1. Introduction
Gravity waves (GWs) play an important role in Earth’s general circulation by transporting energy and momentum vertically, which are deposited wherever the waves are attenuated (McLandress 1998; Fritts and Alexander 2003). The importance of GWs in the general circulation increases with altitude. Nonattenuating vertically propagating gravity waves increase in amplitude with decreasing density, causing them to eventually induce instabilities (e.g., static and/or Kelvin–Helmholtz instabilities) and attenuate. Additionally, as density decreases, the decelerations (and accelerations) associated with the momentum deposited by attenuating GWs [i.e., gravity wave drag per unit mass (GWD)] become increasingly dominant in the momentum budget. GWD plays a primary role in driving the general circulation in the mesosphere and lower thermosphere (Holton 1983; Garcia and Solomon 1985; Holton and Alexander 2000) as well as the tropical stratosphere (Dunkerton 1997), while possibly playing a more secondary role in the extratropical stratosphere. The focus of this study is the propagation and attenuation of gravity waves within the extratropical stratosphere.
In the stratosphere, the important equator-to-pole Brewer–Dobson circulation is driven by momentum deposited in the extratropics by both planetary-scale Rossby waves and GWs (e.g., Holton et al. 1995). Within chemistry–climate models, planetary waves are resolved while the smaller-scale GWs and their GWD are largely unresolved and parameterized. These parameterizations involve free parameters that are typically tuned to produce a realistic general circulation as opposed to being constrained around an observational dataset (Alexander et al. 2010; Geller et al. 2013). Hence, the magnitude of GW driving of the Brewer–Dobson circulation (and other circulation features) is uncertain. This is illustrated in the model intercomparison presented by Eyring et al. (2010, their Fig. 4.10a), where GWD is responsible for little to nearly half of tropopause-level tropical upwelling among model members. Surprisingly, despite variable GWD contributions, the circulation strength was found to be relatively constant, implying changes in planetary wave driving compensate variations in GW forcing (e.g., Cohen et al. 2013) and that the mean transport circulation alone may not strongly constrain GWD parameterizations.
A current common problem in chemistry–climate models is that the Southern Hemisphere pole is too cold in the austral winter stratosphere, resulting in an overly strong stratospheric polar vortex that breaks down too late in spring (Eyring et al. 2010). This cold-pole problem may be due to too little GWD, too little planetary wave drag, or some combination of both acting on the stratospheric polar vortex. McLandress et al. (2012) suggested that this issue is due to missing GWD in these models near 60°S, a latitude band with no major mountain ranges. This missing GWD may be in part due to missing mountain waves launched by mountainous islands near 60°S (e.g., Alexander and Grimsdell 2013), neglected meridional propagation or focusing of GWs into the stratospheric polar vortex jet (e.g., Sato et al. 2009), or underrepresented nonorographic GWs and drag resulting from jet and frontal imbalances near 60°S (e.g., Jewtoukoff et al. 2015) in climate simulations. It is less clear if too little planetary wave drag is part of the cold-pole problem. However, Sigmond and Scinocca (2010) found that increasing orographic GWD significantly reduces the strength of the stratospheric polar vortex primarily by altering planetary Rossby wave propagation and drag. This result suggests that increasing parameterized orographic GWD in chemistry–climate models might reduce the cold-pole problem in free-running climate simulations.
In this paper, the vertical propagation and attenuation of New Zealand mountain waves are studied using deep Weather Research and Forecasting (WRF) Model simulations with realistic topography and initial/boundary conditions. These simulations are extensively validated against research aircraft, radiosonde, and satellite observations collected over New Zealand during the Deep Propagating Gravity Wave Experiment (DEEPWAVE) field campaign during May–July 2014 (Fritts et al. 2016). From these simulations, the vertical fluxes of horizontal momentum and GWD are quantified and compared with DEEPWAVE observations and parameterized quantities within NASA’s Modern-Era Retrospective Analysis for Research and Applications (MERRA) (Rienecker et al. 2011) and MERRA2 (Bosilovich et al. 2010). Throughout the DEEPWAVE period, there was a frequent ambient wind minimum in the lower stratosphere, resulting in significant mountain wave attenuation and GWD. GW dynamics within this layer are the focus of this paper.
The outline of this paper is as follows. The WRF Model configuration and validation are presented in section 2. In section 3, mountain wave propagation and attenuation is investigated in detail over New Zealand for the 2014 austral winter season. Here, vertical fluxes of horizontal momentum and GWD are quantified and controls on vertical mountain wave propagation within the WRF simulations are investigated. Local characteristics of mountain wave attenuation are also presented. In section 4, WRF-simulated momentum fluxes and GWD are quantitatively compared with those parameterized in MERRA and MERRA2. Conclusions are provided in section 5.
2. Model configuration and validation
a. WRF configuration
Two types of WRF simulations are presented in this study: a single “long run” and five “event runs.” The long run is a 6-km-resolution simulation (outer domain in Fig. 1a) initialized once at 0000 UTC 24 May 2014 and run continuously through 0000 UTC 1 August 2014. The long run was effectively only forced by boundary conditions provided by 0.125° × 0.125° resolution operational ECMWF analyses every 6 h. The event runs had a 6-km-resolution outer domain and a 2-km-resolution inner nest centered on the New Zealand region (Fig. 1a) and were completed for five mountain wave events sampled during the DEEPWAVE field campaign. Start and end times, simulation names, and research flights included within the simulations are summarized in Table 1. All New Zealand transects on the 26 (12) research flights flown by the NSF/NCAR Gulfstream V (German DLR Falcon) research aircraft [NGV (DLRF)] during DEEPWAVE were contained within the time–space domain of the long run. Seven (four) NGV (DLRF) research flights were included within the event-run domains. The long-run solution was output every 3 h and event-run solutions were output hourly.
Maps of (a) the WRF domains and (b) the region of interest. The entire region in (a) is contained within the 6-km-resolution outer domain of the event runs and the long-run domain. The inner box is the boundary of the 2-km-resolution nest within the event runs. The boxed region in (b) depicts the region (426 414 km2) considered when area averaging throughout this paper, the black dots show radiosonde launch locations, and the red line segment shows one of the cross-mountain flight legs, in this case traversing Mt. Cook, flown by research aircraft. In both (a) and (b), model terrain height from the 2-km-resolution nest is shown in color shading.
Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0173.1
Summary of completed simulations. All dates are in 2014. NGV and DLRF research flight numbers are preceded by RF and FF, respectively. The resolution provided is that of the innermost domain.
All simulations presented were configured identically to those presented in Kruse and Smith (2015) and so are not discussed in full detail here. The same parameterization selections [see appendix A of Kruse and Smith (2015)] were used for all simulations. No convection parameterization was used and a 10-km upper sponge layer was specified below the domain top at 1 hPa or ~45 km. The ACM2 turbulence parameterization (Pleim 2007) was selected for all simulations. Model terrain within the 6 (2)-km-resolution domains was derived from the 2-arc-min (30-arc-s) digital elevation model (DEM) distributed with WRF. This terrain height was bilinearly interpolated onto the WRF grid and then smoothed with a single pass of the “smoother–desmoother” filter (Grell et al. 1994) to highly damp resolution-scale (2–4Δx) terrain features.
b. Simulation validation
Here, the WRF simulations are compared against observations collected on board the NGV and DLRF research aircraft, radiosondes launched from Hokitika, Haast, and Lauder (see Fig. 1b for locations), and NASA’s Aqua satellite by the Atmospheric Infrared Sounder (AIRS). Comparisons of mean quantities representing the ambient environment, mean vertical flux of zonal momentum, and temperature variance near the top of the simulation domain are presented.
To compare the WRF simulations to the aircraft and radiosonde observations, WRF variables were linearly interpolated in space and time to every observation (sampling frequency of 1 Hz) of a particular flight. The actual and model flights were then postprocessed identically, allowing quantitative comparison. Aircraft quantities were averaged along flight legs, which are defined as a straight and level transect over the Southern Alps of New Zealand (e.g., red line in Fig. 1b). Data along a single cross-mountain flight leg flown through the actual, long-run, and event-run atmospheres are shown in Fig. 2. Qualitatively, the perturbation amplitudes are somewhat underrepresented in the 6-km long run but better represented in the 2-km event run. This was the case for most legs. The agreement between the two simulations and aircraft observations in Fig. 2 was particularly good for this flight leg.
(a) Temperature, (b) zonal wind, (c) vertical wind, and (d) model terrain height along a cross-mountain flight leg (first leg of research flight 16 flown on 4 Jul 2014), in this case traversing Mt. Aspiring (44.3842°S, 168.7283°E). The 1-Hz NGV observations are shown in black. Simulated quantities along this leg from the 2-km-resolution event run and 6-km-resolution long run are shown in red and blue, respectively.
Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0173.1
Observed and simulated mean zonal wind 
Leg-average (a),(d) zonal wind, (b),(e) meridional wind, and (c),(f) temperature from (top) the 6-km-resolution long run and (bottom) the 2-km-resolution event runs plotted vs aircraft observations. Legs flown by the NGV and DLRF are shown in black and red, respectively.
Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0173.1
WRF validation statistics, validating WRF against aircraft observations, for wind speed (m s−1), temperature (K), and MFx (mPa).
A similar comparison of ambient quantities was performed between the WRF simulations and 144, 50, and 95 radiosondes launched from Hokitika, Haast, and Lauder (see Fig. 1b for locations), respectively. Data from observed and simulated radiosonde flights were smoothed with a 4-km vertical moving average and then compared every kilometer. ME and MAE for u and T are shown at every altitude in Fig. 4. For u (and υ, not shown), ME was within ±1 m s−1 at all altitudes except below 5 km. The MAE was relatively high in the troposphere (~2.75 m s−1) and low in the stratosphere (~1.25 m s−1). Temperatures within WRF were generally biased cold, with the cold bias increasing from about −0.2 K at 5 km to −0.9 K near 27 km. MAE increased slightly with height, but was generally at or below 1 K. This sounding comparison was repeated for the 2-km event simulations (not shown), producing similar results. This remarkable validation of mean quantities highlights the accuracy of the ECMWF data assimilation system, likely largely attributable to assimilation of satellite observations in the Southern Hemisphere (e.g., Bouttier and Kelly 2001).
Comparison of long-run ambient zonal winds and temperatures against radiosonde observations. A 4-km vertical moving-average smoother was applied to observed and simulated sonde profiles to estimate ambient quantities. Mean errors (biases) for the (a) zonal wind and (c) temperature are shown. (b),(d) The mean absolute error for these two quantities are shown. (e) The number of radiosonde observations at a given altitude are plotted. This analysis was performed for radiosondes launched from Hokitika (black), Lauder (red), and Haast (blue) (see Fig. 1b for launch locations).
Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0173.1
Below 5 km, the zonal winds within WRF were notably stronger than observed, while the meridional winds were slightly weaker than observed (not shown). This may be due to reduced flow blocking within WRF relative to reality associated with reduced model terrain heights. This issue was modestly improved in the 2-km-resolution event runs (not shown).
Long-run and event-run leg-averaged zonal momentum fluxes 
A comparison of leg-average vertical flux of zonal momentum between the WRF simulations and NGV observations, typically at z = 12.2 km. (a) The NGV [black, after Fig. 5b of Smith et al. (2016)], long-run (green), and event-run (red) leg-averaged zonal momentum fluxes are plotted vs research flight number. The long- and event-run fluxes are offset slightly in time. (b) Long-run and (c) event-run leg-average momentum fluxes are plotted vs aircraft observations, respectively.
Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0173.1
Two-dimensional linear theory suggests that horizontally averaged mountain wave momentum flux is proportional to the cross barrier wind speed and the squared terrain height (e.g., McFarlane 1987). The fact that the model topography in both the long run (max = 2133 m) and event runs (max = 2819 m) is less than the actual terrain height (max = 3724 m) may act to reduce simulated MFx. However, the stronger-than-observed cross-barrier flow may act to increase MFx. These two effects may compensate in the long run so that momentum fluxes are only weakly (~5%) underrepresented. The winds in the 2-km-resolution event runs are slightly weaker than the long-run winds but still 5%–10% stronger than reality. The increased terrain height may explain the stronger momentum fluxes relative to the long run, while the stronger-than-observed cross barrier winds may explain the over predicted momentum fluxes relative to the observations.
The average normalized AIRS weighting function for channels 81 and 82 (average wavelength of 14.9381 μm). The upper horizontal line shows the average height of the top of the long-run domain. The lower-horizontal line shows the start of the damping layer. Note that 88.8% of this weighting function is contained within the long-run domain and 68.3% is contained below the 10-km upper sponge layer.
Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0173.1
Figure 7 shows time series of simulated and observed brightness temperature (
Time series of observed (red) and long-run forward-modeled (black) brightness temperature variances. Variances were computed within the 41°–47°S, 166°–174°E area shown in Fig. 1b.
Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0173.1
In summary, both the 6- and 2-km-resolution long run and event runs were able to quantitatively reproduce ambient horizontal winds and temperatures over the whole DEEPWAVE field campaign between z = 2 and 30 km. This agreement suggests there is little interior drift within the continuously running long run. Despite accurately reproducing slowly varying ambient quantities, there is significant intraevent (<9 h) variability in MFx, both observed and simulated, suggesting MFx averaged along a single aircraft leg may be unpredictable. Higher resolution is important in reproducing the magnitude of this intraevent variability. Despite the lack of predictability, the MFx bias was small relative to the mean (~5% weaker) in the long run but was considerable in the event runs (~50% stronger). Qualitatively, significant observed deep and shallow wave events within satellite temperature observations were also deep and shallow within the long run. We proceed to study wave attenuation in the long run in the next section having established that the ambient atmosphere, wave momentum fluxes, and wave attenuation levels are well represented.
3. Mountain wave attenuation over New Zealand
a. The valve layer
Zonal GWD is computed within WRF using the method presented by Kruse and Smith (2015), where 
Mountain wave events over New Zealand are episodic, evidenced by the transience of both background zonal wind and MFx in Figs. 8a and 8c, respectively. Mountain waves in many events propagate to altitudes greater than 30 km (e.g., 20 June in Fig. 8c), while in other events do not propagate beyond 25 km (e.g., events between 23 June and 5 July). Waves within deep events gradually and relatively smoothly deposit their momentum as they propagate (Fig. 8e), while waves in shallow events are strongly attenuated within a layer between 15 and 25 km, producing a local maximum in zonal GWD in the time-averaged profile (Fig. 8f). This layer is termed a mountain wave “valve layer,” as it restricts mountain wave momentum fluxed into the upper stratosphere, analogous to a valve restricting mass flux of some fluid through a pipe. This valve layer is associated with wind speed minima that occur above tropopause-level wind maxima (Fig. 8a), which cause mountain waves to steepen, become nonlinear (Fig. 8g), and attenuate. Nonlinearity is quantified pointwise by the nonlinearity ratio, 
(left) Height–time and (right) time-averaged plots of (a),(b) area-averaged zonal wind, (c),(d) area-averaged MFx, (e),(f) zonal GWD, (g),(h) area of NLR > 0.25, and (i),(j) modified PV variance within the long run over the boxed region in Fig. 1b.
Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0173.1
This mountain wave valve layer is distinct from a critical level. A critical level is defined as the level where the ambient wind speed through a wave (i.e., wind speed perpendicular to the phase fronts 
Two schematic profiles of zonal wind speed: one with a critical level representative of summer midlatitudes and one with a weak-wind valve layer representative of winter midlatitudes (e.g., New Zealand during the DEEPWAVE period).
Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0173.1
b. GW attenuation and potential vorticity
EPV is conserved assuming the flow is adiabatic 
The horizontal variance of 
c. Local mountain wave attenuation characteristics
In this subsection, the local characteristics of wave attenuation are investigated within a 2-km-resolution event run for the 24 June 2014 mountain wave event. The event run presented here differed from those presented in section 2 in that a 5-arc-min (≈10-km resolution) DEM was used to derive model terrain instead of the 30-arc-s DEM in order to reduce stationary resolution-scale (~2–5Δx) spurious 
The 24 June event is characterized by low-level winds increasing with height, a tropopause-level jet, and winds decreasing to near 10 m s−1 in the lower stratosphere (Fig. 10a). There was little mountain wave attenuation near 12 km within the tropopause-level jet (Figs. 10b and 10c). Mountain waves were strongly and nonlinearly attenuated in the valve layer above this jet, with zonal GWD peaked near 16.5-km altitude (Figs. 10b–d). Stratospheric 
As in Fig. 8, but for the 24 Jun 2014 event simulated at 2-km resolution. Note that color scales here are different from those in Fig. 8.
Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0173.1
In Figs. 11a and 11b, 
Horizontal sections of modified PV [Eq. (6)] plotted at (a) 12- and (b) 16-km levels of little and maximum mountain wave attenuation (Fig. 10c), respectively. Regions where Ri < 0.25 are shown in green. Both panels are valid at 2300 UTC 24 Jun 2014.
Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0173.1
The vertical and cross-mountain distribution of 
Modified PV [Eq. (6)] variance (color shading), average potential temperature (thin black lines; contours every 5 K), and minimum Ri < 0.5 (enclosed within the thick black contours) are shown as a function of distance and height. These quantities were summed, averaged, and minimized, respectively, over the width of the boxed region shown in Fig. 11b. This analysis is valid at 2300 UTC 24 Jun 2014.
Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0173.1
d. What controls deep propagation?
Mountain wave events within the well-validated long run are frequently strongly attenuated within the valve layer between 15 and 25 km. Qualitatively, this attenuation is associated with wind minima (Fig. 8), leading to wave steepening and nonlinear attenuation. However, the incident wave amplitude is important, as large-amplitude vertically propagating waves may be close to breaking, making them more likely to break down at a given altitude than a smaller-amplitude wave. Kaifler et al. (2015) investigated how both of these factors influence the propagation of mountain waves into the mesosphere, finding that mesospheric GW potential energy densities increase with increasing low-level winds and with increasing minimum stratospheric winds to a point, beyond which GW energy densities decreased. Both controls are investigated within the long run here.
Area-averaged MFx at z = 12 and 25 km are plotted versus area-averaged 4-km zonal wind in Figs. 13a and 13b, respectively. There is some relation between the low-level winds and 12-km MFx, but it is not linear as expected from linear theory and there is significant scatter. This situation is worse for the 25-km MFx; low-level winds may be useful in predicting the maximum MFx, but there is more scatter due to valve-layer attenuation.
(a),(b) Long-run MFx at z = 12 km (the altitude of aircraft observations) and z = 25 km (the top of the valve layer) are plotted vs zonal wind at z = 4 km. (c) The 25-km MFx is plotted vs the minimum zonal wind between 12 and 25 km. The red line shows the least squares cubic best fit [Eq. (7)]. (d) The MFx transmission ratio [Eq. (9)] is plotted as a function of 12-km MFx representing wave amplitude and minimum wind speed between 12 and 25 km. All quantities were area averaged over the boxed region in Fig. 1b.
Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0173.1
e. Global context
This valve layer plays an important role in determining the amount of MFx transmitted to the upper stratosphere and middle atmosphere over New Zealand, but does a valve layer exist elsewhere? Zonal-averaged, time-averaged zonal winds and parameterized total (orographic plus nonorographic) zonal GWD within MERRA are shown in Fig. 14a. The averaging period is June and July over the years 2011–15. Between 15° and 50°S and between 15- and 25-km altitude, there is a maximum in zonal GWD associated with a wind minimum above the subtropical jet. This GWD maximum is primarily due to the orographic GWD parameterization, as this region is not far above the nonorographic source level of 400 hPa (Molod et al. 2015) and nonorographic waves are typically launched with amplitudes small enough such that they break in the upper stratosphere and mesosphere. That is, this region of weak winds above the subtropical jet is a mountain wave valve layer, causing mountain waves to attenuate and deposit momentum. This valve layer is also present in the Northern Hemisphere during boreal winter (not shown), suggesting a valve layer similar to that over New Zealand exists above the wintertime subtropical jet (i.e., between latitudes of 15° and 50° and between z = 15 and 25 km) over major mountain ranges in both hemispheres.
Latitude–height cross sections of (a) zonally temporally averaged total (orographic plus nonorographic) parameterized zonal GWD and (b) zonal wind analysis increments from MERRA. Zonal GWD and analysis increments are shown in color shading and the zonally, temporally averaged zonal wind is contoured every 10 m s−1 in both (a) and (b). Quantities were averaged over June and July of 2011–15. The dark-gray-filled region at the bottom of the plots shows the maximum resolved terrain height over all longitudes. The red-filled region shows the maximum subgrid-scale terrain height over all longitudes used by the orographic GWD parameterization.
Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0173.1
4. Comparison of resolved and parameterized GWD
Here total (orographic plus nonorographic) parameterized MFx and zonal GWD within MERRA and MERRA2 are quantitatively compared with those in the well-validated long run. MFx was computed from zonal GWD (Fig. 15b) using Eq. (2) by assuming zero MFx at the uppermost model level (0.1 hPa) and integrating downward. The general circulation model (GCM) in both MERRA and MERRA2 uses the same orographic (McFarlane 1987) and nonorographic (Garcia and Boville 1994) GWD parameterizations; however, the tuning of both parameterizations was changed in MERRA2 (Molod et al. 2015). The most relevant change was to the efficiency or intermittency factor, ε in Eq. (8), which was kept the same as MERRA in the Northern Hemisphere (ε = 0.125), increased by a factor of 2.5 south of 40°S and ramped in between (M. J. Suarez 2016, personal communication).
Height–time plots of area-averaged total (orographic plus nonorographic) (a) parameterized MFx and (b) zonal GWD from MERRA over the same region in Fig. 8. Note that the color contours in Fig. 8c and 8e are 4 times those in this figure.
Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0173.1
MERRA MFx and zonal GWD are shown in Fig. 15 for the same period and area considered in the long run in Fig. 8. Similar figures for MERRA2 are omitted as they were qualitatively similar to those for MERRA (though with larger, i.e., more negative, values). As in the long run, the parameterized momentum flux and GWD are primarily orographic given the small area of interest centered on the South Island (boxed region in Fig. 1b). The vertical and temporal structure of both MFx and zonal GWD are quite similar between WRF and MERRA (cf. Figs. 8c and 8e with Figs. 15a and 15b). Both deep events and valve-layer attenuated shallow events in WRF are also evident in the parameterized fields. Note that the agreement is only qualitative, as color contours in Fig. 15 are a fourth of those in Figs. 8c and 8e. The troposphere is a region of notable disagreement between the simulated and parameterized zonal GWD.
The time-averaged profiles of long run, MERRA, and MERRA2 area-averaged MFx and zonal GWD are shown in Fig. 16. Here, the resolved quantities in MERRA2 are also provided, computed by interpolating MERRA2 fields onto the long-run grid and repeating the method used to compute quantities in the long run. This was not possible in MERRA, as vertical velocity is only provided on a reduced-resolution grid (1.25° × 1.25°); however, MERRA- and MERRA2-resolved quantities should be similar given the similar resolutions. MERRA2-resolved MFx was smaller than that parameterized in both MERRA and MERRA2. The MERRA2-resolved GWD was larger than that parameterized in both MERRA and MERRA2 in the troposphere but still significantly smaller than that in the long run. In the stratosphere, however, resolved MFx and zonal GWD were negligible.
Time-averaged (0000 UTC 24 May–1100 UTC 1 Aug 2014) profiles of area-averaged (boxed region in Fig. 1b) (a) MFx and (b) zonal GWD are plotted vs height. Resolved quantities in the long run and MERRA2 are shown in black and blue, respectively. Parameterized quantities from MERRA and MERRA2 are shown in red and green, respectively. The parameterized zonal GWD in MERRA2 [green in (b)] reached ~−12 m s−1 day−1 near 35 km.
Citation: Journal of the Atmospheric Sciences 73, 12; 10.1175/JAS-D-16-0173.1
In the troposphere, parameterized MFx in both MERRA and MERRA2 is significantly smaller than in the long run and nearly constant with height. This may be due to the constraint that orographic GW source amplitude is limited to the saturation value (McFarlane 1987). As the wind speed typically increases with height (e.g., Fig. 8b), GWs launched at the saturation amplitude might not saturate and attenuate in the troposphere [Eq. (8)], leading to the near conservation of parameterized MFx with height in Fig. 16a. Given little parameterized momentum deposition in the troposphere, parameterized GWD is significantly smaller than that simulated in the long run.
In the valve layer (z = 12–27 km), wave attenuation is represented in both the long-run-resolved and MERRA-/MERRA2-parameterized fields. Here, MFx is 2–4 times smaller in MERRA than in the long run (Fig. 16a). At z = 12 km, where long-run MFx was nearly unbiased relative to aircraft observations (section 2b), the momentum fluxed into the stratosphere in MERRA was about 3.5 times smaller than in the long run. MERRA zonal GWD was 3–6 times smaller than the long run in the valve layer. In MERRA2, MFx and zonal GWD are similar to the long run or slightly underrepresented in the valve layer. These results suggest the mountain wave momentum fluxed into the stratosphere and the lower-stratospheric zonal GWD, at least over New Zealand, may be significantly underrepresented within the MERRA GCM and potentially other GCMs using similar parameterizations and tuning criteria. Increasing the parameterized source MFx, as performed in MERRA2 by increasing ε in Eq. (8), may resolve these issues in the valve layer.
Further evidence of this underrepresentation of valve layer GWD in MERRA is provided by Fig. 14b, showing the zonal, time mean zonal wind analysis increments from MERRA for June and July of 2011–15. Analysis increments are model errors (i.e., the difference between a 6-h forecast by the underlying GCM and an analysis of observations at the same time) divided by the time integrated to express the errors as a tendency. These tendencies are assumed constant and are applied as an additional forcing term in the governing equations to dynamically correct the GCM predictions. Similar analysis increments within the stratosphere were interpreted by McLandress et al. (2012) as missing GWD. In the midlatitude, lower-stratospheric valve layer, negative analysis increments are roughly collocated with negative zonal GWD (e.g., at 30°S, z = 18 km in Figs. 14a and 14b). There are other regions outside of the valve layer where this is also true. These increments also suggest valve-layer GWD is underrepresented within the MERRA GCM. Further, the analysis increments within this region are 4–8 times the MERRA GWD (e.g., increments and zonal GWD of −2−1 and −2−4 m s day−1, respectively, near 30°S and z = 17 km), roughly consistent with the GWD comparison between MERRA and the long run.
Above the valve layer (z = 30−35 km), MERRA2 parameterized MFx is rather sharply deposited, resulting in very large zonal GWD (~−12 m s−1 day−1) relative to long run and MERRA (Fig. 16). This strong deviation from MERRA may be partially due to the increase in ε in MERRA2, as the nonorographic parameterization was unchanged poleward of ±20° latitude (Molod et al. 2015). This tuning parameter modification appears to have resolved the underrepresentation of valve layer GWD in MERRA but also introduced an overrepresentation of GWD by an order of magnitude near z = 35 km. We speculate that this increase in GWD is associated with the fact that increasing ε increases both the source and saturated parameterized momentum fluxes. This modification results in more MFx into the valve layer and more GWD within it but also increases the MFx and wave amplitude transmitted through the valve layer. These larger momentum fluxes and wave amplitudes then allow for more GWD aloft. Modifying ε is inconsistent with Fig. 13c, which suggests MFx transmitted through the valve layer is independent of MFx below it. The overrepresentation of GWD above the valve layer might be addressed by removing the dependence on ε from the saturated MFx relation in GWD parameterizations.
The representation of GWD in GCMs has important implications for simulations of stratospheric and, indirectly, tropospheric climate. For example, increasing the Southern Hemisphere source and saturated orographic momentum flux in the MERRA2 GCM was reported to hasten the springtime breakdown of the stratospheric polar vortex (Molod et al. 2015), bringing the timing of this breakdown closer to observations. Further, Sigmond and Scinocca (2010) found that similarly increasing orographic GWD significantly decreased the strength of the stratospheric polar vortex by altering planetary wave propagation and increasing planetary wave drag on the vortex jet. In addition to addressing the missing GWD near 60°S presented by McLandress et al. (2012), this previous work suggests careful tuning and modification of orographic GWD parameterizations may also help in reducing the common cold-pole problem in chemistry–climate models, and the results presented here provide some justification and guidance for doing so.
5. Conclusions
New Zealand mountain wave propagation into the upper stratosphere is controlled by wave attenuation in a lower-stratospheric mountain wave “valve layer.” A valve layer is distinct from a critical level and is defined as a weak-wind layer containing no wind reversal. In a valve layer, mountain wave momentum flux transmission is primarily controlled by ambient wind speed. During the DEEPWAVE field campaign in May–July 2014, a valve layer was typically present in the lower stratosphere over New Zealand allowing a detailed study of wave attenuation within such a layer. High-resolution, deep (z ≈ 0–45 km) WRF simulations, constrained by operational ECMWF analyses and extensively validated by research aircraft, radiosonde, and satellite observations, were used to reproduce observed mountain wave events and study mountain wave dynamics within this valve layer.
Locally, mountain waves induce regions of low Richardson number (Ri), which cause momentum deposition through the subgrid-scale turbulence parameterization representing unresolved heat and momentum transport in attenuating GWs. Attenuation is horizontally inhomogeneous, likely as a result of horizontal variations of terrain height forcing horizontally varying wave amplitudes. On either side of the many localized regions of low Ri, positive and negative PV anomalies are generated. These anomalies are conservatively advected downstream generating numerous PV banners. Wave attenuation is also inhomogeneous in the vertical and is mostly confined to wave-induced upstream-tilted regions of low Ri.
Within the long run, some mountain wave events are deep (>30 km), while many events are shallow with mountain waves strongly attenuated in a lower-stratospheric valve layer. This valve layer is a climatological feature, present above the wintertime subtropical jet (between latitudes of 15° and 50° and between z = 15 and 25 km) in both hemispheres. Both minimum stratospheric wind, which causes waves to steepen and attenuate, and wave amplitude play a role in determining the percentage of MFx transmitted through the valve layer. However, MFx above the valve layer is primarily controlled by the minimum wind speed within the valve layer alone (i.e., 
The McFarlane (1987) gravity wave drag (GWD) parameterization used in MERRA and MERRA2 was able to qualitatively reproduce the vertical and temporal structure of MFx and zonal GWD over New Zealand within the well-validated long run. However, the long-run-simulated zonal GWD was 3–6 times stronger than that parameterized in MERRA in the valve layer. MERRA zonal wind analysis increments were consistent with this result, suggesting zonal GWD was underrepresented by a factor of 4–8 in the lower-stratospheric valve layer above the wintertime subtropical jet. This underrepresentation of valve-layer momentum flux and GWD in MERRA was significantly reduced in MERRA2 by increasing both the source and saturated momentum fluxes by a factor of 2.5 south of 40°S. However, a significant overrepresentation of GWD was introduced aloft (z = 30–35 km). Future tuning and modification of GWD parameterizations is warranted and should be constrained and guided by direct observations and high-resolution modeling.
Acknowledgments
This work was supported by the National Science Foundation (NSF-AGS-1338655) and the Chief of Naval Research (PE-61153N). High-performance computing was performed on the Yellowstone supercomputer (ark:/85065/d7wd3xhc) with support provided by NCAR’s Computational and Information Systems Laboratory, sponsored by the National Science Foundation. We would like to acknowledge Andreas Dörnbrack for providing the ECMWF analyses, Johannes Wagner for assistance in running WRF with these analyses, and very useful discussions on analysis increments and general circulation with Joan Alexander and William Boos. We would also like to acknowledge useful comments and suggestions on this manuscript by Dale Durran and two anonymous reviewers.
APPENDIX
Spurious Resolution-Scale PV Perturbations
Within event runs using the 30-arc-s digital elevation model, large-amplitude stationary resolution-scale (≈2–5Δx) potential vorticity (PV) perturbations were typically produced on all model levels below 25 km over the highest New Zealand terrain (not shown). These PV perturbations were interpreted as spurious and attributed to the added discretization error introduced when high-amplitude terrain features are poorly resolved and retained in the terrain following model levels (e.g., Schär et al. 2002). The amplitude of the topography retained in the terrain following model levels decreases with height but was only reduced by 10% in the lower stratosphere in these deep (z ≊ 0–45 km) simulations. Using the smoother 5-arc-min DEM largely removed the spurious Π anomalies. Unfortunately, this reduced the model terrain heights and removed an important part of the terrain spectrum. However, stratospheric momentum fluxes and zonal GWD were nearly unaffected.
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