The GW-LCYCLE I campaign took place from 2 to 14 December 2013 in Kiruna, northern Sweden (68∘ N, 20∘ E; see Fig. ). The principal observational platform was the Deutsches Zentrum für Luft- und Raumfahrt (DLR) research aircraft Falcon, based at Kiruna airport in the lee of the Scandinavian mountain range. Airborne observations were complemented by radiosonde measurements launched at the windward side of the mountains at Andenes (69∘ N, 16∘ E; Norway), at the leeward side at the European Space and Sounding Rocket Range Esrange (68∘ N, 21∘ E, Sweden) at Kiruna airport (Sweden) and further downstream at Sodankylä (67∘ N, 27∘ E; Finland). In addition, ground-based lidar systems were operated at the Arctic Lidar Observatory for Middle Atmosphere Research (ALOMAR) in Andenes and at Esrange and provided time series of temperature and wind profiles at altitudes between 30 and 90 km. At Andenes, middle atmospheric winds were measured with the Middle Atmosphere Alomar Radar System (MAARSY). The flight strategy during the campaign focused on synoptic situations with strong westerly cross-mountain flow, which are favourable for the excitation of mountain waves . The planning of the respective research flights was facilitated by the usage of the Mission Support System MSS;, which is a software tool to compute meteorological parameters along virtual flight legs on the basis of numerical weather prediction model output.

Altogether, there were five intensive observation periods (IOPs) with a total of six research flights and 92 radiosoundings (see Table ). IOP 1 and 5 were mountain wave events which were studied with four research flights and are investigated in this paper. No research flight could be conducted during a strong mountain wave event on 11 December 2013 (IOP4) as a downslope windstorm with gale force cross winds made take-off and landing impossible at Kiruna airport. The event during IOP2 was dominated by the winter storm “Xaver”, which passed over northern Germany . This storm caused mountain and jet-induced GWs over southern Scandinavia and deep propagating convective GWs in a strong, convective cold-air outbreak with polar low formation over the Norwegian Sea. Finally, relatively calm conditions prevailed during IOP3, enabling the measurement of polluted air (mainly of SO2), which was advected towards northern Scandinavia from midlatitudes with sources in the US and China (H. Schlager, personal communication, 2013).

The DLR Falcon aircraft was equipped with a downward-looking coherent DWL which operates at a wavelength of 2 µm. Within the last years, this lidar system was successfully deployed in several ground-based and airborne field campaigns for instance for measuring aircraft wake vortices , aerosol optical properties and the three-dimensional wind field over the Atlantic Ocean . Details about the DWL hardware configuration are given by and , and details about the retrieval procedure can be found in .

During the GW-LCYCLE I campaign, the DWL was operated in scanning or nadir modes aiming to measure the vertical profiles of the three-dimensional wind vector or to measure the vertical wind speed, respectively. While operating in scanning mode, a conical step-and-stare scan around the vertical axes with an off-nadir angle of 20∘ is performed, which results in a horizontal resolution of 9 km. During nadir mode operation, the laser beam is pointed in nadir direction and the measured LOS wind equals the vertical wind speed with a horizontal resolution of 200 m. The vertical resolution for both measurement modes is determined by the laser pulse length and is set to be 100 m. A detailed technical description of the DWL measurements during GW-LCYCLE I is given in .

During the GW-LCYCLE I campaign the nadir-operating mode was used most frequently, as it was suitable to detect small-scale gravity waves over the complex orography. An overview of the flight altitudes and flight legs where the lidar operated in nadir and scanning modes during IOP1 and IOP5 is given in Fig. . In this figure the topography height along the flight legs is represented by the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) data set , which has a horizontal resolution of 30 m.

Besides wind lidar observations, in situ measurements of standard meteorological parameters were conducted at flight level during all research flights with a time resolution of 1 s. The measurement of in situ three-dimensional wind is described in and the verification of airborne pressure measurements in . Trace gas measurements were performed at flight level with the water vapour analyser (WARAN) hygrometer and a mass spectrometer for water vapour and SO2, respectively. The University of Mainz Airborne Quantum Cascade Laser-spectrometer UMAQS; was applied to measure nitrous oxide (N2O), which is virtually inert in the UTLS. The transition from nearly constant tropospheric (327.5 ± 0.9 ppbv) to decreasing stratospheric N2O mixing ratios allows for the determination of the chemical tropopause, which was defined by mixing ratios of 326.6 ppbv during GW-LCYCLE I. The main objective of trace gas measurements was to detect GW-induced vertical mixing processes in the tropopause region.

Airborne measurements were complemented by ground-based meteorological observations. During the five IOPs a total of 92 radiosondes was released both on the wind and leeward sides of the mountain range at Andenes (Norway), Esrange (Sweden), Kiruna (Sweden) and Sodankylä (Finland). Depending on wind conditions the sondes drifted up to 390 km horizontally and reached altitudes of more than 30 km in most cases. This data set allows us to study tropospheric GWs and their propagation through the tropopause into the lower stratosphere. In addition to radiosonde observations, the Esrange Rayleigh lidar provided 130 h of temperature profiles of the middle atmosphere between altitudes of 30 to 65 km. The lidar measurements were conducted during the period of 24 November to 14 December 2013. The analysis of the lidar and radiosonde data in combination with mesoscale numerical modelling is described in .

Mesoscale numerical simulations of the two mountain wave events IOP1 and IOP5 are performed with the Weather Research and Forecasting (WRF) model, version 3.7 . Up to three nested domains (D1, D2 and D3) with horizontal resolutions of 7.2, 2.4 and 0.8 km (see Fig. ) are used. For the two coarse domains 138 terrain-following levels with stretched level distances of 80 m near the surface, 160 m near the tropopause and 300 m in the upper stratosphere are used, and the model top is set to 2 hPa (about 39 km altitude). For the innermost domain only 78 vertical levels are applied and the model top is set to 50 hPa (about 20 km altitude) to save computational resources. To avoid numerical instabilities adaptive time stepping was used with a maximum time step of 15 s and a maximum Courant number of 1.2. At the model top a 7 km thick Rayleigh damping layer is applied to prevent wave reflection. Physical parameterizations contain the Rapid Radiative Transfer Model longwave scheme , the Goddard shortwave scheme , the Mellor–Yamada–Nakanishi–Niino boundary layer scheme , the Noah land surface model , the WRF single-moment six-class microphysics scheme WSM6; and the Kain–Fritsch cumulus parameterization scheme . The latter is switched off for the innermost domain. Horizontal diffusion (WRF parameter diff_opt) was not applied in the two innermost domains to increase GW amplitudes in vertical wind fields. The initial and boundary conditions are supplied by ECMWF (T1279 L137, cycle 40r1) operational analyses on 137 model levels with a horizontal resolution of 16 km and a temporal resolution of 6 h. WRF and ECMWF fields are interpolated in space and time on aircraft flight tracks to compare with observational data. For this purpose, a temporal output interval of 5 min is used in the WRF simulations. For ECMWF a 1-hourly output interval is realized by performing short-term forecasts with the ECMWF integrated forecasting system (IFS). In order to compute GW-induced energy and momentum fluxes the diagnostic filtering method of is applied to WRF output.

In addition to the WRF control simulation (CTRL), six sensitivity runs are performed (see Table ): in the NOTOPO and OCEAN simulations the topography height is set to zero everywhere in the domain. In addition, the land use type has properties of a water surface with a roughness length of 0.0001 m everywhere in the domain in the OCEAN runs. The NOTOPO and OCEAN simulations aim to define an atmospheric background state without mountain waves and to investigate the influence of changing surface roughnesses (transition from an ocean to a land surface) on GW excitation. In the SMTOPO simulations the two innermost domains use a smoothed topography, which is the same as in the outermost (D1) model domain. This is done to analyse the effect of unresolved topography on GW structures in a high-resolution model. In the CTRLVR runs the vertical grid resolution is increased, and 188 levels with constant level distances of 80 m and a model top at 50 hPa are used. Horizontal turbulent diffusion is switched on in the HVDIFF runs (WRF parameter diff_opt = 1), and vertical turbulent diffusion is additionally increased by a factor of 2 in the H2VDIFF case by doubling the tendency terms obtained from the boundary layer scheme, which is responsible for subgrid-scale turbulent mixing in the whole atmospheric column (not just the boundary layer). The latter three sensitivity runs are performed to improve simulated energy and momentum fluxes by damping wave amplitudes by unresolved nonlinear processes.

All WRF topographies are based on the Global 30 Arc-Second Elevation (GTOPO30) digital elevation model with a maximum horizontal resolution of about 1 km, while the ASTER data set with a horizontal resolution of 30 m is used as reference topography. Figure  illustrates the different representation of the Scandinavian mountain range in the different model runs by means of two example flight legs during IOP1 and IOP5. The innermost WRF domains D2 and D3 (Δx= 2.4 and 0.8 km) resolve the individual mountain peaks very well in terms of amplitude and horizontal wavelength (note the local peak in the power spectra at about 20 km). Domain D1 and the ECMWF model do not capture the fine-scale mountain peaks and represent the topography as a compact, smooth mountain ridge. The influence of topography resolution on the simulated vertical wind field is investigated in Sect. .

To investigate the complex wave patterns and especially the occurrence of trapped waves in the troposphere, which developed during IOP1 and IOP5, idealized 2-D simulations (IOP1ID and IOP5ID) were performed along the two example cross sections of flight 1, leg 2, during IOP1 and IOP5 (the same as in Fig. ). The simulations were run without moisture and were initialized with averaged upstream profiles of horizontal wind speed and potential temperature of the CTRL D3 real-case simulations at 12:00 UTC on 3 and 13 December. Wind speed was projected to a wind direction of 300∘, which is perpendicular to the Scandinavian mountain range and represents the cross-mountain flow. The model top was set to an altitude of 20 km with a damping layer thickness of 5 km. A horizontal and vertical grid resolution of 800 and 50 m was chosen, respectively, and simulations were run for 10 h.

The computation of EF and MF at flight level according to the method of provides information about GWs in the UTLS region and is applied for both observations and simulations in this study. The leg-averaged fluxes are computed by the following formulas: MFx=ρ‾L∫w′u′dx,MFy=ρ‾L∫w′v′dx andEF=1L∫w′p′dx, with zonal and meridional momentum fluxes MFx and MFy, GW-induced perturbations of zonal wind u′, meridional wind v′, vertical wind w′, pressure p′, leg-averaged density ρ‾, and leg length L. Momentum and energy fluxes of linear GWs are related by the Eliassen–Palm relation : EF=-U×MF, withU×MF=u×MFx+v×MFy, with leg-averaged zonal, meridional and total horizontal wind speeds u, v and U, respectively. The wind and pressure perturbations u′, v′, w′ and p′ are computed by subtracting linear regressions from full wind and pressure fields along flight legs. For pressure, a hydrostatic correction is applied in advance of computing the pressure perturbations as described in .

Further diagnostic variables are used in this study to describe flow and GW characteristics. The gradient Richardson number is the ratio of buoyancy to shear force and is defined as Ri=N2(dUdz)-2 with Brunt–Väisälä frequency N. Typically a flow is dynamically unstable for Ri<0.25.

The Scorer parameter l=N2/U2-1Ud2Udz2 can be used to distinguish between evanescent and vertically propagating waves. Trapped lee waves occur in layers where l is decreasing with height, which means that only waves with horizontal wave numbers smaller than l can propagate vertically. In this study the curvature term is neglected for simplification, and l is computed as l=N2/U2.

Meteorological situations favourable for the generation of mountain waves occurred at the beginning (IOP1) and end (IOP4, IOP5) of the GW-LCYCLE I campaign (see Table ).

The meteorological condition during IOP1 (3 December 2013) was dominated by a strong synoptic low-pressure system, which was located over the northern Norwegian Sea and travelled eastwards from the coast of Greenland towards northern Norway (see Fig. ). At the tropopause level, which was located at an altitude of about 5 km on the upstream side of the mountains, a strong westerly jet moved southwards during IOP1. The cross-mountain flow excited GWs and the related vertical energy fluxes were enhanced in the middle troposphere along the whole Scandinavian mountain range with largest fluxes occurring over the Kiruna region (Fig. c).

The GW event during IOP1 can be divided into three phases, which are marked in the time–height sections for horizontal wind speed, gradient Richardson number, vertical energy flux and Scorer parameter at the location Abisko (68∘ N, 19∘ E; Fig. a to d), which is situated in the centre of the mountain range between Andenes and Kiruna (see the dots in Fig. ). The first GW phase (P1) from 20:00 UTC on 2 December to 03:00 UTC on 3 December was dominated by moderate westerly cross-mountain flow at low levels (30 m s-1 at 850 hPa) within the warm air sector of the synoptic low (not shown) and moderate vertical energy fluxes. The second phase (P2) from 03:00 to 06:00 UTC on 3 December was characterized by weaker low-level winds (15 m s-1) and low GW activity due to calm conditions after the passage of a cold front. At upper levels the tropopause jet was located directly over northern Scandinavia. At about 06:00 UTC on 3 December the third phase (P3) started when low-level winds intensified due to the approaching low-pressure system (cf. Fig. ). During this phase the tropopause dropped to an altitude of about 5 km upstream of the mountains and stratospheric air descended to nearly 2 km altitude in the lee of the mountains, which is visible in a cross section of the Brunt–Väisälä frequency along leg 2 of flight 1 in Fig. a. The stratospheric intrusion on the eastern side of the mountains was also present in the NOTOPO and OCEAN simulations (not shown), which means that it was jet-induced cf. and not generated by mountain waves. Within this tropopause fold weak interfacial waves could develop in the CTRL D3 run (Fig. a) due to decreasing Scorer parameters (not shown). GW excitation stopped at about 03:00 UTC on 4 December when the low-pressure system moved further east. The two research flights of IOP1 took place during phase P3 (see Fig. ).

During IOP5 (13 December 2013) the situation was less complex as northern Scandinavia was located below a strong and quasi-stationary northwesterly tropopause jet (Fig. e) in polar air masses far north of the polar front (not shown). The low-level forcing was weaker than during IOP1 and dominated by a polar-low-like short-wave trough, which developed into a cold-air outbreak south of Svalbard reaching the Norwegian coast at about 06:00 UTC on 13 December. Mountain wave generation was restricted to northern Scandinavia (Fig. f) and started at about 00:00 UTC on 13 December, and EF stopped immediately when the polar low dissolved at about 17:00 UTC on 13 December (Fig. e and f). In the troposphere, interfacial waves formed at a layer with increased stratification between about 2.5 and 5 km altitude. This layer was the residual of a tropopause fold, which passed over northern Scandinavia the day before (not shown) and is visible in the Scorer parameter maximum at about 2.5 to 3 km in Fig. h and in a local maximum of the Brunt–Väisälä frequency in Fig. b. Interfacial waves are visible in this layer by means of potential temperature contour lines, which show wave structures with vertical phase lines. As the upstream profile was already favourable for interfacial waves, wave trapping was stronger during IOP5 than during IOP1.

Because of different cross-mountain flow during IOP1 and IOP5, the vertical wave propagation in the stratosphere was different. While during IOP5 continuously propagating GWs developed, GW breaking occurred at altitudes between about 25 and 30 km during IOP1, which is visible from convective overturning, reduced Richardson numbers Ri, increased nonlinearity ratios NLR; and decreasing energy fluxes in this altitude range during phase P3 in Fig. . As breaking mountain waves slow down the background flow , this turbulent region could also be observed by radiosondes starting at Andenes, which measured strongly reduced horizontal wind speeds (smaller than 10 m s-1) between altitudes of 25 to 30 km (not shown).

To investigate the reason for different propagation conditions in the stratosphere the NOTOPO and OCEAN simulations are analysed. Wind speeds in these simulations can be regarded as atmospheric background state without perturbations due to mountain waves. The solid lines in Fig.  show time series of horizontal wind speeds averaged between 25 and 30 km at Abisko obtained from the NOTOPO and OCEAN simulations and reveal about 10 m s-1 lower wind speeds during IOP1 compared to IOP5. The grey shading in Fig.  indicates maximum and minimum GW-induced wind speed perturbations obtained by subtracting OCEAN from CTRL run fields. During IOP1 weaker background winds and stronger wind perturbations generated regions with winds below 10 m s-1, which favour local mountain wave breaking due to the formation of critical levels. This means that the growing wave amplitude generates regions with nearly zero winds while the vertical wavelength approaches zero. This leads to convective overturning and turbulent wave breaking , which is visible in the regions of reduced Richardson number and increased NLR in Fig. b. During IOP5 wind speeds stayed above 20 m s-1 at this altitude range and enabled wave propagation to altitudes above 30 km (Fig. f). In addition, the comparison of NOTOPO and OCEAN simulations shows nearly no difference in horizontal wind speeds. This indicates that GWs are not generated by changes in roughness lengths in the NOTOPO run, when the flow passes over the ocean and reaches the land surface, as NOTOPO (water and land surfaces) and OCEAN (only water surfaces) simulations generate a similar wind field.

Beside the GW evolution in the lower and middle stratosphere the focus of this study is on GW structures in the UTLS, as this part of the atmosphere was observed by airborne measurements. Differences in the atmospheric background conditions during IOP1 and IOP5 are shown by means of average vertical profiles of wind speed, Scorer parameter and vertical energy flux in Fig. . CTRL upstream profiles of horizontal wind speed were averaged over a region between 69 and 70∘ N and 10 to 15∘ E (see small black boxes over the ocean in Fig. ) and indicate relatively strong and constant horizontal wind speeds between 25 and 30 m s-1 in the troposphere during IOP1. In contrast, a strong increase in wind speed from 10 m s-1 near the surface to 50 m s-1 at the tropopause existed during IOP5. Upstream profiles of the Scorer parameter show continuously increasing values in the troposphere during IOP1 (with a minor local maximum below 2 km altitude), which is not favourable for the formation of trapped waves. During IOP5 maximum values of l occurred at about 2 km altitude and the Scorer parameter was strongly decreasing between 2 and 4 km and between 5 and 8 km altitude during IOP5. This means that during IOP5 background atmospheric conditions were favourable for the formation of interfacial waves. Regionally averaged profiles over the mountain region between 67 to 69∘ N and 15 to 25∘ E (see large black box in Fig. ) of vertical energy fluxes show upward-propagating waves with relatively constant energy fluxes with a height of up to 15 km altitude during IOP1 and a strong peak in energy fluxes in the jet stream region during IOP5.

To simplify the meteorological conditions and to investigate principal differences in wave patterns during IOP1 and IOP5 in the UTLS region, idealized 2-D simulations (IOP1ID and IOP5ID) were performed in addition to real-case simulations. The formation of waves in the idealized 2-D simulations (IOP1ID and IOP5ID) is only determined by the upstream wind profiles, thermal stratification and the mountain peaks at the surface. Effects of horizontal wind shear, convection or 3-D wave propagation are not included. The idealized wave patterns during IOP1 and IOP5 are visualized in Fig. . As already seen in Fig.  the situation during IOP1 was characterized by relatively constant horizontal wind speeds with height in the upstream region. Under these conditions hydrostatic waves formed over the Lofoten Islands and the main mountain range with horizontal and vertical wavelengths of 20 and 6 km and maximum wave amplitudes of 3.3 m s-1 and propagated through the low tropopause into the stratosphere. In the lee of the mountains no tropopause fold with interfacial waves as in Fig. a is visible because the idealized simulations were initialized with upstream CTRL D3 profiles and the tropopause fold was associated with the synoptic upper-level frontal system low approaching from the north.

During IOP5 the strong jet stream and the stratospheric intrusion layer around 5 km altitude dominated the ambient conditions. Over the mountain range waves with maximum amplitudes of 7 m s-1 and horizontal wavelengths of 13 km with nearly vertical phase lines formed between 5 and 10 km altitude due to the strong increase in horizontal wind speed, which caused the increase in the vertical wavelength. Below 5 km altitude waves with shorter horizontal wavelengths of 6 km are visible. On the eastern side of the mountains, interfacial waves with horizontal wavelengths of 8 km formed along the stratospheric intrusion layer and propagated horizontally far in the lee of the mountains. Horizontal wavelengths of interfacial waves in real-case simulations were 10 km (Fig. b) and therefore in the same order as in the IOP5ID simulation. The extremely stable boundary layer in the lee of the mountains represents a typical situation for the development of resonant trapped lee waves . The stratification and the Scorer parameter are continuously decreasing with height, which induces the formation of trapped waves with horizontal wavelengths of 6 km in the IOP5ID case (Fig. d) and 8 km in the CTRL D3 run (Fig. b). Profiles of idealized EF and MF computed along the cross sections (Fig. e) show nearly constant fluxes with height during IOP1. In the IOP5ID case fluxes were very small below an altitude of 5 km due to wave trapping in this altitude range and strongly increased in the jet stream region. Idealized flux profiles are qualitatively similar to fluxes of the CTRL simulations (Fig. ).

To study the agreement between observed and simulated wave structures, vertical wind speeds along flight leg 2 of the respective first research flights during IOP1 and IOP5 are shown in Figs.  and . In all panels the complete flight leg is shown except in panel b where a smaller part of the leg is shown to enlarge the wave structures. Airborne lidar and in situ measurements in panels a and b show alternating up- and downward motions along the flight legs with amplitudes of 2 to 4 m s-1. The strongest signals occur directly over the mountains and extend horizontally up to 300 km eastward in the lee of the mountain range during both IOP1 and IOP5. White areas in lidar observations mark regions where no measurements are available due to cloud coverage . It can be recognized in Figs.  and a and b that waves in the lower troposphere were nearly vertically oriented with weak upstream tilts of the phase lines. During IOP1 (Fig. b) the combination of lidar observations with in situ observations, which were close to the tropopause, enables us to identify a stronger phase tilt in the UTLS compared to waves in the lower troposphere. During IOP5 (Fig. b) both lidar and in situ observations were conducted below the tropopause on the flight leg shown, which means that nearly vertical phase lines observed by the lidar continued in the in situ measurements.

The simulated vertical wind fields in Figs.  and depend strongly on the grid and topography resolution. As the CTRL D1 run does not resolve single mountain peaks (cf. Fig. ), the vertical wind field is large-scale. With a horizontal resolution of 2.4 and 0.8 km, the mountain peaks and related waves are resolved in the CTRL D2 and D3 simulations, however, with weaker maximum amplitudes of 2.4 and 5.3 m s-1 (2.5 and 4.1 m s-1) compared to observed amplitudes of 5.6 m s-1 (4.7 m s-1) during IOP1 (IOP5) mainly due to numeric diffusion. As in the observations waves show nearly vertical phase lines in the troposphere over the mountains, while upward-propagating waves with stronger phase tilts are visible in the stratosphere in the CTRL D2 and D3 runs. The combination of high model resolution with smoothed topography in the SMTOPO D3 simulation (Figs.  and f) results in a vertical wind field, which is very similar to the coarse-resolution CTRL D1 run (Figs.  and c). This shows that realistic vertical wind fields can only be simulated with a model topography that includes single mountain peaks (Fig. ). Similar results were found in for GWs over southern Greenland and in , who analysed WRF simulations of a trapped lee wave event over the Pyrénées. In both cases GWs were not captured appropriately in simulations with grid distances larger than 1.3 and 1 km due to smoothed topography and numerical diffusion.

On the upstream side of the mountains all simulations reveal no vertical winds at flight level in contrast to lidar and in situ observations, which show vertical wind perturbations of up to 1.6 and 0.6 m s-1 during IOP1 and IOP5, respectively. This can be explained by missing perturbations in simulations, e.g. due to convective GWs excited further upstream. It is assumed that the east–west extent of the WRF modelling domains (see Fig. ) would have to be much larger to allow the development of convection-induced GWs in the westerly flow over the ocean. This was, however, not possible in this study due to limitations in computational resources. In addition, missing wave structures in the ECMWF analysis data, which are used as initial and boundary conditions for the WRF model, contribute to the smooth upstream vertical wind fields.

The relation between topography resolution and simulated vertical wind field is demonstrated by comparing Figs.  and . The latter shows vertical wind speeds at flight level in panels a and b along the two example flight legs during IOP1 and IOP5 (the same legs as in Figs.  and ). As seen in Figs.  and , the wave structures cannot be computed in the ECMWF, CTRL D1 and SMTOPO runs but occur in the CTRL D2 and D3 simulations with weaker amplitudes over and in the lee of the mountains compared to observations. The power spectra of observed vertical velocity reveal dominant wavelengths between 15 and 30 km. Similar wavelengths were obtained from the corresponding topographies in Fig. , which indicates that waves observed in vertical wind fields over the Scandinavian mountains were connected to single mountain peaks. The CTRL D2 and D3 runs partially reproduce these wavelengths, however, with significantly smaller amplitudes, while they cannot be resolved by CTRL D1, SMTOPO and ECMWF. Figure  shows the horizontal wind component from a direction of 300∘, which represents the flow across the mountains along the same flight legs as in Fig.  and . During both IOPs a strong jump in horizontal wind speed is visible in the lee of the mountains (Fig. a, b). All WRF simulations compute very similar horizontal winds independently of the horizontal resolution with maximum deviations from the in situ observations of 6.4 and 8.1 m s-1 during IOP1 and IOP5, respectively. In situ observations indicate strong fluctuations in the horizontal wind with amplitudes of up to 5 and 3.6 m s-1 during IOP1 and IOP5. In contrast to the vertical wind, the spectra of the horizontal wind component are dominated by larger wavelengths of 60 to 120 km. In addition, power spectra of in situ observations show secondary maxima for smaller wavelengths of about 25 to 40 km, which are also computed by the CTRL D2 and CTRL D3 simulations during IOP5. The good agreement of horizontal winds and related spectra between all CTRL and SMTOPO simulations indicates that horizontal winds are less dependent on the grid and the topography resolution compared to the waves observed in vertical wind fields.

Airborne observations during IOP1 and IOP5 enable us to verify the simulation of GW-induced energy and momentum fluxes in the UTLS for different grid resolutions. EF and MF at flight level are computed according to the method of (see Sect. ) and are shown in Fig. . During both IOP1 and IOP5, the linear Eliassen–Palm relation between EF and MF is satisfied nearly perfectly in all WRF simulations and indicates upward-propagating mountain waves. Observed EF and MF values show, however, an offset from the identity line and include negative values during IOP5 (Fig. b), which means that nonlinear effects seem to be underestimated by the WRF model. The Eliassen–Palm relation was fulfilled already in other GW campaigns, e.g. over the Sierra Nevada and New Zealand . Note that only data directly above the mountains (cf. black dotted lines in Fig. ) are used for flux computations to avoid nonlinearity effects in observational data in upstream regions. For ECMWF the relatively short lengths of the mountain legs cause inadequate linear Eliassen–Palm relations. Along complete legs (cf. black dashed lines in Fig. ), the linear relation is achieved well for ECMWF (not shown).

Surprisingly, energy and momentum fluxes are significantly larger in the WRF CTRL runs during both IOPs compared to in situ observations (up to 10 W m-2 during IOP5) in spite of smaller wave amplitudes (cf. Figs.  and ). As already seen in Fig. , fluxes were strongest for D3 simulations due to higher vertical wind speeds compared to D1 and D2 simulations (cf. Figs.  and ).

To study the reason for increased fluxes in the model, sensitivity runs with an increased vertical grid resolution of 80 m (CTRLVR) and increased horizontal and vertical turbulent diffusion (HVDIFF, H2VDIFF) were performed (see Table ). The idea of these sensitivity experiments was to improve the representation of small-scale nonlinear effects like wave breaking, which reduces vertical wind speeds and contributes to a reduction in the energy and momentum fluxes. By comparing EF and MF from different simulations, Fig.  shows that an increased vertical grid resolution (CTRLVR) slightly reduces the EF and MF values in the order of 2 W m-2. Probably, an additional increase in the horizontal resolution towards the order of a large-eddy simulation (LES) would be necessary to reduce the simulated fluxes by explicitly resolving wave breaking. By switching on horizontal turbulent diffusion in the HVDIFF simulation, vertical fluxes were reduced by about 2 W m-2, which is similar to the CTRLVR simulation. A clear improvement of vertical flux computation was attained by both applying horizontal diffusion and doubling the vertical mixing tendency term obtained from the boundary layer parameterization scheme in the H2VDIFF simulation. The propagation of wave energy was effectively damped by up to 6 W m-2 compared to the CTRL run.

Grey dots in Fig.  mark smoothed observed fluxes (In-situSM), which were computed by using horizontal wavelengths larger than 15 km. These fluxes are nearly identical to the original in situ fluxes, which means that waves with wavelengths smaller than 15 km did not contribute significantly to GW fluxes at flight level. Similar results were found by for “fluxless” waves with wavelengths between 6 and 15 km over New Zealand during the DEEPWAVE campaign.

Profiles of EF and MF of D3 simulations, which were averaged over all flight legs during IOP1 and IOP5 are shown in Fig. . For the CTRLVR, HVDIFF and H2VDIFF simulations EF and MF fluxes are reduced over the atmospheric column between 2 and 15 km and agree better with in situ observations than fluxes obtained from CTRL runs. CTRLVR and HVDIFF simulations indicate similar flux profiles, while the H2VDIFF runs show clearly reduced fluxes. During IOP5 the largest improvement of the H2VDIFF fluxes compared to CTRL run fluxes can be found in the lower troposphere at altitudes between about 2.5 and 7.5 km. This is at altitudes of the layer where wave trapping occurred (see Fig. ) and localized regions of wave breaking increased turbulent mixing. These processes seemed to be underestimated in the CTRL simulations.

In order to verify the model results of the previous sections, CTRL simulations are compared quantitatively to in situ and lidar observations. Figure  shows correlations of airborne in situ and lidar measurements with numerical models for potential temperature, wind direction, and vertical and horizontal wind speed for all legs during IOP1 and IOP5. Except for vertical wind speed, all variables are captured well by both the WRF and ECMWF model with similar correlation coefficients of up to 0.99 and root mean square errors (RMSEs) independently of the horizontal resolution. This good agreement can be explained as fields of potential temperature and horizontal wind speed are principally dominated by large-scale waves (cf. Fig. ). Vertical winds on the other hand reflect small-scale up- and downdrafts , which are linked to single mountain peaks (cf. Figs.  and ) and may be shifted slightly in space and time in the models, which complicates a pointwise comparison with measurements. As ECMWF is a hydrostatic model, vertical velocity is a diagnostic variable and GW-induced vertical winds cannot be resolved, which results in very low correlation coefficients in Fig. d and f. A separation of correlation coefficients for both IOPs is listed in Table  and indicates that IOP5 was captured better by the models than IOP1 probably due to the less complex meteorological situation (see Sect. ).

To verify vertical velocities in a different way, the distribution of lidar, CTRL and ECMWF vertical winds is computed. Figure a shows the distribution of vertical velocity along all flight legs during both IOP1 and IOP5, where the lidar was operating in nadir-pointing mode. The observed lidar data exhibit a broad distribution with large wave amplitudes of maximum up- and downdrafts of 5.0 and -8.1 m s-1. The CTRL D3, D2, D1 and especially the ECMWF model simulate narrower distributions with maximum and minimum vertical winds of 8.25 and -8.23, 4.7 and -5.3, 0.99 and -0.95 and 0.46 and -0.35 m s-1, respectively.

Figure b shows the relation between the mean vertical velocity amplitude along all nadir-pointing lidar flight legs and the horizontal model resolution (for lidar data a resolution of 800 m was applied; see Sect. ). The largest improvement in simulating vertical velocities is achieved by reducing the horizontal mesh size from 7.2 to 2.4 km (CTRL D1 and CTRL D2) due to the more realistic representation of the topography in CTRL D2 (see Fig. ). The importance of a properly resolved topography for the simulated vertical wind field is further indicated by the SMTOPO runs, which show nearly the same amplitudes as the CTRL D1 run independently of the model grid resolution. Equal values of the NOTOPO and OCEAN simulations indicate that GWs are not induced by a change in roughness length when the flow passes the coast line in the NOTOPO simulation. The more realistic computation of EF and MF in the HVDIFF and H2VDIFF simulations due to increased turbulent diffusion results in reduced vertical wind speeds of up to 0.1 m s-1 on average, while higher vertical grid resolutions in the CTRLVR simulations did not change vertical wind fields significantly.