ACPAtmospheric Chemistry and PhysicsACPAtmos. Chem. Phys.1680-7324Copernicus PublicationsGöttingen, Germany10.5194/acp-17-7941-2017Case study of wave breaking with high-resolution turbulence measurements with LITOS and WRF simulationsSchneiderAndreasa.schneider@sron.nlWagnerJohannesFaberJenshttps://orcid.org/0000-0001-6869-545XGerdingMichaelhttps://orcid.org/0000-0002-5382-4017LübkenFranz-JosefLeibniz Institute of Atmospheric Physics at the University of Rostock (IAP), Kühlungsborn, GermanyGerman Aerospace Center (DLR), Institute of Atmospheric Physics (IPA), Wessling, Germanynow at: SRON Netherlands Institute for Space Research, Utrecht, the NetherlandsAndreas Schneider (a.schneider@sron.nl)30June20171712794179547October201618November201612May201718May2017This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/This article is available from https://acp.copernicus.org/articles/acp-17-7941-2017.htmlThe full text article is available as a PDF file from https://acp.copernicus.org/articles/acp-17-7941-2017.pdf
Measurements of turbulent energy dissipation rates obtained from wind
fluctuations observed with the balloon-borne instrument LITOS
(Leibniz-Institute Turbulence Observations in the Stratosphere) are combined
with simulations with the Weather Research and Forecasting (WRF) model to
study the breakdown of waves into turbulence. One flight from Kiruna
(68∘ N, 21∘ E) and two flights from Kühlungsborn
(54∘ N, 12∘ E) are analysed. Dissipation rates are of the
order of 0.1mWkg-1 (∼ 0.01 Kd-1) in the
troposphere and in the stratosphere below 15 km, increasing in
distinct layers by about 2 orders of magnitude. For one flight covering the
stratosphere up to ∼ 28 km, the measurement shows nearly no
turbulence at all above 15 km. Another flight features a patch with
highly increased dissipation directly below the tropopause, collocated with
strong wind shear and wave filtering conditions. In general, small or even
negative Richardson numbers are affirmed to be a sufficient condition for
increased dissipation. Conversely, significant turbulence has also been
observed in the lower stratosphere under stable conditions. Observed energy
dissipation rates are related to wave patterns visible in the modelled
vertical winds. In particular, the drop in turbulent fraction at
15 km mentioned above coincides with a drop in amplitude in the wave
patterns visible in the WRF. This indicates wave saturation being visible in
the LITOS turbulence data.
Introduction
Gravity waves transport energy and momentum and are thus an important factor
in the atmospheric energetics. Typically, they are excited in the troposphere
and propagate upwards and horizontally. Due to decreasing density, the
amplitudes increase with altitude in the absence of damping. Eventually, the
waves become unstable and break, producing turbulence and dissipation, and
thereby depose their energy and momentum. This mechanism has been suggested
by to explain turbulence in the mesosphere. There are two
variants of wave breaking e.g.Sect. 9: first
catastrophic wave breaking, in which the wave is completely annihilated
e.g., and second wave saturation, in which a wave
loses energy to turbulence so that the amplitude does not increase further,
meaning that the wave breaks only partially
e.g.. defines saturation to
imply that the wave amplitude is at a maximum and the excess energy is shed
by physical processes to prevent further growth. There are several theories
for saturation Sect. 6.3, and the phenomenon
has been observed as well. For example, using a balloon-borne instrument,
measured a gravity wave in winds and temperature with
vertical wavelength of ∼ 1 km and nearly constant amplitude
over ∼ 5 km height. Simultaneously they observed several
turbulent patches collocated with negative temperature gradient and
Richardson numbers between 0.3 and 6. They concluded that clear air
turbulence is related to a long-period wave via shear instability.
The dissipated energy approximately corresponded to the energy loss necessary to keep the wave amplitude constant.
observed gravity waves in the mesosphere with Na
lidar and found upwards-propagating waves still present (with less amplitude)
above an overturning region. Catastrophic wave breaking has been observed,
for example, in the lowermost stratosphere
by and with radar and
radiosonde. Model studies of breaking gravity waves have, for example, been
carried out by and by ,
, who performed direct numerical simulations (DNS) of a
gravity wave superposed by fine-scale shear.
Regarding turbulence measurements, there are two aspects of importance:
first, the energy dissipation, and secondly the diffusive properties. We will
concentrate on the former. Large-scale diffusion in the stratosphere is a
complex process due to the intermittent nature of the turbulence there, as
summarised in some detail by , among others. A relatively extensive data
set exists for the troposphere and tropopause region
e.g., but in the middle stratosphere
observations are sparse. Remote sensing is mainly performed by radars in the
troposphere and lower stratosphere as well as in the mesosphere
seefor an overview, and with satellites in the upper
stratosphere e.g.. In situ observations in the
middle stratosphere have been carried out with balloon-borne instruments.
Pioneering work has been done by and
. An instrument with a similar anemometer has been
developed by . Indirect measurements using the Thorpe
method were taken by , and
others, mainly using standard radiosondes. A recent high-resolution
balloon-borne instrument for the direct measurement of turbulent wind
fluctuations is Leibniz Institute Turbulence Observations in the Stratosphere
(LITOS) , which can resolve the inner scale of
turbulence in the stratosphere for the first time. This state of the art
instrument is used for this study.
To study waves breaking into turbulence, a wide range of scales from
kilometres (the wavelength of GWs) to millimetres (the viscous subrange of
turbulence) have to be resolved. This cannot be performed by a single
instrument. Thus several techniques have to be combined. In this study, LITOS
is used for the turbulence part and radiosonde observations from the
same gondola are used for local atmospheric
background conditions. To put the observations into a geophysical context and
to obtain information about waves, regional model simulations with the WRF
(Weather Research and Forecasting model) driven by reanalysis data are
applied. Three flights are analysed, comprising one from Kiruna (northern
Sweden, 67.9∘ N, 21.1∘ E) and two from Kühlungsborn
(northern Germany, 54.1∘ N, 11.8∘ E).
This paper is structured as follows: Sect. gives an
overview of the instrument LITOS and the data retrieval
(Sect. ) as well as the WRF model set-up
(Sect. ). The results for three different flights are
presented in Sect. . These are interrelated and discussed in
Sect. , and finally conclusions are drawn in
Sect. .
Instrumentation and modelBalloon-borne measurements
LITOS (Leibniz-Institute Turbulence Observations in the Stratosphere) is a
balloon-borne instrument used to observe small-scale fluctuations in the
stratospheric wind field . The wind measurements are
taken with a constant temperature anemometer (CTA) which has a precision of a
few cms-1. It is sampled with 8 kHz yielding a
sub-millimetre vertical resolution at 5 ms-1 ascent rate. Thus
the inner scale of turbulence is typically covered. A standard meteorological
radiosonde (Vaisala RS92 or RS41) is used to record atmospheric background
parameters. LITOS was launched three times as part of a
∼ 120 kg payload from Kiruna (67.9∘ N,
21.1∘ E) within Balloon Experiments for University Students
(BEXUS) 6, 8, and 12 in 2008, 2009, and 2011, respectively
. The second generation of
the small version of the instrument is an improvement on the one described by
and consists of a spherical payload of
∼ 3 kg weight. It is suspended ∼ 180 m below a
meteorological rubber balloon. Two CTA sensors are mounted on booms
protruding at the top of the gondola. The instrument was launched several
times from the IAP's site at Kühlungsborn (54.1∘ N,
11.8∘ E), e.g. on
27 March 2014, 6 June 2014, and 12 July 2015.
In this paper, flights are only taken into account when data from more than
one CTA sensor on the same gondola are available. Summarised, the data
analysis is performed in three steps. First, the dissipation rate is
retrieved similarly to the procedure
described by . Then the ε values from both
sensors are compared to detect sections where one sensor is possibly affected
by the wake of ropes. Finally, the remaining spectra are manually inspected
to sort out cases for which both sensors potentially have been affected.
Another source of artificial turbulence is the wake of the balloon
. Typically, the wake influences both sensors
similarly and cannot be detected by the above methods. Therefore, we limit
our analysis to flights and altitude regions, where wake effects do not play
a role due to sufficient wind shear that brings the payload out of the
balloon's wake.
The details of the retrieval are as follows: the data of the ascent are split
into windows with depths of 5 m altitude with 50 % overlap. In
each window, the mean value is subtracted, and the periodogram is computed,
which is an estimation of the power spectral density (PSD). The periodogram
is smoothed with a Gaussian-weighted running average. The instrumental noise
level is detected and subtracted. Initially, turbulence is assumed to occur
in each window and thus the algorithm attempts to fit the
model for fully developed turbulence in the form
given by and
to the observed spectrum (see
Eq. in
Appendix ). If the fit succeeds, the inner scale
l0 is obtained. This leads to the energy dissipation rate ε
given by
ε=cl04ν3l04,
where ν is the kinematic viscosity (known from the radiosonde
measurement) and cl0 is a constant depending on the type of sensor.
The determination of cl0 for our sensor configurations is described
in Appendix . Non-turbulent (or disturbed) spectra
manifest in bad fits which are sorted out with the following set of criteria:
The noise level detection fails, which usually means that the noise is not
white; i.e. the periodogram is disturbed at small scales.
The mean logarithmic difference between data and fit exceeds a given threshold.
This condition captures cases where the fit does not describe the data well, e.g.
when no turbulence is present so that the periodogram does not follow the form of the turbulence model.
The inner scale l0 lies outside the fit range. This means that the bend in
the spectrum is not within the fit range and thus the fit is not meaningful, allowing
no useful retrieval of ε. That can occur when the spectrum does not have
the expected form of the turbulence model, when the inner scale lies at very small
scales where the periodogram is dominated by noise, or when the periodogram is disturbed.
The fit width is smaller than a threshold; in this case the fit is determined by too few data points.
The value of the periodogram at l0 is too close to the value of the noise
level, which means too small a part of the
viscous subrange is resolved.
The slope of the fit function at the small-scale end is less than a given
threshold (less steep than m-4, where m is the vertical wave number).
This indicates that the bend in the spectrum is not well covered by the fit and the data.
If one of the above conditions applies, the spectrum does not follow the form
for fully developed turbulence; thus ε is set to zero. Requiring
the spectrum to follow Heisenberg's turbulence model may exclude turbulence
that is not fully developed. However, it is not feasible to retrieve
ε in cases where the periodogram does not follow the turbulence
model.
Sometimes a sensor has been located in the wake of a rope supporting the
gondola and the other sensor has not, causing the ε values of both
sensors to differ by up to 5 orders of magnitude. To sort out such sections,
altitude bins for which the dissipation rate from both sensors deviates by more
than a factor of 15 are discarded. For the flights with a small payload,
the remaining spectra have been inspected manually for sections where both
sensors have been affected by the rope wake, and those that look suspicious
have been taken out. A spectrum is regarded as wake-affected if it has a
plateau in PSD near 10 cm spatial scale, which is estimated to be the
extent of a Kármán vortex street originating from the lines supporting
the gondola. This problem of wake effects from the ropes does not occur for
the BEXUS flights, where the sensors were placed further away from the
supporting lines. For all other altitude bins the average of both sensors is
taken.
On the other hand, for the BEXUS flight the distance between the balloon and
the payload was only 50 m, i.e. comparatively small. Thus, the payload flew
through the wake of the balloon for a considerable duration of the flight.
Therefore, only limited altitude sections with large wind shears are
considered for this flight.
To quantify the stability of the atmosphere, the gradient Richardson number
Ri=N2/S2 is used, which is the ratio of the squared
Brunt–Väisälä frequency N2 and the square of the vertical shear of
the horizontal wind S2. The Brunt–Väisälä frequency can be written
as N2=gΘdΘdz, where
Θ is the potential temperature and g is the acceleration due to
gravity. The wind shear is defined as S2=dudz2+dvdz2, where u and v are the
zonal and meridional wind components, respectively. The Richardson number
represents the ratio of buoyancy forces (which suppress turbulence) to shear
forces (which generate turbulence). According to a theory for plane-parallel
flow established by and , turbulence
occurs below a critical Richardson number of Ric=1/4. The
general applicability of that criterion was recently questioned based on
measurements e.g. and model simulations
e.g.. Often the shear is not strictly horizontal so
that the theory by and is not
applicable, as pointed out by . To take into account
slanted shear, proposed a concept of slantwise
instability. However, the Richardson number is still useful as an estimation
of stability. The Richardson number also depends on the scale on which it is
computed . Usually, computing Ri on a
smaller scale yields locally smaller numbers, since for a computation on
larger scales an average over regions with small and large Ri is obtained.
In this study Ri is retrieved from the radiosonde measurements. In order
not to dominate the derivatives by instrumental noise, the potential
temperatures and winds are smoothed with a Hann-weighted running average over
150 m prior to differentiation with central finite differences.
Model simulations
Mesoscale numerical simulations are performed with the Weather Research and
Forecasting (WRF) model, version 3.7 . Two nested
domains with horizontal resolutions of 6 and 2 km and time steps of
15 and 5 s, respectively, are applied. In the vertical direction 138
terrain following levels with stretched level distances of 80 m near
the surface and 300 m in the stratosphere are used and the model top
is set to 2 hPa (about 40 km altitude) for the BEXUS flights
and 5 hPa (about 32 km altitude) for the flights from
Kühlungsborn. At the model top a 7 km-thick Rayleigh damping layer
is applied to prevent wave reflections ; i.e. the top of
the damping layer is the model top. Physical parameterisations contain the
rapid radiative transfer model longwave scheme , the
Goddard shortwave scheme , the
Mellor–Yamada–Nakanishi–Niino boundary layer scheme
, the Noah land surface model , the
WRF single-moment 6-class microphysics scheme WSM6; and
the Kain–Fritsch cumulus parameterisation scheme . The
initial and boundary conditions are supplied by ECMWF (European Centre for
Medium-Range Weather Forecasts) operational analyses on 137 model levels with
a temporal resolution of 6 h. In the WRF a temporal output interval of 1 h
is used, data interpolated along the flight track are output with an interval
of 5 min. Simulations are initialised 5 to 6 h before the launch time of
the balloon. The computation of turbulent kinetic energy (TKE) is done by the
boundary layer scheme and described in . It is
based on a prognostic equation which is solved additionally to the equations
of motion and which includes transport, shear production, buoyancy production
and dissipation terms. Shear and buoyancy terms include deformation and
stability effects of the resolved flow and are related to turbulent motions
by the horizontal and vertical eddy viscosities. The equation operates on the
scale of the grid size.
In this paper WRF simulations are used to get an overview of the
meteorological situation. showed that regions of GW
breaking can be simulated by WRF simulations with horizontal grid distances
of 2 km and a similar model set-up by means of convective overturning
and reduced Richardson numbers. Here, the TKE output from the model is also
used to identify regions of intensified turbulent mixing in the atmosphere
along the balloon flight tracks. This can be a hint that observed turbulence
was caused by large-scale GW breaking. It is not intended to quantitatively
compare observed dissipation rates with simulated regions of enhanced TKE
values.
Observations during the BEXUS 12 flight. (a) Zonal winds
u (blue), meridional winds v (green), and temperatures T (red) from the
radiosonde. The light blue, light green, and orange curves show the
corresponding results from the WRF model interpolated along the balloon
trajectory. (b) Wind direction (blue) and horizontal wind speed
(green) from the radiosonde. (c) Richardson number Ri computed
from the radiosonde data, using a smoothing over 150 m prior to
numerical differentiation. The Ri axis is split at 1 into a linear and a
logarithmic part. The red line shows the critical Richardson number, 1/4.
(d) Energy dissipation rates ε observed by LITOS. The blue
crosses mark single turbulent spectra computed on a 5 m grid with
50 % overlap, the orange curve shows a Hann-weighted running average
over 500 m (non-turbulent bins count as zero in the average). The top
axis gives the heating rate due to turbulent dissipation,
dT/dt=ε/cp. The grey areas mark the
regions with likely wake influence. The horizontal black line in all four
panels marks the tropopause.
(a) Map of horizontal winds at 850 hPa,
(b) vertical section of horizontal winds, (c) vertical
section of vertical winds, and (d) vertical section of turbulent
kinetic energy (TKE) from WRF simulations for 27 September 2011, 18:00 UT.
The black curves visualise the trajectory of the BEXUS 12 flight.
In (a), the blue streamlines show the wind direction, the white
lines visualise coastlines and a latitude/longitude grid, and the black line
indicates the location of the vertical sections. In (b), the white
isolines show potential temperature with labels in Kelvin.
ResultsThe BEXUS 12 flight (27 September 2011)
The BEXUS 12 flight was launched from Kiruna on 27 September 2011 at
17:36 UT.
Figure a and b show atmospheric conditions
observed by the radiosonde on board the payload. Temperatures decreased up to
the tropopause at 10.3 km, excepting some small inversion layers.
Above, there was a sharp increase in temperature known as tropopause
inversion layer (TIL) . Higher up,
temperatures slightly decreased. Winds came from the north-west near the
surface and reversed between ∼ 6 and 10 km. The reversal caused
nearly the opposite wind direction at 9 km altitude compared to
5 km, and a change of sign in both wind components. It further
entailed strong wind shear below the tropopause, causing low Richardson
numbers (below the critical number of 1/4). Above the tropopause the wind
field showed signatures of gravity wave activity with short wavelengths and
no obvious altitude-dependent structure. In the stratosphere, Richardson
numbers were generally larger than in the troposphere.
Same as Fig. , but for the flight from
Kühlungsborn at 27 March 2014. Due to disturbances of the temperature data,
temperatures are smoothed in the plot in (a), and Richardson numbers
are shown only for altitudes lower than 9.4 km. The dissipation
profile excludes the lowermost 650 m due to disturbances from the
launch procedure (dereeling of the payload suspension), and the part above
9.4 km altitude due to potential wake effects from the balloon.
Figure d depicts observed dissipation rates. Each
blue cross corresponds to an altitude bin classified as turbulent (as
described in Sect. ). The orange curve depicts a
Hann-weighted running average over 500 m. Please note that large
sections in the troposphere and stratosphere are subject to wake influence
(marked grey) due to the small distance of only 50 m between the payload and
the balloon. These sections are generally not discussed here. Between 9 and
10 km there was a thick layer with high dissipation. As described
above, this altitude region featured low Richardson numbers caused by high
wind shears. Thus turbulence was presumably induced by dynamic instability.
Additionally, at this altitude a wind reversal was observed which caused
filtering of gravity waves with phase velocities equal to the background
winds (if present). Most probably, these high dissipation rates are not
caused by wake because calculations show that the gondola was outside the
wake in this altitude section due to the large wind shear. Furthermore, the
dissipation rates are even larger than typical wake turbulence.
WRF model simulations were performed for the time and place of the flight. To
show that these produced reasonable results, model winds and temperatures
interpolated along the flight trajectory are plotted in
Fig. a along with the radiosonde profiles.
Observed and modelled results compare very well; the only difference is that
the radiosonde data contain signatures from small-scale gravity waves which
WRF cannot resolve. In Fig. , model snapshots at the middle
of the ascent are shown. Panel (a) depicts horizontal winds at
850 hPa. Westerly winds flowed over the Scandinavian mountains, which
are expected to have excited mountain waves. Another potential source of
gravity waves is geostrophic adjustment. Bending stream lines are visible,
e.g. over the Scandinavian mountains, west of the flight track. Panel (b)
presents a vertical section of horizontal winds and potential temperatures.
It demonstrates that the jet (∼ 7 to 10 km altitude) had a
local structure and involved strong wind shears.
With a grid resolution of 2 km WRF can resolve waves with horizontal
wavelengths larger than about 10 km. These waves can be seen,
for example, in the vertical winds, which
are used as a proxy. This quantity is plotted in Fig. c.
Strong wave-like patterns are visible especially over the Scandinavian
mountains, which correspond to the mountain wave excitation mentioned above.
Weaker wave patterns are visible near the flight trajectory, downstream of
the mountains. Between roughly x=400km and x=550km,
the wave patterns change at tropopause height (approximately 10 km
altitude): above, there is less amplitude than below. This is ascribed to the
wave breaking and filtering mentioned before. Filtering means catastrophic
breaking of waves; i.e. a wave that is filtered is annihilated. Further
upwards the amplitude increases slowly.
Waves can propagate over considerable distances and times. Therefore it is
not sufficient to look at potential sources in the vicinity of the flight
track. Even if sources are found, the waves may have propagated to other
places (away from the point of interest), while waves from sources outside
the domain may have propagated to the location of observation. For resolved
waves the model takes care of these issues. Waves seen in the WRF at the location
of the flight may have travelled from remote places, yet the important
information is not their origin, but that they were present during the
measurement.
To trigger turbulence, wave breaking is necessary. Such events are triggered
by dynamic or convective instabilities or by wave–wave interactions
e.g.. In the WRF, the breakdown to turbulence
is parameterised by solving a prognostic equation for TKE, which is based on
production terms due to shear and buoyancy obtained from the resolved flow.
TKE is plotted in Fig. d. It peaks near 10 km
height at the location of the flight. This corresponds nicely to the intense
turbulent layer observed by LITOS. It is reproduced in the WRF due to the
shear instability on scales resolved by the model, highlighting the
geophysical significance of the layer.
The 27 March 2014 flight
A small LITOS payload of second generation was launched from Kühlungsborn
on 27 March 2014 at 10:10 UT. It was carried by a comparatively small
(3000 g) balloon and a 60 m dereeler.
Figure a shows temperatures smoothed over 15
data points (∼ 150 m) as well as zonal and meridional winds.
The smoothing is necessary because for this flight the temperature
measurement is perturbed by radiation effects as the radiosonde was
incorporated in the main payload; these effects get worse with increasing
altitude. Temperatures decreased up to the tropopause at 9 km.
Between 9 and ∼ 30 km altitude they stayed nearly constant and
started to increase further upwards. Winds were easterly and turned northerly
above ∼ 20 km altitude. A strong southeasterly jet was present
between ∼ 6 and 10 km height. Superposed are signatures of
small-scale gravity waves. Wind shears originating from the jet may have
excited turbulence and/or waves. The effect of the shear is visible as a
layer with enhanced dissipation at this altitude (see below). Richardson
numbers are shown for altitudes below 9.4 km only because they
involve derivatives of the temperature profile, which was disturbed by
radiation effects as described above.
Dissipation rates are presented in Fig. d.
The data below 650 m altitude are affected by the unwinding of the
dereelers while the data above the tropopause are subject to wake influence.
Therefore, these are discarded and not shown in the plot. Dissipation rates
varied over several orders of magnitude within small altitude ranges (typically a few 10 m). The
running average shows some structure in the troposphere, e.g. a few layers
that are standing out with larger rates. Most prominently this can be seen
near 8 km. That is in the same altitude as the wind shear due to the
jet, which speaks for shear-induced turbulence. Precisely, there were two
turbulent layers from 7.5 to 7.9 km and from 8.1 to 8.3 km
height; within both, Richardson numbers were below 1 and partly below 1/4.
Other sheets with large dissipation were detected, e.g. near 6.1 km
and around 3.0 km altitude.
To validate the corresponding WRF simulations, winds and temperatures
interpolated to the flight track are plotted in
Fig. a. They agree very well with the
radiosonde data.
Figure depicts WRF results for the time of the
flight. Panel (a) shows horizontal winds at 850 hPa, which were
easterly or south-easterly. In panel (b) horizontal winds are depicted as
altitude section, showing that the strong jet did not have much structure in
a horizontal direction, while the sharp vertical structure is reproduced as
observed by the radiosonde. Panel (c) shows a vertical profile of vertical
winds. Wave patterns are visible, which stretch over the whole altitude
range. Particularly, a superposition of a wave with long vertical wavelength
(λz≈8km) and nearly horizontal phase fronts and
waves with short horizontal wavelength (10 to 20 km) and phase fronts
in the vertical can be seen. Figure d shows the TKE.
Outside the boundary layer there is an enhancement near 7.5 km
altitude. It corresponds nicely to a thick, strong turbulent layer in the
measurement by LITOS between ∼ 7 and 8.5 km height. Within this
observed turbulent layer, which in fact consists of several layers,
Richardson numbers are smaller than 1 almost everywhere and at times smaller
than 1/4.
The 11/12 July 2015 flight
A night-time flight with LITOS was launched from
Kühlungsborn on 11/12 July 2015, at midnight local
time (22:01 UT on 11 July). A dereeler of 180 m (with a 3000 g balloon)
was used for payload suspension, making balloon wake effects negligible for
this flight. The radiosonde was positioned 60 m below the main
payload to avoid disturbances of the temperature sounding.
The observed background parameters are depicted in
Fig. a and b. Westerly winds prevailed up to
∼ 19 km altitude, whereas above winds came from the east. This
change in direction was not associated with a significant wind shear because
velocities were small in that altitude region. A jet is visible at about
10 km height. Superposed on the winds are signatures of small-scale
gravity waves. Above the tropopause at 11.3 km altitude there was a
small tropopause inversion layer. Higher up temperatures remained rather
constant up to ∼ 20 km, where they started to increase.
Same as Fig. , but for WRF simulations for
27 March 2014, 11:00 UT.
Same as Fig. , but for the flight from
Kühlungsborn at 11/12 July 2015. The dissipation profile excludes the
lowermost 550 m due to disturbances from the launch procedure
(dereeling of the payload suspension).
Same as Fig. , but for WRF simulations for
11 July 2015, 23:00 UT.
Richardson numbers were typically lower than for the other flights,
indicating less stability. There are several layers where the Richardson
number is below the critical limit of Ric (1/4). These layers
are relatively thin.
Energy dissipation rates (data below 550 m are excluded due to
disturbances from the launch procedure) showed a strong patchy structure,
with enhanced dissipation at, for example,
∼ 2.0, 3.8, 7.2, 8.9, 11.0, 12.1, and 14.3 km. These layers of
intense turbulence mostly corresponded to Richardson numbers smaller than
Ric=1/4, or at least to Ri<1. But particularly in the lower
stratosphere between 11 and 15 km, turbulence also occurred for high
Richardson numbers. It should be kept in mind that the Richardson number
depends on the scale on which it is computed
e.g.. A higher resolution (i.e. computing
Ri on smaller scales) may result in locally smaller Ri numbers, because
the computation on large scales yields a kind of average. Similarly, in large
eddy simulations found larger Richardson numbers for
smaller model resolutions (i.e. larger scales). Here, due to measurement
noise a smoothing over 150 m has been applied before computing Ri,
determining the resolution. However, this issue cannot explain the whole
discrepancy. In simulations of gravity waves, found
instabilities and onset of turbulence for Richardson numbers both smaller and
larger than 1/4. He noted that the theory by and
is not applicable to his simulations because the gravity
wave phase propagation and thus the wave-induced shear is slanted. In the
real atmosphere, waves usually propagate at a tilt (i.e. the shear is not
orthogonal to the altitude axis). has already discussed
slantwise static instabilities created by gravity waves. He developed a wave
period criterion for turbulence by comparing the e-folding time of the
(slantwise) instability with the period of the wave. Turbulence is more
likely to occur for slantwise static instability than for vertical static
instability. In the light of these comments, the violation of the Richardson
criterion for the LITOS measurements is comprehensible.
Above ∼ 15 km altitude, hardly any turbulence was detected;
only a few thin turbulent layers were observed. Thus above 15 km the
average dissipation rate (for which no turbulence is counted as zero) was
only 0.01 mWkg-1, while below 15 km it was
0.64 mWkg-1.
Results from corresponding WRF simulations are depicted in
Fig. . Horizontal winds at the 850 hPa level
were mainly westerly. The altitude section shows that the strong jet did not
have much variation in the horizontal direction. Vertical winds reveal wave
patterns that are particularly intense around the tropopause and gradually
become weaker near ∼ 15 km, with less amplitude above. This
drop in wave amplitude is at the same altitude as the drop in observed
dissipation. The TKE has enlarged values around 3 km altitude and
near the tropopause; however the enhancement is small at the flight path.
Correspondingly, the thickness of the strong turbulent layers detected by
LITOS is relatively small, meaning that these dissipative layers are
potentially not resolved in the model.
Discussion
A comparison of the observed dissipation profiles and the wave patterns in
the model vertical winds for the different flights suggests that more
turbulence observed by LITOS comes along with stronger wave patterns visible
in WRF, and vice versa. Particularly, this can be seen at 11/12 July 2015 at
the drop in dissipation and wave amplitude at ∼ 15 km altitude.
A similar feature has been observed during another flight at 6 June 2014 (not
shown). Likewise, LITOS data exhibit a sharp drop in turbulence at
∼ 15 km, and the corresponding WRF simulation shows strong wave
patterns below ∼ 15 km and very weak ones above. For the troposphere,
vertical winds in WRF show similar gravity wave amplitudes for
all Kühlungsborn soundings,
even if the wave structures are different. Accordingly, dissipation rates are
generally similar, showing up as a highly structured profile that is partly
related to shear instabilities measured by the radiosonde. This is also
reflected in the WRF turbulent kinetic energy, attesting that the structures
are sufficiently large to be resolved in WRF. The same is true for the
turbulent layer below the tropopause observed during BEXUS 12.
The relation between waves and turbulence can also be seen in averages over
altitude regions. For 12 July 2015 the most significant drop in mean
dissipation does not happen at the tropopause where the stability increases
due to the changing temperature gradient, but at ∼ 15 km where the
wave activity decreases. Mean energy dissipation rates are
0.64 mWkg-1 below 15 km altitude and 0.01 mWkg-1
above. Consistent with these rates, the average absolute vertical flux calculated from WRF
data as a measure for wave activity is 64 mWm-2 below 15 km and
6.9 mWm-2 above.
We interpret this behaviour as the effect of wave saturation. As described in
the introduction, a saturated wave looses part of its energy to turbulence so
that the amplitude does not grow further. Such effects have already been
observed, for example, by
, who measured a gravity wave with almost constant
amplitude over an altitude range of 5 km and collocated isolated
turbulent patches with a dissipation rate approximately accounting for the
energy loss of the wave. found regions of strong
overturning, and upwards-propagating waves are present below as well as (with
less amplitude) above the overturning region. They argue that, depending on
the amplitude, a breaking wave is not always completely annihilated, but the
amplitude may be modulated in a highly non-linear event.
p. 125 states that “gravity wave and turbulence are
often observed to exist simultaneously.” Via the process of wave saturation,
the occurrence of waves is connected to the intensity of turbulence.
observed intense turbulence in the lowermost
stratosphere during a period of maximal wave intensity using radar at
Aberystwyth (52.4∘ N, 4.0∘ W), which supports the above
hypothesis.
Saturation theories proposed several mechanisms, e.g. linear instability
dynamics due to large wave amplitudes, non-linear damping, or non-linear
wave–wave interactions Sect. 6.3. The present
study cannot answer that debate, yet the relatively large Richardson numbers
hint that non-linear interactions may play a role.
Mean dissipation rates observed by LITOS are of the order of
10-4Wkg-1 (roughly 0.01 Kd-1). This is 2
orders of magnitude below typical solar or chemical heating rates which are
of the order of 1 Kd-1Fig. 4.19b.
However, within thin layers rates of 10-2 to
10-1Wkg-1 (∼ 1 to 10Kd-1) are
observed, which is larger than solar heating. The low mean energy dissipation
rates are not explicitly contained even in high-resolution models, which
cannot describe the large intermittency. Only large layers with highly
increased dissipation, as encountered, for example, during BEXUS 12, are captured.
Observed dissipation rates are partly larger than those reported by other
publications using different methods. obtained values
between 1.4×10-5 and 3.9×10-5Wkg-1 from
balloon measurements. found ε values between
3×10-5 and 6×10-4Wkg-1 in the upper
troposphere from radar measurements. These are lower rates than the averages
in this work, but within the range of the variability.
observed stratospheric dissipation rates between 7×10-4 and
2×10-3Wkg-1, depending on the underlying terrain,
with an aircraft. These results are of a similar order of magnitude to the
averages in this study. reported mean dissipation rates
between 2×10-2 and 5×10-3Wkg-1 for the
altitude range 7 to 26.5 km, using a different retrieval and
potentially including wake effects.
Conclusions
In this paper, high-resolution turbulence observations with LITOS are
complemented by model simulations with WRF to study the relation between
turbulence, waves, and background conditions. Three flights, for which in
each case data from two wind sensors are available, are selected. This allows high-quality assurance.
Furthermore, any data that are possibly influenced by the balloon's wake have
been removed for this study.
Enhanced energy dissipation rates were observed where pronounced
instabilities were detected by the radiosonde. Moreover, measured shear
instabilities and associated enhancements in dissipation on scales resolved
by WRF also coincide with enlarged model turbulent kinetic energy (TKE). For
instance, during the BEXUS 12 flight (27 September 2011), a wind reversal was
observed which caused a large shear instability (indicated by Richardson
numbers smaller than 1/4) as well as potential wave filtering. The
resulting turbulence was detected by LITOS as a region with large dissipation
rates. The model TKE peaks in this region, highlighting the significance of
that layer. Similar effects are observed for some strong layers of the
27 March 2014 and 11/12 July 2015 flights. Thus, in these cases the
geophysical causes of the observed turbulent layers are clearly visible. The
large scale instabilities are resolved by the radiosondes and the model. On
the other hand, many other (less intense) turbulent layers observed by LITOS
are obviously too thin to be related to the much coarser data of the
radiosonde or the WRF results.
Another relation between turbulence detected by LITOS and the presence of
wave-like structures in WRF is noted: for the available summer flights at
6 June 2014 (not shown) and 12 July 2015, a drop in turbulence occurrence at
approximately 15 km altitude with hardly any turbulence above was
observed. In the associated model simulations, wave signatures become weaker
around 15 km. Altogether, observed dissipation is weaker during lower
wave activity (as seen in WRF), and larger where larger wave amplitudes are
seen. These findings can be explained by wave saturation, while a change in,
for example, static stability is less prominent.
Turbulence has been observed for Richardson numbers below as well as above
the critical number of 1/4, partly even for values much larger than 1. Such
a violation of the classical theory by and
has already been described by several researchers, e.g.
. recognised
the limitation of considering only vertical instability (as done when using
the Richardson number) and proposed a concept of slantwise instabilities as
created by gravity waves. He showed that turbulence
is more likely to develop via slanted instability
compared to vertical instability. Thus turbulence for Ri>1/4 is comprehensible.
The results are based on the limited data set from a few flights. More flights
at selected meteorological situations are planned to further study the
relation between waves and turbulence. A redesign of the instrumental set-up
shall eliminate the wake effects of balloon and ropes. Moreover, a direct
measurement of gravity wave activity in combination to the turbulence
observations is preferable.
The data used in this study are available on request to
Michael Gerding (gerding@iap-kborn.de).
Derivation of the constant cl0 in Eq. ()
To retrieve energy dissipation rates from observed spectra, the relation
(Eq. ) between inner scale l0 and dissipation rate
ε, ε=cl04ν3/l04, and especially the
value of the constant cl0 is important. To obtain correct values,
care has to be taken as which component(s) of the spectral tensor are
observed. In the following, the derivation of the constant cl0 is
summarised.
In the inertial subrange, the longitudinal component, transversal component,
and trace of the structure function tensor for velocity fluctuations have the
form
Dxx(r)=Cxxr2/3,
where xx is a placeholder for rr (longitudinal), tt
(transversal), or ii (trace), and the structure constant has the form
Cxx=bxxav2ε2/3 with brr=1,
btt=43, bii=brr+2btt=113p. 54ff and the empirical constant
av2=2.0e.g.p. 193f. In the viscous subrange, the
structure function is
Dxx(r)=C̃xxr2,
with C̃xx=cxxεν and the factors
crr=115, ctt=215, cii=crr+2ctt=13p. 49.
Based on Eq. 28, Eq. 4
gave a form of the temporal spectrum in the inertial and viscous subranges,
which reads, for velocity fluctuations,
W(ω)=Γ(53)sin(π3)2πubCxx(ω/ub)-5/31+ω/ubk08/32,
where ub is the ascent velocity of the balloon, Γ(z):=∫0∞tz-1e-tdt is the gamma function,
and k0 denotes the breakpoint between inertial and viscous subrange. The
normalisation is obtained by considering the limit k≪k0 for the
inertial subrange. Using the relation Φ(k)=-ub22πkdWdω(kub) between temporal and
spatial spectrum Eq. 6.14, the corresponding
three-dimensional spectrum is
Φxx(k)=16πΓ(53)sin(π3)2πCxxk-11/35+21kk08/31+kk08/33.
The constant cl0 in Eq. () can be computed from the
condition of the structure function at the origin
d2Dxxdr2(0)=8π3∫0∞Φxx(k)k4dkp. 49f. Inserting the structure function
(Eq. ) and the spectrum
(Eq. ) into condition
(Eq. ), integrating and
solving for 1/k0 yields
l0=2πk0=2π316Γ(5/3)sin(π/3)bxxcxxav23/4︸=cl0ν3ε1/4.
CTA wire probes are sensitive perpendicular to the wire axis but insensitive
parallel to the wire axis. For the earlier flights, the wires of the CTA
sensors were oriented vertically so that they are sensitive in both
horizontal directions and insensitive in the vertical direction; i.e. for an
ascending balloon both transversal components are measured. Thus bxx=4/3+4/3=8/3 and cxx=2/15+2/15=4/15, which leads to cl0=14.1. For the flight at 12 July 2015, one sensor with the wire oriented
horizontally was flown, which is sensitive in the vertical and one horizontal
direction yet insensitive in the other horizontal direction (parallel to the
wire). In this case bxx=1+4/3=7/3 and cxx=1/15+2/15=3/15 so that cl0=15.8.
Sect. 4 used different components of the structure
function constant yielding cl0=5.7. Since in
Eq. () the constant occurs with cl04, this results
in a difference in ε of a factor of ∼ 50 for the same
l0.
The authors declare that they have no conflict of
interest.
Acknowledgements
The BEXUS programme was financed by the German Aerospace Center (DLR) and the
Swedish National Space Board (SNSB). We are grateful for the support from the
International Leibniz Graduate School for Gravity Waves and Turbulence in
the Atmosphere and Ocean (ILWAO) funded by the Leibniz Association (WGL).
This study was partly funded by the German Federal Ministry for Education and
Research (BMBF) research initiative “Role of the Middle Atmosphere In
Climate” (ROMIC) under project numbers 01LG1206A and 01LG1218A (METROSI),
and by the German Research Foundation (DFG) under project numbers LU 1174
(PACOG) and FOR 1898 (MS-GWaves). We thank Wayne K. Hocking and two anonymous
reviewers for their valuable comments leading to the improvement of this
article. The publication of this article was funded by the Open Access Fund
of the Leibniz Association. Edited by:
Peter Haynes Reviewed by: Wayne K. Hocking and two anonymous
referees
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