Some perspectives on wave clouds

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1 Some perspectives on wave clouds Simon B. Vosper and Douglas J. Parker School of the Environment, University of Leeds Wave clouds, or lenticular clouds, are relatively common features over the British sles, although they are often obscured from view by boundary-layer cumulus. Figure 1 shows a case observed looking north-west from Leeds at 0915G~T on 15 March 2000, and demonstrates the linear nature of the clouds. This is confirmed in the satellite ~ ~ ~ image, Fig. 2, which shows similar clouds covering much of northern Britain. These wave clouds are associated with the formation of internal gravity waves in the atmosphere. Put simply, these waves occur when the atmosphere is suitably stable: if vertical air motions are forced, due to air at low levels flowing over a hill for example, then air parcels will tend to rebound about their initial level (in the same way as the stable interface between a body of water and the air above it will oscillate, in the form of surface waves, if it is disturbed). However, due to the variations of stability and wind speed with height in the atmosphere, the situation is rather more complex than this, and different kinds of wave response can be observed. The type of waves normally associated with long trains of wave clouds, as in Fig. 2, are commonly referred to as trapped waves or lee waves. n this case wave energy is trapped beneath some layer (typically at some mid-tropospheric height), and instead of propagating freely in the vertical and into the stratosphere it is ducted horizontally downwind of the hills. Under conditions of strong trapping, lee waves (and hence wave clouds) can appear for several hundreds of kilometres downwind of any hills. More examples of such trains of lee waves in satellite imagery are shown by Scorer (1986,1990) and Bader et d. (1995). The occurrence of lee waves is important to aviation, as such waves correspond to regions of relatively strong upward and downward Fig. 1 Wave clouds o m the hnines, viewed towards the west jbm LRodhouse Moor in beds, on ~ ~ ~ 1s March 2000 (CP 0 D. 3 Parket) 3

2 F 2 ~ AVHRR channel 2 visible image from 0812 GMT on 15 March 2000 ( Dundee Satellite Receiving Starion, Dundee University) motion. Glider pilots, for instance, may make use of the updraughts for climbing. n extreme cases, rotors may form in association with lee waves, leading to considerable low-level turbulence which is a hazard to aircraft. The nature of the waves over topography is also important in controlling the force balance between the land and the atmosphere (which impacts on numerical weather prediction models). Prediction of the wave characteristics of the airflow is therefore useful. The linearised equations of motion (see, for example, Holton (1992), pp ) can be used to show that the conditions for wave trap- ping are related to the vertical profile of the Scorer parameter, l2 (Scorer 1949), defined by: N2 1 p=---- d2u U2 U dz2 (1) where U(z) is the wind speed, z is the height above the ground and N is the Brunt-Vaisala or buoyancy frequency, defined as: where H(z) is the potential temperature and g is the acceleration due to gravity. The Brunt- 4

3 _--cl-- 9 : 1 Fig. 3 Schematic diagram iuusnating the conditions suitable for wave trapping. See text for further explanah. L Vaisala frequency is the characteristic frequency of vertical motion in the atmosphere. For waves with a horizontal wavelength, A, the atmosphere will support waves where 1 > k 2, where k=2nli. n layers of the atmosphere where Z2 < k 2, the waves will decay with height. Wave trapping is possible when a region of high Scorer parameter (which for a certain wavelength gives 1 > k 2, is bounded by a layer of lower Scorer parameter (in which 12<k2) above. This situation is illustrated by Fig. 3. Lee waves can be expected to occur under such conditions provided that the low-level airstream has sufficient kinetic energy to flow over the hills (thus causing vertical motion) rather than around them. For the case of 15 March 2000, inspection of the observed profile (Fig. 4) obtained from a radiosonde launched at 0929 GMT from the sle of Arran*, south-west Scotland, shows that there was a stable layer at low levels, between around 750 and 850mbar. This is characteristic of subsidence in a high pressure system, and * The radiosonde was launched as part of an extensive field campaign aimed at measuring gravity waves generated over Arran and their influence on the near-surface flow. The fieldwork was coordinated by groups at the University of Leeds, UMST, the Met Office and the Forestry Commission. may have been associated with a warm front which is shown at 0000 GMT in the Met Office surface analysis (Fig. 5). Such a stable layer with much reduced stability aloft is characteristic of the conditions required for trapping. The height dependence of the Scorer parameter, calculated from the high-resolution wind and temperature measurements obtained from the Arran radiosonde, is shown in Fig. 6. A layer of relatively high 1 * can be seen below about 4 km, with lower values in the mid and upper troposphere. Due to the dependence of the wave dynamics on both wind curvature and stability (as expressed in the Scorer parameter) it is necessary to consider the full atmospheric profile and pay special attention to the upper boundary conditions when attempting to diagnose the wave conditions. There have been a number of attempts (e.g. Mobbs and Darby 1989) to use the Taylor-Goldstein equation to diagnose wave conditions from real profiles, and most report considerable difficulty in obtaining reliable solutions. However, during Some recent field campaigns considerable success has been obtained using a threedimensional (3D) linear model to forecast wave activity in the troposphere and stratosphere. The technique involves solving the linear equations of motion (an approximate 5

Fig. 4 Sounding from the sle of Arran, southwest Scotland, for 0929 GMT on 15 March 2000, showing a distinct lower-level stable layer, with much less stable air immediately above it Fig.

4 Fig. 4 Sounding from the sle of Arran, southwest Scotland, for 0929 GMT on 15 March 2000, showing a distinct lower-level stable layer, with much less stable air immediately above it Fig. 5 Met Office surface analysis for 0000 GMT on 15 March 2000 (0 Crown copyright) version of the full nonlinear equations which are valid provided that the wave amplitude is small) on a computer. Given digital terrain data and a background profile of wind and potential temperature, the full 3D wave field can be computed. The advantage of using a linear model over a fully nonlinear model is that considerably less computing time is required, since we can neglect many complex physical processes and consider only simple dynamics. This enables high-resolution gravity-wave forecasts to be made in relatively quick time for special applications. A linear gravity-wave forecast for the sle of Arran on 6

16 f 1 14 8 12 ' E s 10 ' E 8. cb.- " 6 ' " -1 0 1 2 3 l2 /km-2 Fig. 6 Height variation of the Scorer parameter ( 1 *) calculated using the high-resolution Arran radiosonde meamremenu.

5 16 f ' E s 10 ' E 8. cb.- " 6 ' " l2 /km-2 Fig. 6 Height variation of the Scorer parameter ( 1 *) calculated using the high-resolution Arran radiosonde meamremenu. The dashed line corresponds to a wavelength of 9 km. For explanation of k see text E X km Fig. 7 Linear model forecast for the graority-wave vertical velocity field (m s-') at 3 km abow sea-level over the sle of Arran and the Kinlyre peninsula, southwest SCOdand. Forecast is valid for 0600 GMTon 15 March March 2000 is shown in Fig. 7. This fore- obtained from the coarser resolution (0.5') cast is based on a vertical profile of wind and global forecast model of the European Centre potential temperature from an 18-hour forecast for Medium-Range Weather Forecasts. The (valid at 0600GMT on 15 March 2000) linear forecast shows a clear tadded wave 7

6 train, generated by Arran and the Kintyre peninsula, which propagates towards the south-west. Both the horizontal wavelength and the orientation of the waves compare well with waves seen in the high-resolution satellite imagery (Fig. 2). The predicted horizontal wavelength of about 9 km corresponds to a value of 12 of around 0.49 km-2. As shown in Fig. 6, the variation of the Scorer parameter with height is consistent with such a wavelength being trapped in the lower troposphere. Given the occurrence of gravity waves, a layer of the atmosphere must be suitably moist for clouds to appear in the ascent regions of the waves (Fig. 3). n observing wave clouds of the kind seen on 15 March 2000, we are probably seeing only one (moist) level of a deeper wave field. Measuring, understanding and predicting the full 3D wave field remains an important challenge for meteorological research. References Bader, M. J., Forbes, G. S., Grant, J. R., Lilley, R. B. E. and Waters, A. J. (1995) mages in weather forecasting: A practical guide for interpreting satellite and radar imagey. Cambridge University Press Holton, J. R. (1992) An introduction to dynamic meteorology. Harcourt Publishers Ltd (a subsidiary of Harcourt nternational Ltd) Mobbs, S. D. and Darby, M. S. (1989) A general method for the linear stability analysis of stratified shear flows. Q. J. R. Meteorol. SOL., 115, pp Scorer, R. S. (1949) Theory of waves in the lee of mountains. Q. J. R. Meteorol. SOC., 75, pp (1986) Cloud investigation by satellite. Ellis Horwood, Chichester -(1990) Satellite as microscope. Ellis Horwood, Chichester Correspondence to: Dr S. Vosper, School of the Environment, University of beds, Leeds L S~JT. 0 Royal Meteorological Society, How often does severe clear air turbulence occur over tropical oceans? W. T. Roach' and C. E. Bysouth2 ' Crowthorne, Berkshire Met Office, Bracknell The motivation for writing this paper came from a report in Weather of prolonged and severe clear air turbulence (CAT) over the tropical Pacific by Blanchard (1999), followed shortly by a reply from Bysouth (2000) showing that this incident was forecast using the Met Office operational numerical forecast model - or Unified Model (Cullen 1993). This seemed anomalous, since CAT is normally associated with temperate (polar front) and subtropical jet streams usually found poleward of 30" latitude. However, examination of the wind field in Fig. 1 of Bysouth (2000) showed that the Northern Hemisphere subtropical jet stream (NHSTJ) had apparently buckled a few days before (rather like a giant breaking wave) to, form a very long disrupting trough (at the base of the 'breaker') slanting west-south-west to about 10"N. This trough coincided with the area of high CAT index used by the forecast model. Disrupting troughs occur quite often in temperate-latitude jet streams, and have long been known to contain (often severe) CAT. They sometimes form part of the process of detachment of separate vortices - or 'cold pools'. However, subtropical jets in both hemispheres appear to exhibit much more stable behaviour than temperate-latitude jets; subtropical jets rarely buckle and have not been seen to form cold pools in the study presented here. t was therefore decided to make briefcase- 8

How often does severe clear air turbulence occur over tropical oceans?

How often does severe clear air turbulence occur over tropical oceans? train, generated by Arran and the Kintyre peninsula, which propagates towards the south-west. Both the horizontal wavelength and the orientation of the waves compare well with waves seen in the high-resolution