ACPAtmospheric Chemistry and PhysicsACPAtmos. Chem. Phys.1680-7324Copernicus PublicationsGöttingen, Germany10.5194/acp-19-15431-2019Long-lived high-frequency gravity waves in the atmospheric boundary layer: observations and simulationsLong-lived GWs in the ABLJiaMingjiaohttps://orcid.org/0000-0003-4392-4900YuanJinlongWangChongXiaHaiyunhsia@ustc.edu.cnWuYunbinZhaoLijieWeiTianwenWuJianfeihttps://orcid.org/0000-0002-3998-9296WangLuGuSheng-YangLiuLiqunLuDachunChenRulongXueXianghuihttps://orcid.org/0000-0002-4541-9900DouXiankangGlory China Institute of Lidar Technology, Shanghai, 201315, ChinaCAS Center for Excellence in Comparative Planetology, University of
Science and Technology of China, Hefei, 230026, ChinaElectronic Information School, Wuhan University, Wuhan, 430072,
ChinaAnqing Meteorological Bureau, China Meteorological Administration,
Anqing, 246001, ChinaTechnical Support Center for Atmosphere Observation, Anhui Meteorological Bureau, China
Meteorological Administration, Hefei, 230031, China
A long-lived gravity wave (GW) in the atmospheric
boundary layer (ABL) is analysed during a field experiment in Anqing, China
(30∘37′ N, 116∘58′ E).
Persistent GWs with periods ranging from 10 to 30 min over 10 h in the
ABL within a 2 km height are detected by a coherent Doppler lidar from 4 to
5 September 2018. The amplitudes of the vertical wind due to these GWs are
approximately 0.15–0.2 m s-1. The lifetimes of these GWs
are longer than 20 wave cycles. There is no apparent phase progression with
altitude. The vertical and zonal perturbations in the GWs are 90∘
out of phase, with vertical perturbations generally leading to zonal
ones. Based on experiments and simplified two-dimensional computational
fluid dynamics (CFD) numerical simulations, a reasonable generation
mechanism of this persistent wave is proposed. A westerly low-level jet of
∼5 m s-1 exists at an altitude of 1–2 km in the ABL. The wind shear around the low-level jet leads to wave generation
under the condition of light horizontal wind. Furthermore, a combination of
thermal and Doppler ducts occurs in the ABL. Thus, the ducted wave motions
are trapped in the ABL and have long lifetimes.
Introduction
The atmospheric boundary layer (ABL) is the most important atmospheric
environment affecting human life. Gravity waves (GWs) and corresponding
physical processes have important impacts on synoptic systems, atmospheric
models, and aircraft departures and landings in the ABL (Clark et al.,
2000; Fritts and Alexander, 2003; Holton and Alexander, 2000; Sun et al.,
2015b). GWs are ubiquitous in the atmosphere and usually generated by
topography, convection, wind shear, jet streams, frontal systems and other
tropospheric sources (Banakh and Smalikho, 2016; Blumen et al., 1990;
Chouza et al., 2016; Fritts and Alexander, 2003; Plougonven and Zhang, 2014;
Pramitha et al., 2015; Toms et al., 2017; Wu et al., 2018). In general, most
of these GWs will propagate upward into the upper atmosphere, e.g. the upper
troposphere, stratosphere, mesosphere and even thermosphere. This leads to
the transport of energy and momentum from the lower atmosphere to the upper
atmosphere, thus affecting the coupling between the lower atmosphere and
upper atmosphere and the dynamic and thermal structure of the global
atmosphere (Fritts and Alexander, 2003; Holton and Alexander, 2000).
However, trapped GWs, e.g. trapped lee waves and ducted motions with high
frequency and coherent variability, can only propagate horizontally. In the
lower atmosphere, these horizontally propagating GWs may be linked to
low-level turbulence (e.g. rotors), the initiation of convection and
low-level wave drag (Birch et al., 2013; Grubišić et al., 2008;
Lac et al., 2002; Lapworth and Osborne, 2016; Marsham and Parker, 2006;
Tsiringakis et al., 2017). Therefore, such trapped GWs play a key role in
weather forecasts, climate models and aviation safety.
In previous studies, ducted GWs in the ABL (excluding lee waves) are mainly
high-frequency GWs with periods of less than 1 h (Banakh and Smalikho,
2018, 2016; Fritts et al., 2003; Viana et al., 2009).
However, these GWs and their sources are difficult to resolve in global
general circulation models due to smaller spatial and temporal scales. Only
mesoscale and large-scale GWs can be resolved in global atmospheric models
(Preusse et al., 2014; Wu et al., 2018). GW parameterizations are always
used in global models to increase the models' reliability and precision
(Fritts and Alexander, 2003). Thus, we must improve our understanding
of high-frequency ducted GWs and their sources.
However, wave motions in the ABL are usually difficult to detect due to
contamination from strong turbulence. Therefore, most wave motions are
observed in the stably stratified ABL (Banakh and Smalikho, 2016; Fritts
et al., 2003; Mahrt, 2014; Sun et al., 2015a, b; Toms et
al., 2017). These wave motions can be maintained for more than a few periods
if atmospheric-wave-ducting properties are present although such monochromatic
waves are infrequently observed (Mahrt, 2014; Toms et al.,
2017). In addition, due to the capabilities of ground-based measurements,
most of these previous studies are limited to the surface layer within tens
or hundreds of metres of the ground and not the whole ABL.
Numerous instruments have been utilized to detect wave motions in the ABL.
Fixed-point measurements from a tower or at the surface (Einaudi and
Finnigan, 1981; Finnigan and Einaudi, 1981; Poulos et al., 2002; Sun et al.,
2015a, 2004); in situ measurements on a mobile platform, such as
a balloon (Corby, 1957) or an aircraft (Fritts et al., 2003;
Kuettner et al., 2007); and remote sensing measurements such as sodar
(Beran et al., 1973; Hooke and Jones, 1986; Lyulyukin et al., 2015),
radar (Cohn et al., 1997, 2001) and lidar (Chouza et al.,
2016; Mayor, 2017; Neiman et al., 1988; Newsom and Banta, 2003; Poulos et
al., 2002; Witschas et al., 2017) have been widely used in recent decades.
All of these techniques are sensitive to only a certain portion of the wave
spectra and wave characteristics given limited spatial and temporal ranges.
Among these instruments, lidar alone can provide measurements with a
sufficiently long detection range, multi-scanning mode and high
temporal–spatial resolution. Recently, a micropulse coherent Doppler lidar
(CDL) was developed to measure the wind field with a temporal resolution of
2 s and spatial resolution of 60 m in the ABL (Wang et al., 2017). Wave motions such as high-frequency GWs can be revealed from the vertical wind measured by this lidar
in the whole ABL.
Numerical simulations are also used to study GWs. Mesoscale and large-scale
GWs can be resolved in high-spatial and high-temporal resolution models such
as the Whole Atmosphere Community Climate Model (WACCM) and the Weather Research and
Forecasting (WRF) model (Wu et al., 2018). For high-frequency
GWs at smaller scales, high-resolution computational fluid dynamics (CFD)
simulations have been used in recent years (Chouza et al., 2016; Watt et
al., 2015). CFD simulation is able to resolve the flow field at different
spatial scales, ranging from a mesoscale of ∼200 km to an
indoor environment of ∼10 m (Berg et al., 2017; Fernando
et al., 2018; Mann et al., 2017; Remmler et al., 2015; Ren et al., 2018;
Toparlar et al., 2015, 2017; Vasiljević et al., 2017;
Watt et al., 2015). With the help of CFD simulation, the generation
mechanisms and characteristics of GWs can be resolved, as well as the
subsequent evolution of GWs.
In this paper, we report long-lived, high-frequency GWs in the whole ABL
detected by the CDL. The characteristics and the generation mechanisms are
analysed using experiments and CFD simulations. Section 2 describes the
field experiments and instruments used in this study. Section 3 presents the
observational results. The CFD model and simulation results are described
and discussed in Sect. 4. Section 5 gives a discussion of the generation
mechanism of the persistent GWs. Finally, the conclusion is drawn in Sect. 6. If not specified, local time is used in this paper and refers to China standard time.
Experiments and instruments
(a) Terrain elevation map. (b) Enlarged area over Anqing station in the hollow white rectangle in (a). The computational domain is roughly along the
white dash-dotted line in numerical simulations.
A field experiment is conducted to study the generation mechanism of GWs by
the CDL at the National Meteorological Observing Station of Anqing
(30∘37′ N, 116∘58′ E) from 16 August
to 5 September 2018. Anqing is located near the Yangtze River and between
Huangshan (30∘08′ N, 118∘10′ E) to the
southeast and the Dabie Mountains (30–32∘ N, 115–117∘ E) to the
northwest, as shown in Fig. 1a. The station is surrounded by hills with a
relative elevation of 200–600 m, as shown in Fig. 1b. An
airport is located to the southeast of the station.
Coherent Doppler wind lidar
A compact micropulse CDL working at an eye-safe wavelength of 1.5 µm
is used in this study. The pulse duration and pulse energy of the laser are
300 ns and 110 µJ, respectively. A double D-shaped telescope is
employed. The absolute overlap distance and blind distance are
∼1 km and 60 m, respectively. This lidar has full hemispheric
scanning capability with a rotatable transmitting and receiving system.
Benefiting from coherent detection, this lidar can perform all-day
measurement of radial wind speed based on the Doppler effect. Compared with
traditional lidars, this CDL is small in size and robust in stability due to
its all-fibre configuration. More details of this lidar are described in
Wang et al. (2017). The key parameters of the CDL
are listed in Table 1.
The wind field is composited by pointing the rotatable scanner in three
directions during the experiment. First, the laser beam is pointed at two
orthogonal azimuths sequentially, north and west, with a zenith angle of
30∘. Then, the laser beam is pointed vertically upward. In each
direction, the measurement duration is set to 10 s.
The full period of the measurement cycle is 41 s. The observational results,
such as the vertical and horizontal wind components and the carrier-to-noise
ratio (CNR) in the vertical beam, are shown in Appendix A. The blank areas
without measurements are caused by rainy summers. For example, Tropical Storm Rumbia passed by around 17 August 2018. To guarantee the
precision of the wind measurements, the data with a CNR of less than -35 dB are
excluded (Wang et al., 2017, 2019).
Radiosonde
The National Meteorological Observing Station of Anqing is one of 120
operational radiosonde stations in mainland China (excluding Hong Kong; Li, 2006). The China Meteorological Administration has deployed an
L-band (1675 MHz) sounding system at this station. Air temperature,
pressure, relative humidity and wind from the ground to middle stratosphere
can be measured twice a day at 07:15 and 19:15 by this sounding system,
which combines a digital radiosonde with a secondary wind-finding
radar. Previous studies have confirmed the accuracy measured by this type of
radiosonde (Bian et al., 2010). A comparison between the wind
measurements taken by the CDL and the radiosonde was carried out recently by
Wei et al. (2019) to validate the performance of the CDL.
ERA5 reanalysis data
ERA5 is the fifth generation of the European Centre for Medium-Range
Weather Forecasts (ECMWF) atmospheric reanalysis of the global climate. The ERA5
reanalysis assimilates a variety of observations and models in 4 dimensions.
The data resolve the atmosphere with a horizontal resolution of 0.3∘ both longitudinally and latitudinally and using 137 levels from the surface up to an 80 km altitude (Hersbach and Dee, 2016). The hourly temperature data
from the subdaily high-resolution-realization deterministic forecasts of
ERA5 are used to calculate buoyancy frequency near the station in a later
analysis in this study.
Observations and analysisThe long-lived GWs
Height–time cross sections of the (a) vertical wind speed, (b) horizontal wind speed, (c) horizontal wind direction and (d) CNR from the vertical beam obtained by the CDL from 4 to 5 September 2018. The direction is defined as
the angle clockwise from north.
Figure 2a shows the persistent wave motions in the vertical wind lasting longer than
10 h in the ABL between 4 and 5 September 2018. These waves exist for
longer than 20 periods and then dissipate during the evolution of the
convective ABL on the morning of 5 September 2018. The corresponding
horizontal wind speed and wind direction are shown in Fig. 2b and c,
respectively. Two weak low-level jets are observed at heights of
approximately 0.5 and 1.5 km. The lower easterly jet stream lasts only a few
hours with a speed of approximately 5 m s-1, while the higher jet stream
exists during the whole lifetime of the wave motion. The speed of the higher
jet stream is approximately 10 m s-1 and then decreases to
approximately 3–5 m s-1 after 21:00. The corresponding
direction of this northerly jet stream also changes to westerly. The CNR
from the vertical beam is shown in Fig. 2d; it varies slowly with time and is
nearly stratified with altitude. Thus, the ABL seems to be stably stratified
because the CNR may represent the aerosol concentration in some cases.
(a) Mean vertical wind between 600 and 1000 m. (b) Corresponding
wavelet power spectrum of the vertical wind in (a). The brown contours
indicate a significance level of 95 %. The black solid lines represent the
cone of influence.
The periods of these wave motions are typically approximately
10–30 min. The temporal profiles of the average vertical wind
between 600 and 1000 m are plotted in Fig. 3a. Oscillations in the vertical
wind can be seen clearly. The amplitudes of these wave motions are
approximately 0.2 m s-1 before 03:00 and then decrease to approximately
0.15 m s-1, while the periods increased after 04:00. The wavelet power
spectrum of the vertical wind in Fig. 3a is shown in Fig. 3b by using the
Morlet mother wavelet. There are obvious waves with periods of
15–25 min before 03:00 and waves with periods of
20–30 min after ∼04:30. Relatively weak waves
with periods of approximately 10 min are also observed between 03:00 and
05:00. These wave motions could be regarded as quasi-monochromatic waves as
the periods vary within the range of 15–30 min. The change
in periods may be in relation to changes in the background ABL, such as
changes in the height of the upper jet stream.
Zonal wind can be derived from the horizontal wind speed and direction. The
height-averaged perturbations in the vertical wind
w′ and zonal wind
u′ between 600 and 1000 m are
shown in Fig. 4. First, the raw vertical (or zonal) winds are averaged between
600 and 1000 m. Second, the temporal profile of the averaged
vertical (or zonal) winds is smoothed by a 1 h window as the background.
Third, the background is subtracted to remove the trend. Finally, the
perturbation is smoothed by averaging the adjacent three points to reduce
high-frequency noises. It is obvious that wave motions also exist in the
horizontal wind. The periods of zonal perturbations are similar to
those of vertical perturbations. Specifically, the vertical and zonal
perturbations are 90∘ out of phase, with the vertical perturbations
w′ generally leading to zonal perturbations
u′, especially after 02:00. Note that the wave
motions exhibit highly coherent vertical motions with no apparent phase
progression with altitude, as shown in Fig. 2a. These characteristics of wave
motions indicate ducted wave structures within the ABL (Fritts et al., 2003).
Perturbations of vertical wind
w′ (black dash-dotted line, left axis)
and zonal wind u′ (blue solid line,
right axis) obtained between 600 and 1000 m altitude from 22:00 on 4 September to 08:00 on 5 September 2018.
(a) Temperature (black solid line) and potential temperature (blue solid line)
profiles from radiosonde at 07:15 on 5 September and
ERA5 (dash-dotted lines) between 22:00 on 4 September and 08:00 on 5 September. Profiles of temperature (red solid line) and potential temperature (purple solid line) from the radiosonde at 19:15 on 4 September are also plotted. (b) Corresponding buoyancy frequency profiles from radiosonde (black solid line) at 07:15 on 5 September and ERA5 (dash-dotted lines) between 22:00 on 4 September and 08:00 on 5 September. The buoyancy
frequency profile (orange solid line) from the radiosonde at 19:15 on 4 September is
also plotted.
Temperature profiles measured by the radiosonde attached to a weather
balloon and hourly temperature profiles from ERA5 during the wave motions
are shown in Fig. 5a. An inversion layer is observed below an altitude of
∼500 m. The corresponding squares of the buoyancy frequency,
N2=gθ∂θ∂z,
are plotted in Fig. 5b, where g is the gravitational acceleration and
θ is the potential temperature at altitude z. Maxima values of
N2 larger than 5×10-4 rad2 s-2 appear in the inversion
layer from both the radiosonde and ERA5 data, indicating a strongly
stratified stable boundary layer near the ground. Between ∼600
and ∼2000 m altitude, the values of N2 are so small that
they are close to 0 and even negative at 1800–2000 m via
the radiosonde. These results suggest thermal ducting between the ground and
approximately ∼2000 m, in which the wave motions are trapped,
especially under the inversion. This is why such wave motions have a
lifetime longer than 20 periods. The buoyancy periods from Fig. 5b are
typically 2–10 min. Since the background wind speeds are
relatively small, less than ∼10 m s-1, we neglect the
Doppler effects here. These wave motions should be GWs instead of internal
acoustic waves. Therefore, these waves are suggested to be ducted gravity
waves trapped in the ABL.
Background wind
There are complex relationships between GWs and background wind conditions.
Submesoscale wavelike motions, which are defined as any nonturbulent motion
at a horizontal scale smaller than 2 km and with a period at the scale of
tens of minutes, are primarily generated under very weak winds in the
nocturnal boundary layer (Mahrt, 2014). Note that the wind speed from 4
to 5 September 2018 is weakest during the whole field experiment, as shown
in Fig. A2. To understand the relationship between this ducted GW and the
background wind, a spatiotemporal window of 1 h length and 200 m height
and temporal and vertical spatial step shifts of 1 h and 100 m,
respectively, are used. The mean horizontal wind speed and wind direction in
each window during the whole field campaign in Anqing are easily obtained.
Wind rose of horizontal wind in all temporal–spatial
windows during this experiment. It should be noted that the value of the
radius is logarithmic.
The wind rose of the horizontal wind during the field experiment is shown in
Fig. 6. It is apparent that a northeasterly wind and southwesterly wind
prevail around the station in the ABL during the whole field campaign.
The infrequently observed ducted GWs in Fig. 2 accompany an infrequent
westerly wind. It is interesting to note that the long, narrow plain area
along the Yangtze River around Anqing between Huangshan and the Dabie
Mountains is also along the northeast–southwest direction, as shown in Fig. 1a. The typical elevations of Huangshan and the Dabie Mountains are
approximately 1–2 km. Strong winds along a northwest–southeast
direction may be blocked in the ABL, thus leading to weak wind along the
northwest–southeast direction after the wind flows over Huangshan or the
Dabie Mountains and the prevailing wind flows along the northeast–southwest
direction. As the GWs are favourable for generation under weak wind
conditions, we can imagine that the Dabie Mountains and Huangshan may have
an impact on GWs in Anqing. However, the surrounding hills around the
station, as shown in Fig. 1b, may also affect the generation and existence
of GWs. The effect of surrounding hills will be studied by numerical
simulations in the next section.
CFD simulations
Wavelike motions are common in the stably stratified ABL and may be generated
by topography or the jet stream (Mahrt, 2014). There is a complex
topography around the station, as shown in Fig. 1b, and a low-level jet in
the ABL, as shown in Fig. 2. Both of these phenomena may be responsible for
the generation of persistent GWs. To identify the potential source of the
ducted GWs, a numerical simulation based on CFD is performed to simulate the
fluid flow field. The impact of different boundary conditions, e.g. wind
profile and topography, on atmospheric dynamics can be effectively evaluated
by changing them. In addition, the numerical simulations
can provide complete information on the GWs. This information, such as horizontal wavelength or horizontal phase speed, cannot be
obtained by lidar in this experiment. Therefore, CFD simulations are helpful for
investigating GWs in the ABL.
Model description
Reynolds-averaged Navier–Stokes (RANS) simulations have been widely used to
investigate the wind field over the past few decades (Toparlar et al., 2017). Compared with a large eddy
simulation (LES), a RANS simulation has the advantages of low computational cost and
sufficient accuracy. In this study, a two-equation RANS model based on the
renormalization group (RNG) method is used to simulate the wind field. The
RNG k-ε model was developed to renormalize
the Navier–Stokes equations, which account for the effects of small-scale
motions (Yakhot et al., 1992). The RNG k-ε model is a mature model that has been widely verified in the simulation
of wind flow over complex terrain in recent years (El Kasmi
and Masson, 2010; Yan et al., 2015). The RNG k-ε turbulence
model used in this work is based on OpenFOAM. OpenFOAM is the leading free,
open-source software for CFD simulations. The model transport equations are
obtained as follows:
∂∂tρk+∂∂xiρkui=∂∂xjαkμeff∂k∂xj+Gk+Gb-ρε-YM+Sk,∂∂tρε+∂∂xiρεui=∂∂xjαεμeff∂ε∂xj+G1ϵϵkGk+C3εGb-C2ϵρε2k-Rε+Sε,
where t and ρ are time and air density, respectively; k and
ε are turbulence kinetic energy (TKE) and TKE dissipation rate,
respectively; xi and xj are the displacement in dimensions i and
j, respectively; ui is the velocity in dimension i; αk
and αε are the inverse effective Prandtl numbers for
k and ε, respectively; μeff is the effective
viscosity; Gk and Gb represent the generation of TKE due to the
mean velocity gradient and buoyancy, respectively; YM represents the
contribution of the
fluctuating dilatation in compressible turbulence to the overall dissipation
rate; Sk and Sε are user-defined source terms; and
G1ϵ, C2ϵ and C3ε are constants. In
this paper, the input turbulent parameters recommended by OpenFOAM are
applied. The default model coefficients of RNG k-ε are as follows:
G1ϵ=1.42;G2ϵ=1.42;G3ϵ=-0.33;αk=1; and αε=1.22.
(a) The topography used in CFD simulations. A/B
represents west/east hill. The heights of A and B are represented by hA and hB, respectively. (b) The vertical profile of potential temperature
used in the CFD model. (c) The vertical profile of the inlet wind in the CFD
model. (d) The vertical wind perturbation from lidar
00:00–09:00 on 5 September 2018. A mean value is
subtracted. (e) The CFD-simulated results of vertical wind. (f) Observed
(black) and simulated (red) vertical perturbations at 1 km altitude. The
observed perturbation is smoothed with five-point smoothing.
To simplify the numerical simulation processes, a two-dimensional
rectangular computational domain is applied in this study, with a horizontal range of
70 km and a 5 km range vertical from the sea level. The upper interface
extended to 5 km is set as the symmetric condition to prevent the influence
of the upper interface on the region below 2 km. Under this condition, a
zero gradient is set for all vertical physical variables, and the vertical
velocity is set to 0. The vertical height of the first layer of grid
cells is 5 m. The spatial resolution is approximately 20 m in both the
horizontal and vertical planes. The total number of computational grid cells is
875 000. The velocity inlet is westerly and constant in the western boundary
of the computational domain. The easterly interface is set as a
pressure-outlet boundary to improve reversed flow. The topography is set to
have a no-slip wall condition. A rough wall function is adopted, of which
the formula is as follows (Ren et al., 2018):
uu∗=1Kln(EzcCks),
where E=9.793 is the wall constant, C=0.327 is a roughness constant,
K≈0.4 is the von Kármán constant, ks is the roughness
height, zc is the distance to the cell centre of the first adjacent
wall cell, u is the velocity in the cell centre and u∗ is the
friction velocity. The simulation is run with a time step of 0.5 s.
The CFD cases conducted in this study are used to reveal the influence of
topography and wind shear on the generation of persistent GWs. The initial
thermal field is assumed to be horizontally uniform, using the vertical
temperature profile from the radiosonde on 5 September 2018. The topography is
set at a fixed temperature, since the heat flux at the ground was
unavailable. In this work, buoyant flows are developed with low velocity and
small temperature variations in each layer. The Boussinesq approximation, which treats density ρref(z)
as a constant value at altitude z in all solved equations, except
for the gravity and buoyancy terms in the momentum equation, is
applied for each thin layer. The fluctuation
of ρ(z) is caused by temperature T(z), neglecting
the influence of pressure. The density ρ(z) is approximated
as follows:
ρ(z)=ρref(z)-ρref(z)βT(z)-Tref(z),
where β is the thermal expansivity and Tref(z) is the
reference temperature at altitude z. The Boussinesq approximation
is similar to the anelastic approximation in this form. The main difference
between the Boussinesq and anelastic approximations is that the latter considers the influence of both pressure and temperature in
fluctuations of ρ. Considering computational convenience and
convergence, the Boussinesq approximation is adopted in this work.
Numerical simulations
The initial smoothed topography is shown in Fig. 7a. The horizontal location
of the domain is roughly along the zonal white dash-dotted line in Fig. 1b.
This is because the low-level jet and the background wind are mainly in the
zonal (east–west) direction. The influence of terrain on atmospheric flow is
mainly in this direction. The left (west) hill is defined as A with a height
of hA and the right (east) hill is defined as B with a height
of hB in this study. The maximum elevation of A and B are
approximately 250 and 600 m, respectively. The lidar is located between A
and B. The 1 h mean zonal wind under 2 km from the lidar and the zonal
wind above 2 km from the ERA5 reanalysis data at 00:00 on 5 September 2018
are merged into a sustained imported wind profile u0 along the western
boundary of the computational domain. The vertical profiles of potential
temperature and u0 used in the CFD models are shown in Fig. 7b and c,
respectively. The measured vertical wind perturbation w′ with the
mean value subtracted from it is shown in Fig. 7d. The vertical wind from
the CFD simulations is shown in Fig. 7e. The measured and simulated vertical
perturbations at 1.0 km are compared in Fig. 7f. It is obvious that a similar
wave motion with a similar amplitude and period exists in the ABL. This result
verifies the accuracy of the CFD numerical simulation results in this study.
A short video of the zonal wind and vertical wind in the whole computational
domain can be downloaded from the Supplement. From this video, the zonal
wavelength can be estimated as ∼3 km and the corresponding
zonal phase speed as ∼2 m s-1. In addition,
Kelvin–Helmholtz billows exist in the low-level jet around an altitude of 2
km. These billows may be in relation to the GWs.
Based on this result, wind profiles uz with different wind shear and
topography with different height of hills A and B are employed in the CFD
numerical simulations. A detailed list of boundary conditions is presented
in Table 2. The simulated zonal winds and vertical winds above the lidar for
all cases are shown in Fig. 8. It should be noted that a time of 0
represents a steady state, not the real
time after the simulations started running, in all cases except cases 7 and 8. Here, we mean by a steady state
that which pertains when the turbulence is fully developed. In cases 7 and
8, a time of 0 is defined as that when the simulations started running and
the input velocity flowed from the western boundary at the same time.
In case 1, persistent wave motions not only exist in the vertical wind but
also in the zonal wind near and below the low-level jet at approximately 2 km, as shown in Fig. 8. This is consistent with lidar detections, as shown in
Fig. 4. It is obvious that no wave motions are generated, with uniform wind
speeds of 1, 5 and 10 m s-1 in cases 2–4, respectively.
Thus, GWs cannot be excited without wind shear. From the results of cases 1,
5 and 6, the wave amplitudes and frequencies increase with enhancement
in the wind shear. For cases 1, 7 and 8, no persistent wave motions exist
with the increase in wind speed without enhancement in the wind shear. Only
several solitary wavelike motions can be found when the wind flow passes by
the lidar and dissipates rapidly. In addition, the wave motions in cases
1–8 mainly exist under 2.5 km, where the wind speeds are
relatively weak. Therefore, it can be inferred that it is beneficial to the
generation of persistent waves under persistent weak-wind conditions, which
is consistent with the previous result in Sect. 3.2.
The wind profile and topography for each case in CFD simulations.
CaseWind profileTopographyCaseWind profileTopography1uz=u0hA×1,hB×19uz=u0hA×0,hB×02uz=1 m s-1hA×1,hB×110uz=u0hA×0,hB×13uz=5 m s-1hA×1,hB×111uz=u0hA×1,hB×04uz=10 m s-1hA×1,hB×112uz=u0hA×2,hB×05uz=u0×2hA×1,hB×113uz=u0hA×4,hB×06uz=u0×4hA×1,hB×114uz=u0hA×6,hB×07uz=u0+5 m s-1hA×1,hB×115uz=u0hA×0,hB×28uz=u0+10 m s-1hA×1,hB×116uz=u0hA×0,hB×4
What happens when the heights of hills A and B near the lidar location
change? In cases 9–11, persistent wave structures still exist
with only a few changes when hills A and/or B disappear. From cases 9 and
11–13, persistent wave structures always exist and do not
change significantly. When the height of hill A increases to
hA×6 in case 14, i.e. the height of the low-level
jet near a 2 km altitude, the zonal wind structure changes significantly. In
cases 9–10 and 15–16, wave motions also exist
and do not change significantly even though the height of hill B increases
to the height of the low-level jet, hB×4.
The simulated zonal wind u and vertical wind w above the lidar for
all 16 cases as described in Table 2.
Therefore, based on these results from the simulation cases, persistent GWs
are excited by persistent wind shear around the low-level jet. The wave
structures mainly occur under weak winds. The topography, i.e. the hills
near the station, as shown in Fig. 1b, plays a negligible role in GW
generation. Nevertheless, the topography may play a more important role
downstream where the height of the jet is comparable with the height of the
terrain.
Discussion
Based on the above experiments and simulations, the mechanism of the
persistent wave motions can be inferred as follows: a westerly low-level jet
of ∼5 m s-1 exists above the light southeasterly
background wind. The light wind may be understood in relation to Huangshan and the
Dabie Mountains. The weak wind shear around the low-level jet may lead to
the occurrence of wave motions in the light wind. In addition, a strongly
stable thermally stratified ABL with an inversion layer occurs during the
night in Anqing. Negative values of N2 appear near an altitude of
∼2 km. Therefore, the wave motions may be trapped in a ducted
structure with a long lifetime. The GWs exist without apparent phase
progression with altitude in the whole ABL from the surface to a height of ∼2 km.
Such quasi-monochromatic waves with multiple wave cycles and approximately
constant periods and amplitudes are infrequently observed in the ABL
(Mahrt, 2014). Nevertheless, similar quasi-monochromatic wave motions
with multiple wave cycles have been reported in several studies.
Banakh and Smalikho (2016) revealed a coastal mountain lee wave
with a period of ∼9 min during the daytime on 23 August 2015 in
the stably stratified ABL over the shore of Lake Baikal. The wave existed
between the 100 and 900 m height range with a lifetime of approximately 4 h. This wave was suggested to be in relation to the presence of two
narrow jet streams at heights of approximately 200 and 700 m above ground
level. Similar wave motions were also detected in the vertical wind
accompanied with a low-level jet in Banakh and Smalikho (2018). It is
regrettable that the authors did not give a discussion on the contaminated
wavelike motions from 01:00 to 08:00, except with regard to the internal wave with a
period of ∼6 min at 07:00. Fritts et al. (2003)
reported wave motions with typical periods of 4–5 min below a
height of ∼800 m under light wind with low-level jet and
clear-sky conditions throughout the night of 14 October 1999. These wave
motions were interpreted as ducted GWs that propagated horizontally along
the maxima of the stratification and mean wind and were evanescent above and
possibly below and/or between the ducting level(s) (Fritts et
al., 2003). Viana et al. (2009) also reported a ducted mesoscale
gravity wave over a weakly stratified nocturnal ABL. This wave lasted less
than 10 wave cycles, approximately 2 h, with a period of ∼16 min. Román-Cascón et al. (2015) analysed
nonlocal GWs generated by wind shear or the low-level jet trapped within
the stable ABL. With an acoustic echo sounder, similar wave motions were
also observed without apparent phase progression with altitude in a stably
stratified ABL several decades ago (Beran et al.,
1973; Hooke and Jones, 1986).
The wave motions mentioned above were mainly observed in the stable boundary
layer under a height of ∼1000 m or even ∼100 m, while wave motions exist from the surface layer to as high as
∼2000 m in our study due to different measurement capabilities. In addition, the lifetime of the ducted GWs is more than 10 h and 20 wave cycles, while in the previous studies listed above most
of the lifetimes are shorter in duration with several wave cycles. These
characteristics make these ducted GWs unique and novel. However, in one of
our previous studies, obvious wave motions with periods of 10–30 min in the vertical wind were observed in the whole residual layer from 1 to 2 June 2018 by a similar CDL system (Wang et al., 2019).
The mechanism of these long-lived GWs is consistent with that of other
similar wave motions referenced above in some aspects. The low-level jet or
wind shear is one of the main sources of such wavelike motions in the ABL. A
stably stratified ABL usually leads to effective quasi-monochromatic ducted
wave motions with a long lifetime and multiple wave cycles. Although wind shear
near the low-level jet is the main source of GWs as discussed in Sect. 4.2,
weaker wind shear is more favourable to the existence of high-frequency GWs.
Similarly, the surrounding hills play a negligible role in generating the
ducted GWs while the Dabie Mountains and Huangshan may have an impact on the
generation and existence of GWs.
The vertical structure of GWs is described by the Taylor–Goldstein equation
(Gossard and Hooke, 1975):
m2=N2ci2+u‾zzci-kh2-14H2,
where m is the vertical wavenumber, ci is the intrinsic phase speed in
the direction of propagation, u‾zz is the second derivative with
the height of the mean wind in the direction of wave propagation, kh is
the horizontal wavenumber, and H is the scale height. A sufficiently deep
atmospheric layer is required for a wave duct with positive values of
m2. To resolve this equation, the vertical profile of squared
buoyancy frequency, which is calculated by the temperature profile measured
by the radiosonde, is shown in Fig. 5b. Simultaneous hourly mean wind, which
is required to resolve ci and u‾zz, can be obtained from the
lidar measurements. However, the horizontal structures of this wave motion,
i.e. ci and kh, are still unclear in this study. The horizontal
structures of wavelike motions in the ABL can be detected by airborne lidar
(Chouza et al., 2016; Witschas et al., 2017) and ground-based lidar with
range–height indicator (RHI) scans (Poulos et al., 2002; Wang, 2013) or
plan position indicator (PPI) scans (Mayor, 2017). GW parameters, such as
horizontal phase speed, horizontal wavelength, propagation direction, and
intrinsic frequency, can be resolved from these measurements. Nevertheless,
we try to illustrate the characteristics of this ducted wave to determine a
plausible propagation direction and horizontal wavelength in accordance with the CFD
simulations. The propagation direction is assumed to be westerly here, as
the simulated wave is westerly according to the video available in the Supplement. Thus, the
horizontal wavelength is equal to the zonal wavelength, which is estimated
as ∼3 km in Sect. 4.2.
The vertical profile of the vertical wave number squared is shown in Fig. 9. The
singular point of the relative maxima m2 towards the right-hand side of the figure is caused by
a critical level where the intrinsic frequency is Doppler-shifted close to
0. A ducting process occurs between ∼1.5 km altitude and
the ground where m2>0. This is the result of a
combination of thermal and Doppler ducts. The thermal duct is dominant under
the temperature inversion with a maximum buoyancy frequency squared for all
propagation directions, as shown in Fig. 5. The Doppler duct is dominant
between the ∼0.5 and ∼1.5 km altitude range
due to the critical level induced by the low-level jet of wind maximum in a
particular direction. Thus, the ducted motions give a plausible explanation
for the long-lived trapped GWs in the ABL.
The vertical profile of the vertical wave number squared. The dotted
line represents the zero line.
It should be noted that the retrieval of horizontal wind is based on the
hypothesis of a homogeneous wind field on a horizontal plane. Accompanying
the wave activities, the radius of the scanning beam cone leads to a bias in
the retrieved horizontal wind. If the radius is equivalent to or larger than
the scale of the horizontal wavelength of the GWs, these biases may
significantly affect the result in the horizontal plane, especially the amplitude
of the retrieved GWs. Nevertheless, the bias in the period of the wave
motion is negligible. If the radius is smaller than the scale of the
horizontal wavelength of the GWs, the biases in both amplitude and period
can be ignored. In this study, the horizontal wavelength is estimated to be
∼3 km in Sect. 4.2. The radii are approximately 580 m and 870 m at 1 km and 2 km altitude, respectively. Thus, the retrieved bias
can be ignored in this study.
A 2-D model is used in this simulation rather than a 3-D model which in
principle can more accurately simulate the atmospheric flow. Considering the
direction of the low-level jet and the maximum background wind flow, the
zonal transect in this case is appropriate for a 2-D model; the influence of
terrain on atmospheric flow is mainly in this direction. However, the 2-D
model cannot simulate the information in another dimension, e.g. lateral
flow around the hillside and the blocking effect of the low terrain on both
sides, leading to errors compared with a 3-D model. Nevertheless, comparison
between numerical simulation results and field experiments show that 2-D
models can simulate the actual topographic flow well in some cases
(Miller and Davenport, 1998; Toparlar et al., 2017; Walmsley et al.,
1984). Furthermore, some basic theories and empirical formulas of complex
mountain wind fields are built on the basis of a 2-D model. In
addition, a 2-D model consumes many fewer computing resources and much less time than 3-D
models. Therefore, the 2-D terrain simulation of the mountain
wind field has wide-ranging theoretical significance and applicability.
By using this simplified 2-D model, the influence of terrain on GWs can be
analysed.
Conclusions
A persistent wave motion was investigated by experiments and numerical
simulations. From 4 to 5 September 2018, GWs with periods of
10–30 min were observed in the whole ABL from the ground to a
height of ∼2 km by a coherent Doppler lidar during a field
experiment in Anqing. The amplitudes of these GWs were approximately
0.15–0.2 m s-1 in the vertical wind direction. These GWs existed
for longer than 20 wave cycles. The periods were approximately
15–25 min before 03:00 and 20–30 min after
03:00. A westerly low-level jet was observed at an altitude of
1–2 km in the ABL with maxima speeds of 5–10 m s-1. Simultaneous temperature profiles from radiosonde measurements and
ERA5 reanalysis data confirmed the existence of a strong stably stratified
ABL. There was an inversion layer below the altitude of ∼500 m and a negative buoyancy frequency squared near the height of
∼2 km. Note that there was no apparent phase progression with
altitude for these GWs. Moreover, the vertical and zonal perturbations in
the GWs were 90∘ out of phase with the vertical perturbations
generally leading zonal perturbations. These characteristics suggested that
such GW motions are ducted GWs trapped in the ABL, which is also verified by
the vertical structure of the wave motions. Based on simplified 2-D CFD
numerical simulations, the generation mechanisms of such GWs were discussed.
The low-level jet streams were considered to be responsible for the
excitation of GW motion in the present study. Wave motions mainly occurred
under weaker wind conditions, which was consistent with other studies of
ducted waves. The contributions from wind flow over the surrounding hills
could be ignored.
The current study contributes to our understanding of the GW generation
mechanism in the ABL, which plays a key role in atmospheric dynamics.
Furthermore, the National Meteorological Observing Station of Anqing is
close to an airport, as shown in Fig. 1b, which will be affected by clear-air turbulence caused by breaking GWs and rotors affected by the trapped
GWs. The application of such a coherent Doppler lidar will enhance
measurement capability generating high-quality data in the ABL, thus enriching our
knowledge and improving aviation safety, weather forecasting and climate
modelling in the future. However, the horizontal structures of GWs are still
unclear in this study. Simultaneous measurements with multiple lidars and multiple
scanning modes are required in additional studies.
Data availability
The ERA5 data sets are publicly available from the ECMWF website at https://cds.climate.copernicus.eu/cdsapp#!/home
(last access: 1 March 2019; C3S, 2017). The elevation data are available on the Shuttle Radar Topography Mission (SRTM) website at http://srtm.csi.cgiar.org (last access: 1 March 2019; Jarvis et al., 2008). Lidar and radiosonde data can be downloaded from
http://www.lidar.cn/datashare/Jia_et_al_2019.rar (last access: 16 March 2019; Jia et al., 2019).
Video supplement
A video of vertical wind and horizontal wind simulated by a CFD model in the whole 2-D computational domain for case 1 in Table 2 is provided (10.5446/41847, Jia and Yuan, 2019).
Lidar observational results during the experiment
The vertical wind, horizontal wind speed, wind direction and CNR during the
field experiment from 16 August to 5 September 2018 are shown in Figs. A1–A4, respectively.
Time–height cross section of vertical wind speed per day during
the experiment. Dates are shown in the top left of each panel, and are read
as YYYY/MM/DD.
Similar to Fig. A1 but for horizontal wind speed.
Similar to Fig. A1 but for horizontal wind direction.
Similar to Fig. A1 but for CNR.
Author contributions
HX conceived of and designed the study. YW, LZ CW and MJ performed the lidar
experiments. MJ, CW and TW performed the lidar data analysis. LL, DL and RC
provided the field experiment site and the radiosonde data. JW analysed ERA5
data. JY performed the CFD numerical simulations. MJ and JY carried out the
analysis and prepared the figures with comments from the other coauthors. MJ,
HX, XX and XD interpreted the data. MJ, JY and HX wrote the manuscript. All
authors read and approved the final manuscript.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
We acknowledge the use of ERA5 data sets from the ECMWF website at https://www.ecmwf.int/en/forecasts/datasets/ reanalysis-datasets/era5 (last access: 1 March 2019). We
acknowledge the use of elevation data sets from the SRTM website at http://srtm.csi.cgiar.org (last access: 1 March 2019).
Review statement
This paper was edited by Geraint Vaughan and reviewed by two anonymous referees.
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