Journd of Almwphsric
Terresrrial Physics, Vol.56. No. 8. pp. 939-947, 1994 Copyright 0 1994 Else&r Science Ltd
Printed inGreatBritain. All rightsreserved 00X-9169194 $7.00+0.&l
Gravity waves in the stratosphere and troposphere observed by lidar and MST radar N. J.
and I. T.
Department of Physics, University College of Wales. Aherystwyth, Dyfed, U.K. (Recriwd
1 JWIP I993 : ucwpturl IO June 1993)
Abstract-Co-ordinated lidar and MST observations of the stratosphere and troposphere have been made at Aberystwyth (52.4”N, 4.1’W). Density and temperature profiles derived from lidar observations of Rayleigh backscatter above about 21 km have been combined with MST radar measurements of winds to investigate gravity waves at heights between 2 and 50 km. The measurements made by each technique reveal that long-period quasi-monochromatic motions frequently dominate the stratospheric gravity-wave field. Characteristic vertical wavelengths range from I-2 km in the lower stratosphere to some 5-8 km at the greater heights. Vertical wavenumber and frequency spectra are derived for both tropospheric and stratospheric data. Wave energy per unit mass is used as a tracer of wave activity and is combined with vertical wavenumber spectra to investigate wave-field saturation. The significance of measured frequency spectral indices as a function of height is discussed in relation to possible Doppler shifting by the mean wind
1. lNTRODUCTlON It is now recognized that gravity waves play a significant part in determining the global circulation of the middle atmosphere through the process of momentum transfer at heights where wave saturation occurs (LINDZEN, 1981; HOLTON, 1983). MST/ST radar measurements with good height resolution and time continuity have helped to interpret quasiperiodic ~uctuations of winds at heights up to the lower stratosphere in terms of inertia-gravity waves (e.g. SATO and WOODMAN, 1982 ; CORNISHand LARSEN, 1989 ; THOMAS et al., 1992). Analogous lidar measurements of density and temperature by Rayleigh scatter, at levels free from subst~tn~ial aerosol ~on~ent~dtion, have provided information on waves and saturation processes at heights between about 25 and 50 km (e.g. SHIBATA ct al.. 1986 ; MII-CHELLet (I[., 1991 ; WILSON el ul.. 1991).
Here we present preliminary results from six sets of co-ordinated measurements, made at Aberystwyth (52.4 N, 4.1 ‘W) during the period 25 September 1990.-22 January 1991, in which MST radar observations of winds at heights up to about 20 km are combined with lidar observations of temperature and density at greater heights.
AND METHOD OF ANAtYSlS
The lidar and MST radar systems located at Aberystwyth have been described by THOMAS et al. (1983) and SLATER cr ul. (1992). respectively. In the present
study, lidar data were recorded in height channels of 0.5~s duration giving a height resolution of some 75m. The photon counts in each channel for 5000 laser shots were pre-integrated in the receiver hardware before being recorded by the controlling minicomputer. The laser was operated at a p.r.f. of 10 Hz. so the consequent time resolution was 8.3 min. Profiles of absolute temperature and molecular density were calculated following the procedure described by HAUCHEC~RNE and CHANIN (1980). The use of vertical profiles of molecular density to study gravity waves relies on the ability to distinguish waveinduced density perturbations, P’(Z), from the background mean state of the atmosphere, p(z). MITCHELL et al. (1990) examined a number of possible analytic techniques. and the method employed here is that detailed in MITCHELL ef ~1. (1991). The MST radar observations of winds involved measurements of radial velocities using three beams ; one directed vertically and two in orthogonal planes at 6 from the zenith. A height resolution of 300m was used and data were recorded with time resolutions of l-2 min, subsequently averaged to 7-12 min to increase the signal-to-noise ratio and to Facilitate comparisons with the lidar data. Pertur~tions of the recorded wind field attributable to gravity waves were identified by band-pass filtering successive derived profiles of zonal and meridional winds to reveal structures with vertical wavelengths between 600m and 5 km [a procedure more fully described in THOMASrf al. (1992)]. In all cases a second-order Butterworth filter was used. 939
J. MITCHELL er af.
The duration of the co-ordinated measurements was limited by the requirement of clear skies at night for the lidar observations. The dates and approximate durations of the lidar observations were as follows: 25 September 1990: IOh; 13 December 1990: 14h; 14 December 1990: 4h; 16 January 1991: 4h; 21 January 1991: 14 h; 22 January 1991 : 2.5 h. In general, the radar observations on these dates were of considerably greater duration and both preceded and followed those of the lidar. To compare the gravity-wave induced perturbations of density and wind measured by the lidar and MST radar, respectively, use was made of the gravity-wave dispersion relation expressed in the form (GOSSARD and HOOKE, 1975):
where U’ is the wind perturbation in the direction of propagation of the gravity wave, N is the BruntVhisHlHfrequency-which can be calculated from the lidar observations using the derived temperature profile. u is the wave’s intrinsic frequency (that measured in the frame of reference of the mean flow), g the acceleration due to gravity, and f the inertial frequency. It is to be noted that the square-root term has a value near 1 for f <
Prior to spectral analysis, inspection of the timeheight contours of density perturbation and wind derived from the lidar and MST radar observations can reveal gross properties of the wave field. The contours presented in Fig. 1(a) and l(b) illustrate typical wave field perturbations derived from lidar and MST radar measurements, respectively. The Iidar data are for the night of 16 January 1991 and have been band-passed in the vertical between limits of 0.6 and 15 km; those for the MST radar are for the approximate period 1400 on 21 January 1991 to 1000 on 22 January 1992 and have been band-passed between 0.6 and 5.0 km. The different upper bandpass limits employed in the two sets of data were chosen to allow for the observed increase in the characteristic vertical wavelength with height (e.g. SMITH et al., 1987). In the lidar observations, the wave fields in the middle and upper stratosphere frequently appear dominated by long-period quasi-monochromatic waves with vertical wavelengths of some 510 km and fractional density perturbation amplitudes
of up to about 2%. In the radar data, such long-period quasi-monochromatic motions are again frequently present in the accessible region of the lower stratosphere and often appear to be radiating from some height near the tropopause. In the tropospheric portion of the data, such features are not usually so coherent. Characteristically, vertical wavelengths for waves observed in the lower stratosphere are some l-2 km, and representative amplitudes are about 3m ss’. In both sets of observations, waves whose apparent periods exceed the inertial value, 15.1 h at Aberystwyth, are frequently recorded ; such periods have been explained by SHIBATA ef al. (1986) in terms of Doppler shifting by the mean flow. It is not generally meaningful to compare timeheight contours of the perturbation fields revealed by each technique because the lidar observations of density perturbation can be combined with the BruntV&ill profile and assumptions about (or knowledge of) wave intrinsic frequencies to reveal onty u’, whereas the radar observations record both u’ and the transverse oscillatory component, o’, where I“ = i(,f‘/o)u’. However, the comparison can be based on the wave energy per unit mass deduced from the two sets of measurements, after the lidar observations of density perturbation are converted to equivalent horizontal winds by use of equation (1). Since the spectral composition of the wave field is known to fluctuate appreciably over time scales of several hours (e.g. MARSH et al., 1991), it was decided to restrict the time interval over which the energy density was evaluated to the length of the appropriate lidar data set. The energy density per unit mass, E, was therefore calculated using the expression : (2) where W, and w2 are frequency limits corresponding to periods equal to the duration of the lidar data set and 1 h, respectively, and u0 is the wave amplitude at frequency w. The MST radar results have been derived by calculating mean spectra of the zonal and meridional winds. The short period limit was chosen to avoid possible noise contamination at the greater heights in the lidar data. Additionally, a noise value calculated from the high-frequency part of the spectrum was subtracted at all frequencies. Finally, to ensure that the same components of the wave field were being observed by each technique, both data sets were band-passed in the vertical between limits of 600 m and 5.0 km prior to spectral analysis. Figure 2 presents the vertical profile of E calculated for measurements made by each technique during
D.P. (%) n
II m w
0.7 1.3- -
-1.3 -“‘7- -2.o-
-0.7 O.O -1.3
Fig. I. Height-time contours of (a) percentage density perturbation derived from lidar measurements on the night of 16 January 1991. The contoured profiles represent 8 min means and have been band-passed between 600 m and 15 km in the vertical. (b) Meridional winds for 21-22 January 1991 band-passed between 600 m and 5.0 km in the vertical.
N. J. MITCHELL et al
Fig. 7. Heif;ht-time contours of estimated fl values for heights in the stratosphere.
0 PER UNIT MASS)
Fig. 2. Profiles of wave energy per unit mass derived from radar and lidar observations for the night of 25 September
1990. A growth curve corresponding to conservative motions, with an arbitrary starting point, is indicated for comparison.
40? c.c f
9.75 h of observation on the night of 25 September 1990. The profiles have been subjected to a 1 km smoothing and are similar in general form to the profiles derived from the data recorded on other nights of observation. Also indicated is a line corresponding to the conservative growth curve for gravitywave energy (i.e. that in the absence of saturative or dissipative processes). The frequency spectra of horizontal winds can be used to investigate the distribution of energy as a function of apparent frequency within the wave field. Spectra calculated as described above were used to determine the frequency spectral index, p, where the frequency power spectral density, S,,(o), is assumed to scale as S,,(U) CCwmP. Values of p were determined by means of a linear regression fit to the log-log plot of S,,(o). Vertical profiles of p were calculated from both lidar and radar observations for each period of co-ordinated observation. Figure 3(a) and (b) presents the profiles derived for the nights of 13 December 1990 and 21 January 1991, respectively. In each case the apparent frequency interval considered corresponds to the period range 1-8 h and the spectral indices were calculated as means over height intervals of 4 km. Vertical wavenumber spectra can provide a valuable insight into the nature of the gravity-wave field. Such spectra are especially useful because the vertical wavenumber, unlike the frequency, is largely unaffected by possible Doppler shifting of the waves by the
8 I zo-
01 -1 (b)
I 2 SPECTRAL
Fig. 3. The spectral index, p, for wave periods l-8 h as a function of height for (a) the night of 13 December 1990, (b) the night of 2 I January I99 1.The range of heights over which observations were made by each technique is indicated, as is a line corresponding top = 513.
mean flow. Vertical wavenumber power spectral densities of horizontal winds, S,,(m), derived from MST radar observation between 2246 and 0734 on 13-14 December 1991 at heights from 10.45 to 18.05 km are presented in Fig. 4; the spectra were derived in the rotary form (THOMPSON, 1978) from profiles of zonal and meridional winds, but only the total component is shown for reasons of clarity. In all the rotary spectra for stratospheric data, the clockwise component was found to make the dominant contribution to the total spectrum, indicating a preponderance of upwardly propagating waves. Also indicated in the figure is the spectrum derived from the corresponding lidar profiles of inferred horizontal winds from 22.06 to 29.78 km for this period. An arbitrary line of slope
N. J. MITCHELLt’t ~1.
944 Vertical Wavelength (km) 6.0
1.0 0.8 0.6
-3.6 -3.4 -3.2 -3.0 log(l0) Wavenumber (cyclm)
Fig. 4. Vertical wavenumber spectra of horizontal winds, S,,(N). derived from radar observations between 10.45 and 18.05 km and 29.78 199 I. For line
- 3. that
(dashed line) and lidar observations between 22.06 km (continuous line) on the night of21L22 January clarity, only alternate error bars are indicated. A of gradient - 3 is indicated for comparison.
theory of SMITH for comparison.
by the saturation
rl al. (1987), is included
The comparatively restricted data set available in the present co-ordinated study prevents more than general conclusions being drawn, especially since only three of the lidar observations were of greater than 12 h duration. However, the domination of the stratospheric wave field by quasi-monochromatic waves has been reported by a number of authors using lidar. radar and various other techniques (e.g. THOMPSON, 1978 ; MAEKAWA et ul. 1984; SHIBATA Pt ul., 1986 ; MITCHELL et al., 1991 ; WILSON et rd., 1991 ; THOMAS et al., 1992) and this may well represent the normal condition of this region. The increase with height of the vertical wavelength of these dominant waves agrees well with the behaviour of the characteristic vertical wavenumber, m*, described by SMITH et al. (1987). The vertical profiles of wave energy per unit mass presented in Fig. 2 appear to show a smooth con-
tinuation between the wave fields observed by the radar and lidar techniques, the actual transition being obscured by loss of coverage near 20 km. This continuation provides confidence in the use of equation (1) by which density and wind perturbations are related. At stratospheric heights the energy growth with height appears less rapid than would be the case for a conservative wave field, suggesting that wave energy is being lost through a dissipative or saturative process. The analysis of lidar data made by MITCHELL et cd. (1991) and MAKSH ct rd. (1991) at heights above 30 km suggests that this is usually the case in all but the summer months at Aberystwyth. The present observations suggest that such processes might be active, at least on the limited number of occasions examined hcrc. in both the stratosphere and troposphere. The frequency spectra derived from the MST radar observations provide values of the spectral index, p, close to the value of 5/3 commonly observed throughout the atmosphere for the gravity-wave part of the motion field (e.g. VANZANIX, 1983). However, for some of the vertical profiles of p considered in this study, it was noticed that there are suggestions of vertical structure. In particular, there appears to be some association between the profiles of p and those of the mean radar-measured wind speed in the troposphere and lower stratosphere. Figure 5(a) and (b) prcscnts profiles of the mean wind speed measured over times coincident with the lidar and MST radar data on 13 December 1990 and 21 January 1991 ; i.e. data used to calculate the vertical profiles of p contained in Fig. 3(a) and (b). respectively. The mean wind speed has been estimated by low-pass filtering to remove structure on scales smaller than 5 km. The profiles of p and mean wind speed for I3 December 1990 [Figs 3(a) and 5(a)] reveal that p decreases from values near 1.6 at 8 km to just below 1.O at 16 km. and over the same height interval the mean wind speed increases from about 5 to about l6ms ‘. The corresponding profiles in Figs 3(b) and 5(b) for 21 January 1991 appear to show a similar association. Similarly, minimum values of p are associated with maximum values of wind speed, about I. 15 and 27 m s ‘, respectively, at heights near 12 km. To clarify this association, the 4 km mean spectral indices and wind speeds are presented graphically in Fig. 6. An explanation for this relationship is proposed in terms of Doppler shifting of the wave field by the mean flow. FRITTS and VANZANDT (1987) examined theoretically the effects on observed wave spectra of variations in the ratio, 8, of the mean wind speed, u, and wave horizontal phase speed, c,. The authors assumed an intrinsic frequency spectrum of gravity
Fig. 6. The variation of the spectral index, p, as a mean over 4 km, with the mean wind speed at the appropriate height for the nights of I3 December 1990 and 2 I January 1991.
Fig. 5. Mean wind speeds for (a) the night of 13 December 1990 and (b) the night of 21 January t991, over times coincident with the radar and lidar observations on those nights.
waves of the form S,(w) CCCL-* for N > w 2.f with zero power outside this frequency range, rather than the commonly reported S,(w) CCo-5:3 which is usually assumed to represent the intrinsic frequency spectrum. Furthe~ore, these authors considered wave propagation azimuths to be aligned with the mean flow. Both these steps were taken in order to simplify the necessary calculations. However, the general conclusions are at least qualitatively applicable to the observational data presented in this study. The authors found that one effect of increasing b values is to redistribute energy from the low frequency end of the spectrum to higher frequencies [see, for example,
their Fig. 6(a)]. Thus as /I increases, the spectral index [calculated by a linear regression fit to the log-log plot of S,,(o)] for apparent frequencies near the inertial value becomes progressively smaller, and significant differences in k were shown to occur for values of fi as small as 2. An increase in mean wind may therefore result in a decrease in spectral index, as observed here. To investigate this effect further, crude estimates were made of representative monthly mean /I values. Horizontal phase speeds for the dominant components of the wave field were estimated by using the relation c , e N/m and substituting values of m corresponding to the observed dominant vertical wavenumbers~ m*, for various heights within the stratosphere. Values of m* used correspond to characteristic vertical wavelengths of 2 km at a height of 20km, 4km at 30km, 8km at 40km and 12km at 50 km. These values were selected as typical of those reported from observations of the stratosphere (e.g. SMITH et al., 1987 ; MITCHELL et al.. 1991 ; WILSON et al., 1991 ; THCB~AS rf uf., 1992). The monthly mean
N. J. MITCHELL
wind speed at these heights was estimated from the annual profiles of zonal and meridional wind recorded at Primrose Lake (53”N) presented by MANSON et al. (1985). No attempt was made to calculate representative p values for the stratosphere below 20 km because of the occurrence of tropopause level jet streams at these heights; also, no attempt was made to allow for wave propagation azimuths other than those aligned with the mean wind. The p values should thus be regarded as rough indications of maximum possible values only. Figure 7 presents contours of monthly mean [j values so calculated. Despite the above limitations, the figure does suggest that J values are likely to be low, i.e. < 1.5, throughout much of the stratosphere from late March to October and hence Doppler shifting may not be significant in this period. The vertical wavenumber spectra developed from the MST radar and lidar observations (Fig. 4) indicate that there is little, if any, increase in ,S,,(nz)between the height ranges corresponding to the lower and middle stratosphere for vertical wavenumbers greater than about IO- “cycles/m ; this value corresponding to a vertical wavelength of about 2 km. However, at small wavenumbers, there is an increase in power between these two altitude ranges. This behaviour has been explained by SMITH et ul. (1987) in terms of saturated and unsaturated wavenumber regimes. However, the mean gradient of the two spectra at wavenumbers
above 1O-‘-3cycles/m (vertical wavelengths less than about 2 km), determined by means of a linear regression fit to the Iog-log plot of S&B), has a value of -2.1 iO.2, rather than the value of -3 predicted by Smith et uf. 5. CONCLUSIONS
Lidar and radar observations of gravity waves in the stratosphere have been combined in the preliminary investigation presented to examine gravity waves throughout the stratosphere, a range of observation not possible by using either technique alone. During the co-ordinated observations the stratosphere appeared dominated by quasi-monochromatic gravity waves, although such a situation did not exist in the troposphere. The growth of wave energy per unit mass suggests that the wave-field is not conservative in the stratosphere or troposphere and this inference is reinforced by observations of an apparently saturated wave-field at high wavenumbers in the lower and middle stratosphere. However, in at least some of the observations, the wavenumber spectral index appears nearer 2 than the predicted value of 3. The variation of the frequency spectral index with height has been observed to be influenced by the mean wind, and this relationship is explained in terms of a Doppler shifting of the wave spectra by this wind.
REFERENCES CORNISH C. R.
and LAKSENM. F.
Observations of low-frequency inertia-gravity waves in the lower stratosphere over Arecibo. .I. atmos. Sci.
FKITTSD. C. and VANZANDTT. E.
GOSSARDE. E. and HOOKE W. M. HA~J~~~~ORNE A. and CHANINM.-L.
Effects of Doppler shifting on the frequency spectra of atmospheric gravity waves. J. geophys. Res. X,9723. Wmes in rhe Atmosphere. Elsevier, Amsterdam. Density and temperature profiles obtained by lidar between 35 and JO km. Geophys. Res. Left. 7, 565. The influence of gravity wave breaking on the general circulation of the middle atmosphere. J. IIZ~~IOS. Sci.
MAEKAWAY., FUKAOS., SATOT., KATO S. and WOOUMANR.
MANSONA. H., MEEKC. E., VINCENTR. A.
Turbulence and stress owing to gravity wave and tidal breakdown. J. geophys. Res. 86,9707. Internal inertia-gravity waves in the tropical lower stratosphere observed Sci. 41, 2359.
MARSI~A. K. P. M., MITCHELLN. J. and THOMASL. MITCHELLN. J., T~OOMAS L. and MARSHA. K. P.
MITCHELLN. J.. THOMASL. and MAKSHA. R. P.
by the Arecibo radar. J. atmos.
Mean winds of the mesosphere (60-80 km) as measured by M.F. radars. Handbook for MAP 16,36. Lidar studies of stratospheric gravity-wave spectra. Planet Space Sci. 39, 1541. Lidar studies of stratospheric gravity waves: a comparison of analysis techniques. AHFZ.Geo$ys. 8,705. Lidar observations of long-period gravity waves in the stratosphere. Ann. Geopizyx 9, 588.
T. and W~~DMAN R. F.
T., FUKUDA T. and MAEDA M.
SLATER K., STEVENSA. D., PEARMAINS. A. M., ECCLES D.. HALL A. J., BENNETTR. G. T.. FRANCE L., ROBERTSG., OLIWI~Z Z. K. and THOMAS L. SMITH S. A., FRITTS D. C. and VANZANUT T. E.
THOMAS L., JEI*~KINS D. B., WAKING D. P. and FAKRINGTON M. THOMAS L., PRICHARU 1. T. and ASTIN I.
THOMPSON R. 0. R. Y.
VANZANDT T. E.
WILSON R. A.. HAU~HECORNE A. and CHANIN M.-L.
947 Fine altitude resolution observations of stratospheric turbulent layers by the Arecibo 430MHz radar. J. atmos. Sci. 39, 2546. Density fluctuations in the middle atmosphere over Fukuoka observed by XeF Rayleigh lidar. Geophys. Res. Lerl. 13, 1121. Overview of the MST radar system at Aberystwyth. Proceedings of the fifth workshop on technical and scientific aspects of MST radar, 479. Evidence of a saturated spectrum of atmospheric gravity waves. J. aimos. Sci. 44, 1404. Laser observations in mid-Wales of aerosol from the El Chichbn eruption. Nature 304, 248. Radar observations of an inertia-gravity wave in the troposphere and lower stratosphere. Ann. Geophys. IO, 690. Observation of inertial waves in the stratosphere. Q. JI R. Met. Sot. 104, 691. A universal spectrum of buoyancy waves in the atmosphere. Geophys. Res. Letr. 9, 575. Gravity waves in the middle atmosphere observed by Rayleigh lidar. 1. Case studies. J. geophxs. Rex. 96, 5153.