1. Introduction
The Momentum Budget over the Pyrenées (PYREX) experiment took place around the Pyrenean chain during October and November 1990. It was devoted to the study of the dynamical influence of the Pyrenees on the atmospheric circulation. The program and the scientific purposes were decribed by Bougeault et al. (1990) and some preliminary first results were presented by Bougeault et al. (1993). One of the main purposes was the study of lee waves. The third intensive observation period (IOP3), occurring between 1800 UTC 14 October 1990 and 1200 UTC 15 October 1990 was precisely a case of strong lee waves induced by a south to southwesterly wind over Spain and France. Thanks to the particular shape of the Pyrenees, the locations where the different instruments operated, and the fact that the incident wind was very close to the chain transect during the whole IOP3, the data could be analyzed and interpreted using the 2D approximation. This means that the wave structure in all vertical planes perpendicular to the crest line is maintained.
The theoretical aspects concerning lee waves can be summarized as follows. When the wind is perpendicular to a mountain chain, the air accumulation on the upwind side creates a high pressure zone, which slows down the incident flow. Part of the air is deflected upward, giving rise to mountain waves. In the context of the 2D linear theory [see Scorer (1949) or, more recently, Atkinson (1981)], when the Scorer parameter vertical profile, that is, the ratio of the atmospheric stability to the horizontal wind, increases with the height or is roughly uniform, this wave radiates upward and downwind. In this case, the air motion amplitude very rapidly decreases from the crest, following the horizontal direction, thus leading to a short wave horizontal extent. On the other hand, if the Scorer parameter decreases with the height, the wave is reflected downward and some wave energy can be ducted, creating a train of waves extending several wavelengths downstream of the mountain. In such conditions the wave is called a trapped lee wave. In any case, if the upstream atmospheric conditions are constant in time, these waves are stationary, which means that the wave field is still, relative to the ground. Otherwise, there is a possible vertical propagation for the nontrapped case (e.g., Lott and Teitelbaum 1993) or a horizontal propagation for the trapped case (Ralph et al. 1992a). A more detailed discussion about the gravity wave duct existence and its dependence on the atmospheric stability and wind vertical profiles, is given, for example, by Chimonas and Hines (1986), Fritts and Yuan (1989), and Ralph et al. (1993a).
Our purpose is to give a description in space and time of the lee wave that occurred during the IOP3 and to show that a very high frequency stratosphere-troposphere (VHF ST) radar installed in a suitable site is an efficient tool for determining the vertical structure and stationarity of the mountain waves. We will consider the wave system to be quasi-stationary as soon as its motion with respect to the ground, also called wave drift, is sufficiently slow to induce no significant radar data temporal variation. Airborne data are used to give, at different altitudes and times, the position, the wavelength, and the vertical velocity amplitude of the lee wave, whereas radar data allow the temporal variability of the wave field to be studied from a fixed site. The upwind air mass characteristics are obtained from radiosoundes. It is noticeable that all the experimental results presented below can be interpreted in terms of orographically induced processes only, since no strong meteorological perturbation, such as a surface front, upper-level front, or cutoff low passage, occurred during the period studied.
Lee wave observations using VHF ST radars installed in very different kinds of mountainous areas have been intensively reported (e.g., Ecklund et al. 1982; Ecklund et al. 1985; Balsley and Carter 1989; Sato 1990). In those papers radiosounding data were used for the geophysical interpretation of the radar data. In particular, Ralph et al. (1992a) have already shown that the vertical profiles of vertical air motions measured by ST radars in the lee of mountains provided a method for continuously monitoring the vertical structure of lee waves. Here it is proposed to significantly extend similar conclusions.
The main originality of the present paper concerns the use of data from two VHF ST radars, one located on the mean crest line and the other one 35 km downwind in the lee wave field, to investigate the stationary nature of the wave event. To our knowledge, this is the first time such a comparison has been made. Another originality is the intercomparison of the measurements of the vertical air motion obtained independently by VHF ST radar, aircraft, and constant volume balloons. This constitutes further experimental results relevant to the debate over the reliability of direct measurement of vertical air motion by ST radars during lee wave events.
2. Experimental technique
Upstream radiosoundes (RS), made every 6 h at Saragoza, Spain, 120 km south of the mean crest line, allowed horizontal wind speed and atmospheric stability profiles, and consequently Scorer parameter profiles, to be obtained.
For all the other instruments presented below, the relevant parameter used is the air vertical velocity W. The reason for this choice is that this quantity properly reflects the lee wave structure and is measured by all the instruments at different times and/or locations. Therefore, among all the quantities that have been measured, only the experimental accuracy and the reliability of W measurements are discussed.
Aircraft measurements made along the Pyrenean chain transect documented, at a given time and altitude, the horizontal structure of the wave, which, thanks to the high aircraft speed, is considered to be frozen. Indeed, the horizontal transect B1–B4 (see Fig. 1 and Fig. 2) is 200 km long. With an aircraft velocity of 100 m s−1 one pass across the mountain range took 30 min along the wind direction and 40 min in the opposite sense, whereas one pass across the lee wave field, which is about 40 km long, took 6–8 min. Aircraft measurements of W within a lee wave field have already been reported by Cruette (1976). In the present study the research airplane Fokker 27 ARAT (Avion de Recherche Atmosphérique et de Télédétection, a teledetection and atmospheric research aircraft) operated by a group of French institutes [Centre National d’Etudes Spatiales (CNES), Institut National des Sciences de l’Universés (INSU), Météo-France, and Institut Geographique National (IGN)] is used. It is equipped with a 5-m-long nose boom on the tip of which are installed the fast-response sensors. They consist of a Rosemount 858 probe that measures static and dynamic pressure, and attack and sideslip angles. An inertial navigation system (INS) installed close to the aircraft center of gravity measures the aircraft horizontal geographical position, the ground velocity vector, and the attitude angles of the aircraft (pitch, roll, and true heading). The vertical velocity is deduced from the air speed, attack, and sideslip angles; aircraft attitude angles; and vertical acceleration (Attié 1994; Druilhet et al. 1978). The W measurement’s absolute accuracy is estimated to be 0.5 m s−1. The data were originally acquired at 32 Hz but those used here have been averaged over 1 s. Four flights, A1, A2, A3, and A4, are taken into account in our study.
Several previous studies have demonstrated the capabilities of constant volume balloons (CVB), also called constant level balloons, to analyze the properties of lee waves (occurrence, location, strength) above complex mountains such as the Alps (Gerbier and Bergenger 1961), White Sands Missile Range (Reynolds et al. 1968), and the central Colorado Rocky Mountains (Vergeiner and Lilly 1970). Here, two CVBs described by Benech et al. (1987) and launched from the Pic du Midi gave Lagrangian measurements by following the airstream perturbed by the wave. They were tracked by a radar in Lannemezan 28 km north of their launch site. As for the aircraft, the W measurement’s absolute accuracy is 0.5 m s−1, whereas the time resolution is 10 s. The data from two flights, CVB1, and CVB2, are used here.
Two VHF ST radars observed in a fixed vertical direction the temporal evolution and the vertical distribution of the vertical velocity field. The first one located on the crest is called crest radar (CR) and the second one to the north of the Pyrenees, thus below the lee wave field, is called lee radar (LR). Details concerning the physical and technical aspects relative to ST radar wind measurements have been described by Gage and Balsley (1978), Larsen and Röttger (1982), and more recently by Crochet (1990). In summary, W is estimated from the frequency corresponding to the mean Doppler shift obtained in the radar vertical echo. The W-estimation error depends upon the signal to noise ratio, which itself depends upon the altitude investigated, the vertical and time resolution, and the frequency resolution of the corresponding Doppler spectrum. For tropospheric measurements made with a signal to noise ratio greater than 0 dB, the estimation error of the Doppler shift frequency relative to the frequency resolution has been found to be between two-thirds and one (Yamamoto et al. 1988; Ferrat and Crochet 1994). The two radars involved in the present study were of the same type but not in the same experimental conditions, therefore the corresponding estimation errors were not the same. Although details concerning the CR and LR experimental conditions will be given in sections 3b(1) and 3b(2), respectively, it can be immediately noticed that the W-estimation errors were about 3–4 cm s−1 for CR and 20–30 cm s−1 for LR. For other purposes than lee wave investigations, such an accuracy was suitable for ST radar dynamic studies of vertical motions in various mesoscale atmospheric phenomena such as a jet stream (Gage and Clark 1978), a strong extratropical cyclone (Crochet et al. 1990), or gravity waves of frontal origin (Ralph et al. 1993a; Ralph et al. 1993b). Actually, for our purpose, we are more interested in the overall errors made in the lee wave amplitude measurement than in the W-estimation errors only. This overall error bar includes not only the W-estimation error but also the W-fluctuation range due to the background vertical motions that always exist independantly of lee waves. For both the radars used here, the overall error bars were 20 cm s−1 for CR and 40 cm s−1 for LR [see 3b(1) and 3b(2), respectively, for the evaluation method].
The problem of VHF ST radar W-measurement errors, due to off-horizontal tiltings of the backscattering and/or reflecting layers, is currently discussed (e.g., Larsen and Röttger 1991; Larsen et al. 1991; van Baelen et al. 1991; Yoe and Rüster 1992). During a lee wave event such tilted layers may sometimes exist above the radar but previous studies using UHF and VHF data comparison have shown that the W estimation is actually not too contaminated (MacAfee et al. 1994; MacAfee et al. 1995). As will be seen in section 4b, it was also the case here. Furthermore, for stationarity investigations, we are less interested in the accurate W values than their temporal variations. Roughly, if the wave is quasi-stationary, the backscattering layer is fixed with respect to the ground and the W values, even biased, are constant in time.
In short, under a quasi-stationary regime, the radar W profiles are nearly constant in time. On the other hand, as long as the wave is unstationary, significant temporal variations are observed. The quasi-stationary nature of the waves can be investigated using radar data but, as already explained, cannot be directly related here to upstream condition variations.
The geographical coordinates of the relevant sites taken into account in our analysis are reported in Table 1. A topographic map of the Pyrenees, showing those relevant sites, is given in Fig. 1, whereas the orographical situation of the radars and the space–time position of the airborne measurements, using a horizontal projection on the vertical plane above the chain transect, are shown in Fig. 2. The acronyms noted in these figures are those presented above. The chain transect used here is the ground vertical projection of the aircraft flights (see the B1B4 dotted line of Fig. 1). Finally, the chain mean axis, or the mean crest line, is taken as the straight line that is perpendicular to the chain transect and that passes over the CR installation site (see the dashed line of Fig. 1).
3. Experimental results
a. Radiosounding and airborne measurements
The experimental results obtained by RS, CVB, and aircraft have already been reported and analyzed by Attié (1994) and Benech et al. (1994). They have been interpreted in the context of the 2D linear theory. A good agreement, in time and altitude, was found between the horizontal wavelengths measured by the airborne instruments and those calculated from the upstream Scorer parameter profiles deduced from RS. The three available profiles are presented in Fig. 3. Those obtained at 0000 UTC and 0600 UTC were compatible with a trapped lee wave situation since a decrease of the Scorer parameter with the altitude was found, essentially due to an increase of the wind, that is, from less than 16 m s−1 below 3000 m to more than 25 m s−1 above 6000 m. As a confirmation, a wave horizontal extent of 55 km was observed from the crest by the A1 flight almost at the same time as the 0600 UTC RS. On the other hand, the 1200 UTC profile shows that the lee wave was no longer trapped and its amplitude was thus weaker when observed downstream. It should be noticed that the Scorer parameter was calculated by neglecting the curvature of the horizontal wind vertical profile. This approach is quite sufficient here, since we are more interested in a mean behavior of the Scorer parameter profile than in a very accurate one with a high vertical resolution. The Scorer parameter profile obtained from the 0600 UTC RS, calculated with a 500-m vertical resolution and using the curvature term has been presented by Tannhauser and Attié (1995). That profile resampled every kilometer is close to that of Fig. 3b, which a posteriori justifies our simple calculation.
Between 0600 UTC and 1030 UTC, the airborne instruments measured maximum amplitudes in the 3–5 m s−1 range for the air vertical velocity.
A lee wave parameter used in our study is the horizontal extent of the train of waves observed downstream of the mountain. Here, this wave horizontal extent was measured from the mean crest line using the W values obtained along each airborne instrument flight and presented in Fig. 2. In this same figure, the limits of the train of waves are indicated by the thick vertical dashes. For each flight, it was determined to be the first location where W reached zero immediately after the last significant wave crest, be it positive or negative. As shown in Fig. 2, the values obtained reveal that, during the airborne measurements, the radar LR was below the wave field most of the time, except maybe around 1000 UTC, which corresponds to the CVB2 and A4 flights. All the lee wave parameters obtained from the four aircraft flights and the two constant volume balloons are reported in Table 2.
To study strictly temporal variations and to avoid any ambiguity in their interpretation due to possible vertical variations, only the airborne measured values obtained in a same altitude range should be taken into account. Such is the case here for CVB1, A3, A4, and CVB2, since their measurements were made in a same atmospheric layer of about 1000-m thickness (see Table 2). For these flights, the observed temporal variations of the wavelength, the amplitude, and the wave horizontal extent are significant. Wave crest position variations with altitude and time were also observed between successive flights (see Fig. 2). Those observed nonstationarities may be interpreted as changes in characteristics associated with a given type of wave, trapped or nontrapped, but also with transitions between those two regimes. Such behavior was already reported by Ralph et al. (1992a) and Ralph et al. (1992b), in case of two different situations of trapped lee wave above two very different kinds of mountainous area. In any case, time variations for the upstream Scorer parameter profile should be simultaneously observed. Unfortunately, such an RS profile was only obtained every 6 h, which is obviously too infrequent to be directly related to the airborne data. Nevertheless, the difference between the 0600 UTC and the 1200 UTC profiles proves that nonstationarities should have occurred during this time interval. This difference was due to variations of the cross-mountain wind speed and the static stability, which is calculated here as the Brunt–Väisälä pulsation. The situation observed by RS can thus be summarized: 1) the cross-mountain wind speed, at 0600 and 1200 UTC, was, respectively, 17 and 21 m s−1 at 4000 m, and 25 and 23 m s−1 at 6000 m, whereas it remained constant with a value of 12 m s−1 at 1000 m; 2) with respect to the same times, the static stability was 0.017 and 0.007 rad s−1 at 1000 m, and 0.013 and 0.011 rad s−1 at 6000 m; and 3) the upstream wind direction range was 210°–240° at 0600 UTC, whereas it was 180°–210° at 1200 UTC. These results, consistent with those obtained downstream by the airborne instruments, indicate that a temporal variation of the upstream conditions is a possible cause of the lee wave nonstationarities. The same conclusion was drawn by Tannhauser and Attié (1995) on the basis of the same airborne data but analyzed to study the impact of the nonstationarities on the momentum flux profile.
Recently, it was also established by Bogar Nance (1995) from numerical simulations that observed lee wave nonstationarities may be produced by nonlinear instabilities leading to wave amplitude temporal variations even if the upstream atmospheric conditions are constant with time. This possibility is mentioned here but is not actually discussed since variations of the upstream profile were observed.
b. ST radar measurements
1) The crest radar (CR)
The Centre National des Recherches Meteorologiques (CNRM) VHF ST radar of 45-MHz frequency (Petitdidier et al. 1990) CR was installed at St. Lary almost exactly on the Pyrenees’ mean axis (see Fig. 1). This location was nevertheless in a valley, which explains its low altitude, 600 m, compared with that of the mean crest, 2800–3300 m. A vertical profile of W was obtained every 12 min using vertical complementary high and low resolution modes, 375 m below 8 km and 2250 m above 8 km, respectively, these values being due to pulse widths of 2.5 and 15 μs, respectively. On the other hand, the gate length was always of 2.5 μs, leading to an overlapping of the radar cells and to a smoothing of the W-vertical profiles above 8 km of altitude. The detection range was between 1600 and 15 100 m. The altitude range above 2725 m is only presented to avoid ambiguous data interpretation locally due to the valley influence. The horizontal resolution for the W measurement is given by the radar beamwidth, here 5.5° at −3dB, and ranged from 260 m, at 2725 m of height, to 1450 m at 15 100 m. The corresponding W time series are shown in Fig. 4. Knowing that the Doppler spectra were calculated on 256 points corresponding to W values extended from −5.0 to +0.5 m s−1 and that up to 8 km of altitude the signal to noise ratio remained greater than 0 dB, the W-estimation error was, at least for this altitude range, between 3 and 4 cm s−1.
Classic W profiles above the crest in mountain–lee wave event, be it trapped or vertically propagating, exhibit negative W values in the first height range above the crest. Earlier mesoscale studies, such as those of Queney (1948), Sawyer (1960), and several others reviewed in the works of Gossard and Hooke (1975), Atkinson (1981), or Gill (1982), have shown this behavior when both the lee wavelength and the mountain width are in the mesoscale range, that is, from a few kilometers to a few tens of kilometers, which is precisely the case in our study. At these scales, all the air flow simulations presented in these works exhibited downward motion in the first height range above the crest due to the upstream tilt of mountain waves with height. This result is still usually obtained by numerical simulations using recent 2D nonhydrostatic models (e.g., Yang 1993). Besides, such simulations have been made in the particular case of the IOP3 of PYREX, using the 0600 UTC upstream RS of Saragoza and, as expected, the same behavior was obtained (Elkhalfi and Carrissimo 1993; Satomura and Bougeault 1994). It should nevertheless be noticed that such a behavior is theoretically obtained for idealized, smooth orography. The real topography of the Pyrenean chain is, of course, more complex (see Fig. 2), and some apparent inconsistencies between the theory and the experimental results are a priori not excluded.
The altitudes above the crest corresponding to W sign shifts are of high interest since they are directly related to the upstream atmospheric conditions. The altitude range, including respective positive and negative W values as a function of time, was computed from the CR data presented in Fig. 4. Figure 5 shows this experimental result in a height–time cross-section representation. The NO_WAVES-period, from 1800 to 0040 UTC, is so called because W is positive immediately above the crest, which is incompatible with a lee wave situation. It is precisely from the data obtained during this period, thus relative to an atmospheric situation not perturbed by lee waves, that the overall error bar on the mountain wave amplitude measurement was estimated. This error was actually given by the standard deviation of the W values, calculated from 1800 UTC to 0040 UTC and averaged for the four time series obtained between 2725 and 3850 m of altitude, that is, for the time series corresponding to W successive values without any change of sign (see Figs. 4 and 5). A value of 23 cm s−1 was exactly found but, for our purpose, a 20 cm s−1 value can be noted.
After 0040 UTC and until 1120 UTC, the data indicate that the wave system is established, except for the 0840–0945 UTC time interval where they suggest that the wave regime temporarily stopped. Nevertheless, during the same period, the A3 flight detected lee wave activity (see Fig. 2). This inconsistency is probably an example of the problem due to the real topography of the Pyrenees. A transition regime, between 0005 and 0040 UTC, is also visible and suggests an upward air motion from the crest to the radar detection altitude limit. In the same figure, C1, C2, and C3 indicate periods longer than 48 min during which the vertical distribution of the sign of W is constant with time according to an accuracy of 750 m, that is, ±375 m. This suggests the lee wave was quasi-stationary within these periods, on the basis of our assumption that wave field motion was sufficiently slow to produce no significant radar data time variations. These periods were objectively found as corresponding to series of at least four successive vertical profiles for which the altitudes where a W sign shift is observed remained in the same 750-m interval.
2) The lee radar (LR)
The Laboratoire des Sondages Electromagnetiques de l’Environnement Terrestre (LSEET) VHF ST radar (Crochet 1990) LR of the so-called Platteville radar type was installed at Lannemezan, 35-km north of the mean crest line, where it was almost always below the lee wave field (see Figs. 1 and 2). The data consist of radar measurements of W with a VHF radar frequency around 45 MHz, a pulse length of 5 μs and 28 gates of 5 μs length. A W vertical profile was obtained, every 4 min 50 s, from 1500 to 21 750 m of altitude with a vertical step and resolution of 750 m. In our study we used data obtained from 2250 to 15 000 m, which is a range where the data were not contaminated by receiver saturation effects and a too-weak signal to noise ratio. The horizontal resolution for the W measurement is given by the radar beamwidth, here 5.5° at −3 dB, and ranged from 200 m, at 2250 m of height, to 1450 m, at 15000 m. Knowing that the Doppler spectra were calculated on 64 points corresponding to W values extended from −9.7 to +9.7 m s−1 and that up to 9 km of altitude the signal to noise ratio remained greater than 0 dB, the W-estimation error was, at least for this altitude range, between 20 and 30 cm s−1.
For the height range studied, and during the whole IOP3, the time series of W are shown in Fig. 6. Maximum W amplitudes of 5–6 m s−1 are recorded between 3750 and 5250 m at 0145 UTC, between 4500 and 5250 m at 0430 UTC, and between 3000 and 4500 m at 0645 UTC. From 0600 to 1030 UTC, the maximum W values obtained by LR were very close to the maximum wave amplitudes obtained by the airborne instruments. More particularly, the W time series of Fig. 6 show significant time variations that occurred simultaneously, coherently, and without any vertical sign shift in the 2250–9000-m altitude range between 2315 and 0230 UTC, and between 0330 and 0830 UTC. It means that, for these periods, the wave moved horizontally and had quasi-vertical wave fronts, which was also found by numerical simulations (Elkhalfi and Carrissimo 1993; Satomura and Bougeault 1994). As already shown by Ralph et al. (1992a), this behavior can be interpreted as the signature of a trapped lee wave. As a consequence, we can vertically average the time series without smoothing the temporal variations, at least for these height and time intervals. In order to avoid attenuating the W-values too much, only the first six time series, that is, up to 6000 m, are taken into account in the average. These averaged values as a function of time are presented in Fig. 7.
This time, the NO_WAVES period corresponds to small W values, ranging from −40 to 40 cm s−1, classically observed by ST radars installed close to a mountain range such as the Pyrenees when no wave disturbs the atmospheric situation. This range of values is directly related to the overall error bar on the lee wave amplitude measurement, which is this time estimated by the standard deviation of the W time series obtained between 2250 and 9000 m during the NO WAVES period. A value of 43 cm s−1 was exactly found but, for our purpose, a 40-cm s−1 value can be noted and used.
On the other hand, the period of wave activity, where the W values are much stronger than + or −40 cm s−1, is well identified between 2315 and 0840 UTC and less apparent after. In Fig. 7, L1, L2, L3, L4, and L5 indicate the time intervals, included in the wave activity period and longer than 35 min, during which W is constant according to a −40 to 40 cm s−1 possible fluctuation range and thus quasi-stationarity is suggested. This time, such periods correspond to series of at least seven successive averaged W values so that their fluctuations remain in the same 80-cm s−1 interval.
In Fig. 6, no wave activity is clearly visible above 11250 m, which means, using the interpretation of Ralph et al. (1992a), that vertically propagating episodes did not clearly occur. This suggests that, during the IOP3 of PYREX, the Pyrenees have essentially forced trapped lee wave modes.
4. Data comparison and geophysical discussion
The W values obtained by all the instruments were generally found to be in agreement, taking into account their features, locations, and acquisition times (Bougeault et al. 1993). In this section we present a more detailed data comparison, allowing a geophysical discussion.
a. Lee radar/crest radar data comparison
The first comparison between both radars concerns their detection of the wave and no wave periods. As already mentioned, LR continuously detected wave activity from 2315 to 1200 UTC (see Figs. 6 and 7). On the basis of the assumption that observations of downward motions immediately above the crest reveal the presence of lee waves, CR detected wave activity from 0040 to 0840 UTC and from 0945 to 1120 UTC (see Fig. 5). For the comparison, a time lag must be considered between the data, corresponding to the delay for the train of waves to reach downstream the vertical above LR from the vertical above CR. This delay is derived from the velocity of propagation of the wave energy, that is, the group velocity. Using the values of the lee wave number k, the incident wind U, and the Scorer parameter l, averaged between 2300 and 1200 UTC and in the 1000–6000-m altitude range, the horizontal component Vgx of the group velocity is found to be very close to 50 km h−1. Such a value is obtained from the classic expression Vgx = Uk2/l2 valid in nonhydrostatic cases (e.g., Stein 1992). Since the downstream distance between CR and LR is 35 km, a time lag of 40 min is to be taken into account to cross compare the wave and no wave periods detected by both the radars. A total of 3 h 15 min of CR data are found to be inconsistent with the theoretical behavior of the W profiles above the crest. As already explained, these inconsistencies, which occur during 21% of the total period studied, are probably due to the real topography of the Pyrenees. Nevertheless, the good agreement obtained for 79% of the radar data consitutes an encouraging result concerning the ability of an ST radar located on a mountain crest to detect lee wave activity.
Although the duration of C1 was roughly the double of L2, general agreement is found concerning the simultaneous detection of the C1, C2, and C3 periods of Fig. 5 and the L2, L3, and L4 periods, respectively, of Fig. 7. Their time locations and durations are clearly visible in these figures and a rather good agreement is found between them. Clearly, the periods during which W kept the same sign, at a given altitude above the crest, coincided rather well with the periods of quasi-stationarity observed in the lee of the mountain.
The quasi-stationarity found by LR during the L5 period of Fig. 7 is only apparent and partly due to the averaging made on the data. At that time there were vertical W sign shifts that caused the small averaged values in the corresponding interval. Besides, around 1000 UTC the A4 and CVB2 flights found the wave horizontal extent at 31–33 km to the north from the mean crest line, whereas the LR ground position is at 35 km. This can explain that, even without averaging, W values are not very high. Note that the L1 period corresponds to W values included in the 21% of inconsistent CR data already discussed.
b. Airborne instruments–lee radar data comparison
At a given time, the wave field is assumed to be two-dimensional and the wave fronts were found by LR to be vertical planes. Therefore the W values measured by the airborne instruments can be compared to those measured by LR using a projection following a horizontal direction parallel to the wave fronts. According to the 2D linear theory, this direction should not be far from being parallel to the mountain mean axis. Nevertheless, for local comparisons, a possible deviation from this direction is to be considered. In details, for a given direction, the vertical plane parallel to this direction and that contains the radar beam was determined. The data obtained at the intersections between this plane and the six airborne instrument paths were compared to those obtained by the radar at the corresponding time and altitude. The most favorable comparison should be found when the direction tested is that of the actual wave front, since in this case, at a given altitude, the wave amplitude should be the same, and both the radar and airborne corresponding data should thus be very close. To make this comparison objective, the root-mean-square (rms) difference between the set of the six airborne data and that of the six corresponding radar data was calculated. It has been made for a set of possible horizontal directions corresponding to angles ranging from −40° to 40°, with a 5° step and using an east-to-north rotation around the mountain mean axis direction. The result of these successive calculations is shown in Fig. 8. The best agreement between both the datasets was found for an angle of −5° for which a minimum rms value of 0.58m s−1 was obtained. The direction corresponding to this angle and the mountain mean axis direction are indicated, respectively, by the dotted and dashed lines of Fig. 9. In this same figure, the projections onto a horizontal plane of the aircraft and balloon paths are depicted in full lines, whereas the mean radar beam is shown by the thick black circle.
Using the projection direction shown by the dotted line of Fig. 9, the LR W values were then compared to the airborne measured values. The result of this comparison is shown in Fig. 10. As for the previous rms calculation, the airborne W values used for the comparison were obtained by averaging data over intervals equivalent to the radar beamwidth, ranging from 200 to 600 m and from 2250 up to 6000 m, respectively. By taking into account the measurement error bars, that is, 0.5 m s−1 for the airborne instruments and 0.4 m s−1 for the radar, a good agreement is objectively found regarding the rms difference minimum value of 0.58 m s−1 previously calculated. This agreement, obtained for each flight time and at the local scale studied, allows the assumption of vertical wave fronts parallel to the mountain mean axis to be a posteriori reasonably justified, which is consistent with the 2D linear theory. Here, the local scale is the horizontal distance between the radar vertical lobe and the flight paths, and ranges from 2.5 km for the closest flight, A3, to 7.5 km for the farthest, CVB2. This agreement also suggests that the possible contamination by lee waves of the W measurement did not strongly appear in the data presented here.
c. Lee wave detailed description around 0600 UTC
The best period for a detailed description of the wave is around 0600 UTC since the RS, A1 flight, CR, and LR data are simultaneously available. At that time RS and A1 suggest a trapped lee wave, whereas CR and LR indicate a quasi-stationary regime, from 0550 to 0635 UTC (see C3 in Fig. 5) and from 0610 to 0655. UTC (see L4 in Fig. 7), respectively. The horizontal wavelength, the amplitude, and the wave horizontal extent, measured at 4950 m of altitude, were 10 km, 3.9 m s−1, and 55 km, respectively. Furthermore, the W time series presented in Fig. 6 also reveal that the wave fronts were vertical planes that moved horizontally above the LR installation site, from 0330 to 0840 UTC. This conclusion can be drawn since, as already noted, the significant W-time variations occurred simultaneously, coherently, and without any vertical sign shift. Such a behavior shows that the atmosphere acted as a duct from at least 2250 m and up to 7500–9000 m of height, which constitutes a trapped lee wave signature.
5. Conclusions
The lee wave that occurred during the IOP3 of PYREX has been described in space and time thanks to the air vertical velocity measured by an aircraft, two constant volume balloons, and two VHF ST radars suitably installed. The two radars observed the temporal evolution and the vertical structure of the wave above the mean crest line with a time resolution of 12 min for the first one and directly in the lee wave field with a time resolution of 5 min for the second one. The airborne instruments documented the lee wave horizontal structure every hour.
The wave activity was detected from the radar installed downstream when an increase of the vertical velocity was observed, that is, for values much greater than 1 m s−1 instead of less than 0.5 m s−1 when no lee wave disturbs the air flow. For the radar installed on the mean crest line, a technique to identify wave activity by the presence of downward vertical motion immediately above the crest altitude was tested. Although that test was made on an 18-h period only, a favorable comparison with the observations made by the other radar and the airborne instruments was found for about 79% of the IOP3 duration. The remaining 21%, that is, the inconsistent data, should probably be due to the fact that the Pyrenees do not have an idealized, smooth topography such as that used in the theory. The comparison between the data simultaneously obtained by both the radars allowed the identification of three periods of quasi-stationarity of 35–90, 80, and 45 minutes’ duration. For timescales longer than 45 min, and except for the three previous cases, the lee wave was found to be very nonstationary. The data from the airborne instruments showed that the nonstationarity observed by the radar installed below the lee wave field were mainly due to time variations of the wavelength but also of the amplitude and the wave horizontal extent.
During most of the lee wave activity period, this same radar observed temporal variations of the vertical velocity that coherently and simultaneously occurred for all the altitudes investigated between 2250 and 7500–9000 m. As already interpreted by Ralph et al. (1992a), this behavior is the signature of a trapped lee wave having vertical wave fronts and horizontally propagating in a tropospheric wave duct. In our case study, no wave activity was clearly obtained above 11 250 m of altitude, which suggests that the Pyrenees did not force a significant vertically propagating mode.
During the IOP3, three upstream Scorer parameter profiles were obtained every 6 h, which was obviously not frequent enough to be related to the direct experimental observations made by ST radar and by airborne instruments. A difference between the upstream conditions at 0600 and 1200 UTC was nevertheless obtained and due to changes in the cross-mountain wind speed and direction, and static stability. Furthermore, for the 0600 UTC-case, the upstream Scorer-parameter profile was found to be compatible with a trapped lee wave situation, which was no longer the case at 1200 UTC.
The data from the radar installed downstream and that from the airborne instruments were cross compared by assuming the wave fronts to be vertical planes. The most favorable comparison was obtained for wave fronts oriented in a horizontal direction very close to that of the mountain mean axis and for a root-mean-square difference between the data of the order of the instrumental error bars. These results a posteriori justify the assumption of vertical planes parallel to the mountain axis for the wave fronts and thus the use of the 2D approximation. These also constitute further experimental evidence of the reliability of the vertical velocity measurements by a VHF ST radar in a lee wave situation.
Finally, it should be noted that all the results presented here confirm the earlier conclusions drawn by Ralph et al. (1992a) about the ability of a VHF ST radar to monitor the vertical structure and the temporal variability of a lee wave, but that the present paper has extended those results through detailed intercomparison of data from two radars, four aircraft flights, and two constant volume balloons.
Acknowledgments
The PYREX experiment was made possible by the participation of a large number of institutes and funding agencies. The participating institutes are CNRM, CRPE, LA, LAMP, LMD, LSEET, SA, EDF, France; INM, UV, UIB, Spain; and DLR, Germany. Funding was provided by Météo-France, INM, INSU (ARAT, PATOM, and PAMOY programs), CNES, EDF, DLR, and Région Midi-Pyrénées. Much technical help was provided by CEV, ENM, and the French and Spanish Airforce and Air Control authorities. We would like to express our gratitude to J.C. André, D. Cadet, D. Guédalia, and A. Ascaso Liria for their help in the planning of this program. We also would like to express our deep appreciation to the many colleagues who have taken part in the success of the experiment through enormous personal commitment. We are finally indebted to P. Bougeault and D. Tannhauser for very helpful scientific discussions, and to F.M. Ralph and two anonymous reviewers for the very precise comments and suggestions made in the review of this paper.
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Geographical and topographical situation of the crest radar CR, lee radar LR (see the white disks), and the meteorological radiosounding station RS, of Saragoza (see the black disk). The ground vertical projection of the four aircraft flights is the B1–B4 dotted line, which is also the Pyrenean transect used in our study. The mean crest line, which is the straight line passing over CR and perpendicular to B1–B4, is shown by the dashed line. The wind direction during the IOP3 is schematically represented by the arrows. The three numbered white triangles indicate the location of the three main peaks, and their corresponding numbers, names, and altitudes are given in the upper left part. The scales used for the altitude and the horizontal distance representation are indicated in the upper and lower part, respectively.
Citation: Journal of the Atmospheric Sciences 54, 14; 10.1175/1520-0469(1997)054<1821:STDONT>2.0.CO;2
Orographic situation of the radar and airborne measurements using an orthogonal projection onto the vertical plane above B1–B4. The mean Pyrenean profile along the transect B1–B4, which is taken here as the x axis, is depicted in black in the lower part. The acronyms A1, A2, A3, and A4 refer to the first, second, third, and fourth aircraft flights, respectively, whereas CVB1 and CVB2 refer to the first and second constant volume ballon launched from the Pic du Midi (white triangle). Their UTC launch times are noted, as are the UTC times of the aircraft passages above B1 and B4. The four upper horizontal dashed lines and the superimposed small black arrows show the flight ways of the aircraft, the corresponding full line curves show the W successive values it measured, and the thick vertical dashes indicate the downstream horizontal extent of the train of waves it detected. Because the measurements were made in the same altitude range, that is, 3000–4000 m, two separate boxes are used for the representation of the W values measured by the balloons, CVB1 and CVB2. For all the airborne data, the scale used for the W values is indicated in the left part. The vertical dashed lines show the radar sounding directions, the radar name and position being shown by the two black triangles on the x axis. The upstream wind is schematically represented by the gray arrows. The altitudes are indicated in the right part along the y axis.
Citation: Journal of the Atmospheric Sciences 54, 14; 10.1175/1520-0469(1997)054<1821:STDONT>2.0.CO;2
Upstream Scorer parameter profiles obtained at Saragoza, Spain, during the IOP3 lee wave event. The profile values are indicated (in km−1) on the x axis and are calculated every km by averaging the RS data over a 1-km vertical window. The RS UTC times are indicated in the upper part. The first two profiles show a decrease with the altitude, whereas the third one is fairly uniform.
Citation: Journal of the Atmospheric Sciences 54, 14; 10.1175/1520-0469(1997)054<1821:STDONT>2.0.CO;2
The W time series obtained by CR from altitudes of 2725–15 100 m. The corresponding altitudes are indicated by the horizontal dashed lines associated with the values, in km, on the left part. These dashed lines also show, for each time series, the W = 0 straight line. The W scale, in m s−1, is given by the thick vertical dash superimposed on the left part of the lower time series. The W value corresponding to the separation between two successive dashed lines is 2 m s−1. The x axis indicates the time in UTC.
Citation: Journal of the Atmospheric Sciences 54, 14; 10.1175/1520-0469(1997)054<1821:STDONT>2.0.CO;2
Height–time cross section of W, measured by CR above the mean crest-line altitude (dashed line), in single isocontour plot. The isocontour value is W = 0. The shaded regions correspond to negative W values, whereas the white area is associated with positive W values. The NO_WAVES, C1, C2, and C3 periods are defined in the text. The thick vertical dash on the left shows the accuracy, here 750 m, for the estimation of the altitudes where W = 0. The x axis indicates the time in UTC.
Citation: Journal of the Atmospheric Sciences 54, 14; 10.1175/1520-0469(1997)054<1821:STDONT>2.0.CO;2
The W time series obtained by LR from altitudes of 2250–15 000 m. Same as in Fig. 4 except for the separation between two dashed lines, which is now 4 m s−1.
Citation: Journal of the Atmospheric Sciences 54, 14; 10.1175/1520-0469(1997)054<1821:STDONT>2.0.CO;2
Time evolution of W, measured by LR in the wave field, vertically averaged in the 2.25–6.00-km altitude range. The x axis indicates the time in UTC hours. The periods named NO_WAVES, L1, L2, L3, L4, and L5 are defined in the text. The thick vertical dash superimposed on the NO_WAVES data indicates the W fluctuation range, that is, −40 to +40 cm s−1. It is considered to be the noise level in W values obtained in the wave field.
Citation: Journal of the Atmospheric Sciences 54, 14; 10.1175/1520-0469(1997)054<1821:STDONT>2.0.CO;2
Values of the rms difference between the radar and the airborne W measurements for different possible orientations of the wave front from the mountain mean axis. The data taken into account are those that were obtained along different straight lines crossing at the same time and altitude the radar vertical beam and the path of the airborne instrument concerned. The angles corresponding to the horizontal direction of those vertical planes, and for which the rms value calculation were made, are indicated in the x axis. Positive values indicate a rotation of the wave front from east to north.
Citation: Journal of the Atmospheric Sciences 54, 14; 10.1175/1520-0469(1997)054<1821:STDONT>2.0.CO;2
Projection onto a horizontal plane of the radar vertical beam (shaded circle) and of the airborne instrument paths (full lines). The system is referenced from the lee radar ground position. The dashed line shows the direction parallel to the mountain mean axis, whereas the dotted line shows the direction rotated from −5° versus the mountain mean axis. It corresponds to the minimum of the rms difference obtained in Fig. 8.
Citation: Journal of the Atmospheric Sciences 54, 14; 10.1175/1520-0469(1997)054<1821:STDONT>2.0.CO;2
Comparison between the vertical velocity measured at the same time and at the same altitude by the lee radar (rectangles) and by the airborne instruments (vertical dashes) using the horizontal projection obtained from Fig. 8 and shown by the dotted line of Fig. 9. The x axis indicates the time of measurement in UTC hours. The airborne W values are the result of a data averaging over an interval equivalent to the radar beamwidth. The lengths of the rectangles and of the dashes correspond to the measurement error bars, + or −0.4 m s−1 for radar data, and + or −0.5 m s−1 for airborne data, respectively. The width of the rectangles indicates the time resolution, 4 min 50 s, of the radar measurements, whereas the thickness of the vertical dashes indicates the time necessary for the airborne instrument to travel over the averaging interval, that is, 4–8 s for the aircraft and 50–70 s for the constant volume balloons.
Citation: Journal of the Atmospheric Sciences 54, 14; 10.1175/1520-0469(1997)054<1821:STDONT>2.0.CO;2
Experimental setup geographical coordinates.
Lee wave parameters from airborne measurements.
