Inertia-gravity waves observed by the UK MST radar

Transcription

1 QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY Q. J. R. Meteorol. Soc. 133: (S2) (2007) Published online in Wiley InterScience ( Inertia-gravity waves observed by the UK MST radar G. Vaughan* and R. M. Worthington University of Manchester, UK ABSTRACT: We present an analysis of eight years data from the UK MST radar at Aberystwyth, Wales, to determine the occurrence and properties of long-period, quasi-monochromatic oscillations in the wind vector identified with inertia-gravity waves. Wave perturbations were first isolated by filtering out background wind variation in the vertical, then the continuity of the radar measurements was exploited to apply band-pass filters in time to select quasi-monochromatic oscillations with periods 4 8 hours or hours. By searching for altitude regions where the wind vector rotates systematically with height, and fitting ellipses to such sections, the properties of inertia-gravity waves can be derived. To guard against contamination by short-intrinsic-period mountain waves, cases were discarded when the vertical velocity measured by the radar exceeded 15 cm s 1. Results show that waves in the stratosphere are dominated by upward energy propagation (clockwise rotation) and those in the troposphere by downward propagation, consistent with the dominant source for inertia-gravity waves being at tropopause level. Long-period waves (> 12 hours) are observed 70% of the time in the lower stratosphere, roughly twice as often as the shorter-period waves, and 10 20% of the time in the troposphere. There is a winter maximum in occurrence in the troposphere and for the short-period stratospheric waves; however, the dominant long-period waves show little seasonal dependence. Likewise, they show only a weak correlation with jet-stream velocity or direction, unlike the other categories which are preferentially associated with strong jet streams and propagate along the jet. Inertia-gravity waves observed by the radar have typical amplitudes 1 2 m s 1 and vertical wavelength 2 km. The intrinsic wave period, estimated for non-jet-stream conditions, is similar for the two band-passed series, pointing to the importance of Doppler shifting in generating the observed oscillations. Copyright 2007 Royal Meteorological Society KEY WORDS jet stream; band-pass filters Received 6 February 2007; Revised 16 July 2007; Accepted 23 July Introduction The spectrum of atmospheric gravity waves extends from the Brunt Väisälä frequency, N, to the inertial frequency, f. This paper is concerned with very lowfrequency waves, near to the inertial frequency, which are a ubiquitous feature of the lowermost stratosphere. We refer to this class of wave, irrespective of the generating mechanism, as inertia-gravity waves (IGWs). Despite their ubiquity, there remains considerable theoretical uncertainty about the generating mechanisms for these waves and the role they play in redistributing atmospheric momentum. Breaking IGWs may also be an agent of mixing in the lowermost stratosphere, a region of the atmosphere largely free of convection, characterized by laminar flow punctuated by occasional patches of turbulence. The aim of this work is to use measurements from the UK mesosphere-stratosphere-troposphere (MST) radar at Aberystwyth, Wales (52.4 N, 4.1 W) to gain a better understanding of the occurrence and properties of IGWs. An excellent example of an IGW measured by the Aberystwyth MST radar was reported by Pavelin et al. * Correspondence to: G. Vaughan, School of Earth, Atmospheric and Environmental Sciences, University of Manchester, Manchester M13 9PL, UK. geraint.vaughan@manchester.ac.uk (2001). This was a near-monochromatic wave lasting for four days above the radar between the tropopause and 16 km, with ground-based period of 13.8 hours, vertical wavelength 2 km and horizontal velocity amplitude 8ms 1. It occurred during a period of very light winds at tropopause level associated with pronounced ridging of the jet-stream flow over the UK. During the early part of the event turbulence was observed by the radar (as a layer of enhanced spectral width) where the wind shear due to the wave was greatest. Turbulence in the lower stratosphere observed by the Aberystwyth radar is often associated with an IGW either by itself as in Pavelin et al. (2001), intensifying the shear layer above the jet (e.g. Vaughan and Worthington, 2000), or setting up critical layers for mountain waves to break (Pavelin, 2002). There are several theories in the literature for the generation of IGWs, e.g. diurnal variation in convection (Sato et al., 1995), instability of a horizontal shear line (Ford, 1994), instability of a vertical shear layer (Scinocca and Ford, 2000) and flow over mountains (Hines, 1989; Sato, 1994). The most popular is probably that of spontaneous or geostrophic adjustment relaxation of the atmosphere to a balanced state after the distortion of a jet stream by a weather system. Viudez and Dritschel (2006), for instance, predicted that waves generated by this mechanism in the Northern Hemisphere would have dominant frequencies near the inertial frequency and Copyright 2007 Royal Meteorological Society

2 180 G. VAUGHAN AND R. M. WORTHINGTON a clockwise-rotating horizontal velocity consistent with monochromatic wave solutions. O Sullivan and Dunkerton (1995) simulated wave generation in a high-resolution 3D model and predicted wave trains generated around highly curved regions of the polar jet stream, consistent with geostrophic adjustment. More idealised modelling by Reeder and Griffiths (1996), using 2D anelastic equations, showed that strong IGWs are emitted during upper-level frontogenesis when there is cold advection at jet-stream level, and that the strength of the waves depend on the strength of the cross-front circulation. These theories imply that a departure of the atmosphere from geostrophic balance leads to cross-flow acceleration and consequent inertial-type oscillations executed along sloping isentropic surfaces. They predict that regions of the Earth which frequently experience frontogenesis and large meridional distortions of the jet stream would be favoured locations for IGWs; Western Europe, being at the end of the Atlantic storm track, is an obvious example. Plougonven et al. (2003) analysed 224 radiosondes during the FASTEX experiment in the Eastern Atlantic and found that IGWs were most intense near the jet axis and where the jet was strongly curved, consistent with geostrophic adjustment. A related study (Moldovan et al., 2002) found narrow layers of mixing coincident with the waves. However, despite a number of reported case studies, there have been no climatological studies of IGWs over Europe. Statistical surveys of IGWs have been reported at other locations around the globe using data from MST radars. The first of these was by Sato (1994) based on three years data from the MU radar in Japan (34.9 N, E). This site experiences a marked seasonal cycle in the background wind near the tropopause, with the very strong subtropical jet stream being dominant in winter while much weaker winds are found in summer. In this work IGWs were defined as fluctuations with vertical wavelengths shorter than 4 km and periods longer than 10 h. In common with earlier studies Sato found a peak in lower stratospheric IGW intensity in winter and a secondary maximum in April. Vertical wavelengths were generally in the range 1 3 km, horizontal wavelengths km, and propagation direction southward in winter below 18 km; in summer there was no preferred direction. Sato examined the results in detail for evidence of generating mechanisms and concluded that there was strong evidence in winter for a mountain wave source above 18 km, but not between 14 and 18 km. Geostrophic adjustment at the jet axis as the major source was not consistent with the observed propagation of waves towards as well as away from the jet core. Recently, Nastrom and Eaton (2006) reported on 6 years MST radar data from White Sands, New Mexico (32.4 N, W) and Vandenberg Air Force base, California (34.8 N, E). They found a marked enhancement in IGW energy near the inertial period, particularly in summer, with peak amplitude 2 m s 1, vertical wavelengths around km and horizontal wavelengths around km. An example of an IGW climatology derived from radiosonde profiles was presented by Guest et al. (2000) based on observations from Macquarie Island, far from any orography in the Southern Ocean. Without the continuous observations of MST radars, hodograph analyses of radiosonde data are subject to more uncertainties (Zhang et al., 2004) but are still basically valid. The Macquarie Island results showed a predominant upward propagation of wave energy in the stratosphere (consistent with the MST radar results) and downward in the troposphere, suggesting a source at jet-stream level. IGWs are generated by high-resolution dynamical models of the atmosphere (Le Sommer et al., 2006), but there is some doubt whether they are correctly represented Plougonven and Teitelbaum (2003), for example, concluded that the ECMWF model produces waves at the right location and time but with the wrong properties, probably because of limitations in model resolution. There is a continuing need therefore for observations of IGWs to serve as a check on the performance of such models. Here we report on the occurrence and properties of IGWs in a database of highresolution wind profiles measured from 1990 to 2004 with the UK MST radar. 2. Method 2.1. General principles The UK MST radar is a VHF radar (46.5 MHz) providing vertical profiles of winds, echo power and turbulence from 2 to around 18 km. Commissioned in 1990, the radar has been in continuous operation since 25 October 1997, with observations around 98% of the time (there are occasional short interruptions due to power cuts, lightning or scheduled maintenance). In this paper, we use the dataset between 1998 and the end of 2005, i.e. eight complete years continuous measurements. The radar uses Doppler beam swinging to obtain radial wind profiles at the zenith and 6 off-zenith in four orthogonal azimuths; these are then combined to give wind profiles with a time resolution of around 2 minutes. Although the radar is capable of measurements with 150 m vertical resolution, better coverage and signal:noise ratio are obtained with longer radar pulses and the data used in this paper were all taken with 300 m vertical resolution. The altitude range of wind profiles starts at 2 km in all cases, but the vertical extent varies with atmospheric conditions: it is generally in the range km. More details on the MST radar may be found in Vaughan (2002). Recently, the MST radar analysis software has been rewritten to improve the derivation of winds, particularly in the lower stratosphere. The new algorithms have improved the signal processing and implemented consensus algorithms to ensure radial and temporal continuity of the wind fields. Comparisons with radiosonde profiles show an average difference between the two techniques of order 1 m s 1, a comparable value to the radar precision.

3 INERTIA-GRAVITY WAVES 181 The MST radar is fixed in one location and observes gravity waves as oscillations in the measured wind profiles. The frequency of these oscillations, ω, is known as the ground-based wave frequency. This however is not the oscillation frequency of air parcels disturbed by the wave this is the intrinsic frequency,. Thetwo frequencies are related by the Doppler expression: = ω k U, (1) where k is the horizontal wavenumber and U the mean background wind. For a trapped lee wave, for instance, ω = 0, so that (in this case equal to N, the Brunt Väisälä frequency), has a direct relation to k. In general, however, there is no direct way to relate ω and, and we must use indirect methods. Here, we exploit the fact that for long-period waves (ω f,where f is the inertial frequency or Coriolis parameter) the air parcels follow elliptical paths on planes inclined by small angles to the horizontal i.e. if the wave perturbation velocity V is (u,v,w ), its horizontal projection (u,v ) rotates, either with time at a fixed location or with displacement at a given time, tracing out an ellipse. In the absence of background wind shear, the ratio R between the minor and major axes of the ellipse is equal to the ratio f/ thus allowing to be derived without prior knowledge of k. By fitting an ellipse to measured wind perturbations we may derive not only but also the direction of the group velocity, the horizontal component of which lies along the major axis of the ellipse. The corresponding vertical component depends on the sense of rotation of the wind vectors: clockwise rotation in the Northern Hemisphere indicating upward energy propagation. This analysis of IGWs by fitting ellipses to the rotating wind vectors is often referred to as the hodograph method. A confounding issue in employing the hodograph method is the effect of mountain waves. Hines (1989) argues that a mountain wave propagating into a background wind shear perpendicular to the wave vector k will induce an elliptical hodograph even though there is no long-period wave present. We return to this point in section 2.3, where we examine the distribution and properties of fitted hodographs for potential mountain-wave influences. A related complication, alluded to above, is that background wind shear enters the relationship between and f, precluding the use of R to derive directly (Thomas et al. 1999); correction for this is possible but requires unambiguous knowledge of the wave alignment. For this reason, results presented in section 3.2 on the distribution of intrinsic frequencies are confined to conditions of low wind shear. (In practice this means low background wind.) A further critique of the hodograph method was presented by Zhang et al. (2004). They simulated a nearmonochromatic wave of intrinsic period 3f using the MM5 mesoscale model, then used the hodograph method to derive wave parameters. As expected, in a region of background wind shear neither the intrinsic frequency nor the horizontal wavelength could be reliably derived, but the vertical wavelength was generally accurate. In a further simulation, they showed how the method breaks down when there is a superposition of waves, a problem first identified by Eckermann and Hocking (1989). For this reason we exploit the time continuity of the MST radar data to apply band-pass filters to the data in time, to ensure that the hodograph analysis is confined to nearmonochromatic oscillations Analysis algorithm To derive long-period IGWs from the radar data, the raw 2-minute radar winds were first median-averaged over 30 minutes. (Medians rather than means were used because the random errors in the radar winds are distinctly non-gaussian, with occasional outliers.) These 30-minute average zonal and meridional wind profiles were high-pass filtered in the vertical, using a fourthorder Butterworth filter with cut-off 5 km, to remove the background wind variation. A further median average of these perturbation winds was performed to generate a time series of 3-hourly profiles. These products were the basis of the search for elliptical hodographs. Firstly, fourth-order Butterworth filters were applied in the time dimension at each altitude, to generate two separate time series with nominal pass bands 4 8 hours and hours. This choice of pass bands was intended to allow oscillations near to the inertial frequency to be distinguished from a sample at higher frequency, to find whether they had different properties. As the 3-hourly averaging makes the shortest wave period distinguishable in the time series equal to 6 hours, and gravity waves cannot exist beyond the inertial period (15.2 hours at this location), these filters effectively selected oscillations with periods 6 8 hours and hours. Rotating hodographs typical of IGWs were identified using a pattern-matching algorithm, to find where the perturbation wind vector moved through four consecutive quadrants in either a clockwise or anticlockwise sequence, starting in any quadrant, and with 1 10 data points ( km height interval) in each quadrant. Provided the perturbation wind speed remained greater than 0.5 m s 1 in each quadrant, and the wind vector rotated by more than 360, IGW parameters were then derived by fitting ellipses to the perturbation wind vector. The vertical wavelength was measured from the average rotation rate of the hodograph over the four quadrants, while the ellipse-fitting algorithm supplied hodograph major and minor axes, alignment, and the sum of squares of residuals. Hodographs were accepted as valid if the root mean square residual < 0.5 ms 1. To check the operation of the algorithm, it was used to analyse a time series of random wind profiles (u and v selected from a Gaussian distribution with σ = 3ms 1 ). IGWs were found in fewer than 0.5% of profiles, far fewer than the results below using the measured winds. Tropopause height was derived from the maximum gradient of vertical echo power with height, below the

4 182 G. VAUGHAN AND R. M. WORTHINGTON echo power maximum in the lower stratosphere; this follows the method of Vaughan et al. (1995). The radar tropopause algorithm was modified to find the lowest of multiple tropopauses in IGWs Possible influence of mountain waves The vertical velocity measured by the MST radar was used to screen the profiles for the possible influence of mountain waves. In Figure 1, we present the percentage occurrence of detected ellipses as a function of w max, the maximum absolute vertical velocity coinciding with waves detected in that profile. The figure also shows the distribution of vertical velocity, with a pronounced peak at 0.1 m s 1. This is an artifact of the radar spectral processing algorithm caused by the need to remove ground clutter the point at zero Doppler shift and the two either side are replaced by values interpolated from the rest of the spectrum. Thus, the MST radar (in common with all radars of this type) cannot measure very small Doppler shifts; hence, the peak at 0.1 m s 1 is indistinguishable from zero. Figure 1 shows that the vast majority of detected waves did not coincide with mountain waves indeed for the clockwise-rotating waves (which, as we show below, are found in the stratosphere) the incidence decreases with vertical velocity. For the anticlockwise-rotating waves the opposite is true and contamination by mountain waves cannot be ruled out. For this reason, we exclude from the analysis below (for clockwise and anticlockwise rotation) all profiles where w max exceeded 0.15 m s Results 3.1. Occurrence of inertia-gravity waves Figure 2 shows the percentage of profiles for which the algorithm found an ellipse, as a function of season and divided according to the direction of rotation and observed wave period. Clearly shown in this figure is the prevalence in the MST radar data of longperiod (> 12 hours) clockwise-rotating waves, which are detected by the algorithm 70% of the time, largely independent of season. By contrast, the shorter-period clockwise waves are twice as prevalent in winter (45% occurrence) as in summer (20%). Anticlockwise rotation is less common ( 15% occurrence) and shows a similar seasonal pattern to the shorter-period clockwise waves. Figure 1. Probability of an ellipse being detected in a profile as a function of w max, the maximum absolute vertical velocity coinciding with a wave detected in that profile: (a) clockwise-rotating and (b) anticlockwise-rotating hodographs. Figure 2. Probability of an inertia-gravity wave being detected in 3-h averaged wind profiles as a function of time of year, for w max < 0.15 m s 1 : (a) upward energy propagation, and (b) downward energy propagation.

5 INERTIA-GRAVITY WAVES 183 The distribution of detected waves with respect to height (Figure 3) clearly shows that clockwise rotation is mainly found in the stratosphere with anticlockwise rotation in the troposphere. This points unambiguously to the tropopause region as the primary source of IGWs a result previously found in case studies (e.g. Hirota and Niki, 1985) but here shown to be a definite climatological feature. Figure 3 shows that the algorithm also detects clockwise rotation in the troposphere 5% of the time and anticlockwise rotation in the stratosphere 1% of the time. Examination of individual cases showed that the former generally correspond to breaking mountain waves at low levels an example is shown in Figure 4. Here the vertical velocity measured by the radar early in the day is large below 4 km, but very small above the signature of a breaking mountain wave. The zonal filtered wind component shows a maximum wave amplitude where the mountain wave is breaking, with clockwise-rotating hodographs. Less easily explained are the anticlockwise-rotating ellipses detected in the stratosphere. Some are due to noise: the 1% occurrence is comparable to the 0.5% detected by the algorithm from random noise. In such cases a time-height plot of the hodographs shows isolated single examples with anticlockwise rotation. Of more interest are clusters of such hodographs, as shown in Figure 5. For the first 15 hours of this day, the hodographs in the stratosphere rotate clockwise in the normal fashion. However, from 1900 UTC onwards a large-amplitude feature (> 5ms 1 ) is detected by the filtered winds between 10 and 15 km, corresponding to the region around the tropopause (12 km). The anticlockwise hodographs are prominent near the tropopause but disappear by a few kilometres above it. They correspond in fact to a thin layer of enhanced wind shear at km, from 1900 UTC onwards, which also corresponds to a layer of turbulence. As already explained, wind shear interferes with the hodograph method, changing the properties of the derived ellipse (e.g. Thomas et al., 1999) Properties of detected inertia-gravity waves The horizontal velocity amplitude of a wave is defined as the semi-major axis of the fitted ellipse. The distribution of these amplitudes and vertical wavelengths for the detected waves are shown in Figures 6 and 7. The threshold amplitude of 0.5 m s 1 used in the detection algorithm sets the lower limit for Figure 6, which clearly shows the vast majority of waves having amplitudes <3 ms 1. The peak amplitude is around 1ms 1, extending to slightly larger values for the most commonly-observed features the long-period, clockwise-rotating waves in the lower stratosphere. As with Figure 2, the other three categories show a very similar distribution. However, this is not the case with vertical wavelength, λ v, (Figure 7), where both clockwise (stratospheric) categories show a peak at 2.2 km and almost no cases beyond 4 km, whereas the anticlockwise (tropospheric) ellipses display longer wavelengths, particularly for the longer-period waves. We can derive the intrinsic frequency from the hodograph ratio R for each wave provided background wind shear is negligible. Such conditions are found when background winds throughout the profile are weak defined here as 20 m s 1 anywhere in the profile. The results are shown in Figure 8. They show that the distribution of intrinsic periods is the same, whether the observed wave period is > 12 hrs or 4 8 hrs. Tests on the ellipse-fitting algorithm in the presence of noise showed a broadening of the spectrum but no average shift in frequency. This suggests that the preponderance of very long-period waves in the observed dataset is a result of Doppler shifting of higher-frequency waves to near the inertial period, at least for those waves with low background wind velocities. To provide the observed shift in frequency with a wind speed 15 m s 1, a horizontal wavelength of order 200 km would be needed. The intrinsic wave frequency is related to the horizontal wavenumber k and the vertical wavenumber m by: 2 = (f 2 m 2 + N 2 k 2 )/(k 2 + m 2 ). (2) Figure 3. Probability of non-zero inertia-gravity wave activity as a function of height from the tropopause (measured by radar using vertical-beam echo power), for w max < 0.15 m s 1 : (a) upward energy propagation, and (b) downward energy propagation.

6 184 G. VAUGHAN AND R. M. WORTHINGTON Figure 4. Example of clockwise-rotating hodographs in the troposphere upward energy propagation from breaking mountain waves at low levels (shown by the vertical velocity). Vertical black stripes denote missing radar data for those times. Using f = s 1 (corresponding to a period of 15.2 hrs) and N = s 1 for the stratosphere and 0.01 s 1 for the troposphere (corresponding to periods of 5 and 10 minutes respectively), we can use Equation (2) and Figure 7 to estimate other wave parameters, taking the range of intrinsic frequencies to be 6 12 hrs. In the stratosphere (1.5 <λ v < 3km), = 6 hr waves have horizontal wavelengths λ h ranging from 118 to 235 km, while λ h for = 12 hr waves ranges from 354 to 707 km. Corresponding values for the troposphere (noting that λ v extends to 4 km for the longer-period waves) are km and km. The horizontal component of ground-relative group velocity, c g decreases with wave period and is in the range 6 18 m s 1 for the stratospheric waves and m s 1 in the troposphere. For the wave shown by Pavelin et al. (2001), a period of 13.8 hours and vertical wavelength of 2 km corresponds to λ h = 800 km and c g = 5.5 ms 1. This wave persisted for four days, suggesting a wave packet 1730 km in extent about two wavelengths. Most observed IGWs persisted for a day or less in the observations, suggesting wave packets less than around 1000 km for 12-hour waves in the stratosphere and 300 km for the their tropospheric equivalents. It follows that such waves will seldom have more than one complete wavelength in the wave group. For shorter-period waves persisting for 24 hours in the MST radar observations, the wave packet would be around 1400 km in the stratosphere and 500 km in the troposphere, enough for several complete wavelengths.

7 INERTIA-GRAVITY WAVES 185 Figure 5. As Figure 4, but for anticlockwise-rotating hodographs in the stratosphere. Figure 6. Probability of non-zero IGW activity as a function of wave amplitude, for w max < 0.15 m s 1 : (a) upward energy propagation, and (b) downward energy propagation.

8 186 G. VAUGHAN AND R. M. WORTHINGTON Figure 7. Probability of non-zero IGW activity as a function of vertical wavelength, for w max < 0.15 m s 1 : (a) upward energy propagation, and (b) downward energy propagation. Figure 8. Probability of occurrence of derived intrinsic period from the ratio of the ellipse axes, for w max < 0.15 m s 1 and maximum background wind < 20 m s 1 : (a) upward energy propagation, and (b) downward energy propagation Relation to the jet stream Given the tropopause level source for the waves identified in section 3.1 above, the question arises of the relation between waves and the jet stream. Jet streams are associated with baroclinic instability, strong ageostrophic winds and sharp wind gradients on their upper and lower edges. All these features are potential wave sources. Figure 9 presents the distribution of wave occurrence as a function of the maximum background wind speed in the vertical profile. The dashed line in this figure is the probability distribution of the winds themselves low probability here indicates that the wave occurrence statistics are based on small samples and are not reliable. For the short-period clockwise category, and for both anticlockwise categories, there is a a clear association between waves and the strength of the jet stream. This is especially strong for the shorter period waves, which are more than three times more common when maximum winds are > 60 m s 1 than for winds < 20 m s 1. The association is weaker with the dominant long-period waves in the lower stratosphere. Unlike the other three categories, such oscillations are almost as common at low wind speed as they are above strong jet streams, which indeed is necessary given that they are observed around 70% of the time (Figure 2). Two possible explanations for this are that (i) these waves are more persistent and able to propagate further from their source region than the other categories and (ii) the source regions themselves are more widely distributed. Given that group velocity decreases with wave period, there is no reason to expect the long-period waves to propagate further than shorter period waves, so the hypothesis of a more extensive source region would appear more likely. As already mentioned, fitting an ellipse to a hodograph allows the propagation direction of the wave to be calculated from the orientation of the major axis. There is an ambiguity in direction of 180, and the technique is more reliable for shorter-period waves where the hodographs are more elliptical (so the fitted orientation is less susceptible to noise). In principle, the vertical velocity measured by the radar may be used to resolve the ambiguity in direction, but, as already explained, this dataset specifically excludes cases with significant vertical velocity. In Figures 10 and 11, we present the distribution of wave alignments with respect to the direction of the maximum background wind. Looking first at the whole dataset (Figure 10), little angular dependence is seen for

9 INERTIA-GRAVITY WAVES 187 Figure 9. Probability of non-zero IGW activity as a function of jet-stream speed, for w max < 0.15 m s 1 : (a) upward energy propagation, and (b) downward energy propagation. Figure 10. Probability of non-zero IGW activity as a function of wave alignment with respect to the maximum wind direction, for w max < 0.15 m s 1 : (a) upward energy propagation, and (b) downward energy propagation. Figure 11. Probability of non-zero IGW activity as a function of wave alignment with respect to the jet-stream direction, for maximum wind > 40 m s 1 and w max < 0.15 m s 1 : (a) upward energy propagation, and (b) downward energy propagation. any of the categories although there is a slight preference for an alignment to the clockwise side of the maximum wind. Restricting the datasets to jet-stream cases (max wind speed > 40 m s 1 ) a greater dependence of alignment appears, with preferred direction clockwise of the jet stream. This is consistent with Zhang et al. (2004), who found an artificial bias in direction for fitted hodographs, rotated to the right of the correct direction, possibly (according to them) because of varying background winds. As Figure 11 uses data from conditions where vertical wind shear will be present, we conclude that the apparent bias in direction is a similar artifact.

10 188 G. VAUGHAN AND R. M. WORTHINGTON 4. Conclusions This work has investigated the incidence of long-period, short-vertical-wavelength oscillations in the wind fields measured by the UK MST radar which have properties consistent with IGWs. It is the first climatological investigation of this kind conducted for a site near the end of the storm tracks, where generation of IGWs by baroclinic instability should be observed. By a combination of vertical and temporal filtering of the data, wave components could be isolated from variations in the background wind and restricted to a narrow frequency range. Further demanding that the winds rotate through four quadrants with altitude meant that non-igw perturbations could be strongly discriminated against. Further, to remove possible contamination by mountain waves, occasions when the vertical velocity in the wave field exceeded 15 cm s 1 were discarded. We find that IGWs are much more common in the stratosphere than the troposphere, with greater incidence near the inertial frequency, in line with previous studies (Sato, 1994; Nastrom and Eaton, 2006). Long-period (> 12 h) waves in the lower stratosphere are observed around 70% of the time, with a slight preference towards the winter season. They are not preferentially associated with a jet stream and have very long ( 500 km) horizontal wavelengths. This is in marked contrast to shorter-period (6 8 h) waves in the stratosphere and waves of all periods in the troposphere which are clearly associated with jet streams and generally propagate along them. The shorter-period stratospheric waves were observed around 30% of the time and both category of tropospheric wave around 10% of the time. Typical vertical wavelengths of 2 km and amplitudes of 1 3 m s 1 were found. Because of the effect of background wind shear on ellipse properties, it was only possible to investigate the wave intrinsic frequency under conditions of low background wind speed (and thus also low wind shear). For this subset of IGWs the distribution of intrinsic frequencies was the same, whether the waves were observed with longer or shorter periods (or indeed on which side of the tropopause they were found). This suggests that Doppler shifting of waves from higher frequencies is an important factor in generating the observed preponderance of longer-period waves. The overwhelming majority of waves propagate energy upwards in the stratosphere and downwards in the troposphere, consistent with the source of these waves being at jet-stream level. However, incidences were observed of upward-propagating waves in the troposphere resulting from breaking mountain waves at low levels. Rarer incidences of downward propagation of energy in the stratosphere are best explained by the effect of a strong shear layer on the analysis method. Acknowledgements This work was funded by the NERC UTLS Ozone thematic programme, and the paper is published with help from the COST-723 project ( We thank the NERC MST radar facility for the data used here. The ellipse-fitting algorithm was taken from craigm/idl/idl.html. References Eckermann SD, Hocking WK Effect of superposition on measurements of atmospheric gravity waves: A cautionary note and some reinterpretations. J. Geophys. Res. 94: Ford R Gravity wave radiation from vortex trains in shallow water. J. Fluid Mech. 281: Guest FM, Reeder MJ, Marks CJ, Karoly DJ Inertia-gravity waves observed in the lower stratosphere over Macquarie Island. J. Atmos. Sci. 57: Hines CO Tropopausal mountain waves over Arecibo: a case study. J. Atmos. Sci. 46: Hirota I, Niki T A statistical study of inertia-gravity waves in the middle atmosphere. J. 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