Observations of cross-ridge flows across steep terrain

Transcription

1 QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY Q. J. R. Meteorol. Soc. 134: (2008) Published online 27 May 2008 in Wiley InterScience ( Observations of cross-ridge flows across steep terrain H. W. Lewis, a * S. D. Mobbs a and M. Lehning b a Institute for Atmospheric Science, University of Leeds, UK b Swiss Federal Institute for Snow and Avalanche Research, Davos, Switzerland ABSTRACT: A field experiment, Gaudex, has been conducted to address the need for quantitative measurements of turbulence in the vicinity of steep terrain. A dense network of automatic weather stations and turbulence towers was deployed along cross-ridge transects over Gaudergrat, a steep triangular cross-section ridge in eastern Switzerland. A new feature, whereby ridge-normal cross-ridge flows develop at the crest even when the flow in each valley is oriented parallel to the ridge axis, is identified. This occurs independently of whether the flow is thermally or synoptically driven. Pressure measurements across the ridge show that this flow is driven by a cross-ridge pressure gradient. Two mechanisms for generating cross-ridge flows have been identified from measurements of pressure, wind and temperature. In most cases the pressure gradient arises from a difference in flow speeds between the two sides of the ridge, caused by different valley geometries. Less commonly, the cross-ridge flow is explained by linear speed-up of the ridge-normal flow. Copyright 2008 Royal Meteorological Society KEY WORDS Bernoulli function; Gaudex; microbarograph; orography Received 26 October 2007; Revised 2 April 2008; Accepted 14 April Introduction The influence of surface undulations on the motion of Earth s atmosphere can lead to a wide variety of phenomena on a range of scales. An understanding, quantification and parametrization of these features has proved to be important in improving both local weather forecasts and the accuracy of operational numerical weather-prediction models on a global scale. The influence of smaller-scale orography on the atmosphere is becoming increasingly significant as such models begin to resolve it explicitly. It is well understood that individual hills may induce dynamic features such as crest speed-up, flow blocking, lee waves, slope flows and turbulent wakes (e.g. Carruthers and Hunt, 1990). These processes have a considerable influence on the dynamics of the atmospheric boundary layer above complex terrain. One approach used to predict the flow pattern over an isolated hill is to assume that modifications to the initial background state are small, so that the governing equations of motion can be linearized (Jackson and Hunt, 1975). This method has proved to be highly successful, and has been verified and extended as a result of much subsequent analytical, numerical and observational research (Taylor et al., 1987). However, it is limited by its restriction to shallow topography and its failure to describe complex flow in the wake region, which may develop in the lee of hills and mountains. In reality, most hills are not of sufficiently low slope, and the flow behaviour can become highly nonlinear. * Correspondence to: H. W. Lewis, Met Office, Fitzroy Road, Exeter, EX1 3PB, UK. huw.lewis@metoffice.gov.uk Recent work has concentrated on understanding flows within more complex environments. The most comprehensive observational and modelling studies to date were during the Mesoscale Alpine Programme. Mayr et al. (2007) have summarized the achievements in understanding gap flows that resulted from a high-resolution observation campaign in the Wipp Valley with associated modelling work. A similar approach in the Riviera Valley has yielded new understanding of the interaction between thermally-driven flows and the nearsurface turbulence structure (e.g. Weigel and Rotach, 2004). The Gaudergrat Experiment (Gaudex) was devised to meet a need for quantitative measurements of the nearsurface flow in the vicinity of steep terrain, primarily for the verification of numerical simulations of flow in such environments. The main aim was to provide a detailed description of flow separation and turbulence in the lee of steep hills. A variety of measurements were conducted over Gaudergrat, a steep ridge in eastern Switzerland, during the summer of In this paper we provide some background to the Gaudex measurement campaign, and present new observations of a cross-ridge flow phenomenon. The Gaudex measurements are described in Section 2. The meteorology at the time of the campaign is summarized in Section 3, and the dominant mean-flow features are identified in Section 4. Evidence of the crossridge flow phenomenon is presented in Section 5. In Section 6, the measurements are used to identify a mechanism to explain its occurrence. Conclusions are drawn in Section 7. Copyright 2008 Royal Meteorological Society

2 802 H. W. LEWIS ET AL. 2. The Gaudex field measurements A dense instrument network was deployed across Gaudergrat, a steep-sided ridge located on the Alpine plateau in eastern Switzerland (46.46 N, 9.80 E), for over 100 days between June and October More limited flow measurements have been conducted across the ridge by the Swiss Federal Institute for Snow and Avalanche Research (SLF) for several years (Doorschot et al., 2001): this is because it is known that small-scale flow features such as separation, recirculation and turbulence can result in inhomogeneous snow distributions on mountains, and increase the risk of avalanches. Terrain-induced flow separation is known to be facilitated by both a steep lee slope and a sharp ridge crest. Photographs of these features on Gaudergrat are shown in Figure 1. A maximum slope angle in excess of 40 is clearly greater than typical values for the critical lee slope predicted by Wood (1995) for the onset of separation in neutral turbulent flow over hills Field site A map of the Gaudergrat orography is shown in Figure 2. Gaudergrat is approximately triangular in cross section Figure 1. Photographs of the Gaudergrat field site. Crest and east slope. Automatic weather station located on the sharp crest. along its 1.5 km length, running NNE SSW between two U-shaped valleys. Cross sections of the ridge-crest and valley-floor profiles, and of the cross-ridge profile, are shown in Figure 3. The eastern valley is about 150 m deep and 500 m wide: significantly narrower than the western valley, which is about 1.5 km wide. The ridge rises to a peak of 2305 m a.m.s.l. towards its southern end, where it joins the surrounding terrain. At its northern end, the ridge crest falls away to the height of the surrounding valleys over a distance of about 200 m. The ridge may therefore be considered as quasi-twodimensional over the majority of its length. The task of defining typical length scales for the Gaudergrat terrain profile is complicated by the fact that the west and east valley floors are at different altitudes. In addition, Figure 3 illustrates how the eastern valley deepens with down-valley distance towards the north. The average of the valley depths h 1 and h 2 along the central transect (Figure 3) gives a representative hill height h = (h 1 + h 2 )/2 = m. The half-width at half the hill height is estimated to be L h = 152 m for this central transect Instrumentation The instrument network deployed across Gaudergrat during Gaudex is shown in Figure 2. A total of 27 automatic weather stations (AWSs) were distributed along three cross-ridge transects and around the northern ridge end, where three-dimensional mean-flow features were expected to be most significant. Site positions along the crest and in the east and west valleys are also shown in Figure 3. The AWSs at sites are operated by SLF to provide long-term wind-speed measurements at heights of 5 m, 3 m and 2 m (within the inner layer) at 1 s and 10 s resolution. These stations were supplemented during Gaudex with an additional 20 AWSs provided by the University of Leeds, which recorded surface pressureandwindspeedanddirectionat2mheightat 1 s time resolution. Temperature and relative humidity were recorded every 4 s. The AWS deployed at site 28 was supplied by the University of Innsbruck (IMGI), and provided 60 s measurements of pressure, temperature, relative humidity, and wind speed and direction, which served as reference surface data for the radiosondes launched from that location. The Leeds AWSs have been developed over a number of years, and have been employed in several field campaigns above complex terrain. These include measurements of the mean flow associated with Black Combe, Cumbria (Vosper and Mobbs, 1997), the Isle of Arran (Vosper et al., 2002), the Falkland Islands (Mobbs et al., 2005) and the Wipptal (Mayr et al., 2007). The basic design used during Gaudex is shown in Figure 1. Each AWS consisted of a propeller anemometer mounted on a 2 m lattice mast, aspirated temperature and relative-humidity sensors housed in a radiation shield, and a sensitive microbarograph. The

3 OBSERVATIONS OF CROSS-RIDGE FLOWS AWS (Leeds) AWS (SLF) 28 AWS (IMGI) Turbulence tower Sodar Radiosonde Figure 2. Orographic map showing the location of instrument sites across the Gaudergrat region during the Gaudex campaign. Each grid square is 1 km 1km. Altitude (m) West AWS Crest East Along-ridge distance (m) L 1 Crest L 2 Altitude (m) West h h 2 1 L h h East Across-ridge distance (m) Figure 3. Two-dimensional cross sections of the Gaudergrat ridge. Top: profiles along the ridge crest (bold), and the west (dotted) and east (dashed) valley-floor transects. Bottom: cross-ridge profile across a central transect. Symbols are defined in Figure 2. data from each sensor were processed by a circuit board housed inside the white microbarograph box, and stored, together with the time according to an internal clock, on a PCMCIA flash card for later retrieval. The microbarographs were calibrated against a high-precision barometer to account for their temperature dependence (Vosper et al., 2002). The pressure data presented are considered to have an associated error of 0.24 hpa (Lewis, 2006). In order to maintain all logger clocks in close synchronization (essential for making instantaneous comparisons of measurements from instruments in close proximity), each logger included a GPS receiver and and was synchronized to GPS every 12 h. In addition, turbulence measurements were made using ultrasonic anemometers mounted on towers across the ridge crest on the central cross-ridge transect at sites 31,

4 804 H. W. LEWIS ET AL. 32 and 33. The operational details of these instruments, as well as an analysis of the data, is provided by Lewis (2006). Remote measurements of wind and turbulence profiles were gathered with sodars in each valley at sites 29 and 30. These surface-based measurements were complemented by daily radiosonde ascents, launched about 1 km to the northeast of Gaudergrat from site Meteorological overview The Gaudex observation period was characterized by generally slack synoptic-scale pressure gradients across Europe, occasionally interrupted by isolated convective storms. During the campaign, 14 days were characterized by mainly southerly flow and 21 days by mainly northerly flow, evident at most sites. All other days were identified as valley-wind days, since a well-defined diurnal cycle of wind directions was observed along the east and west valleys on each day. This cycle corresponds to local thermally-driven flows, up-valley during daytime and down-valley at night (Whiteman, 1990). The longest period of successive valley-wind days during Gaudex lasted for over two weeks, between 1 August and 16 August Measurements show the daytime up-valley flow to accelerate with distance along the east valley, driven by an up-valley temperature gradient of up to 1.5 K over an along-valley distance of about 700 m (Lewis, 2006). A corresponding pressure difference of about 0.1 hpa was measured over the same distance, with flow towards the region of lower pressure. The valley wind speed was approximately linearly related to the along-valley flow-induced pressure difference, and daytime up-valley flow speeds were inversely related to the along-valley temperature difference. An average daytime wind speed at 2 m of 3.5 ms 1 was measured on valley-wind days at site 02 on the east valley floor (Figure 2). Flow speeds were generally lower in the west valley than in the east valley, with an average of 1.5 ms 1 measured at site 10. This difference may be due to the larger size of the west valley, reducing the terrain-induced alongvalley temperature gradient, and the shallower valleyfloor slope, reducing night-time drainage-flow speeds. In addition to the along-valley temperature gradients observed, temperature measurements from AWSs at various positions along each slope show a clear diurnal temperature variation across Gaudergrat as a result of its north south orientation. Figure 4 shows profiles of near-surface potential temperature θ measured along the west and east slopes during a typical valley-wind day, 8 August Potential temperatures relative to site 07 are plotted every 2 h. An average near-surface temperature gradient θ/ z on each slope can be estimated for each time period by performing a linear regression of the temperature at each AWS along the slope with station height. These results are plotted in Figure 4. At night, the valley layer is stably stratified, with temperatures at the valley-floor sites up to 5 K cooler than at the ridge crest ( θ/ z 15 Km 1 ). Stability within each valley tends to increase with time until a peak at about 0300 UTC. The temperature profiles at 0600 UTC (see Figure 4) illustrate how the eastern profile warms earlier than the western profile, in response to the eastern slope becoming sunlit while the western slope remains shaded behind the ridge. The resulting cross-ridge temperature gradient persists above an altitude of about 2280 m (between sites 09 and 05) until about 1000 UTC, while the gradient between sites 08 and 06 across the ridge crest lasts throughout the morning. On 8 August, the peak temperature difference across the crest of 4.7 K was measured at 0710 UTC. By midday, the profiles show approximately neutral behaviour, and θ values that are reasonably constant with height. The afternoon temperature-profile evolution mirrors the morning pattern, with the eastern-slope profile cooling in response to local shadowing from about 1500 UTC. A maximum afternoon cross-ridge horizontal temperature gradient between sites 08 and 06 of 1.4 K was measured at 1730 UTC considerably smaller than the temperature gradient associated with the morning shadowing effect. Altitude (m) q (k) Time of Day (hours, UTC) +5 dq/dz (Km -1 ) East valley West valley Time of Day (hours, UTC) Figure 4. Evolution of vertical potential-temperature profiles along the east (solid) and west (dashed) slopes during 8 August 2003, as measured by AWSs along the central transect (see Figure 3). Average vertical potential-temperature gradient θ/ z through each profile with time of day. Symbols show 10 min values on 8 August 2003; solid lines show the average diurnal pattern over all valley-wind days.

5 OBSERVATIONS OF CROSS-RIDGE FLOWS Terrain-induced flow patterns The dominant near-surface wind patterns measured across Gaudergrat are illustrated by the wind roses plotted in Figure 5, which show the wind-direction frequency distributions at each AWS site. The steep terrain has a clear influence on local wind patterns, with systematic differences in the flow characteristics within a small spatial area. Data at sites located near the ridge end (17, 18, 20, 19) display evidence of flow around the ridge end. This is illustrated by comparing the flow directions at sites 16 and 17, located within 50 m of each other but with site 16 located on the ridge crest (Figure 3). While cross-ridge flows are prevalent at site 16, the mean flow at site 17 tends to follow the terrain contours. Southwesterly winds at sites 19 and 20 may be indicative of flow separation from the ridge end. Measurements along the east (01, 02, 03, 21, 22) and west (10, 27) valleys show ridge-parallel near-surface flows. These are associated with the diurnal cycle of valley winds, northeasterly up-valley during the daytime and southwesterly down-valley at night. Even when flows are driven by larger-scale pressure gradients, the mean flow may still be parallel to the ridge axis because of channelling. Wind roses for locations on the east (05, 06, 11, 12, 23) and west (08, 09, 13, 25) ridge slopes in Figure 5 show a more even flow distribution than along the valley floor, with less than 5% of data from any 5 sector. The prevailing wind directions are oriented across each slope at an angle to the terrain contours. Flow at these sites also tends to follow a diurnal cycle, with measurements on the east slope showing northeasterly flows during the daytime and southwesterly flow at night, while those on the west slope tend to be northwesterly during the daytime and southeasterly at night. This is consistent with thermally-forced slope flows, upslope during the day and downslope at night (Whiteman, 1990). The orientation of the mean wind direction across the slope is perhaps an indication of an interaction between the valley and slope wind systems. These directions are also consistent with dynamically-induced flow across the ridge and lee-slope separation. The dominant flow patterns observed at sites along the ridge crest (24, 14, 15, 07, 16) are strikingly different. While flows in either valley tend to be ridgeparallel, Figure 5 shows a strong tendency for flow at the ridge-crest sites to be oriented at right angles to the ridge axis. For example, 54.4% of all wind directions measured at site 07 on the central cross-ridge transects were from within a 60 range, between 275 and 335. On average, a change in flow direction of almost 90 occurs within a 50 m distance on the eastern side of Gaudergrat crest between sites 07 and 06 (Figure 2). This feature is replicated between sites 24 and 23 on the southern transect, where the ridge-normal wind direction is northwesterly Figure 5. Wind-rose plots showing the wind-direction frequency and mean wind-speed distributions at each site, calculated from 1 s data during the Gaudex campaign. Wind directions are split into 5 sectors. The radial axis of each rose ranges between zero and 5% (frequency) and between zero and 5 ms 1 (wind speed). The position of site 28 has been moved for clarity (see Figure 2). Terrain contours are plotted at 25 m intervals.

6 806 H. W. LEWIS ET AL. 5. Evidence of cross-ridge flows Figure 5 illustrates the dominant phenomenon observed during the Gaudex campaign: cross-ridge flows at the ridge crest when the flow in each valley is oriented parallel to the main ridge axis. In this section, we will describe the periods when cross-ridge flows were observed. Case studies have been selected from those periods when steady southerly or southwesterly flows were measured along each slope (i.e. all 10 min mean AWS wind directions within a sector between 158 and 248 ). Such flows account for 10% of the Gaudex dataset, and are typically associated with thermally-driven nighttime flows down both valleys. In Section 6, we will further analyse the cross-ridge flow phenomenon using all measured data. 5m/s 08/08/ UTC 5.1. Thermally-driven night-time flow Figure 6 illustrates a typical night-time flow pattern measured on a valley-wind day during the Gaudex campaign (8 August 2003). The influence of thermal forcing is clear, with southerly down-valley flow parallel to the ridge axis at sites 01, 02, 03 and 22 in the east valley and at sites 10 and 27 on the west-valley floor. These flows are driven by the along-valley temperature and pressure gradients discussed in Section 3. In contrast, flow vectors at the crest demonstrate westerly flow across the ridge, while the flow elsewhere is generally along-ridge. For example, there is a shift of almost 90 between wind-direction measurements at site 08 on the west slope and site 07 on the ridge crest during this time. This feature is apparent at crest sites along the entire ridge length, while measurements at the ridge end are consistent with the southerly down-valley wind direction. A further example of this situation is shown in Figure 7. At this time, measurements at sites along the east slope show some downslope flow behaviour, driven by horizontal temperature gradients between the slope and the surrounding environment (Whiteman, 1990). Cross-ridge profiles of the flow-induced pressure perturbation p, the Bernoulli parameter ρ 0 u 2 /2 and the potential-temperature perturbation θ measured along the central transect during night-time southerly-flow periods are plotted in Figure 7. Pressure perturbations p are calculated by first reducing the measured pressure at each AWS to a mean reference height (2284 m a.m.s.l.). This removes the hydrostatic-pressure component, estimated using a polytropic atmosphere profile and by fitting linear vertical temperature profiles to the east- and west-valley data (Figure 4). The background synoptic pressure, estimated as the spatially-averaged reduced pressure in each time interval, is then subtracted from the reduced pressures. The calculation is estimated to have an error in p of 0.24 hpa (Lewis, 2006). The background atmospherictemperature gradient is subtracted from temperature measurements to give θ estimates. Figure 7 illustrates two features which are consistent with the sense of cross-ridge flow and which may (c) 5m/s 5m/s 09/08/ UTC 09/08/ UTC Figure min-average wind vectors at 2330 UTC, 0000 UTC and (c) 0030 UTC on 8 9 August 2003, showing examples of night-time flow patterns across Gaudergrat. prove important in determining its origin. One possible factor is that the θ profiles show generally higher temperatures at east-slope sites than on the west slope. This is perhaps a result of the east valley being more enclosed. Assuming the air on both sides of the ridge to be in hydrostatic balance, a cross-ridge temperature difference will result in a difference of pressure between the two

7 OBSERVATIONS OF CROSS-RIDGE FLOWS /08/ UTC 5 m/s p (hpa) ru 2 /2 (hpa) UTC UTC UTC UTC 1.5 q (K) Cross-ridge distance (m) Figure 7. Example of night-time southerly flow in the west valley, and westerly ridge-normal cross-ridge flow along the crest. 10 min-mean 2 m wind vectors at 2120 UTC on 24 August Cross-ridge profiles of 10 min-mean flow-induced pressure perturbation p, Bernoulli parameter ρ 0 u 2 /2 and potential-temperature perturbation θ measured at sites along the central transect. Mean values are plotted as a grey line, with error bars showing the standard deviation of each point. The profile measured at 2120 UTC on 24 August is plotted in bold with black squares.

8 808 H. W. LEWIS ET AL. sides of the ridge. Smith (1978) estimated the pressure difference p halfway up a ridge of height h that would result from a temperature difference θ as p ρg θ θ h 2. For example, the largest difference between average temperatures on the two slopes shown in Figure 7 is 0.7 K, measured between sites 05 and 08. Such a temperature difference induces a cross-ridge pressure difference of 15 hpa, with the westerly cross-ridge wind being consistent with flow from regions of higher pressure to regions of lower pressure. The second feature highlighted in Figure 7 is the presence of generally stronger down-valley wind speeds in the east valley than in the west valley. This may be a result of the steeper valley-floor inclination in the east valley (Figure 3) and larger along-valley temperature contrasts driving faster flow in the east valley. Assuming p to vary inversely with ρ 0 u 2 /2, the data suggest that the east slope is a region of lower pressure than the west slope. The observed westerly cross-ridge flow is consistent with flow towards the region of faster-moving, lowerpressure air. Unfortunately, the p values in Figure 7 are inconclusive in such light-wind conditions, being of similar magnitude to the estimated error associated with the p calculation and an order of magnitude greater than the temperature-induced pressure gradient Synoptically-driven flow The strongest wind speeds measured during the Gaudex field campaign occurred during periods of synopticallydriven southerly flow (Section 3). Figure 8 shows one such case on 28 August 2003, when a 2 m cross-ridge wind speed of 13.0 ms 1 was measured at site 07 on the crest while steady southerly flows of 6.2 ms 1 and 10.2 ms 1 were measured in the west and east valleys respectively. The along-valley flow illustrated in Figure 8 is clearly not thermally-driven, since the typical flow pattern at 1430 UTC would involve northerly daytime up-valley winds along each valley. The remarkable feature shown in Figure 8 is the presence of strong ridge-normal flow measured at all sites along the crest. The ridge-crest flow vector at site 07 is aligned perfectly with the central cross-ridge AWS transect at this time, and deviates by more than 90 from the wind direction measured immediately downstream at site 06. A similar contrast can be seen over an even shorter distance between sites 24 and 23 along the south transect. This feature first became established at 0800 UTC on this day, and persisted until 1500 UTC, when it was briefly interrupted by easterly winds across the whole Gaudergrat region. We do not know whether such striking behaviour has previously been measured or reported, but it certainly not a widely known or understood phenomenon of flows in the vicinity of steep ridges. The flow pattern illustrated in Figure 8 is very reminiscent of that shown in Figure 7, where thermally-driven night-time southerly winds dominate in each valley. It seems likely that the same forcing mechanism must account for both cases. This idea is developed in Section 6. The profiles of cross-ridge potential temperature θ plotted in Figure 8 show generally higher temperatures in the east valley during periods of synopticallydriven southerly flows. The θ cross section measured at 1430 UTC on 28 August 2003 shows an average θ value at sites in the west valley of 0.38 K, and at sites in the east valley of 0.21 K. This is in clear contrast to the typical behaviour at this time on valley-wind days, when solar heating is strongest on the west slope (Figure 4). Following the analysis of Smith (1978), such a temperature difference would lead to different hydrostatic balances on the two sides of the ridge, and result in a cross-ridge pressure difference of about 13 hpa. The westerly cross-ridge flow is therefore consistent with flow towards the region of higher temperature and lower pressure in the east valley. Figure 8 also shows that the synoptically-driven southerly flows tend to be stronger in the east valley than in the west valley. For example, the average value of ρ 0 u 2 /2 in the east valley for the 28 August case shown is 0.38 hpa, while that at west-valley sites is 0.21 hpa. This trend is replicated in all cases plotted in Figure 8. Peak wind speeds are associated with the cross-ridge flow at the ridge crest, where maximum ρ 0 u 2 /2 values of up to 0.8 hpa occur. The increased wind strength observed during these synoptically-driven cases leads to flow-induced pressure perturbations that can be resolved beyond the level of error associated with their measurement and calculation. Values at west-valley sites show a region of higher pressure, with average p values of 0.22 hpa for the case in Figure 8, while values at east-valley sites show lower pressure, with an average of 3 hpa. Measurements across the ridge crest itself show that the cross-ridge flow is associated with a cross-ridge pressure difference between sites 06 and 08 of 0.54 hpa. A measurable pressure gradient therefore exists, driving flow at the crest normal to the ridge axis towards the region of lower pressure. Comparison of the cross-ridge ρ 0 u 2 /2andp profiles in Figure 8 shows excellent correspondence between the spatial variations of the two quantities. This is best illustrated by the maximum p values at the ridge crest associated with minimum ρ 0 u 2 /2 values; but increases or decreases in ρ 0 u 2 /2 between adjacent sites can also be associated with corresponding decreases or increases in p between those sites. The strength of this correlation is highlighted in Figure 9, which shows the variation of p with ρ 0 u 2 /2, where differences are measured for sites 08 and 06 relative to ridge-crest values. Linearregression correlation coefficients of 0.74 and 0.40 can be calculated for the differences between sites 07 and 08 and between sites 07 and 06 respectively. The relationship between p and ρ 0 u 2 /2 for the two pairs of measurements can be estimated as ρ 0 u 2 /2 = 0.36 p.no

9 OBSERVATIONS OF CROSS-RIDGE FLOWS /08/ UTC 5 m/s p (hpa) ru 2 /2 (hpa) UTC UTC UTC UTC q (K) Cross-ridge distance (m) Figure 8. Example of synoptically-driven southwesterly flow in the west and east valleys and westerly ridge-normal cross-ridge flow along the crest. 10 min-mean 2 m wind vectors at 1430 UTC on 28 August Cross-ridge profiles of 10 min-mean flow-induced pressure perturbation p, Bernoulli parameter ρ 0 u 2 /2 and potential-temperature perturbation θ measured at sites along the central transect. Mean values are plotted as a grey line, with error bars showing the standard deviation of each point. The profile measured at 1430 UTC on 28 August is plotted in bold with black squares.

10 810 H. W. LEWIS ET AL. such correlation is found between p and θ,since θ values tend to zero for large p. This is in response to mixing of temperature gradients in the presence of strengthened cross-ridge flow. By Bernoulli s theorem, the quantity ρ 0 u 2 /2 + p + ρgz, (1) is constant along a streamline. Although the flow measurements across Gaudergrat clearly show that sites are not on the same streamline, there is a strong relationship between the ρ 0 u 2 /2andp measurements. Vosper and Mobbs (1997) derived an expression for the difference in the quantity (1) along two streamlines that pass over a hill, assuming that the streamlines originate from a region of horizontally-homogeneous inviscid flow far upstream, where they are separated by a small vertical distance δ u z, if δ u is a small difference in wind speed between the two levels. In this case, 1( u u 2 1 ( 2) + p ρ 1 p 2) (1 + δu 2 u2) = 0. Assuming that streamlines at sites across the ridge originate from regions of similar wind speed, it can be expected that differences in wind speed will be related to differences in flow-induced pressure. The more separated the upstream origins of the two streamlines, the weaker the inverse correlation between p and ρ 0 u 2 /2. Dissipative processes that may be dominant close to the surface will also weaken the correlation (Vosper et al., 2002). Figure 9 shows that significant inverse correlation remains in this case despite these factors Easterly cross-ridge winds Synoptically-driven southerly winds persisted during most of 28 August Figure 10 shows the flow pattern at 1840 UTC. While the flow in each valley is apparently very similar to that observed during the afternoon (Figure 8), measurements at the ridge crest show easterly cross-ridge winds. The flow vector at site 08, located immediately downwind of the crest at this time, has a significant upslope component, indicative of hillinduced flow separation on the lee slope. Figure 10 shows that the easterly cross-ridge flow is associated with a cross-ridge pressure difference between sites 08 and 06 of 0.14 hpa. While this is consistent with easterly flow from a region of higher pressure to a region of lower pressure, the cross-ridge profiles of ρ 0 u 2 /2 and θ are very similar to those shown in Figure 8 during westerly cross-ridge flow periods. For example, the average value of ρ 0 u 2 /2intheeastvalley for the case shown in 0.56 hpa, while that at westvalley sites is 0.23 hpa. Wind speeds and temperatures generally remain higher in the east than in the west valley during southerly-flow periods, apparently independent of the cross-ridge wind direction. The profiles plotted in Figure 10 show good correspondence of ρ 0 u 2 /2 and p changes between adjacent sites, although the magnitudes of those changes are less well matched than in Figure 8. For example, the highest p values occur in the east valley while the lowest ρ 0 u 2 /2 values continue to be measured in the west valley. Figure 11 shows the correlation between p and ρ 0 u 2 /2 for all southerly-flow periods when easterly cross-ridge winds were observed. The correlation between p and ρ 0 u 2 /2 measured between sites 06 and 07 is similar to that shown in Figure 9 for the cases of westerly cross-ridge flow. There is no correlation between p and ρ 0 u 2 /2 values calculated between sites 07 and 08, however, suggesting that the easterly cross-ridge winds are independent of conditions downwind of the ridge crest. The generally reduced p values between sites 07 and 08 shown in Figure 11 are consistent with slackened pressure gradients associated with the occurrence of flow separation downwind of an obstacle. As in Figure 9, the variation of p with θ in Figure 11 shows the largest p values to be associated with near-zero values of θ.most θ values plotted in Figure 11 show temperatures at the crest and east slope to exceed those on the west slope, highlighting the tendency for most cases of easterly cross-ridge flow to take place during the morning (Figure 4). Figure 9. Correlation of 1 min-mean differences of pressure perturbation p with differences of Bernoulli parameter ρ 0 u 2 /2 and potential-temperature perturbation θ measurements, at the crest and above the west (site 08) and east (site 06) slopes during periods of westerly cross-ridge flows at the ridge crest.

11 OBSERVATIONS OF CROSS-RIDGE FLOWS /08/ UTC 5 m/s p (hpa) ru 2 /2 (hpa) UTC UTC UTC UTC q (K) Cross-ridge distance (m) Figure 10. Example of southerly flow in the west and east valleys and easterly ridge-normal cross-ridge flow along the crest. 10 min-mean 2 m wind vectors at 1840 UTC on 28 August Cross-ridge profiles of 10 min-mean flow-induced pressure perturbation p, Bernoulli parameter ρ 0 u 2 /2 and potential-temperature perturbation θ measured at sites along the central transect. The profile measured at 1840 UTC on 28 August is plotted in bold with black squares. 6. Cross-ridge flow mechanism The results of Section 5 highlight the occurrence of ridge-normal flows at the ridge crest even when the flow in each valley is oriented along-valley. The Gaudex campaign provides the first field measurements of such a feature. The majority of cases involve westerly crossridge flow during periods of southerly winds along each

12 812 H. W. LEWIS ET AL. Figure 11. Correlation between 1 min-mean differences of pressure perturbation p with differences of Bernoulli parameter ρ 0 u 2 /2and potential-temperature perturbation θ measurements, at the crest and above the west (site 08) and east (site 06) slopes during periods of easterly cross-ridge flows. valley, independent of whether that flow is driven by local thermal forcing or synoptic-scale pressure gradients. This suggests that the same process must account for this feature in both cases, and analysis of all flow types is required to determine the factors that influence and drive this cross-ridge flow. For sufficiently high wind speeds, it is clear that the westerly flows are driven by a cross-ridge pressure gradient. This pressure difference is well correlated with the cross-ridge difference of ρ 0 u 2 /2. Easterly cross-ridge flows were also observed in apparently similar conditions. Characterization and prediction of flows in the vicinity of steep terrain requires an understanding of the conditions under which easterly or westerly cross-ridge flows develop Geographic scale Our first consideration is that the ridge-crest flow pattern may reflect a larger-scale wind feature that occurs above the east- and west-valley layers, rather than being orographically induced, so that, in effect, the valley-wind direction is determined by the terrain rather than by that at the crest. The validity of this suggestion is difficult to assess from the available network of near-surface AWSs, which are all influenced to some extent by the ridge. Measurements away from the Gaudex study region are too far from the ridge in both the horizontal and the vertical directions to be assured of relevance to conditions across Gaudergrat. Figure 12 compares radiosonde (site 34) and sodar (site 30) measurements made at heights of 150 m, 500 m and 1000 m above the west valley with the closest 10 min-mean crest-wind direction to that measurement time (site 07). All available values are plotted, independent of flow conditions and crest-wind direction. The distribution of wind-direction measurements by the westvalley sodar shown in Figure 12 is very similar to that measured by the co-located AWS on the west-valley floor at site 10. The absence of systematic correlation between the AWS data and radiosonde or sodar measurements above and below crest height demonstrates that the perpendicular crest flow is restricted to the ridge crest, rather than being part of a larger-scale feature Speed-up Coppin et al. (1994) measured flow deviations of up to 20 towards ridge-normal for flow within 40 of perpendicular to the crest of a two-dimensional hill with 10 slopes. This was explained as being consistent with linear theory, which predicts that only the ridge-normal wind-speed component is accelerated as it crosses a two-dimensional ridge. Figure 13 shows the difference between wind directions measured at sites 10 and 07 on the ridge crest, plotted against wind direction, for all periods with crest-wind directions greater than 180. This reflects the strong tendency for cross-ridge flows to occur for all such incident flow directions. Figure 13 shows the flow deviation but with the crest-wind direction recomputed to neglect the ridge-normal component of flow speed-up. The observed deviation for small angles of incidence (±45 ) can be accounted for by neglecting the ridge-normal component of flow speed-up. This is not the case for the deviation associated with larger angles of incidence (Section 5), which involves considerable flow acceleration in the cross-ridge direction and along-ridge deceleration. The westerly cross-ridge flows are therefore not simply due to ridge-induced speed-up. Figure 14 shows similar behaviour between wind directions at the ridge crest with those at site 02 in the east valley, for those periods when crest-wind directions are less than 180. The variation between incident wind directions and the ridge-crest flow deviation is not as well defined as for westerly flows (Figure 13). This is perhaps due to the influence of flow channelling in the narrower east valley, restricting wind directions at site 02. Flow speed-up cannot explain the observed 90 shifts of wind direction. For lower angles of incidence and southerly along-valley flow directions (relative wind direction greater than 0 ), the scatter of flow deviations is removed by accounting for flow speed-up, and values tend to zero. It is interesting to note that all cases of easterly cross-ridge flow described in Section 5.2 involve flow deviations of only about 45. In the absence of further evidence, it is possible that these flow patterns could be accounted for by flow speed-up of the cross-ridge windspeed component. The strong correlation between p

13 OBSERVATIONS OF CROSS-RIDGE FLOWS 813 Radiosonde (site 34) wind direction ( ) m 500 m 150 m Ridge crest AWS (site 07) wind direction ( ) West valley SODAR (site 30) wind direction ( ) Ridge crest AWS (site 07) wind direction ( ) Figure 12. Correlation between ridge-crest wind direction at site 07 and wind-direction measurements at heights of 150 m (white squares), 500 m (stars) and 1000 m (black circles), by radiosondes and west-valley sodar. Crest - Upwind dir. change ( ) Upwind wind direction - Ridge normal ( ) Upwind wind direction - Ridge normal ( ) Figure 13. Difference between wind directions measured at sites 10 and 07 for westerly ridge-crest flow directions during Gaudex, as a function of incident wind direction (at site 10) relative to ridge-normal. Only periods when u 07 > 1ms 1 are included. As, but showing the difference between incident and crest wind directions after removing the cross-ridge speed-up component. Crest - Upwind dir. change ( ) Upwind wind direction - Ridge normal ( ) Upwind wind direction - Ridge normal ( ) Figure 14. As Figure 13, but for wind directions measured at sites 02 and 07 for easterly ridge-crest flow directions during Gaudex. and ρ 0 u 2 /2 measured between sites 07 and 06 during easterly-flow periods shown in Figures 10 and 11 then highlights flow acceleration towards the ridge crest driven by an along-slope pressure gradient. This idea implies that flow along the east valley with an easterly upslope component is necessary for easterly cross-ridge flow at the ridge crest Thermally-driven plain-basin flow It has been shown (see, for example, Figure 4) that the Gaudergrat region is subject to significant thermal gradients over small distances. All the evidence presented in Section 5 showed higher temperatures at sites along the east slope than along the west slope. It was shown that the

14 814 H. W. LEWIS ET AL. resulting difference between the hydrostatic balance on the two sides of the ridge in such conditions would produce a cross-ridge pressure difference of about 15 hpa. The sense of θ plotted in Figure 9 shows cross-ridge flow towards the region of higher temperatures and lower hydrostatic pressure. However, θ values are not correlated with measured pressure differences, and, as shown in Section 5.1, the magnitude of θ is too small to account for the observed p values using the analysis of Smith (1978). This indicates that the observed pressure gradient and resulting cross-ridge flows are not thermally induced. p (hpa) Dynamically-driven pressure-gradient flow The correlation between differences of flow speed and pressure perturbation measured at the ridge crest and immediately upwind and downwind at sites 08 and 06 during periods of westerly cross-ridge flow shown in Figure 9 demonstrates an association between ridge-crest and along-valley flow conditions. Figure 15 shows the correlation between 1 min-mean values of the ridgecrest wind speed and the cross-ridge pressure gradient calculated between sites 08 and 06 for all flow conditions during Gaudex. For westerly cross-ridge flows, Figure 15 shows that the cross-ridge flow speed is correlated with the cross-ridge pressure gradient (R 2 = 0.44). The strongest 2 m wind speeds, of up to 15 ms 1, are associated with p values of 1.5 hpa. Figure 15 confirms that this pressure difference is related to the wind-speed difference across Gaudergrat. Cases when ρ 0 u 2 /2 > 0 correspond to cases of hill-induced flow separation downwind of the crest and reduced wind speeds at site 06. Significantly fewer positive values of ρ 0 u 2 /2 are calculated for cross-ridge wind-speed differences between measurements at sites 10 and 02, where the flows are purely along-valley. Easterly ridge-crest wind speeds are less well correlated with p (R 2 = 0.22). This reflects the independence of p and ρ 0 u 2 /2 between sites 08 and 07 shown in Figure 11. Conversely, easterly crest-wind speeds are well correlated with the cross-ridge values of ρ 0 u 2 /2(R 2 = 0.77). These results are consistent with the suggestion that easterly cross-ridge flows at the crest are associated with speed-up of flow along the east slope (Section 6.2). The easterly crest-wind speed increases with upwind flow speed at site 06, while for strong crossridge flows, wind speeds downwind at site 08 are reduced as a result of flow separation. Figure 10 shows an example of this process. The lack of correspondence between the variation of the ridge-crest wind speed with p and ρ 0 u 2 /2 for easterly and westerly ridge-crest wind directions also suggests that different mechanisms account for the two flow conditions. We therefore propose the following mechanism to account for westerly cross-ridge flow across Gaudergrat. A schematic illustration is provided in Figure 16. Alongvalley flow past Gaudergrat is driven in the east and west r u 2 /2 (hpa) -1.5 Easterly Westerly u ridge-crest (ms -1 ) Easterly Westerly u ridge-crest (ms -1 ) Figure 15. Correlation between 1 min-mean ridge-crest 2 m wind speed at site 07 and the cross-ridge difference in flow-induced pressure perturbation p and Bernoulli parameter ρ 0 u 2 /2, calculated between sites 08 and 06. For easterly crest winds, u crest < 0; for westerly crest winds, u crest > 0. valleys by synoptic-scale or thermally-induced pressure gradients, with wind speed in the east valley increased relative to that along the west valley (ρ 0 u 2 /2 < 0). This is due to the difference in valley geometries, perhaps because the east valley is considerably narrower and shallower than the west valley, encouraging flow convergence and acceleration in the east valley. The cross-sectional areas of the east and west valleys along the central transect shown in Figure 3 are estimated to be at least 46 km 2 and 0.17 km 2 respectively. The effect of this areal difference will be accentuated for southerly flows by the steeper valley-surface elevation along the east valley. The faster-flowing airstream in the east valley generates low pressure relative to the slower west-valley flow. This pressure difference has

15 OBSERVATIONS OF CROSS-RIDGE FLOWS 815 little influence within each valley, where the flow is constrained by the topography and driven by alongvalley acceleration. In contrast, the ridge crest forms the boundary between the two airstreams, and is a region of considerable cross-ridge pressure gradient, which induces strong flow perpendicular to the ridge crest. Similar phenomena might be expected to occur in other steep-terrain environments where differences in valley geometry or surface properties exist on each side of a ridge. In summary, the Gaudex measurements have highlighted cross-ridge flow at the ridge crest perpendicular to flow directions in either valley. Easterly cross-ridge flows originate from flow deviating as speed-up accelerates the ridge-normal component of incident flow. Westerly cross-ridge flows are driven by a cross-ridge pressure gradient that develops in response to faster along-valley flow in the smaller east valley. Note in particular that the two mechanisms identified here depend only on two commonly-occurring features of steep orography: preferential topographic channelling on one side of the ridge, and speed-up at the crest. It can therefore be expected that the cross-ridge flow phenomena observed here occur much more widely. A modelling study, although challenging and at the limit of current capabilities to represent flows over steep orography, could begin to explain the circumstances under which each of the two mechanisms dominates. This would need to be supported by observations at other sites. 7. Conclusions Measurements from a dense surface AWS network deployed during the Gaudex field campaign, complemented by sodar and radiosonde data, have been analysed p U crest U - p + U + p - WEST p U crest CREST EAST U upstream p upstream Figure 16. Schematic illustration of a cross-ridge flow mechanism observed across Gaudergrat inducing westerly flow perpendicular to the ridge towards a valley of faster-flowing (U + ), lower-pressure (p ) air. to investigate new observations of ridge-normal crossridge flows in the vicinity of steep terrain. This locallydriven feature develops at the ridge crest even when the flow in each valley is oriented parallel to the ridge axis, independent of whether that flow is thermally or synoptically driven. This can lead to large changes of wind direction within only 50 m of the crest. Calibrated pressure measurements indicate that the westerly cross-ridge flow is accelerated by a pressure difference across the ridge crest of up to 1.5 hpa within a horizontal distance of 100 m. This pressure gradient is a result of the local terrain shape, with the ridge forming a boundary between faster along-valley wind speeds within the narrower, steeper east valley and slower flow in the deeper, broader west valley. Cross-ridge pressure gradients are therefore well correlated with differences of ρ 0 u 2 /2 between the two valleys. Easterly cross-ridge flows originate from flow speed-up accelerating the ridgenormal component of incident flow, and are associated with a region of flow separation in the lee. The factors identified from the Gaudex observations as driving the cross-ridge flows are sufficiently generic that they are likely to be of relevance in other regions of complex terrain where steep terrain separates valleys with differing geometry. A systematic modelling study is required to further investigate the cross-ridge flow mechanism and assess the importance of the factors identified in this study to explain its occurrence. This would depend on an extremely accurate reproduction of thermally-driven flows, however, and would be at the limits of the numerical resolution and physical modelling currently possible. Ongoing work to model the wind flow over Gaudergrat provides some preliminary evidence that the crossridge flow feature can be simulated (e.g. Lehning et al., 2008), although these simulations are highly dependent on boundary conditions and are not time-dependent. More developed modelling of thermally-driven flows has been successful for much less steep terrain than Gaudergrat only when all the significant contributions to the surface energy balance are accurately modelled (e.g. Chow et al., 2006). Analysis of measurements in environments with similarly complex terrain would also shed light on the significance of cross-ridge flows in other regions of steep terrain. Acknowledgements The authors are indebted to the large number of staff and students from the University of Leeds, the Swiss Federal Institute for Snow and Avalanche Research and the University of Innsbruck for their involvement in the Gaudex field campaign. This study would not have been possible without their commitment and hard work. Particular thanks are due to Martin Hill, for developing much of the instrumentation, and to Barbara Brooks, Norbert Raderschall, Thomas Exner and Francoise Faure, for their contributions. The work was funded by the Natural Environment Research Council (NERC). H. W. Lewis was