1. Introduction
Mountain waves under transient tropospheric forcing conditions were frequently observed during the Deep Propagating Gravity Wave Experiment (DEEPWAVE) in austral winter 2014 (Fritts et al. 2016). These events occurred episodically and were associated with migratory low pressure systems impinging the South Island (SI) of New Zealand (NZ; Gisinger et al. 2017). During these events, the conditions for wave excitation and propagation varied temporally. Continuous ground-based lidar observations in the lee of New Zealand’s Alps during DEEPWAVE revealed enhanced gravity wave activity in the stratosphere and mesosphere, which lasted about 1–3 days and alternated with quiescent periods (Kaifler et al. 2015). The gravity wave forcing due to passing weather systems, the appearance of tropopause jets, and the middle atmosphere wave response were all observed with a similar frequency and duration of 2–4 days (Fritts et al. 2016; Gisinger et al. 2017).
The episodic nature of mountain wave events due to traversing cyclones was already observed during the Mesoscale Alpine Programme (MAP) and the Terrain-Induced Rotor Experiment (T-REX; Smith et al. 2007; Grubišić et al. 2008; Strauss et al. 2016). During T-REX, the transient formation of rotors and lee waves was investigated (Kühnlein et al. 2013), as well as the onset of downslope wind storms with shifting wave patterns aloft (Strauss et al. 2016). During both field campaigns, the observations focused on processes within the troposphere, including the boundary layer. Deep propagation of mountain waves was almost impossible during MAP, as directional wind shear in the midtroposphere acted like a critical level, except for above the western Alpine arc (Smith et al. 2007).
The design of DEEPWAVE allowed, inter alia, to measure orographically induced gravity waves from their excitation over the mountains of the Southern Alps up to their dissipation in the middle atmosphere (Fritts et al. 2016; Bramberger et al. 2017). The SI of NZ is located at about 45°S, just between the polar front jet to the south and the subtropical jet to the north. The frequent appearance of frontal systems allows one to study the transient forcing conditions for mountain-wave excitation and their impact on the gravity wave activity in the middle atmosphere. The nearly unidirectional westerly winds from the troposphere to the stratosphere during austral winter are strong enough that total critical levels are unlikely (Kim et al. 2003; Fritts et al. 2016). For an inviscid, adiabatic, nonrotating, steady, Boussinesq flow across mountains, linear theory gives total critical levels whenever the scalar product of horizontal wind 
The steady-state assumption is the basis of linear mountain-wave theory (Smith 1979). Moreover, there are numerous numerical studies about transiently forced mountain waves. Lott and Teitelbaum (1993a,b) investigated the wave dynamics in a 2D linear time-dependent model with transient incident stably stratified flow. Chen et al. (2005, 2007) and Hills and Durran (2012) extended the work of Lott and Teitelbaum (1993a,b) and studied the impact of the flow of a time-dependent barotropic planetary square wave in a uniformly stratified atmosphere over an isolated 3D mountain in idealized numerical simulations. Martin and Lott (2007) further addressed the large-scale effect of inertia–gravity wave generation due to the passage of an idealized front over a 3D mountain range. Recently, Menchaca and Durran (2017) simulated an idealized cyclone passing an isolated ridge in a baroclinically unstable environment and investigated the wave structures and the flow morphologies in the course of the idealized event. Lott and Teitelbaum (1993a,b), as well as Chen et al. (2005, 2007) and Hills and Durran (2012), prescribed the cross-mountain wind variation during 2 and up to 8 days with cosine functions, increasing the wind from zero to a maximum of 20 m s−1 and returning to zero afterward. With such a time-varying incident flow, hydrostatic wave perturbations no longer appeared over the mountains, but were shifted downstream or upstream under accelerating or decelerating forcings, respectively. For low mountains, wave momentum flux was accumulated during accelerating forcing due to conservation of wave action. In contrast, the flow over higher mountains generated gravity wave breaking at lower levels. Here, the accumulated maximum of the zonal momentum flux during the high-drag state occurred shortly after the time of maximum wind.
So far, no real-world case studies exist investigating a mountain-wave field excited by transient low-level forcing and propagating into the middle atmosphere. In this case study, a mountain-wave event that occurred in the period of 28 June–1 July 2014 [intensive observing period (IOP) 9] is investigated. The overall questions are as follows:
Which tropospheric and stratospheric quantities control the transience of the event?
How do flux values, wave amplitudes, and wave scales in the upper troposphere and lower stratosphere (UTLS) respond to the varying conditions?
Does the transient tropospheric forcing favor the excitation of certain horizontal wavelengths?
Can the wave response in the UTLS be described by a sequence of individual steady states?
How does the transient low-level forcing affect the wave activity in the mesosphere?
The paper is structured as follows. First, a description of the used dataset and the applied methods is given in section 2. The following section 3 provides a detailed description of the meteorological evolution during IOP 9. The results are presented separately for the wave response in the UTLS (section 4a) and for the deep vertical wave propagation into the mesosphere (section 4b). The findings are discussed and related to literature in section 5. The research questions are answered in section 6. The appendix gives an overview of the extended wavelet transform used in this paper.
2. Methodology
IOP 9 took place from 28 June to 1 July 2014. Altogether, six coordinated flights of the NSF/NCAR Gulfstream V (GV; RF11–RF14) and the DLR research aircraft Falcon (FF01 and FF02) were conducted. During IOP 9, different flight patterns were flown (Fig. 1). Flight altitudes and times can be extracted from Fig. 2.
Map of the SI of NZ with colored flight transects Mt. Cook 1a and 1b (hereinafter Mt-C-1a and Mt-C-1b, respectively), Mt-A-2b, the radiosonde stations Haast and Lauder, and the radiosonde flight tracks during the IOP 9. The thin red line close to the Mt-A-2b flight transect marks FF01 leg 1. In addition, the upstream point (44.2°S, 167.5°E) used in the ECMWF analyses is shown. Triangles denote the location of Mt. Aspiring and Mt. Cook in the respective color coding.
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0080.1
ECMWF IFS Brunt–Väisälä frequency 
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0080.1
The analysis presented in this paper focuses on observations along the Mt. Aspiring 2b (hereinafter Mt-A-2b) transect (Fig. 1), a mountain-wave flight track with a direction of 300° from northwest to southeast over Mt. Aspiring (44.38°S, 168.73°E). During IOP 9, a total flight duration of 9.5 h was spent along this transect comprising 19 flight legs (RF12: six legs, FF01: three legs, RF13: six legs, FF02: four legs). One flight leg (FF01 leg 1) was flown along a slightly shifted flight track, compared to the Mt-A-2b transect (thin red line in Fig. 1), and is only included in the analysis where specifically stated.
The topography of the SI is rough and structured with a sequence of valleys oriented parallel to the mountain range. Along the Mt-A-2b transect, several individual peaks can be identified. These peaks are labeled in Fig. 3a, and their respective names, latitudes, and longitudes are listed in Table 1. Their positions on the map can be found in Fig. 3b. Mt. Aspiring is the highest peak along this track. The outstanding peak at 20-km distance belongs to the Dunstan Mountains in central Otago, located directly upstream of the radiosonde and Rayleigh lidar station in Lauder (Fig. 1). All GV flight legs were flown within the stratosphere at around 12- and 14-km altitude, whereas the Falcon crossed the tropopause during both FF01 and FF02 (Table 2, Fig. 2).
(a) WRF topography with the finest obtainable resolution of 30 arc s along the Mt-A-2b transect with labeled peaks. For the projection upon the flight tracks, the Lambert projection is used, with a 1-km grid spacing and the topography data bilinearly interpolated to the flight track coordinates. The middle of the island along the transect is taken as the reference point (distance = 0 km). (b) Map over the SI of NZ with the identified mountains along the Mt-A-2b transect (via Google Earth view 2015).
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0080.1
Identified mountains along the Mt-A-2b transect from west to east with their respective latitudes and longitudes. The letters and distances refer to the marked peaks in Fig. 3a and their respective distance to the reference point (middle of the island along the cross section).
Serial leg numbers as counted in Fig. 2, research flight (RF: GV; FF: Falcon), flight leg number, respective forcing phase [accelerating (acc), maximum (max), decelerating (dec)], day, mean leg time, leg-averaged flight altitude, flight transect (Mt. Aspiring, Mt. Cook), and status of cross-mountain legs during DEEPWAVE IOP 9. A checkmark in the status column is provided for Mt-A-2b flight legs that were analyzed in more detail in this paper.
For this study, the 1-Hz in situ flight-level data of the GV and Falcon were used. For the GV, general measurement uncertainties are given in Smith et al. (2016). For the Falcon, measurement uncertainties can be found in Rotering (2011) and Giez et al. (2017). Only GPS height data (no differential GPS) are available for the Falcon during the DEEPWAVE campaign. On board the GV, upper-atmosphere observations were performed using an Advanced Mesospheric Temperature Mapper (AMTM) imaging system. This instrument measures the intensity and rotational temperature of the bright OH airglow layer located at ≈87-km altitude. OH is a vibrationally excited molecule of oxygen (O) and hydrogen (H). It is produced by the chemical reactions of either H + O3 or O + HO2 (see Snively et al. 2010). In statistical thermodynamics, the rotational temperature is the temperature at which the thermal population of the rotational states is such as to give rise to the observed rotational spectrum, in terms of the relative intensities of the different transitions. The equivalence of the OH rotational temperature and the temperature of the emitting atmosphere, established by Wallace (1962), allows us to measure the mesopause temperature at the altitude of the OH airglow layer. Therefore, this emission has been extensively used to study waves propagating through the mesosphere–lower thermosphere (MLT) region (e.g., Pautet et al. 2014; Bossert et al. 2015; Pautet et al. 2016; Eckermann et al. 2016).
Altogether, 23 radiosondes were launched from Haast on the upstream side of the Southern Alps and from Lauder in the lee of the main ridge of the Southern Alps. The locations of radiosonde stations and the balloon trajectories are given in Fig. 1. These soundings (eight from Haast and 15 from Lauder) complemented the airborne measurements with respect to vertical observations from the ground up to the stratosphere. A maximum altitude of 36 km was achieved, and the average flight duration was 2.5 h.
In addition, DLR operated a mobile middle atmosphere Rayleigh lidar at Lauder. On the basis of integrated range-corrected photon count profiles (which are proportional to atmospheric density profiles), temperatures are retrieved assuming hydrostatic equilibrium. Temperature profiles are available from the middle stratosphere up to the mesosphere from ~30- to 80-km altitude. Details of the instrumentation of the lidar can be found in Kaifler et al. (2015). Measurement uncertainties, as well as the calculation of the temperature perturbations 
Six-hourly operational analyses valid at 0000, 0600, 1200, and 1800 UTC and 1-hourly high-resolution forecasts at intermediate lead times (+1, +2, +3, +4, +5, +7, +8, +9, +10, and +11 h) of the 0000 and 1200 UTC forecast runs of the Integrated Forecast System (IFS) of the European Centre for Medium-Range Weather Forecasts (ECMWF) are further used to visualize the temporal evolution of the upstream conditions at 44.20°S, 167.50°E (Fig. 1). The IFS cycle 40r1 has a horizontal resolution of about 16 km, 137 vertical model levels, and a model top at 0.01 hPa, with numerical damping starting at 10 hPa (Jablonowski and Williamson 2011).
Moreover, mesoscale numerical simulations with the Weather Research and Forecasting (WRF;1 Skamarock et al. 2008; Skamarock and Klemp 2008) Model are performed. With the use of Advanced Research WRF version 3.7, atmospheric simulations are generated processing operational ECMWF analyses as initial and boundary conditions. Two nested model domains are centered at 43°S, 169°E over the SI of NZ. The inner domain has a horizontal resolution of 2 km with 553 × 505 grid points in the x–y plane, and the outer domain has a resolution of 6 km with 440 × 430 grid points. There are 138 terrain-following levels used in the vertical, with level distances stretching from 85 m near the surface to about 170 m at 1-km altitude. Level distances are kept nearly constant at 170 m in the troposphere. Above 10-km altitude, they are further stretched from 170 m to 1.5 km at the model top, which is set at 2 hPa (about 40 km). Implicit damping of the vertical velocity (Rayleigh damping layer; Klemp et al. 2008) is applied to the uppermost 7 km of the model domain. This damping layer impedes wave reflection at the model top. The flow structure up to 25-km altitude is only marginally influenced when using damping layers of 10- and 15-km thickness (not shown). The WRF simulations are initialized at 1800 UTC 28 June 2014 with IFS operational analyses and are run for 54 h until 0000 UTC 1 July 2014. The usefulness of the combination and comparison of the high-resolution output of the WRF simulations with lidar, aircraft, and radiosonde data was already demonstrated by Ehard et al. (2016) and Wagner et al. (2017).
To investigate the flow development along the Mt-A-2b cross section under quasi-steady background conditions, six simulations are performed with the WRF Model in a two-dimensional idealized setup covering the core period of the transient event. The model domain has a horizontal extent of 400 km and a model top at 40 km. The same vertical levels as in the real case simulations are used, and the lower boundary is defined by the topography along the Mt-A-2b cross section. These runs are initialized with vertical profiles of horizontal wind and potential temperature taken at the first upstream point of the Mt-A-2b cross section from the innermost domain of the transient simulation. The six upstream profiles are taken every 6 h between 0000 UTC 29 June and 0600 UTC 30 June and are kept constant throughout each simulation, covering 48 h. In the 2D WRF Model, open boundary conditions are used in flow direction. Note that horizontal winds are projected to a wind direction of 300° (
From both the WRF and the in situ flight-level data, vertical energy and momentum fluxes are calculated according to the method of Smith et al. (2008), with a leg integration of 
3. Meteorological evolution during IOP 9
The tropospheric flow during IOP 9 started as a so-called trough–northwest regime characterized by a low-level northwesterly flow (28–30 June 2014) and proceeded to a trough regime with more westerly low-level flow on 1 July 2014 (Table 1 and Fig. 2f in Gisinger et al. 2017). Figure 4 illustrates the eastward propagation of a Rossby wave train by means of the 700-hPa meridional wind component υ averaged between 40° and 45°S. During the period from 28 to 29 June 2014, υ swapped sign from positive to negative over the SI. This indicates the passing ridge axis prior to the trough in the west. This transition caused increasing northwesterly and westerly winds, associated with a passing occluding frontal system (Figs. 5a,b). At 1200 UTC 29 June, a broad band of horizontal winds 
Hovmoeller diagram of the meridional wind component (m s−1) at 700 hPa obtained from the ECMWF IFS. Data were spatially averaged between 40° and 45°S. The dashed lines mark the location of the SI. Black contour lines are shown for 12, 24, and 48 m s−1. DL in the longitude axis marks the date line.
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0080.1
(a),(c),(e) ECMWF IFS equivalent potential temperature and (b),(d),(f) horizontal wind with wind barbs and 20-m-spaced contours of geopotential height at 700 hPa at 1200 UTC 29 Jun, 0000 UTC 30 Jun, and 1200 UTC 30 Jun 2014. The transect Mt-A-2b is superimposed as a black line in the individual panels. The location of Mt. Aspiring is marked with a red dot.
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0080.1
In Fig. 6, the time series of the IFS upstream cross-mountain wind component (
ECMWF IFS upstream cross-mountain wind speed (at 44.2°S, 167.5°E) during IOP 9 from 0000 UTC 28 Jun to 0600 UTC 1 Jul 2014. Mean upstream values were calculated as averages over the lowest 4 km (blue). Green and orange triangles depict the respective values for the Lauder and Haast sondes. Up to 5 m s−1 wind speed, the forcing is referred to as “weak,” from 5 to 15 m s−1 is “moderate,” and more than 15 m s−1 is “strong.” The dotted–dashed vertical lines refer to the division into accelerating, maximum, and decelerating forcing. Also, periods of synoptic events like passing fronts and convection are marked. The dashed black curve marks an approximation of the transient forcing following 
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0080.1
From Fig. 6, it is found that IOP 9 is centered on a strong forcing period of 
According to the findings of Gisinger et al. (2017), the peculiarity of IOP 9 was the southward deflection of the core of the subtropical jet stream (STJ) to about 40°S in the region of NZ (also see Fig. 7b). The southward deflection of the subtropical jet is evident at 200 hPa, especially at early times (Fig. 7b). Later, the 200-hPa winds decreased markedly over the SI (Figs. 7d,f). At lower levels, a branch of the STJ separated from the main jet and diverted south (Fig. 7a). This branch of the STJ passed the SI during the displayed sequence (Figs. 7a,c). At 1200 UTC 30 June 2014, 300-hPa winds increased again, with the approaching front reaching about 35 m s−1 over the SI (Fig. 7e). This changing upper-tropospheric wind conditions resulted in varying propagation conditions in the UTLS region for the excited mountain waves during IOP 9.
ECMWF IFS horizontal wind speed with wind barbs and 40-m-spaced contours of geopotential height at (a) 300 and (b) 200 hPa at 0000 UTC 29 Jun, (c) 300 and (d) 200 hPa at 0000 UTC 30 Jun, and (e) 300 and (f) 200 hPa at 1200 UTC 30 Jun 2014.
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0080.1
Figure 8a displays vertically smoothed and temporally averaged profiles of 
ECMWF IFS upstream (a) cross-mountain wind speed and (b) Scorer parameter smoothed over 750 m in the vertical during 3-h windows of maximum forcing phase part I (0800–1000 UTC 29 Jun), part II (1400–1600 UTC 29 Jun), early (2300–0100 UTC 29 Jun), and late (1700–1900 UTC 30 Jun) decelerating forcing phases. In red, the critical wavenumbers and wavelengths for propagation based on an argument from steady-state theory are given for different periods in (b). Waves are able to propagate as long as the ambient Scorer parameter is larger than the selected wavenumber. From bottom to top, the altitude range of inhibited propagation for waves shorter than 50-km horizontal wavelength during maximum forcing phase part I (0800–1000 UTC 29 Jun), of strong negative shear during maximum forcing phase part II (1400–1600 UTC 29 Jun), and during early decelerating forcing phase (2300–0100 UTC 29 Jun) are shaded in gray.
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0080.1
At the end of 29 June 2014, the lower-level split-branch jet had moved downstream the SI (Fig. 7c), and only a weak wind maximum remained at ≈10-km altitude (green line in Fig. 8a). At this time, the edge of the STJ was located over the SI (Fig. 7d), with maximum upstream 
The analysis of the meteorological situation around the SI revealed the low-level forcing and the propagation conditions in the UTLS region. Both will have an influence on the observed wave activity at flight level.
Finally, Fig. 9 illustrates the mesoscale flow by means of the vertical wind component and isentropic surfaces from the innermost domain of the WRF simulations interpolated along the Mt-A-2b transect. Four different times are selected to cover the maximum and decelerating forcing phases. At all times, up- and downdrafts, apparently associated with individual mountain peaks, dominate the vertical wind field in the troposphere. The tropopause, marked by decreasing spacing of the isentropes, descended during the displayed period, and the TIL weakened (cf. Figs. 9a,d). In the lower stratosphere, propagating waves of varying intensity and vertical extent appear mainly over the mountain peaks and are characterized by vertical wavelengths of 5–6 km. During the decelerating forcing phase (Figs. 9c,d) and with the weakening of the TIL (Fig. 2), the amplitudes of the simulated gravity waves in the stratosphere become larger with more than 3 m s−1 (Fig. 9d). Most pronounced in Fig. 9c, isentropes become very steep in the altitude region between ≈15 and ≈20 km. Near the end of IOP 9, gravity waves of even larger amplitudes, having horizontal wavelengths of about 20 km, and large vertical wavelengths are found at the lower edge of the PNJ (Fig. 9d, orange profile above 30 km in Fig. 8a).
WRF vertical wind along the Mt-A-2b transect up to 33-km altitude (sponge layer is excluded) with 5-K-spaced isentropes up to 320 K and 10-K-spaced isentropes above at (a) 0900, (b) 1500, and (c) 2300 UTC 29 Jun and (d) 1800 UTC 30 Jun.
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0080.1
4. Results
Aircraft observations along the Mt-A-2b transect exist only during maximum (covered by RF12) and decelerating (covered by FF01, RF13, and FF02) forcing phases. These different phases are further divided into maximum forcing phases part I and II and in early, mid-, and late decelerating forcing phases, according to the changing propagation conditions in the UTLS (see Fig. 2, Table 2). In this section, we analyze the wave response in the UTLS (section 4a) by means of vertical displacements and along-track momentum fluxes. The vertical propagation into the mesosphere is investigated in section 4b.
a. Wave response in the UTLS
1) Vertical displacements
Figure 10 illustrates the varying wave activity over the Mt-A-2b transect by means of vertical displacement 
Vertical displacement for the flight legs of (a) RF12 and (b) FF01 on 29 Jun 2014 and (c) RF13 and (d) FF02 on 30 Jun 2014 with underlying topography along the Mt-A-2b transect. For the Falcon legs, the topography originates from the WRF Model with the finest obtainable resolution of 30 arc s. For the GV flight tracks, the topographic height was provided by the NCAR Earth Observing Laboratory (EOL). In (b), an estimated phase line (black) of the long waves (
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0080.1
During the maximum forcing phase, η decreases slightly from the upstream locations to the middle of the main mountain ridge, where a pronounced increase of about 1300 m is found [RF12; Fig. 10a; see also Fig. 9a in Smith et al. (2016)]. Small-amplitude fluctuations of η extend downwind over the SI. Especially for leg 1 and leg 18, those fluctuations show small horizontal scales of 
The beginning of the decelerating forcing phase was covered by the subsequent Falcon research flight FF01 (Fig. 10b). It reveals vertical displacements with peak-to-peak amplitudes up to 1500 m extending over the main mountain ridge (around distance = −80 km). This part of the η curves is dominated by long waves with 
During the mid- and late decelerating forcing phases, the observed wave activity is strongly reduced. While peak-to-peak η amplitudes of up to 1500 m are found during RF12 and FF01, they are reduced during RF13 and FF02, reaching maximum values of around 500 m (Figs. 10c,d). The large-scale waves that showed up in the vertical displacements of FF01 can no longer be clearly found for RF13 and FF02 (Figs. 10c,d). In addition, the small-scale η oscillations do not show a strong connection to underlying dominant topographic features toward the end of IOP 9 (Fig. 10d). The interim occurrence of horizontally long waves and the pronounced temporal decay of the η amplitudes in the decelerating forcing phase are the key findings of the vertical displacement analyses.
2) Momentum fluxes
The transience of the wave response during IOP 9 is further quantified by means of vertical fluxes of along-track momentum 
(a) Time series of leg-integrated vertical flux of along-track momentum (
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0080.1
The observed 
The simulated tropospheric 
The simulated 
For linear, steady, nondissipating mountain waves, the Eliassen–Palm relation links the vertical energy flux to the scalar product of horizontal wind U and horizontal momentum flux (MF): 
Test of the linear Eliassen–Palm relation between the energy flux (
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0080.1
In the following, we investigate if the evolution and magnitude of 
Figure 13 shows the leg-integrated 
WRF leg-integrated 3-h-smoothed vertical flux of along-track momentum of quasi-steady runs at 13-km altitude as a function of run time after the respective initialization. All runs were simulated for 48 h. The light gray shading gives the time interval (30–48-h run time) during which the simulations are assumed to reach a quasi-steady state. This time interval is used to average the flux values and to compare to the “transient” WRF simulation and the observations in Fig. 11.
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0080.1
Error bars with the minimum, mean, and maximum 
3) Momentum-carrying wave scales
The amount of wave momentum carried by gravity waves depends on the horizontal wavelength 
The peaks in the total simulated tropospheric 
During the transition from maximum to decelerating forcing phase, both short and long waves contribute to the broad peaks of the total simulated 
During the mid-decelerating forcing phase, both simulations and observations reveal a trend of decreased fluxes of large-scale waves with about similar values. Apparently, the excitation of long waves has ceased since the beginning of the decelerating forcing phase. Therefore, the oscillating character of the total simulated 
The wavelength decomposition of 
Transiently simulated and observed flux values for 
Summarizing, the long waves dominate the transient behavior in the stratosphere. Observations reveal that the small-scale wave contributions have small flux values and do not vary much in time. Large positive and large negative flux values of the small-scale waves occur in the troposphere and stratosphere, respectively, during the early decelerating forcing phase. The WRF simulations are able to represent the general evolution of the large-scale component, whereas the small-scale contributions are overestimated.
4) Local scale-dependent fluxes
The previous analysis concentrated on the temporal evolution of the leg-integrated along-track momentum fluxes. Next, the extended wavelet transform, as described in the appendix, is applied to quantify the horizontal wavelengths associated with locations of significantly enhanced (5% significance level) vertical energy flux 
During the maximum forcing phase part I, the GV RF12 leg 6 (at around 12-km altitude) is dominated by positive spectral amplitudes of 
(a) 
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0080.1
In the maximum forcing phase part II, the GV detected strong turbulence along the flight leg 22 (altitude of 13.5 km) above the main mountain range between −100- and −80-km distance (Figs. 14c,d). This enhanced turbulence is reflected by significant flux values in the wavelength range 400 m 
During the early decelerating forcing phase, the Falcon flight FF01 observed strong, upward-propagating mountain waves in leg 2 (8 h later than GV leg 22), with 
(a),(b) and (c),(d) As in Figs. 14a and 14b, respectively, but for Falcon FF01 leg 2 on 29 Jun and leg 4 on 30 Jun 2014 during early decelerating forcing phase of the IOP 9.
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0080.1
The mid- and late decelerating forcing phases were already characterized by considerably decreased wave amplitudes observed during RF13 and FF02, as described above for the leg-integrated fluxes (Fig. 11a) and the vertical displacements (Figs. 10c,d). At around 9-km altitude within the tropopause, positive smaller energy flux values of 
(a),(b) and (c),(d) As in Figs. 14a and 14b, respectively, but for Falcon FF02 legs 2 and 3 on 30 Jun during late decelerating forcing phase of the IOP 9. Note the different limits of the distance axis for leg 3 in (c),(d).
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0080.1
The subsequent leg 3 of FF02 was conducted at around 10.5-km altitude above the tropopause. The Falcon observed a significant upward-propagating wave of 20–30-km wavelength, with 
Previously identified contributions of small-scale and large-scale waves [section 4a(3)] to leg-integrated fluxes were now attributed to different mountain peaks and ranges. Upward-propagating large-scale waves were detected only during the maximum forcing phase over the main mountain ridge. Small-scale waves with larger flux values dominated the decelerating forcing phase. Because of downward-propagating waves, leg-integrated fluxes are small or even of reversed sign at stratospheric levels in the decelerating forcing phase.
b. Vertical propagation into the mesosphere
As mentioned above (section 3), the vertical wave propagation during the maximum forcing phase part I is influenced by the existence of a low-stability layer associated with the passing STJ. To illustrate this effect, we show approximated and density-corrected vertical velocity perturbations 
Density-corrected, approximated vertical velocity fluctuation and potential temperature of the radiosoundings launched at Lauder at (a) 1129 UTC (maximum forcing phase part I), (b) 1725 UTC (maximum forcing phase part II), and (c) 2333 UTC 29 Jun (early decelerating forcing) and at (d) 2035 UTC 30 Jun (late decelerating forcing). Density-corrected refers to the multiplication of 
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0080.1
During the maximum forcing phase part II, 
During the early decelerating forcing phase, large-amplitude vertical velocity fluctuations of, on average, ±1.5 m s−1 exist within the troposphere and extend up to around 19-km altitude (2333 UTC 29 June Lauder sonde; cf. Fig. 17c). Below 19-km altitude, wave amplitudes decrease slightly with altitude, attaining mean peak-to-peak amplitudes of around 3 m s−1. Above, peak-to-peak wave amplitudes are more strongly attenuated to around 1 m s−1. The horizontal projection technique of Lane et al. (2000) was applied to determine the horizontal and vertical wavelengths of the large-amplitude signal of the 2333 UTC 29 June sounding: this reveals a horizontal wavelength of around 10 km with a vertical wavelength varying around 4–8 km in the stratosphere.
Another remarkable finding of the radiosounding at 2333 UTC 29 June 2014 is the distinct staircase structure of the potential temperature profile in the stratosphere (Fig. 17c). The staircase structure is further quantified by detecting several stratospheric layers where 
In the sounding launched during the late decelerating forcing phase (2035 UTC 30 June Lauder sonde), the vertical velocity fluctuations show locally strong wave excitation at the ground, but decreasing amplitudes around the tropopause (Fig. 17d). Further aloft, 
These soundings during the different forcing phases especially illustrated the effects of the changing propagation conditions. The soundings could prove the strong damping character of the low-stability layer in the upper troposphere (Fig. 17a) and could identify the minimum wind layer between the peaks of the double jet as a mixing region (Fig. 17b). Stratospheric wave activity increased from the maximum forcing phase to early decelerating forcing phase. During the latter phase, wave-breaking layers were found in the stratosphere between about 15- and 25-km altitude (Fig. 17c). Thereafter, stratospheric wave activity decreased (Fig. 17d).
As was indicated by the 2333 UTC 29 June radiosounding, attenuated gravity waves existed above the gravity wave breaking layers from ≈15- to ≈24-km altitude during the early decelerating forcing phase. Hence, the question arises if orographic gravity wave activity is observed even further aloft. A measure of stratospheric and mesospheric gravity wave activity is given by the GWPED, calculated from temperature fluctuations of the Rayleigh lidar measurements from Lauder (Fig. 18). Nine hours of measurements on 30 June 2014 show a transient behavior. In particular, the mesospheric gravity wave activity reached peak values of GWPED of around 110 J kg−1 between 1500 and 1600 UTC in the decelerating forcing phase. The stratospheric gravity wave activity is continually decreasing, from a GWPED maximum of about 30 J kg−1 at around 1130 UTC to 5 J kg−1 at around 1930 UTC. The stratospheric and mesospheric maxima, with a plateau of wave activity in the stratopause in between, are time shifted by around 4 h. Assuming an upward propagation of hydrostatic mountain waves, the propagation time 
One-hourly mean of GWPED, logarithmically averaged over the upper stratosphere (violet dots), stratopause (black dots), and mesosphere (blue dots). In addition, the thin dotted lines denote the 1-hourly running mean of the 2-min GWPED data during the Rayleigh lidar measurement at Lauder, NZ, on 30 Jun. In general, the GWPED increases with height due to wave amplification with decreasing air density.
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0080.1
Airborne AMTM observations obtained during the two GV research flights RF12 and RF13 on 29 and 30 June, respectively, confirm the delayed appearance of those long mountain waves in the mesosphere: while the observations of RF12 during the maximum forcing phase show no clear large-scale structures above the SI (≈1100 UTC 29 June; Fig. 19a), the airglow observations of RF13 reveal elongated maxima of the airglow brightness temperatures parallel to the main mountain ridge and a minimum directly above the SI (≈1400 UTC 30 June; Fig. 19b). The estimated horizontal wavelength amounts to about 200 km and agrees with 
Keograms (time–distance sections constructed from collocated time series of narrow AMTM image slices) of the AMTM observations during (a) RF12 on 29 Jun and (b) RF13 on 30 Jun 2014.
Citation: Monthly Weather Review 146, 6; 10.1175/MWR-D-17-0080.1
5. Comparison with previous studies and discussion
In this section, we discuss our results in the context of numerical studies of transiently forced mountain waves, as well as in the context of previous investigations of MAP, T-REX, and DEEPWAVE studies.
A detailed and quantitative comparison of our findings for this complex transient wave event with existing theoretical and idealized numerical simulation studies (Lott and Teitelbaum 1993a,b; Chen et al. 2005, 2007) is hardly possible. The analyzed wave event is not only influenced by transient tropospheric forcing, but also by changing propagation conditions in the UTLS region. Previous studies focused on mountain waves generated during only transient tropospheric forcing (Lott and Teitelbaum 1993a,b; Chen et al. 2005, 2007). In these studies, forcing and propagation conditions varied temporarily at all altitudes in the same way. In contrast, our case study reveals the importance of the varying propagation conditions. They include the passing upper-tropospheric low-stability layer with a correspondingly strong TIL, the double peak structure of the STJ, and the wave breaking in the UTLS and in the stratospheric wind minimum. Nevertheless, the observed temporal dependence of the low-level cross-mountain flow, with an approximated 
The low-stability layer in the upper troposphere (Fig. 2) occurred in the maximum forcing phase part I and resulted in decreasing values of the Scorer parameter 
Another peculiarity of the time-varying propagation conditions in the UTLS is the wave breaking between the double peaks of the STJ. There, the cross-mountain wind was reduced by 15 m s−1 over less than 2-km altitude (second shaded area in Figs. 8a, 17b). Radiosonde observations revealed a mixing layer in this minimum wind layer (Fig. 17b). As the GV flew within this layer, the observed nonlinearity and turbulence at flight level (Figs. 14c,d) suggests mountain wave breaking. Because of this wave breaking, the observed leg-integrated momentum fluxes for 
Vertically stacked mixing layers observed in the stratospheric wind minimum by the radiosounding during the early decelerating forcing phase (Fig. 17c) coincide with simulated wave breaking. The simulated wave breaking and the resulting mixing is indicated by steep isentropes at around 17-km altitude (Fig. 9c). Interestingly, downward-propagating waves in the lower stratosphere were detected in the flight-level data during this period (Figs. 15c,d). The similarity of the horizontal wavelength band and the same location of upward- (leg 2, Figs. 15a,b) and downward- (leg 4, Figs. 15c,d) propagating signals suggest that the observed downward-propagating wave results from partial wave reflection by the breaking region located above the flight leg. Observations of downward-propagating waves extend further into the late decelerating forcing phase (Fig. 16). The numerical simulations support the assumption of reflected mountain waves in this phase, too, as a gravity wave-breaking region is present in the stratospheric wind minimum near 19-km altitude (Fig. 9d). Upward- and downward-propagating waves influence the wave response at the subjacent stratospheric flight levels in such a way that the observed leg-integrated momentum fluxes become negligible (Fig. 11). The observational and numerical evidence of the existence of a stratospheric gravity wave-breaking layer confirms the findings of the so-called “valve” layer within the stratospheric wind minimum (Kruse et al. 2016). This valve layer attenuates upward-propagating waves when wave breaking occurs. Indeed, attenuated waves were observed above, indicating a leakage of wave energy into the upper stratosphere during IOP 9 (Figs. 9c, 17c). In general, the existence of the stratospheric wind minimum is not related to the transient mountain-wave event, but to the location of NZ and the seasonal shift of the PNJ (Fritts et al. 2016). The valve layer as a breaking layer depends on the amplitudes of waves that are able to propagate beyond the UTLS in comparison to the magnitude of the stratospheric wind (Kruse et al. 2016). As wave amplitudes in the lower stratosphere are largest during the early decelerating forcing phase, wave breaking in the stratospheric valve layer was mainly limited to this phase. Therefore, the appearance of the valve is also transient.
Kruse and Smith (2015) classified observed mountain-wave cases of the DEEPWAVE campaign into shallow and deep events, depending on the reduction of horizontal stratospheric wind by 20 or 10 m s−1, respectively, from a lower-stratospheric value of 30 m s−1. Based on this classification, the reduction of 
In the UTLS, vertically propagating mountain waves achieved along-track momentum flux (vertical energy flux) values varying from about zero up to ≈130 kN m−1 (≈4000 kW m−1). Smith et al. (2016) classified all DEEPWAVE IOPs into weak and strong flux events, applying a threshold value of 
The flow across the rugged terrain of the Southern Alps excites a broad spectrum of gravity waves. During IOP 9, horizontally long waves of 
The comparison of the 2D quasi-steady runs with the transient WRF run and the observations was focused on the UTLS along-track momentum fluxes. To a large extent, the quasi-steady momentum fluxes in the UTLS agree quantitatively with the transiently simulated and observed values. Agreement was found for the maximum and the mid-decelerating forcing phase, when the variability of the steady runs is considered (error bars in Fig. 11). The steady-state runs do not capture the retarded enhancement of momentum fluxes extending further into the early decelerating forcing phase in the observation of FF01 leg 2 and in the transient run. This finding encourages the hypothesis that UTLS momentum fluxes, as observed along the Mt-A-2b transect, seem to be reproducible by individual quasi-steady 2D runs, except for the retarded flux enhancement during the early decelerating forcing phase. However, this statement is only based on leg-integrated momentum fluxes. We did not investigate particular wave structures in the transient and the stationary runs, as done by Menchaca and Durran (2017) for simulations of a crossing cyclone over an isolated ridge.
6. Conclusions
The DEEPWAVE case study presented here combines in situ and remote sensing measurements to follow the deep vertical propagation of mountain waves from the troposphere to the mesosphere. The observational findings of a mountain-wave event under transient tropospheric forcing were complemented by numerical simulations covering the atmosphere up to about 33-km altitude. Among a series of transient mountain-wave events during DEEPWAVE, the analyzed IOP 9 was the only transient case of the campaign that was observed in such detail and duration, especially by the successive deployment of the two research aircraft NSF/NCAR GV and the DLR Falcon. In this way, our study extends previous theoretical and numerical considerations of transient mountain wave events of Lott and Teitelbaum (1993a,b) and Chen et al. (2005, 2007).
Although the observed low-level forcing roughly follows the sinusoidal temporal dependence of the cross-mountain wind used in these studies, our case study reveals the importance of the time-varying propagation conditions during the period when a migrating trough and connected fronts controlled the transient forcing over NZ. With the evolving synoptic situation, the upper-tropospheric stability, the wind profile, and the tropopause strength and altitude changed and controlled the transience of the event together with the low-level forcing. In particular, the occurrence of the low-stability layer and the double jet resulted in wave attenuation and mountain wave breaking in the UTLS. In contrast, upper-stratospheric conditions changed only marginally due to the presence of a nearly steady PNJ.
During the event, maximum vertical displacements 
Small-scale waves (
Other wave-breaking layers were observed between 15- and 25-km altitude inside the stratospheric wind minimum. As indicated by Kruse et al. (2016), the ratio of amplitudes of wave-induced velocity perturbation to the magnitude of stratospheric wind controls whether wave breaking occurs. We further found that in the case of wave breaking in the stratospheric wind minimum, upward-propagating small-scale waves seem to be reflected at this layer, explaining the observed downward-propagating waves above the tropopause.
In accordance with the decreasing low-level wind in the decelerating forcing phase, the observed short-wave along-track momentum fluxes in the UTLS diminished and achieved nearly the same small values as during the maximum forcing phase. Corresponding simulated values were higher. Wagner et al. (2017) explain this overestimation of the numerical simulations by a lack of turbulent diffusion that comes into effect when the propagation conditions also allow for the shortest waves to propagate upward.
The temporal appearance and intensity of horizontally longer waves differs from the small-scale waves during this event. The spectral analysis revealed that long waves (
Moreover, it was investigated whether the wave response in the UTLS can be described by a sequence of individual steady states. For this purpose, along-track momentum flux values were simulated by six 2D WRF runs initialized at different times in the course of the event. As a result, UTLS momentum fluxes seem to be reproducible by individual quasi-steady 2D runs, except for the flux enhancement during the early decelerating forcing phase. The well-satisfied Eliassen–Palm relation for the flight-level observations further suggests a quasi-steady state behavior of the nearly linear mountain waves in the UTLS (Smith et al. 2008, 2016). Indeed, parts of the wave event can be described by individual steady states. On the other hand, our results also reveal the importance of including the total transience of the event. The effect of temporally shifted wave activity in the mesosphere, compared to the UTLS, due to dispersive wave propagation cannot be captured by quasi-steady simulations. This higher-altitude effect, including the excitation and modified propagation of various wave scales, can be considered to be another major extension to existing idealized and numerical studies of transient mountain-wave events.
Acknowledgments
Part of this research was funded by the German research initiative Role of the Middle Atmosphere in Climate (ROMIC), funded by the German Ministry of Research and Education in the project Investigation of the life cycle of gravity waves (GW-LCYCLE) and by the Deutsche Forschungsgemeinschaft (DFG) via the Project MS-GWaves (GW-TP/DO1020/9-1, PACOG/RA1400/6-1). Mesoscale simulations were performed at the Leibniz Institute for Atmospheric Physics (IAP) in Kühlungsborn, Germany. The special project HALO Mission Support System allowed the access to the ECMWF data. Gulfstream V (GV) data were provided by NCAR/EOL under sponsorship of the National Science Foundation (http://data.eol.ucar.edu/). The development of the GV AMTM was funded by the NSF Grant AGS-1061892, and its operations during the DEEPWAVE campaign by the NSF Grant AGS-1338666. We further thank the DLR facility Flight Experiments for providing the Falcon noseboom data.
APPENDIX
Wavelet Analysis
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Freely available: www2.mmm.ucar.edu/wrf/users/download/get_source.html
However, it has to be noted that 
