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

Transcription

1 Q. J. R. Meteorol. Soc. (26), 1, pp Influence of lee waves on the near-surface flow downwind of the Pennines By P. F. SHERIDAN 1, V. HORLACHER 1, G. G. ROONEY 1, P. HIGNETT 1, S. D. MOBBS 2 and S. B. VOSPER 1 1. Met Office, UK 2. University of Leeds, UK Submitted 7 December 26, revised and resubmitted 24 April 27 SUMMARY 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 was the improvement of wind forecasts downstream of orography. Trapped lee waves commonly occur in westerly flow in this region and there were numerous occasions of apparent flow separation indicating the formation of lee-wave rotors during the experiment. The spatial variability of the near-surface flow in these circumstances was 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 normalised pressure perturbation amplitude. For a group of lee-wave cases during which the cross-mountain flow is strong, a rapid decrease of the Scorer parameter within the lower portion of the troposphere appears to be a pre-requisite for rotors to form. However, this does not guarantee their occurrence. For a fixed Scorer parameter profile, idealised two-dimensional simulations indicate that the lee wave induced 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 are required for rotors to develop. KEYWORDS: Flow separation Automatic weather station Microbarograph Orography 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 25), two classifications of rotors have emerged; type I rotors, which form beneath the crests of a lee wave train, and type II rotors, the continuously stratified analogue of a hydraulic jump. Both types of flow are potentially associated with severe turbulence and pose a difficult challenge to weather forecasting. This study concerns type I rotors. The formation of rotors under a variety of conditions has been investigated by several authors using idealised two-dimensional (2-D) simulations, such as Doyle and Durran (22), Vosper (24), and Vosper et al. (26). These authors note the importance of surface friction in allowing rotors to form. The most recent of these studies by Vosper et al. focused on type I rotors, and showed how as the wave amplitude increases, rotors form when a critical value of the normalised pressure perturbation amplitude, p/ρu 2, 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 normalisation 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. Though many pioneering measurements of rotor flows were made around the mid 2th century (e.g. Kuettner 1939, in the Alps, Holmboe and Klieforth 1957, in the Sierra Nevada, Manley 1945, in the UK), a number of field experiments during the past decade provide new insights into the rotor phenomenon. Notable examples include studies by Corresponding address: Met Office, FitzRoy Road, Exeter EX1 3PB, UK. peter.sheridan@metoffice.gov.uk c Royal Meteorological Society, 26. The Met Office contribution is Crown copyright. 1

2 2 P. F. SHERIDAN ET AL. Ralph et al. (1997) and Darby and Poulos (26) who mapped the flow structure of rotors downstream of the Colorado Rockies using LIDAR, 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 26 (Grubisic and Kuettner 24). In a recent field campaign carried out in the Falkland Islands, South Atlantic (Mobbs et al. 25), 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 24). However, such an inversion 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. Note that the way trapped waves of this kind interact with the nearsurface flow has recently been the focus of several studies (e.g. Smith et al. 26, Jiang et al. 26, Vosper et al. 26). This study describes the results of a field experiment aimed at measuring the nearsurface flow over the Pennines in northern England during periods of strong lee-wave activity. Idealised 2-D simulations have also been performed in support of the field analysis, since they offer the ability to isolate the different factors involved in rotor formation. A description of the experiment is provided in section 2. Section 3 describes the method used for the idealised simulations. In section 4, case studies from the field experiment are used to demonstrate the typical upstream conditions required for large amplitude waves and explore the link between rotor formation and the lee-wave induced pressure field. Subsequently in section 5, the results of the idealised simulations are discussed. In section 6, the implications of the simulation results for forecasting are examined. Final conclusions are presented in section 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 October 23 April 25. Observations focused on the Vale of York, which lies 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 (NWP) models. Historically, aircraft reports of severe turbulence in the region in conjunction with lee-waves are 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 ( 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 the Facility for Airborne Atmospheric Measurement (FAAM) BAe 146 aircraft also formed part of the campaign, though these data 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 south-east of the image. The positions of thirteen 2 m automatic weather stations (AWSs) and four 2 m turbulence masts are marked by

3 INFLUENCE OF LEE WAVES ON THE NEAR-SURFACE FLOW DOWNWIND OF THE PENNINES 3 filled circles and white crosses, respectively. A cluster of AWSs were placed close to Leeming air base (depicted in panel (a) of Fig. 1), with one (SH) located to the east of Leeming, while three stations were sited at other airfields named Topcliffe, Dishforth and Linton-on-Ouse (panel (b) of Fig. 1). Finally, one AWS was located at Hazelrigg, to the west of the Pennines near Lancaster (labelled Lan ). The four turbulence masts were collocated with four of the AWS sites, at Hazelrigg, Leeming, Dishfoth and Linton. Only the data from the Hazelrigg mast is 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, for most part, to the lee waves themselves, rather than due to local variations in the topography. Figure 1. The orography of the Pennines with locations of all automatic weather stations marked as filled circles. Four 2 m turbulence masts are indicated by white crosses. Insets (a) and (b) show zoomed images of areas marked by rectangles within the main panel. Terrain heights are contoured, with an interval of 1 m. See text for further details. The AWS instruments measured the 2 m wind speed and direction, and the surface pressure with a practical accuracy of.5 hpa, in addition to the temperature and relative humidity. The full details of the AWS sensors are contained in Mobbs et al. (25) and

4 4 P. F. SHERIDAN ET AL. references therein. A local effect (possibly sheltering) at station L3 appears to result in wind data which represent the larger scale flow poorly, and therefore the wind data from L3 have not been used in this study. On each of the turbulence masts, two Gill- Solent horizontally symmetric (HS) ultrasonic anemometers allowed the measurement of all three velocity components. The skycam consisted of an Axis 212 Network Camera with a Pentax mm f1.4 auto-iris lens, whose centre-of-view was oriented towards 284 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, though 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 (2.78 W, 54.1 N), starting in November 23. The launch time was chosen for the convenience for those participating. These were supplemented with more frequent releases, both upwind and downwind of the Pennines during intensive observation periods (IOPs). IOPs were carried out when forecast conditions were conducive to strong lee-wave formation, such as 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 east of the Pennines from either Leeming airfield or Dallow Moor (marked DM in Fig 1). Only the upstream radiosonde data are discussed in this study. Hourly SYNOP cloud base data have also been used. These data originate from a laser cloud base recorder which was part of a permanent Semi-Automatic Meteorological Observing System (SAMOS) station at Leeming. 3. NUMERICAL SIMULATION METHOD (a) Model description A series of numerical simulations of lee waves have been performed in support of the field work. These allow us to examine various factors which may influence the formation of rotors in a controlled, systematic manner. 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, 23; Vosper, 24). The model configuration used is identical to that used by Vosper et al. (26), except that a domain of 512 km length, instead of 124 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 setup is given by Vosper et al. (26) from which some important details are repeated below, followed by a description of the upstream profiles used. The model as used in this study employs the shallow Boussinesq approximation. At the lower boundary, a no-slip 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(x) = H/(1 + x 2 /L 2 ), (1) where the mountain height, H, is 3 m and the mountain half-width, L, is 2 km. (b) Upstream profiles The simulations involve idealized flow whose basic-state consists of a sinusoidal westerly jet described by, U(z) = U +U t sin(πz/z m ), (2)

5 INFLUENCE OF LEE WAVES ON THE NEAR-SURFACE FLOW DOWNWIND OF THE PENNINES 5 where U is the surface wind speed, and the maximum wind speed, U MAX = U +U t, occurs at a height z m /2. A value of 2 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 Fig. 2. According to linear theory, the vertical structure of a wave mode is determined by the equation, d 2 ŵ dz 2 + ( l 2 k 2) ŵ =, (3) where ŵ(k,z) is the Fourier transform of the vertical velocity and k is the horizontal wavenumber. The degree to which waves are trapped is determined by the Scorer parameter, l 2 (z) (Scorer 1949), which for the shallow-convection form of the Boussinesq equations is given by, l 2 (z) = N2 U 2 1 d 2 U U dz, (4) 2 where N is the Brunt-Väisälä frequency. In general a decrease with height of l 2 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 changes in 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, and then the profile of N (and hence potential temperature, θ) can be computed by inverting Eq. (4) for each model level. The profile of l 2 chosen is shown in Fig. 3. When U = 5 ms 1 and U t = 28 ms 1 this l 2 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 are shown in Fig. 2(a) and 2(b). Figure 2(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 (1-D) solution was first obtained using a 1-D version of the model which was run to a steady state in order to provide an initialisation for the 2-D configuration. This resulted 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 Fig. 2(c). Despite the effort to keep the profile of l 2 fixed, some variation occurred at low levels due to differences in the boundary layer, depending on the initial wind and temperature profiles. For larger values of U, a deeper boundary layer formed and the lee-wave wavelength was found to be shorter. Wavelengths ranged overall between 9.5 km and 11.5 km. Meanwhile, the variation with height of the vertical velocity amplitude (normalised by its maximum value) was found not to change significantly upon increasing U, despite the change in wavelength. The 2-D simulations were all run until a steady solution was obtained. 4. OBSERVATIONAL RESULTS In this section we examine the field measurements as follows. Initially, case studies are discussed at length in order to demonstrate the typical flow behaviour in lee wave and rotor events. Subsequently, 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.

6 6 P. F. SHERIDAN ET AL θ (K) (a) (b) (c).6 z (km) 1 z (km) 5 z (km) U (ms -1 ) θ (K) U (ms -1 ) Figure 2. The 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 (dashed), U = 6.5 ms 1 and U t = 36.4 ms 1 (solid), U = 4 ms 1 and U t = 36 ms 1 (dot-dashed). (c) The wind and potential temperature profile in the U = 5 ms 1, U t = 28 ms 1 simulation 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). Also, only the lowest portion of the profile is shown in (c) as above the boundary layer the profile is unmodified. 1 8 z (km) l 2 (km -2 ) Figure 3. Scorer parameter profile for the lowest 1 km of the domain corresponding to Eq. (4) (solid line with filled circles) with U = 5 ms 1, U t = 28 ms 1, and with N=.1 s 1 throughout the depth of the domain. The Scorer parameter profile computed using wind and temperature data from a radiosonde ascent from Hazelrigg at 11:49 UTC on 17 March 25 (case 2) is shown (dashed) for comparison. (a) Examples of lee wave and rotor activity Here we focus on two cases: 9 February 25 and March 25, which will be referred to as case 1 and case 2 respectively. IOPs occurred during both of these periods. Cases 1 and 2 were chosen because strong, ostensibly similar lee waves were observed in both cases. However, rotors appeared to occur only in case 2, with no rotor activity detected in case 1. The synoptic conditions occurring over the UK during cases 1 and 2 are shown in Figs. 4(a) and 4(b), respectively. Both cases correspond to warm sector westerly flows. The warm sector generally contains stable air, and these are the

7 INFLUENCE OF LEE WAVES ON THE NEAR-SURFACE FLOW DOWNWIND OF THE PENNINES 7 typical conditions for strong lee waves. Profiles of wind and potential temperature taken (a) (b) Figure 4. Synoptic analysis charts showing the mean sea level pressure (hpa) and the positions of surface fronts for (a) 12: UTC on 9 February 25 and (b) 18: UTC on 17 March 25. from upstream radiosonde ascents during case 1 and case 2 are shown in Figs. 5(a)-(c) and 5(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 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 Fig. 5(e) for case 2 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 25 ms 1 to 16 ms 1 for the two sondes shown. The potential temperature (panels (c) and (g)) profiles confirm that there were stable conditions on both days. There is a degree of negative curvature in θ for both cases, particularly in case 2, 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 which was present to the south. Scorer parameter profiles have been calculated from the radiosonde data for cases 1 and 2 using Eq. (4) and are shown in Figs. 5(d) and 5(h) respectively. In order to compute the Scorer parameter, the winds have been resolved in the direction of the average wind vector below 2 km. Due to the high sensitivity of l 2 (z) to noise in the profile, smoothing was applied to the wind and θ profiles, and to the resulting profiles of N 2 and d 2 U/dz 2, before calculating l 2 (z). Note that care was taken not to remove features of particular relevance to the wave structure through smoothing. For instance, the largest filter scale corresponded to roughly 1 m in the vertical, so that features comparable to the mountain wave vertical wavelength (which is much larger than 1 m) were not strongly affected. In both case 1 and case 2, 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 2 the curvature of the θ profile makes the stronger contribution. Visible satellite images recorded during case 1 and case 2 are shown in Figs. 6(a) and 6(b), respectively, and contain clear evidence of lee waves in the form of crossflow banding of cloud over the Pennines and the Vale of York. Images were available

8 8 P. F. SHERIDAN ET AL. case 1 case 2 Figure 5. Vertical profiles of (a) wind speed, (b) wind direction, (c) potential temperature and (d) Scorer parameter, measured by radiosondes released at 1:1 UTC (solid) and 17:27 UTC (dashed) on 9 February 25 (case 1) from Hazelrigg. Panels (e) (h) show the equivalent profiles for 17 March 25 (case 2) at 1:8 UTC (solid) and 16:41 UTC (dashed). at intervals of 15 minutes 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, whilst in case 2 the bands move to the west over time. This coincides with an increase (decrease) in wavelength over time in case 1 (case 2). The evolution with time of the wind profile decreases (increases) the value of l 2 in the trapping layer for case 1 (case 2), primarily via the first term in Eq. 4. According to linear theory (Scorer 1949), this will result in an increase (decrease) in wavelength for case 1 (case 2), like that observed. Ralph et al. (1997) noted similar motions of wave clouds associated with lee-wave wavelength changes downstream of the Colorado Rockies, and these were attributable to changes in the terms of Eq. 4. Stations F3 and L4 are close to Leeming and around 5 km apart, and as such are good candidates for studying the variation of the winds across the portion of the AWS array close to Leeming. Timeseries of the 2 m wind speed and direction measured by the AWS at Hazelrigg and at stations F3 and L4 are shown for case 1 in Fig. 7(a) and 7(b), and for case 2 in Fig. 8(a) and 8(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 2, there are periods of even more pronounced unsteadiness and spatial variability; a number of periods of strongly accelerated or slack winds occur. At times the wind direction 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, South Atlantic (Mobbs et al. 25). These effects can be clearly seen in Figs. 9(a) and 9(b), which show plots of the 1 minute average 2 m wind vectors

9 INFLUENCE OF LEE WAVES ON THE NEAR-SURFACE FLOW DOWNWIND OF THE PENNINES 9 (a) (b) 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: on 9 February 25 and (b) 1: on 17 March 25. at the AWS locations at 51 UTC on 9 February 25 (case 1) and at 21 UTC on 17 March 25 (case 2), respectively. The winds within the area of the array around Leeming display high spatial variability. Again, this is most pronounced in case 2, with accelerated winds in the west portion of the array, and slack winds in the east portion of the array. 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 2 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 timeseries of wind for one such period on 18 March 25 during which particularly clear and eventful skycam cloud images were obtained. Note this period is not included in Fig. 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 Fig. 1 are shown in Figs. 11(a)-(f). Dashed lines have been added to Fig. 11 to indicate each cloud or cloud edge 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 between 36 m and 42 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 Fig. 11(b) and subsequent images, and the second appears in Fig. 11(e), and further upstream in Fig. 11(f). The cloud visible in the majority of the image in Fig. 11(a) is at a high level and is distinct from the low-level bands, though one low-level band can be seen relatively far upstream, close to the horizon. The The colours in Fig. 9 depict measured pressure perturbations, which will be discussed later.

10 1 P. F. SHERIDAN ET AL. wind speed (ms -1 ) wind direction (º) (a) (b) (c) Hazelrigg F3 L4 p (hpa) Time (UTC, 9 Feb 25) Figure 7. Timeseries of (a) the wind speed, (b) wind direction and (c) the pressure perturbation at AWS sites F3 (solid), L4 (dashed), and at Hazelrigg (wind only, solid bold) between 22: UTC on 8 February 25 and 22: UTC on 9 February 25 (case 1). The vertical dotted line indicates the time shown in Fig. 9(a). horizontal distance of a cloud s position from the camera is trigonometrically related to the cloud base height and the cloud s angular position within the camera field-of-view. Positions have thus been calculated for the low-level clouds in Fig. 11. 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 was used. The cloud leading (i.e. windward) edge just over halfway down the image in Fig.11(b) is found to be 1.9 km away from the camera. Clearly the wave crest is passing overhead in the period between 12: and 12:3 UTC. Since the cloud bands run roughly northsouth, this crest will also have passed over the AWS L4 (which is located 9 m directly south of the camera), and Fig. 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 trailing edges of the cloud are visible (Fig. 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 (Fig. 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: (Fig. 11(d)) and 15: UTC (Fig. 11(f)), during which time L4 and F3 again experience decelerated winds. Figure 11(e), taken in the middle of this period at 14:2 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 re-orientation of the axis of the wave crest in a roughly The uncertainty associated with this method depends on the elevation angle of the object, but an analysis for the images used indicated that this is typically between 1% and 15%

11 INFLUENCE OF LEE WAVES ON THE NEAR-SURFACE FLOW DOWNWIND OF THE PENNINES 11 wind speed (ms -1 ) wind direction ( ) p (hpa) (a) (b) (c) Hazelrigg L4 F Time (UTC, Mar 25) Figure 8. As Fig. 7, but for the period 4: UTC, 17 March 25 to 4: UTC, 18 March 25 (case 2). The vertical dotted line indicates the time shown in Fig. 9(b). NE-SW direction over the array, and this may explain why flow deceleration occurs simultaneously at both L4 and F3 at this time (since the locations of F3 and L4 are on a roughly NE-SW line). Figure 11(f) shows that the crest has resumed a roughly N-S 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 antiphase 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 Eq. (3) (e.g. Vosper and Mobbs 1996, Vosper et al. 26) using the wind and temperature profiles from a radiosonde release at 9:27 UTC on 18 March, which yields a single dominant trapped mode with a horizontal wavelength of 6.6 km. At around 15:1 UTC, the upstream motion of the crests slows to a near halt, and during the remainder of the period depicted in Fig. 1 no further low-level clouds pass through the camera field-of-view. A similar analysis of the skycam and surface winds for several other cases was possible, and revealed similar correspondence between the surface winds and the positions of wave crests and troughs. Having discussed the perturbations of the surface flow, we now turn our attention to the surface pressure perturbations associated with the lee waves. The perturbations, p, to the surface pressure were estimated by subtracting a synoptic component and a hydrostatic component from the pressure measurements at each site. The hydrostatic component was obtained using the same method as Mobbs et al. (25). Subsequently the synoptic component was obtained by averaging the hydrostatically corrected pressures of the stations involved. In order to prevent significant contamination of p by the Note that a similar calculation for data from a radiosonde release at 15:36 UTC on the previous day of case 2, 17 March 25, yields a wavelength twice as large. The waves clearly underwent significant change over 24 hours, as the synoptic conditions evolved.

12 12 P. F. SHERIDAN ET AL. (a) (b) (c) (d) Figure 9. Snapshots of the 1 minute average 2 m wind vectors measured at the AWS sites at (a) 51 UTC on 9 February 25 (case 1), (b) 21 UTC on 17 March 25 (case 2), (c) 121 UTC on 23 December 24 (case 8) and (d) 112 UTC on 3 December 24 (case 9). The Hazelrigg AWS site is shown inset. Sites where no vector is plotted were not operating or produced bad data at the time shown. Colour contours indicate the pressure perturbations (units hpa) at each site in the array surrounding Leeming. Terrain contours are depicted by solid lines with an interval of 5 m. synoptic pressure gradient, the analysis was 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 revealed an overall maximum uncertainty of.23 hpa in the resulting pressure perturbation. The pressure perturbations at 5:1 UTC during case 1 and at 2:1 UTC during case 2 are depicted in Figs. 9(a) and 9(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 Fig. 9(a) (case 1) increases by roughly.6 hpa over about 5 km, while the flow decelerates through around 3 ms 1 over the same distance. In case 2, the adverse pressure gradient is larger, and the flow deceleration across the array is more pronounced. The

13 INFLUENCE OF LEE WAVES ON THE NEAR-SURFACE FLOW DOWNWIND OF THE PENNINES 13 Figure 1. Timeseries of the 1 minute average 2 m windspeed at AWS sites F3 (solid), L4 (dashed) and at Hazelrigg (bold) between 8: UTC and 18: UTC on 18 March 25. Vertical lines mark the times of skycam images shown in Fig. 11(a)-(f), with letters denoting the relevant panel of the latter figure. pressure perturbation increases by close to 1 hpa over 5 km, while the flow decelerates through about 7 ms 1. Figures 7(c) and 8(c) show the timeseries of pressure perturbations at F3 and L4 for cases 1 and 2, respectively. These show that the dramatic flow perturbations occurring during case 2 in the latter half of Fig. 8(a) are accompanied by simultaneous large pressure perturbations. Meanwhile, the pressure perturbations during case 1 are significantly smaller. Of the two downwind AWS sites shown in Figs. 7 and 8, the one which measures the largest wind speed at a given time also 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 2 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. Note, however, that Vosper et al. (26) highlight also the additional importance of the background near-surface flow in determining whether or not rotors form. More precisely, flow separation will occur under the lee wave crests when the normalised pressure amplitude, p/ρu 2, reaches some critical value. We have attempted to estimate this quantity from the field data. For the present study, p is simply considered as half of the largest difference in p between any pair of AWSs within the array at a given time, based on 1 minute averages. The ideal gas law was used to determine ρ from the 1 minute average pressure and temperature at each station. Finally, values of u were obtained as 1 minute averages from the turbulent shear stress measurements (approximated in terms of the vertical flux of horizontal momentum) at 2 m at the upwind site, Hazelrigg. It was necessary to use an upwind measurement of u since measurements within the Vale of York were highly disturbed during rotor events and not representative of the background flow. Timeseries of p/ρu 2 have been plotted for case 1 and case 2 in Fig. 12(a) and 12(b) respectively. A dashed line at a nominal value of p/ρu 2 = 6 has been added as a guide to the eye. In case 1, p/ρu 2 seldom exceeds 4. Meanwhile, larger values occur during case 2, approaching 6 or higher, particularly during the period between 8: UTC and 1: UTC and after 16: UTC when the wind timeseries contain large accelerations and

14 14 P. F. SHERIDAN ET AL. Figure 11. Skycam images taken at (a) 12: UTC, (b) 12:3 UTC, (c) 13: UTC, (d) 14: UTC, (e) 14:2 UTC, and (f) 15: UTC on 18 March 25. The horizontal orientation of the skycam is 284. The image colours have been desaturated to provide a black and white image, and the images have been darkened slightly. In addition, dashed lines have been added to mark out some leading and trailing edges of clouds which are discussed in the text. flow reversals. Large values of p/ρu 2 occur between 1: and 13: UTC, but are not accompanied by strong wind perturbations. A warm front passed through the area in this time interval, and it is possible that the pressure gradients involved were associated with phenomena other than lee waves, such as convective cells. Overall, the magnitude of p/ρu 2 seems to distinguish the two cases, suggesting that this normalised pressure perturbation amplitude, in the absence of other mesoscale influences, has a controlling influence on rotor formation. It should be stated that, 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 2 was roughly double 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 Fig. 12 are somewhat smaller than the typical critical normalised pressure

15 INFLUENCE OF LEE WAVES ON THE NEAR-SURFACE FLOW DOWNWIND OF THE PENNINES 15 p/ρu * (a) Time (UTC, 9 Feb 25) p/ρu * (b) Time (UTC, Mar 25) Figure 12. Timeseries of p/ρu 2 based on 1 minute average data for the AWS stations L1 L4 and F1 F4 for (a) the period 22: UTC on 8 February 25 to 22: UTC on 9 February 25 and (b) 4: UTC on 17 March 25 to 4: UTC on 18 March 25. A line marking p/ρu 2 = 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 2 were not availaible. amplitudes found by Vosper et al. (26). Since lee-wave wavelengths occurring in cases 1 and 2 are fairly typical, this sampling issue is likely to affect most lee wave cases. Cases 1 and 2 provide a useful illustration of the factors potentially implicated in the formation of rotors which may be summarised as follows: (i) The decrease of l 2 with height over the lowest 4 km of the troposphere. This is sharper during case 2 than during case 1 (revealed by a close inspection of Figs. 5(d) and 5(h)), which should result in more efficient wave trapping. (ii) The wind close to the mountain-top level. At 7 m, the wind is stronger in case 2 (25 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. (iii) 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 further 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 2, while conversely strong tropospheric wind shear and relatively uniform stratification occur in case 1. These factors may also influence the background flow in the boundary layer, which plays a crucial rôle in rotor formation. A larger magnitude of p/ρu 2 occurs during case 2, presumably because of the above three factors.

16 16 P. F. SHERIDAN ET AL. (b) Flow response to the lee-wave pressure amplitude In the interests of a more thorough investigation of the correspondence between the magnitude of the normalised lee-wave pressure amplitude and the occurrence of flow separation, a total of twelve prominent lee-wave cases containing large downstream wind and pressure perturbations will be examined. The characteristics of these twelve cases are summarised in table 1. Case 2 is included, but has been split into two cases, 2a and 2b, since some characteristics on 18 March are rather different to those on 17 March. The remaining cases are numbered The lee-wave wavelength has been calculated using data from the appropriate radiosonde releases, as for 18 March 25 earlier. Cases 2a 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 (6.43 W, 54.5 N, Northern Ireland) 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 re f, measures the degree of acceleration or deceleration of the downstream flow relative to the flow upstream, s re f = u u re f u re f, (5) where u re f is the 1 minute average AWS wind speed (measured at 2 m) at Hazelrigg and u is the component of the 1 minute average wind at a downstream AWS, resolved in the direction of the wind at Hazelrigg. When the maximum value of s re f 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 di f, indicates the degree of wind variation which occurs within the downstream array, s di f = u max u min 2u re f, (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 minute average winds measured at 2 m. Values of s di f have been calculated for the duration of the experiment using stations L1, L2, L4 and F1 F4. During times when a rotor is present, we might expect the value of s di f measured by the array to exceed unity. As the cases in table 1 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 di f 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 di f as a function of p/ρu 2 still gives a valid insight into the response of the flow to the lee-wave induced pressure perturbations. Meanwhile, the variation of the maximum s re f with p/ρu 2 is likely to be less informative since s re f is affected in a different way by this sampling issue. The variation of s di f as a function of p/ρu 2 for cases 2a, 3, 6, 8, 9, 1, 11, and 2b is shown in Fig. 13(a) (h) respectively. Data have been plotted either for a 24-hour period covering 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 1. The high degree of scatter which occurs in the data appears

17 INFLUENCE OF LEE WAVES ON THE NEAR-SURFACE FLOW DOWNWIND OF THE PENNINES 17 TABLE 1. 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 EQ. (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 QUOTED CORRELATION COEFFICIENT, R, IS YIELDED FROM A LINEAR FIT (WHERE PERFORMED) OF s di f VS. p/ρu 2. Case Start Duration Radiosonde wavelength < u re f > < u > p max R (UTC, date) (hrs) release time (km) (ms 1 ) (ms 1 ) (Pa) 2a 15:36 17/3/5 8:24 16: b : 18/3/5 14:24 9: : 15/11/4 14:24 9: :24 17/11/4 21:36 14: : 22/11/4 2:24 9: : 6/12/4 18: 9: ** : 22/12/4 24: 11: ** : 23/12/4 24: 11: ** : 3/12/4 24: 11: : 3/1/5 14:24 9: ** : 8/1/5 14:24 11: : 19/1/5 24: 9: 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.592. This is reminiscent of the behaviour found for the numerical simulations of Vosper et al. (26), where data from a range of simulations show a high degree of collapse when plotted on axes of s vs. p/ρu 2. It is also noteworthy that the values of p/ρu 2 at which s di f approaches 1 are similar to the critical normalised pressure perturbation amplitude values for rotor formation found by Vosper et al. The lower gradient evident in panel (h) (case 2b) is probably an effect of a relatively high degree of scatter which results from small magnitudes of u and u re f. Case 8 (panel (d)) and case 9 (panel (e)) also appear slightly different to the other cases, with relatively low correlation coefficients and fit gradients. This is because of a period within both cases when p/ρu 2 is large, but s di f 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 minute average 2 m wind vectors and pressure perturbations shown in Fig. 9(c) and 9(d). It seems plausible that these periods are examples of a non-linear response of the wind when the pressure gradient becomes large, or when the critical normalised pressure perturbation amplitude for flow reversal is reached. The wind and pressure data for the remaining four cases in table 1 were not plotted in Fig. 13 because, although large values of s di f and p/ρu 2 were observed during these cases, these did 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 normalised pressure expression by the 2 m wind speed at Hazelrigg gives similar (but re-scaled) results for the cases plotted in Fig. 13. (c) 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 bulk average Scorer parameter value for the lowest 3 km of each radiosonde ascent, termed l 1, has been calculated. This is based on the potential temperature at the top and bottom of the layer, and the mean wind vector. A similar value, l 2, 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 2 is

18 18 P. F. SHERIDAN ET AL. 1 (a) (b) (c) (d) s dif.5 1 (e) (f) (g) (h) s dif p/ρu * p/ρu * p/ρu * p/ρu * Figure 13. The variation of s di f as a function of p/ρu 2, based on 1 minute average 2 m wind data at AWS locations L1, L2, L4 and F1 F4, for a selection of the lee wave periods detailed in table 1: cases (a) 2a, (b) 3, (c) 6, (d) 8, (e) 9, (f) 1, (g) 11, and (h) 2b. Straight lines in each panel indicate a linear fit to the data, for which the correlation coefficient is quoted in table 1. significantly lower than l 1, some waves which 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 1 all satisfy l 1 /l 2 > 2. 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 eight hour period centred on the radiosonde release. These criteria are: (i) westerly flow, defined by an upstream 2 m wind direction between 22 and 32, (ii) average upstream 2 m wind speed for the eight hour period > 4 ms 1, (iii) l 1 /l 2 > 2. Criterion (iii) ensures that the atmospheric profile accommodates the formation of lee waves, while (ii) 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 re f have been calculated for the AWS stations in the Vale of York (11 stations) using the 1 minute average 2 m wind data for the duration of the experiment. Cases of rotor activity are identified by occasions when the maximum s re f exceeds unity within the eight hour period centred on the radiosonde release. A period as long as eight hours is not ideal for this purpose, since the variation of the synoptic flow in this time could be significant. However, due to the relative infrequency (once per day) of routine radiosonde releases, this period gave the best compromise between coverage of episodes of rotor turbulence and retaining 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 re f exceeded unity. An inspection of the Scorer parameter profiles suggests that the rate of decrease of l 2 within the lowest 4 km influences whether or not this occurs. In order to capture this rate of decrease, two more average Scorer parameter values were calculated for each of the 45 radiosonde ascents: l a for the lowest 2 km of

19 INFLUENCE OF LEE WAVES ON THE NEAR-SURFACE FLOW DOWNWIND OF THE PENNINES 19 the atmosphere and l b for the layer between 2 km and 4 km. These represent the mean of the Scorer parameter profile in the respective layer. The ratio l a /l b was found to be above 1.1 for all 16 cases where s re f exceeded unity. Meanwhile, the majority (62%) of the remaining cases were 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 rôle in determining whether or not rotors will form, and 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 Fig. 4 of Vosper et al. (26). In some of the simulations, rotors form beneath the lee wave crests, in others they do not, despite all simulations being initialised 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 leewave 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 2 in order to check if the correlation between these quantities found by Vosper et al. (26) also occurs for the simulations from this study. The fractional deceleration was 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 windspeed averaged over a wave cycle. The variation of s as a function of p/ρu 2 has been plotted in Fig. 14(a) for the simulations described in section 3. For simulations where U was below 5 ms 1 the wave structure was observed to change considerably with decreasing U, and since we are trying to isolate the effect 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 2 until a critical value is reached at which s = 1 and rotors begin to form. Further, the critical values of p/ρu 2 are similar to those found by Vosper et al.. Therefore the original result appears to be robust 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 lines plotted in Fig. 14(a) demonstrates the effect of changing U t without altering U. Reducing U t causes the wind in the boundary layer to decrease. The value of u scales with this decrease, but the wave amplitude proves less sensitive, causing p/ρu 2 to increase. Thus larger values of p/ρu 2 in Fig. 14(a) tend to correspond to simulations with weaker jets. As shown in Fig. 2, for a weak jet the corresponding potential temperature profile exhibits negative curvature (due to the constraint on the Scorer parameter profile), resulting in a decrease of N with height. This type of profile often occurs in reality, such as in case 2 from section 4, where its occurrence may have contributed to rotor formation.