Reference simulation: TDT climatology
The REF simulation includes solar, nonlinear and gravity wave forcing for all
wave numbers. Therefore, it serves as a reference for all the experiments. The
following results are given as a mean of the 11 ensemble members, owing to
the nudging of reanalysis data for the years 2000–2010 (color shading)
with the respective standard deviations (contour lines).
In Fig. we provide a background climatology of the MUAM
zonal mean circulation for solstice (Fig. a–c) and
equinox (Fig. d–f) for the parameters zonal wind (a, d),
meridional wind (b, e) and temperature (c, f). The color coding denotes the
11 year means, while the standard deviations are given as black contour
lines.
Comparing the MUAM climatology with empirical climatologies such as CIRA86
, the radar based GEWM or the
satellite based UARS we find good agreement but
with slightly larger westerly jets and weaker easterly jets during January in
MUAM.
Terdiurnal component of thermal tendency terms in the REF simulation
for January conditions (a, c, e, g) and April conditions (b, d, f, h). Amplitudes are
scaled by exp{-z(2H)-1}. Results are an average of the 11 ensemble
members (color shading). Standard deviations (σ) are added as gray
contour lines. (a, b) Temperature advection (nonlinear component
of Eq. ), (c, d) adiabatic heating (nonlinear component of
Eq. ), (e, f) heating due to gravity wave activity (tendency term
from gravity wave parameterization), and (g, h) solar heating (tendency term from
solar radiation parameterization). Note that the color scale is not linear.
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Terdiurnal component of zonal and meridional wind acceleration terms
in the REF simulation for January conditions (a, c, e, g) and April conditions
(b, d, f, h). Amplitudes are scaled by exp{-z(2H)-1}. Results are an
average of the 11 ensemble members (color shading). Standard deviations
(σ) are added as gray contour line. (a, b) Zonal wind
advection (nonlinear component of Eq. ), (c, d) meridional wind
advection (nonlinear component of Eq. ) and (e, f) zonal and (g, h) meridional
acceleration due to gravity waves (tendency terms from gravity wave
parameterization).
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We notice that the model produces small year-to-year variations below
100 km in the Southern Hemisphere and south of 30∘ N. There, the
standard deviation σ is very small, mostly below σ(T)=1 K
(σ(u)=2 m s-1, σ(v)=0.25 m s-1). Model variations
for middle and high latitudes in the Northern Hemisphere are larger with
standard deviations up to σ(T)=6 K (σ(u)=12 m s-1,
σ(v)=2 m s-1) during January and σ(T)=2 K
(σ(u)=2 m s-1, σ(v)=0.75 m s-1) for April. Maxima
of the standard deviation are located at about 60∘ N. These
variations have their origin in the year-to-year variability of the polar
vortex for which a range of several K, especially during winter, is
realistic. Due to the fact that MUAM assimilates the zonal mean temperature
up to 30 km altitude, this model variability represents a realistic
atmospheric variability, too.
Figures and show the terdiurnal
component of all forcing terms that our analysis takes into account, namely
solar forcing, nonlinear forcing and forcing due to gravity wave–tide
interactions. All forcing terms are scaled by exp{-z(2H)-1}. This
factor is associated with the conservation of wave energy which normalizes
the wave growth with height due to the decrease in density. Therefore, the
figures show the source region of tidal excitation but they do not provide
any information about propagation conditions.
Figure refers to thermal parameters including temperature
advection (a, b), the nonlinear component of adiabatic heating (c, d), heating
due to gravity waves (e, f) and direct solar heating (g, h). Note that the
color scales in Fig. are equal but not continuous in order
to cover the magnitudes of all forcings while keeping them comparable to each
other. For the thermal forcing of the TDT it can be seen that the direct
solar forcing dominates in the troposphere and stratosphere. This is because
of the strong absorption of solar radiation by tropospheric water vapor and
stratospheric ozone. In the mesosphere (80–100 km), nonlinear effects
are mainly responsible for the forcing of terdiurnal fluctuations. Due to
absorption of EUV radiation, there is again some solar forcing in the lower
thermosphere (Fig. g, h at about 120 km altitude) that is
comparable to nonlinear thermal forcing (Fig. a, b). In this
region, heating due to gravity wave effects (Fig. e, f)
plays a major role. The nonlinear adiabatic heating effect
(Fig. c, d) is weak everywhere compared to the other
forcings and will therefore be neglected in our further considerations.
Figure is similar to Fig. but refers to
wind parameters. These are also scaled by the amplitude's growth rate
exp{-z(2H)-1}. The figure shows nonlinear zonal (a, b) and meridional
(c, d) wind advection as well as zonal (e, f) and meridional (g, h) acceleration
due to gravity waves. In the zonal wind, in the troposphere and stratosphere,
the nonlinear forcing is clearly dominating over gravity wave effects. Zonal
gravity wave forcing becomes strong above 100 km. In January, there is an
additional maximum of gravity wave induced terdiurnal forcing
(Fig. e) near 80 km between 30 and 60∘ N
which cannot be observed in April (Fig. f). For meridional
wind patterns, gravity wave forcing only plays a role between 80 and
100 km (Fig. g, h), its magnitude being comparable to
those of the advective nonlinear forcing (Fig. c, d). In the
stratosphere and mesosphere, nonlinear advection is the most important source
for the meridional component.
Generally, direct solar forcing is weaker during April
(Fig. h) than during January (Fig. g),
but most nonlinear forcings (Figs. a, b and a–d) become stronger in April and are therefore more
dominant during an equinox.
Product of DT and SDT amplitudes, scaled by exp{-z(2H)-1}
for temperature (a), zonal wind (b) and meridional wind (c); January
conditions. Results are an average of the 11 ensemble members (color
shading). Standard deviations (σ) are added as gray contour lines.
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As described above, the nonlinear terdiurnal forcing is a result of
interactions between the migrating DT and the migrating SDT. These
interactions can only take place if both DT and SDT have a considerable
amplitude. To test this relation between the different harmonics, the product
of DT and SDT amplitudes serves as a proxy for the terdiurnal nonlinear
forcing. Due to the fact that the forcing terms in Figure
are scaled by the growth rate of the amplitudes, we also scaled the product
of DT and SDT amplitudes to show the source region of the possible nonlinear
interaction. As an example, Fig. shows the results for
temperature (a), zonal wind (b), and meridional wind amplitudes (c) during
January.
Zonal mean TDT amplitudes (colors, REF). (a, d) Temperature, (b, e) zonal wind,
(c, f) meridional wind. (a–c) Solstice (January) conditions.
(d–f) Equinox (April) conditions. Standard deviation (σ) are added
as gray contour lines.
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It can be seen that the scaled product of DT and SDT amplitudes exhibits
similar structures to the nonlinear terdiurnal forcing terms in
Figs. a and a, c. For example, the
zonal and meridional component (Fig. b, c), have regions of
enhanced amplitude near 50 km extending from low latitudes poleward to
high latitudes and with a minimum over the equator. This is in good agreement
with the nonlinear zonal and meridional forcing in Fig. a, c.
The similarities for the temperature component (Figs. a and a) are less clear but we want to emphasize that the
multiplied amplitudes of DT and SDT only serve as proxy. The pure existence
of an overlapping DT and SDT source region does not necessarily induce an
interaction.
Zonal mean TDT phases (REF). (a, d) Temperature, (b, e) zonal
wind, (c, f) meridional wind. (a–c) Solstice (January) conditions. (d–f) Equinox
(April) conditions.
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TDT amplitudes are presented for January (Fig. a–c) and
April (Fig. d–f). In contrast to the forcing terms, they
are not scaled. Zonal wind amplitudes become stronger in April
(Fig. e) compared to January (Fig. b)
above 110 km but this is not the case for the temperature and meridional
wind amplitude. Amplitudes at 100 km altitude reach only about 1.5 K
and 4 m s-1 (zonal/meridional wind). This is much smaller than
observed by radars
e.g., and by
satellite measurements e.g.,.
They reported amplitudes of about 5–6 m s-1 at 90 km
during equinoxes and local winter with
a minimum during summer. These radars are located between 40 and 50∘ N and in these regions, Fig. also shows larger wind
amplitudes during winter and equinoxes. and
observe a maximum larger than 10 m s-1
(95 km) during autumn and early winter and a smaller one during spring. The
absence of a mid-winter maximum can be explained by the location of the
radars (>50∘ N) which is north of the region with a winter maximum
as can be seen in Fig. b, c.
However, considering only the maxima does not give a good comparison between
seasons, and the height-latitudinal structure is more important. Especially
in temperature (Fig. a) and zonal wind
(Fig. b) we note a double-peak structure in January with
maxima at very low latitudes and a minimum at the equator. This turns into a
triple-peak structure in April (Fig. d, e) with maxima
slightly more poleward (30∘ N or S) and directly at the equator. This
structure is also visible in SABER measurements reported by
for March and December. In the meridional wind, the
structure of the TDT is not as clear in January (Fig. c),
with several maxima between ±60∘ , the strongest one appearing
near the equator. In April (Fig. f), it has four distinct
peaks with maxima at low and midlatitudes but, in contrast to temperature and
zonal wind, a minimum at the equator. This pattern of superposed maxima on
minima and vice versa between the zonal and meridional wind components is
expected from the wave structure itself.
The standard deviation of tidal amplitudes is relatively small, not more than
10 % of the total amplitude. Thus, our results prove to be robust in
structure and strength.
REF monthly mean TDT amplitudes at an altitude of ≈106 km.
From left to right: (a) temperature, (b) zonal wind component, (c) meridional wind
component.
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The TDT phases are shown in Fig. . At each latitude, the
corresponding vertical wavelength can be obtained from the vertical phase
gradient. The wavelength is taken as the vertical distance between two points
of identical phases. A full span of phases should be covered between these
points, and for upward propagating waves, the phase gradient for the
determination should be negative. Where the amplitude is large, vertical
wavelengths turn out to be longer, i.e., the vertical phase gradients are
small. Where the amplitude is small, wavelengths are shorter with larger
phase gradients. , and
report a similar relationship with vertical wavelengths
being short in summer when the amplitude minimizes. Typically, the
wavelengths in Fig. reach 100 km and more. In January
(Fig. a–c), the structure of phases appears to be more
complex while in April (Fig. d–f) there are large areas
of constant phase, especially at low latitudes.
Figure presents the seasonal cycle of TDT amplitudes at an
altitude of 106 km. Results of satellite data analyses have frequently
been presented at 90 and 110 km
, and therefore we choose an altitude
between these heights. The temperature TDT at this altitude
(Fig. a) appears to be strongest during equinoxes near the
equator (3.0 K) and at midlatitudes (30–40∘ N or S). The
amplitudes in autumn (2.2 K) are larger than those in spring (1.6 K).
Further maxima are present during local winter at 30–40∘ N or S
(2.6 K at Northern Hemisphere and 2.3 K at southern Hemisphere).
For latitudes poleward of 50∘ N or S, amplitudes are much lower and peak during summer (<1.1 K).
The structure of MUAM temperature amplitudes is generally confirmed by SABER
measurements e.g., who reported
maxima of about 5 K during equinoxes near the equator at 90 km
altitude. Note that this amplitude is almost twice as large as the one
obtained from our model simulations even though the altitude is smaller. For
midlatitudes, also found maxima during northern winter
(3–4 K at 30–50∘ N, 90 km) but not during southern
winter. This is in contrast to the results of and
who found maxima during equinoxes and local winter in both
hemispheres (110 km altitude) which qualitatively agrees well with our
results at 106 km near 40∘ N or S.
Maxima in zonal wind (Fig. b) and meridional wind TDT
(Fig. c) are also found during local winter at midlatitudes.
They are slightly larger in the Northern Hemisphere (5.9 m s-1 in
both components) than in the Southern Hemisphere (4.7 m s-1 in both
components). During equinoxes, the maxima are smaller and located close to
the equator (zonal wind only, <4.0 m s-1), at low latitudes
(meridional wind only, <4.3 m s-1) and at midlatitudes
(zonal and meridional wind <3.8 m s-1).
Zonal and meridional amplitudes at midlatitudes (40–50∘ N or S)
agree well with TIDI measurements showing maxima during
equinoxes at both hemisphere and during southern winter. However, the
northern winter maximum is not seen in the zonal wind analysis by
. Another meridional wind peak is reported by
near 30∘ N during July which can be found in our simulations, as
well. However, amplitudes tend to be underestimated by a factor of about
3–4.
Some differences between model results and satellite measurements may be
explained by the orbit of the satellite passing high latitudes less
frequently and leading to larger uncertainties at these latitudes. However,
this cannot explain the large discrepancies in the magnitude of the TDT.
Smaller model amplitudes may be due to processes that are not included in the
simulations such as latent heat release.
As in Fig. but for NO_SOL simulation.
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Zonal mean TDT phases (NO_SOL). (a, d) Temperature,
(b, e) zonal wind, (c, f) meridional wind. (a–c) Solstice (January) conditions.
(d–f) Equinox (April) conditions.
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Separating the forcings
In order to determine the effect of each individual forcing on the amplitude
of the TDT we performed the simulations with different forcings switched off,
as listed in Table .
Difference of TDT amplitudes between NO_NLIN and REF simulation.
Red colors denote larger NO_NLIN simulation amplitudes and blue colors
denote larger REF simulation amplitudes. Significant areas (α<0.01)
are hatched. (a, d) Temperature, (b, e) zonal wind, (c, f) meridional wind.
(a–c) Solstice (January) conditions. (d–f) Equinox (April) conditions.
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Difference of TDT amplitudes between NO_NLIN and REF simulation,
scaled by exp{-z(2H)-1}. Red colors denote larger NO_NLIN simulation
amplitudes and blue colors denote larger REF simulation amplitudes. Areas of
destructive interferences (120∘ ≤ΔΦ≤240∘)
between NO_NLIN and NO_SOL phases are hatched. (a, d) Temperature,
(b, e) zonal wind, (c, f) meridional wind.
(a–c) Solstice (January) conditions. (d–f) Equinox
(April) conditions.
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NO_SOL represents a TDT that is only due to nonlinear and gravity wave
effects because wave number 3 direct solar heating is removed in the whole
model domain. Therefore, possible sources of this wave are nonlinear
interactions between other tides, i.e., between the DT and the SDT, and
gravity wave–tide interactions only. The resulting amplitudes and phases are
shown in Figs. and . As
expected, the amplitudes are strongly reduced. However, they are not
completely extinguished. In all parameters there is a clear maximum at
northern midlatitudes (about 60∘ N) during January reaching 4 K ±0.6 K (temperature), 5 m s-1±1.2 m s-1 (zonal
wind) and 4 m s-1±0.8 m s-1 (meridional wind) above
120 km. In the zonal wind component there is a secondary maximum at about
30∘ N as well. During April, the maxima are shifted towards the
equator with amplitudes similar to those in January. This indicates that
secondary terdiurnal forcing is most evident during local winter as is
confirmed from the annual cycle of the NO_SOL simulation (not shown here).
TDT phases from this simulation (Fig. ) are much more
irregular in comparison to the REF simulation (Fig. ) and
show vertical wavelengths shorter than 50 km for those latitudes where TDT
amplitudes are strong.
The simulation NO_NLIN only includes direct solar forcing and gravity
wave–tide interactions. Therefore, it does not include nonlinear
interactions. Figure shows the mean amplitude
differences between the NO_NLIN and REF ensembles where red (blue) colors
denote larger (smaller) amplitudes in NO_NLIN. Welch's t test was applied
and areas with α<0.01 are hatched. It turns out that
decreased amplitudes are not the only consequence of the removed nonlinear
forcing since there are also areas where the amplitude has increased. This
result occurs primarily during January in all parameters. The strongest
increase of about 3 K (3 m s-1) is located where the REF
amplitude reaches its maximum. There, the amplitude in the NO_NLIN
simulation is about 25 % larger compared to the REF simulation. Another
large red area is located at about 60∘ N at an altitude of
110 km. In this area the amplitudes in the REF simulation are relatively
small (not more than 2 K and 2 m s-1), but the differences
between the simulations are similar so that the NO_NLIN amplitudes are twice
as strong as the REF amplitudes.
In April only weak enhancements of about 0.5–1.5 K (0.5–2 m s-1)
appear for individual grid points and these are not located in the areas of
larger amplitudes. Generally, the negative amplitude differences dominate and
areas of positive change are negligible.
We do not show the phases of the NO_NLIN simulation and the NO_GW
simulation here because both of these simulations still include the solar
forcing which dominates the other remaining forcing. As a result, the phases
are almost identical to those shown in Fig. for the REF
simulation.
In order to investigate the reason for the positive difference in amplitude
it is useful to compare phase shifts Δϕ between the NO_NLIN TDT
(with solar and gravity wave forcing) and the NO_SOL TDT (with nonlinear and
gravity wave forcing). The gravity wave forcing appears in both simulations
and therefore the phase shift between the tides associated with these
simulations can be mainly attributed to the phase shift between a pure solar
wave and a pure nonlinear wave. The differences in the background wind and
therefore tidal propagation conditions between the simulations are small. For
120∘ <Δϕ<240∘destructive interference occurs and
leads to a decrease in amplitude for the case of superposition.
Figure shows the amplitude differences as presented in
Fig. but now scaled by the growth rate (factor
exp{-z(2H)-1}) to show the source of the positive amplitude
differences. Here, the hatched areas show regions of destructive interference
(120∘ <Δϕ<240∘) between the phases of NO_NLIN and
NO_SOL occur. It is clear that the red areas and the destructive
interferences match almost perfectly for both January and April conditions,
and for all parameters.
Figure shows the mean amplitude differences between the
NO_GW and REF ensembles. For this simulation, positive amplitude differences
occur at several heights/latitudes, when the gravity wave–tide interaction as
a forcing of TDTs is removed. In this case destructive interference seems to
be more independent of the season as can be seen in January and April.
However, the regions where the zonal wind amplitude has increased are rather
small. This increase is most apparent around 60∘ N and 110 km
altitude during January. Note that this area is positive for both the
meridional and zonal wind and also appears in the NO_NLIN simulation
(Fig. ). For the temperature and meridional wind
component we find, as in Fig. , that amplitudes in
regions with strong REF amplitudes are enhanced even when the wave number 3
gravity wave forcing is removed. Furthermore, the amplitude changes in
Fig. are larger during April compared to January. This
is consistent with the larger TDT reference amplitudes occurring during
April. Generally, all amplitude differences are stronger for NO_GW than for
NO_NLIN.
As in Fig. but for NO_GW simulation.
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As in Fig. but for CTRL simulation. Note that
scales are different.
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The CTRL simulation provides a measure of TDT amplitudes due to effects that
have not been considered in the previous simulations. The presence of regions
of significant amplitude indicates that there still exist other sources in
the model. Figure shows the TDT amplitudes for the CTRL
simulation. Note that the scale is different from Fig.
so that the smaller magnitudes can be seen. The structure of this remaining
tide is not completely irregular. However, the amplitudes are small with
maximum values below 1 K, 1.2 m s-1 (zonal wind) and
1.4 m s-1 (meridional wind). During January, maxima are located in
the Northern Hemisphere at low and midlatitudes and during April at the
equator (temperature) and at southern low and midlatitudes (wind).