ISSN 00014338, Izvestiya, Atmospheric and Oceanic Physics, 2015, Vol. 51, No. 2, pp. 193–202. © Pleiades Publishing, Ltd., 2015. Original Russian Text © V.S. Lyulyukin, M.A. Kallistratova, R.D. Kouznetsov, D.D. Kuznetsov, I.P. Chunchuzov, G.Yu. Chirokova, 2015, published in Izvestiya AN. Fizika Atmosfery i Okeana, 2015, Vol. 51, No. 2, pp. 218–229.
Internal GravityShear Waves in the Atmospheric Boundary Layer from Acoustic Remote Sensing Data V. S. Lyulyukina, M. A. Kallistratovaa, R. D. Kouznetsova, b, D. D. Kuznetsova, I. P. Chunchuzova, and G. Yu. Chirokovac a
Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Pyzhevskii per. 3, Moscow, 119017 Russia b Finnish Meteorological Institute, FI00101 Helsinki, Finland c Colorado State University, CIRA/CSU, Fort Collins, CO, USA email:
[email protected] Received September 24, 2013; in final form, July 22, 2014
Abstract—The yearround continuous remote sounding of the atmospheric boundary layer (ABL) by means of the Doppler acoustic radar (sodar) LATAN3 has been performed at the Zvenigorod Scientific Station of the Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, since 2008. A visual analysis of sodar echograms for four years revealed a large number of wavelike patterns in the intensity field of a scat tered sound signal. Similar patterns were occasionally identified before in sodar, radar, and lidar sounding data. These patterns in the form of quasiperiodic inclined stripes, or cat’s eyes, arise under stable stratifica tion and significant vertical wind shears and result from the loss of the dynamic stability of the flow. In the foreign literature, these patterns, which we call internal gravityshear waves, are often associated with Kelvin–Helmholtz waves. In the present paper, sodar echograms are classified according to the presence or absence of wavelike patterns, and a statistical analysis of the frequency of their occurrence by the year and season was performed. A relationship between the occurrence of the patterns and wind shear and between the wave length and amplitude was investigated. The criteria for the identification of gravityshear waves, mete orological conditions of their excitation, and issues related to their observations were discussed. Keywords: internal sheargravity waves, Kelvin–Helmholtz waves, atmospheric boundary layer, ground based remote sensing, sodar DOI: 10.1134/S0001433815020103
1. INTRODUCTION The existence of mesoscale wavelike patterns (with a wavelength from 100 m to several kilometers) in the lower troposphere was known as early as two centuries ago from observations of clouds of unusual form. A schematic depiction of the shapes of these patterns and examples of the photographs of clouds in the form of billows with a characteristic vorticity in their upper part and in the form of inclined stripes are given in Fig. 1. Such patterns arise when the airflow loses sta bility because of a jump in air density and wind speed at the top of the cloud and are a typical example of Kelvin–Helmholtz waves (KHWs). The wavelike cloud patterns shown in Fig. 1 exist a few minutes and disperse afterward. Laboratory investigations of sheared flows in a two layer fluid, which had been started in the 1970s [1] and continued later [2], demonstrated the generation and breakdown of KHWs, the shapes of which agree well with both the observed wavelike patterns in clouds and the numerical modeling results [3]. However, in a cloudless atmospheric boundary layer (ABL), such patterns were not identified until the development of
groundbased remote sensing instruments (sodars, radars, and lidars). With the advancement of the sounding technology providing the highresolution visualization of mesos cale turbulence structures, wavelike patterns were occasionally detected in lowlevel jets, which have place in a stably stratified ABL and are characterized by strong wind shears. Then, with the appearance of scanning Doppler radars and lidars, these patterns were detected not only in the field of refractive index fluctuations, but also in the wind field. Note that there is still no commonly accepted ter minology for wavelike motions in the cloudless atmo sphere in the Russian or foreign literature. In many publications abroad, the patterns we consider are called Kelvin–Helmholtz waves, although they are only a partial case which occurs in the atmosphere with a density and velocity discontinuity of a medium. We will therefore use the term “internal gravityshear waves” (IGSWs). One of the most important problems of dynamic meteorology is the generation, propagation, and decay of internal gravity waves in the atmosphere, because
193
194
LYULYUKIN et al. (а)
i
ii (b)
iii
(c)
Fig. 1. Kelvin–Helmholtz waves (KHWs) in the atmo sphere. (a) Schematic picture of (i) billows, (ii) cat’s eyes, and (iii) inclined stripes. (b, c) Examples of clouds with KHWs, Voskresensk district, Moscow region, October 2013: (b) billows, time 14:37:02 and (c) inclined stripes, time13:45:54 (photo: of G.Yu. Chirokova).
they accomplish the vertical transport of heat, momentum, and water vapor through stable layers. Several hundred journal papers on IGSWs have been published over the last three decades. Most of these publications are theoretical studies of waverelated hydrodynamic problems (e.g., [4–6]) or the numeri cal modeling studies of mesoscale and largescale wave processes [7–10]. Far less attention is paid to observa tions of the waves in the atmosphere, their climatol
ogy, and measurements of their parameters. The same tendency is clearly seen in the wellknown mono graphs [11–13]. Among the experimental IGSW studies, radar observations of the waves in the upper troposphere, lower stratosphere, and ionosphere have a major place [14–16]. This is related to the widespread networks of continuous atmospheric sensing by pulsed veryhigh frequency (VHF) and highfrequency (HF) radars, which often record ISGWs at heights of 2–20 and 50– 100 km. The vertical resolution of such radars (100 to 200 m) is insufficient to investigate a stably stratified ABL. In the atmospheric boundary layer, remote obser vations of IGSWs are scarce and there is little or no cli matological information. Evidently, this is explained by the absence of the ABL monitoring network and occasional sounding of this layer. As far as we know, only about a dozen of papers have been published since 1968 on the detection of IGSW trains at heights of up to 1 km by frequencymodulated continuos wave (FMCW) radars, sodars, and lidars which have a vertical resolution (2–20 m) sufficient for a detailed study of structure formations. However, comparisons of IGSW observations in the ABL with theoretical models were made only in several papers. The com parisons were qualitative, rather than quantitative [17–19]. Studies of ISGWs are quite important specif ically in the atmospheric boundary layer, because these waves may have a significant influence on the develop ment of turbulence and heat and mass exchange [20]. Understanding of the role of gravityshear waves is important for correcting parametrizations of a stable boundary layer in numerical models of atmospheric circulation. The studies of the waves in the ABL are also essential for solving many applied problems related to shortrange pollution transport and wind farm efficiency (see, e.g., [21]). The goal of this paper is to study statistics of the occurrence of IGSWs; altitudes of their location; and their duration, amplitude, period, and wavelength, as well as to compare some parameters of IGSWs with parameters of lowlevel jets (LLJs) using data from multiyear 24h acoustic (sodar) atmospheric sounding in the Moscow region [22, 23]. Section 2 gives exam ples of IGSW visualization by means of groundbased remote sensing. Section 3 describes instrumentation and setup for acoustic atmospheric sounding at the Zvenigorod Scientific Station of the Obukhov Institute of Atmospheric Physics, Russian Academy of Sci ences, and formulates criteria for the identification of the IGSW in sodar echograms. Section 4 outlines sta tistics obtained from the 2009–2011 sounding data. Finally, conclusions are presented and some unre solved problems of experimental IGSW studies are formulated.
IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
Vol. 51
No. 2
2015
INTERNAL GRAVITYSHEAR WAVES IN THE ATMOSPHERIC BOUNDARY LAYER
2. SHAPES OF INTERNAL GRAVITYSHEAR WAVES DETECTED BY RADARS, SODARS, AND LIDARS
The development of Doppler sounding opened up the opportunity for visualizing the waves in the wind speed field [19, 29]. Figure 3 shows examples of spa cial images of IGSWs in the horizontal extent–height coordinates recorded by modern instruments: a scan ning Doppler radar and a scanning pulsed highreso lution radar. The spatial structure in the form of bil lows is clearly seen in the field of the radial wind veloc ity in a shallow surface inversion (Fig. 3a); cat’s eyes were identified in the field of the vertical wind shear in an elevated inversion (Fig. 3b). Such spatial patterns allow the sizes of IGSW trains and wavelengths to be IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
600
Height, m
500 03:52
03:54
03:56
250 200 150 03:28
03:30 (b)
03:32
Height, m
300 200 100 0 08:10
08:20 (c)
08:30
600 Height, m
Examples of first records of internal gravityshear waves in the cloudless ABL in radar and sodar echograms in height–time coordinates are shown in Fig. 2 [24–27]. The degree of shading corresponds to the strength of a received signal from radio waves or sound backscattered by inhomogeneities of the refrac tive index of air. Since the strength of the received sig nal is proportional to the structure parameter of turbu lent temperature fluctuations CT2 (for sodar) or humid ity C q2 (for FMCW radar) [28], the darker the color of the pattern in the echogram is, the more the pattern is turbulized. Trains of wavelike patterns are clearly seen in the echograms. The IGSWs in the form of cat’s eyes and billows (Fig. 1a) recorded by a FMCW radar in a thin elevated inversion layer are shown in Fig. 2a. Sodar echograms with IGSWs in the form of cat’s eyes and inclined stripes in elevated inversions are dis played in Figs. 2b and 2c. Cat’s eyes in a shallow inver sion recorded by a minisodar with a high space reso lution (3.5 m) and a high time resolution (1 s) are shown in Fig. 2d. The altitudes of the location of the IGSWs, their amplitudes, and their periods in Figs. 2a–2d differ significantly from each other (the height and time scales in these graphs are different), but the shapes of these wave formations extending through the entire depth of the elevated or surface temperature inversion are easy to distinguish. They look nothing like a nearsinusoidal shape of traveling internal gravity waves, which are also occasionally recorded in the echograms as undulation of the inver sion layer boundaries.
(а)
400 200 06:30
07:00
07:30
08:00
(d)
100 Height, m
In investigations of the statically stable ABL by groundbased remote sounding, the time scan of the echosignal intensity reveals typical wavelike patterns. They are similar in shape to the Kelvin–Helmholtz waves shown in Fig. 1 and are usually associated with the IGSWs. The first cases of the IGSWs in the cloud less atmospheric boundary layer detected by radars and sodars date back to the mid1960s. A comprehen sive verbal description of the objects we study here is rather difficult to give; we therefore present some examples of IGSW visualization below.
195
50
0 02:25
02:30
02:35 Local time
02:40
02:45
Fig. 2. Visualization of IGSWs in radar and sodar echograms: (a) FMCW radar, San Diego: (top) June 23, 1970 and (bottom) June 25 1970; (b) Sodar, Oklahoma, September 6, 1971; (c) sodar, Colorado, March 2, 1971; and (d) sodar, ZSS IAP RAS, March 28, 1991. Adapted from [24–27].
estimated without using the Taylor hypothesis of fro zen turbulence. Of all the remote sensing facilities suitable for visu alization and research of IGWs in the ABL, sodar is the simplest and most costefficient instrument [30]. Modern highfrequency minisodars of high spatial resolution (~2 m) [31] allow the wave processes in the lower part of the ABL to be investigated in detail. Vol. 51
No. 2
2015
196
LYULYUKIN et al.
Height, km
(а) 50
Height, m
0 400 800 1200 Distance from radar, km Radial velocity, m/s 0 5 10 (b) 2 1 0 15 20 25 30 Distance from radar, m Velocity shear, (m/s)/km –20 0
10
35 20
Fig. 3. Visualization of gravityshear waves in space coor dinates: (a) billows in a twodimensional field of the radial wind velocity from scanning radar data, October 6, 1999, Kansas; and (b) cat’s eyes in a twodimensional field of the vertical wind shear from scanning pulsed radar data, Deptember 6, 1995, Chilbolton, England. Adapted from [19, 29].
Images of IGSWs analogous to those shown in Fig. 2 were obtained from the sodar measurements at the Zvenigirod Scientific Station (ZSS) of the Obukhov Institute of Atmospheric Physics (IAP), Russian Academy of Sciences, in 2008–2013. 3. MEASUREMENT SITE, EQUIPMENT, AND CRITERIA FOR IDENTIFICATION OF INTERNAL GRAVITYSHEAR WAVES An investigation into IGSWs was carried out using measurements of the ABL parameters at a permanent site of groundbased remote sensing at the ZSS. This station operated year round since 2008. In this paper we used measurements mainly for 3 years, from 2009 to 2011, and some measurements in 2008. The Zvenigorod Scientific Station is located 50 km west of Moscow (55°42′ N, 36°47′ E) in a wooded countryside at an elevation of 150 m above sea level. The landscape around the station is mostly flat, slop ing gently (~1°) to the Moskva River with smooth hills. The elevation difference within 10 km does not exceed 40 m. There are several low buildings around the station. A motor road runs nearby. With nocturnal surface inversions in the summer and almost 24h inversions in the winter, lowlevel jets regularly arise over the ZSS area with winds in the core of the jet stream of 10–15 m/s. There is usually dead calm near the ground, and the vertical wind shear often attains 7–9 m/s per 100 m [23].
Measurements were taken with LATAN3 research sodars designed and produced at IAP [32]. The three component Doppler sodar LATAN3 has been oper ated at a carrier frequency of 2000 Hz and had a verti cal resolution of 20 m, a time resolution of 15 s, and an altitude range from 30 to 300–800 m (depending on the intensity and vertical distribution of the refractive index fluctuations and on the level of ambient acoustic noise). The instrumental accuracy is ±0.5 m/s for the horizontal wind components and ±0.1 m/s for the ver tical wind velocity. Examples of recording IGSWs in sodar exhograms in the height time coordinates are shown in Fig. 4. On the right is the scale of the echosignal intensity in decibels. The sodar profiles of the horizontal wind speed and direction averaged over 30 min are displayed below each echogram. Wind speeds of low statistical probability (more than 75% of instantaneous values were excluded from averaging according to the signal tonoise ratio) are denoted by solid lines. The vertical bands at the top of the echograms are caused by the acoustic noise from motor vehicles driving on the road near the site where the sodar is installed. Zero or decreased mean wind speeds at a height of 150 m are an artifact caused by the reflection of a sodaremitted sound pulse from a watertower located at the ZSS at a distance of 150 from the sodar. The patterns of the type of cat’s eyes were recorded rarely by the ZSS. There were only several cases of these patterns over 4 years. All of them occurred in ele vated inversions. The cat’s eyes shown in Fig. 4a were formed at 400 m, in the upper part of a weak jet, where the mean wind speed decreases with height. Not a sin gle case of IGSWs in the form of billows was recorded. Therefore, all statistical characteristics in Section 3 refer to wavelike patterns in the form of inclined stripes, similar to the examples in Figs. 4b–4d, which correspond to the schematic shape (iii) in Fig. 1a. Such stripes usually arose in the lower part of strong jet streams, where the maximum wind speed was 10– 15 m/s and the wind speed increased with height by more than 4–5 m/s per 100 m. The speed dropped sharply at the top of the inversion layer, which was identified by a decrease in the echosignal intensity [33]. The wind enhancement with height in the LLJs was often accompanied by a significant wind shift. However, there were cases where the IGSWs occurred at much lower maximum wind speeds and shears. Surprisingly, not a single case of the transition from one IGSW pattern to another was recorded at the ZSS. At the same time, the simplified linear theory of IGSWs [13, 34] shows that the three IGSW patterns (Fig. 1a) occur successively when the IGSWs develop and break down. These theoretical conclusions were quantitatively confirmed in laboratory experiments [2]. It is unclear whether the lack of evolution and decay of the IGSW trains in the sodar echograms is a consequence of the insufficient sensitivity and resolu tion of LATAN3 and of the fact that sodar provides
IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
Vol. 51
No. 2
2015
INTERNAL GRAVITYSHEAR WAVES IN THE ATMOSPHERIC BOUNDARY LAYER
Height, m
(а) 600 01.09.2009
02.09.2009
400 200 0 600
00:00
01:00
N E S W N E S W N E S W N E S W N Rhumb
400 200 0 0 2 4 6 0 2 4 6 0 2 4 6 0 2 4 6 V, m/s 09.08.2008
(b) 400 200 0
07:00
08:00
N E S W N E S W N E S W N E S W N Rhumb
200 00 2 4 6 0 2 4 6 0 2 4 6 0 2 4 6 V, m/s 05.11.2008 (c)
400 dB 70
200 Height, m
only the temporal evolution of events at a single site and gives no spatial information. The lack of evolution can also be attributed to a specificity of the behavior of the IGSWs in a real ABL, where the waves may be affected by many factors missing in the theory (includ ing air viscosity, surface stress, reflection from the boundaries of a jet stream, etc.). Note also that no influence of IGSWs on the variance of the vertical wind velocity was found in [33], where the intensities of vertical turbulent mixing in lowlevel jets with IGSWs were compared with those without IGSWs. Moreover, it is possible that the evolution of the IGSW patterns is not recorded in the echograms because of the lower intensity of sound scattering from the parts of the wave where there is no turbulence [35]. In order to obtain climatological statistics of IGSWs, it is necessary to formulate criteria for their identification in the echograms. Such criteria are largely subjective and, moreover, depend on the reso lution of the equipment. In the sodar data measured at the ZSS in 2009–2011, the IGSW episodes were iden tified in the echograms visually by two operators sepa rately using the following criteria: 1. The shape of wavelike patterns corresponds to the schematic pattern (iii) in Fig. 1a. 2. The minimum period of wavelike patterns at least 12 times greater than the time resolution, given by the period of transmission of sounding pulses (i.e., >3 min). 3. The thickness of the layer of wave activity (i.e., double wave amplitude) is at least three times greater than the height resolution of the sodar (>60 m). 4. The depth of modulation of the background echosignal level by a wave structure exceeds 5 dB. 5. The train of wavelike structures contains at least three wave periods. The recognition of patterns with smaller periods, duration, amplitudes, and modulation depths is unreliable. Note, that the parameter set of LATAN3 sodar at ZSS in 20092011 was not optimal for IGW observations, so smaller and shorter waves are missing from the statistics obtained in the next section. The used parameter set was chosen primarily for other applications, such as wind observations.
197
0
03:00
04:00
N E S W N E S W N E S W N E S W N
400
50
200 0
60
40 0 2 4 6 0 2 4 6 0 2 4 6 0 2 4 6 V, m/s 09.11.2010
(d) 600 400 200 0
09:00
10:00
N E S W N E S W N E S W N E S W N Rhumb
400 200
4. STATISTICS OF THE OCCURENCE OF INTERNAL GRAVITYSHEAR WAVES AND THEIR CHARACTERISTICS IN THE ABL The statistical data given below involve measure ments for 3 years, from 2009 to 2011. The structure of the IGSWs in the echograms in Fig. 4 is clearly seen because the echosignal intensity modulation by “stripes” reaches 15–20 dB. In addition to these pat terns, a number of less distinct IGSWs were identified IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
0
0 2 4 6 0 2 4 6 0 2 4 6 0 2 4 6 V, m/s Local time
Fig. 4. Visualization of IGSWs by sodar LATAN3, ZSS IAP: (a) cat’s eyes and (b) inclined stripes. Below echograms are the 30minaveraged profiles of the magni tude of horizontal velocity (dots connected by lines) and wind direction in rhumbs (dots without lines). Wind speeds with low statistical probability are shown by solid lines. Vol. 51
No. 2
2015
198
LYULYUKIN et al. 35 2009 2010 2011
30
Total duration, hour
25 20 15 10 5 0 Jan. Feb.
March May July Apr. June
Sept. Aug.
Nov. Oct.
Dec.
Fig. 5. Monthly distribution of the total duration (in hours) of recording gravityshear waves in sodar echograms, Zvenigorod Sci entific Station, 2009–2011.
with a modulation depth of just 5 to 10 dB. The cases were not classified according to the modulation depth, because this did not result in any significant changes in statistical distributions of the wave parameters. Overall 3 years of 24h LATAN3 echograms, there were 234 cases of IGSWs with a duration of wave trains from 15 min to several hours. The total duration of the IGSW cases was about 400 h. This is roughly 6% of the total lifetime of inversion layers observed at the ZSS. The distribution of the total duration of the identi fied IGSWs by months is given in Fig. 5. The largest number of IGSWs occurred in January and Septem ber, and the smallest number was in February, October, and December. However, the interannual variability of the number exceeds the variability from season to sea son, so this distribution gives no way of making any conclusion about the annual cycle of the IGSW fre quency at the ZSS. Their formation does not seem to be related directly to the mean air temperature and wind speed and direction, which vary seasonally. The mean period of the IGSWs for every case was determined visually from the echogram. The distribu tion of the IGSWs by oscillation periods is shown in Fig. 6. The distribution demonstrates a rapid decrease in the number of cases with periods above 3 min. At the same time, several episodes of IGSWs were detected with anomalously long periods, which correspond to wavelengths of 5–8 km. The skewness of this distribu tion is caused by a choice of the IGSW identification criteria determined by a resolution of the sodar.
Using the Taylor hypothesis of frozen turbulence, it is possible to estimate the length of the observed wave as the period, determined from the echogram, multi plied by the mean wind speed in the layer with an IGSW. This parameter allows a qualitative comparison with modeling results for IGSWs. Howard’s semicircle theorem [34] says that a necessary condition for insta bility is Richardson number criterion: Ri < 1/4 some where within in the layer. Gravityshear waves with a positive growth rate dependent on the wave number and the Richardson number can then arise in a medium. The ratio of the internal gravityshear wave length L to the waveactivity layer thickness h, in dif ferent models, depends on the assumed vertical pro files of air density and wind speed. The most likely values for different models lie in the range 4.4 < L/h < 7.5 [34]. The dependence of the spatial period (wavelength) L calculated under the hypothesis of frozen turbulence on the layer thickness h, which corresponds to a dou ble fluctuation amplitude determined visually in the echogram, is shown in Fig. 7. The accuracy of the visual determination of a wave period and amplitude is limited by the resolution of the sodar. The mean ratio L/h calculated for 234 cases was found to be 9.2 ± 0.3, a value that is comparable to L/h = 7.5, which corresponds to the most rapidly growing mode in a model with linear velocity and den sity profiles [34]. A theoretical relation is also given in Fig. 7. Earlier, in analyzing the IGSW parameters obtained from sodar measurements at the ZSS [36], the ratio was calculated to be L/h = 8.5 ± 0.3, which
IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
Vol. 51
No. 2
2015
INTERNAL GRAVITYSHEAR WAVES IN THE ATMOSPHERIC BOUNDARY LAYER
Number of occurrences
140 120 100 80 60 40 20 0
3
4
5
6
7 8 Т, min
9
10
11
Fig. 6. Distribution of stripes periods, ZSS, 2009– 2011.
was caused by more rigorous criteria for a choice of IGSW cases. To find a connection between wind shear and IGSWs generation, wind shears were calculated sepa rately in the lower part of all LLJs observed at the ZSS in 2009 and in those jets in which IGSWs were recorded. In the literature there is no conventional method for estimating wind shear in the layer because of a wide variaty of shapes of vertical profiles of wind speed. In our paper, the wind shear in the layer was defined as a difference between the maximum and minimum wind speeds normalized to the layer thick ness. Figure 8 shows a distribution of the total duration
199
of IGSWs for different wind shears in 2008–2011 and a distribution for 1haveraged wind shear in noctur nal LLJs for 2009 determined from the echograms. The shapes of the distributions do not differ much: both are nearnormal distributions peaked at a shear of 3.5 m/s per 100 m and slightly skewed toward large shears. Thus, our observations did not show any direct (i.e., without temperature gradient) effect of wind shear on the formation of IGSWs. Overall, the results in Figs. 5–8 for the first time give extensive statistics of the IGSW parameter distri butions. However, they are insufficient to classify the frequency of occurrence of IGSWs and their parame ters with respect to external factors or determine con ditions for the development of IGSWs in the atmo spheric boundary layer. It is of interest to compare the IGSW parameters obtained at the ZSS with those available in the litera ture. The table lists nearly all publications we have found in which waveactivity parameters are consid ered [17, 19, 24, 25, 27, 35, 37–41]. Most of these publications present data only for one or two IGSW episodes lasting from a few minutes to 1 h. It is seen from the table that internal gravityshear waves in the ABL in the Northern Hemisphere midlat itudes (from 32° N to 56° N) have similar parameters at all measurement sites: on the Atlantic [35] and Pacific [24] coast of the United States, in arid plains of central America [25, 37, 19], and in a wooded nonuni form terrain [27, 38, 39]. The waves arise mainly at a height of 60–300 m, with strong as well as weak wind shears. The ratio of the wavelength to amplitude gen erally agrees with model results, but has a significant
Spatial period L, m
6000
4000
2000
0
200
400 Layer thickness, m
600
Fig. 7. Spatial period L of internal gravityshear waves versus the waveactivity layer thickness h, ZSS, 2009–2011: the experi mental regression L = 9.2 h (solid line) and theoretical L/h = 7.5 valid for a model with linear velocity and density profiles (dashed line). IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
Vol. 51
No. 2
2015
200
LYULYUKIN et al.
Experimental Data on WaveActivity Layer Characteristics and Parameters of Internal GravityShear Waves in the ABL Midlayer height, m
Year, site, equipment
Layer shear, ms–1 per 100 m
Layer thickness h, m
IGSW wavelength L, m
Ratio L/h
1966, Wallops Island, Virginia, US, scan ning radar [35]
600
0.8
400
1500
3.8
1969, San Diego, US, FM radar [40]
300
0.35
50
230
4.6
1970, San Diego, US, FM radar [24]
560 250
n/a n/a
50 100
370 300
7.4 3.0
1971, Oklahoma, US, sodar [25]
200
n/a
200
3100
15.5
1969, Haswell, Colorado, US, sodar [17]
55 60
8 11
30 27
150 100
5.2 3.4
1971, Haswell, Colorado, US, sodar [37]
115
10
70
300
4.3
1972, Haswell, Colorado US, three sodars [41]
750
n/a
200
3500
17.5
1975, Chaniers, France, sodar [38]
160 100 160
8 7.5 10
130 100 130
1050 750 1090
8.1 7.5 8.4
1985, Chicago, US, minisodar [39]
100
5.0
80
500
6.3
1991, ZSS, Moscow region, Russia, mini sodar [27]
60
12
50
350
7.0
1999, Kansas, US, scanning lidar [19]
50
17
50
320
6.4
90–400
1–15
50–500 220**
650–8900 2020**
3.8–36.0 9.2 ± 0.3**
2009–2011, ZSS, Moscow region, Russia, sodar * n/a—not available; ** average of 234 episodes.
scattering of the values. The longterm continuous sensing of the ABL has significantly broadened a range of the IGSW parameters compared to that obtained earlier from occasional observations. The ZSS has detected several cases of very large values of the ratio L/h.
500
Total duration, h
400 300 200 100
0
1
2
3 4 5 6 7 Wind shear, ms–1/100 m
8
9
Fig. 8. Distribution of the total duration (in hours) of IGSWs for different vertical wind shears in LLJs in 2008– 2011 (light gray) and distribution of the duration of record ing nocturnal LLJs with different vertical shears in 2009 (dark gray).
10
5. CONCLUSIONS Groundbased remote sensing give valuable infor mation on atmospheric wave activity, providing a visual twodimensional picture of mesoscale wavelike structures in the field of fluctuations of refractive index or in the wind velocity field. Longterm continuous sodar measurements of the atmospheric boundary layer parameters performed at the Obukhov Institute of Atmospheric Physics, Rus sian Academy of Sciences, provided the possibility of compiling an extensive catalog of the cases of occur rence of internal gravityshear waves in the atmo spheric boundary layer. Over the period from 2009 to 2011, the Zvenigorod Scientific Station recorded 234
IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
Vol. 51
No. 2
2015
INTERNAL GRAVITYSHEAR WAVES IN THE ATMOSPHERIC BOUNDARY LAYER
episodes of IGSWs lasting from 15 min to a few hours. The waves occurred mainly in the form of “inclined stripes” at a height of 100–300 m with wind shears of 3–5 m/s per 100 m. Distributions of the occurrence of IGSWs and their wavelengths were constructed. No significant seasonal dependence on the number of IGSWs was found. Typical parameters of the observed waves are as follows: the wavelength 400–2000 m, double amplitude (waveactivity layer thickness) 60– 300 m, and mean ratio of the wavelength to layer thic ness L/h = 9.2. This ratio slightly exceeds theoretical model predictions. Despite more than a century of the experience in studying Kelvin–Helmholtz instability and a large number of publications on this topic, investigations of IGSWs in the atmospheric boundary layer are far from being complete. Many problems are not yet solved, and even approaches to their solution are not always obvious. For example, it is unclear what conditions are sufficient for the formation of IGSWs, because the Richardson number criterion, Ri < 0.25, is only a nec essary condition. It is unclear how the amplitude and lifetime of IGSWs are related to external conditions. Overall, the ZSS has recorded a relatively small number of IGSW episodes (with a total duration of 6% of the total lifetime of inversions in the ABL) and such episodes were observed very rarely in previous investi gations. This raises the question of whether the IGSWs have a real influence on the turbulent exchange in a statically stable ABL, which is often assumed signifi cant. A search for answers to these questions is compli cated by a wide variety of the morphology of the IGSWs recorded in echograms [42] and by a broad range of parameters of the observed waves. Many of the published cases of IGSW observations are poorly documented: data from the auxiliary measurements of temperature, wind speed and direction, and turbu lence intensity are not available, nor are there any descriptions of weather conditions. This complicates a classification of IGSWs according to external condi tions, which is an important step to understanding this phenomenon. The question also arises of whether the sodar and radar recording of IGSWs in the field of refractive index fluctuations is representative. There are limita tions related to the resolution of the equipment, which make it difficult to record the smallest waves. Besides, it is unclear to what extent the modulation of the field of refractive index fluctuations by waves is informative and how the depth of the echosignal modulation is related to the mean temperature gradient and turbu lence intensity. Spatial observations of the waves in the wind field with scanning pulsed Doppler radars are clearer in this context. However, the latters usually have a large dead zone and insufficient resolution for measurements in the ABL. The recording of IGSWs in the wind field by a scanning Doppler radar seems to be more promising. IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
201
However, this method also has limitations. Moreover, the equipment for such measurements is complicated, and, as far as we know, there is only one lidar HRDL in the world [43] suitable for such measurements. ACKNOWLEDGMENTS This study was supported by the Russian Founda tion for Basic Research (project no. 120531399, 13 0500846) and by Finnish Academy (project ASTREX). Data analysis and processing was sup ported by the Russian Science Foundation (project no. 142700134). REFERENCES 1. S. A. Thorpe, “Experiments on Instability and turbu lence in a stratified shear flow,” J. Fluid Mech. 61, 731–751 (1973). 2. M. D. Patterson, C. P. Caulfield, J. N. McElwaine, and S. B. Dalziel, “Timedependent mixing in stratified Kelvin–Helmholtz billows: Experimental observa tions,” Geophys. Res. Lett. 33, L15608 (2006). 3. W. R. Peltier and C. P. Caulfield, “Mixing efficiency in stratified shear flows,” Annu. Rev. Fluid Mech. 35, 135–167 (2003). 4. N. N. Romanova and I. G. Yakushkin, “Stabilization of a linearly unstable wave participating in a threewave resonant interaction,” Izv., Atmos. Ocean. Phys. 46 (3), 360–368 (2010). 5. N. A. Bakas and B. F. Farrell, “The role of nonnormal ity in overreflection theory,” J. Atmos. Sci. 67, 2547– 2558 (2010). 6. M. V. Kalashnik and O. G. Chkhetiani, “Wave genera tion on an interface by vortex disturbances in a shear flow,” Fluid Dyn. 49 (3), 384–394 (2014). 7. Z. N. Kogan and N. P. Shakina, “Numerical investiga tion of internal waves in jet streams including nonlinear effects,” BoundaryLayer Meteorol. 5, 79–93 (1973). 8. W. D. Smyth, “Kelvin–Helmholtz billow evolution from a localized source,” Q. J. R. Meteorol. Soc. 130, 2753–2766 (2004). 9. X. Liu, J. Xu, H. Gao, and G. Chen, “Kelvin–Helm holtz billows and their effects on mean state during gravity wave propagation,” Ann. Geophys. 27, 2789– 2798 (2009). 10. H. Pham and S. Sarkar, “Internal waves and turbulence in a stable stratified jet,” J. Fluid Mech. 648, 297–324 (2010). 11. N. P. Shakina, Hydrodynamic Instability in the Atmo sphere (Gidrometeoizdat, Leningrad, 1996) [in Rus sian]. 12. Yu. A. Stepanyants and F. L. Fabrikant, Wave Propaga tion in Shear Flows (Naukafizmatlit, Moscow, 1996) [in Russian]. 13. C. J. Nappo, "An introduction to atmospheric gravity waves," in International Geophysics, (Academic Press, 2012), Vol. 102, 360 p. 14. J. J. Hicks, “Radar observations of a gravitational wave in clear air near the tropopause associated with CAT,” J. Appl. Meteorol. 8, 627–633 (1969). Vol. 51
No. 2
2015
202
LYULYUKIN et al.
15. A. Muschinski, “Local and global statistics of clearair Doppler radar signals,” Radio Sci. 39, RS1008 (2004). 16. S. Fukao, H. Luce, T. Mega, and M. K. Yamamoto, “Extensive studies of largeamplitude Kelvin–Helm holtz billows in the lower atmosphere with VHF middle and upper atmosphere radar,” Q. J. R. Meteorol. Soc. 137, 1019–1041 (2011). 17. C. B. Emmanuel, “Richardson number profiles through shear instability wave regions observed in the lower planetary boundary layer,” BoundaryLayer Meteorol. 5, 19–27 (1973). 18. W. Blumen, R. Banta, S. P. Burns, et al., “Turbulence statistics of a Kelvin–Helmholtz billow event observed in the nighttime boundary layer during the CASES field program,” Dyn. Atmos. Oceans 34 (2), 189–204 (2001). 19. R. K. Newsom and R. M. Banta, “Shearflow instabil ity in the stable nocturnal boundary layer as observed by Doppler lidar during CASES99,” J. Atmos. Sci. 30, 16–33 (2003). 20. B. CushmanRoisin, “Kelvin–Helmholtz instability as a boundaryvalue problem,” Environ. Fluid Mech. 5, 507–525 (2005). 21. R. B. Smith, “Gravity wave effects on wind farm effi ciency,” Wind Energy 13, 449–458 (2009). 22. M. Kallistratova, R. Kouznetsov, D. Kuznetsov, et al., “Summertime lowlevel jet characteristics measured by sodars over rural and urban areas,” Meteorol. Z. 18 (3), 289–295 (2009). 23. M. A. Kallistratova and R. D. Kouznetsov, “Lowlevel jets in the Moscow region in summer and winter observed with a sodar network,” BoundaryLayer Meteorol., 143, 159–175 (2012). 24. E. E. Gossard, J. H. Richter, and D. R. Jensen, “Effect of wind shear on atmospheric wave instabilities revealed by FM/CW radar observations,” Boundary Layer Meteorol. 4, 113–131 (1973). 25. W. T. Cronenwett, G. B. Walker, and R. L. Inman, “Acoustic sounding of meteorological phenomena in the planetary boundary layer,” J. Appl. Meteorol. 11, 1351–1358 (1972). 26. F. F. Hall, “Acoustic remote sensing of temperature and velocity structure in the atmosphere,” in Proceed ings of NATO Advanced Study Institute, Statistical Meth ods and Instrumentation in Radio Meteorology, Apri1 15–22, 1971, Ed. by A. G. Kjelaas (Teknologisk Forlag, Oslo, 1971), pp. 167–180. 27. M. A. Kallistratova and I. V. Petenko, “Aspect sensitiv ity of sound backscattering in the atmospheric bound ary layer,” Appl. Phys. B 57, 41–48 (1993). 28. V. I. Tatarskiì, The Effects of the Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translations, Jerusalem, 1971).
29. D. Chapman and K. A. Browning, “Radar observations of windshear splitting within evolving atmospheric Kelvin–Helmholtz billows,” Q. J. R. Meteorol. Soc. 123, 1433–1439 (1997). 30. R. L. Coulter and M. A. Kallistratova, “The role of acoustic sounding in a high technology era,” Meteorol. Atmos. Phys. 71, 3–13 (1999). 31. S. Argentini, G. Mastrantonio, I. Petenko, et al., “Use of highresolution sodar to study surfacelayer turbu lence at night,” BoundaryLayer Meteorol. 143, 177– 188 (2012). 32. R. D. Kouznetsov, “Latan3 sodar for investigation of the atmospheric boundary layer,” Atmos. Oceanic Opt., 20(8), 684–687 (2007). 33. M. A. Kallistratova, R. D. Kouznetsov, V. F. Kramar, and D. D. Kuznetsov, “Profiles of vertical wind speed variances within nocturnal lowlevel jets observed with a sodar,” J. Atmos. Oceanic Technol. 30, 1970–1977 (2013). 34. E. Gossard and W. Hooke, Waves in the Atmosphere (Elsevier, Amsterdam, 1975). 35. J. J. Hicks and J. K. Angell, “Radar observations of breaking gravitational waves in the visually clear atmo sphere,” J. Appl. Meteorol. 7, 114–121 (1968). 36. V. S. Lyulyukin and D. D. Kuznetsov, “Features of Kelvin–Helmholtz billows in lowlevel jets derived from sodar data,” in Extended Abstracts of 16th ISARS, Boulder, Colorado, USA, June 5–8, 2012, pp. 150–152. 37. D. Atlas, J. I. Metcalf, J. H. Richter, and E. E. Gossard, “The birth of CAT and microscale turbulence,” J. Atmos. Sci. 27, 903–913 (1970). 38. W. H. Hooke, F. F. Hall, and E. E. Gossard, “Observed generation of an atmospheric gravity wave by shear instability in the mean flow of the planetary boundary layer,” BoundaryLayer Meteorol. 5, 29–41 (1973). 39. A. G. Kjelaas, D. W. Beran, W. H. Hooke, and B. R. Bean, “Waves observed in the planetary boundary layer using an array of acoustic sounders,” J. Atmos. Sci. 31, 2040–2045 (1974). 40. L. Eymard and A. Weill, “A study of gravity waves in the planetary boundary layer by acoustic sounding,” BoundaryLayer Meteorol. 17, 231–245 (1979). 41. R. L. Coulter, “A case study of turbulence in the stable nocturnal boundary layer,” BoundaryLayer Meteorol. 5, 75–91 (1990). 42. V. S. Lyulyukin, R. D. Kouznetsov, and M. A. Kallis tratova, “The composite shape and structure of braid patterns in Kelvin–Helmholtz billows observed with a sodar,” J. Atmos. Oceanic Technol. 30, 2704–2711 (2013). 43. R. M. Banta, “Stableboundarylayer regimes from the perspective of the lowlevel jet,” Acta Geophys. 56, 58–87 (2008).
Translated by N. Tret’yakova
IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
Vol. 51
No. 2
2015
