1. Introduction
Mountain waves generated by stratified flow passing over a topographic barrier have a fundamental influence on the atmosphere on a variety of spatial scales ranging from turbulence and wave breaking associated with downslope windstorms to the aggregate effects of wave drag and fluxes on the momentum balance of the atmospheric general circulation and climate (e.g., see reviews in Smith 1989; Fritts and Alexander 2003). The stratified flow response to idealized two-dimensional obstacles (Durran 1986; Doyle et al. 2000) and three-dimensional terrain (Smolarkiewicz and Rotunno 1989; Ólafsson and Bougeault 1996, 1997) has been extensively addressed in the literature. In contrast, relatively few investigations have considered the flow response to realistic topography, particularly for large-scale mountains such as Greenland, the Antarctic Peninsula, and Tibetan Plateau that have the potential to have a significant impact on the circulation through the generation of large-amplitude mountain waves and planetary waves (e.g., Grose and Hoskins 1979; Smolarkiewicz et al. 2001).
Vertically propagating mountain waves increase in amplitude with height because of decreasing air density (Hines 1960; Lindzen 1967) or reverse wind shear layers (Smith 1989; Shen and Lin 1999), either of which independently or synergistically may lead to wave steepening, overturning, and subsequent turbulent breakdown, particularly in the stratosphere or mesosphere (e.g., Bacmeister and Schoeberl 1989; Fritts and Alexander 2003). An increase in the atmospheric stability such as the transition across the tropopause can reduce the vertical wavelength and increase the potential for wave breaking (VanZandt and Fritts 1989). Additionally, mountain waves may overturn and break as they approach a critical level (Clark and Peltier 1984; Dörnbrack 1998), a level at which the wave phase speed is equivalent to the wind component projected along the horizontal wave vector. High-resolution three-dimensional studies of wave breaking associated with overturning of isentropic surfaces highlight the role of nonlinear interactions that occur in the transition to turbulence (e.g., Fritts et al. 1996). Mountain wave breaking has a significant influence on the atmosphere for a number of reasons that include the impact of orographic drag on the large-scale circulation (Bretherton 1969; Palmer et al. 1986); downslope windstorms (Peltier and Clark 1979; Durran 1986); vertical mixing of water vapor, aerosols, and chemical species (Dörnbrack and Dürbeck 1998); potential vorticity generation (Schär and Smith 1993) and associated upscale forcing (Thorpe et al. 1993; Aebischer and Schär 1998); and clear-air turbulence that poses an aviation hazard (Lilly 1978; Ralph et al. 1997; Clark et al. 2000).
Although there have been numerous observational studies documenting mountain wave characteristics (e.g., Shutts 1992; Vosper and Mobbs 1996; Doyle and Smith 2003), direct observations of mountain wave breaking are relatively rare. The in situ observations of the windstorm and wave breaking in the lee of the Front Range of the Rockies on 11 January 1972 (Lilly and Zipser 1972; Lilly 1978) still may be the most complete set of observations of large-amplitude mountain wave breaking to date. The establishment of the link between resonant mountain wave amplification positioned beneath upper-level wave breaking regions that contain “wave induced” critical levels and downslope windstorm and gravity wave drag enhancement was motivated in part by these observations (Peltier and Clark 1979). The downslope windstorm has been subsequently shown to be consistent with internal hydraulic theory based on theoretical considerations (Smith 1985) and numerical simulations (Durran 1986). Other more recent observational evidence of mountain wave breaking has been documented, for example, above the Front Range of the Rockies (Clark et al. 2000), the Alps (Jiang and Doyle 2004), and the Welsh Mountains (Worthington 1998).
Many of the numerical studies reported upon in the literature have used two- and three-dimensional basic terrain shapes with idealized initial states to establish the characteristics of gravity wave breaking (e.g., Clark and Peltier 1984; Bacmeister and Schoeberl 1989; Ólafsson and Bougeault 1996, 1997; Epifanio and Durran 2001). There are relatively few studies that have used complex terrain and real-atmospheric initial states to simulate wave breaking. Examples include the Clark et al. (2000) study that used a high-resolution model to simulate a downslope windstorm and clear-air turbulence event over the Rockies and documented the generation of horizontal vortex tubes within wave breaking regions along a jet stream in the upper troposphere. Schmid and Dörnbrack (1999) simulated lower stratospheric wave breaking over the Alps associated with a critical level above the jet stream. Leutbecher and Volkert (2000) found that the simulation of mountain waves generated by Greenland were sensitive to the horizontal model resolution and surface friction representation. The multiscale terrain of the Alps was shown by Jiang and Doyle (2004) to promote wave breaking and increase wave drag. Although several of these previous real-data simulations have replicated the limited observations of the wave breaking evolution with reasonable accuracy, the predictability of wave breaking is not well established. For example, simulations of the 1972 Boulder windstorm using 11 different numerical models, all with identical initial states and two-dimensional terrain, exhibit diverse wave breaking evolution in some cases (Doyle et al. 2000). Outstanding issues regarding gravity wave breaking in the real atmosphere that are potentially important for mesoscale numerical weather prediction include turbulent mixing and wave overturning processes, mountain wave drag, downstream effects, and predictability of wave breaking. The current limit in our understanding of gravity wave breaking can be partially attributed to lack of observations.
During the Fronts and Atlantic Storm-Track Experiment (FASTEX) (Joly et al. 1997), a large-amplitude gravity wave was observed in the lee of Greenland on 29 January 1997 (e.g., see Doyle and Shapiro 1999). Data collected during FASTEX represents a unique opportunity to study topographically forced gravity wave breaking and to assess the ability of high-resolution numerical models to predict the structure and evolution of such phenomenon. The topography of Greenland (Fig. 1) is characterized by extremely steep terrain near the coastlines and an ice-covered plateau exceeding 3000 m with an average ice thickness of 1790 m and a thickness maximum of 3400 m (Dolgushin and Osipova 1989). The terrain of Greenland is complex and characterized by a spectrum of mountain shapes ranging from half-widths of less than 150 km in the south to greater than 500 km in the central portion. The study of flow impinging on Greenland and the generation of mountain waves is important for a variety of reasons that include its formidable topography and ice sheet, the proximity to the semipermanent Icelandic cyclone (Petersen et al. 2003), influence on synoptic-scale systems (Schwierz and Davies 2003), polar stratospheric cloud generation (Chan et al. 1993), katabatic winds (Bromwich et al. 2001), clear-air turbulence (Lester et al. 1989) and wave breaking (Leutbecher and Volkert 2000), contribution to large-scale mountain torque (Wei and Schaack 1984), tip jets and associated high-latitude air–sea interaction processes (Doyle and Shapiro 1999; Pickart et al. 2003), and the emerging significance of Greenland for the climate system (Murphy et al. 2002).
In the present study, a nonhydrostatic model simulation is evaluated with continuous research aircraft and dropwindsonde observations from the National Oceanic and Atmospheric Administration (NOAA) G-IV aircraft. Real data and idealized model simulations are used to document the evolution, characteristics, and dynamics of the breaking gravity wave event. An overview of the numerical model is presented in section 2. The observations of the wave breaking event are discussed in section 3. The results from a series of numerical simulations performed with real data and idealized flows are presented in section 4. The relationship between diabatic cooling within the boundary layer and wave amplitude is explored in section 5. Section 6 contains the summary and conclusions.
2. Numerical model description
The atmospheric portion of the U. S. Naval Research Laboratory’s Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS; Hodur 1997) is utilized for the numerical simulations of observed and idealized flows in this study. COAMPS is based on a finite-difference approximation to the fully compressible, nonhydrostatic equations and uses a terrain-following vertical coordinate transformation. In this application, the finite difference schemes are of second-order accuracy in time and space. The compressible equations are integrated efficiently using a time splitting technique with a semi-implicit formulation for the vertical acoustic modes (Klemp and Wilhelmson 1978).
The planetary boundary layer and free-atmospheric turbulent mixing and diffusion are represented using a prognostic equation for the turbulence kinetic energy (TKE) budget for both real data and idealized simulations. The surface fluxes are computed following the Louis (1979) formulation, which makes use of a surface energy budget based on the force–restore method. The subgrid-scale moist convective processes are parameterized using an approach following Kain and Fritsch (1993). The grid-scale evolution of the moist processes are explicitly predicted from budget equations for cloud water, cloud ice, raindrops, snowflakes, and water vapor (Rutledge and Hobbs 1983). The shortwave and longwave radiation processes are parameterized following Harshvardhan et al. (1987). The real-data simulations use the full suite of physical parameterizations. For simplicity, the idealized simulations are adiabatic with a free-slip lower boundary condition and include free-atmosphere vertical diffusion derived from the explicitly predicted TKE.
The real-data simulations are initialized using an incremental update data assimilation procedure that enables mesoscale phenomena to be retained in the analysis increment fields (Barker 1992). The initial fields for the model are created from multivariate optimum interpolation analyses of upper-air sounding, surface, commercial aircraft, and satellite data that are quality controlled and blended with the 12-h COAMPS forecast fields. Lateral boundary conditions for the outermost grid mesh are derived from the U. S. Navy Operational Global Analysis and Prediction System (NOGAPS) forecast fields.
The domain configuration for the real-data simulations, as shown in Fig. 2, contains four horizontally nested grid meshes of 81 × 81, 73 × 73, 133 × 133, and 223 × 223 points with horizontal grid increments on the computational meshes of 45 km, 15 km, 5 km, and 1.7 km, respectively. The model contains 80 vertical levels on a nonuniform vertical grid consisting of an increment of 10 m at the lowest level that gradually increases to 250 m at 12 km, 1000 m at 18 km, and continues with a 1000-m increment to the model top at 30 km. A radiation upper boundary condition is applied to mitigate the reflection of vertically propagating gravity waves. The topographic data for the simulations are based on the Global Land One-kilometer Base Elevation (GLOBE) dataset, made available by NOAA National Geophysical Data Center, which enables orographic characteristics, such as steep slopes of the Greenland ice sheet and the complex coastal orography, to be well represented, as shown in Figs. 1 and 2.
3. Observations
Several different sources of observations are used to describe the synoptic-scale and mesoscale atmospheric conditions on 29 January 1997, as well as the mountain waves over Greenland. This set of observations includes the routine radiosondes, satellite imagery, and research aircraft measurements that include continuous flight level data and Global Positioning System (GPS) dropwindsondes.
a. Synoptic-scale flow
A broad region of deep southwesterly flow extended from eastern Canada to northeast of Greenland, as illustrated by the COAMPS 12-h forecast of wind speed at 700-, 500-, and 250-hPa levels valid at 1200 UTC 29 January 1997 (Fig. 3). Synoptic-scale features of interest include a shortwave trough positioned over eastern Canada, a shortwave ridge located upstream and to the southwest of Greenland, and an upper-level front and deformation zone situated near Iceland. The southwesterly flow was strongest over the southern one-third of Greenland with winds upstream of Greenland attaining speeds from 7.5 to 15 m s−1 at 700 hPa (Fig. 3a) and 15 to 30 m s−1 at 500 hPa (Fig. 3b). At higher latitudes north of 70°N, there is relatively weak flow across the Greenland topography. The relatively strong southwesterly flow upstream of Greenland is confirmed by the radiosonde and dropwindsonde observations along western and southern Greenland shown in Figs. 3a,b. The relatively small vertical shear of the horizontal wind direction, as indicated by the 700- and 250-hPa winds (Figs. 3a,c), was conducive for deep propagation of gravity waves due to the lack of directional critical levels (e.g., Shutts 1998).
The visible satellite image from NOAA-12 valid at 1446 UTC 29 January, shown in Fig. 4, indicates that a southwest–northeast oriented band of lower- and middle-level clouds was present near Iceland, associated with the synoptic-scale baroclinic system. A broad region of lower- and middle-level clouds was present upstream of Greenland and a clear region was evident to the east, indicative of flow descent. Figure 5 presents the surface wind speeds at 1431 UTC 29 January 1997 derived from Special Sensor Microwave Imager (SSM/I) with an effective resolution of 25 km and rmse of ∼5 m s−1. The SSM/I winds indicate that a swath of surface wind speeds were in excess of 20 m s−1 upstream of Greenland. A weak region of wind speed with a minimum of approximately 5 m s−1 was present in the lee of Greenland along the eastern shore consistent with surface properties of a large-scale wake (e.g., Pan and Smith 1999; Doyle and Shapiro 1999; Petersen et al. 2003).
Radiosonde soundings taken at the southern tip of Greenland at Narssarssuaq, valid at 0000 and 1200 UTC 29 January 1997, are shown in Figs. 6a and 6b. At 0000 UTC 29 January, relative strong westerlies are present in the 850–500-hPa layer with wind speeds exceeding 20 m s−1 at 500 hPa. The layer between the surface and 5 km is characterized by a relatively strong static stability, corresponding to a Brunt–Väisälä frequency, N, of ∼0.013 s−1, similar to the stability in the 5–8.5 km layer that contains a mean N of ∼0.015 s−1. A marked change in the tropospheric stratification and winds occurs in the following 12-h period such that a three-layer stratification develops by 1200 UTC 29 January (Fig. 6b). A strong stable layer, which contains several shallow inversions, is present below 5 km (∼500 hPa) and has a corresponding mean N of ∼0.015 s−1. The 500–300-hPa layer is characterized by a much weaker stability, N ∼ 0.008 s−1, relative to the more stable lower troposphere and lower stratosphere. In the lowest 2 km, the flow is weak with a pronounced vertical speed shear in the 2–3-km layer. Observed wind speeds range from 12 m s−1 at 700 hPa, which is near the maximum height of the southern Greenland topography, to 30 m s−1 at 500 hPa and further increasing to 49 m s−1 near the tropopause level.
b. Research aircraft measurements
Measurements from the NOAA G-IV research aircraft were used to document the evolution and dynamics of a large-amplitude gravity wave event over Greenland, which also provide mesoscale observational validation data for the numerical simulations. During the research flight, 20 dropwindsondes were deployed along the flight path from an altitude of approximate 12 km (Fig. 2). The flight path was oriented in an east–west direction approximately along the large-scale wind direction and spanned across the entire Greenland ice shelf at ∼64.5°N. The in situ 25-Hz flight level (∼180 hPa or 12 km) u wind component, vertical velocity, and potential temperature are shown in Fig. 7 for the section of the flight path between 46° and 36°W. A large-amplitude wave signature with a horizontal scale in excess of 200 km is apparent in the u wind component (Fig. 7a), and the potential temperature (Fig. 7c) above the steep eastern slope of the Greenland ice sheet. The wave breaking is associated with horizontal shear of the cross-mountain wind component in excess of 10−3 s−1 and a 25-K potential temperature perturbation across the large-scale wave. The wind speed downstream of the breaking wave decreases by 30 m s−1, resulting in the reduction of the cross-mountain flow to near zero with localized flow reversal regions. The maximum vertical velocity magnitude approaches ∼10 m s−1 during the turbulent episode associated with the wave breaking (Fig. 7b). Gravity wave activity characterized by shorter horizontal wavelengths (less than 15 km) is evident in the velocity and potential temperature fields downstream of the prominent larger-scale wave breaking signature and extends to a distance of over 150 km. Due to the encounter with the extreme turbulence, the research aircraft ascended from 12.5 to 13.1 km ASL (Fig. 7d).
Manual vertical cross-section analysis of continuous flight level and dropwindsonde data, with a 50-km horizontal spacing, document the presence of the large-amplitude breaking gravity wave that extends from the 12-km level downward to 5 km ASL (Fig. 8a). Analysis of dropwindsondes 15 and 16 and the in situ flight level data suggest that phase lines tilt upshear with height in the upper portion of the wave similar to that of mountain waves in the hydrostatic regime (e.g., Smith 1989). The dropsonde spacing is insufficient to conclusively deduce the tilt of the phase lines in the lower portion of the wave, such as in the 3–6-km layer, where the analysis indicates the phase lines tilt somewhat downstream with height. Convectively unstable layers of depths greater than 2 km were measured by dropwindsonde 15 above the steep leeside slope, suggestive of wave breaking and associated isentropic overturning. The cross-mountain wind component analysis (Fig. 8b) indicates a wind speed maximum near the lower portion of the mountain wave at 7.5 km ASL and a region of weak and reversed flow near the flight level at 12 km ASL, once again consistent with wave breaking. A wind speed maximum greater than 28 m s−1 is positioned near the surface along the steep lee slope. The strong near-surface downslope winds rapidly transition to weak flow in the lee coincident with abruptly ascending isentropes, which is consistent with a hydraulic-like flow response (e.g., Durran 1986).
c. Wave breaking characteristics
To illustrate some of the characteristics of the wave breaking episode, TKE, momentum flux, and heat flux were computed from the research aircraft flight level data and are shown in Fig. 9. In these calculations, the perturbation fields are separated into scales less than 5 km, which is referred to as turbulence scale, and scales larger than 5 km, referred to as wave scale. The turbulence-scale perturbations are defined as: A′ = A − 〈A〉, where angle brackets represent a moving average over 5 km. The wave-scale perturbations are derived using A′ = 〈A〉 − 〈〈A〉〉, where the second-level average is computed over a 200-km length scale.
The TKE derived from the research aircraft data (Fig. 9a) indicates that an approximately 50-km wide maximum exists in the wave breaking zone with a long tail extending more than 180 km downstream, likely due to contributions from advection and local production. The TKE is displayed in Fig. 9a for each component, u′2/2, υ′2/2, and w′2/2, where u, υ, and w are the zonal, meridional, and vertical wind components, respectively. The magnitudes of the three TKE components are comparable, indicative of quasi-isotropic turbulence.
The vertical flux of the horizontal momentum is shown in Figs. 9b,c. The portion of the vertical flux of the zonal momentum, ρ〈u′w′〉, associated with turbulence-scale mixing is positive in the wave breaking zone, and the corresponding meridional flux, ρ〈υ′w′〉, is negative, where ρ is the air density. The zonal momentum flux due to wave-scale perturbations is negative and similar to the horizontal scale of the gravity wave. The signature in the momentum flux is consistent with the characteristics of the large-amplitude wave. The meridional momentum flux is comparatively small.
The in situ research aircraft data is used to compute the vertical heat flux, Cpρ〈θ′w′〉, where Cp is the specific heat capacity at constant pressure. The vertical heat flux associated with turbulence-scale perturbations, shown in Fig. 9d, indicates two major negative peaks within and downstream of the large TKE zone. If we assume that the mixing of heat is downgradient as well, the negative fluxes suggest that the layer is statically stable in the turbulence zone, which would limit turbulence production. In a recent study, Jiang and Doyle (2004) analyzed aircraft in situ measurements over a turbulent wave breaking zone in the middle troposphere in the central Alps. In the first flight transect analyzed in the Alpine study, the turbulence was nonisotropic and heat flux was positive, suggestive of turbulence in a development phase. During the second leg, the turbulence became near isotropic and the heat flux became negative, indicative of decaying turbulence. The characteristics of the turbulence measured by the research aircraft in this study was similar to that observed during the second flight leg in Jiang and Doyle. Thus, the turbulence may have been in a decay phase at the time of observation, although beneath the flight level turbulence production may be still active as indicated by the superadiabatic zone revealed by GPS dropsonde analysis. For a linear gravity wave, potential temperature and the vertical wind component should be in quadrature with zero heat flux averaged over one horizontal wavelength. In this case, the wave-scale vertical heat flux shows a large-scale negative maximum or downward heat flux in the region of the observed gravity wave, which may be due to nonlinearities in the wave breaking region.
The characteristics of the turbulence in the wave breaking zone measured by the research aircraft are further illustrated in Fig. 10 by the power spectrum in frequency and wavelength of the vertical velocity for 1140–1220 UTC 29 January, which is the time period that encompasses the wave breaking episode. The major peak in the vertical velocity spectrum, which occurs at a ∼10 km wavelength, is a manifestation of the shorter-scale waves evident in the vertical velocity observations upstream and downstream of the most intense breaking region (Fig. 7). These short-wavelength features are likely associated with the nonlinear breaking processes rather than a reflection of the dominant wavelength of the terrain (wavelength of the topography is approximately 300 km), which is clearly larger than this spectral peak. Additional peaks in the spectrum occur at ∼1–5 km wavelengths, which may be indicative of vigorous mixing dominated by large eddies consistent with a deep layer of isentropic overturning associated with large-amplitude wave breaking (Fig. 8a). At wavelengths less than approximately 1 km, an approximate slope of 2.7 to the energy spectrum is apparent, which deviates somewhat from the k−5/3 slope found in a number of studies including kinetic energy spectra derived from aircraft measurements (Nastrom and Gage 1985) and spectra derived from a B-57 aircraft during penetration of a region of severe turbulence (Lilly and Kennedy 1973). The velocity spectrum of the u wind component is dominated by a k−5/3 slope for the high-frequency portion.
4. Numerical simulations of mountain wave breaking
High-resolution numerical simulations of the 29 January 1997 mountain wave breaking event were conducted using the COAMPS model with the objectives of assessing the ability of an operational modeling system to forecast wave breaking and documenting the characteristics and dynamics of the mountain wave evolution and breaking. Additional simulations were conducted using synthetic initial conditions in order to gain insight into the relationship between the wave breaking and steep terrain.
a. Numerical simulations of 29 January 1997 wave breaking event
To accurately simulate mountain waves generated by complex terrain, the large-scale flow must be realistically represented because of the sensitivity of gravity wave characteristics, such as the amplitude and wavelength, to the upstream wind and stability profiles (e.g., Durran 1986; Smith 1989). The COAMPS simulated wind field on the 45-km resolution mesh, valid at 1200 UTC 29 January (12-h simulation time), agrees reasonably well with the radiosonde and GPS dropwindsonde observations for 700, 500, and 250 hPa, as shown in Figs. 3a–c. The relatively strong southwesterly flow over Greenland in the lower and middle troposphere are in agreement with the wind observations. The simulated winds are weakest over northern Greenland and strongest near the southern tip, also in agreement with the observations. The radiosonde and model-derived (based on the 15-km resolution mesh) soundings at Narssarssuaq for 0000 and 1200 UTC 29 January, are shown in Figs. 6a and 6b. The model-derived sounding at the initialization time, 0000 UTC 29 January, agrees well with the radiosonde. The profiles indicate that the model captures the increase of the lower-tropospheric static stability and decrease of the upper-level stability over the 12-h time period with reasonable skill. The simulated wind speed maximum near 300 hPa at 1200 UTC 29 January is ∼40 m s−1, in contrast to the observed wind speed maximum of 49 m s−1. Several of the smaller-scale structures in the sounding including shallow inversions are not particularly well represented; however, the model does capture the overall stability and wind profiles accurately.
Vertical cross sections of potential temperature and cross-mountain wind speed, based on the 5-km resolution mesh and oriented along a portion of the research aircraft transect, are shown in Figs. 11a and 11b, valid at 1000 UTC 29 January (10-h simulation time). The simulated upper-level wave breaking, as diagnosed by the region with TKE in excess of 5 m2 s−2, vertically spans the 8–11-km layer above the lee slope and extends ∼100 km downstream (Fig. 11a). The isentropic cross section has a number of characteristics in common with the analysis based on the observations (Fig. 8a), which includes the weak stability layer in the upper troposphere and the deformed tropopause associated with the wave amplification and breaking. However, the simulation differs from the analysis in several respects. One primary difference is that the simulated wave amplitude and breaking region has a considerably smaller amplitude than indicated by the dropsonde analysis. The analysis contains a layer of weaker static stability layer in the middle and upper troposphere upstream of the Greenland crest relative to the simulation. The implication of this static stability difference is that the simulated hydrostatic vertical wavelength, 2πU/N, may be underestimated. The mean stability between mountaintop level (i.e., 3000 m) and wave breaking level (∼9000 m), estimated using dropsonde 18 and the 1200 UTC COAMPS simulation time at the same location, is 0.0139 and 0.0141 s−1, respectively. Since the static stability differences are rather small over the 3–9-km layer depth, the hydrostatic vertical wavelengths are nearly identical: 11.3 km based on the dropsonde and 11.1 km for the simulation. The static stability differences in the 5–9-km layer are somewhat greater, which implies a larger vertical wavelength based on the observations relative to the simulation. The differences in the upstream profiles apparently do not completely explain the nature of the discrepancy between the simulated and observed wave amplitude. Other factors that may impact the wave amplitude include vertical shear, nonlinearities, and baroclinicity. It is also noteworthy that the phase lines of the simulated vertically propagating waves in the stratosphere have a greater tilt upstream than indicated by the analysis, which is likely due to the limitations imposed by the relatively coarse dropsonde spacing.
The vertical cross section of the cross-mountain wind speed indicates a maximum of 54 m s−1 located near 9 km (Fig. 11b), in general agreement with the observed 48 m s−1 wind speed maximum (Fig. 8b). The strong downslope winds located just above the surface along the lee slope are in excess of 35 m s−1, similar to the shooting flow diagnosed from the dropwindsonde data. A region of weak flow is present in the 10–12-km layer coincident with the wave breaking in both simulated and analyzed cross-mountain winds. The region of weak cross-mountain wind speed extends upstream with height in the lower stratosphere similar to other simulations of wave breaking (e.g., Doyle et al. 2000). Weak flow is also present just above the strong downslope winds and coincident with a gravity wave feature that exhibits internal hydraulic jump characteristics similar to those depicted in the analysis based on the dropwindsondes (Fig. 8b). In the upstream region, the dropsondes indicate that stronger vertical shear is present in the 3–9-km layer relative to the simulation.
The simulated wind speed, potential temperature, and TKE derived from the 1.7-km resolution grid mesh was interpolated to a portion of the research aircraft flight transect at the nearest available model output time (1130 UTC 29 January 1997) and is displayed in Fig. 12 along with the in situ aircraft observations. To illustrate the spread and variability of the simulated flow in the vicinity of the flight track, the model results interpolated to 0.25° north and south of the flight path are shown by the gray dotted lines in Fig. 12. The perturbation potential temperature is shown for ease of comparison. The highest-resolution grid mesh accurately captures the gross large-scale features of the wave. For example, the model and observations both exhibit a wind speed perturbation of nearly 30 m s−1 associated with the gravity wave (Fig. 12a) and a potential temperature perturbation greater than 25 K (Fig. 12b). Downstream of the highly turbulent region, the observations indicate several wavelike structures in the winds; however, in the model the amplitude of the simulated short wavelength features is substantially weaker. Additionally, the mean wind speed in the simulation downstream of the breaking region is 2.5 to 7.5 m s−1 too large. The model does not reduce the wind speed as much as observed in the strongest portion of the wave breaking; however, this is likely due to a sampling issue as other nearby grid points show larger TKE and weaker wind speeds. The TKE predicted by the model and derived from the 25-Hz research aircraft observations are shown in Fig. 12c. To facilitate a meaningful comparison between the aircraft observations and the model simulation for the fourth grid mesh (Δx = 1.7 km), scales less than 1.7 km are considered turbulence. The model simulated TKE shows two distinct peaks. One maximum occurs in the observed region of minimum wind speed and highest frequency activity, however, the model-simulated TKE maximum of 2 m2 s−2 is considerably less than the derived TKE maximum of 10.5 m2 s−2 based on the aircraft data. In the simulation, a second maximum exists 25 km downstream of the initial breaking zone, apparently associated with strong buoyancy and shear contributions. The surrounding grid points just north and south of the flight track indicate considerable variability and appear to match better with the flight level data for the western TKE maximum.
The TKE at 12 km ASL, obtained from the fourth grid mesh (1.7-km horizontal resolution) for 1130 UTC 29 January is shown in Fig. 13a. The simulated TKE indicates a widespread region of wave breaking occurs above the steepest portion of the leeside topography and decays with distance downstream. The cross-mountain wind component at 12 km ASL, shown in Fig. 13b, indicates a strong horizontal gradient in the wind speed is present associated with the wave breaking. For example, the region of wind speed in excess of 40 m s−1 upstream of the breaking transitions over a relatively short distance of 5–10 km to weak or reversed flow in the downstream. Downstream of the wave breaking, the cross-mountain wind field contains rich structure comprised of streams of weak and strong flow. The source of the weak or reversed flow plumes are linked with the more intense regions of dissipation associated with wave breaking, in contrast to the stronger flow maxima that appear to be associated with regions of relatively weak breaking and dissipation (Fig. 13a), similar to the characteristics of lower-tropospheric gap winds and wakes (e.g., Pan and Smith 1999).
The temporal variability of the wave breaking is illustrated by the time–distance diagram of the cross-mountain wind component at 12 km ASL, shown in Fig. 14. The time section is constructed along a portion of the research aircraft flight path shown in Fig. 13a. The wave breaking is most intense in the 1000–1300 UTC time period, as indicated by the region of TKE in excess of 10 m2 s−2. During this time period, the cross-mountain wind speed is a maximum just upstream of the breaking zone, suggestive of an amplifying wave. The wake that forms downstream of the wave breaking, characterized by a region of weak wind speed, expands with time due to advection.
b. Impact of the Greenland terrain slope on wave breaking
A series of three-dimensional numerical simulations were conducted using the atmospheric portion of COAMPS applied in an idealized configuration in order to explore the sensitivity of wave breaking to the terrain slope. Lilly and Klemp (1979) noted that an asymmetric mountain shape with a gentle upwind slope and a steeper downwind slope tended to generate stronger downslope winds than a symmetric profile for a single layer flow. Miller and Durran (1991) found that the downslope windstorms were most sensitive to terrain asymmetry for two-layer flows. Miller and Durran considered several atmospheric states and noted that for inviscid flows the steepness of the leeside slope has more of an influence on the downslope windstorm than the terrain asymmetry. However, the relationship between the terrain slope and wave breaking for a topographic obstacle similar to the size of Greenland, which may be influenced by rotation and nonlinear effects, is not clear.
The three-dimensional idealized simulations are adiabatic and make use of a free-slip lower boundary condition. Simulations are performed with and without the effects of the earth’s rotation. The simulations with rotation are performed with a Coriolis parameter f = 1.26 × 10−4 s−1, corresponding to a 60°N latitude, consistent with that of Greenland. The simulations are initialized as a horizontally homogeneous initial state with N = 0.01 s−1, that is, hydrostatically balanced and a zonal wind component U = 20 m s−1. The initial state is in geostrophic balance for the simulations with rotation. The idealized simulations make use of two horizontally nested grid meshes of 91 × 91, and 265 × 265 points with horizontal grid increments on the computational meshes of 45 and 15 km, respectively. Open lateral boundary conditions are applied for the outermost grid mesh using a constant phase speed approximation. The inner mesh boundary lateral conditions use a one-way interactive nesting technique. The model contains 99 vertical levels on a nonuniform vertical grid consisting of an increment of 200 m in the lowest 10 km, with a gradual increase to 500 m at ∼24 km and continues with a 500-m increment to the model top at ∼32 km. A sponge layer of 8-km depth at the model top is used to mitigate spurious reflection of vertically propagating waves.
Vertical cross sections through the ridge centerline (hm = 3000 m) illustrate the sensitivity of wave breaking to the terrain slope as shown in Fig. 16. In these idealized simulations the model is integrated to 12 hours, which is a reasonable time period to assume steady synoptic-scale flow. Several simulations conducted using longer integration times indicate that the wave response at 12 hours is similar to that of 24 hours or later, although some differences are apparent in the wave breaking regions. The most intense regions of wave breaking are denoted by hatched areas, which correspond to TKE of 2 m2 s−2 or greater. The simulation with s = 1 without rotation (Fig. 16a) indicates that a large-amplitude wave is generated in the lee of the bell-shaped terrain. Wave breaking is confined to the lower troposphere below 6 km. The corresponding s = 3 simulation (Fig. 16b) indicates that much stronger and deeper wave breaking is generated by the steeper leeside terrain, consistent with the results from Lilly and Klemp (1979) and Miller and Durran (1991). Large-amplitude mountain waves generated by the steep terrain vertically propagate and subsequently amplify and break in the upper levels above 14 km. The inclusion of rotation significantly decreases the wave amplitude for the s = 1 terrain (Fig. 16c), similar to the results of Ólafsson and Bougeault (1997), particularly for the portion of the ridge south of the centerline. The wave breaking generated by the steeper terrain (Fig. 16d) appears to be less sensitive to rotational effects. The steeper terrain essentially has an effective Rossby number, Ro = U/fa, that is increased relative to the bell-shaped terrain because of the narrow width of the plateau slopes. For example, Ro ∼ 0.5 for the s = 1 terrain (Fig. 16c), in contrast to the s = 3 terrain (Fig. 16d), which has an effective Ro ∼ 1.5.
5. Impact of diabatic cooling on wave amplitude
The ice-covered surface of Greenland undoubtedly has an important influence on the near-surface energy balance and boundary layer response (e.g., Oerlemans and Vugts 1993). The stable boundary layer evident in the soundings (Fig. 6) and dropwindsondes (Fig. 8) for 29 January 1997 is likely a manifestation of airmass cooling over the relatively colder ice sheet through radiation and surface flux processes. The influence of diabatic cooling/heating within the boundary layer on mountain waves has been suggested to be important based on observational and theoretical evidence. Several observational studies of downslope wind frequency indicate that windstorms near Boulder, Colorado, in the lee of the Front Range tend to be more frequent at night and a minimum during the daytime (Brinkmann 1974; Whiteman and Whiteman 1974). Raymond (1972) solved a nonadiabatic form of Long’s equation and found that boundary layer cooling over a mountain ridge contributes to an increase in the wave amplitude and boundary layer heating has the opposite impact.
6. Summary and conclusions
A large-amplitude mountain wave event was observed during FASTEX on 29 January 1997 by several different observing systems including the NOAA G-IV research aircraft equipped with continuous flight level instrumentation and GPS dropwindsondes. The synoptic scale was characterized by deep southwesterly flow over Greenland with the strongest cross-mountain wind speeds located over the southern portion. Surface wind speeds derived from SSM/I indicated the presence of a large region of weak winds in the lee likely associated with an internal hydraulic jump and wave breaking. Radiosondes and dropwindsondes indicated that strong low-level flow was forced to ascend the Greenland ice sheet and was characterized by a several kilometer deep layer of strong static stability in the lower troposphere positioned beneath a weaker stability layer in the upper troposphere, which was conducive for mountain wave generation. Linear theory and idealized nonlinear numerical simulations suggest that boundary layer cooling acts to increase the effective mountain height for relatively wide obstacles such as Greenland, which enhances the wave amplitude and increases the potential for wave breaking.
The evolution and characteristics of the large-amplitude mountain wave event generated by flow over Greenland was documented through the use of in situ measurements and GPS dropwindsondes deployed from the research aircraft. A large-amplitude gravity wave signature with a horizontal scale of approximately 200 km was evident in the velocity and potential temperature in situ measurements, with an ∼25 K potential temperature and ∼10 m s−1 vertical velocity perturbations associated with the gravity wave. The 50-km spaced dropwindsondes and flight level data depict a large-amplitude wave that deformed the tropopause and lower stratosphere in the 5–12-km layer. One of the dropsondes measured an ∼2 km deep convectively unstable layer, suggestive of wave breaking. Near the surface, wind speeds were approximately 30 m s−1 in the lee that transitioned to weaker flow downstream of an internal hydraulic jump feature. The horizontal location of the overturning layer was well correlated with large turbulence values derived from the in situ measurements. The TKE components based on the zonal, meridional, and vertical wind perturbations derived from the flight level data are of comparable magnitude, indicative of quasi-isotropic turbulence. The momentum fluxes associated with the turbulence-scale perturbations exhibit vigorous mixing of momentum with much weaker wave-scale fluxes. The vertical heat flux calculations suggest that turbulence was in a decay phase at the observation time, although other levels of active turbulence production may have existed. Peaks in the power spectrum occurred at ∼10 km and 1–5-km wavelengths, indicative of vigorous mixing consistent with the deep layer of isentropic overturning.
The large-amplitude wave breaking event was simulated using the nonhydrostatic COAMPS using four nested grids with a finest horizontal resolution of 1.7 km. The simulated gravity wave structure derived from the 5-km resolution mesh contained many common characteristics with observations and analysis of the dropwindsondes including (i) a large-amplitude wave with deformed tropopause, (ii) wave overturning layers, (iii) a near-stagnant cross-mountain wind component in the breaking zone, (iv) strong downslope windstorm near the surface and a low-level internal hydraulic jump, and (v) a local wind speed maximum of 50 m s−1 at the base of the wave near 9 km ASL. However, the simulation had a smaller amplitude wave than analyzed based on the research aircraft data. The numerical simulation underscores the difficulty in accurately reproducing a large-amplitude wave associated with a flow characterized by a wide range of spatial scales. The 1.7-km resolution inner grid mesh simulation compared well with the research aircraft data with regard to the wave breaking amplitude, location, and timing. For example, the perturbation wind speed of 30 m s−1 and perturbation potential temperature of 26 K associated with the mountain wave compared well with the research aircraft measurements of 35 m s−1 and 25 K. A phase error in the TKE maximum was apparent, which may be related to sampling issues within the wave breaking region. The winds and TKE at 12 km, which is the approximate flight level, exhibited rich small-scale structures associated with the wave breaking, with wakelike plumes that extend downstream from the dissipative regions. The simulated wave breaking was quite transient with the duration of the strongest wave overturning occurring over a 2-h period, which corresponds to the period of maximum momentum flux divergence. The observations and real-data numerical simulation both indicate that wave amplification and breaking occurred above the steep leeside slope of Greenland. A series of idealized simulations suggest that the steep terrain slope increases the effective Rossby number of the relatively wide Greenland topography, and as a result the wave characteristics are less sensitive to rotational effects.
The advancement of knowledge and prediction of mountain wave breaking has been limited by a lack of companion observations, which are necessary for model evaluation and elucidation of the dynamical processes. Gravity wave breaking is considered to be very localized and transient, which presents a challenge for conventional observing systems. The observations, taken from the NOAA G-IV research aircraft during FASTEX on 29 January 1997, included in situ measurements and GPS dropwindsonde data that provided a relatively rare depiction of large-amplitude wave breaking forced by the large-scale topography of Greenland. Although the objective of the research mission was to observe mountain waves generated by Greenland and was inspired by large-scale numerical model forecasts, the in situ and dropwindsonde measurements of the large-amplitude wave breaking near the geographic region of maximum wave activity and within the narrow time window of maximum wave breaking was serendipitous in many respects.
There are a number of outstanding issues regarding gravity wave breaking generated by large-scale topography such as Greenland and the Tibetan Plateau including (i) wave overturning processes and the significance of turbulent mixing including stratospheric–tropospheric exchange issues and polar stratospheric cloud generation; (ii) wave drag for large-scale obstacles, which is only partially resolved in extended-range forecast and climate models; (iii) predictability of clear-air turbulence; (iv) the linkage between low-level wave breaking that result in strong gradients of surface fluxes and air–sea interaction processes; (v) upscale energy transfer from the wave breaking to the planetary scale; (vi) the relationship between wave breaking, downslope windstorms, and thermally forced flows such as katabatic winds; and (vii) the aggregate effect of these microscale and mesoscale processes on the climate system. Future progress in the dynamical processes and prediction of orographic flows, and in particular mountain wave breaking, will require high-resolution numerical models capable of resolving the wave breakdown processes in concert with airborne and remotely sensed observing systems deployed during future field campaigns.
Acknowledgments
Support was provided by the Office of Naval Research’s Program Element 0601153N, with computing time supported in part by a grant of HPC time from the Department of Defense Major Shared Resource Center, Aberdeen, MD. COAMPS is a registered trademark of the Naval Research Laboratory. Jeff Hawkins of NRL graciously provided the NSCAT and SSM/I data through the support of the Office of Naval Research (PE 060243N) and the Space and Naval Warfare Systems Command, PMW-185 (PE 0603207N). The authors wish to acknowledge Robert Gall for helpful discussions and contributions to the planning and execution of the NOAA G-IV research flight over Greenland during FASTEX. The authors are grateful for the outstanding support of the NOAA Aircraft Operations Center (AOC) and for providing the platform and measurements. Comments by three anonymous reviewers substantially improved an earlier version of this manuscript.
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Three-dimensional depiction of the Greenland relief.
Citation: Journal of the Atmospheric Sciences 62, 9; 10.1175/JAS3528.1
The outer-grid mesh (Δx = 45 km) topography and inner-grid mesh locations for the numerical simulation. The contour interval is 200 m. The NOAA G-IV flight track and dropsonde locations are indicated by the solid line and gray circles, respectively.
Citation: Journal of the Atmospheric Sciences 62, 9; 10.1175/JAS3528.1
The 12-h simulated wind speed (grayscale every 5 m s−1) valid at 1200 UTC 29 Jan 1997 for (a) 700, (b) 500, and (c) 250 hPa. Radiosonde and dropwindsonde winds are shown by the station model wind vectors with full and half barbs representing 5 and 2.5 m s−1, respectively, and a pennant 25 m s−1.
Citation: Journal of the Atmospheric Sciences 62, 9; 10.1175/JAS3528.1
The NOAA-12 visible satellite image valid at 1446 UTC 29 Jan 1997 (obtained from the University of Dundee).
Citation: Journal of the Atmospheric Sciences 62, 9; 10.1175/JAS3528.1
Near-surface wind speed derived from SSM/I for 1431 UTC 29 Jan 1997. The wind speed is represented by the color scale (m s−1).
Citation: Journal of the Atmospheric Sciences 62, 9; 10.1175/JAS3528.1
Skew T–logp diagram (temperature, dewpoint, and wind profiles) for Narssarssuaq, Greenland (solid black soundings), valid at (a) 0000 and (b) 1200 UTC 29 Jan 1997. The model soundings are shown by the gray lines. The wind speeds (m s−1) from the model (right) and radiosonde (far right) are shown along the right side of the diagram with full and half barbs representing 5 and 2.5 m s−1, respectively, and a pennant 25 m s−1.
Citation: Journal of the Atmospheric Sciences 62, 9; 10.1175/JAS3528.1
The NOAA G-IV 25-Hz flight level (180 hPa or ∼12 km) measurements of the (a) horizontal velocity (m s−1), (b) vertical velocity (m s−1), and (c) potential temperature (K) for a portion of the flight path that extended from central Greenland to 150 km offshore. (d) The terrain height (km) (black, left axis) interpolated to the flight path and aircraft altitude (km) (gray, right axis).
Citation: Journal of the Atmospheric Sciences 62, 9; 10.1175/JAS3528.1
Vertical cross-section analyses based on the NOAA G-IV in situ and dropwindsonde observations for (a) potential temperature (K) (isentrope interval 4 K) and (b) section-parallel wind speed (m s−1) (black, isotach interval 4 m s−1) and isentropes (gray) valid at 1200 UTC 29 Jan 1997.
Citation: Journal of the Atmospheric Sciences 62, 9; 10.1175/JAS3528.1
Diagnostics derived from the NOAA G-IV 25-Hz flight level measurements consisting of (a) turbulence kinetic energy components, (b) vertical flux of horizontal momentum for the turbulence scales (less than 5 km), (c) vertical flux of horizontal momentum for the wave scale (greater than 5 km), and (d) vertical heat flux for turbulence and wave scales. The computations are performed along the identical segment as shown in Fig. 7.
Citation: Journal of the Atmospheric Sciences 62, 9; 10.1175/JAS3528.1
Power spectrum in frequency and wavelength of the vertical velocity for the wave breaking episode (1140–1220 UTC 29 Jan). The k−5/3 slope is shown by the gray line.
Citation: Journal of the Atmospheric Sciences 62, 9; 10.1175/JAS3528.1
Vertical cross sections derived from the COAMPS grid mesh 3 (Δx = 5 km) simulation for (a) potential temperature (K) (isentrope interval 4 K) with turbulent kinetic energy greater than 5 m2 s−2 hatched and (b) section parallel wind speed (m s−1) (isotach interval 4 m s−1) with regions of wind speed less than 4 m s−1 hatched. The cross sections are valid at 1000 UTC 29 Jan 1997 (10-h simulation time). The tick marks along the abscissa are shown every 50 km.
Citation: Journal of the Atmospheric Sciences 62, 9; 10.1175/JAS3528.1
The NOAA G-IV 25-Hz flight level measurements (solid lines) of the (a) wind speed (m s−1), (b) perturbation potential temperature (K), and (c) turbulence kinetic energy (m2 s−2) for a portion of the flight path that extended from central Greenland to 125 km offshore. (d) The terrain interpolated to the flight path. The model-simulated values are interpolated to the flight path from the finest-resolution grid mesh (Δx = 1.7 km) shown by the dashed lines and the model results interpolated to 0.25° north and south of the flight path are shown by the gray dotted lines.
Citation: Journal of the Atmospheric Sciences 62, 9; 10.1175/JAS3528.1
The model-simulated (a) TKE (grayscale every 2.5 m2 s−2) and (b) wind vectors and cross-mountain wind component (grayscale every 4 m s−1) valid at 1130 UTC 29 Jan 1997 (11.5-h simulation time) at 12 km ASL for the finest-resolution grid mesh (Δx = 1.7 km). The model topography is shown in (a) with a 200-m contour interval.
Citation: Journal of the Atmospheric Sciences 62, 9; 10.1175/JAS3528.1
Time–distance diagram of the model-predicted cross-mountain wind component (grayscale every 5 m s−1) valid from 0900 to 1500 UTC 29 Jan 1997. TKE greater than 10 m2 s−2 is represented by the hatched regions. The location of the time–distance section is along segment AA′ shown in Fig. 13a. The tick marks along the abscissa are shown every 50 km.
Citation: Journal of the Atmospheric Sciences 62, 9; 10.1175/JAS3528.1
Time–height diagram of the model-predicted vertical flux of horizontal momentum (grayscale every 0.1 × 1011 N) for the 1.7-km resolution mesh.
Citation: Journal of the Atmospheric Sciences 62, 9; 10.1175/JAS3528.1
Vertical sections of potential temperature (K) based on idealized three-dimensional simulations with hm = 3000 and (a) s = 1 and without rotation, (b) s = 3 and without rotation, (c) s = 1 with rotation ( f = 1.26 × 10−4 s−1), and (d) s = 3 with rotation ( f = 1.26 × 10−4 s−1). The contour interval is 4 K. TKE greater than 2 m2 s−2 is denoted by the hatched regions; tick marks along the abscissa are shown every 100 km.
Citation: Journal of the Atmospheric Sciences 62, 9; 10.1175/JAS3528.1
Simulated nondimensional cross-mountain pressure drag as a function of the normalized terrain slope f (s), as defined by Eq. (5). The drag is normalized by the two-dimensional linear drag.
Citation: Journal of the Atmospheric Sciences 62, 9; 10.1175/JAS3528.1
Vertical cross section of the parcel displacement field (gray shading every 1 km) from linear theory with hm = 1000 m and a = 300 km for (a) adiabatic flow and (b) diabatic flow with Q = −0.2 for a 1-km boundary layer depth. The vertical velocity is shown at an interval of 0.01 m s−1.
Citation: Journal of the Atmospheric Sciences 62, 9; 10.1175/JAS3528.1
