Alpine gravity waves: Lessons from MAP ... - Wiley Online Library

QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY Q. J. R. Meteorol. Soc. 133: 917–936 (2007) Published online in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/qj.103

Alpine gravity waves: Lessons from MAP regarding mountain wave generation and breaking Ronald B. Smitha *, James D. Doyleb , Qingfang Jiangc and Samantha A. Smithd a

b

Yale University, New Haven, Connecticut, USA Naval Research Laboratory, Monterey, California, USA c UCAR, Monterey, California, USA d MetOffice, Exeter, UK

ABSTRACT: The two-month special observing period of the Mesoscale Alpine Programme (MAP) in autumn 1999 included a variety of complex mountain wave events. Seven wave events were carefully analyzed, compared with numerical models and described in published papers. These detailed investigations revealed some common dynamical elements, i.e. the importance of low-level processes involving the slow-moving boundary layer, low-level wind shear causing either wave absorption or decoupling/spilling, upstream blocking, and latent heat release. Based on these studies, it is clear that any quantitative prediction of mountain wave generation must take full account of these lower troposphere processes. The newest numerical models show significant skill in simulating these effects. Using these models, the climatology of waves over the Alps can be studied. Copyright  2007 Royal Meteorological Society KEY WORDS

internal gravity waves; numerical modelling; Mesoscale Alpine Programme

Received 10 October 2006; Revised 31 January 2007; Accepted 27 April 2007

1.

Introduction

Mountain waves have interested meteorologists for more than 70 years because of their impact on aviation, their formation of beautiful lenticular clouds, the occurrence of severe downslope windstorms, and the ‘action-at-adistance’ idea that waves carry momentum and energy vertically into the stratosphere to influence turbulence, mixing, chemistry and large-scale overturning, as well as acting as a drag on the planetary circulation momentum budget. They also modulate the surface patterns of wind and precipitation. Some useful reviews of the subject are given by Queney (1947), Smith (1979, 1989a), Blumen (1990), Baines (1995), Wurtele et al. (1996), Smith et al. (2002), Fritts and Alexander (2003), and Kim et al. (2003). In the autumn of 1999, after several years of planning, the special observing period (SOP) of the Mesoscale Alpine Programme (MAP) was carried out in the European Alps. This project was perhaps the largest scientific field campaign ever carried out in the field of mountain meteorology (Bougeault et al. 2001). The programme was diverse, both in its participation and in its objectives. Scientists and equipment were contributed from nearly a dozen countries. The overall objectives of MAP were broad, including projects on orographic precipitation, valley wind effects and gravity waves (Volkert and Gutermann, 2007). The objective of project P6 was summarized in the MAP * Correspondence to: Ronald B. Smith, Yale University, New Haven, CT, USA. E-mail: [email protected] Copyright  2007 Royal Meteorological Society

Design Proposal (Scientific Overview Document) in this way: To improve the understanding of 3D gravity wave breaking and associated wave drag in order to improve the parametrization of gravity wave effects in numerical weather prediction and climate models.

The goal of this survey on project P6 is to put MAP gravity wave research into a historical and scientific context (see also Bougeault et al., 2001). We will summarize its most important discoveries. In addition, we will try to understand how MAP drew from previous work and how it stimulated subsequent research. Corresponding reports on related MAP objectives can be found in the current issue of this journal. Rotunno and Houze (2007) describe orographic precipitation studies, Mayr et al. (2007) describe gap flow and Drobinski et al. (2007) describe föhn in the Rhine Valley. An overview of the entire project is provided in the MAP Design Proposal (http://www.map.meteoswiss.ch/map-doc/proposal.htm). In Sections 2 and 3, we review pre-MAP field programmes and theory. In Sections 4 and 5, we discuss the new observing strategies used in MAP and introduce the seven MAP wave events described in the literature. In Section 5, we describe the three types of airflow dynamics that dominated the seven events. Section 6 describes the progress in numerical modelling associated with P6 in MAP. Subsequent modelling and theory motivated by MAP is outlined in Section 7.

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Pre-MAP field projects

The state of research on mountain waves prior to MAPSOP in 1999 can be characterized by mentioning a few diverse theoretical and observational projects active in the middle and late 1990s. In Table I, we list four successful field projects in this period. Of these projects, the Pyrenees Experiment (PYREX; Bougeault, 1997) was the most direct precursor of the MAP mountain wave subproject. Using a multiple-aircraft strategy, wave patterns were observed simultaneously at several altitudes. These results were surprising in at least one respect: the gravity wave amplitudes and the frequencies of wave breaking over the Pyrenees were less than expected, given the impressive size of the mountain barrier and the strong flows across them. These results led to the speculation that low-level processes were reducing the efficiency of wave generation. Waves over the southern tip of Greenland have recently been studied in two projects using research aircraft. Leutbecher and Volkert (2000) report on stratospheric data from the U2. In their simulation of mountain waves generated by Greenland, the waves were sensitive to the horizontal model resolution and surface friction representation. During the Fronts and Atlantic Storm-Track Experiment (FASTEX), the Gulfstream-IV aircraft of the US National Oceanic and Atmospheric Administration (NOAA) flew through a large-amplitude mountain wave generated by the southern tip of Greenland (Doyle et al., 2005). The authors conclude that the spectacular amplitude of the wave may have been favoured by the strong low-level winds hitting the terrain, and the smoothness of the ice-covered mountains. The smooth ocean and thin marine boundary layer (BL) surrounding Greenland’s tip may have favoured the strong ambient winds. Dörnbrack et al. (2002) used the Falcon aircraft of the German Aerospace Research Establishment (DLR), airborne lidar, and high-resolution models to study waves and wave clouds in the stratosphere over Scandinavia. They found that these waves were long enough to feel the effect of the Coriolis force, and that they could modify stratospheric chemistry through cloud generation. Several factors favour the propagation of mountain waves in this region. First is the strong deep westerly winds that prevent wave breaking and dissipation until they reach the middle stratosphere. A second factor might be the relatively smooth and broad terrain of Scandinavia. Due to recent ice-sheet glaciation, the terrain is missing

the sharp peaks and cirques found in the midlatitude Alps. While these three aircraft studies were examining the local properties of mountain waves, satellites were beginning to monitor waves and turbulence in the upper atmosphere. One method uses a microwave limb sounder (MLS) to detect regions of enhanced variation of index of refraction around the globe (Jiang et al., 2002). Index of refraction variations at these high levels indicate temperature fluctuations from the waves themselves or associated turbulence. The results were highly seasonal, with the winter season giving the strongest waves. The most energetic regions were found to be the mountain areas in high latitudes of both hemispheres. Intense wave activity was found over Greenland and the Scandinavian mountains in the Northern Hemisphere and over the southern Andes (Patagonia) and the Antarctic peninsula in the Southern Hemisphere (Figure 1). As discussed above, these areas have persistent deep westerlies and thin BLs. They are exposed to strong oceanic winds. The Alps in Europe were found to produce little persistent wave energy in the upper atmosphere. Perhaps this is not too surprising. The Alps are primarily aligned east to west, and thus produce a lesser barrier to westerly winds. When a northerly or southerly wind does hit the Alps, it is part of a complex baroclinic cyclone system. With directional wind shear aloft, gravity waves are likely to encounter critical levels (i.e. levels with zero wave intrinsic frequency) before they reach the stratosphere. In addition, the Alps are geometrically complex, with their special history of glacial erosion acting to roughen rather than smooth the terrain. Sharp peaks and ridges separate deep intersecting valleys. At night and in the cool seasons, layers of cold air lie still in the valleys while only the peaks feel the force of the large-scale winds. With these insights, it was clear that MAP would not be a field study with predominant strong deep gravity waves. The east–west orientation of the Alps has more in common with the Pyrenees, rather than north–south ranges such as Greenland, Scandinavia, Sierra Nevada, the southern Andes and the Antarctic Peninsula. This suggested that Alpine waves would be relatively rare and typically shallow. Indeed, the Alpine Experiment (ALPEX) in 1982, while it did not include exhaustive mountain wave surveys, reported few cases of strong gravity waves in the middle and upper troposphere. The strong cases of deep gravity waves during southerly flow (Hoinka, 1985) may be the ‘exception that proves the rule’.

Table I. Some pre-MAP mountain wave observations. Location

Observations

Reference

Pyrenees Greenland Scandinavia Global

Multiple aircraft One aircraft One aircraft Satellite UARS-MLS

Bougeault et al. (1997) Modest waves over complex terrain Leutbecher and Volkert (2000); Doyle et al. (2005) Large-amplitude tropospheric waves Dörnbrack et al. (2002) Stratospheric wave clouds Jiang et al. (2002); Preusse et al. (2002) Upper-atmosphere gravity waves

Copyright  2007 Royal Meteorological Society

Characteristics

Q. J. R. Meteorol. Soc. 133: 917–936 (2007) DOI: 10.1002/qj

MOUNTAIN WAVE GENERATION AND BREAKING

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Figure 1. The global distribution of gravity wave intensity in the upper atmosphere, derived from the Microwave Limb Scanner (Jiang et al., 2002), for (a) December–February and (b) June–August. These waves have vertical wavelengths greater than 10 km and horizontal wavelengths less than 100 km. The temperature variance (K2 ) is shown in colour and the dotted contours are the 34–44 km mean winds (m s−1 ) from the UK Met Office. The waves are strongest are in high latitudes during the winter season. Note the lack of signal over the Alps. This figure is available in colour online at www.interscience.wiley.com/qj

3.

Pre-MAP theoretical and numerical studies

We characterize the state of pre-MAP theoretical research by describing just six examples (Table II). Our selection is not meant to cover all the interesting areas of mountain wave research. At least since the work of Richard et al. (1989), it has been recognized that the atmospheric BL can reduce ´ the amplitude of terrain-generated waves. Olafsson and Bougeault (1997) extended this work with a systematic numerical study of BL effects, including the influence of the Coriolis force. As mountain waves propagate upwards, their amplitude and steepness is modulated by the variation in static stability and wind speed, and by persistently decreasing air density. Under this influence, the waves must eventually break down to turbulence and then to heat. The mechanism of the wave breaking includes the possibility that secondary waves may be generated as the primary waves destroy themselves (Satomura and Sato, 1999; Afanasyev and Peltier, 2001; Vadas et al., 2003). Wave breaking at lower altitudes in Alpine-relevant geometries were modelled by Schneidereit and Schär (2000) and Epifanio and Durran (2001).

The idea that a zero-wind level in the atmosphere will act as a ‘critical level’, absorbing gravity waves and preventing further propagation, goes back to Booker and Bretherton (1967). A more intricate (and realistic) case is when the wind turns with height so that a particular wind component might become zero. The Coriolis force also complicates the situation. The simple back-shear case has been studied by Shen and Lin (1999). Coriolis force and wind turning has been added by Shutts (2001, 2003). He found that the wave component with zero intrinsic frequency will indeed be absorbed at the critical level, but the horizontal location of absorption is spread widely laterally and downstream. Because of this wide distribution, localized intense turbulence is unlikely. In many circumstances, the atmospheric stability structure has a sharp jump that encourages the atmosphere to act in discrete layers. This behaviour permits a ‘hydraulic’ description of waves and wave breakdown. The layered approach is the only way that quasi-analytic solutions can be found to nonlinear wave breaking problems. While the theory of single-layer hydraulics (e.g. in rivers and channels) is simple and well understood, the theory of multiple layers was incomplete and contained inconsistencies (Baines, 1995). For example, the

Table II. Some recent theoretical and numerical studies of mountain waves. Problem

Approach

References

Boundary-layer effect on gravity waves

Numerics

Gravity wave breaking and regeneration

Numerics

Gravity wave critical levels with rotation and directional shear Two-layer hydraulic jumps Momentum flux

Theory and numerics

´ Richard et al. (1989); Olafsson and Bougeault (1997) Vadas et al. (2003); Afanasyef and Peltier (2001); Satomura and Sato (1999) Shen and Lin (1999); Shutts (2001)

Model comparison

Numerics


Theory and numerics Numerics

Jiang and Smith (2000, 2001a,b, 2003) Lott and Miller (1997); Webster et al. (2003); Brown (2004) Doyle et al. (2000)


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jump conditions for two-layer jumps had multiple roots of unknown realizability. Dissipation computed from these models was not always positive, as it should be. Recent work by Jiang and Smith (2001a,b, 2003) has addressed these problems and identified new possibilities such as bifurcation, hysteresis and double jumps. In a double jump, the flow experiences an ‘external jump’, in which both layers decelerate, followed by an ‘internal jump’, in which only one layer decelerates. Inspired by the need to incorporate unresolved gravity waves into climate models, efforts are under way to parametrize wave effects in terms of terrain geometry and the mean atmospheric profile. Recent pre-MAP progress has been reported by Clark and Miller (1991) and Lott and Miller (1997). As numerical models have grown to play a key role in mountain wave research, the question of model dependence (with regard to resolution, initial and boundary conditions, and model formulations) has become more important. While agreement between different numerical models does not guarantee that they are correct, it does add confidence to the method. Doyle et al. (2000) reported on an eleven-model intercomparison of a simulation of the 1972 Boulder windstorm. In many respects the models agreed, but not in the downstream extent of the windstorm. This result was not too surprising, as simple hydraulic models of ‘shooting’ flow indicate a delicate sensitivity to the downstream boundary condition. It is clear from these examples that remarkable progress had been made in the theory and numerical modelling of gravity waves prior to MAP (e.g. Volkert et al., 2003). It remained to be seen if the existing conceptual, analytical and numerical models could handle the complexity of the 3D Alpine gravity wave environment. An attempt to classify complex Alpine flows into discrete regimes was reported by Schneidereit and Schär (2000), following an earlier more idealized attempt by Lin and Wang (1996). 4. New observing methods in MAP Due to the complexity of Alpine flows and the challenging objectives of the MAP gravity wave sub-project, it was essential to have available some powerful new observing tools and methods. Seven new tools are listed in Table III. MAP was not necessarily the first project to use each method, but they had not been used in a co-ordinated manner before.

One long-standing problem with aircraft surveys of mountain waves is the uncertainty in the steady-state assumption. Almost the entire body of mountain wave theory is built on this critical assumption. Unfortunately, travelling and other transient gravity waves are common in the atmosphere. As a surveying aircraft moves to a different altitude and finds a different wave field, it is unclear whether the changed time or the changed location of the observation is responsible for the observed flow field differences. In MAP, we chose a conservative ‘repeat leg’ strategy. Each aircraft flew several repeat upwind and downwind legs at the same altitude and along the same track along the forecasted wind direction (as recommended by Doyle et al., 2002). In most cases, good to excellent agreement between repeat legs was found, validating the steady-state assumption. This additional confidence in the basic steady assumption allowed deeper questions to be asked of the flight-level datasets. The penalty for this conservative approach, the lack of vertical sampling, was not excessively troublesome in MAP as we often had three aircraft that could simultaneously monitor three altitudes. The early development of mountain wave theory and many of the early field projects limited their analyses by the assumption of two-dimensionality. According to this assumption, the wave pattern is independent of the coordinate running along the range. This approach assumes that there is a well-defined and uniform crestline. In the Alps of course this assumption would never hold! The terrain is fully 3D, and so are the linear and fullnumerical models that we wish to test. To carry out a careful quantitative comparison of data and model, the research aircraft was ‘flown through the model’. That is, the precise Global Positioning System (GPS) track of the aircraft was superposed on the 3D model output array, allowing the computed field to be sampled in a way that is consistent with the observations. This technique allowed the analysts to ask more penetrating questions concerning the accuracy of the models. In all previous mountain wave projects, it has been impossible to simultaneously probe the wave generation region in the BL and the wave propagation region in the middle troposphere. In cloud-free ‘visual flight rules (VFR)’ conditions, small aircraft or gliders could operate locally in broad valleys but such surveys connect poorly in time and space with the broad-scale overflights by high-performance aircraft aloft. In cloudy, windy

Table III. New observing methods and technologies in MAP. Method

Purpose

Repeated aircraft legs ‘Fly’ the aircraft through the model DIAL and SABL down-looking lidars GPS drop(wind)sondes Rapidscan Meteosat Constant-volume balloons Wind profilers

Validation of steady state Better model testing Detection of cloud patterns and inversions Detect low-level inversions, shear layers and stagnant layers Discrimination of steady and moving clouds, identify lee waves and föhn clearing Track air parcels, gravity wave analysis Continuous wind profile monitoring



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wave generation. Based on forecasts for cross-mountain wind speed and wave generation, a number of Intensive Observing Periods (IOPs) were declared and research aircraft were deployed. As shown in Table IV, the number of aircraft used for each event varied from one to three. All missions used dropsondes and lidar. The locations and prevailing wind directions for the seven cases are shown in Figure 2. The three research aircraft used for mountain wave research were the DLR Falcon, the UK Met Office C-130 and the NCAR Electra. The Falcon was stationed at Oberpfaffenhofen in southern Germany, while the C-130 and Electra were flown from the operations centre in Innsbruck, Austria. In the years that followed the MAP field phase, several research groups analysed the aircraft and the auxiliary datasets event by event. The reader is referred to these original papers for the details of each analysis (Table IV). Of particular interest are those events for which two independent analyses have been carried out, as they illustrate different approaches to the interpretation. In the sections below, we reorganize the material in these casestudies on the basis of dynamical process.

conditions, safe aircraft operations are impossible within one kilometer above the highest peaks, thus eliminating all possibility of direct BL probing with manned aircraft. In MAP, two ‘remote-sensing’ methods were used to probe the wave generation region directly below the wave survey aircraft. First was the GPS dropwindsonde (DWS). During each wave transect, several DWSs could be dropped from the aircraft along the track. As they fell to earth, they sent information back to the aircraft about temperature, humidity and wind. The second method used down-looking lidar: the Scanning Aerosol Backscatter Lidar (SABL) on the National Center for Atmospheric Research (NCAR) Electra and the Differential Absorption Lidar (DIAL) in the DLR Falcon. The lower-flying Electra could see the pattern of cumulus clouds often marking the top of the BL or cold-air layer in the valleys. The higher-flying Falcon could, if the clouds were not too dense, map out the full stack of clouds in the troposphere, including cirrus, lenticular and cumulus (Figures 4, 5). Three other observation methods complemented the aircraft data. The rapid-scan images from Meteosat allowed transient wave cloud patterns to be monitored (Bolliger et al., 2003; Smith et al., 2002). To diagnose cloud conditions along a specified flight track, time–distance (i.e. Hovmöller) brightness diagrams could be constructed. Additional information on the low-level flow was available from the occasional launch of a constant-level balloon. These data could be compared with trajectories computed from the model fields. VHF and UHF wind profilers were also used in MAP, giving continuous wind data though events (Caccia et al., 2001) Together, these new methods allowed us to ask more penetrating questions and to more thoroughly evaluate the model predictions.

5.

5.1. Low-level blocking and stagnant layers The first mountain wave event in MAP to be analyzed in detail was the Mt. Blanc case on 2 November 1999 (Table IV). In spite of the historical role of Mt. Blanc in mountain meteorology (Saussure, 1796), and its stature as the highest mountain in Europe (4807 m), this was the first observation of its mountain waves. Under conditions of southwesterly airflow (Figure 3), three research aircraft flew repeatedly through waves in the middle and upper troposphere and the low stratosphere. A remarkable visualization of the waves was possible using the downlooking lidar on the DLR Falcon aircraft (Figure 4). The lidar was able to penetrate three layers of cloud (cirrostatus, lenticular and cumulus) and detect the wave modulation. A photograph of those clouds is shown as Figure 5.

Major results from MAP

During the MAP field phase, a number of baroclinic disturbances moved through the Alpine region, bringing a variety of wind and stability environments for gravity

Table IV. Seven gravity wave cases in 1999 in the literature from MAP. Case Date Location

1

20 Sep Hohe Tauern Wind direction S Wind shear No. of aircraft 1 Dropsondes Y Lidar Y Comment Latent heat; lee waves References Doyle and Smith (2003); Jaubert and Stein (2003)

2

3

4

5

6

21 Oct ¨ Otztaler Alpen SW Reverse 1 Y Y Föhn

25 Oct Hohe Tauern SSW

2 Nov Mt. Blanc massif SW Forward 3 Y Y No lee wave

7 Nov Dinaric Alps NE Reverse 2 Y Y Bora

8 Nov Monte Rosa massif N

Jiang and Doyle (2004)

Volkert et al. (2003)

Smith et al. (2002); Smith and Broad (2003)

Grubiˇsić (2004); Jiang and Doyle (2005)


1 Y Y Föhn

7

13 Nov Dauphiné Alps SE Directional 3 3 Y Y Y Y Blocking; föhn; Blocking lee waves Jiang et al. Doyle and (2005); Smith Jiang (2006) (2004)


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Figure 2. A plan view of the Alps showing the locations of seven gravity wave events observed during the MAP field program in autumn 1999. Arrow orientation indicates the ambient wind direction. Details are given in Table IV. This figure is available in colour online at www.interscience.wiley.com/qj

Figure 3. Soundings for the 2 November case, representing conditions during the flights. Data from three aircraft (F,C,E), eight Electra dropsondes (D) between 10 : 31:58 UTC and 11 : 15:47 UTC and the nearby Payerne (P) sounding (06 and 12UTC) are combined to derive a reference sounding. Points (X) are extrapolated from the dropsondes and the Payerne temperature soundings. Variables shown are the potential temperature (PT), wind direction (DD) and speed (FF), and the simplified Scorer parameter (N/U , km−1 ). The idealized Scorer profile is shown dashed. Note the stagnant layer below 3 km. (Smith et al., 2002). Copyright  2007 Royal Meteorological Society



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Figure 4. The vertical section of DIAL backscatter coefficient (colourshading) from the first Falcon traverse over Mt. Blanc on 2 November 1999. Also shown are the vertical parcel displacements (solid black curves), computed from vertical velocity data from the three research aircraft Electra, C-130 and Falcon. Only the even-numbered legs of the Electra are shown. Near an altitude of 9.5 km, the lower edge of the cirrostratus layer is deformed by a mountain wave. Note the lenticular cloud at altitude 7.5 km. The backscatter from the low-level cumulus clouds show plunging flow over Mt. Blanc. Vertical exaggeration is about 10 : 1. A corresponding photograph is shown in Figure 5. (Smith et al., 2002). This figure is available in colour online at www.interscience.wiley.com/qj

Figure 5. Photograph taken from the cockpit of the C-130 on 2 November 1999 showing cloud types present during the mission: cirrostratus aloft, lenticularis at flight level, and cumulus below. This figure should be compared with Figure 4. (Smith et al., 2002). This figure is available in colour online at www.interscience.wiley.com/qj Copyright  2007 Royal Meteorological Society


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The waves observed by the aircraft were modest in amplitude, in spite of the high Mt. Blanc terrain, with vertical velocities seldom exceeding 4 m s−1 . The waves were also remarkably stationary, judged by the similar wave patterns found on subsequent flight legs. The wave steadiness and small amplitude allowed the classical steady linear theory of Scorer (1949) to be applied and tested. As expected, the strong jet stream and weak static stability in the upper troposphere put the waves into an ‘evanescent’ structure there. Surprisingly however, the decay aloft was not accompanied by the occurrence of a periodic train of trapped lee waves. According to classical theory, trapped lee waves will occur whenever a ‘wave duct’ occurs in the atmosphere. A duct for internal gravity wave energy occurs when a jet stream reflects waves downward and the Earth’s surface reflects them upwards. In previous work, it had been assumed that the lower reflector would always be present. The lee wave occurrence would only depend on the ‘Scorer criterion’ that the ratio N/U decreased strongly aloft (where N is the Brunt–Väisälä frequency, and U is the horizontal wind speed). An important clue to the resolution of this paradox was the discovery of a region-wide stagnant layer of air below 2.5 km, probably caused by the drag and blocking by the complex surrounding terrain. While the aircraft could not safely penetrate these lower layers around Mt. Blanc, numerous dropsondes from the aircraft provided evidence of the quiescent layer (Figure 3). Subsequent analysis verified a dual role for the stagnant layer. First, as only winds above the stagnant layer hit the mountain peak, the waves were generated only by those terrain elements that poked above 2.5 km. This effective reduction in mountain height explains the modest amplitude of the observed waves. Second, as the downwardpropagating waves reflected from the jet stream encounter the stagnant layer, they are absorbed instead of reflected (Figure 6). Thus, the ‘wave duct’ is absent in spite of the upper reflector. In Figure 7, we show the difference in the linear model wave field caused by the elimination of reflected waves from the Earth’s surface. An important property of the wave field is the vertical flux of horizontal momentum. As the Alps are highly complex, the wave field generated aloft is also very complex. The apparent wave field observed by aircraft is therefore highly dependent upon the exact track along which it flies. This was demonstrated by Smith (2004) for the 8 November case using high-resolution Met Office Unified Model (UM) simulations. The smallscale waves apparent in the vertical velocities were produced by many different peaks in the experimental region, and those wave trains sampled by the aircraft had differing orientations. A very slight displacement of the Electra flight track on this day observed a much larger wave magnitude by passing directly over the peak of Monte Rosa, which the first track narrowly missed, demonstrating the highly 3D nature of the wave field. Two larger-scale wave trains were sampled by the Falcon at an angle, so that their separation appeared Copyright  2007 Royal Meteorological Society

Figure 6. Schematic of the resonant cavity for lee waves. The triangles represent the lower mountains, with one higher peak (i.e. Mt. Blanc) penetrating into the ambient flow. The dashed line labelled Zref , is the top of the stagnant layer and the bottom of the linear theory domain. The upper dashed line represents the level of wave reflection due to decreasing Scorer parameter. The slanting wave rays are parallel to the local group velocity. The down-going wave amplitude, B, is reduced by partial absorption at Zref , characterized by the reflection coefficient q. (Smith et al., 2002).

to be a longer wavelength than was actually present. Interpretation of these observations required information about the 3D wave field provided by the UM simulation. One of the objectives of the MAP field campaign was to provide data with which to verify numerical models. However, it has been shown that the determination of a flight path on such days can be quite difficult. The resulting incoherent sampling of the wave field makes for a difficult verification of simulated wave fields. The momentum flux in this Mt. Blanc case was estimated by Smith et al. (2002) and analyzed more extensively by Smith and Broad (2003). The latter study pointed out a surprising variability in the momentum flux, in spite of the apparent steadiness of the wave field (Figure 8). In the mid-troposphere, both large positive and negative flux values were found in subsequent aircraft penetrations. Two explanations were explored. First, the reduced Scorer parameter in the upper troposphere would reflect waves downwards. Short aircraft transects may penetrate regions of downward dominance and positive flux. Second, the wind shear aloft (Figure 3) was observed to increase with time, possibly causing shear instability and downward wave generation. Other MAP events showed the influence of blocking as well, but in other forms. On September 19–20, the southerly flow changed from flow-around to flowover as the wind speed increased. This shift also influenced the föhn, low-level wave breaking and hydraulic jumps (Jaubert and Stein, 2003). On 8 November 1999, a northerly airflow across the central Alps was again studied with three aircraft (Table IV). Upstream, to the north of the Alps, a blocked layer reduced the effective height of the Alps. Downstream however, the airflow descended strongly to the ground causing a ‘föhn clearing’. Lee waves found by aircraft, constant-volume balloons and satellites images indicated that a complete waveguide must exist, in spite of the upstream blocking (Smith, Q. J. R. Meteorol. Soc. 133: 917–936 (2007) DOI: 10.1002/qj


Figure 7. Plan view of the linear theory vertical displacement field at z = 5.5 km for 2 November 1999 with the reflection coefficient (a) q = 0.9, and (b) q = 0.0. The small X marks the location of Mt. Blanc. Disturbances generated by other high mountains are seen to the east of Mt. Blanc. Note the differences in the lee-wave field along the flight track. More oscillations are seen in (a). (Smith et al., 2002).

2004; Jiang et al., 2005). The momentum flux in this case was discussed by Smith (2004). Blocking was also a factor in the 13 November case (Doyle and Jiang, 2006). 5.2. Critical layers, wave breaking and hydraulic jumps When waves propagate upwards in a wind environment with reverse shear or strong turning, they will eventually reach a critical level. According to linear theory, waves will then amplify, contract their scale, break and probably be absorbed (Booker and Bretherton, 1967). A different description arises from nonlinear analysis of the problem, derived from laboratory experiments and numerical simulations. The critical level will cause the low-level flow to decouple from the flow aloft, producing layer-like flow below (Durran, 1986; Figure 9). The shallow layer can spill over terrain and may even produce hydraulic jumps. Copyright  2007 Royal Meteorological Society

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Analytical solutions to nonlinear spilling can be obtained in special cases (Smith, 1985; Jiang and Smith, 2003) In the complex Alpine terrain, these complicated critical-layer flows are difficult to locate and observe with aircraft or any other observing technology. Nevertheless, a few cases of wave breaking were identified in MAP. On 21 October 1999, a strong southsouthwesterly flow developed against the central Alps, associated with a cyclone over France (Jiang and Doyle, 2004). While the incoming wind speed reached 20 m s−1 in the lower troposphere, it decreased to nearly zero at an altitude of 6 km. This layer accelerated and spilled, creating a downslope windstorm ¨ over the Otztaler Alps (Figure 10). After some descent, the layer seemed to decelerate and jump upwards in a structure resembling a hydraulic jump. Vertical motions approaching 9 m s−1 and turbulent kinetic energies of 10 m2 s−2 were found. A smaller-amplitude example of critical-level absorption was found on 13 November 1999 in the French Alps (Table IV) (Doyle and Jiang, 2006). Moderate southeasterly flow weakened and turned aloft. Three aircraft flew during this event. The decrease in wave amplitude aloft suggested that waves were being absorbed at a critical level. Numerical simulation results indicated the presence of low-level wave breaking above the highest Alpine peaks, along with trapped waves and directional criticallevel absorption. Spilling and hydraulic jumps also played a central role in the bora case on 7 November 1999 in the Dinaric Alps. As in the Alpex bora cases from 1982 (Smith, 1987), the MAP bora case had a low-level stable layer and a decreasing wind aloft, forcing decoupling and layer-like behaviour. As the layer spills over the lower coastal passes, severe downslope winds are produced that extend for several kilometres out over the Adriatic Sea (Figure 11). As the layer spills over higher coastal peaks, strong hydraulic jumps occur almost immediately (Grubiˇsić, 2004; Jiang and Doyle, 2005). The jumps dissipate flow energy and reduce the Bernoulli function for each airstream that passes through them. Crosssections through two different airstreams are shown in Figures 12(a) and (b). The cross-stream variation in the jump strength results in lateral gradients in Bernoulli function and, in turn, gradients in potential vorticity (PV; Schär and Smith, 1993; Pan and Smith, 1999). The concept of Bernoulli gradients caused by wave breaking and jumps was also invoked in the study of the mistral and the tramontane in the gap region between the Pyrenees and Alps (Jiang et al., 2003). Aircraft observations of these massive jets show PV gradients on their flanks associated with Bernoulli losses over the highest terrain. The combination of föhn and turbulence down inside Alpine valleys was described by Lothon et al. (2003) and Gohm and Mayr (2004). For an overview of gap-related research during MAP, see Mayr et al. (2007) and Drobinski et al. (2007). Q. J. R. Meteorol. Soc. 133: 917–936 (2007) DOI: 10.1002/qj

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Figure 8. Profiles of the vertical flux of along-track momentum near Mt. Blanc for 2 November 1999. Symbols represent aircraft measurements, and curves represent fluxes from numerical simulations. (a) is calculated from simulated wind fields along the actual track, and (b) and (c) are from two adjacent tracks. Note the variability from track to track. A data point with positive momentum flux may signify downward-propagating waves, either reflected or generated aloft. (Smith and Broad, 2003).

Figure 9. Numerical simulations of a two-layer atmosphere over a 600 m high ridge. Airflow is from left to right and the top of the stable layer is at (a) 1571 m (one quarter of a vertical wavelength) and (b) 3142 m (one half of a vertical wavelength). The latter corresponds to a nonlinear resonance, causing violent plunging flow and an undular jump downstream. The resonance condition is derived using a hydraulic approach to continuous stratification based on Long’s model. (Durran, 1986).

5.3.

Latent heat effects

While most events during MAP were classified as primarily ‘wet’ or ‘dry’ events, and analyzed accordingly, at least one event was examined from both points of view. This was the orographic precipitation event of 20 September 1999. As a trough progressed across Spain, a strong moist southerly flow impacted on the southern side of the Alps. Heavy rains shifted slowly eastwards starting in the Lago Maggiore area and ending in the Friuli area of the eastern Alps north of the Adriatic Sea. Copyright  2007 Royal Meteorological Society

This event brought the largest rainfall totals in the MAP period and caused flooding in several catchments. This interesting event has become one of the best-studied cases of orographic precipitation in the history of mountain meteorology (Georgis et al., 2003; Asencio et al., 2003; Jaubert and Stein, 2003; Medina and Houze, 2003; Smith et al., 2003; Doyle and Smith, 2003; Rotunno and Ferretti, 2003; Rotunno and Houze 2007). Readers wishing to compare different scientific analyses of the same natural event have an ideal opportunity here. Several MAP aircraft and surface radars mapped out the inflow region Q. J. R. Meteorol. Soc. 133: 917–936 (2007) DOI: 10.1002/qj


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¨ Figure 10. Cross-section through the central Otztaller Alps on 21 October 1999 showing spilling flow with a dividing streamline and turbulent zone (Jiang and Doyle, 2004). The observations include vertical displacement at the flight level (the bold wavy curve at 6 km), Electra SABL backscatter (dBZ, grey shading), isentropes (K, solid contours), and dropsonde trajectories (dashed lines). Dropsondes are numbered along the abscissa. Turbulent regions near an altitude of 4 km are marked with hats. The flow pattern is suggestive of the classic model plunging flow with turbulence above. Vertical exaggeration is about 20 : 1.

over the Po Valley and Piedmont. During this event, one research aircraft was deployed directly over the Alps to monitor mountain wave activity and föhn descent. This aircraft found spilling flow and well-defined lee waves (Figure 13).

Figure 11. Plan view of the MAP bora event on 7 November 1999. Airflow is from northeast to southwest. Red colours represent high wind speed near the surface of the Earth. High-speed winds are first generated as the air descends to the sea over the Dinaric Alps. Note the jet/wake structures over the Adriatic Sea. Cross-sections B and C are shown in Figure 12. (Jiang and Doyle, 2005). This figure is available in colour online at www.interscience.wiley.com/qj Copyright  2007 Royal Meteorological Society

To isolate the role of latent heat in mountain wave generation, Doyle and Smith (2003) used a numerical model to simulate the observed flows, with and without the latent heat effect (Figure 14). The impact of latent heat was profound. The release of latent heat in the low and mid-troposphere had the effect of reducing the static stability aloft. This reduced stability allowed the Scorer criterion for lee waves to be met. This factor helped to explain the observed strong lee waves with maximum vertical velocities in excess of 9 m s−1 and potential temperature perturbations of 10 K. Even more dramatic was the influence of latent heat on lee-side descent. Numerical experimentation showed that if the upstream latent heating was strong and shallow, the lee-side descent was significantly increased. Once again, the physics of this shift in flow pattern involves the reduction of static stability aloft. According to the theory of severe downslope winds, reduced winds or stability aloft can decouple the low-level flow and allow it to flow like a shallow layer. When the depth and speed of this layer satisfy the critical-state criterion (Smith, 1985; Baines, 1995), the layer will spill over the obstacle like water spilling over a dam. Such an impact of latent heating is far from intuitive, but it may help to resolve the old question about föhn: How can the warm (and therefore buoyant) air be made to Q. J. R. Meteorol. Soc. 133: 917–936 (2007) DOI: 10.1002/qj

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Figure 12. Two cross-sections through the strong MAP Bora event on 7 November. The locations of the sections (a) line B–B’, and (b) line C–C’ are shown in Figure 11. The flow is from right to left, and the flow in both sections spills over the Dinaric Alps ridgeline. In (a), the fast flow lifts off the surface by the action of an internal hydraulic jump (dashed box). In (b), the fast flow hugs the sea surface. (Jiang and Doyle, 2005). This figure is available in colour online at www.interscience.wiley.com/qj

Figure 13. Lidar and aircraft data combined on a north–south cross-section for 20 September 1999. The lidar backscatter (dBZ) is shown in colour and the vertical displacement (km) derived from the velocity measured at flight levels is shown as dark curves. The airflow is from left (south) to right (north). There is evidence of spilling flow and strong trapped lee waves. This event had significant precipitation on the south side of the Alps. (from Doyle and Smith, 2003). Vertical exaggeration is about 30 : 1. This figure is available in colour online at www.interscience.wiley.com/qj




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Figure 15. Frequency (% of time) when w ≥ 2 m s−1 , based on the COAMPS reanalysis for the period of the MAP SOP (15 September–15 November 1999), for the (a) 5000 m and (b) 10 000 m levels. The shading interval for frequency is 0.4%. Strong vertical motions are present more than 5% of the time in a few “hot spots”. Figure 14. Cross-section of stratified airflow over the Central Alps, as simulated in COAMPS for 20 September 1999. Airflow is from south (left) to north (right): (a) with and (b) without latent heating. Note the spilling airflow in (a). The shallow upslope heating has tuned the atmosphere for a nonlinear resonance. This case provides some evidence for a link between latent heating in föhn and strong descent. Vertical exaggeration is about 10 : 1. (from Doyle and Smith, 2003).

descend on the lee side of the Alps? It is not known how often latent heat plays a role in decoupling and criticalstate development.

6.

Numerical modelling progress and challenges

6.1. Climatological issues The results from the MAP gravity wave studies suggest that the quality of mountain wave simulations from the current generation of non-hydrostatic numerical models is now sufficient to begin addressing new classes of scientific questions and problems, such as gravity wave climatological issues. In order to gain a better understanding of the climatological distribution of mountain waves generated by the Alps, a series of high-resolution reanalysis simulations were conducted using the Coupled Atmosphere–Ocean Mesoscale Prediction System (COAMPS , see Hodur, 1997). The reanalysis consists Copyright  2007 Royal Meteorological Society

of 15-hour forecasts executed twice daily using three horizontally nested grids with resolutions of 45, 15 and 5 km and 40 vertical levels. The initial fields for each reanalysis forecast are created from multivariate optimum interpolation (MVOI) analyses of upper-air sounding, surface, commercial aircraft, and satellite data that are quality controlled and blended with the previous 12-hour COAMPS forecast fields. Lateral boundary conditions for the outermost grid mesh are based on the US Navy Operational Global Analysis and Prediction System (NOGAPS) forecast fields. The model output was archived at a 1-hour frequency during the forecast, and statistics were computed based on the 4- to 15-hour forecast period in order to avoid spin-up and balance issues that may impact on the gravity wave fields in the first few hours following the analysis and initialization stages. The horizontal distribution of the frequency of occurrence of small- to moderate-amplitude mountain waves (w ≥ 2 m s−1 ) for the time period spanning the MAP SOP (15 September to 15 November 1999) is shown in Figure 15. The gravity waves frequency at 5 km amsl (Figure 15(a)) contains several frequency maxima in the western Alps, such as Monte Rosa, Berner, and Maritime ranges, as well as maxima in the eastern Alps near the Hohe Tauern. The maxima in the western Alps arise from predominantly westerly, southwesterly, or northwesterly Q. J. R. Meteorol. Soc. 133: 917–936 (2007) DOI: 10.1002/qj

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mean flow (e.g. the 2 and 8 November cases) with a much smaller contribution from easterly flow events (e.g. 13 November). The maximum in the eastern Alps is located along the Hohe Tauern crest, which is an east–west oriented range and is one of the few quasi-2D sections within the Alps making it a preferred location for gravity waves launched under northerly or southerly föhn conditions (e.g. 20 September, 25 October, 6 November). The mountain wave frequency distribution (w ≥ 2 m s−1 ) for the 10 km level (Figure 15(b)) indicates that the largeramplitude mountain waves penetrate to the tropopause and above more frequently along the western Alps. This may be an indication that the waves in the central and eastern Alps are more frequently trapped or experienced a critical level due to directional shear. 6.2.

Model intercomparisons

w (m s-1)

During the pre-MAP research stage, 2D simulations of the 11 January 1972 Boulder windstorm, obtained from eleven diverse non-hydrostatic models, were intercompared with special emphasis on the turbulent breakdown of topographically forced gravity waves (Doyle et al., 2000). The results from the simulations were encouraging in that all models produced upper-level wave breaking in horizontal and vertical locations. However, significant differences among the simulations were apparent in the movement of the hydraulic jump and the depth of the breaking layers, which may be an indication of the sensitivity of these phenomena to numerical dissipation, numerical representation of the advection and the lateral boundary conditions. Although no systematic model intercomparison was conducted in the post-MAP SOP, several detailed studies of MAP cases have been performed using multiple models. For example, simulations were conducted for the 2 November and 8 November gravity wave events

10 8 6 4 2 0 −2 −4 −6 −8 −10

using linear theory models and the nonlinear UM and COAMPS. The 2 November case was characterized by a stationary mountain wave forced by southwesterly flow over Mont Blanc. The model simulations from UM (Smith and Broad, 2003) and COAMPS (Smith et al., 2002) were in reasonable agreement with the research aircraft observations and the linear theory (Smith et al., 2002). Both UM and COAMPS simulated a very steady wave-train response that damped out quite rapidly downstream associated with the BL absorption mechanism proposed by Smith et al. (2002). Interestingly, both UM and COAMPS appeared to overpredict the amplitude of the vertical velocity of the first two waves, which may be an indication that the multi-scale blocking is too shallow in both models. The agreement between the nonlinear models and observations was not as close for the 8 November wave event (Smith, 2004; Jiang et al., 2005). Even though the large-scale stability and winds were well simulated by the 1 km resolution UM and COAMPS, as diagnosed by the available upstream dropsondes and radiosondes, the UM systematically underpredicted the amplitude of the larger gravity waves and COAMPS exhibited errors in amplitude as well, although not obviously systematic. The underprediction in the UM was attributed to erroneously large static stability near the surface arising from the semi-Lagrangian advection scheme (Smith, 2004). 6.3.

Resolution dependence

The research aircraft measurements for a number of the MAP gravity wave IOPs indicate that the horizontal wavelengths of the dominant mountain wave signature was typically in the range of 3–15 km. Given the relatively small-scale nature of these waves, it is not surprising that the model simulations are quite sensitive to horizontal resolution. For example, in the 20 September case, which featured large-amplitude trapped waves

Electra COAMPS - 1 km COAMPS - 3 km COAMPS - Cold Start COAMPS Topography

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Figure 16. Vertical velocity (m s−1 ) for the Electra (thin solid) and COAMPS simulation (x = 1 km) interpolated to the aircraft positions (bold) at 1234–1258 UTC and 5500 m. Vertical velocities from a cold-start initialization experiment and the third mesh (x = 3 km) are also shown. The model terrain for the innermost mesh (x = 1 km) interpolated to the aircraft position is shown along the abscissa (Dyle and Smith, 2003). Copyright  2007 Royal Meteorological Society



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shown in Figure 17(b), illustrates the potential differences in the terrain characteristics arising from resolution issues. Smith et al. (2006b) used three different modelling systems to investigate the resolution dependence of the resolved surface pressure drag for seven MAP mountain wave case-studies. They found that for the case with larger-amplitude waves resulting from relatively strong cross-mountain wind speeds near the crest level, the drag increased significantly as the grid spacing was reduced. The resolved drags converge to the value derived from a 4 km horizontal resolution mesh for cases with smallamplitude waves and weaker wind speeds near mountain crest level. In these situations, most of the drag was produced by low-level flow splitting around the Alpine barrier.

6.4. Vertical coordinate issues

Figure 17. Numerical wave simulations with various model resolutions: (a) Data extracted from the 8 November UM simulations along the research aircraft transect for the 1200 UTC vertical velocity time series at a height of 5670 m, and (b) model orography. Only with the finest resolution (x = 1 km) do the waves reach their full amplitude.

generated by the Hohe Tauern, a 1 km horizontal resolution simulation accurately captured the wavelength and amplitude of the waves, as shown in Figure 16. However, the 3 km horizontal resolution mesh produced wave amplitudes that were reduced by up to 75% and substantially disagreed with the research aircraft observations. Similarly, Smith et al. (2006b) explored the resolution sensitivity for the 8 November gravity wave event. The wave amplitude and phase were found to be very sensitive to resolution changes, with a reduction in resolution from 2 to 1 km resulting in as much as a 100% or greater increase in the vertical velocity for a specific wave, as shown in Figure 17(a). General guidelines suggest that 6–8 grid points across one horizontal wavelength is needed to adequately resolve a wave. Thus, small-scale waves such as those observed during the 13 November event, which featured horizontal wavelengths of 3 km or less (Doyle and Jiang, 2006), may require subkilometre-scale horizontal resolutions. Additionally, the Alpine terrain is sufficiently complex and contains substantial energy at the small scales such that resolving the local terrain characteristics may be needed to accurately simulate the wave characteristics including launching. The representation of the terrain at various resolutions along the aircraft transect during the 8 November case, Copyright  2007 Royal Meteorological Society

In nearly all current-generation numerical modelling systems, a terrain-following coordinate system is employed as the vertical coordinate. The accurate representation of the horizontal pressure gradient force can be particularly challenging in terrain-following coordinate systems. Spurious mountain waves and PV that were apparent during MAP in real-time forecasts from the Canadian Mesoscale Compressible Community Model (MC2) motivated Schär et al. (2002) to improve upon some of the shortcomings of the commonly used terrain-following coordinate systems. They proposed a new smooth level vertical (SLEVE) coordinate that results in smooth and relatively flat coordinate surfaces at mid- and upper levels through the use of a non-local coordinate transformation, which features a scale-dependent vertical decay of the underlying topography. The new vertical coordinate reduced the truncation errors and resulted in a substantial reduction of the high-frequency noise in the MC2 model. Following the Schär et al. (2002) study, Klemp et al. (2003) found that the terrain transform metric terms appearing in the pressure gradient and advection terms need to be treated consistently so that cancellation will occur when transformed back to the Cartesian system. Spurious gravity waves arise when the metric terms are not treated in a consistent manner. These tests were carried out using the Weather Research and Forecasting (WRF) and MC2 modelling systems. Klemp et al. noted that the spurious waves generated by the inconsistencies in the metric terms are most serious when the terrain spectrum contains dominant forcing scales near the wave number N/U . Horizontal diffusion is commonly used in numerical models to control nonlinear instability and aliasing. Typically, horizontal diffusion is performed along the terrain-following coordinate surfaces that may result in spurious mixing of atmospheric properties along sloping surfaces. Diffusion along sloping sigma surfaces may lead to potentially serious errors when strong vertical Q. J. R. Meteorol. Soc. 133: 917–936 (2007) DOI: 10.1002/qj

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gradients are present, such as inversions or moist layers within or at the top of the BL. Zängl (2002) proposed a horizontal diffusion scheme that uses vertical interpolation to produce a true horizontal diffusion with respect to sea level rather than the sloping terrain surface. Zängl showed that the new diffusion scheme greatly improves the ability of the Pennsylvania State University/NCAR mesoscale model (MM5) to simulate topographic flows. 6.5.

Predictability issues and challenges

Despite the progress made through the MAP-related research, explicit prediction of mountain waves generated by complex 3D terrain remains a formidable challenge. The results from a number of the MAP gravity waves studies, such as 20 September (Doyle and Smith, 2003), 25 October (Volkert et al., 2003), and 2 November (Smith et al., 2002; Smith and Broad, 2003), indicate that accurate simulations of mountain waves relative to the research aircraft observation is indeed possible. In general this group of cases was characterized by stationary, non-breaking gravity waves. The results from several other studies, such as 21 October (Jiang and Doyle, 2004), 8 November (Smith, 2004; Jiang et al., 2005), and 13 November (Doyle and Jiang, 2006), indicate larger discrepancies between the model simulations and the observations. These gravity wave events tended to be characterized by non-stationary waves with complex large-scale patterns. For example, the 21 October case exhibited non-stationary characteristics associated with relatively strong low-level wave breaking. The 13 November case contained significant directional wind shear associated with a large-scale depression. The waves generated in this particular case were small in amplitude and non-stationary as well. The 8 November event was dominated by multi-scale blocking that apparently modulated the wave response. In all of these cases, the models appear to accurately represent the large-scale conditions and compared well with the upstream dropsondes. A pre-MAP study of nonstationary waves generated during a south föhn event also indicated substantial deficiencies in the predictive capability of these events (Doyle et al., 2002). Despite the accuracy of the large-scale forcing, current generation non-hydrostatic models are still not capable of accurately simulating these non-stationary wave events. Other issues that may contribute to deficiencies in the predictive capabilities include the representation of BLs associated with absorption of downward-propagating waves (Smith et al., 2002), multi-scale blocking (Jiang et al., 2005), and moist processes (e.g. Doyle and Smith, 2003; Rotunno and Houze, 2007). The complexity of these gravity-wave events support the straightforward aircraft observing strategy employed during MAP, which featured linear flight segments oriented along the crossmountain wind direction and repeated segments to document the transience of the flow, coupled with remotesensing and dropsonde observations. Copyright  2007 Royal Meteorological Society

7.

Recent research inspired by or related to MAP

As seen in the above sections, the MAP project P6 identified a number of physical problems regarding mountain wave generation in complex wind and terrain environments. In this section we report on some recent research, stimulated by or related to these MAP results. We will mention some progress regarding momentum flux in time-varying flows, distinguishing between drag by blocking and drag by wave generation, linear theory representation of BL effects, rotors and BLs, and PV generation. 7.1.

Momentum flux in time-varying flows

One of the characteristics of the Alpine region is the variability of the synoptic wind field as frontal cyclones traverse the area. The study of unsteady mountain waves had begun prior to MAP (e.g. Lott and Teitelbaum, 1993), but without consideration of their interaction with synoptic systems. Chen et al. (2005) have made some significant progress by their numerical studies of an idealized periodic pattern of high and low pressure systems drifting past a fixed finite mountain ridge. The hydrostatic waves generated by the ridge vary in time, both because the wind speed across the ridge varies and because the vertical wave number, N/U , aloft varies. In general, larger downward momentum fluxes were found during the accelerating phase of the synoptic cycle. This behaviour could be explained using classical ideas of wave action. Even slow accelerations can exhibit this effect because of the extra time it takes the mountain wave field to develop over the full depth of interest. While some evidence of reversed momentum fluxes were found in the Chen et al. simulations, these were only seen on the large scales and are seemingly unconnected with the positive momentum fluxes discussed in Section 5.1. 7.2. Improved parametrization of drag from complex terrain As seen in several MAP cases, low-level blocking modified the generation and the fate of downward reflected mountain waves (section 5.1). Blocking also makes its own contribution to the total pressure force on a mountain range by piling up dense air on one side (Hafner and Smith, 1985; Davies and Phillips, 1985; Carissimo et al., 1988). For the purposes of drag parametrization it is important to distinguish between blocking and wave generation drag components. Some progress along these lines was reported from PYREX (Bessemoulin et al., 1993). Often too, when the waves encounter a critical level, their relatively small drag contribution can be reduced further. When these two effects are conflated, it seems that only a small fraction of the mountain drag will reach the upper troposphere in the form of wave momentum flux. Using these ideas, Webster et al. (2003) has recently proposed a mountain drag parametrization scheme for general-circulation models which assigns nearly 70% of Q. J. R. Meteorol. Soc. 133: 917–936 (2007) DOI: 10.1002/qj

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the mountain pressure drag to blocking. Of the remaining 30%, only a small portion reaches the stratosphere. A related issue is the scale dependence of drag parametrization schemes. In Smith et al. (2006b), mesoscale simulations of MAP cases were carried out at horizontal resolutions between 60 km and 4 km. As the resolution increases, the resolved drag should converge towards its real value while the parametrized drag should reduce to zero. Instead the magnitude of the resolved drag was found to increase monotonically with resolution. The lack of convergence suggests that individual peaks and valleys, which are not yet fully resolved, are as important as longer orographic features in producing drag. Momentum flux profiles indicate that the largest proportion of the drag is felt below the level of the highest mountain peaks, demonstrating the importance of representing drag due to low-level flow blocking. Additional discussions on the effect of terrain properties on drag are given by Brown (2004), Kim and Doyle (2005), and Rontu (2006). 7.3. Boundary-layer effects on wave generation and absorption The confirmation in MAP that the BL can have a strong influence on gravity waves has led to more detailed physical studies in the post-MAP era. Numerical studies by Peng and Thompson (2003) and Jiang et al. (2006) isolated the effects of the BL on wave generation and absorption. In simple wave generation problems, the BL reduces the wave amplitude. In trapped lee wave problems, the BL caused the lee wave to decay downstream. To clarify the interaction of waves and BLs, a linearized theoretical approach has been outlined by Smith et al., (2006a) and Smith (2007). They showed that the bulk response properties of the BL, when subjected to wave-induced pressure gradients, can be captured in the ‘compliance coefficient’, C, defined as the ratio of the BL-top displacement, ηT , to the imposed pressure field, p. Expressing this ratio in terms of the spatial Fourier transform of each field gives C(k) =

ηˆ T , pˆ

(1)

where the hats denote the Fourier transform and k is the horizontal wave number. The name ‘compliance coefficient’ conjures an image of testing a foam mattress to see how its displacement responds to various loading patterns. This concise complex representation of the BL can be used to specify a lower boundary condition for linearized mountain wave problems: Aˆ = −qˆ Bˆ +

hˆ , 1−B

(2)

where Aˆ and Bˆ are the (complex) amplitudes of the up- and down-going wave near the lower boundary. The Copyright  2007 Royal Meteorological Society

symbol hˆ is the Fourier transform of the terrain shape. The physical properties of the BL enter (2) through B(k) =

iN 2 C(k) , m(k)

(3)

where m(k) is the vertical wave number. The complex reflection coefficient in (2) is qˆ = (1 + B)/(1 − B). Equation (2) describes the influence of the BL depth changes on wave generation and wave reflection. According to Peng and Thomson (2003), Smith et al. (2006a), Jiang et al. (2006) and Smith (2007), the effect is quite sensitive to the wind profile in the BL as influenced by surface roughness and heat flux. 7.4. Potential vorticity banners When low-level flow splitting or wave breaking occurs, dissipative processes in the turbulent regions generate PV that streams downwind in ‘PV banners’ (e.g. Smith, 1989a). Occasionally, these streams of vorticity will wrap up into pairs of eddies of opposite signs. Just prior to MAP, Aebischer and Schär (1998) predicted that the irregular peak and pass structure of the Alpine ridgeline would generate multiple PV banners. While it was not possible to probe the 3D structure of the wavebreaking region with aircraft, it was possible to detect the PV banners downstream. Flamant et al. (2004) observed and described the PV banners streaming south from the central Alps over the Po Valley. The famous mistral wind, shooting through the Rhine Valley gap between the Alps and the Pyrenees, is bounded on both sides by mountaininduced PV banners. Often, this wind is divided into two airstreams (mistral and tramontane) by PV banners shed from Mt. Lozere and other peaks in the Massif Central (Jiang et al., 2003; Schär et al., 2003). Over the Adriatic, the bora wind is broken into gap jets and wakes by PV generation from the Dinaric Alps (Grubiˇsić, 2004; Jiang and Doyle, 2005). Since the end of MAP, the details of PV generation have been further clarified by high-resolution numerical simulation (e.g. Epifanio and Rotunno, 2005). 7.5. Rotors and boundary layers Shortly after the MAP results began to appear, a new approach to the problem of rotor formation was reported by Doyle and Durran (2002). Rotors are intense vortices with horizontal axes, associated with lee waves or hydraulic jumps. The study of rotors, while partly independent of MAP, nonetheless advanced a central theme of MAP, i.e. the role of the BL in wave structure. The authors concluded that rotors will form when a strong trapped lee wave generates a strong decelerating pressure gradient causing the BL to separate from the Earth’s surface. The sensitivity of slow BL flow to pressure gradients (discussed above in Section 7.1) has been quantified by Vosper et al. (2006). A subsequent numerical study by Hertenstein and Kuettner (2005) pointed out that the Q. J. R. Meteorol. Soc. 133: 917–936 (2007) DOI: 10.1002/qj

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pressure gradient can also arise from lee-side hydraulic jumps. They proposed a two-part classification scheme for rotors: type A caused by lee waves and type B caused by jumps. These new ideas and hypotheses quickly generated excitement for a new field project devoted to rotors. A logical location for a rotor experiment was the famous Owens Valley site in California where the original Sierra Wave Project was first carried out (Grubiˇsić and Lewis, 2004), in the 1950s. At the time of writing, two field experiments, the Sierra Rotor Project and the Terraininduced Rotor Experiment (T-REX), have been carried out in 2004 and 2006. 8.

Conclusions

During the MAP-SOP in autumn 1999, three research aircraft were used to observe seven different cases of gravity wave generation around the Alps. In these investigations, several new observational methods were used including airborne dropwindsondes, down-looking lidar and a repeated flight leg strategy. New highresolution numerical models were tested against these new data and then used for 3D flow interpretation and hypothesis testing. In this survey, we review the gravity wave discoveries in MAP and show how they have stimulated subsequent development of theoretical and numerical models. Three types of stratified airflow dynamics were found to dominate the seven Alpine wave events. First is the effect of blocked or frictional BLs near the Earth’s surface. These slow-moving layers have two impacts. By immersing part of the terrain in stagnant flow, the effective heights of the mountain peaks are greatly reduced, and so is the wave generation. Also, by absorbing waves reflected downwards from the jet stream, the stagnant layer prevents the trapping of lee waves. The second type of flow dynamics observed above the Alps is the interaction of waves with a critical level. For weak waves in directional shear, the linear theory prediction of wave absorption appears to be confirmed. The wave amplitude decays rapidly aloft. More often, however, nonlinear effects dominate. In this case, the critical layer, or the weak stability aloft, decouples the flow, allowing the lower layer to act independently. Like a shallow layer of water spilling over a dam, the cold low-level air spills over high terrain and undergoes a hydraulic jumps over the lee slopes. The third type of flow dynamics involves precipitation. With sufficient latent heating upstream, the upper-level stability is reduced and the flow decouples. As with the other decoupling cases, the flow can spill down lee slopes, generating föhn. MAP included several detailed tests of numerical models in regard to wave generation and breakdown. The general ability of numerical models to simulate and predict the steady aspects of complex Alpine gravity waves was judged to be moderate to good, but very sensitive to spatial resolution, vertical coordinate, horizontal diffusion and the treatment of the turbulent BL. The use of Copyright  2007 Royal Meteorological Society

improved models allows an analysis of Alpine wave climatology. Results suggest that the western Alps are more likely to generate waves that reach the stratosphere. Acknowledgements The authors gratefully acknowledge the contributions of Dr. Joachim Kuettner to the success of the gravity wave objectives in MAP. In the 1930s in Germany and again in the Sierra Wave Project in the 1950s, he identified some of the fundamental properties of mountain waves and showed how airborne instruments could be applied to their investigation. Over his long career, he has contributed to a tradition of well-designed field projects successfully revealing the secrets of atmospheric dynamics. The initial impetus for both large international mountain meteorological field projects ALPEX and MAP came from Kuettner. Joach’s leadership in the organization and execution of international field projects is admired by all those who have worked and learned under his tutelage. Joach has encouraged a generation of young atmospheric scientists. The contributions to this research came from the gravity wave team: David Fritts, Greg Poulos, and Joachim Kuettner. Philippe Bougeault, Peter Binder, Joachim Kuettner, Herbert Pümpel and many others assisted in organizing MAP. Hans Volkert encouraged the MAP ‘harvest’ process that led to this review. Support for this work came from the National Science Foundation (ATM-0531212), the Naval Research Laboratory, Office of Naval Research (ONR) program element 0601153N, and the UK Met Office. COAMPS is a registered trademark of the Naval Research Laboratory. References Aebischer U, Schär C. 1998. Low-level potential vorticity and cyclogenesis to the lee of the Alps. J. Atmos. Sci. 55: 186–207. Afanasyev YD, Peltier WR. 2001. Numerical simulations of internal gravity wave breaking in the middle atmosphere: The influence of dispersion and three-dimensionalization. J. Atmos. Sci. 58: 132–153. Asencio N, Stein J, Chong M, Gheusi F. 2003. Analysis and simulation of local and regional conditions for the rainfall over the Lago Maggiore Target Area during MAP IOP2b. Q. J. R. Meteorol. Soc. 129: 565–586. Baines PG. 1995. Topographic effects in stratified flows. Cambridge University Press: Cambridge, UK. Bessemoulin P, Bougeault P, Genoves A, Clar AJ, Puech D. 1993. Mountain pressure drag during PYREX. Beitr. Phys. Atmos. 66: 305–325. Blumen W. (ed.) 1990. Atmospheric processes over complex terrain. Meteorol. Monograph 45: American Meteorol. Society: Boston, Mass. Bolliger M, Binder P, Rossa A. 2003. Tracking cloud patterns by METEOSAT rapid scan imagery in complex terrain. Meteorol. Zeitschrift 12: 73–80. Booker JR, Bretherton FP. 1967. The critical layer for internal gravity waves in a shear flow. J. Fluid Mech. 27: 513–539. Bougeault P, Benech B, Bessemoulin P, Carissimo B, Jansa Clar A, Pelon J, Petitdidier M, Richard E. 1997. PYREX: A summary of findings. Bull. Am. Meteorol. Soc. 78: 637–650. Bougeault P, Binder P, Buzzi A, Dirks R, Houze Jr RA, Kuettner J, Smith RB, Steinacker R, Volkert H. 2001. The MAP special observing period. Bull. Am. Meteorol. Soc. 82: 433–462. Brown AR. 2004. Resolution dependence of orographic torques. Q. J. R. Meteorol. Soc. 130: 3029–3046. Q. J. R. Meteorol. Soc. 133: 917–936 (2007) DOI: 10.1002/qj

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