Introduction
Noctilucent clouds (NLCs) are a phenomenon of the mesopause region from midlatitudes to
high latitudes. During summer temperatures fall below 150 K and cause the
few ppmv of water vapor at these altitudes to freeze. The result is tiny ice
particles which are observable with the naked eye. First documented observations
were made during summer 1885
and the altitude of
the clouds was determined to about 83 km by optical triangulation
.
It has been shown that NLCs consist of aspherical ice particles of a few tens
of nanometers, with a number density of about 100 per cm3
e.g.,. NLC
displays often show pronounced variability, which provides information about
dynamic processes like horizontal wind and wave motions in their environment
. Mesospheric ice particles are extremely sensitive to
changes of atmospheric background parameters, like temperature and water
vapor, and have been demonstrated to respond to various scales of
variability, ranging from seconds to years
e.g.,.
One particular scale of interest is variations with solar time
e.g.,.
Such oscillations have been found to be persistent, even when epoch averaging
over many years is applied, and were attributed to impacts of atmospheric
thermal tides e.g.,. Solar tidal
oscillations are globally forced due to absorption of solar irradiance
throughout the day. Diurnal and semidiurnal components have a prominent
influence; they are stimulated by absorption of solar radiation in the
near-infrared bands of tropospheric water vapor and solar ultraviolet
radiation by stratospheric ozone and mesospheric molecular oxygen,
respectively e.g.,.
The moon forces gravitational tidal signatures not only in Earth's oceans but
also in the atmosphere. published the first
reliable identification of lunar tidal signatures in surface pressure data.
The semidiurnal lunar tide is the most significant component and was found in
several parameters, even in the mesosphere and lower thermosphere like winds,
temperatures and airglow emissions
e.g.,. Studies of
lunar tidal signatures in NLCs are sparse and mostly based on ground-based
visual observations
e.g.,. Only
recently was the lunar semidiurnal tide identified in multiyear data sets of
satellite instruments . Ground- and
satellite-based results partly differ from each other, especially for the
lunar tidal amplitude.
In general, available observation methods of tides in NLCs have different pros
and cons. Ground-based visual data can only be obtained around solar midnight
hours when the lower troposphere is dark but sunlight still illuminates the
upper mesosphere and is scattered at the ice particles. This hampers the
identification of both solar and lunar tidal signatures. Ground-based lidars
can cover the entire solar diurnal cycle and are thus able to identify solar
and lunar tides. As they operate at fixed locations, the superposition of all
tidal components above the instrument is measured, with the migrating
components giving the distinct variations with solar time. Solar and lunar
semidiurnal periods are close to each other (12.0 vs. 12.4 solar hours) and a
separation requires adequate sampling and data accuracy. Satellite
instruments usually operate in sun-synchronous orbits and cover only few
solar times during longer time periods. On the one hand this hampers the
identification of solar tidal signatures, and on the other hand they have less
deterioration of the lunar signal by solar impacts. Moon's orbit around the
Earth as well as Earth's rotation around its axis are of identical direction;
however, Moon's orbital speed is slower. For this reason its apparent Earth
revolution takes about 50 min longer than 24 h, which accumulates to a full
day within a month's period. Hence it takes 1 month for sun-synchronous
satellites to cover all lunar times.
In this study, for the first time, we will extract solar and lunar tidal
signatures in NLCs simultaneously from a multiyear data set obtained using ground-based lidar. Moreover, phase progressions will be addressed
through the investigation of altitude-resolved tidal parameters.
Data analysis
We use data obtained by the Rayleigh–Mie–Raman (RMR) lidar at the ALOMAR
research station in northern Norway (69∘ N, 16∘ E). The lidar
has been in regular operation since 1997 and is intensely used during the summer
months for NLC detections whenever weather conditions permit. Because of the
technical setup, NLCs are detectable during all local times, even during the
highest solar elevation angles around 44∘. NLCs above ALOMAR usually
occur between the beginning of June and mid-August, leading to our definition of
the season length from day of year (DoY) 152 (1 June) to 227 (15 August). The
data set covers 6400 measurement hours during 21 seasons. A subset of
3100 h contains NLCs, yielding a mean probability of ∼48 % of observing NLCs at this location.
The lidar transmitter emits light at 532 nm wavelength with approx. 50 MW
power per laser pulse. Part of it is backscattered by air molecules and NLC
particles and detected by the receiver, together with sunlight scattered by
the atmosphere. After background subtraction the received signal is first
converted into a backscatter ratio R(z), which is a measure for the
presence of aerosol particles and defined as the ratio of the measured total
signal to the molecular signal βM(z). Then the volume
backscatter coefficient of NLC particles
βNLC(z)=(R(z)-1)×βM(z) is calculated;
βM(z) is calculated from air densities for the lidar location
. From the altitude profile βNLC(z) we
determine the maximum value βmax, the total backscatter coefficient
βtot (integral over the vertical layer extension) and the
centroid altitude (zc). The ratio of time with NLC signatures
over total measurement time yields the occurrence frequency (OF). For more
details the reader is referred to . To maintain
homogeneous conditions during 21 seasons, the data were pre-integrated in
time and altitude for about 15 min and 150 m.
In a next step, the measurements were sorted by local time; i.e., the
individual pre-integrations were accumulated and averaged in their
corresponding hourly time slots. This method is usually called superposed
epoch analysis and was applied for solar times as well
as lunar times separately. Lunar, like solar, time follows from the azimuth
position of the celestial body relative to the observer. For a given solar
time Moon ephemerides were calculated using the PyEphem library
(https://rhodesmill.org/pyephem/, last access: 6 November 2018). To
extract tidal information from the temporal variations of NLC parameters,
least-square fits of the sum of sinusoidal functions with periods of 24, 12,
8, and 6 h to the hourly mean values (solar as well as lunar epoch
averages) were performed. Confidence intervals of the estimated fit
parameters were calculated with the bootstrap method by resampling the data
set within the uncertainties of the means e.g.,. The
mean NLC parameters are randomly diversified within their error bars (1000
times for each hour), which results in an equivalent number of time series
for which the fits are determined. Finally, the statistics of the
distribution of each fit parameter is calculated, resulting in a mean value
and its error.
Results and discussion
Variations with solar time
Figure shows the mean variations of NLC occurrence
frequency and brightness with altitude and time. The plots contain 6400
measurement hours including 3100 h with NLCs and were composed using
individual altitude profiles from 1997 to 2017. NLCs above ALOMAR can
virtually exist in the entire altitude range between 78 and 90 km. They
occur most often and have the largest vertical extent between midnight and
06:00 local solar time (LST), which was attributed to thermal tides at
83 km altitude . The altitude of maximum occurrence
decreases by about 1 km during the morning hours. A second and weaker
occurrence maximum is visible around 15:00 LST. The clouds reach their
maximum brightness between 03:00 and 09:00 LST, which is 3 h later compared
to the occurrence maximum. Nevertheless relatively strong (brighter) clouds
contribute to this occurrence maximum. The secondary occurrence maximum,
however, is caused only by fainter (dimmer) clouds. The altitude structure of
brightness mirrors the growth-sedimentation scenario of NLC particles. They
nucleate at low temperatures in the mesopause region around 88 km, grow in
size by the uptake of water vapor and decrease in altitude due to selective
turbulent diffusion and gravitation. The observed brightness depends strongly
on particle size (∝ r6). Temperature increases with decreasing
altitude, which causes the ice particles to sublimate. This leads to a sharp
brightness decrease at the lower border of the particle existence range.
Mean altitude and solar time variations of NLC occurrence
frequency (a) and brightness (b) between 1 June and
15 August from 1997 to 2017. The plots are composed of altitude profiles
covering 3100 h of NLC detections; panel (a) contains 6400 h total
measurement time.
We would like to point out that one cannot prove from measurements at one location
that observed local-time-dependent features are caused by tides. However, the
persistence of features in our 21 year data set shown in Fig. is a strong indication for atmospheric tides. Imprints
of variability sources uncorrelated to solar time, like gravity waves, should
cancel out on these multiyear timescales. Furthermore we observe a
superposition of all existing tidal modes at a given time and cannot
differentiate between migrating and nonmigrating parts.
Mean solar (red) and lunar (blue) time variations of NLC occurrence
frequency (OF), altitude and the maximum and integrated brightness
(βmax, βtot) between 19 June and 29 July from
1997 to 2017. Symbols are hourly mean values and vertical bars errors of the
means. Solid lines are harmonic fits with periods of 24, 12, 8 and 6 h to
the mean values. The relative variations of the fits over day Δ=(max-min)/mean are indicated.
Simultaneous solar and lunar tidal variations
We investigate the mean local time dependence of NLC parameters using a
representative brightness value for each altitude profile. This method was
applied earlier for our data set and is commonly used for ground-based lidars
as well as satellite instruments. We determine for each altitude profile the
value of the maximum brightness βmax as well as the
integrated brightness βtot over all altitudes. Local time
variability of NLC parameters depends on cloud brightness and its observation
is additionally impacted by instrument sensitivity
e.g.,. For these reasons we usually
apply a minimum brightness limit. In this study, however, we aim at identifying weak lunar signals embedded in a larger background of solar
variability. The frequency distribution of brightness values satisfies an
exponential law (cf. Fig. 1 in ) with a high
occurrence of dim clouds. As a result, the application of our long-term
brightness limit (βmax>4×10-10 m-1 s-1) reduces the NLC detections by
48 % from 3100 to 1600 h. Sensitivity tests showed that data reductions
of such extent prevent a reliable extraction of the lunar signal from our
data set. It turned out that an exclusive limitation to the core of the
season (without application of any brightness limit) is better suited as it
restricts the sampling to stable summer conditions with high NLC occurrences.
Therefore we choose a time period for which the daily NLC occurrence frequency
exceeds the seasonal mean value, which is roughly the case between DoY 170
(19 June) and 210 (29 July); cf. Fig. 3 in and
Fig. 2 in . This reduces the NLC detections by
35 %.
The resulting solar and lunar time variations are shown in
Fig. . The plots contain 3450 measurement hours including
2030 h with NLCs from 1997 to 2017. Throughout the solar day the results
match the variations seen in Fig. . We again find the
highest NLC occurrence between midnight and 06:00 LST and a weaker maximum
around 15:00 LST. The maximum brightness is observed between 03:00 and
08:00 LST. The highest altitudes are reached around midnight and 14:00 LST, and the
mean altitude variation during the solar day is ∼1.1 km. The daily
variations of brightness and altitude are anti-correlated (r=-0.84); i.e.,
the brightest clouds occur at lowest altitudes and vice versa, which fits the
above-mentioned growth-sedimentation scenario of mesospheric ice particles.
Such distinct variations throughout the solar day were first observed in
1997 at ALOMAR and have been found by ground-based lidar at other locations
as well
e.g.,.
Satellites mostly operate in sun-synchronous orbits and are thus not able to
cover NLC local time variations, with some exceptions
e.g.,. NLC variability during
the solar day was also investigated by models
e.g.,. In general,
maximum values for occurrence and brightness are found in the first half of
the solar day, which is attributed to temperature tides and tidal variations
in background water vapor.
Amplitudes (A) and phases (P) of solar and lunar tidal oscillations
as determined from harmonic fits with periods of 24, 12, 8 and 6 h to
the data from 1997 to 2017. Amplitudes are given both in absolute and
relative units. Absolute units (abs) are occurrence frequency (OF) in %,
altitude (zc) in km, maximum brightness (βmax) in
10-10 m-1 s-1 and total brightness (βtot) in
10-7 sr-1. Relative units (rel) are in % with respect to the mean
value. Fit quality is given as the correlation coefficient r.
Solar
Lunar
Parameter
OF
zc
βmax
βtot
OF
zc
βmax
βtot
A24 (abs)
13.40 ± 1.23
0.33 ± 0.02
2.54 ± 0.14
3.86 ± 0.20
1.68 ± 1.16
0.04 ± 0.02
0.34 ± 0.14
0.79 ± 0.19
A12 (abs)
7.32 ± 1.22
0.33 ± 0.02
1.23 ± 0.14
1.56 ± 0.20
3.92 ± 1.27
0.08 ± 0.02
0.16 ± 0.13
0.21 ± 0.17
A08 (abs)
2.92 ± 1.25
0.05 ± 0.02
0.22 ± 0.14
0.31 ± 0.19
2.68 ± 1.23
0.06 ± 0.02
0.19 ± 0.14
0.47 ± 0.19
A06 (abs)
1.31 ± 1.10
0.03 ± 0.02
0.16 ± 0.12
0.37 ± 0.19
1.04 ± 1.00
0.07 ± 0.02
0.27 ± 0.14
0.47 ± 0.19
A24 (rel)
23.46 ± 2.16
0.40 ± 0.03
31.86 ± 1.76
39.09 ± 2.04
2.91 ± 2.01
0.04 ± 0.02
4.21 ± 1.78
7.75 ± 1.85
A12 (rel)
12.81 ± 2.14
0.40 ± 0.03
15.38 ± 1.76
15.80 ± 1.93
6.80 ± 2.20
0.10 ± 0.03
1.96 ± 1.63
2.09 ± 1.72
A08 (rel)
5.11 ± 2.18
0.06 ± 0.03
2.74 ± 1.75
3.10 ± 1.89
4.64 ± 2.14
0.07 ± 0.03
2.37 ± 1.69
4.63 ± 1.85
A06 (rel)
2.30 ± 1.92
0.04 ± 0.03
2.02 ± 1.56
3.76 ± 1.93
1.80 ± 1.73
0.08 ± 0.03
3.27 ± 1.73
4.59 ± 1.85
P24
1.83 ± 0.36
18.13 ± 0.26
4.60 ± 0.21
4.42 ± 0.20
7.37 ± 3.58
0.37 ± 2.73
14.16 ± 1.74
14.48 ± 1.02
P12
3.22 ± 0.32
0.66 ± 0.13
5.73 ± 0.23
5.23 ± 0.24
1.99 ± 0.63
0.94 ± 0.51
5.87 ± 2.46
4.41 ± 2.66
P08
6.70 ± 0.55
3.64 ± 0.65
5.11 ± 0.93
4.24 ± 0.92
2.56 ± 0.62
0.93 ± 0.49
5.05 ± 1.23
5.65 ± 0.58
P06
0.75 ± 2.34
3.92 ± 0.75
1.36 ± 4.08
0.37 ± 2.00
4.28 ± 1.93
1.91 ± 0.31
4.90 ± 0.57
5.13 ± 0.44
r
0.99
0.99
0.98
0.99
0.95
0.79
0.60
0.72
Figure shows also the NLC parameters as a function of local
lunar time (LLT) and we find variations in all parameters. NLCs occur most
often around 03:00 and 11:00 LLT. The highest altitude is reached around
02:00 LLT, which is connected with a minimum in brightness. Variations with
LLT are smaller compared to those with LST. The relative variation Δ=(max-min)/mean during solar (lunar) day is 60.9 % (21.5 %)
for occurrence frequency, 1.4 % (0.4 %) for altitude, 74.4 %
(15.8 %) for maximum brightness and 92.8 % (25.7 %) for total
brightness.
To compare the impact of solar and lunar tides on NLCs we extracted amplitudes
(A) and phases (P) of fits up to the fourth harmonic of the day to the data. The
results are listed in Table . For checking purposes we
calculated the fits additionally for only two harmonics (24 and 12 h periods).
It turned out that the fit algorithm is fairly robust; the amplitudes and
phases resulting from both fit versions are close to each other. For example,
for the 12 h component of the maximum brightness the deviations between
including/omitting 8 and 6 h periods are 1.7 % for amplitude value,
1.0 % for amplitude error, 8.7 % for phase value and 3.9 % for
phase error. We note the only moderate correlation coefficients for altitude
and especially brightness variations with the lunar day, indicating these
parameters to be additionally impacted by other sources of variability. Solar
tidal variations are dominated by diurnal and semidiurnal periods. Amplitude
ratios A24 / A12 are 1.8, 2.1 and 2.5 for occurrence frequency
and brightness (maximum, total), respectively. For altitude both periods
identically contribute to solar time variations.
Investigations of NLCs regarding lunar tidal signatures are sparse and mostly
based on ground-based visual observations. Such observations are limited to a
couple of hours around midnight because of the illumination conditions of
mesospheric altitudes by the sun. The results partly differ from each other
and show lunar variations of the NLC occurrence with amplitudes from 4 %
to 30 % in a monthly period
e.g.,. Only
recently were lunar tides in NLCs identified in multi-decade data sets of SBUV
(Solar Backscatter Ultraviolet) satellite instruments
. The authors found clear lunar semidiurnal tidal
signatures in NLC occurrence frequency, albedo, and ice water content. For
the Northern Hemisphere (55–75∘ N) they extracted a relative
amplitude A12(rel) of 5.2 % and a phase P12 of 3.3 h LLT for
the NLC occurrence frequency, which is so far the only value determined by
instrumental observations. The present study is the first identification of
lunar tidal signatures in ground-based lidar observations. Our values of
A12(rel) = 6.8 % and P12 = 2.0 h LLT are in good
agreement with . From visual NLC observations
published by , maximum NLC occurrences around 3 h
LLT follow (cf. discussion in ). Thus three independent
data sets show occurrence maxima between 2 and 3 h LLT, which indicates a
robust determination of the corresponding semidiurnal lunar tide. One should
keep in mind that sun-synchronous satellite instruments cannot distinguish
between the semidiurnal and the semimonthly lunar tide and thus measure a
superposition of both components. It is commonly expected that the
semidiurnal component dominates, which is, however, still debated (cf.
discussion in ).
suggested temperature variations in the mesopause
region as the main driver of lunar tidal signatures in NLCs. They investigated
7 years of satellite temperature data from the MLS (Microwave Limb Sounder)
instrument and found consistent features at 83 km altitude with respect to
lunar NLC variations, namely minimum temperatures from 1 to 4 h LLT.
analyzed 9 years of data from the SOFIE (Solar
Occultation for Ice Experiment) satellite instrument and found temperature
variations with LLT as well. In general temperature variations with lunar
time are very small, with maximum amplitudes of about 0.2 K.
Brightness-related parameters (albedo, ice water content) were determined by
to be A12(rel) ∼ 6 % and
P12 ∼ 3 h LLT. In SOFIE data, found
A12(rel) = 2.5 % and P12 = 2.5 h LLT for the ice water
content in the Northern Hemisphere. Our values of
A12(rel) = 2.1 % and P12 = 4.4 h LLT for brightness
(βtot) match the satellite data reasonably. We notice,
however, that the semidiurnal component is the weakest of all extracted
harmonic components for our NLC brightness (cf. Table ). The
superposition of all four oscillations results in a brightness minimum
around 2 h LLT, compared to a maximum in the satellite observations.
also extracted lunar tidal NLC altitude variations,
which were determined to A12(abs) = 60 m and P12 = 2.2 h
LLT. This fits remarkably our values of A12(abs) = 80 m and
P12 = 0.9 h LLT. A difference between satellite results and the
present study is the phasing of altitude to brightness. Whereas
find them to be in phase (clouds with larger ice
water content are at higher altitudes), our results show the common
anti-phase behavior known from solar tidal variations (cf.
Fig. ). When only the semidiurnal components are taken into
account, the lunar phases of altitude and brightness (βtot)
differ by about 3.5 h, which is midway between in phase and anti-phase. We
make the reader aware that the statistical significance for our brightness
fits is relatively low and thus this particular result should not be
overestimated; see also below.
From Table we find solar tidal amplitudes to be always larger
than lunar ones, which is expected. For example, the ratios of semidiurnal
solar to lunar amplitudes are ∼1.9 for occurrence frequency, ∼4.1
for altitude and ∼7.5 for brightness. extracted
this ratio to ∼7.7 for horizontal winds from radar measurements in the
mesopause region at 68∘ N. For our data set we notice that the
extracted harmonics contribute differently to the observed lunar tidal
behavior of the NLC parameters. For occurrence frequency and altitude, the
semidiurnal component is dominant, whereas it is the weakest one for
brightness. From models, it is shown that a diurnal lunar tide is anticipated to be
significantly smaller compared to the semidiurnal lunar tide
e.g.,.
found a diurnal modulation of the lunar tide and suggested this to be caused
by interactions with solar tides during upward propagation of the lunar tide;
cf. also . Concerning the 8 and 6 h LLT oscillations
we see no resilient reason to attribute it to be directly caused by the Moon
and will estimate the robustness of extracted lunar oscillations in the
following chapter.
Reliability of tidal parameters
For analysis of simultaneous solar and lunar tidal variations we use 41 days
in the core of the NLC season (DoY 170–210). As our measurements cover many
solar times, and solar tidal amplitudes are large, the actual distribution of
measurements times during each year might cause a residual impact on the
extracted lunar amplitudes (sampling issue). This would introduce a
systematic error on top of the statistical error of the lunar tidal
parameters. We investigated this topic using the following simulations.
First the mean solar time dependencies for NLC occurrence frequency,
altitude and brightness were reconstructed using amplitudes and phases of the
harmonic solar periods. Then the constructed NLC parameter value at the solar
time of each actual measurement was taken and assigned to the corresponding
lunar time (method 1). This results in mean lunar time dependencies for the
NLC parameters which should be ideally flat curves representing the mean
values of the NLC parameters. We find deviations from this ideal case
indicating residual impacts of solar tidal parameters on lunar tidal parameters (thick
green curves in Fig. a, c, and e). For occurrence frequency
enhanced values are visible from 04:00 to 06:00 LLT and from
11:00 to 16:00 LLT. For altitude, enhanced values are shown, especially from
10:00 to 12:00 LLT, and decreased values are shown from 16:00–18:00 LLT. The measured
hourly mean values with respect to lunar time are also shown for reference
(blue symbols and curves in Fig. a, c and e). Comparing
these curves with the simulations we find that NLC occurrence frequency as well as
altitude are only little impacted during the lunar morning, whereas during the lunar
afternoon solar impacts are large compared to the measured values. For NLC
brightness the situation is worse. Here solar impacts reach larger values
during extended lunar time periods, even during the lunar morning.
We also calculated a second simulation (method 2). For this purpose,
artificial solar times were randomly generated, with the total number matching
the number of measurements. Then, like in the first simulation, the
constructed NLC parameter value at each artificial generated solar time was
taken and assigned to the corresponding lunar time. This procedure was
executed several times. The results are the thin green curves in Fig. a, c and e. Again we find residual solar tidal
impacts; however, they do not exceed the ones from the first simulation.
Simulated residual impact of solar on lunar (a, c, e) and
lunar on solar (b, d, f) tidal variations, as introduced by the
distribution of measurement times between 19 June and 29 July from 1997 to
2017. Method 1: actual times (thick green curves). Method 2: randomly
generated times (thin green curves). Causative variations were reconstructed
from harmonic fits with periods of 24, 12, 8 and 6 h; see
Table . For details see text. NLC parameters are occurrence
frequency (a, b), altitude (c, d) and brightness (e, f). (a, c, e) Measured lunar dependence
(blue) and simulated impact from solar variations (green).
(b, d, f) Measured solar dependence (red), simulated impact from
lunar variations (green).
In general, the actual sampling of the measurements concerning solar time
impacts the extracted lunar time dependence of NLC parameters. This impact is
smallest for occurrence frequency, moderate for altitude and largest for
brightness. We notice that 1.7 times more data are available for
determination of occurrence frequencies (entire measurement time) compared to
NLC layer parameters (only NLC measurement time). Thus, enhanced lunar
amplitudes especially for the higher harmonics (8 and 6 h lunar periods) of
altitude and brightness might be caused by an insufficient amount of data,
although the data set covers 21 seasons.
For completeness we performed the same investigations regarding lunar
residual impacts on solar tidal parameters. The results are shown in Fig. b, d, and f and indicate only negligible effects.
Mean solar amplitudes (a, b) and phases (c, d) of
NLC occurrence frequency (OF, a, c) and brightness
(βNLC, b, d) between 1 June and 15 August from 1997
to 2017. Diurnal components are in red, and semidiurnal components are in green. Black
numbers at the panels a and b are correlation coefficients of the harmonic fits
for the corresponding altitudes. Colored numbers in panels c and d are
vertical wavelengths as calculated from the phase slopes (dashed lines),
separated for altitudes below and above 84 km (gray dotted line).
(a) Mean variations of NLC occurrence frequency with
altitude and lunar time from 1997 to 2017. The plot contains 3450 h of
lidar measurements between 19 June and 29 July. (b) Semidiurnal
amplitudes and phases determined from data of (a). Black numbers are
correlation coefficients of the harmonic fits for the corresponding
altitudes.
Altitude dependence of tidal parameters
Now we study altitude-resolved tidal parameters. For this purpose the
altitude range between 80 and 88 km was divided into eight slices of 1 km
extent each (cf. Fig. ). For each altitude slice
amplitudes (A24, A12) and phases (P24, P12) of diurnal
and semidiurnal harmonic oscillations were extracted. The result for solar
tides is shown in Fig. . Amplitudes of the occurrence
frequency reach values up to 10 %. The lower half of the altitude range is
dominated by the diurnal component, being partly 1.9 times stronger compared
to the semidiurnal component. At higher altitudes the amplitudes of both
components decrease and are nearly identical. The brightness shows roughly a
similar behavior. The diurnal component dominates by a factor up to 2.2.
However, the altitude dependences of A12 are different for occurrence
frequency and brightness. While the former has its maximum at 84.5 km, the
one of the brightness is monotonically decreasing with increasing altitude.
Phases for both tidal components of occurrence frequency and brightness
decrease continuously with altitude, as is expected for upward propagating
tides, with only one exception (P12 of brightness). We notice the
existence of two altitude ranges with different phase progressions, separated
at about 84 km. From the slopes we determined corresponding vertical
wavelengths λz, which are also shown in Fig. .
For the occurrence frequency, vertical wavelengths in the lower altitude
range are -31 km (P24) and -21 km (P12). Values increase in
the upper altitude range to -125 km (P24) and -56 km (P12).
For brightness we extract vertical wavelengths of -68 km (P24) and
-17 km (P12) below 84 km altitude. Above this limit the progression
of P24 increases substantially, whereas the progression of P12 tends to
change sign. This phase behavior, however, is accompanied by small amplitude
values and might lack robustness. We notice that vertical wavelengths
connected with diurnal phases have generally larger absolute values compared
to those of semidiurnal phases.
Hough modes of classical tidal theory are distinguished by their vertical
wavelength . Wavelengths between 17 and 21 km as they
were observed for the semidiurnal tide below 84 km correspond to higher
order Hough modes H(2,9)–H(2,11). For the diurnal tide we find solely
wavelengths ≥31 km, which indicates negative Hough modes. We note,
however, that the excitation intensity of modes decreases towards higher
latitudes according to linear theory. Thus at 69∘ N nonlinear wave
interactions might play a major role.
To the best of our knowledge, vertical phase progressions in NLCs have never been
published so far. Thus we compare our results to other parameters like
temperature and horizontal winds measured in the summer mesopause region.
investigated thermal tides at Davis (69∘ S) by
means of a resonance lidar. During January 2011 they found downward
progressing P24, with a vertical wavelength of -30 km between 84 and
89 km altitude. P12 shows the opposite behavior, namely upward
progression (their Fig. 3). published a climatology of
tides in the Antarctic mesosphere determined by radar wind measurements. They
found between December and February in the 80 to 86 km range vertical
wavelengths from -37 to -55 km for P12 (migrating), but also values
marked as large. Vertical wavelengths associated with P24 are
large or even positive; cf. their Fig. 7. At midlatitudes
(Figs. 2 and 3) found tidal temperature variations between 84 and 89 km
altitude during summer, corresponding to vertical wavelengths of -27 km
(P12) and -19 km (P24), using a resonance lidar. Again at
midlatitudes, from lidar temperature soundings by vertical wavelengths of -9 km (P12) and -14 km (P24)
follow at around 85 km altitude in July (cf. their Fig. 7). These numbers might not be
representative, as their results show large variabilities during the summer
period.
In general, solar tidal phases determined from our NLC observations show a
consistent behavior, indicating that corresponding vertical wavelengths are
robust. The wavelengths fall within the range of values extracted from other
measurements published in the literature. We notice the variability of
λz values which might be caused by different time periods covered by
the measurements (days to years) as well as the tidal variability itself.
Changes in phase progressions around 84 km altitude could be caused by
the combined effects of tracer (ice particles) and background atmosphere. With
increasing altitude, the particle size decreases towards the mesopause at
around 89 km where they nucleate. Simultaneously, turbulent mixing of the
background atmosphere increases with altitude, which impacts the microphysical
properties of NLC particles. found a correlation
between particle size and distribution width for mean sizes up to 40 nm,
which are reached at an altitude of about 84 km. For larger particles (lower
altitudes) the distribution width is roughly constant. Following this, one
could speculate that tidal impacts might depend on the turbulent regime of
the atmosphere.
We have shown that occurrence frequency is the most robust NLC parameter of
our data set concerning lunar time variations. Therefore we investigated the
altitude dependence of its semidiurnal component by applying the same
procedure like for solar time variations. The results are shown in
Fig. . The semidiurnal component maximizes shortly above
the altitude of maximum occurrence frequency. Phases vary between 1.5 and
4.4 h LLT; their progression is positive below 84 km and negative above.
Corresponding vertical wavelengths are approx. -27 and +36 km.
Phase progressions of the lunar semidiurnal tide in layered phenomena of
the summer mesopause region have not been studied so far. In temperature data of the SABER (Sounding of
the Atmosphere Using Broadband Emission Radiometry) satellite instrument, found both
positive and negative phase progressions between 80 and 90 km altitude,
depending on latitude. They also identified several modes of the lunar
semidiurnal tide, including nonmigrating, and suggested an interaction
between lunar tide and other tides and/or waves at higher altitudes.