as a function of time, we determined the standard deviation of the anomaly values in adjacent 100-day 100 time bins.The red solid lines in the panels of Figure 2 display the time variation of these standard deviations.The standard deviation of the SPH anomaly is on the order of several hundred meters, which is significantly larger than solar 27-day signature extracted below using the SEA.Applying the same procedure to the LYA series, we found similar results, as expected (not shown).
Maxima in solar activity associated with the sun's differential rotation are identified automatically The epoch-averaged standard phase height anomaly exhibits a periodic 27-day signature with an amplitude of about 50 m and with a minimum occurring a few days before maximum solar activity.

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This finding is discussed below in section 4, where we also investigate the dependence of the SEA results on solar activity (applying different F10.7 cm flux thresholds) and on season.

Significance testing
Periodic signatures in the epoch-averaged anomalies may also be introduced by effects entirely unrelated to changes in solar forcing.A single major anomaly in the time series, e.g., related to a major 120 stratospheric warming, will only cancel out in the analysis, if a sufficiently large number of epochs is available for analysis.Note that such an anomalous event may also lead to periodic variations in the epoch-averaged anomalies, if overlapping epochs are used, i.e., if the major anomaly occurs after local solar maximum in one epoch and before local solar maximum in the following epoch.In other words, a repeating pattern in the epoch-averaged anomaly with a period of about 27 days is not 125 necessarily an indication of the presence of a solar 27-day signature in the analyzed time series.
In order to test the significance of the obtained results, we applied the following Monte-Carlo test: Rather than choosing the epochs centered at local solar maxima, the epochs are chosen randomly, using the same number of epochs as for the actual analysis.The SEA with randomly selected epochs   in standard phase height is very likely related to solar variability.

Results
In section 4.1 we apply the band-pass filtering method based on wavelet analysis after Torrence and Compo (1998) in order to identify for the selected anomaly time series a comparable variability as 140 the studied solar induced 27-day variation.The motivation comes from the result of the SEA (Figure 4) that already showed that a 27-day signature is present in the SPH time series which is strongly anti-correlated to the F10.7 cm solar flux or the Lyman-α flux.The used standard band-pass filter has a half width of about 10 % (∼ 3 days) of the fundamental period of 27 days, i.e. a band-pass filter of 24 -31 days is applied.These filtered time series are also used for a cross-correlation analysis.145 Furthermore, in section 4.2 we apply the superposed epoch analysis using F10.7 cm solar flux data in order to investigate the identified 27-day signature (Figure 4) in more detail.In section 4.3 we apply a regression analysis to the standard phase height time series as well ERA-Interim (Dee et al., 2011) andCMAM (McLandress et al., 2014) temperature and geopotential height time series to examine a possible link to atmospheric processes like planetary wave propagation and evolution.clear dominance for the winter months.Figure 7 shows as a typical example the winter 1985 -1986 with an amplitude ratio exceeding 1 during solar minimum (note: with moderate LYA amplitudes and larger SPH amplitudes).In summer the two band-pass-filtered time series are out-of-phase, as 160 expected from photo-ionisation by Lyman-α, but phase changes during winter time may be due to atmospheric processes.
In addition to Figure 7, the phase relationship is studied over the whole time series of 58 years.
We examine the phasing between the SPH, and LYA, SFL, SPN anomaly series over all seasons.
The results of a cross correlation analysis (not shown) between those time series reveal a very weak 165 anti-correlation between SPH and LYA, SFL, SPN, as expected.But the SPH shows a negative lag of 1 -3 days for all three cross-correlations that means that on average the SPH minimum leads the maxima in solar activity proxies by a few days.This time lag is consistent with the time lag obtained from applying the superposed epoch analysis (see section 4.2).Note that the cross-correlation was run over all seasons and all 58 years.This result supports the hypothesis that atmospheric processes 170 determine the mean cross-correlation and finally the variability of SPH.Especially in winter during solar minimum it seems that atmospheric processes are dominant.

Superposed epoch analysis
The SEA result displayed in Figure 4 already demonstrated that a 27-day signature is present in the SPH time series.The Monte-Carlo significance test described above showed that the fitted amplitude 175 to the epoch-averaged SPH anomalies did not reach the actual amplitude for any of the 1000 random ensembles, indicating that the 27-day signature in SPH in Figure 4 is very likely caused by the solar 27-day cycle.The 27-day signature in SPH has an amplitude of about 50 m and is thus significantly smaller than the overall SPH variability (see bottom panel of Figure 2).
The SEA was so far applied to the entire time series covering the period from 02/1959 to 02/2017 180 and for a window width of 41 days when determining the anomaly time series.In the following subsections we investigate, how the SEA results depend on solar activity (applying different thresholds for the F10.7 cm flux), on season, and on the width of the window.As will be seen, the sensitivity values are dependent on all of these assumptions.anomaly is then shifted by the corresponding time lag (4 days for the results displayed in Figure 4), followed by the linear regression.For a smoothing window width of 41 days and considering all available epochs a sensitivity of -0.365 ± 0.043 km (100 sfu) −1 is obtained.
We also determined the sensitivity of the SPH to the 11-year solar cycle.This is done by defining a regular F10.7 cm flux grid with a step size of 10 sfu, followed by averaging all daily F10.7 cm solar 195 flux values -and the corresponding SPH values -for each 10 sfu bin.The resulting bin-averaged solar flux and SPH values are then plotted in a scatter plot and the sensitivity is given by the slope of a line fitted by linear regression.The obtained value of the standard phase height sensitivity to solar forcing at the 11-year time scale is -0.436 (± 0.049) km (100 sfu) −1 .This value agrees within combined uncertainties with the standard phase height sensitivity for the 27-day solar cycle of -200 0.365 (± 0.043) km (100 sfu) −1 , which suggests similar driving mechanisms.This aspect will be discussed further in section 5. We also note that the 11-year SPH sensitivity derived here is in good agreement with the value based on the results by Peters and Entzian (2015) of -0.387 km (100 sfu) −1 .
Peters and Entzian (2015) used the Lyman-α flux as solar proxy, so that a conversion to the F10.7 cm flux was required to convert their sensitivity value to units of km (100 sfu) −1 .This was done using 205 a linear fit to the Lyman-α flux as a function of F10.7 cm radio flux (see Figure 8) for all available data between 02/1959 and 02/2017.

Dependence of results on solar activity
Different tests were performed to study the dependence of the 27-day sensitivity of SPH on solar activity.First, we apply different solar activity thresholds (from 60 sfu up to 200 sfu in steps of 10 210 sfu) and only consider epochs for which the solar activity exceeds the assumed threshold on all days.
The results of this test are listed in Table 1 and the dependence of the derived 27-day SPH sensitivity on solar activity is shown in Figure 9. Table 1 lists the number of epochs available for the different solar activity thresholds, the temporal shift applied before performing the linear fit, the amplitude of the fitted sine, as well as the results of the significance tests and the 27-day sensitivity value.The 215 number of epochs decreases with increasing solar activity threshold, as expected.For the lowest three solar activity thresholds, the significance test did not yield a single random ensemble with amplitudes exceeding the amplitude obtained in the actual analysis.The fraction generally increases with increasing solar activity threshold and reaches about 35 % for a F10.7 cm flux threshold of 200 sfu.The shift or time lag varies somewhat between -1 and -4 and the negative sign implies that 220 the minimum in standard phase height precedes the maximum in solar activity.The reasons for this behavior are currently not well understood and will be discussed in section 5.  dash-dotted line corresponds to the value determined in the study by Peters and Entzian (2015), based on the same SPH data set.
Next, we tested how the results differ between periods of low and enhanced solar activity.This was done by selecting epochs for which the F10.7 cm flux was either lower or greater than 130 sfu.

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The epoch-averaged SPH anomaly for F10.7 > 130 sfu is shown in the upper panel of Figure 10 and the one for F10.7 < 130 sfu in the bottom panel of this Figure .Surprisingly, the amplitude of the extracted solar 27-day signature in SPH is larger for low solar activity than for higher solar activity.Because the absolute amplitude of the 27-day F10.7 cm flux variations for low solar activity is significantly smaller than during solar maximum, the SPH sensitivity to solar forcing at the 27-235 day scale and for low solar activity is with a value of -1.54 ± 0.38 km (100 sfu) −1 also significantly larger than the value reported above.

Dependence of results on season
In addition, we investigated whether the solar 27-day signature in standard phase height depends on the season.For this purpose we consider "winter" to include the months October, November, 240 December, January and February."Summer" includes May, June, July, August and September.We use more than 3 months for each season in order to increase the number of epochs available for analysis.The smoothing window width is again 41, as above.2. The number of epochs used for the summer (243) and winter (244) seasons is almost identical and the phase shift only differs by one day.However, the obtained amplitude is about a factor of 2 larger 245 for the winter season than for summer.The SPH 27-day sensitivity for summer (-0.454 ± 0.077) agrees within uncertainties with the all-year value (-0.365 ± 0.043), but for winter, the value is with -0.488 ± 0.052 slightly larger.Potential reasons for this behavior are discussed below in section 5.

Dependence of results on window width
Next, we tested the effect of different smoothing windows -used to determine anomaly time series -250 on the results.The window width (w) was increased from 30 days to 80 days in steps of 5 days.The obtained SPH sensitivities to solar forcing at the 27-day scale changed from -0.343 (± 0.029) km (100 sfu) −1 (w = 30 days) to -0.405 (± 0.047) km (100 sfu) −1 (w = 80 days).In addition, in subsection 4.3.2we apply a regression analysis between the SPH time series and the 3-dimensional geopotential height field (GH) taken from CMAM, in order to examine the possible 270 link between SPH evolution (band-pass filtered) and the hemispheric variability of the planetary wave field on a daily basis.

Comparison of time-series over Eifel-mountain
The ERA-Interim (red) and CMAM (blue) temperature evolutions at about 1 hPa over the Eifel   2016)) -and an anti-correlation to stratopause temperature.In each winter we found also a strong anti-correlation in the temperature variability between both layers induced by planetary wave activity which appears also in other meteorological fields due to the quasi-geostrophic balance.This ultra-long wave activity extends into the mesosphere as known from to the vertical propagation of ultra-long planetary waves (Charney and Drazin,

Regression of standard phase heights and CMAM geopotential heights
Following classical textbooks (e.g., Taubenheim, 1969) the regression between two times series is  The vortex weakening is linked with an intrusion of subtropical air into the polar region over the North Atlantic, as known from some major stratospheric warming events in wintertime (e.g., Peters et al., 2014).A dominant wave 1 pattern occurs with a strong wave 2. In general the results reveal an

Discussion
In this study we investigated variability in SPH at temporal scales close to the solar 27-day cycle.
Different analysis techniques -i.e.cross-correlation analysis and superposed epoch analysis -were applied to extract a potential solar driven 27-day signature in SPH data covering almost six solar cycles.

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The SEA, when applied to the entire SPH data set, yields evidence for a clear periodic 27-day signature with an amplitude of about 50 m, which is very likely caused by the solar 27-day cycle, as demonstrated by a Monte-Carlo significance analysis.An independent piece of evidence indicating that the identified 27-day signature in SPH is caused by solar forcing, is the finding that the determined SPH sensitivity to solar variability at the 27-day scale is good agreement with the sensitivity for the 11-year solar cycle.SPH is more or less anti-correlated to solar forcing, which is consistent with the simple picture that enhanced photo-ionisation of NO leads to an increase in free electron density and subsequently to a decrease in SPH.However, several of our findings cannot be reconciled with a purely photochemical mechanism.
First, both the SEA and the cross-correlation analysis consistently show that the minimum in SPH 360 precedes the maximum in solar forcing by a few days, indicating the action of other forcings or atmospheric effects.
Second, not only the SPH sensitivity to solar forcing is larger for periods of low solar activity, even the amplitude of the potential solar 27-day signature is larger during solar minimum, which is currently not understood at all.Interestingly, Gruzdev et al. (2009) find in their HAMMONIA model 365 studies generally a non-linear atmospheric response to solar forcing with sensitivities increasing with decreasing forcing.This is in part consistent with our results.However, Gruzdev et al. (2009) emphasize that the amplitude of the atmospheric response does not increase with decreasing forcing, which is inconsistent with our results on the SPH response to solar forcing.The apparent increase in the amplitude of the potential 27-day signature in SPH with decreasing solar activity may also 370 be an artifact and caused by effects unrelated to solar variations.If this is the case, it is, however, unexpected that the phase relationship between solar forcing and the potential response in SPH essentially remains the same, independent of solar activity.This could be a synchronization effect.
In this context it is important to mention that Ebel et al. (1981) performed a cross-spectral analysis of the solar F10.7 cm flux and planetary wave activity at pressure levels between 10 and 50 hPa.In order to investigate the influence of planetary waves, temperature data taken from the ERA-Interim Reanalysis as well as from model simulations with a nudged version of CMAM were used in the current study.The presented results provide clear evidence that planetary waves are associated with spectral power in the quasi 27-day period range and lead to corresponding variations in SPH.

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The different analysis techniques provide complementary approaches to investigate different sources of variability in SPH.While the SEA allows a robust identification of a solar-driven 27-day signature, the regression analysis applied to SPH and CMAM GH allows separating dynamical effects.The presented investigations allowed improving the scientific understanding of several aspects of solar and dynamical influences on SPH.However, an overall and coherent picture is still missing, as 400 several of the reported effects are difficult to quantify and understand.In addition, a potential impact of solar variability on planetary wave activity is not well understood.
In the context of 27-day variations in SPH it is also relevant that a solar 27-day signature in noctilucent cloud (NLC) altitude was recently discovered (Thurairajah et al., 2017;Köhnke et al., 2018).The signature has an amplitude of about 100 -200 m.Köhnke et al. (2018) provide a 405 qualitative explanation for phase relationship of the identified 27-day signature in NLC altitude, NLC occurrence rate and temperature at the polar summer mesopause.The 27-day signature in NLC parameters is likely mainly driven by dynamical effects (see Köhnke et al. (2018)).The main reason is that the phase relationship between the 27-day signatures in temperature and H 2 O mixing ratio at the summer mesopause found by Thomas et al. (2015) is inconsistent with a purely photochemical 410 process, but easily explained by a solar modulation of the upwelling in the polar summer mesosphere.
Further insight into the underlying processes may be gained by dedicated model simulations using a general circulation model, coupled to an ion chemical module capable of modelling all relevant physical (particularly dynamical) and chemical processes.

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by searching for local maxima in the F10.7 cm flux time series smoothed with 5-day running mean filter.These local solar maxima are the centers of the analyzed epochs, each epoch covering 61 days, i.e., center date ± 30 days.Then the standard phase height anomalies for every epoch are written to the rows of a N × 61 matrix, N being the number of epochs analyzed.The main step of the SEA consists of averaging the matrix column-wise, yielding the epoch-averaged standard phase 110 height anomaly.Figure 4 shows the epoch-averaged F10.7 cm flux and the standard phase height anomalies for the entire data set from 1959 to 2017.The epoch-averaged F10.7 cm flux anomaly peaks at day 0 relative to local solar maximum, indicating that the epochs were selected correctly.

Fig. 2 .
Fig. 2. Anomaly time series of standard phase height (top panel), solar Lyman-α flux (middle panel) and F10.7 cm solar flux (bottom panel), determined by removing a 41-day running mean from the time series shown in Figure 1.The red lines correspond to 1 standard deviation determined in adjacent 100-day time bins.

Fig. 3 .
Fig. 3. Power spectra of the Lyman-alpha (LYA) and the standard phase height (SPH) time series starting in February 1959.

Fig. 4 .
Fig. 4. Epoch-averaged F10.7 cm solar flux and standard phase height (SPH) anomalies for a total of 584 epochs.The thick blue line corresponds to the epoch-averaged F10.7 cm solar flux anomaly and the thin blue lines show the standard errors of the mean for each day relative to local solar maximum.The grey thin line corresponds to the unsmoothed epoch-averaged SPH anomaly, also shown smoothed by a 5-day running mean in red.The thin red lines represent the standard error of the mean of epoch-averaged anomalies about the daily mean value and plotted around the smoothed anomaly to improve clarity.The black dashed line is a sinusoidal fit to the unsmoothed epoch-averaged standard phase height anomaly, with an amplitude of about 50 m.

Fig. 5 .
Fig. 5. Illustration of the Monte-Carlo significance test.The red line shows the amplitude of a sinusoidal fit to the extracted 27-day signature in SPH.The black line shows the fitted amplitudes to epoch-averaged SPH anomalies for 1000 randomly chosen epoch ensembles.See text for more detailed information.
4.2.1 Sensitivity of standard phase height to the 27-day and 11-year solar cycles 185 The sensitivity parameter (or simply sensitivity) that quantifies the SPH dependence on solar activity is easily determined using the epoch-averaged F10.7 flux and SPH anomalies displayed in Figure 4.The anomalies are plotted against each other in a scatter plot and the sensitivity parameter is given by the slope of a linear regression line.Before the linear regression is performed, we determine the 10 Atmos.Chem.Phys.Discuss., https://doi.org/10.5194/acp-2018-799Manuscript under review for journal Atmos.Chem.Phys.Discussion started: 24 August 2018 c Author(s) 2018.CC BY 4.0 License.phase lag between solar maximum and SPH minimum using time-lagged cross correlation.The SPH 190

Fig. 8 .
Fig. 8. Scatter plot of daily values of Lyman-α flux and F10.7 cm radio flux for the period from 02/1959 to 02/2017.The red line corresponds to a linear regression to the data points.

Fig. 9 .
Fig. 9. SPH sensitivity to solar forcing for the 27-day and the 11-year solar cycle.The red circles show the 27-day sensitivity for different solar activity thresholds as described in the text.The blue line corresponds to the 11-year sensitivity determined in this study and the dotted line show the uncertainties.The black dash-dotted line displays the 11-year sensitivity determined byPeters and Entzian (2015).

Figure 9 F10
Figure 9 illustrates that the SPH sensitivity to solar forcing at the 27-day time scale depends on the solar activity threshold, but no simple or monotonous dependence is obvious.The Figure also displays the SPH sensitivity to solar forcing for the 11-year solar cycle.The blue line shows the 225

Fig. 10 .
Fig. 10.Top panel: similar to Figure 4, but for epochs with solar activity exceeding 130 sfu.Bottom panel: similar to Figure 4, but for epochs with solar activity lower than 130 sfu.

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to average changes in sensitivity of about 0.01 km (100 sfu) −1 , corresponding to a relative change of about 3 %.We can therefore conclude, that the obtained sensitivities are only weakly dependent on the smoothing window width.4.3 Comparison of standard phase heights with ERA-I and CMAM In subsection 4.3.1,we compare the variability of three data sets: the SPH time series, measured over the Eifel mountain (50 • N, 6 • E; Western Germany) at about 82 km altitude (details are described in section 2), temperature profiles averaged over the Eifel mountain region (40 • -58 • N, 0 • -12 • E) from ERA-Interim data (Dee et al., 2011) and from the Extended Canadian Middle Atmosphere Model (CMAM-Ext, CMAM30 results, McLandress et al. (2014)).Model data were downloaded from the following web-page: http://climate-modelling.canada.ca/climatemodeldata/cmam/-265cmam30/era interim adjustment/index.shtmlNote that the CMAM-Ext model is nudged up to 1 hPa with ERA-Interim data, i.e., CMAM-Ext and ERA-Interim show a similar temporal evolution in the troposphere and stratosphere.
mountain region are in good agreement, as shown in the upper panel of Figure 11.This is expected, 275 because of the nudging procedure used in CMAM.This is demonstrated as an example for the decade from 1979 to 1989.A stratopause warming is found in each summer season and a highly disturbed winter evolution mainly due to the action of planetary waves.Results of a band-pass filter analysis are shown in the lower panel of Figure 11 indicating large amplitudes of about 1 -5 K for a 24 -

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They found significant correlations between solar variability and the amplitude of planetary waves.Third, the amplitude of the potential solar 27-day signature in SPH is about a factor of two larger during winter than during summer.It is well known that due to the winter anomaly the SPH amplitudes are increased in winter by larger downward transport of NO from the thermosphere and amined the electron density anomalies in the boreal D region in a coupled model with neutral and ion photochemistry, as well as transport by planetary waves.They found that anomalies can be understood in terms of auroral production of nitric oxide in polar night and its subsequent transport and ionization.In particular, their results indicate the importance of horizonal ultra-long planetary wave transport for many of the observed features.In addition,Hendricks et al. (2015)  clearly demonstrated 385 the impact of the 27-day solar cycle on NO production in the Auroral zone in satellite measurements during events of energetic particle precipitation (EPP).The authors found larger amplitudes of the EPP-driven 27-day signature in NO during winter than during summer, which may contribute to the larger amplitudes of the 27-day signatures in SPH reported here.Gruzdev et al. (2009) also discuss seasonal variations of the atmospheric response to the solar 27-day cycle.For extra-tropical latitudes 390 they report that the sensitivities are for many parameters larger in winter than in summer.

Table 1 .
Overview of the results for different solar activity thresholds ( * Amplitude of fitted sinusoidal function; † Fraction of random realizations with amplitudes larger than actual data).

Table 2 .
Overview of the results for different seasons ( * Amplitude of fitted sinusoidal function; † Fraction of random realizations with amplitudes larger than actual data).
The dependence of the Atmos.Chem.Phys.Discuss., https://doi.org/10.5194/acp-2018-799Manuscript under review for journal Atmos.Chem.Phys.Discussion started: 24 August 2018 c Author(s) 2018.CC BY 4.0 License.sensitivity on window width is not truly monotonous, but larger window widths have a tendency to be associated with larger absolute sensitivity values.Changing the window width by 10 days, leads