Influence of lee waves on the near-surface flow downwind of the Pennines

Transcription

1 QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY Q. J. R. Meteorol. Soc. 133: (7) Published online in Wiley InterScience ( Influence of lee waves on the near-surface flow downwind of the Pennines P. F. Sheridan, a * V. Horlacher, a G. G. Rooney, a P. Hignett, a S. D. Mobbs b and S. B. Vosper a a Met Office, UK b University of Leeds, UK ABSTRACT: The results of a recent field experiment focusing on the near-surface pressure and flow fields downstream of the Pennines in northern England are presented. The main aim of the experiment is the improvement of wind forecasts downstream of orography. Trapped lee waves commonly occur in westerly flow in this region, and during the experiment there were numerous instances of apparent flow separation, indicating the formation of lee-wave rotors. The spatial variability of the near-surface flow in these circumstances is closely linked to the positions of lee-wave crests and troughs aloft, and appears to be a response to pressure gradients induced by the lee waves. For large-amplitude waves, it has been possible to demonstrate a correlation between the fractional change of the flow speed across the measurement array (which if large enough may lead to flow separation) and a normalized pressure-perturbation amplitude. For a group of lee-wave cases during which the cross-mountain flow is strong, a rapid decrease in the Scorer parameter within the lower portion of the troposphere appears to be a prerequisite for rotors to form. However, this does not guarantee their occurrence. For a fixed Scorer-parameter profile, idealized two-dimensional simulations indicate that the lee-waveinduced pressure-perturbation amplitude, and hence the occurrence of rotors, is controlled largely by the strength of the wind upstream close to the mountain-top level. It seems that the combination of a favourable Scorer-parameter profile and sufficiently strong low-level winds is required for rotors to develop. Crown Copyright 7. Reproduced with the permission of Her Majesty s Stationery Office. KEY WORDS flow separation; automatic weather station; microbarograph; orography Received 7 December 6; Revised 7 April 7; Accepted 9 May 7 1. Introduction When trapped lee waves form downstream of orography, they may be accompanied by rotors: turbulent regions of air recirculating about a horizontal, cross-wind axis. In recent literature (e.g. Hertenstein and Kuettner, 5), two classes of rotors have emerged: type-i rotors, which form beneath the crests of a lee-wave train, and type-ii rotors, the continuously-stratified analogues of a hydraulic jump. Both types of flow are potentially associated with severe turbulence, and present a difficult challenge to weather forecasting. This study is concerned with type-i rotors. The formation of rotors under a variety of conditions has been investigated by several authors using idealized two-dimensional (D) simulations (e.g. Doyle and Durran, ; Vosper, 4; Vosper et al., 6). These authors note the importance of surface friction in allowing rotors to form. The most recent of these studies (Vosper et al., 6) focuses on type-i rotors, and shows how, as the wave amplitude increases, rotors form when a critical value of the normalized pressure-perturbation amplitude, p, ρu * Correspondence to: P. F. Sheridan, Met Office, FitzRoy Road, Exeter EX1 3PB, UK. peter.sheridan@metoffice.gov.uk is reached. Here p is the amplitude of the wave-induced pressure perturbation at the surface within a lee-wave cycle, ρ is the air density, and u is the friction velocity. The involvement of u in the normalization expresses the fact that the velocity scale near the surface in addition to the adverse pressure gradient induced by the lee waves is important in determining whether or not rotors occur. Although many pioneering measurements of rotor flows were made in the mid-twentieth century (for example, in the Alps, (Kuettner, 1939) in the Sierra Nevada, (Holmboe and Klieforth, 1957) and in the UK (Manley, 1945)) a number of field experiments performed during the past decade provide new insights into the rotor phenomenon. Notable examples include studies mapping the flow structure of rotors downstream of the Colorado Rockies using LIDAR (Ralph et al., 1997, Darby and Poulos, 6), and the Terrain-Induced Rotor Experiment (T-REX), involving the deployment of various in situ and remote-sensing techniques in the Sierra Nevada in March April 6 (Grubisic and Kuettner, 4). In a recent field campaign carried out in the Falkland Islands in the South Atlantic (Mobbs et al., 5), the occurrence of rotors was found to be linked to the presence of an upstream temperature inversion, whose strength and height largely determine the nature of the trapped-wave response (Vosper, 4). However, such an inversion Crown Copyright 7. Reproduced with the permission of Her Majesty s Stationery Office.

2 1354 P. F. SHERIDAN ET AL. is not a prerequisite for rotor formation. As we shall see, rotors are commonly observed beneath the trapped lee waves generated by the hills in northern England. Strong temperature inversions are relatively uncommon in these flows, and wave-trapping is instead controlled by the gradual variation of temperature and wind with height through the troposphere. The way in which trapped waves of this kind interact with the near-surface flow has recently been the focus of several studies (e.g. Jiang et al., 6; Smith et al., 6; Vosper et al., 6). This study describes the results of a field experiment aimed at measuring the near-surface flow over the Pennines in northern England during periods of strong lee-wave activity. Idealized D simulations have also been performed in support of the field analysis, since they enable us to isolate the different factors involved in rotor formation. A description of the experiment is provided in Section. Section 3 describes the method used for the idealized simulations. In Section 4, case studies from the field experiment are used to demonstrate the typical upstream conditions required for large-amplitude waves, and to explore the link between rotor formation and the lee-wave-induced pressure field. In Section 5, the results of the idealized simulations are discussed. In Section 6, the implications of the simulation results for forecasting are examined. Conclusions are presented in Section 7.. Description of experiment The field campaign was carried out in the Pennines, northern England, as a collaborative effort between scientists from the Met Office (Cardington Met Research Unit (MRU)), the University of Leeds and the University of Lancaster. Data were recorded continuously over the period from October 3 to April 5. Observations focused on the Vale of York, which lies to the east of the Pennines, and contains numerous airfields. During periods of lee-wave activity in westerly flow, the Vale is often subject to high degrees of near-surface horizontal wind shear, and gusty winds, whose strength is poorly forecast by numerical weather prediction models. Historically, aircraft reports of severe turbulence in the region in conjunction with lee waves have been quite common (e.g. Cashmore, 1966). The main instrumentation consisted of a network of automated sites at the surface, which operated continuously during the experiment. A unidirectional sky camera, or skycam, was placed within the surface array, and the measurements were supported by radiosonde releases to the west of the Pennines. Flights over the Pennines on two occasions by BAe 146 aircraft operated by the Facility for Airborne Atmospheric Measurement (FAAM) also formed part of the campaign, though the data from these are not presented here. Figure 1 depicts the area covered by the experiment, showing the terrain and the overall layout of surface-based instruments, with two extra panels depicting zoomed areas. Running north south through the centre of the large panel of the figure are the Pennines. The Vale is the lowland area in the east and southeast of the image. The positions of thirteen m automatic weather stations (AWSs) and four m turbulence masts are marked by filled circles and white crosses, respectively. The cluster of AWSs depicted in panel (a) of the figure were located close to Leeming air base, with one ( SH ) located to the east of Leeming; three stations were located at other airfields (Topcliffe, Dishforth and Linton-on-Ouse panel (b)); and one was located at Hazelrigg, to the west of the Pennines near Lancaster ( Lan ). The four turbulence masts were all located at AWS sites (Hazelrigg, Leeming, Dishfoth and Linton). Only the data from the Hazelrigg mast are used in this study. The skycam was situated roughly halfway between AWS stations L1 and L4 at Leeming airfield. The Vale of York, being a broad and relatively flat area, represents a good location for studying the influence of lee waves on the near-surface flow, since flow disturbances detected by the AWS array are expected to be due mainly to the lee waves themselves, rather than to local variations in the topography. The AWS instruments measured the m wind speed and direction, and the surface pressure with a practical accuracy of.5 hpa, in addition to the temperature and relative humidity. Full details of the AWS sensors are given in (Mobbs et al., 5) and references therein. A local effect (possibly sheltering) at station L3 appears to lead to wind data that represent the larger-scale flow poorly; therefore the wind data from L3 have not been used in this study. On each of the turbulence masts, two Gill-Solent horizontally-symmetric ultrasonic anemometers allowed the measurement of all three velocity components. The skycam consisted of an Axis 1 Network Camera with a Pentax mm f1.4 auto-iris lens, whose centre of view was oriented towards 84 in the horizontal, and at an elevation of around 16 above the horizon. The field of view (measured manually) was 41 in the vertical and 55 in the horizontal; however, the images used in this study have been cropped in order to exclude areas of military operations within the field of view. Radiosondes were routinely released daily at around 9 UTC from Hazelrigg (54.1 N,.78 W), starting in November 3. This launch time was chosen for the convenience of those participating. These releases were supplemented with more frequent releases, both upwind and downwind of the Pennines, during intensive observation periods (IOPs). IOPs occurred when forecast conditions were conducive to strong lee-wave formation: for example, a warm sector with strong westerly flow across northern England. Eleven IOPs occurred, each of which consisted of a day of roughly-hourly radiosonde releases, from Hazelrigg to the west, and from either Leeming airfield or Dallow Moor ( DM in Figure 1) to the east of the Pennines. Only the upstream radiosonde data are discussed in this study. Hourly SYNOP cloudbase data have also been used. These data originate from a laser cloud-base recorder that was part of a permanent Semi-Automatic Meteorological Observing System (SAMOS) station at Leeming.

3 INFLUENCE OF LEE WAVES DOWNWIND OF THE PENNINES 1355 Figure 1. The orography of the Pennines, with locations of automatic weather stations marked as filled circles. Four m turbulence masts are indicated by white crosses. Insets (a) and (b) show zoomed images of the areas marked by rectangles within the main panel. Terrain heights are contoured, with an interval of 1 m. See text for further details. 3. Numerical-simulation method 3.1. Model description A series of numerical simulations of lee waves have been performed in support of the field work. These allow us to examine, in a controlled and systematic manner, various factors that may influence the formation of rotors. The numerical simulations were performed using the Met Office BLASIUS model (Wood and Mason, 1993), which has been used extensively for a range of orographic flow studies (e.g. Wood, 1995; Ross and Vosper, 3; Vosper, 4). The model configuration used is identical to that used in a previous study (Vosper et al., 6), except that a domain length of 51 km, instead of 14 km, has been used in the interests of computational efficiency. This change was found to have negligible impact on the results. A full description of the model and simulation set-up is given in (Vosper et al., 6); some important details are repeated below, followed by a description of the upstream profiles used. The model used in this study employs the shallow Boussinesq approximation. At the lower boundary, a noslip condition is applied with a constant roughness length of z =.5 m, and a zero-surface-heat-flux condition is also applied. The Coriolis force is imposed with f = 1 4 s 1. The ridge considered in this study is specified by H h(x) = 1 + ( x, (1) L ) where the mountain height H is 3 m and the mountain half-width L is km. 3.. Upstream profiles The simulations involve idealized flow whose basic state consists of a sinusoidal westerly jet described by U(z) = U + U t sin(π z ), () z m where U is the surface wind speed, and the maximum wind speed U max = U + U t occurs at height z m /. A value of km was used for z m, resulting in a jet maximum at 1 km. Examples of some of the wind profiles used are shown in Figure. According to linear theory, the vertical structure of a wave mode is determined by the equation d ŵ dz + (l k )ŵ =, (3) where ŵ(k, z) is the Fourier transform of the vertical velocity and k is the horizontal wave number. The degree

4 1356 P. F. SHERIDAN ET AL. (a) (b) 1 15 z (km) 1 z (km) U (ms -1 ) θ (K) (c) θ (K) z (km) U (ms -1 ) Figure. Idealized profiles of (a) U and (b) potential temperature (before modification by boundary-layer mixing) used in the simulations, with: U = 15 ms 1 and U t = 15 ms 1 (dashed); U = 6.5 ms 1 and U t = 36.4 ms 1 (solid); U = 4ms 1 and U t = 36 ms 1 (dashed-dotted). (c) Wind and potential-temperature profiles in the simulation with U = 5ms 1 and U t = 8 ms 1 after modification by boundary-layer mixing with a roughness length of.5 m. Panel (b) focuses on the bottom half of the domain in order to better illustrate the shape of the θ profile (note that N is symmetric about 1 km). In (c), only the lowest portion of the profile is shown, as the profile is unmodified above the boundary layer. to which waves are trapped is determined by the Scorer parameter l (z) (Scorer, 1949), which for the shallowconvection form of the Boussinesq equations is given by l (z) = N U 1 d U U dz, (4) where N is the Brunt Väisälä frequency. In general, a decrease with height of l indicates that the profile will be conducive to wave-trapping. For the simulations in this study, the Scorer parameter is fixed, while the profiles of N and U are varied. This allows us to isolate the effect of changes to the wind profile and stratification from the effect of changes to the horizontal wavelength and vertical structure of the resonant wave mode. For each simulation, the wind profile is defined by choosing values of U and U t ; then the profile of N (and hence of potential temperature θ) can be computed by inverting Equation (4) for each model level. The chosen profile of l is shown in Figure 3. When U = 5ms 1 and U t = 8 ms 1,this l profile corresponds to a constant N value of.1 s 1 throughout the depth of the domain. These conditions result in simulated lee waves with a wavelength of around 1.5 km. Values of U between 1 ms 1 and 3 ms 1 have been used, and for each U, a range of different relative jet strengths, U t /U, between and 9 have been simulated. A selection of these wind and θ profiles is shown in Figure (a) and (b). Figure (b) demonstrates that, because the Scorer-parameter profile is always the same, there is negative curvature of the θ profile with height in the lowest 1 km of the domain when U t /U < 5.6 and positive curvature when U t /U > 5.6. For each simulation, a one-dimensional (1D) solution is first obtained, using a 1D version of the model, which

5 INFLUENCE OF LEE WAVES DOWNWIND OF THE PENNINES 1357 z (km) l (km - ) Figure 3. Scorer-parameter profile for the lowest 1 km of the domain corresponding to Equation (4) (solid line with filled circles) with U = 5ms 1, U t = 8 ms 1 and N =.1 s 1 throughout the depth of the domain. For comparison, the dashed line shows the Scorer-parameter profile computed using wind and temperature data from a radiosonde ascent from Hazelrigg at 1149 UTC on 17 March 5 (case ). has been run to a steady state in order to provide an initialization for the D configuration. This results in a modification to the wind and temperature profile due to the formation of a neutrally-stratified boundary layer. An example of this effect is shown in Figure (c). Despite the effort to keep the profile of l fixed, some variation occurs at low levels because of differences in the boundary layer, depending on the initial wind and temperature profiles. For larger values of U, a deeper boundary layer forms and the lee-wave wavelength is found to be shorter. Wavelengths range overall between 9.5 km and 11.5 km. The variation with height of the vertical-velocity amplitude (normalized by its maximum value) is found not to change significantly when U is increased, despite the change in wavelength. The D simulations are all run until a steady solution is obtained. 4. Observational results In this section we examine the field measurements. First, case studies are discussed at length, in order to demonstrate the typical flow behaviour in lee-wave and rotor events. Then, the relationship between the flow and pressure fields is explored using a set of strong-lee-wave cases. Finally, the importance of the Scorer parameter in the formation of rotors is demonstrated Examples of lee-wave and rotor activity Here we focus on two cases, those of 9 February 5 and March 5, referred to as case 1 and case respectively. IOPs occurred during both of these periods. These particular cases were chosen because strong, ostensibly similar lee waves were observed in both; however, rotors appeared to occur only in case, with no rotor activity detected in case 1. The synoptic conditions over the UK during cases 1 and are shown in Figure 4(a) and (b), respectively. Both cases correspond to warm-sector westerly flows. The warm sector generally contains stable air, and these are the typical conditions for strong lee waves. Profiles of wind and potential temperature taken from upstream radiosonde ascents during cases 1 and are shown in Figure 5(a) (c) and (e) (g) respectively. Two examples are shown for each case, from the morning (solid lines) and evening (dashed lines) of each day, illustrating the temporal variation of the upstream conditions. In both cases, the wind direction (panels (b) and (f)) is close to westerly, and changes little throughout the troposphere except for turning in the boundary layer. Figure 5(a) indicates that strong winds occur in case 1: the wind at 7 m is 18 ms 1, compared to a mean value of about 1 ms 1. There is also a jet aloft, peaking in strength at the tropopause. In Figure 5(e), for case, the profile also indicates strong winds, initially roughly constant with height above the boundary layer. The winds weaken significantly during the day, decreasing at 7 m from 5 ms 1 to 16 ms 1 for the two sondes shown. The potential-temperature profiles (panels (c) and (g)) confirm that conditions are stable on both days. There is a degree of negative curvature in θ for both cases, particularly in Figure 4. Synoptic analysis charts showing the mean sea-level pressure (hpa) and the positions of surface fronts for (a) 1 UTC on 9 February 5 and (b) 18 UTC on 17 March 5.

6 1358 P. F. SHERIDAN ET AL. case 1 case Figure 5. Vertical profiles of (a, e) wind speed, (b, f) wind direction, (c, g) potential temperature, and (d, h) Scorer parameter, measured by radiosondes released from Hazelrigg at: (a d) 11 UTC (solid lines) and 177 UTC (dashed lines) on 9 February 5 (case 1); (e h) 18 UTC (solid lines) and 1641 UTC (dashed lines) on 17 March 5 (case ). case, where the low-level Brunt Väisälä frequency is unusually high. This enhanced stability is consistent with mid-level descent, which could have been occurring in association with an anticyclone that was present to the south. Scorer-parameter profiles have been calculated from the radiosonde data for cases 1 and using Equation (4), and are shown in Figure 5(d) and (h) respectively. In order to compute the Scorer parameter, we have resolved the winds in the direction of the average wind vector

7 INFLUENCE OF LEE WAVES DOWNWIND OF THE PENNINES 1359 below km. Because of the high sensitivity of l (z) to noise in the profile, smoothing has been applied to the wind and θ profiles, and to the resulting profiles of N and d U/dz, before calculating l (z). Care has been taken not to remove features of particular relevance to the wave structure through smoothing. For instance, the largest filter scale corresponds to roughly 1 m in the vertical, so that features comparable to the mountainwave vertical wavelength (which is much larger than 1 m) are not strongly affected. In both cases, the Scorer parameter exhibits a decreasing trend with height in the lower troposphere, indicating conditions conducive to wave-trapping. In case 1, this is largely brought about by the general increase with height of the wind profile, while in case the curvature of the θ profile makes the stronger contribution. Visible satellite images recorded during cases 1 and are shown in Figure 6(a) and (b), respectively. They show clear evidence of lee waves, in the form of cross-flow banding of cloud over the Pennines and the Vale of York. Images were available at intervals of 15 min, and showed that the waves in each case were not stationary. In case 1, the cloud bands downstream of the orography move to the east with time during the event, whereas in case the bands move to the west over time. This coincides with an increase (decrease) in wavelength over time in case 1 (case ). The evolution with time of the wind profile decreases (increases) the value of l in the trapping layer for case 1 (case ), primarily via the first term in Equation (4). According to linear theory (Scorer, 1949), this will result in an increase (decrease) in wavelength for case 1 (case ), like that observed. Similar motions of wave clouds which have been observed downstream of the Colorado Rockies were also associated with lee-wave wavelength changes, attributable to changes in the terms of Equation (4) (Ralph et al., 1997). Stations F3 and L4 are close to Leeming and around 5 km apart, and so are well placed for studying the variation of the winds across the portion of the AWS array close to Leeming. Time series of the m wind speed and directionmeasuredbytheawsathazelriggandatstations F3 and L4 are shown for case 1 in Figure 7(a) and (b), and for case in Figure 8(a) and (b). During case 1, the winds at F3 and L4 differ significantly from the flow upstream at Hazelrigg, and are variable over time. In case, there are periods of even more pronounced unsteadiness and spatial variability: several periods of strongly accelerated or slack winds occur. At times, the wind is from an easterly quadrant, i.e. reversed with respect to the upstream wind direction. Such examples of reversed wind detected during the experiment tended to be small in magnitude and intermittent. Similar intermittence of flow reversal was found to occur in measurements of downstream turbulence during strong lee-wave events over East Falkland in the South Atlantic (Mobbs et al., 5). These effects can be clearly seen in Figure 9(a) and (b), which show plots of the 1 min-average m wind vectors at the AWS locations at 51 UTC on 9 February 5 (case 1) and at 1 UTC on 17 March 5 (case ), respectively. Note that the colours in Figure 9 indicate measured pressure perturbations, which will be discussed later. The winds within the area of the array around Leeming exhibit high spatial variability. Again, this is most pronounced in case, with accelerated winds in the Figure 6. High-resolution visible satellite images of cloud formations over the UK recorded by the Meteosat Second Generation (MSG) geostationary satellite at (a) 13 UTC on 9 February 5 and (b) 1 UTC on 17 March 5.

8 136 P. F. SHERIDAN ET AL. western portion of the array, and slack winds in the eastern portion. This picture is consistent with flow separation and possible rotor formation. It is possible to demonstrate the connection between the variability of the flow in case and the presence of lee waves aloft using skycam images taken during the periods of highly perturbed flow. Figure 1 shows a zoomed view of the time series of wind for one such period on 18 March 5, during which particularly clear and eventful skycam cloud images were obtained. Note that this period is not included in Figure 8, in order to focus the latter figure on a shorter period of time, for the sake of clarity. Selected skycam images recorded at the times marked by vertical lines in Figure 1 are shown in Figure 11. Dashed lines have been added to Figure 11 to indicate the clouds or cloud edges discussed in the text. Hourly cloud-base data from the SAMOS station at Leeming indicate that during the period corresponding to the skycam images shown, the cloud base lay at a height of between 36 m and 4 m. For simplicity, a rough cloud-base height of 4 m has been assumed. Figure 11 illustrates the motion of two low-level lee-wave-induced cloud bands in an upstream direction (i.e. into the image) above the camera position. The first of these is clearly visible in Figure 11(b) and subsequent images, and the second appears in Figure 11(e), and further upstream in Figure 11(f). The cloud visible in the majority of the image in Figure 11(a) is at a high level, and is distinct from the low-level bands, although one low-level band can be seen relatively far upstream, close to the horizon. The horizontal distance of a cloud s position from the camera is trigonometrically related to (a) wind speed (ms -1 ) 1 5 (b) 36 wind direction ( ) (c) p (hpa) Time (UTC, 9 Feb 5) Hazelrigg F3 L4 Figure 7. Time series of (a) wind speed, (b) wind direction, and (c) pressure perturbation, at AWS sites F3 (thin solid lines), L4 (dashed lines), and Hazelrigg (wind only, thick solid line), between UTC on 8 February 5 and UTC on 9 February 5 (case 1). The vertical dotted line indicates the time shown in Figure 9(a). the cloud-base height and the cloud s angular position within the camera s field of view. Positions have thus been calculated for the low-level clouds in Figure 11 (the uncertainty associated with this method depends on the elevation angle of the object; an analysis for the images used indicates that it is typically between 1% and 15%.). The obvious distortion in the images, which causes the horizon to appear curved, does not affect this calculation, since the central vertical portion of the field of view of the camera is used. The cloud leading (i.e. windward) edge just over halfway down the image in Figure 11(b) is found to be 1.9 km away from the camera. Clearly the wave crest is passing overhead in the period between 1 and 13 UTC. Since the cloud bands run roughly north south, this crest will also have passed over the AWS L4 (which is located 9 m due south of the camera), and Figure 1 shows that by the end of this period the wind at L4 is strongly decelerated relative to that upstream. Meanwhile, the wind at F3, which is about 3 km upstream, is accelerated. By 13 UTC, both the leading and the trailing edges of the cloud are visible (Figure 11(c)), and the leading edge is now found to be around 3 km upstream of the camera, placing the wave crest directly between F3 and L4. The wind speeds at the two AWS sites now become roughly equal to the upstream value. Subsequently, the crest s motion upstream continues, and by 14 UTC (Figure 11(d)) the wave crest has passed over F3, the leading edge of the cloud being 7 km away from the camera. In the same period, a deceleration of the flow occurs at F3, while at L4 the flow is accelerated. The second cloud passes above the camera and moves upstream over the two stations between 14 UTC (Figure 11(d)) and 15 UTC (Figure 11(f)), during which time L4 and F3 again experience decelerated winds. Figure 11(e), taken (a) wind speed (ms -1 ) 1 5 (b) 36 wind direction ( ) (c) p (hpa) Time (UTC, Mar 5) Hazelrigg Figure 8. As Figure 7, but for the period from 4 UTC on 17 March 5 to 4 UTC on 18 March 5 (case ); the vertical dotted line indicates the time shown in Figure 9(b). L4 F3

9 INFLUENCE OF LEE WAVES DOWNWIND OF THE PENNINES 1361 Figure 9. Snapshots of the 1 min-average m wind vectors measured at the AWS sites, at (a) 51 UTC on 9 February 5 (case 1), (b) 1 UTC on 17 March 5 (case ), (c) 11 UTC on 3 December 4 (case 8), and (d) 11 UTC on 3 December 4 (case 9). The Hazelrigg AWS site is shown inset. Sites where no vector is plotted either were not operating or produced bad data at the time shown. Colour contours indicate the pressure perturbations at each site in the array surrounding Leeming. Terrain contours are shown by solid lines with an interval of 5 m. in the middle of this period at 14 UTC, suggests that the cloud shape deviates temporarily from the simple banding seen in the other images. The cloud leading edge marked in the figure suggests a brief reorientation of the axis of the wave crest in a roughly northeast southwest direction over the array, and this may explain why flow deceleration occurs simultaneously at both L4 and F3 at this time (since F3 and L4 lie roughly on a northeast southwest line). Figure 11(f) shows that the crest has regained a roughly north south orientation by 15 UTC. At the same time, the behaviour of the wind at L4 and F3 returns to that which occurred before 14 UTC, with deceleration at one station and acceleration at the other. This anti-phase variation of the wind strength at the two stations suggests that they are roughly half a wavelength apart in the streamwise sense: in other words, that the wavelength is roughly 6 km. This appears to be confirmed by a resonant-mode calculation, based on Equation (3) (e.g. Vosper and Mobbs, 1996; Vosper et al., 6), using the wind and temperature profiles from a radiosonde release at 97 UTC on 18 March, which yields a single dominant trapped mode with a horizontal wavelength of 6.6 km. At around 151 UTC, the upstream motion of the crests slows to a near halt, and during the remainder of the period represented in Figure 1 no further low-level clouds pass through the camera s field of view. The waves underwent significant change over 4 h, as the synoptic conditions evolved. This is revealed by a further resonant mode calculation for data from a radiosonde release at 1536 UTC on the previous day of case, 17 March 5, which yields a wavelength twice as large as the result for 18 March. Analyses of the skycam and surface winds for several other cases reveal a similar correspondence between the surface winds and the positions of wave crests and troughs as for case. Having discussed the perturbations of the surface flow, we now turn our attention to the surface-pressure perturbations p associated with the lee waves. These are estimated by subtracting a synoptic component and a hydrostatic component from the pressure measurements

10 136 P. F. SHERIDAN ET AL. Figure 1. Time series of the 1 min-average m wind speed at AWS sites F3 (thin solid line) and L4 (dashed line) and at Hazelrigg (thick solid line), between 8 and 18 UTC on 18 March 5. Vertical lines mark the times of skycam images shown in Figure 11, with letters indicating the relevant panels of that figure. at each site. The hydrostatic component is obtained using the same method as in a previous study (Mobbs et al., 5). The synoptic component is then obtained by averaging the hydrostatically-corrected pressures of the stations involved. In order to prevent significant contamination of p by the synoptic pressure gradient, the analysis is confined to the portion of the array close to Leeming (L1 L4, F1 F4). An error analysis using typical error values for the AWS sensors reveals an overall maximum uncertainty of.3 hpa in the resulting pressure perturbation. The pressure perturbations at 51 UTC during case 1 and at 1 UTC during case are depicted in Figure 9(a) and (b), respectively, using colour contours. The colours indicate an adverse pressure gradient across the array at these times, accompanying the deceleration of the flow from west to east. The pressure perturbation in Figure 9(a) (case 1) increases by roughly.6 hpa over Figure 11. Skycam images taken at (a) 1 UTC, (b) 13 UTC, (c) 13 UTC, (d) 14 UTC, (e) 14 UTC, and (f) 15 UTC, on 18 March 5. The horizontal orientation of the skycam is 84. The image colours have been desaturated to yield a black-and-white image, and the images have been darkened slightly. The superimposed dashed lines indicate some leading and trailing edges of clouds that are discussed in the text.

11 INFLUENCE OF LEE WAVES DOWNWIND OF THE PENNINES 1363 about 5 km, while the flow decelerates through about 3ms 1 over the same distance. In case, the adverse pressure gradient is larger, and the flow deceleration across the array is more pronounced. The pressure perturbation increases by about 1 hpa over 5 km, while the flow decelerates through about 7 ms 1. Figures 7(c) and 8(c) show the time series of pressure perturbations at F3 and L4 for cases 1 and, respectively. They show that the dramatic flow perturbations occurring during case in the latter half of Figure 8(a) are accompanied by simultaneous large pressure perturbations. The pressure perturbations during case 1 are significantly smaller. Of the two downwind AWS sites shown in Figures 7 and 8, the one that measures the highest wind speed at a given time measures the lowest pressure perturbation, suggesting that the wave-induced pressure perturbations are driving the flow perturbations. It would appear that the occurrence of rotors in case is perhaps linked to the presence of waves whose amplitude is larger than those in case 1, leading to larger adverse pressure gradients at the surface. However, the additional importance of the background near-surface flow in determining whether or not rotors form has previously been highlighted (Vosper et al., 6). More precisely, flow separation will occur under the leewave crests when the normalized pressure amplitude p/ρu reaches some critical value. We have attempted to estimate this quantity from the field data. For the present study, p is simply considered to be half of the largest difference in p between any pair of AWSs within the array at a given time, based on 1 min averages. The ideal-gas law is used to determine ρ from the 1 minaverage pressure and temperature at each station. Finally, values of u are obtained as 1 min averages from the turbulent-shear-stress measurements (approximated in terms of the vertical flux of horizontal momentum) at m at the upwind site, Hazelrigg. It is necessary to use an upwind measurement of u, since measurements within the Vale of York are highly disturbed during rotor events and not representative of the background flow. Time series of p/ρu have been plotted for cases 1 and in Figure 1(a) and (b) respectively. A dashed line at a nominal value of p/ρu = 6 has been added as a guide to the eye. In case 1, p/ρu seldom exceeds 4. Larger values occur during case, reaching 6 or higher, particularly during the period between 8 and 1 UTC and after 16 UTC when the wind time series contain large accelerations and flow reversals. Large values of p/ρu occur between 1 and 13 UTC, but are not accompanied by strong wind perturbations. A warm front passes through the area in this time interval, and it is possible that the pressure gradients involved are associated with phenomena other than lee waves, such as convective cells. Overall, the magnitude of p/ρu seems to distinguish between the two cases, suggesting that this normalized pressure-perturbation amplitude, in the absence of other mesoscale influences, has a controlling influence on rotor formation. Since the east west extent of the measurement array is around 7 km, while the lee-wave wavelength calculated both for case 1 and for the first day of case is roughly twice this, the value of p based on the measurements is likely to significantly underestimate the true pressure amplitude. Indeed, it is notable that the values in Figure 1 are somewhat smaller than the typical critical normalized pressure amplitudes found in idealised simulations (Vosper et al., 6). Since the lee-wave wavelengths occurring in cases 1 and are fairly typical, this sampling issue is likely to affect most lee-wave cases. Cases 1 and provide a useful illustration of the factors potentially involved in the formation of rotors. These may be summarized as follows: The decrease of l with height over the lowest 4 km of the troposphere. This is sharper during case than during case 1 (as revealed by a close inspection of Figure 5(d) and (h)), and should result in more efficient wave-trapping. The wind close to the mountain-top level. At 7 m, the wind is stronger in case (5 ms 1 at the start of the event, compared to 18 ms 1 in case 1). According to linear theory, the lee-wave amplitude is proportional to the flow speed over the mountain. Wind shear and variation of stability with height. While the Scorer-parameter profile defines the vertical structure of the waves, and the mountain-top wind then dictates the waves vertical-velocity amplitude, the near-surface pressure and wind fields are expected to be influenced by the precise variation of wind and stability with height. For instance, roughly-uniform wind speed within the troposphere is accompanied by concentrated low-level atmospheric stability in case ; and conversely, strong tropospheric wind shear and (a) p/ρu * p/ρu * 1 5 (b) Time (UTC, 9 Feb 5) Time (UTC, Mar 5) Figure 1. Time series of p/ρu based on 1 min-average data for the AWS stations L1 L4 and F1 F4, for the periods: (a) UTC on 8 February 5 to UTC on 9 February 5; (b) 4 UTC on 17 March 5 to 4 UTC on 18 March 5. A dashed line marking p/ρu = 6 has been added as a guide to the eye. Periods for which no data are plotted correspond to times when one or more of the measured quantities required to calculate p/ρu were not available.

12 1364 P. F. SHERIDAN ET AL. relatively uniform stratification occur in case 1. These factors may also influence the background flow in the boundary layer, which plays a crucial role in rotor formation. A larger magnitude of p/ρu occurs during case, presumably because of the above three factors. 4.. Flow response to the lee-wave pressure amplitude In the interests of a more thorough investigation of the correspondence between the magnitude of the normalized lee-wave pressure amplitude and the occurrence of flow separation, twelve prominent lee-wave cases containing large downstream wind and pressure perturbations will be examined. The characteristics of these twelve cases are summarized in Table I. Case is included, but has been split into two cases, a and b, since some characteristics on 18 March are rather different from those on 17 March. The remaining cases are numbered 3 1. The lee-wave wavelength has been calculated using data from the appropriate radiosonde releases, as for 18 March 5 earlier. Cases a and 4 correspond to IOPs, and one representative radiosonde release has been selected from each date. On some days, the daily Hazelrigg radiosonde release was not performed, and therefore radiosonde releases from Castor Bay in Northern Ireland (54.5 N, 6.43 W) have been substituted in some cases. We adopt two measures to indicate the degree to which the near-surface flow is perturbed during each case. The first, s ref, measures the degree of acceleration or deceleration of the downstream flow relative to the flow upstream: s ref = u u ref, (5) u ref where u ref is the 1 min-average AWS wind speed (measured at m) at Hazelrigg and u is the component of the 1 min-average wind at a downstream AWS, resolved in the direction of the wind at Hazelrigg. When the maximum value of s ref exceeds unity, the streamwise perturbation of the wind speed at one or more of the AWS locations is larger in magnitude than the upstream wind speed. Thus the flow perturbations are sufficient to reverse the flow, as would happen in a rotor. The second measure, s dif, indicates the degree of wind variation that occurs within the downstream array: s dif = u max u min u ref, (6) where u max and u min are the maximum and minimum components (resolved in the direction of the wind at Hazelrigg) of the 1 min-average winds measured at m. Values of s dif have been calculated for the duration of the experiment using stations L1, L, L4, and F1 F4. During times when a rotor is present, we might expect the value of s dif measured by the array to exceed unity. As the cases in Table I indicate, however, the lee-wave wavelength is frequently greater than the east west extent of the measurement array around Leeming (roughly 7 km), and s dif in most cases will not capture the full extent of flow acceleration and deceleration beneath the lee wave. As stated earlier, the same issue affects the measurement of p, causing it to underestimate the true pressure amplitude. However, because both quantities sample the variation over the same part of the wave cycle, the behaviour of s dif as a function of p/ρu still gives a valid insight into the response of the flow to the lee-wave-induced pressure perturbations. The variation of the maximum s ref with p/ρu is likely to be less informative, since s ref is affected by this sampling issue in a different way. The variation of s dif as a function of p/ρu for cases a, 3, 6, 8, 9, 1, 11 and b is shown in Figure 13. Data have been plotted either for a 4 h period covering Table I. Date/time and flow characteristics of twelve cases of westerly flow giving rise to strong lee waves during the period of the experiment. The lee-wave wavelength is based on a resonant-mode calculation involving Equation (3) applied to the radiosonde data, as described in the text. Cases where operational radiosonde releases from Castor Bay have been used are marked **. The correlation coefficient R is obtained from a linear fit (where performed) of s dif versus p/ρu Angle brackets indicate a time average at Hazelrigg over the indicated duration. Case Start Duration Radiosonde release Wavelength u ref u p max R (UTC, dd/mm/yy) (h:min) time (UTC) (km) (ms 1 ) (ms 1 ) (Pa) a 1536, 17/3/5 8: b, 18/3/5 14: , 15/11/4 14: , 17/11/4 1: , /11/4 : , 6/1/4 18: , /1/4 4: , 3/1/4 4: , 3/1/4 4: , 3/1/5 14: , 8/1/5 14: , 19/1/5 4:

13 INFLUENCE OF LEE WAVES DOWNWIND OF THE PENNINES 1365 each case or for a shorter period in which large perturbations of the near-surface wind and pressure occur. Positive correlations occur for all the cases, and correlation coefficients resulting from linear fits of the data in each panel are quoted in the final column of Table I. The high degree of scatter in the data appears to be associated with typical background noise in both quantities, and this scatter is one of the reasons for confining the analysis to cases in which a strong near-surface disturbance occurs. The data fits in panels (a), (b), (c), (f) and (g) have similar gradients, between.366 and.59. This is reminiscent of the behaviour found in idealised numerical simulations (Vosper et al., 6), where data from a range of simulations show a high degree of collapse when plotted on axes of s versus p/ρu. It is also noteworthy that the values of p/ρu at which s dif approaches 1 are similar to the critical normalized pressure-perturbation amplitudes for rotor formation found by Vosper et al. Thelowergradient evident in panel (h) (case b) is probably an effect of a relatively high degree of scatter resulting from small magnitudes of u and u ref. Case 8 (panel (d)) and case 9 (panel (e)) also appear slightly different from the other cases, with relatively low correlation coefficients and fit gradients. This is because of a period within both cases when p/ρu is large but s dif remains relatively small. Note, however, that the pressure- and wind-perturbation fields are still highly correlated spatially during such periods, as demonstrated by snapshots of the 1 min-average m wind vectors and pressure perturbations shown in Figure 9(c) and (d). It seems plausible that these periods are examples of a nonlinear response of the wind when the pressure gradient becomes large, or when the critical normalized pressure-perturbation amplitude for flow reversal is reached. The wind and pressure data for the remaining four cases in Table I are not plotted in Figure 13 because, although large values of s dif and p/ρu are observed during these cases, these do not occur simultaneously. The reasons for this behaviour are not clear. Note that, as expected given the close relationship between the low-level wind and u, replacing u in the normalizedpressure expression by the m wind speed at Hazelrigg gives similar (but rescaled) results for the cases plotted in Figure The Scorer-parameter profile We now return to the influence of the Scorer-parameter profile on the formation of rotors. In order to quantify differences between Scorer-parameter profiles, a bulkaverage Scorer-parameter value l 1 for the lowest 3 km of each radiosonde ascent has been calculated. This is based on the potential temperature at the top and bottom of the layer, and the mean wind vector. Similarly, a value l is defined as the lowest bulk value that occurs for any 3 km-deep layer above the first layer. It is expected that when l is significantly lower than l 1, some waves that can propagate vertically within the first layer are unable to propagate in the second layer, and are thus trapped. For instance, the cases in Table I all satisfy l 1 /l >. The investigation is restricted to a subset of westerly lee-wave cases, defined according to several objective criteria applying to the radiosonde profile and the AWS data within an 8 h period centred on the radiosonde release. These criteria are: 1. westerly flow, defined by an upstream m wind direction between and 3 ;. average upstream m wind speed for the 8 h period exceeding 4 ms 1 ; 3. l 1 /l >. (a) (b) (c) (d) 1 s dif.5 1 (e) (f) (g) (h) s dif p/ρu * p/ρu * p/ρu * p/ρu * Figure 13. The variation of s dif as a function of p/ρu, based on 1 min-average m wind data at AWS locations L1, L, L4, and F1 F4, for a selection of the lee-wave periods detailed in Table I: cases (a) a, (b) 3, (c) 6, (d) 8, (e) 9, (f) 1, (g) 11, and (h) b. Straight lines indicate linear fits to the data, for which the correlation coefficient is quoted in Table I.

14 1366 P. F. SHERIDAN ET AL. Criterion 3 ensures that the atmospheric profile accommodates the formation of lee waves, while criterion ensures that only cases of significant wind strength are considered (and to some extent constrains the wave amplitude). The subset comprises 45 cases. Values of s ref have been calculated for the eleven AWS stations in the Vale of York using the 1 min-average m wind data for the duration of the experiment. Cases of rotor activity are identified by occasions when the maximum s ref exceeds unity within the 8 h period centred on the radiosonde release. A period as long as 8 h is not ideal for this purpose, since the variation of the synoptic flow in this time could be significant. However, because of the relative infrequency (once per day) of routine radiosonde releases, this period gives the best compromise between coverage of episodes of rotor turbulence and retention of mutual relevance of the near-surface and upper-air measurements. Of the 45 lee-wave cases in the subset, there were 16 during which s ref exceeded unity. An inspection of the Scorer-parameter profiles suggests that the rate of decrease of l within the lowest 4 km influences the magnitude of s ref. In order to capture this rate of decrease, two more average Scorer-parameter values are calculated for each of the 45 radiosonde ascents: l a for the lowest km of the atmosphere, and l b for the layer between km and 4 km. These represent the mean of the Scorer-parameter profile in the respective layers. The ratio l a /l b is found to be above 1.1 for all 16 cases where s ref > 1. The majority (6%) of the remaining cases are found to have l a /l b < 1.1. This result demonstrates the importance of a rapid decrease with height of the Scorer parameter, which presumably results in more efficient wave-trapping, increasing the likelihood of rotor formation. Clearly other factors must also play a role in determining whether or not rotors will form. These will be examined in the following section. 5. Numerical simulations The numerical simulations described in Section 3 result in trapped lee-wave flows similar to that depicted in (a) a previous numerical study (Vosper et al., 6, figure 4). In some of the simulations, rotors form beneath the lee-wave crests, while in others they do not, despite all simulations being initialized with conditions corresponding to the same Scorer-parameter profile. The purpose of this section is primarily to understand how factors other than the upstream Scorer-parameter profile affect the formation of rotors. We will establish the influence of the upstream profiles of wind and potential temperature on the lee-wave amplitude and on the background near-surface flow, both of which are important variables in rotor development. It is useful to examine the relationship between the fractional deceleration beneath a wave crest and p/ρu, in order to check whether the correlation between these quantities found previously (Vosper et al., 6) also holds for the simulations in this study. The fractional deceleration is defined by Vosper et al. as s = U min U λ U λ, (7) where U min is the minimum wind speed beneath a wave crest, and U λ is the wind speed averaged over a wave cycle. The variation of s as a function of p/ρu has been plotted in Figure 14(a) for the simulations described in Section 3. For simulations where U is below 5 ms 1, the wave structure is observed to change considerably with decreasing U ; since we are trying to isolate the effects of factors other than the wave structure, these simulations have been excluded from the plot. As demonstrated by Vosper et al. for a fixed model roughness length and upstream profile, s decreases with increasing p/ρu until a critical value is reached at which s = 1 and rotors begin to form. Furthermore, the critical values of p/ρu are similar to those found by Vosper et al. Therefore the original result appears to be robust with respect to variations of the upstream profile that do not significantly alter the Scorer-parameter profile. It is worthwhile to examine why some upstream profiles of wind and stratification lead to rotor formation while others do not. For example, any one of the (b) s u = 5 ms -1 u = 6.5 ms -1 u = 8.5 ms -1 u = 1 ms -1 u = 15 ms -1 s U t /u = U t /u = 1 U t /u = U t /u = 3 U t /u = 4 U t /u = 5.6 U t /u = 6.5 U t /u = 9 U t /u = p/ρu * Φ/ρu * Figure 14. Variation of s with (a) p/ρu and (b) /ρu, for the idealized D numerical simulations. Symbols indicate different values of U in panel (a), and values of U t /U in panel (b) (see legends).