Introduction
According to the first Kepler law, the Earth travels in a good
approximation on an elliptical trajectory around the Sun. Within a year the
distance between both celestial bodies changes. During the
northern-hemispheric (NH) winter the range is approximately 3.29 % shorter than in
the NH summer. Due to the inverse square law, where the intensity I of the
radiation is inversely proportional to the Earth–Sun distance squared, this
shorter distance between the Sun and the Earth during boreal winter leads to
an increased heating of the mesosphere and lower thermosphere (MLT) resulting
in an expansion of the MLT and thermosphere, compared to the annual mean.
Another effect on the expansion–shrinking of the MLT is given by the
variability of solar radiation due to the 11-year solar cycle effect.
Figure shows a scheme of the Earth–Sun constellation and the
resulting effects, which will be explained in the following. Previous studies
such as , , ,
and showed that solar cycle variations affect the
atmospheric density, temperature, chemical composition, and winds over the
whole atmosphere, but in particular in the MTI
(mesosphere–thermosphere–ionosphere) system. A model simulation by
showed responses to changes in the 11-year solar cycle for the whole atmosphere.
For example, they showed that due to differences in the solar radiation between
solar maximum and solar minimum temperature changes by over 100 K occur in
the lower thermosphere. Further, they showed the occurrence of tropospheric wind and temperature
changes due to changes in solar radiation. But they also mention that changes
in the climatology due to solar radiation are too complex to be explained by
simplified methods. showed that a solar cycle effect
between 2002 and 2013 led to changes in the neutral density within the MLT
region by up to 2.5 %. Furthermore, satellite measurements showed on
global scales a neutral density decrease by up to ∼30 % between
solar maximum and solar minimum at about 400 km . For the
2009–2010 winter season, showed a connection between the
neutral density and the expansion–shrinking of the atmosphere by using meteor
radar (MR) winds, lidar, and Microwave Limb Sounder (MLS) satellite
temperature measurements. Further, they showed a strong anti-correlation of
neutral air density and prevailing zonal winds. This indicates that an
increase/decrease in the neutral density occurs almost simultaneously with a
decrease/increase in zonal wind speed, respectively.
Schema of Earth and Sun correlation and the resulting effects on the
thickness of the atmosphere and the Earth's rotation velocity.
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Changes in the thickness of the atmosphere, resulting from differences in the
distance between the Earth and Sun as well as from solar cycle effects, go along
with changes in the Earth's rotation speed. Based on the conservation of
angular momentum L, the angular velocity ω for an altitude-defined
atmospheric layer a, with the thickness ao-ai, can
be estimated by
L=Jω=25mao5-ai5ao3-ai3ω,
where J is the moment of inertia for a spherical shell, which rotates about
an axis through the center; ai and ao are the inner and outer radius
of the spherical shell; and m is the atmospheric mass. On this occasion the
atmospheric mass is calculated according to by
m=∫r0∞∫02π∫-π/2π/2ρr2cosϕdϕdλdr,
where ρ=ρ(λ,ϕ,r) is the density of air at longitude
λ and latitude ϕ, and r is the distance from the Earth's
center, while r=r0 at the surface of the Earth. In a good
approximation the Earth's surface can be described as an ellipsoid r02=a2(1-2αsin2ϕ), where a is the equatorial radius,
α=(a2-b2)/2a2 is related to the flattening, and b is
the polar radius. With respect to the height above the surface z, this
results in r2=(a+z)2(1-2αsin2ϕ) and
dr=(1-2αsin2ϕ)12dz.
Further, under the assumption that ρ=ρ1(r)ρ2(λ,ϕ), the atmospheric mass can be derived by
m=∫02π∫-π/2π/2[∫0∞ρ1(z)a+z2dz]ρ2(λ,ϕ)1-2αsin2ϕ32cosϕdϕdλ.
The integral with respect to z and the relation to the measurements of the
surface pressure ps can be estimated by solving
ps=∫0∞ρ1(z)g(z)dr,
where g is the acceleration due to gravity. Considering that g is a
function of height and latitude, the total atmospheric mass can be written in
numerical terms as m=5.22371×1015p‾s,
where m is given in kilograms and p‾s is given in
hectopascal, for standard gravity at 45∘ latitude. More detailed
information about the estimation of the total mass of the atmosphere can be
found in . According to the
total mean mass of the atmosphere is 5.148×1018 kg and varies
slightly on annual scales mainly due to the amount of available water vapor.
A method to measure variations in the rotation speed of the solid Earth is
estimating the time the Earth needs for a full rotation. In the following, we
define the crust, mantle, and core of the Earth as solid Earth. To estimate
the percentage of the atmospheric rotation velocity from the solid Earth
rotation velocity, their rotation rate and their variations are necessary.
The time the Earth needs for a full rotation is not constant. The rate of
rotation and the orientation of the Earth's axis varies in time and space.
Perturbations in the Earth's rotation rate are caused either by external
forces, such as the influence of celestial bodies, or by internal torques,
which are large-scale geophysical processes .
These internal torques are a combination of relative movements and mass
reallocation of Earth's core, mantle, crust, oceans tides, and the
atmosphere. Geographical differences in wind pattern and oceans cause shifts
in the air and in the water masses. Earthquakes displacing the Earth's mantle
might also influence the Earth's rotation on longer timescales
.
On timescales less than a year the dominant geophysical process to influence
the duration of the Earth's rotation is the atmosphere .
Every large-scale momentum exchange in the Earth's atmosphere on the Earth's
surface increases or decreases the Earth's surface rotation, due to the law of conservation
of total angular momentum within its system. The total angular momentum of
the Earth's atmosphere M can be approximately written as
M=∫vρapcLapcdV=∫vρapcr×(urel+ω×r)dV,
where Lapc is the angular momentum of an air parcel of unit mass,
ρapc the density of the air parcel, urel the
relative velocity, and ω×r the velocity due to the rotation
of the Earth .
The total angular momentum and the velocities can be split into two parts.
The mass part Mω represents the value the angular momentum would
take if the atmosphere were vertically and horizontally stationary relative
to the ground, and the relative part Mr describes the part of the
atmosphere angular momentum that is due to the motion of the atmosphere
relative to the Earth's rotation. Following ,
, and these parts of angular momentum
can be written as
M=Mω+Mr=r4ωg∫02π∫-π/2π/2psfccos3θdθdλ+r3g∫01000∫02π∫-π/2π/2urelcos2θdθdλdp.
Thus, changes in the atmospheric angular momentum depend on the sum of
different torques dM/dt=TF+TM+ others. Here TF is the friction torque, TM is the
mountain torque, and others torques include, for example, the gravity wave
torque, which is small compared to the other two mentioned. The friction
torque is exerted on the Earth's surface mainly due to frictional forces
between the wind and the surface. If eastward-directed surface winds are
prevailing on a global scale, this torque leads to an increase in the
rotation rate due to a transfer of angular momentum from the atmosphere to the
Earth's surface. The mountain torque is based on the surface pressure and
orography, and it is the torque which is exerted on the Earth's surface due
to a difference in pressure on two sides of a mountain. Both torques vary
according to their global location and reach values in the range of
1019 Nm . The dominant
exchange of the angular momentum between the atmosphere and Earth takes place in
the atmospheric boundary layer, which, depending on the orography and
latitude, has a typical thickness of about 1 km at midlatitudes
.
Already in the 1960s and 1970s scientists showed that fluctuations in the
orientation of the Earth's rotation axis, on seasonal timescales, are
associated with changes in the east–west tropospheric wind on a global scale
and therefore accompanied with a transfer of angular momentum between the
Earth's crust and the atmosphere (). Changes
in the speed of the Earth's rotation axis can be seen in fluctuations in the
duration around a day. These fluctuations have been measured since the 1960s
using the very long baseline interferometry (VLBI) technique. The fluctuation
in the day length is the difference between the astronomically determined
duration of a full day 2π/D and the standard 86 400 s, whereby
D is the angular velocity . Henceforth, we use the
acronym LOD for the fluctuations in the length of day. The LOD can be written
as
LOD(t)=2πD-86400s.
Within the estimation of the LOD the sidereal time gets converted into solar
time, by taking into account the Earth's position, nutation, precession, and
motion with respect to the stars. Detailed information about the
transformation from sidereal time into solar time can be found in
e.g.,.
studied the influence of geophysical processes of the
atmosphere on the duration of a day. They showed that, when the globally
averaged mean winds from east to west increase, the rotation rate of the
Earth decreases and the day gets longer. showed that the
effect of the wind on the LOD decreases with heights, by showing that winds
in the atmospheric layer between 1000 and 10 hPa contribute 0.5 ms, winds from
10 to 1 hPa contribute 0.03 ms, and winds above 1 hPa contribute less than
4 µs to the interannual LOD budget. The impact of large-scale
geophysical processes like El Niño e.g.,
and the stratospheric quasi-biennial oscillation (QBO) can also be seen in
the LOD (e.g., ).
On short timescales a change in the Earth rotation can lead to an uneven
heating of the Earth's surface, which results in temperature differences
between the surface and the atmosphere above. This can further cause
convection currents, which leads to pressure differences in the atmosphere
and results in a different wind formation, which can influence the day
length. The influence of the solar radiation is stronger for higher altitudes and also for longer time series.
An increase in the solar radiation, which can be caused due to a slowing of the Earth's rotation, leads to an
expansion of the higher atmosphere, which further results, due to the
conversion of angular momentum, in a slower rotation of the atmosphere.
What further needs to be considered is, for example, the influence of volcanic
eruptions, which influence the Earth's rotation as well as the atmospheric
chemistry and temperature e.g.,. Changes in these parameters
can further lead to changes in the neutral density.
Within this study, we focus on heights between 60 and 100 km. These heights
are sensitive enough to density changes due to the changes in the intensity
of solar radiation. After we describe the data we used in this study in
Sect. 2, we show results and discuss the theoretical change in the rotation
speed due to an expanding–shrinking atmosphere in Sect. 3. We will show that
due to the expansion–shrinking effect, even under the assumption of equal
density distribution between the Northern and Southern Hemisphere (SH),
differences in the prevailing wind occur. Furthermore, we will show a
connection between the LOD and the prevailing wind by showing correlations in
the MLT region by using MR and MLS data for one polar and two midlatitude
locations. We use the LOD data to show how deep the influence of solar
radiation penetrates into the atmosphere. The conclusions are found in
Sect. 4.
Data
The wind data we use in this study are derived from MR and MLS satellite
measurements. The MRs are located at the northern high-latitude station
Andenes (32.5 MHz; 69.3∘ N, 16.0∘ E; Norway), the
midlatitude stations Juliusruh (32.5 MHz; 54.6∘ N,
13.4∘ E; Germany) and Collm (36.2 MHz; 51.3∘ N,
13.0∘ E; Germany) on the Northern Hemisphere, and the southern
high-latitude station Davis (33.2 MHz, 68.6∘ S, 78.0∘ E,
Antarctic). The radars cover an altitude range between 75 and 110 km and the
obtained winds have an hourly temporal resolution and a vertical altitude
resolution of 2 km in the applied analysis. At 90 km altitude, the observed
volume of each radar has a diameter of approximately ∼400 km, and the
mean wind above each station is a weighted average over this volume. In the
case of the Andenes, Davis, and Collm, MR data are available between 2005 and
2016 and for Juliusruh since 2008. We focus on an altitude range between 78
and 100 km where we obtain continuous measurements. The statistical
uncertainties of winds are obtained from a fitting procedure by taking into
account the number of detected meteors per altitude and time bin, as well as
a full nonlinear error propagation of the radial wind errors. Therefore the
resulting uncertainties for the hourly winds vary in a range between 2 and
6 m s-1 with larger errors at the upper and lower part the of the meteor
layer. More information about the all-sky meteor radars and the wind
estimation method used can be found in ,
, and . For this research, we focus
primarily on the zonal wind component, because a connection between winds and
changes in day length will be mainly seen in the main rotation direction of
the Earth.
In addition to local radar observations, we use satellite data from the
Microwave Limb Sounder to extend the vertical coverage. MLS onboard the
Aura satellite () has a global coverage
from 82∘ N to 82∘ S and an useful height range from
approximately 11 to 90 km (261 to 0.001 hPa). The vertical resolution
varies between ∼4 km in the stratosphere and ∼14 km at the
mesopause . The geometric heights are approximately
estimated from pressure levels as described in : h=-7⋅ln(p/1000), where h is the altitude in km and p the pressure in
hPa. Furthermore, we are aware about a difference between the geometric and
geopotential heights, which increase especially above 80 km. Therefore, we
focus in this work on the height range between 60 and 80 km (if not otherwise
specified) to investigate a connection between the LOD and the density
depending on zonal wind within these heights. Daily quasi-geostrophic winds for
the years between 2005 and 2016 are derived from MLS geopotential height
observations. For this study we use three different horizontal grids which
are located around Andenes (70∘ N and 0–20∘ E) and around
Juliusruh and Collm (50–60∘ N, 0–20∘ E), which are further
referred to as northern high- and midlatitude stations, respectively. For the
SH we use a horizontal grid around Davis (70∘ S,
60–80∘ E).
Further we use in this study combined data from the international Earth
Rotation and Reference System Service . The use of interferometry
between several stations, which observe radio sources, leads to fundamental
geodetic information such as changes in the Earth's spinning or in the Earth
orientation (). Based
on this information the mean rotation rate and the astronomical duration of
the day were computed according to Eq. () . The
IERS provides uncertainties for the day length measurements, which most of the
time vary by ∼5 %. More information about the data provided by
IERS and their algorithm to estimate the duration of a day can be
found in .
Composites of zonal wind for the Northern Hemisphere stations
Andenes (a), Juliusruh (b), and Collm (c).
(d) shows the southern-hemispheric station of Davis. The
composite for Andenes, Collm, and Davis includes 12 years of meteor radar data
and that of Juliusruh includes 9 years. Positive values correspond to
eastward-directed winds and negative to westward-directed winds.
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Results and discussion
LOD and neutral air density at the MLT
Figure shows composites of zonal winds from MR
measurements at Andenes, Juliusruh, Collm, and Davis. These data are
estimated by using a mean wind adaptive spectral filter .
It uses a 1-day sliding window, which mainly removes the impact of short-term
variations, such as atmospheric tides and gravity waves. All three NH stations
show almost similar wind patterns, with typical mesospheric eastward-directed
winds during the winter, with mean values of up to 10 m s-1, and a
wind reversal during spring. The spring wind reversal occurs earlier at
midlatitudes than at polar latitudes. During the summer considerable vertical
wind shear is present with westward-directed winds below 90 km for Andenes,
below 88 km for Juliusruh, and below 85 km for Collm. Above these heights a
strong eastward jet occurs. The westward and the eastward jets reach wind
values of up to 40 m s-1 at all three locations. These annual wind
climatologies are consistent with previous studies, e.g., ,
, and . Compared to Andenes a nearly
opposite wind pattern can be seen for Davis. A dominant eastward-directed
wind occurs between March and September for the complete observation range.
Between September and March a vertical wind shear occurs, which reaches
heights above 100 km around October. Compared to the NH stations the summer
vertical wind shear remains mainly below 90 km.
Composite of zonal wind for the high-latitude location (a) and
midlatitude location (b). The composite of both figures includes
12 years of wind data derived from MLS geopotential height data.
Positive values corresponds to eastward-directed winds and negative to
westward-directed winds. The altitude is given in geopotential height.
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Besides the radar data, we additionally use MLS data within this study to
extend the vertical coverage down to 60 km. In
Fig. the zonal wind is shown for the
high-latitude location of Andenes, for middle latitudes at Collm, and for the
southern latitude location Davis. The altitude ranges between ∼60 and
∼90 km geopotential height. A comparison of the MLS composite winds
with MR composite winds results in a qualitatively good agreement for the
seasonal amplitudes and phases. Both NH locations show eastward-directed
winds between September and April for nearly all altitudes, with values of up
to 40 m s-1 for the high-latitude area and up to 60 m s-1 for
the midlatitudes. During summer westward-directed wind dominates below 95 km
and reaches values of up to 30 m s-1 for the high latitudes. For the
middle latitude, below 90 km, the wind reaches values of up to
50 m s-1. A similar pattern of an eastward-directed wind occurs in
both cases during summer above 90 km geometric height. The SH location also
shows a similar wind pattern to the observed MR data. In the following
discussion we will focus on the MLS altitude range 60–80 km and use the MR
data for the altitudes between 80 and 100 km.
According to previous studies such as and
, a connection exists between the thickness of an
atmospheric layer and the density fluctuation within that layer.
explained the occurrence of this connection by showing
variations in the neutral density, based on MLS and MR observations, together
with changes in the MLT geometric height. Furthermore they showed a strong
anti-correlation between the simultaneous occurrence of the zonal wind and
the density change within the mesosphere.
Theoretical change in the rotation speed (left side) for a rigid
atmospheric layer. In black we show the theoretical rotation speed of the Earth's
atmosphere and in colors the change due to a density increase of 1 %
according the legend. On the right side the density progress is shown for
specific altitudes.
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To underline this statement, we show in the following part the connection
between the expanding MLT and the atmospheric rotation speed.
Figure shows, as an example, the theoretical
variation in the atmospheric rotation velocity with height due to a density
increase up to 1 % between 70 and 100 km. The calculation is done in
2 km height layers and for the latitude of 45∘. Different latitudes
lead to slightly different values of g, which is used in Eq. ().
The density increase takes place for longer timescales during a solar
maximum e.g., and on annual timescales during the
winter, when the Earth–Sun distance is smaller. Both cases influence the
temperature within this atmospheric layer as well as their expansion compared
to the annual mean. Overall the density variation during an 11-year solar
cycle is stronger than the variation caused by the changes in the Earth–Sun
distance. According to Eqs. ()–(), we estimated for
three different cases (linear, red; exponential, green; and a Gaussian-shaped, blue, density increase)
the resulting theoretical change in the rotation
speed within these heights, with the solid Earth rotation speed (black) as
background flow. Based on the conserved quantity of the angular momentum
within a narrow atmospheric layer (2 km vertical) this sums up, according to
each case, to a decrease in the rotation speed by up to
∼2–4 m s-1, with the strongest variation within the Gaussian-shaped curve.
These results fit to the observations by
and show the dependence of the rotation speed within an atmospheric layer due
to changes in the neutral density. However, we are not able to extract a
specific wind value only based on wind measurements.
Based on ERA40 data, showed that the global mean of
the surface pressure is nearly constant, and surface pressure anomalies at
the Northern and the Southern Hemisphere are nearly identical, but the
fluctuations are opposite in sign. These anomalies are mainly due to the
changing amount of available water vapor in the atmosphere. Under the
assumption of opposite surface pressure anomalies within both hemispheres and
therefore by neglecting other factors such as different gravity wave forcing
between the hemispheres, we assume, on annual scales, similar pressure values
within the MLT region. Therefore the prevailing wind within the MLT region
should be similar in magnitude between Andenes and Davis, which are located
at the same latitude in the Northern and Southern Hemisphere. To underline
the influence of the intensity of the solar radiation on the density and also
on the amplitude of the zonal wind, we compare the evolution of the seasonal
mean wind measurements from the NH station Andenes (69.3∘ N) and SH
station Davis (68.3∘ S). Figure shows, for
both stations, the winter and summer mean wind for the altitudes at 88 and
96 km. The northern winter includes the mean of the months of December,
January, and February and the southern winter the months June, July, and August. The
northern winter period comes along with the perihelion, which is the point
where the Earth comes nearest to the Sun. At the perihelion, the intensity of
the solar radiation on the upper atmosphere is stronger during the aphelion.
While during the winter season the wind values are higher over Davis for both
altitudes, they are higher over Andenes during the summer season, especially
at 96 km, with values of up to 10–20 m s-1. Both seasonal wind
differences are consistent with the change in the average density within the
upper mesosphere, resulting from the different distance between the Earth and Sun
and leading to the variation of the averaged zonal wind, as shown in
. We have to note that others factors exists, which are
more dominant for the wind differences between both locations at theses
altitudes. Other physical processes also have a strong effect on the
hemispheric wind differences, e.g., the topography, chemical composition of
the atmosphere (), and the occurrence and
propagation of gravity waves. These waves are the main drivers of the
atmospheric wind circulation and therefore also influence the local wind
differences at both hemispheres. Furthermore, gravity waves lead, compared to
the annual mean, to a colder summer mesosphere and a warmer winter mesosphere
e.g.,. These temperature differences also fit well to
the atmospheric expansion–shrinking. Unfortunately, we are not able to estimate a precise value
on how strong the connection is between mean zonal wind and the LOD based only on wind
measurements. For a more detailed
understanding of these phenomena global density observations would be
required.
Zonal wind amplitudes for the winter and summer season at 96 and 88 km
for Andenes and Davis.
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Correlation of mean winds and LOD
In the following we want to show that the LOD (fluctuations in the length of
a day) correlates with the prevailing wind from the four stations. If the
Earth's rotation is constant the LOD should be zero; however, small wobbles
of the Earth's rotation between the days cause tiny fluctuations in the day
length. These have to be compensated for by a momentum transfer between the
different parts of the Earth including the atmosphere. As the atmosphere is
slaved to the Earth crust, because the atmospheric momentum and mass are much
smaller than that of the Earth core, the atmosphere has to respond to changes
in the rotation velocity. So far we use the LOD explicitly as reference for the
changes in the rotation speed, which can be seen in the zonal wind, as well
as to verify up to which height the solar-driven density effect is dominant.
Therefore, Figs. and
show wind values for Andenes, Collm, and Davis at different altitudes and the
LOD by using the same filtering method as done for the winds. Two different
altitudes in the MLT are considered from the MR winds for all locations:
(1) 80 km, where within a year a change between eastward- and
westward-directed wind occurs; and (2) 96 km, which is the altitude where the wind, during
each hemispheric summer, shows the opposite direction compared to at 80 km (see
Fig. ). Positive wind values correspond to
eastward-directed winds and positive LOD values correspond to a longer duration of the
day. If not explicitly mentioned, the results of the two midlatitude
stations are nearly identical. Therefore we only show the results for the
location around Collm.
Smoothed zonal wind (blue) values based on meteor radar wind data at
80 km and smoothed LOD (black) values. The modulation of the smoothed zonal
wind is displayed in red after removing the impact of the solar cycle. All curves are done by
smoothing over several days, without removing the day-to-day variations, to show the
seasonal pattern of the parameters. The dashed lines correspond to the
tendency of the wind and LOD based on linear regression.
![]()
Same as Fig. , but for 96 km.
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At 80 km (Fig. ) the oscillation pattern of the
smoothed zonal wind (blue) and the smoothed LOD (black) are similar for
Andenes. According to previous studies the LOD consists of superpositions of
several periods, such as 0.5 years, 1 year see also, 2–3 years , 5.9 years ,
and others (e.g., ). According to an
accurate estimation of the impact of the solar radiation is quite
complicated, due to the fact that internal oscillations in the climate system
show variations with the same frequency as the 11-year solar cycle. Further,
support this statement and mention that the problem is
further complicated due to the small influence of the solar forcing on the
climate. Nevertheless, showed that, based on a
decomposition of the LOD, the solar activity (10.47 years) is included. Also
the zonal wind includes a superposition of several periods such as the solar
cycle, diurnal and semidiurnal tides, and more (e.g.,
). Therefore, we additionally show with
the red line a smoothed zonal wind after removing variations due to the
11-year solar cycle. The influence of the solar cycle on the daily zonal wind
is relatively small; therefore the smoothness of the red line is enhanced for
better visualization. Changes in the LOD are sluggish compared to variations
in the wind, due to the amount of momentum which is needed to influence the
Earth's rotation speed. According to , a direct
effect between the stratospheric and tropospheric zonal wind and the day
length exists on annual timescales due to long-term geophysical effects, such as
QBO and El Niño. They found that the stratosphere cannot be
neglected in the Earth's angular momentum. Around 20 % of the LOD
relative to the atmosphere below 100 hPa belongs to the impact of the
stratosphere. Furthermore, they mentioned a small lag (10–20 days) between
the LOD and variations in the angular momentum, but the lag does not appear
to be statistically significant. Therefore only comparisons on seasonal and
longer timescales are useful to consider. All parameters which are
displayed in Fig. show a seasonal pattern. First we
describe the results for the NH stations. For the NH the zonal wind and the
LOD show decreasing values during summer and increasing values during
winter. Beside the striking seasonality, short time fluctuations within a
year are observable during the winter in the zonal wind for some years.
During the winter of 2010 and 2011, and on even shorter timescales such as a few
months during the winter 2006, 2014, and 2015, decreases in the LOD together
with decreases in the zonal wind are visible. The LOD varies between -1 and
4 ms. The LOD oscillation shows seasonal variations of a fluctuation with
shorter day lengths during NH summer and longer day lengths during winter,
which fits to the density increase and decrease in the MLT as described
above. For the midlatitude station the oscillation patterns in the LOD and the
wind are qualitatively similar, but shifted in time. The wind peaks occur
earlier in the year than the LOD peaks, which goes along with the earlier
wind transition at midlatitudes that can be seen in
Fig. . For Davis a time shift of approximately 6 months
occurs between the zonal wind and the LOD, due to the opposite seasonal wind
pattern.
Zonal MLS wind (red) and LOD (black) at ∼80 km geometric
height for 0–20∘ E. The left part shows the values for the Southern
Hemisphere and the right for the Northern Hemisphere for every 10∘
latitude. The black correlation coefficients (r) are estimated for the mean
between 0 and 20∘ E, and the green coefficients correspond to the
global average over all longitudes.
![]()
Correlation coefficients between the zonal wind and the LOD. Positive values corresponds to the occurrence of
an eastward-directed mean zonal wind together with a positive fluctuation in the LOD.
Altitude (km)
80
82
84
86
88
90
92
94
96
98
Andenes
0.57
0.56
0.52
0.42
0.21
-0.13
-0.45
-0.61
-0.67
-0.69
Juliusruh
0.43
0.36
0.23
0.04
-0.23
-0.48
-0.62
-0.67
-0.68
-0.68
Collm
0.3
0.19
-0.01
-0.3
-0.54
-0.65
-0.68
-0.68
-0.66
-0.64
Davis
-0.37
-0.37
-0.38
-0.39
-0.41
-0.42
-0.41
-0.38
-0.35
-0.32
In the summer wind transition altitude, a time shift occurs between both
parameters. The altitude of the wind transition in these cases is defined as
the height between the above-located eastward and the below-located westward
wind during summer. At these heights the wind and the LOD are almost
uncorrelated. Above the summer wind transition altitude the oscillation
patterns between the LOD and the winds are quite opposite to those for 80 km
altitude, with a 180∘ shift between both parameters, which can be
seen in Fig. . The phase shift, which is pronounced
during the summer, obviously results from the opposite wind regime compared
to the 80 km altitude. Nevertheless, above the transition height, changes in
the density, due to the intensity of the solar radiation, are more pronounced
than at lower heights. Therefore the existing seasonal wind pattern fits well
to the atmospheric density increase and decrease at these layers.
Additionally, we show in Table correlation coefficients for
the four locations for the altitudes between 80 and 98 km. Positive correlation
values correspond to the occurrence of an eastward-directed wind together
with an increased LOD. The values of the NH follow a similar pattern, with
positive coefficients below the vertical transition height and negative ones
above. Davis shows a different pattern, with overall negative correlation
coefficients. This is owing to the opposite zonal wind pattern compared to
the NH. Theoretically, a time shift of ∼6 months would lead to a
similar correlation pattern to that in the NH.
Annual mean values for the LOD (black) and the zonal wind (red), for
the station Collm, after removing seasonal variations and the solar cycle for
the altitudes between 80 and 100 km. The error bars correspond to the
standard deviation. The dashed lines represents the tendency.
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Same as Fig. , but for Davis.
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Figure shows the mean zonal wind at ∼80 km geometric
height, based on MLS data, and the LOD. These mean zonal winds include wind
values within the longitude grid between 0 and 20∘ E, which is
comparable to the NH stations. The figure is divided in 10∘ latitude
steps centered at latitudes from 80 to 10∘ S/N. Each latitude grid
includes values for ±6∘. For the MLS observations the comparisons
between the wind and the LOD are similar to the 80 km meteor results at the
respective latitudes. Furthermore, the occurrence of a time shift of 6 months
between both polar hemispheres can be seen. A 180∘ phase shift would
lead to the wind–LOD pattern of the opposite hemisphere. Furthermore, the
strongest correlation between both parameters can be seen at northern polar
latitudes. Due to an increase in the difference between the geometric and
geopotential heights, we do not show comparisons for higher altitudes. We
added correlation coefficients (black) between the mean zonal wind and the
LOD for each latitude. A correlation increase towards the northern high
latitudes is visible. The same would be seen if a 180∘ phase shift is
added to the time series. Additionally, we present global correlations
(green) by averaging mean zonal wind data over all longitudes, whereby
possible stationary planetary waves are filtered. The global correlation
coefficients are nearly similar to the values for previous average winds
between 0 and 20∘ E. The shape of the curves between the global average
winds is also nearly equal; therefore we did not add them in the figure.
In Figs. and , long-term
changes in annual LOD (black) and annual mean zonal winds (red) are shown for
Collm and for Davis. At this point, we have to mention that the tendency over
a long time series is not linear in time. Parameters which influence the
tendency of the wind and the LOD also vary over time. Such changes are often
approximated by a piecewise linear trend model (e.g., ), where different linear fit tendencies are
estimated for different time periods. Nevertheless, due to the length of the
available data series we decided not to use a piecewise linear trend model.
The wind values exclude seasonal and solar cycle variations and the LOD
excludes the seasonal variations. As an example for the location of Collm
(Fig. ), the altitudes between 80 and 96 km are
displayed. The error bars correspond to the annual variance for each height
and the dotted lines show the long-term tendency for each parameter.
Figure shows that a long-term increase in the LOD
occurs together with a long-term decrease in the zonal wind. Above 94 km the
tendency reverses into a slightly positive wind. This reversal can be
explained by the stronger influence due to gravity wave filtering, which has
to be considered and cannot be excluded by filtering the data. The tendencies
of an increased value for the LOD and a decreased value for the mean zonal
wind can be seen for all midlatitude locations and also for Davis (see
Fig. ). Andenes shows for all altitudes an
increased tendency in the zonal wind (not shown). The results indicate that the
connection between the LOD and the wind is more pronounced at lower
latitudes and is simply explainable by the rotation velocity, which is
higher at the middle latitude stations than at the polar latitudes like at
Andenes and Davis. The results of an increase in the LOD and a decrease in
zonal wind agree with the relation between fluctuations in the neutral
density and the zonal wind, as shown in .
Conclusions
Within this work we show that the mesospheric winds are affected by an
expansion–shrinking of the upper atmosphere that takes place due to changes
in the intensity of the solar radiation, which affects the density within the
atmosphere. A reason for this, besides the solar cycle effect, is the annual movement
of the Earth around the Sun, which leads to a shorter distance between both
celestial bodies during the NH winter and a longer distance during summer.
This leads to a shrinking/expansion of the atmosphere during the NH
summer/winter. This shrinking effect mainly takes place in the upper
atmosphere, where the amount of mass is small enough to be sensitive enough
to changes to the intensity of solar radiation, as well as temperature
changes. According to an increase in the neutral density
together with a decrease in the zonal wind in the MLT region occurs. Based on
these findings we showed that a theoretical density increase of 1 %
between 70 and 100 km leads to a decrease in the atmospheric rotation speed,
within a defined layer, of up to 4 m s-1. The influence of the
Earth–Sun distance on the wind speed was further investigated using winds
from four stations in total, whereby two stations are located at similar high
latitudes for the Northern and Southern Hemisphere. The other two meteor
radar systems are located at the northern midlatitudes. Based on summer and
winter mean wind, we found that during the perihelion, where the MLT expands,
a decrease in the zonal wind speed for the respective location occurs
together with an increase in the LOD. During the opposite aphelion, an
increase in the zonal wind occurs beside a decrease in the day length.
Further, we showed that even after removing the seasonal and the 11-year
solar cycle variations the zonal wind and the LOD (fluctuations in the length
of a day) are connected. We showed on the basis of annual timescales
that an increase in the LOD occurs together with a
stronger pronounced westward-directed wind for the middle latitude locations.
This effect is weaker at the polar station and is, on the one hand,
due to a smaller radius, which affects the rotation speed of the atmospheric
layer. On the other hand, there are further natural factors, such as the
gravity wave drag, that strongly influence these tendencies. Further, we were
only able to investigate the connection between these parameters on timescales which are at least 1 year.
On shorter timescales a connection
between the LOD and the winds cannot be figured out; the LOD consists of
oscillations with at least a 6-month period and with the currently
available data we are not able to fully resolve the superpositions of both
parameters. Future work remains necessary to fully understand these effects
when global density data measurements are available. Additionally, in future
work the estimation of a time lag between the LOD and the winds needs to be
considered.
We want to mention that based on our findings a connection between the zonal
wind and the LOD exists, which we explain by the variation of the available
atmospheric density. Furthermore, we only compare global LOD data with local
measurements, and within the MLT stronger geophysical effects which
drive the wind regime at these altitudes exist. Within this work we only want to
point out this effect, and for closer investigations we need global longtime
density data.