1. Introduction
The advent of satellite radiance assimilation has required many operational numerical weather prediction (NWP) centers to raise the upper boundaries of their global forecast models. Assimilating radiances from nadir-viewing sensors in particular can have large positive impacts on NWP due to the high density, precision, and global coverage of these observations (e.g., Langland and Baker 2004), but can be challenging because of vertically deep contribution functions that can extend into the stratosphere and mesosphere [see Rosenkranz et al. (1997), their Figs. 1 and 2]. Accurate assimilation of the atmospheric information contained in these measurements requires, inter alia, accurate forecast background fields at all contributing altitudes, so that forward radiative transfer models provide accurate background radiances and thus meaningful analysis increments (Hoppel et al. 2013). Thus, extending NWP systems through the stratosphere has promoted a virtuous cycle of improved upper-level forecasts and improved assimilation of nadir radiances, leading to increases in 0–5-day forecast skill not just in the stratosphere, but in the troposphere as well (Gerber et al. 2012; Charron et al. 2012).
Another motivating factor for extending the upper boundaries of NWP systems is an emerging requirement to forecast well beyond 5 days, and potentially out to intraseasonal and seasonal time scales. Over these longer time scales, stratosphere-resolving models are needed to forecast deep dynamical coupling (Gerber et al. 2012). A well-known example is stratospheric anomalies in the strength of northern annular mode (NAM) during wintertime vortex disturbance or intensification events, which can significantly impact surface weather over subsequent weeks and months (e.g., Thompson et al. 2002; Baldwin et al. 2003; Boer and Hamilton 2008; Folland et al. 2012; Sigmond et al. 2013).
The quasi-biennial oscillation (QBO), which is characterized by alternating tropical easterlies and westerlies at 10–70 hPa [~(20–30)-km altitude] with a period of ~(18–34) months, also plays an important role in both troposphere–stratosphere and tropical–extratropical dynamical coupling (Baldwin et al. 2001). Winds are weaker and temperatures are higher in the polar winter stratosphere during easterly QBO phases relative to westerly phases (Baldwin et al. 2001; Pascoe et al. 2005, 2006; Hurwitz et al. 2011a). This teleconnection occurs primarily because QBO winds modify refractive indices for planetary-wave propagation, leading to greater poleward focusing of planetary waves during QBO easterly phases. This in turn increases extratropical planetary-wave drag, which weakens winds and enhances downwelling that warms the stratosphere adiabatically (Holton and Tan 1980). In addition to this Holton–Tan mechanism, QBO-induced meridional circulation anomalies and planetary wave propagation in the subtropical lower stratosphere can also contribute to this teleconnection (e.g., Anstey et al. 2010; Garfinkel et al. 2012). The QBO’s influence can extend to the extratropical troposphere as well, either through QBO-modulated wave–mean flow interactions between the extratropical stratosphere and troposphere (Baldwin and Dunkerton 2001; Coughlin and Tung 2001; Thompson et al. 2002; Ribera et al. 2008; Garfinkel and Hartmann 2010), or through modification of the Hadley circulation in the upper troposphere (Liess and Geller 2012).
The QBO is driven by selective dissipation of a broad spectrum of upward-propagating planetary and gravity waves generated in the tropical troposphere by deep convection [for a complete review, see, e.g., Baldwin et al. (2001), and references therein]. Global models typically do not spontaneously generate a QBO, a problem that has been variously ascribed to insufficient vertical resolution, excessive stratospheric diffusion, inaccurate parameterization of deep tropical convection, and inadequately resolved gravity wave forcing (e.g., Takahashi 1999; Scaife et al. 2000; Giorgetta et al. 2002; Boer and Hamilton 2008). For short-range NWP (0–5 days), this inability to generate a QBO is generally of little concern, particularly if realistic QBO structure is assimilated operationally (e.g., from tropical radiosondes), since the slow radiative relaxation rates in the tropical lower stratosphere allow QBO initial conditions to persist largely unaltered in these types of forecasts. Over longer forecast time scales, however, the forecast QBO can start to decay and revert to an unrealistic model climatology (Boer and Hamilton 2008) unless the model physics has been modified to generate and maintain a realistically evolving QBO (Marshall and Scaife 2009).
This paper describes the implementation of a new gravity wave drag (GWD) parameterization along with several key modifications that were needed to produce a realistic QBO in a high-altitude NWP forecast model while at the same time maintaining computational efficiency. The latter point is important, since NWP systems always operate near the limits of available computational resources. Standard methods used to generate a QBO in research models, such as large increases in stratospheric vertical resolution and implementation of expensive nonorographic gravity wave drag parameterizations, involve significant increases in computational overhead that may exceed what operational NWP centers can currently accommodate. This paper also demonstrates how an internally generated QBO in an NWP model can positively impact seasonal forecasts during Northern Hemisphere (NH) winter.
The forecast model and sequence of experimental tests are described in section 2, which highlights the importance of horizontal and vertical resolution, parameterized gravity wave drag, resolved tropical waves from deep convection, and sources of diffusive damping in producing a QBO in the model. Section 3 presents results from a series of 12-month free-running simulations designed to test the model’s ability to generate a QBO. Results from a 10-yr model integration designed to evaluate the long-term behavior of the modeled QBO are discussed in section 4. Section 5 presents results from ensembles of 120-day model simulations over the December–March period showing that a QBO generated with a modified stochastic GWD parameterization improves seasonal forecasts of equatorial lower-stratospheric winds, and in so doing produces significant changes in surface weather patterns during NH winter. The major findings of this study are discussed and summarized in section 6.
2. Model description and experimental design
Our forecast model is the advanced-level physics, high-altitude (ALPHA) prototype of the Navy Operational Global Atmospheric Prediction System (NOGAPS). The dynamical core of the NOGAPS-ALPHA forecast model is hydrostatic, Eulerian spectral in the horizontal, and finite differenced in the vertical (Hogan and Rosmond 1991). The basic model configuration is described in section 2.1 of Eckermann et al. (2009). In this section we first provide a brief overview of this configuration and then describe changes that were made to the model’s physical parameterizations in order to generate a realistic QBO. We also describe the model initialization and boundary conditions used to carry out the 120-day, 12-month, and 10-yr free-running simulations.
a. Horizontal resolution
It is generally accepted that the wave driving of the QBO comes from a combination of planetary-scale equatorial waves and smaller-scale gravity waves generated by tropical deep convection (Baldwin et al. 2001). The major components of the planetary wave driving consist of wavenumber-1 Kelvin waves with periods of ~(10–15) days for the QBO’s westerly phase (Wallace and Kousky 1968), and mixed Rossby–gravity waves of wavenumbers ~(3–6) with periods of 4–6 days for the QBO’s easterly phase (Yanai and Maruyama 1966). Faster equatorial modes tend to propagate higher and drive semiannual oscillations (SAOs) of the upper stratosphere and mesosphere, whereas slower modes typically remain in the troposphere where they are relevant, for example, to the Madden–Julian oscillation (MJO). However, the momentum fluxes associated with the Kelvin and Rossby–gravity waves are not large enough to drive the QBO (Sato and Dunkerton 1997; Ern and Preusse 2009), and it is now believed that the majority of the QBO wave driving comes from the broad spectrum of smaller-scale tropical gravity waves generated by deep convection (Dunkerton 1997; Kawatani et al. 2010).
For the present study, the NOGAPS-ALPHA model was triangularly truncated at wavenumber 79 (T79), corresponding to a 1.5° spacing in latitude and longitude on a quadratic Gaussian grid, which is more than adequate to resolve the horizontal scales of the dominant Wallace–Kousky and Yanai–Maruyama modes as well as most other planetary-scale equatorial wave modes (e.g., Horinouchi et al. 2003). It is insufficient, however, to resolve the smaller-scale tropical gravity waves that also drive the QBO. Since small-scale gravity waves are under resolved even at much higher horizontal resolutions used for operational NWP (e.g., Orr et al. 2010), in this work we retain T79 resolution, so as to make multiyear simulations computationally feasible, and parameterize the missing small-scale tropical gravity wave flux (see section 2c).
b. Vertical resolution
Although their horizontal wavelengths are large, the vertical wavelengths of the Wallace–Kousky and Yanai–Maruyama modes are short: typically 5–10 and 4–8 km, respectively. The combined effects of these modes and smaller-scale gravity waves drive the QBO, which is characterized by relatively narrow (~5 km) zones of high vertical wind shear that descend at a rate of ~1 km month−1. Not surprisingly, then, simulated QBOs in models have proven sensitive to vertical resolution in the stratosphere. The standard NOGAPS-ALPHA configuration uses the hybrid σ−p vertical coordinate of Eckermann (2009) with 68 model levels (L68) extending to an upper boundary of 
Vertical grid spacing (km) as a function of altitude in the 139-level (black), 84-level (red), and 68-level (blue) versions of the NOGAPS-ALPHA forecast model.
Citation: Monthly Weather Review 143, 6; 10.1175/MWR-D-14-00208.1
c. Gravity wave drag parameterization
As discussed in Geller et al. (2013), several differently formulated parameterizations of subgrid-scale nonorographic GWD have been used to generate a QBO in global models. Some examples include the spectral parameterization of Warner and McIntyre (2001) implemented in the Met Office Unified Model (Scaife et al. 2000, 2002), the Doppler-spread parameterization of Hines (1997) implemented in the middle atmosphere version of the ECHAM5 model (Giorgetta et al. 2002), the parameterization of Lindzen (1981) using a combination of frontal and convective sources in the Whole Atmosphere Community Climate Model (Richter et al. 2014), and the convectively generated parameterization employed in the Goddard Institute for Space Studies model (Rind et al. 2014). A common feature of all of these different approaches is to account for sources of momentum flux from unresolved tropical gravity waves generated in the troposphere.
The NOGAPS-ALPHA forecast model parameterizes the forcing by subgrid-scale nonorographic gravity waves using the method of Eckermann (2011), which replaces a deterministic multiwave scheme based on Lindzen (1981), and described in appendix A of Garcia et al. (2007), with a single-wave stochastic analog. As shown in the study of Eckermann (2011), general circulation model (GCM) experiments using this stochastic analog produce time-mean zonal wind fields and kinetic energy spectra that are nearly identical to those produced with the original deterministic multiwave scheme. The main advantage of the stochastic approach is that it reduces the computational expense of the GWD parameterization by a factor of ~10. Piani et al. (2004) and, more recently, Lott et al. (2012) have used stochastic GWD parameterizations to generate a QBO in a GCM for research purposes. Here we describe how the stochastic GWD parameterization in NOGAPS-ALPHA is applied to produce a realistic internally generated QBO suitable for NWP applications.
The original GWD parameterization incorporates waves with short horizontal wavelengths and fast phase speeds that tend to deposit most momentum in the mesosphere (Eckermann 2011), whereas the QBO is driven by waves with longer horizontal wavelengths and slower phase speeds. In the present study, the original parameterization is augmented to use two separate source spectra. Both incorporate a Gaussian distribution of source-level wave momentum as a function of phase speed with a width of 30 m s−1, following Garcia et al. (2007).
The first spectrum is applied at all latitudes using parameters based on the original formulation of Eckermann (2011). Waves are launched at a source level of 500 hPa. Waves propagate zonally at a phase speed chosen randomly within a ±80 m s−1 intrinsic phase speed range (i.e., the phase speed relative to the 500-hPa zonal wind) and are assigned a constant horizontal wavelength of 100 km (see Fig. 2a). The phase speed in turn sets the wave’s source-level momentum flux according to the deterministic Gaussian momentum flux spectrum. The peak value of this source-level flux spectrum varies with latitude and season as shown by the broken curves in Fig. 2b. The GWD calculation incorporates a deterministic efficiency factor (ε) = 15, as defined in Garcia et al. (2007). This value is rescaled in the single-wave stochastic formulation, following Eckermann (2011), to give the same time-mean flux and drag values as the deterministic scheme.
(a) Latitude dependence of the original (dashed) and modified (solid) horizontal wavelengths used in the stochastic gravity wave drag parameterization. (b) Latitude dependence of the original source-level momentum flux for January (dotted) and July (dashed) compared with values of the modified tropical flux (solid).
Citation: Monthly Weather Review 143, 6; 10.1175/MWR-D-14-00208.1
A second tropical spectrum is launched at 100 hPa between 30°S and 30°N only. Wave phase speeds are zonal and assigned randomly between ±30 m s−1 relative to the ground and, as depicted in Fig. 2a, are assigned horizontal wavelengths that vary smoothly with latitude from 100 km at ±30° latitude to 500 km at the equator. As shown in Fig. 2a, the peak values of the Gaussian momentum flux spectrum are time invariant but vary with latitude. GWD is calculated using ε = 0.06.
The time-mean source momentum flux from each spectrum can be derived by integrating the deterministic Gaussian momentum flux spectrum across its assigned phase speed range, then scaling by ε. These values will vary with time and position (see Fig. 2b) but yield estimates in the range of those diagnosed from earlier GCM studies by Geller et al. (2013). Note from Fig. 2b that although peak tropical flux values are larger for the second spectrum compared to the first spectrum, the phase speeds of the second spectrum are restricted to ±30 m s−1 and thus sum over a smaller part of the Gaussian momentum flux spectrum than the first spectrum, which spans the ±80 m s−1 range of intrinsic phase speeds.
Initial tests of the modified GWD spectrum found that the higher source level and reduced phase speed range were necessary for generating westerly flow in the equatorial stratosphere. Increasing the horizontal wavelength parameter and decreasing the efficiency factor were both found to increase the QBO period. In particular, changing the horizontal wavelength parameter in the tropics avoided phase locking between the QBO and the annual cycle, as described in the study by Hurwitz et al. (2011b). The use of longer horizontal wavelengths in the tropics is supported by the observations and modeling results reviewed by Alexander et al. (2010), which show that higher wavenumber Kelvin waves with horizontal wavelengths of up to ~1000 km play a role in forcing the westerly phase of the QBO in the tropical lower stratosphere.
d. Convective parameterization
Equatorial wave spectra in global models are sensitive to the method used to parameterize subgrid-scale tropical deep convection due to the large differences in the space–time variability of the diabatic tendencies generated by different schemes (Ricciardulli and Garcia 2000; Horinouchi et al. 2003). Convective precipitation and the associated transport of heat and momentum are parameterized in NOGAPS-ALPHA using the method of Emanuel and Zivkovic-Rothman (1999), with modifications as described by Peng et al. (2004). Figure 3 compares the geographic distribution of convective precipitation over the January–March period from a T79L139 NOGAPS-ALPHA experiment initialized 1 January 2005 with corresponding mean values derived from daily analyses provided by the Global Precipitation Climatology Project (GPCP; Adler et al. 2003). While there is good qualitative agreement in the distribution of modeled and observed precipitation, the model tends to produce higher peak values of precipitation that are more localized than the observations indicate. To evaluate the temporal variability in the modeled convective precipitation over this time period, Fig. 4 plots longitude–time variations in equatorial (±10° latitude) convective precipitation rates over a 30-day period (10 January–9 February) from 3-hourly T79L139 output and from corresponding GPCP fields. As Fig. 4 shows, the Emanuel parameterization in NOGAPS-ALPHA produces regions of intense precipitation over highly localized regions, while the GPCP convective precipitation is distributed more broadly in longitude. This result is consistent with earlier modeling studies (e.g., Hamilton et al. 2008; Maury and Lott 2014) showing that the Emanuel scheme generates less variance in the space–time spectrum of convectively generated waves compared to observations.
Geographic distribution of convective precipitation rates averaged over the January–March period from (a) daily T79L139 NOGAPS-ALPHA model output for a simulation initialized on 1 Jan 2005 and (b) the Global Precipitation Climatology Project (GPCP) daily analyses from 1 Jan to 31 Mar 2005. Contour interval is 2.5 mm day−1.
Citation: Monthly Weather Review 143, 6; 10.1175/MWR-D-14-00208.1
Longitude–time plots of daily convective precipitation rates (mm day−1) averaged over 10°S–10°N from (a) days 10–40 of the T79L139 NOGAPS-ALPHA simulation in Fig. 3, and from (b) GPCP daily analyses for 10 Jan–9 Feb 2005.
Citation: Monthly Weather Review 143, 6; 10.1175/MWR-D-14-00208.1
To illustrate how this reduced variance impacts the resolved wave activity in the model, Fig. 5 compares wavenumber–frequency power spectra derived from equatorial mean (±10° latitude) convective precipitation anomalies using the first 90 days of output from NOGAPS-ALPHA (top row) and daily GPCP convective precipitation rates (bottom row) for the period 1 January–31 March 2005. The spectra in Fig. 5 are based on anomalies from the 3-month mean precipitation fields and are plotted using the energy-content form described in Horinouchi et al. (2003, their appendix A). The modeled spectra in Figs. 5a and 5b show relatively little power at the wavenumbers and frequencies associated with the Wallace–Kousky and Yanai–Maruyama modes compared to the observed spectra in Figs. 5c and 5d. This is not an unprecedented finding for NWP-focused models, which tend to place the greatest emphasis on accurate prediction of large-scale convective features having the greatest impact on surface NWP, and may even suppress space–time variability to improve skill scores based on forecast error variances.
Power spectra of (left) eastward- and (right) westward-propagating convective precipitation anomalies over the period 1 Jan–31 Mar 2005. (a),(b) Results from 3-hourly L139 NOGAPS-ALPHA model output initialized 1 Jan 2005. (c),(d) Results from the daily GPCP data for 2005. Solid black contours are drawn at values of 0.01, 0.1, 0.3, 0.5, 1.0, and 3.0 mm2 day−2. Dashed lines indicate zonal phase speeds of 2, 5, 10, 20, and 50 m s−1.
Citation: Monthly Weather Review 143, 6; 10.1175/MWR-D-14-00208.1
While the horizontal resolution of the T79 NOGAPS-ALPHA model can resolve the types of planetary-scale equatorial waves that contribute to the wave driving of the QBO, our analysis shows that the model’s convective parameterization does not provide sufficient forcing from these types of waves. For the purposes of this study, the resulting systematic underprediction of resolved equatorial wave activity is viewed as a missing wave flux that must be parameterized in order to generate a QBO.
e. Vertical diffusion
Vertical mixing of momentum and heat is parameterized in NOGAPS-ALPHA using the method of Louis (1979), as modified for NWP applications by Louis et al. (1982); additional implementation details for NOGAPS are provided in section 7b of Hogan and Rosmond (1991). Though primarily focused on the planetary boundary layer (PBL), the scheme is designed to operate at all levels in the free atmosphere, including the stratosphere (see, e.g., Louis et al. 1982, section 4). In initial tests using the T79L139 NOGAPS-ALPHA configuration, this scheme often yielded unrealistically large vertical mixing tendencies within tropical lower-stratospheric layers where the vertical shear in zonal winds was large. This problem was eventually traced to the vertical mixing parameterization. When sharp vertical shear layers developed in the tropical lower-stratospheric zonal winds, the vertical mixing parameterization would activate in these layers to reduce the vertical shear, which reduced the parameterized GWD driving the QBO. This effect is discussed in more detail in section 3.
Palmer et al. (1990) diagnosed a similar problem and implemented major changes to the scheme, such that it activated in the free atmosphere only in regions of diagnosed static instability. For the purposes of this study, we are more interested in the sensitivity of the QBO simulation to levels of vertical diffusion in the tropical stratosphere. Since observations indicate that turbulent vertical diffusivities in the tropical lower stratosphere are several orders of magnitude lower than those encountered in the troposphere (e.g., Wilson 2004) we performed a series of tests in which vertical mixing tendencies from the Louis scheme were reduced by a factor of 10, 100, and 1000 at heights above the 700-hPa level. Best results were found when the tendencies were reduced by a factor of 100. Analysis of modeled kinetic energy spectra in section 3 indicates that this reduction increases the amount of resolved wave energy in the lower stratosphere at the small scales.
f. Horizontal diffusion
Typically, the treatment of horizontal diffusion in a spectral NWP model is tuned to provide optimum performance over the time frame of a 5–10-day forecast rather than the seasonal and interannual time scales relevant for the QBO. In this section, we describe modifications to the specified horizontal diffusion in the NOGAPS-ALPHA model that facilitate the generation of an internal QBO. We then evaluate this treatment of horizontal diffusion within the context of other global spectral models used for both NWP and climate studies.
Ideally, 
Values of the fourth-order horizontal momentum diffusion time scale at the truncation wavenumber N, 
Citation: Monthly Weather Review 143, 6; 10.1175/MWR-D-14-00208.1
For the T79 configuration of NOGAPS-ALPHA used in this study, we adopt a value of 
Preliminary T79L139 NOGAPS-ALPHA simulations found that both the amplitude and period of the modeled QBO below the 10-hPa level were less than observed when using 
g. Model initialization and boundary conditions
All free-running model simulations were initialized using analyzed wind, temperature, and constituent fields from NOGAPS-ALPHA data assimilation runs, which are based on a production configuration described in Eckermann et al. (2009). To determine the statistical significance of the QBO’s impact on seasonal forecasts during NH winter (see section 5), 15-member ensembles of 120-day simulations with and without the modified tropical GWD were generated over the December–March period. The first three members of each ensemble were initialized using NOGAPS-ALPHA analyses for 0000 UTC 1 December, 5 December, and 9 December 2007. The next three members were initialized using the model output fields at hour 12 from the first three simulations. Additional ensemble members were generated similarly using model output from hours 24, 36, and 48 of the original three simulations.
Boundary conditions for the 120-day and 12-month simulations were specified using archived twice-daily (0000 and 1200 UTC) global analyses of sea surface temperature (SST) and sea ice fraction provided by the Fleet Numerical Meteorology and Oceanography Center (FNMOC). Boundary conditions for the 10-yr simulation were specified using monthly mean climatological values of SST and sea ice fraction for the 1979–2005 period, which were obtained from the National Centers for Environmental Prediction (NCEP) reanalysis (Kistler et al. 2001). Since the 120-day experiments use specified ocean conditions, these are not true seasonal forecasts. A coupled ocean–atmosphere model would be required in order to produce a true seasonal forecast, a capability that is not currently available in NOGAPS-ALPHA.
3. Results from 12-month model simulations
a. Description of experiments
This section presents results from a series of 12-month NOGAPS-ALPHA simulations that were performed to determine optimal configurations of the model’s vertical levels, horizontal diffusion, vertical diffusion, and parameterized GWD for generating an internal QBO. Table 1 summarizes each of these model experiments.
Description of gravity wave drag (GWD) and numerical diffusion used in the NOGAPS-ALPHA model experiments.
First, the sensitivity of the modeled QBO to vertical resolution was tested with a set of three 12-month simulations using the NOGAPS-ALPHA configurations plotted in Fig. 1, designated L68, L84, and L139. These three simulations all used the same parameterized GWD, horizontal diffusion, and vertical diffusion as described in section 2.
To determine the role of the GWD parameterization in producing a QBO, two additional 12-month L139 simulations were performed using the same settings for the horizontal and vertical diffusion. The L139-OS experiment listed in Table 1 uses only the original stochastic GWD spectrum (i.e., the additional tropical spectrum is not included); the L139-NS experiment has no parameterized GWD.
To further explore the sensitivity of the modeled QBO to specified values of horizontal and vertical diffusion in the lower stratosphere, two additional 12-month simulations were performed, designated L139-HDF and L139-VDF, respectively. These two experiments differ from the L139 experiment as follows. L139-HDF employs a constant value of 
Figures 7a, 7b, and 7c plot the monthly zonal mean zonal wind over the equator (5°S–5°N) from the L68, L84, and L139 experiments, respectively. Both L68 and L84 experiments produce alternating periods of weak (~10 m s−1) easterly and westerly winds in the equatorial lower stratosphere with a period of ~6 months. The L139 experiment (Fig. 7c), on the other hand, produces westerly winds that slowly descend into the equatorial lower stratosphere, similar to the observed QBO. Figure 7d shows that using the original stochastic GWD parameterization without the augmented tropical spectrum of wave momentum flux produces persistent easterly flow in the equatorial lower stratosphere. In the absence of any parameterized GWD, the L139-NS experiment (Fig. 7e) produces easterly flow throughout most of the equatorial stratosphere. Figure 7f shows that using 
Monthly zonal mean zonal winds over the equator from the (a)–(g) 12-month NOGAPS-ALPHA simulations listed in Table 1: Contour interval is 10 m s−1 with dashed contours representing easterly and solid westerly flow.
Citation: Monthly Weather Review 143, 6; 10.1175/MWR-D-14-00208.1
b. Momentum budget calculations
To examine the relative roles of resolved and parameterized wave driving in the sensitivity experiments, Figs. 8 and 9 compare monthly zonal mean zonal wind tendencies calculated from the EP flux divergence with monthly mean values of the parameterized GWD for the month of March, when QBO westerlies first begin to descend into the lower stratosphere (i.e., below the 10-hPa level). Also plotted in Figs. 8 and 9 are corresponding vertical profiles of the monthly zonal mean zonal wind over the equator for each 12-month experiment. A comparison of the resolved and parameterized wave driving during March in the L68, L84, and L139 experiments (Fig. 8) shows that parameterized GWD is producing the majority of the westerly acceleration at this time. Westerly accelerations near 10 hPa due to both resolved and parameterized waves are strongest in the L139 simulation (see Figs. 8g,h). This is due to the fact that the reduced vertical spacing (Δz = 500 m) better captures the selective dissipation of eastward-propagating waves that drives the sharp vertical shear zone separating regions of peak easterly and peak westerly flow over the equator. In the L68 and L84 experiments, westerly accelerations due to parameterized wave drag are much smaller (Figs. 8b and 8e) and thus do not drive as sharp a shear zone separating descending westerlies and easterlies.
Monthly mean values of the zonal mean zonal wind tendency due to (a),(d),(g) the Eliassen–Palm flux divergence and (b),(e),(h) the parameterized gravity wave drag for the month of March from the (top) L68, (middle) L84, and (bottom) L139 experiments. Contours are drawn at ±0.1, 0.2, 0.4, 0.6, 0.8, 1, 2, and 3 m s−1 day−1. Solid (dashed) contours represent westerly (easterly) accelerations. (c),(f),(i) Corresponding zonal mean zonal wind profiles over the equator. Gray contour (in middle column) denotes the location of the zero zonal wind line.
Citation: Monthly Weather Review 143, 6; 10.1175/MWR-D-14-00208.1
As in Fig. 8, but for the (top) L139-OS, (middle) L139-HDF, and (bottom) L139-VDF experiments.
Citation: Monthly Weather Review 143, 6; 10.1175/MWR-D-14-00208.1
The relationship between the model vertical grid spacing and the westerly accelerations produced by the parameterized GWD is further illustrated by comparing profiles of zonal mean zonal wind over the equator for March from each experiment (Fig. 8, right column) with values of the parameterized GWD (Fig. 8, middle column). Of the three experiments, the largest westerly acceleration (~0.6 m s−1 day−1) occurs in the L139 case, in close proximity to the location of the zero wind line (indicated by the solid gray contour). Note that all three experiments (L68, L84, and L139) use the exact same source fluxes in the stochastic GWD parameterization; the increased GWD within the shear zone in the L139 experiment (Fig. 8h) is due to the increased vertical resolution that allows wave drag to drive a narrower sharper vertical shear zone.
Figure 9 presents a similar comparison among the resolved wave driving, parameterized wave driving, and zonal wind profiles for the L139-OS, L139-HDF, and L139-VDF experiments. Again, we find the westerly accelerations in the equatorial stratosphere due to the parameterized GWD are larger than those due to the resolved waves at this time. In the L139-OS experiment (Figs. 9a–c), the original stochastic GWD parameterization (i.e., without the additional tropical GWD) produces a westerly acceleration in excess of 1.4 m s−1 day−1 in the upper stratosphere (1–5 hPa). However, in the absence of additional parameterized tropical wave flux, no westerly accelerations develop below the 10-hPa level.
Comparing the results from the L139-HDF experiment (Figs. 9d–f) with the L139 experiment (Figs. 8g–i) shows that changing the amount of horizontal diffusion between 10 and 70 hPa produces little change in the amount of parameterized GWD or the resultant zonal wind profile in March. The increased amount of horizontal diffusion in the L139-HDF experiment does produce moderate reductions in the amount of resolved wave driving in the subtropical lower stratosphere at this time (Fig. 9d), and similar reductions are also found over the equator later in the year, as discussed below. The larger vertical diffusion in the L139-VDF experiment reduces both the resolved westerly accelerations over the equator (Fig. 9g) and the parameterized GWD driving near 10 hPa (Fig. 9h) at this time by eliminating the narrow vertical shear zone essential for producing a realistic QBO (Fig. 9i).
In addition to the direct effects of resolved and parameterized wave driving, numerous modeling studies (e.g., Dunkerton 1997; Scaife et al. 2002; Giorgetta et al. 2006; Kawatani et al. 2010) have shown that the amplitude and period of the QBO also depend on the strength of equatorial stratospheric upwelling (
To evaluate the upwelling produced in the sensitivity experiments, Fig. 10 depicts the time evolution of monthly mean values of 
Monthly zonal mean values of the transformed Eulerian mean residual vertical velocity 
Citation: Monthly Weather Review 143, 6; 10.1175/MWR-D-14-00208.1
A key feature of the QBO is the descent of westerly flow into the lower stratosphere (i.e., below the 10-hPa level). The L139 experiment, with reduced horizontal and vertical diffusion in the lower stratosphere, produces QBO westerly winds in the range of 15–18 m s−1 at 30 hPa during the July–December period (Fig. 7c). In the L139-HDF experiment, the westerly winds at 30 hPa are in the range of 5–10 m s−1 during this time (Fig. 7f). In the L139-VDF experiment, westerly winds do not descend below the 10-hPa level (Fig. 7g). To examine how the amount of horizontal and vertical diffusion affects the development of QBO westerlies below the 10-hPa level, Fig. 11 plots time series of the terms representing monthly mean EP flux (red curves), parameterized GWD (dark blue curves), vertical momentum advection (yellow curves), and horizontal momentum advection (light blue curves) in the zonal wind tendency equation in (2) at 30 hPa. Also plotted in Fig. 11 is the sum of these terms (black curves). The contribution from the Coriolis torque was found to be small in each case and can be neglected for the purposes of this analysis.
Monthly time series of individual terms in the transformed Eulerian mean zonal momentum budget at 30 hPa averaged between 5°S and 5°N latitude for the (a) L139, (b) L139-HDF, and (c) L139-VDF experiments. The solid black line represents the sum of these terms.
Citation: Monthly Weather Review 143, 6; 10.1175/MWR-D-14-00208.1
Figure 11a shows that westerly accelerations from a combination of parameterized GWD, resolved wave driving, and horizontal momentum advection drive the westerly QBO phase in the equatorial lower stratosphere in the L139 experiment. In the L139-HDF case (Fig. 11b), the increased horizontal diffusion between 10 and 70 hPa reduces the resolved westerly wave forcing during July and August compared to the L139 case, leading to the relatively weak westerly winds (5–10 m s−1) at 30 hPa over the July–December period seen in Fig. 7f. In the L139-VDF case (Fig. 11c), the enhanced vertical diffusion strongly damps the resolved wave driving in June and July, with the result that westerly winds do not descend below the 30-hPa level during the latter half of the year (see Fig. 7g).
Although the resolved equatorial wave driving is insufficient to initiate development of the QBO on its own, the results in Fig. 11 indicate that the amount of resolved wave activity in the model can impact the development of the QBO westerly phase below the 10-hPa level. The following section further discusses the sensitivity of the resolved waves to the specified horizontal and vertical diffusion in the lower stratosphere.
c. Kinetic energy spectra at 50 hPa
To determine how changes in the specified numerical diffusion affects the model dynamics in the lower stratosphere, we examined spectra of kinetic energy per unit mass (KE) as a function of total wavenumber n between 10 and 70 hPa. These spectra were computed from spherical harmonic coefficients of vorticity and divergence, using the methods outlined in Koshyk et al. (1999). Here we discuss results at one representative level (50 hPa), and note that similar results were obtained at the other levels we examined.
Figure 12 shows spectra of total KE at the 50-hPa level, as well as the contributions to this total from divergent and vortical motions, for the L139 (Fig. 12a), L139-HDF (Fig. 12b), and L139-VDF experiments (Fig. 12c). These spectra were averaged over the period 1–31 January. In interpreting Fig. 12, it is important to remember that spectra derived from spherical harmonic coefficients are global means, encompassing the bulk KE distributions in the summer and winter extratropics as well as the tropics. The shapes of the spectra in Fig. 12 are broadly similar to those seen in other GCM experiments, with a peak at n ~ 2–3 followed by power-law reductions with increasing n (Koshyk et al. 1999). High-resolution GCM integrations report n−3 shapes at synoptic wavenumbers due to vorticity-conserving dynamics, followed by a transition to n−5/3 spectral shapes at n ≥ 20–40 (e.g., Koshyk et al. 1999; Burgess et al. 2013), in broad agreement with observed spectra from stratospheric aircraft measurements (e.g., Bacmeister et al. 1996). Blue and red curves in Fig. 12 show these n−3 and n−5/3 power-law forms, respectively.
Kinetic energy spectra at 50 hPa as a function of total wavenumber n averaged over the month of January from the (a) L139, (b) L139-HDF, and (c) L139-VDF experiments. Red and blue curves illustrate theoretical power-law forms anticipated in transitioning from synoptic-scale (n−3) to mesoscale (n−5/3) dynamics, respectively.
Citation: Monthly Weather Review 143, 6; 10.1175/MWR-D-14-00208.1
The L139 spectra in Fig. 12a transition from a steeper KE spectrum at n < 30 to shallower spectra at n > 30. This transition at n ~ 30 occurs when divergent and vortical KE become roughly equal, as is observed at this transition wavenumber in other GCM studies (Koshyk et al. 1999). The divergent KE spectrum in Fig. 12b retains this n−5/3 shape at all n values. Note also that there is no upturned tail (i.e., 
Moreover, the L139-HDF experiment, which uses more typical GCM levels of horizontal diffusion in the stratosphere, yields a KE spectrum at 50 hPa (Fig. 12b) that is suppressed at large n and retains an n−3 shape out to the truncation scale, without any evident transition to a shallower spectral form. Vortical KE in particular is heavily suppressed at large n relative to the L139 experiment, such that divergent KE dominates at short horizontal wavelengths. Similar features are observed even more strongly in the L139-VDF experiment (Fig. 12c), when tropospheric values of the vertical momentum mixing are retained throughout the stratosphere. The KE spectrum in Fig. 12c is again heavily suppressed at large n, with the effect most noticeable in vortical KE, which falls off precipitously at large n such that no break from n−3 to n−5/3 occurs in total KE. At large n, the total KE spectral levels from the L139-VDF experiment (Fig. 12c) are almost an order of magnitude smaller than those in the L139 experiment (Fig. 12a).
The spectra from the three experiments in Fig. 12 reveal that horizontal and vertical diffusion suppress KE at larger n in the lower stratosphere, reducing the amount of resolved wave flux. Changes in the amount of vertical diffusion in the L139-VDF experiment had the largest impact, which is consistent with the greatly reduced westerly acceleration from resolved waves in the lower stratosphere (Fig. 11c).
Overall, the results of the 12-month sensitivity tests indicate that several key modifications are needed to generate an internal QBO in the T79L139 version of NOGAPS-ALPHA. These include increased vertical resolution, a representation of subgrid-scale GWD that includes tropical sources, and reduced amounts of numerical diffusion in the lower stratosphere compared to values typically employed in operational NWP models. These modifications allow the parameterized GWD to provide the majority of the QBO forcing given that the model’s convective parameterization underpredicts resolved tropical wave activity.
Since the spectrum of resolved waves can vary dramatically from one model to another depending on the type of convective parameterization being used (Horinouchi et al. 2003), in practice the amounts of parameterized GWD needed to generate a QBO can be viewed as values to be “tuned” to give optimal results. However, the results of the 12-month sensitivity tests can provide some guidance on how to best choose values for the other key modifications. First, the model vertical resolution should be able to capture the narrow (~5 km) vertical shear zones in equatorial zonal winds that selectively filter the eastward and westward momentum fluxes generated by the GWD parameterization. Second, the amounts of horizontal and vertical diffusion applied in the equatorial lower stratosphere should produce realistic kinetic energy spectra throughout the model’s spatial domain, thus retaining as much resolved wave activity as possible.
In the following section, we present results from a 10-yr free-running simulation using these modifications to examine the behavior of the modeled QBO over multiple cycles.
4. Results from a 10-yr simulation
Based on the findings from the 12-month experiments described in the previous section, a 10-yr free-running T79L139 simulation (designated Q10YR) was carried out using the modified stochastic GWD parameterization with reduced horizontal and vertical diffusion (i.e., using model settings identical to those used in the 12-month L139 experiment listed in Table 1). The monthly zonal mean zonal winds averaged over 5°S–5°N latitude from this experiment, plotted in Fig. 13, show overall good agreement with the observed QBO. For example, alternating phases of westerly and easterly flow originate above the 10-hPa level and descend to the 100-hPa level. Within this region, a peak westerly wind speed of 19 m s−1 occurs at 25-km altitude and a peak easterly wind speed of −34 m s−1 occurs at 30-km altitude. The westerly phase descends faster than the easterly phase, and there is asymmetry in the duration of the phases such that above the 30-hPa level, the easterly phase is longer than the westerly phase, while below this level the westerly phase is longer than the easterly phase. The periods of the modeled QBO, determined by the times when winds transition from easterly to westerly at 30 hPa, are 33, 29, and 30 months. Although these values are are slightly longer than the observed long-term mean QBO period of 28 months (Baldwin et al. 2001) they fall within the observed range of variability in QBO period (Pascoe et al. 2005).
Monthly zonal mean zonal winds over the equator as a function of height and time from a 10-yr free-running T79L139 NOGAPS-ALPHA model simulation using the stochastic GWD parameterization with additional tropical wave flux. Contour interval is 10 m s−1. Periods used to compute QBO easterly and westerly composite differences are indicated in red by “E” and “W,” respectively.
Citation: Monthly Weather Review 143, 6; 10.1175/MWR-D-14-00208.1
To illustrate how the QBO affects the model dynamics in the extratropical stratosphere during NH winter, Fig. 14 plots composite differences in zonal mean zonal wind and temperature averaged over the months of December–January–February–March (DJFM). The composites for westerly (QBOW) and easterly (QBOE) phases are based on NH winters when the value of the modeled 30-hPa monthly mean zonal wind averaged between 5°S and 5°N exceeds 15 m s−1 during all four months. Using this criterion, the QBOE and QBOW composites each contain three winters, as indicated by “W” or “E” in Fig. 13. The composite zonal wind differences in Fig. 14a (defined as QBOW minus QBOE) indicate, on average, stronger westerly flow throughout much of the NH extratropical stratosphere under QBOW conditions, with an enhancement in the subtropical jet between 0.1 and 1 hPa of up ~15 m s−1. The composite temperature differences (Fig. 14b) indicate that NH polar temperatures near 10 hPa are up to 10 K cooler during QBOW compared to QBOE conditions.
Composite differences in (a) zonal mean zonal wind and (b) zonal mean temperature between westerly and easterly QBO phases (QBO W − QBO E) averaged over the December–March period from the 10-yr free-running T79L139 NOGAPS-ALPHA simulation in Fig. 13. Contour intervals are 1 m s−1 and 1 K for wind and temperature differences, respectively.
Citation: Monthly Weather Review 143, 6; 10.1175/MWR-D-14-00208.1
Although the 10-yr simulation is not long enough to demonstrate a statistically significant QBO signal in extratropical stratosphere, the composite zonal mean zonal wind and temperature anomalies in Fig. 14 are both qualitatively and quantitatively consistent with observed QBO signals in the NH winter extratropical stratosphere (e.g., Pascoe et al. 2005; Lu et al. 2008), with stronger zonal flow and lower polar temperatures during the westerly QBO phase as compared to the easterly QBO phase. These results indicate that NOGAPS-ALPHA is producing a realistic extratropical response to the internally generated QBO. In the next section, we examine in more detail the physical mechanism for the extratropical response to the QBO westerly phase using daily output from ensembles of 120-day simulations during NH winter.
5. Results from seasonal simulations
The previous section demonstrates how a stochastic GWD parameterization can generate a realistic QBO in the T79L139 NOGAPS-ALPHA model. To characterize the impact of the modified tropical GWD on a seasonal forecast, we next examine results from a case study using two 15-member ensembles of 120-day free-running simulations. The first ensemble, designated Q120D, uses the stochastic GWD parameterization with the modified tropical source spectrum as in the L139 and Q10YR experiments. The second ensemble, designated noQ120D, uses the original stochastic GWD parameterization as in the L139-OS experiment (see Table 1). Both sets of ensembles use reduced horizontal and vertical diffusion in the stratosphere as described in section 2. A total of 15 pairs of 120-day simulations (i.e., with and without the modified tropical GWD) were initialized using a combination of NOGAPS-ALPHA analyses and forecasts for early December 2007, as described in section 2g. We note that differences between the Q120 and noQ120 experiments will not completely represent the effects of the QBO alone, since the additional tropical GWD source introduced in the Q120 case represents a significant new forcing to the model climatology. To completely resolve the QBO effect, forecast ensembles for both QBO east and QBO west conditions generated with the modified tropical GWD need to be examined. The aim of the present study, however, is to highlight the differences between long-term forecasts in which the persistent easterly bias in equatorial stratospheric winds is replaced by a more realistic easterly-to-westerly transition produced by the stochastic GWD parameterization augmented with an additional source of tropical wave momentum flux.
To examine these differences, Fig. 15a compares ensemble mean time series of the daily zonal winds over the equator at 30 hPa from the Q120D and noQ120D simulations. In the noQ120D case (Fig. 15a, blue curve), the model produces persistent easterly flow throughout the tropical lower stratosphere, which is consistent with the results of the 12-month L139-OS experiment in Fig. 7d. In the Q120D case (Fig. 15a, red curve), the ensemble-mean 30-hPa-zonal wind transitions from easterly to westerly by mid-February. To illustrate the variability in the zonal mean 30-hPa zonal wind among the members of the Q120D ensemble, the standard deviation σ among ensemble members was computed. Gray curves in Fig. 15a show ±1σ ranges about the ensemble means. For the noQ120D case, there is very little variation among the ensemble members and so the ±1σ curves are indistinguishable from the ensemble mean curve (plotted in blue).
(a) Daily time series of zonal mean zonal winds over the equator at 30 hPa for the ensemble means of the noQ120D experiments (blue curve) and the Q120D experiments (red curve). Also plotted are ±1σ values of the Q120D ensemble means (gray curves) and values of monthly mean zonal wind from the NCEP reanalysis for December 2007–March 2008 (black curve and symbols). (b) Daily ensemble mean temperature differences (Q120D − noQ120D) averaged over 75°–90°N latitude; contour interval is 3 K. (c) Daily ensemble mean zonal wind differences averaged over 60°–80°N latitude; contour interval is 2 m s−1.
Citation: Monthly Weather Review 143, 6; 10.1175/MWR-D-14-00208.1
Also plotted in Fig. 15a are monthly mean values of the equatorial zonal winds at 30 hPa from the NCEP reanalysis (black curve) for the December 2007–March 2008 period. Over this time period, the modified tropical GWD in the Q120D experiment (red curve) produces, on average, a transition from easterly to westerly flow at this level that is similar to the behavior of the QBO in the NCEP reanalysis. This result is consistent with the recent study of Scaife et al. (2014), which found that stratosphere-resolving NWP models with an internal QBO could forecast its evolution with reasonable skill out to at least 12 months.
Figure 15b plots daily values of the ensemble mean temperature differences (ΔT = Q120D − noQ120D) averaged over 75°–90°N latitude. An initial warming of ~3 K first appears in early January between 1 and 10 hPa, then evolves into a pattern of cooling throughout the stratosphere (1–100 hPa) and warming in the mesosphere (0.1–1 hPa) during February and March. This pattern of stratospheric cooling and mesospheric warming is characteristic of extratropical wave–mean flow interactions throughout the middle atmosphere in winter seen in earlier NOGAPS-ALPHA modeling studies (see, e.g., Coy et al. 2005; Siskind et al. 2007). The polar stratospheric cooling peaks at just over 12 K in mid-February and again at ~9 K in mid-March, while the polar mesospheric warming of 3–6 K persists throughout most of February and March.
Figure 15c plots the ensemble mean differences in zonal mean zonal winds (ΔU) between the Q120D and noQ120D experiments averaged over the 60°–80°N region. There is little difference in polar stratospheric zonal winds between the two sets of simulations throughout most of December. Differences of 6–8 m s−1 emerge in January, with positive differences indicating generally stronger westerly flow near 10 hPa and negative differences indicating weaker westerly flow near 1 hPa. During February, a region of positive zonal wind differences up to 8 m s−1 emerges between 0.1 and 5 hPa. In March, positive differences up to 16 m s−1 are found between 0.1 and 100 hPa throughout the month.
The results in Fig. 15 indicate that the change from easterly to westerly flow in the equatorial lower stratosphere over NH winter in the Q120D experiment produces generally colder temperatures and stronger zonal flow in the northern winter polar stratosphere compared to the noQ120D experiment, where easterly flow persists throughout the equatorial stratosphere. To characterize further the dynamical response of the extratropical NH winter stratosphere to differences in equatorial stratospheric zonal wind, Figs. 16 and 17 plot the monthly zonal mean zonal wind and temperature distributions for December to March based on the ensemble averages from the Q120D experiment (top row) and the noQ120D experiment (middle row). Also plotted in Figs. 16 and 17 are the differences in the ensemble mean zonal wind and temperature distributions for each month (bottom row). To determine the statistical significance of these differences, a Student’s t test was performed using the two sets of 15-member ensembles.
Latitude–altitude distributions of ensemble mean zonal winds from (a)–(d) the Q120D experiment, (e)–(h) the noQ120D experiment, and (i)–(l) the differences (Q120D − noQ120D) for (left to right) December through March. Contour intervals are 10 m s−1 for zonal winds and 5 m s−1 for the differences. Shading indicates regions where ensemble mean differences are statistically significant at the 90% level.
Citation: Monthly Weather Review 143, 6; 10.1175/MWR-D-14-00208.1
As in Fig. 16, but for mean temperatures. Contour intervals are 10 K for temperatures and 2.5 K for the differences.
Citation: Monthly Weather Review 143, 6; 10.1175/MWR-D-14-00208.1
The ensemble mean zonal wind distributions from the two experiments in Fig. 16 show statistically significant differences over the equator of up to 20 m s−1 in all four months. Significant monthly mean differences of 10–15 m s−1 are also found during winter between 40°–80°N and 0.1–10 hPa, with stronger westerly flow at high latitudes in the Q120D experiment. In addition, a small (1.5–2.0 m s−1) but statistically significant zonal wind response is found in March near the surface between 65° and 80°N. Figure 17 shows significant temperature differences over the equator of up to 5 K during all four months. A pattern of statistically significant stratospheric cooling–mesospheric warming emerges in January between 25° and 50°N. This pattern strengthens as it moves poleward and downward during February and March, ultimately producing a cooling of 10 K near 10 hPa and a warming of 7.5 K near 0.1 hPa over the pole in March. Despite the considerable magnitude of this high-latitude temperature response, it is not significant at the 90% confidence level. A larger number of ensemble members may be needed to isolate a statistically significant extratropical temperature response because of the high degree of dynamical variability in the NH winter.
The zonal wind and temperature differences in Figs. 16 and 17 are similar to both observed and modeled differences in extratropical stratospheric winds and temperatures produced by the QBO (e.g., Baldwin et al. 2001; Pascoe et al. 2005; Lu et al. 2008; Anstey et al. 2010; Yamashita et al. 2011). To investigate if these differences can be explained in terms of changes in planetary wave propagation between the Q120D and noQ120D experiments, we computed the monthly mean values of EP flux and its divergence using daily NOGAPS-ALPHA output from each of the 15-member ensembles. Figure 18 plots the ensemble mean EP flux vectors along with the zonal wind tendencies computed from the EP flux divergence for each month from December to March for the Q120D experiment (top row) and the noQ120D experiment (middle row). Ensemble mean differences in the EP fluxes and zonal wind tendencies are also plotted (bottom row). In all four months, the ensemble mean EP fluxes indicate upward and equatorward propagation of planetary wave EP fluxes, and the convergence of these waves provides a net easterly acceleration on the zonal winds in the extratropical stratosphere. The differences in EP fluxes between the two experiments in early winter (Figs. 18i–j) indicate more equatorward propagation in the Q120D case than in the noQ120D case. In February (Fig. 18k), however, the EP flux differences indicate less vertical propagation in the Q120D case between 50° and 75°N. There is no strong overall pattern in the EP flux differences in March (Fig. 18l). Statistically significant differences in the zonal wind tendencies associated with the EP flux divergence are found in all four months (Figs. 18i–l), with the largest differences occurring in February over a broad region of the extratropics between 1 and 5 hPa. In this case, the ensemble mean easterly (i.e., negative) accelerations in this region are reduced up to 6 m s−1 day−1 in the Q120D case, meaning that the onset of the westerly QBO phase over the equator leads to reduced planetary wave drag in the extratropical stratosphere.
As in Fig. 16, but for mean EP fluxes (arrows) and zonal wind tendencies of the EP flux divergence . Solid (dashed) contours denote westerly (easterly) tendencies and are drawn every 2 m s−1 day−1. For reference, the horizontal arrow in (a) has a magnitude of 1.0 × 107 kg s−2. For plotting purposes, EP flux vectors are multiplied by a vertical scale factor 
Citation: Monthly Weather Review 143, 6; 10.1175/MWR-D-14-00208.1
The high-latitude zonal wind differences noted near the surface during March (Fig. 16) between the Q120D and noQ120D experiments suggest that differences in the equatorial lower-stratospheric zonal winds (Fig. 15a) may also impact extratropical circulation patterns near the surface through changes in planetary wave propagation. To investigate this possibility, Fig. 19 plots ensemble mean differences in sea level pressure (SLP) for the months of December, January, February, and March between the Q120D and noQ120D experiments. The SLP differences are initially small (1–2 hPa) in December and grow over the course of the winter, reaching ±6 hPa in February and March. Throughout January and February (Figs. 19b and 19c), the SLP differences resemble a zonal wavenumber-2 pattern. In March, statistically significant decreases are found over the pole while significant increases are found over the midlatitudes from 300° to 330°E.
Differences in ensemble mean (Q120D − noQ120D) sea level pressure for (a) December, (b) January, (c) February, and (d) March. The contour interval is 1 hPa. Green contours enclose regions where ensemble mean differences are statistically significant at the 90% level.
Citation: Monthly Weather Review 143, 6; 10.1175/MWR-D-14-00208.1
The spatial pattern of the March SLP differences in Fig. 19d resembles anomalies related to the NAM teleconnection pattern, which is the leading mode of variability in monthly mean SLP over the NH extratropics in winter (Thompson and Wallace 2000). In its positive phase, the NAM exhibits positive SLP anomalies over the NH midlatitudes and negative anomalies over the pole, with a related intensification of the midlatitude jet stream. As reviewed by Baldwin et al. (2001), the spatial patterns of surface pressure differences between westerly and easterly phases of the QBO resemble the positive phase of the NAM teleconnection pattern, suggesting that the QBO can influence the NAM teleconnection pattern. The results in Fig. 19 are consistent with this hypothesis, and demonstrate that including the east–west transition in equatorial stratospheric winds over the NH winter in a stratosphere-resolving NWP model can have a significant impact on long-term forecasts of NH winter surface weather patterns by facilitating a NAM-like SLP response to the QBO.
6. Discussion and conclusions
Through a series of detailed sensitivity experiments, a QBO with realistic amplitude and period was produced in free-running simulations with a high-vertical resolution version of the NOGAPS-ALPHA global forecast model using an augmented form of the stochastic GWD parameterization of Eckermann (2011) in conjunction with reduced horizontal and vertical diffusion in the lower stratosphere. Results from a 10-yr free-running NOGAPS-ALPHA simulation show that the modeled QBO produces a dynamical response in the NH winter stratosphere consisting of colder polar temperatures and stronger zonal flow in the NH winter extratropics. Ensembles of 120-day NOGAPS-ALPHA simulations show that the augmented stochastic GWD parameterization eliminates the persistent easterly bias in equatorial stratospheric winds commonly found in NWP models, and instead produces a transition from easterly to westerly flow over the course of the NH winter that is consistent with the observed behavior of the equatorial lower-stratospheric winds. These changes in the model equatorial stratospheric winds alter the propagation of planetary waves in a manner that is broadly consistent with the Holton–Tan mechanism, which in turn has an effect on surface weather patterns. Specifically, we find that when the model winds over the equator are near the 10-hPa transition from easterly to westerly during NH winter, the resulting surface pressure differences over the Arctic polar cap resemble the positive phase of the NAM teleconnection pattern. The results of this study should be seen as preliminary steps toward addressing the impact of the QBO on long-term forecast skill. Additional simulations are needed to more completely characterize dynamical variability produced during both easterly and westerly QBO phases using the modified stochastic GWD parameterization. For example, future simulations should ideally incorporate atmosphere–ocean coupling to some degree, which is necessary for skillful forecasting over seasonal time scales.
Based on the results of this initial study, and given the reduced computational overhead of the stochastic GWD parameterizations used here, relative to more conventional multiwave parameterizations used in other GCM studies, it may now be feasible to include the effects of the QBO in operational NWP models that have sufficiently high vertical resolution. This could alleviate possible biases in seasonal forecasts of NH winter resulting from, for example, persistent easterly flow in the equatorial lower stratosphere in models that lack a QBO. In this regard, our findings are consistent with recent studies that have found improved seasonal prediction skill by simply increasing vertical resolution in the stratosphere (e.g., Kuroda 2008; Roff et al. 2011). More specifically, Weare et al. (2012) reported improved simulations of the Madden–Julian oscillation, a dominant source of intraseasonal atmospheric variability, in a GCM with high vertical resolution in the stratosphere and an internally generated QBO.
However, generating and maintaining the QBO in the NOGAPS-ALPHA model required reductions in the amount of diffusion in the lower stratosphere. As discussed in section 2, NWP models used in operational forecast–assimilation systems typically employ relatively high amounts of diffusion in an effort to preserve short-term forecast skill by tightly constraining the background (i.e., modeled) atmospheric state to large-scale observations. Using a highly diffusive NWP model for seasonal forecasting applications may not allow a realistic simulation of the QBO, either through the direct effects of diffusion on the QBO itself or indirectly by suppressing the types of waves that drive the QBO. The challenge for extending operational NWP forecasting out to seasonal time scales will be to accommodate the QBO and other modes of internal variability within NWP systems that are constrained by finite computational resources and operationally specified run times in order to capture the relevant physical mechanisms that influence teleconnection patterns coupling the stratosphere and troposphere. For example, our work here and that of others (e.g., Richter et al. 2014) suggest that a model vertical grid spacing of ~500 m in the stratosphere is a minimum requirement for a realistic QBO. The increased number of vertical model levels to achieve this (e.g., Fig. 1) involves additional computational overhead that operational centers may not be able to accommodate easily. As this study shows, ensemble forecasts that generate a QBO using a model with higher vertical resolution, but with reduced (e.g., T79) horizontal resolution, may be one possible way to generate more skillful seasonal forecasts for the NH winter period at a reasonable computational cost.
Acknowledgments
This research was supported by the Office of Naval Research through the Departmental Research Initiative “Predictability of Seasonal and Intraseasonal Oscillations” and by the Chief of Naval Research through the Naval Research Laboratory’s base 6.1 research program. Additional support was provided by the DoD High Performance Computer Modernization Program via grants of computer time at the U.S. Army Engineer Research and Development Center (ERDC) and Navy DoD Supercomputing Resource Center. GPCP data provided by the NOAA/ESRL/Physical Sciences Division in Boulder, Colorado, from online (http://www.esrl.noaa.gov/psd).
REFERENCES
Adler, R. F., and Coauthors, 2003: The Version-2 Global Precipitation Climatology Project (GPCP) monthly precipitation analysis (1979–present). J. Hydrometeor., 4, 1147–1167, doi:10.1175/1525-7541(2003)004<1147:TVGPCP>2.0.CO;2.
Alexander, M. J., and Coauthors, 2010: Recent developments in gravity-wave effects in climate models and the global distribution of gravity-wave momentum flux from observations and models. Quart. J. Roy. Meteor. Soc., 136, 1103–1124, doi:10.1002/qj.637.
Andrews, D. G., J. A. Holton, and C. B. Leovy, 1987: Middle Atmosphere Dynamics. Academic Press, 489 pp.
Anstey, J. A., T. Shepherd, and J. Scinocca, 2010: Influence of the quasi-biennial oscillation on the extratropical winter stratosphere in an atmospheric general circulation model and in reanalysis data. J. Atmos. Sci., 67, 1402–1419, doi:10.1175/2009JAS3292.1.
Bacmeister, J. T., S. D. Eckermann, P. A. Newman, L. Lait, K. R. Chan, M. Loewenstein, M. H. Proffitt, and B. L. Gary, 1996: Stratospheric horizontal wavenumber spectra of winds, potential temperature, and atmospheric tracers observed by high-altitude aircraft. J. Geophys. Res., 101, 9441–9470, doi:10.1029/95JD03835.
Baldwin, M. P., and T. J. Dunkerton, 2001: Stratospheric harbingers of anomalous weather regimes. Science, 294, 581–584, doi:10.1126/science.1063315.
Baldwin, M. P., and Coauthors, 2001: The quasi-biennial oscillation. Rev. Geophys., 39, 179–229, doi:10.1029/1999RG000073.
Baldwin, M. P., D. B. Stephenson, D. W. J. Thompson, T. J. Dunkerton, A. J. Charlton, and A. O’Neill, 2003: Stratospheric memory and extended-range weather forecasts. Science, 301, 636–640, doi:10.1126/science.1087143.
Boer, G. J., and K. Hamilton, 2008: QBO influence on extratropical predictive skill. Climate Dyn., 31, 987–1000, doi:10.1007/s00382-008-0379-5.
Boville, B. A., 1991: Sensitivity of simulated climate to model resolution. J. Climate, 4, 469–485, doi:10.1175/1520-0442(1991)004<0469:SOSCTM>2.0.CO;2.
Boville, B. A., and W. J. Randel, 1992: Equatorial waves in a stratospheric GCM: Effects of vertical resolution. J. Atmos. Sci., 49, 785–801, doi:10.1175/1520-0469(1992)049<0785:EWIASG>2.0.CO;2.
Burgess, B. H., A. R. Erler, and T. G. Shepherd, 2013: The troposphere-to-stratosphere transition in kinetic energy spectra and nonlinear spectral fluxes seen in ECMWF analyses. J. Atmos. Sci., 70, 669–687, doi:10.1175/JAS-D-12-0129.1.
Charron, M., and Coauthors, 2012: The stratospheric extension of the Canadian Global Deterministic Medium-Range Weather Forecasting System and its impact on tropospheric forecasts. Mon. Wea. Rev., 140, 1924–1944, doi:10.1175/MWR-D-11-00097.1.
Coughlin, K., and K.-K. Tung, 2001: QBO signal found at the extratropical surface through northern annular modes. Geophys. Res. Lett., 28, 4563–4566, doi:10.1029/2001GL013565.
Coy, L., D. E. Siskind, S. D. Eckermann, J. P. McCormack, D. R. Allen, and T. F. Hogan, 2005: Modeling the August 2002 minor warming event. Geophys. Res. Lett.,32, L07808, doi:10.1029/2005GL022400.
Dunkerton, T. J., 1997: The role of gravity waves in the quasi-biennial oscillation. J. Geophys. Res., 102, 26 053–26 076, doi:10.1029/96JD02999.
Eckermann, S. D., 2009: Hybrid coordinate choices for a global model. Mon. Wea. Rev., 137, 224–245, doi:10.1175/2008MWR2537.1.
Eckermann, S. D., 2011: Explicitly stochastic parameterization of nonorographic gravity wave drag. J. Atmos. Sci., 68, 1749–1765, doi:10.1175/2011JAS3684.1.
Eckermann, S. D., and Coauthors, 2009: High-altitude data assimilation system experiments for the northern summer mesosphere season of 2007. J. Atmos. Sol.-Terr. Phys.,71, 531– 551, doi:10.1016/j.jastp.2008.09.036.
Emanuel, K. A., and M. Zivkovic-Rothman, 1999: Development and evaluation of a convection scheme for use in climate models. J. Atmos. Sci., 56, 1766–1782, doi:10.1175/1520-0469(1999)056<1766:DAEOAC>2.0.CO;2.
Ern, M., and P. Preusse, 2009: Wave fluxes of equatorial Kelvin waves and QBO zonal wind forcing derived from SABER and ECMWF temperature space-time spectra. Atmos. Chem. Phys., 9, 3957–3986, doi:10.5194/acp-9-3957-2009.
Folland, C. K., A. A. Scaife, J. Lindesay, and D. B. Stephenson, 2012: How potentially predictable is northern European winter climate a season ahead? Int. J. Climatol., 32, 801–818, doi:10.1002/joc.2314.
Garcia, R. R., D. R. Marsh, D. E. Kinnison, B. A. Boville, and F. Sassi, 2007: Simulation of secular trends in the middle atmosphere, 1950–2003. J. Geophys. Res.,112, D09301, doi:10.1029/2006JD007485.
Garfinkel, C. I., and D. L. Hartmann, 2010: Influence of the quasi-biennial oscillation on the North Pacific and El Niño teleconnections. J. Geophys. Res.,115, D20116, doi:10.1029/2010JD014181.
Garfinkel, C. I., T. A. Shaw, D. L. Hartmann, and D. W. Waugh, 2012: Does the Holton–Tan mechanism explain how the quasi-biennial oscillation modulates the Arctic polar vortex? J. Atmos. Sci.,69, 1713–1733, doi:10.1175/JAS-D-11-0209.1.
Geller, M. A., and Coauthors, 2013: A comparison between gravity wave momentum fluxes in observations and climate models. J. Climate,26, 6383–6405, doi:10.1175/JCLI-D-12-00545.1.
Gerber, E. P., and Coauthors, 2012: Assessing and understanding the impact of stratospheric dynamics and variability on the earth system. Bull. Amer. Meteor. Soc., 93, 845–859, doi:10.1175/BAMS-D-11-00145.1.
Giorgetta, M. A., E. Manzini, and E. Roeckner, 2002: Forcing of the quasi-biennial oscillation from a broad spectrum of atmospheric waves. Geophys. Res. Lett.,29, doi:10.1029/2002GL014756.
Giorgetta, M. A., E. Manzini, E. Roeckner, M. Esch, and L. Bengtsson, 2006: Climatology and forcing of the quasi-biennial oscillation in the MAECHAM5 model. J. Climate, 19, 3882–3901, doi:10.1175/JCLI3830.1.
Hamilton, K., Y. O. Takahashi, and W. Ohfuchi, 2008: Mesoscale spectrum of atmospheric motions investigated in a very fine resolution global general circulation model. J. Geophys. Res.,113, D18110, doi:10.1029/2008JD009785.
Hines, C. O., 1997: Doppler-spread parameterization of gravity-wave momentum deposition in the middle atmosphere. Part 2: Broad and quasi monochromatic spectra, and implementation. J. Atmos. Sol.-Terr. Phys.,59, 387–400, doi:10.1016/S1364-6826(96)00080-6.
Hogan, T., and T. Rosmond, 1991: The description of the Navy Operational Global Atmospheric Prediction System’s spectral forecast model. Mon. Wea. Rev., 119, 1786–1815, doi:10.1175/1520-0493(1991)119<1786:TDOTNO>2.0.CO;2.
Holton, J. R., and H.-C. Tan, 1980: The influence of the equatorial quasi-biennial oscillation on the global circulation at 50 mb. J. Atmos. Sci., 37, 2200–2208, doi:10.1175/1520-0469(1980)037<2200:TIOTEQ>2.0.CO;2.
Hoppel, K. W., S. D. Eckermann, L. Coy, G. E. Nedoluha, D. R. Allen, S. D. Swadley, and N. L. Baker, 2013: Evaluation of SSMIS upper atmosphere sounding channels for high-altitude data assimilation. Mon. Wea. Rev.,141, 3314–3330, doi:10.1175/MWR-D-13-00003.1.
Horinouchi, T., and Coauthors, 2003: Tropical cumulus convection and upward-propagating waves in middle-atmospheric GCMs. J. Atmos. Sci., 60, 2765–2782, doi:10.1175/1520-0469(2003)060<2765:TCCAUW>2.0.CO;2.
Hurwitz, M. M., P. A. Newman, L. D. Oman, and A. M. Molod, 2011a: Response of the Antarctic stratosphere to two types of El Niño events. J. Atmos. Sci., 68, 812–882, doi:10.1175/2011JAS3606.1.
Hurwitz, M. M., I.-S. Song, L. D. Oman, P. A. Newman, A. M. Molod, S. M. Frith, and J. E. Nielsen, 2011b: Response of the Antarctic stratosphere to warm pool El Niño events in the GEOS CCM. Atmos. Chem. Phys., 11, 9659–9669, doi:10.5194/acp-11-9659-2011.
Kawatani, Y., K. Sato, T. J. Dunkerton, S. Watanabe, S. Miyahara, and M. Takahashi, 2010: The roles of equatorial trapped waves and internal inertia–gravity waves in driving the quasi-biennial oscillation. Part I: Zonal mean wave forcing. J. Atmos. Sci., 67, 963–980, doi:10.1175/2009JAS3222.1.
Kistler, R., and Coauthors, 2001: The NCEP–NCAR 50-Year Reanalysis: Monthly means CD-ROM and documentation. Bull. Amer. Meteor. Soc., 82, 247–267, doi:10.1175/1520-0477(2001)082<0247:TNNYRM>2.3.CO;2.
Koshyk, J. N., B. A. Boville, K. Hamilton, E. Manzini, and K. Shibata, 1999: Kinetic energy spectrum of horizontal motions in middle-atmosphere models. J. Geophys. Res.,104, 27 177–27 190, doi:10.1029/1999JD900814.
Kuroda, Y., 2008: Role of the stratosphere on the predictability of medium-range weather forecast: A case study of winter 2003–2004. Geophys. Res. Lett.,35, L19701, doi:10.1029/2008GL034902.
Langland, R., and N. Baker, 2004: Estimation of observation impact using the NRL atmospheric variational data assimilation adjoint system. Tellus, 56, 189–201, doi:10.1111/j.1600-0870.2004.00056.x.
Liess, S., and M. A. Geller, 2012: On the relationship between QBO and distribution of tropical deep convection. J. Geophys, Res., 117, D03108, doi:10.1029/2011JD016317.
Lindzen, R. S., 1981: Turbulence and stress owing to gravity wave and tidal breakdown. J. Geophys. Res., 86, 9707–9714, doi:10.1029/JC086iC10p09707.
Lott, F., L. Guez, and P. Maury, 2012: A stochastic parameterization of non-orographic gravity waves: Formalism and impact on the equatorial stratosphere. Geophys. Res. Lett.,39, L06807, doi:10.1029/2012GL051001.
Louis, J.-F., 1979: A parametric model of vertical eddy fluxes in the atmosphere. Bound.-Layer Meteor., 17, 187–202, doi:10.1007/BF00117978.
Louis, J.-F., M. Tiedtke, and J. F. Geleyn, 1982: A short history of the operational PBL parameterization at ECMWF. ECMWF Workshop on Planetary Boundary Parameterizations, Reading, United Kingdom, ECMWF, 59–79.
Lu, H., M. P. Baldwin, L. G. Gray, and M. J. Jarvis, 2008: Decadal-scale changes in the effect of the QBO on the northern stratospheric polar vortex. J. Geophys. Res., 113, D10114, doi:10.1029/2007JD009647.
Marshall, A. G., and A. A. Scaife, 2009: Impact of the QBO on surface winter climate. J. Geophys. Res.,114, D18110, doi:10.1029/2009JD011737.
Maury, P., and F. Lott, 2014: On the presence of equatorial waves in the lower stratosphere of a general circulation model. Atmos. Chem. Phys.,14, 1869–1880, doi:10.5194/acp-14-1869-2014.
Orr, A., P. Bechtold, J. Scinocca, M. Ern, and M. Janiskova, 2010: Improved middle atmosphere climate and forecasts in the ECMWF model through a nonorographic gravity wave drag parameterization. J. Climate, 23, 5905–5926, doi:10.1175/2010JCLI3490.1.
Palmer, T., C. Brankovic, F. Molteni, and S. Tibaldi, 1990: Extended-range predictions with ECMWF models: Interannual variability in operational model integrations. Quart. J. Roy. Meteor. Soc., 116, 799–834, doi:10.1002/qj.49711649403.
Pascoe, C. L., L. J. Gray, S. A. Crooks, M. N. Juckes, and M. P. Baldwin, 2005: The quasi-biennial oscillation: Analysis using ERA-40 data. J. Geophys. Res.,110, D08105, doi:10.1029/2004JD004941.
Pascoe, C. L., L. J. Gray, and A. A. Scaife, 2006: A GCM study of the influence of equatorial winds on the timing of sudden stratospheric warmings. Geophys. Res. Lett., 33, L06825, doi:10.1029/2005GL024715.
Peng, M. S., J. A. Ridout, and T. F. Hogan, 2004: Recent modifications of the Emanuel convective scheme in the Navy Operational Global Atmospheric Prediction System. Mon. Wea. Rev., 132, 1254–1268, doi:10.1175/1520-0493(2004)132<1254:RMOTEC>2.0.CO;2.
Piani, C., W. A. Norton, and D. A. Stainforth, 2004: Equatorial stratospheric response to variations in deterministic and stochastic gravity wave parameterizations. J. Geophys. Res., 109, D14101, doi:10.1029/2004JD004656.
Ribera, P., C. Peña-Ortiz, J. A. Añel, L. Gimeno, L. de la Torre, and D. Gallego, 2008: Quasi-biennial modulation of the Northern Hemisphere tropopause height and temperature. J. Geophys. Res.,113, D00B02, doi:10.1029/2007JD009765.
Ricciardulli, L., and R. R. Garcia, 2000: The excitation of equatorial waves by deep convection in the NCAR Community Climate Model (CCM3). J. Atmos. Sci., 57, 3461–3487, doi:10.1175/1520-0469(2000)057<3461:TEOEWB>2.0.CO;2.
Richter, J. H., A. Solomon, and J. T. Bacmeister, 2014: On the simulation of the quasi-biennial oscillation in the Community Atmosphere Model, version 5. J. Geophys. Res. Atmos.,119, 3045–3062, doi:10.1002/2013JD021122.
Rind, D., J. Jones, N. K. Balachandran, G. A. Schmidt, and J. Lean, 2014: The QBO in two GISS global climate models: 1. Generation of the QBO. J. Geophys. Res. Atmos., 119, 8798–8824, doi:10.1002/2014JD021678.
Roff, G., D. W. J. Thompson, and H. Hendon, 2011: Does increasing model stratospheric resolution improve extended-range forecast skill? Geophys. Res. Lett.,38, L05809, doi:10.1029/2010GL046515.
Rosenkranz, P. W., K. R. Hardy, and M. S. Davis, 1997: An assessment of the impact of satellite microwave sounder incidence angle and scan geometry on the accuracy of atmospheric temperature profile retrievals. J. Atmos. Oceanic Technol., 14, 488–494, doi:10.1175/1520-0426(1997)014<0488:AAOTIO>2.0.CO;2.
Sato, K., and T. J. Dunkerton, 1997: Estimates of momentum flux associated with equatorial Kelvin and gravity waves. J. Geophys. Res.,102, 26 247–26 261, doi:10.1029/96JD02514.
Scaife, A. A., N. Butchart, C. D. Warner, D. Stainforth, W. Norton, and J. Austin, 2000: Realistic quasi-biennial oscillations in a simulation of the global climate. Geophys. Res. Lett.,27, 3481–3484, doi:10.1029/2000GL011625.
Scaife, A. A., N. Butchart, C. D. Warner, and R. Swinbank, 2002: Impact of a spectral gravity wave parameterization on the stratosphere in the Met Office Unified Model. J. Atmos. Sci., 59, 1473–1489, doi:10.1175/1520-0469(2002)059<1473:IOASGW>2.0.CO;2.
Scaife, A. A., and Coauthors, 2014: Predictability of the quasi-biennial oscillation and its northern winter teleconnection on seasonal to decadal timescales. Geophys. Res. Lett.,41, 1752–1758, doi:10.1002/2013GL059160.
Shibata, K., and M. Deushi, 2005: Partitioning between resolved wave forcing and unresolved gravity wave forcing to the quasi-biennial oscillation as revealed with a coupled chemistry-climate model. Geophys. Res. Lett., 32, L12820, doi:10.1029/2005GL022885.
Sigmond, M., J. F. Scinocca, V. V. Kharin, and T. G. Shepherd, 2013: Enhanced seasonal forecast skill following stratospheric sudden warmings. Nat. Geosci., 6, 98–102, doi:10.1038/ngeo1698.
Simmons, A. J., and C. Temperton, 1997: Stability of a two-time-level semi-implicit integration scheme for gravity wave motion. Mon. Wea. Rev., 125, 600–617, doi:10.1175/1520-0493(1997)125<0600:SOATTL>2.0.CO;2.
Simmons, A. J., D. M. Burridge, M. Jarraud, C. Girard, and W. Wergen, 1989: The ECMWF medium-range prediction models development of the numerical formulations and the impact of increased resolution. Meteor. Atmos. Phys., 40, 28–60, doi:10.1007/BF01027467.
Siskind, D. E., S. D. Eckermann, L. Coy, J. P. McCormack, and C. E. Randall, 2007: On recent interannual variability of the Arctic winter mesosphere: Implications for tracer descent. Geophys. Res. Lett.,34, L09806, doi:10.1029/2007GL029293.
Skamarock, W. C., 2004: Evaluating mesoscale NWP models using kinetic energy spectra. Mon. Wea. Rev., 132, 3019–3032, doi:10.1175/MWR2830.1.
Takahashi, M., 1999: Simulations of the quasi-biennial oscillation in a general circulation model. Geophys. Res. Lett., 26, 1307–1310, doi:10.1029/1999GL900188.
Takahashi, Y. O., K. Hamilton, and W. Ohfuchi, 2006: Explicit global simulation of the mesoscale spectrum of atmospheric motions. Geophys. Res. Lett.,33, L12812, doi:10.1029/2006GL026429.
Thompson, D. W. J., and J. M. Wallace, 2000: Annular modes in the extratropical circulation. Part I: Month-to-month variability. J. Climate, 13, 1000–1016, doi:10.1175/1520-0442(2000)013<1000:AMITEC>2.0.CO;2.
Thompson, D. W. J., M. P. Baldwin, and J. M. Wallace, 2002: Stratospheric connection to Northern Hemisphere wintertime weather: Implications for prediction. J. Climate, 15, 1421–1428, doi:10.1175/1520-0442(2002)015<1421:SCTNHW>2.0.CO;2.
Wallace, J. M., and V. E. Kousky, 1968: Observational evidence of Kelvin waves in the tropical stratosphere. J. Atmos. Sci., 25, 900–907, doi:10.1175/1520-0469(1968)025<0900:OEOKWI>2.0.CO;2.
Warner, C. D., and M. E. McIntyre, 2001: An ultra-simple spectral parameterization for nonorographic gravity waves. J. Atmos. Sci., 58, 1837–1857, doi:10.1175/1520-0469(2001)058<1837:AUSPFN>2.0.CO;2.
Weare, B. C., C. Cagnazzo, P. G. Fogli, E. Manzini, and A. Navarra, 2012: Madden-Julian Oscillation in a climate model with a well-resolved stratosphere. J. Geophys. Res.,117, D01103, doi:10.1029/2011JD016247.
Wilson, R., 2004: Turbulent diffusivity in the free atmosphere inferred from MST radar measurements: A review. Ann. Geophys., 22, 3869–3887, doi:10.5194/angeo-22-3869-2004.
Yamashita, Y., H. Akiyoshi, and M. Takahashi, 2011: Dynamical response in the Northern Hemisphere midlatitude and high-latitude winter to the QBO simulated by CCSR/NIES CCM. J. Geophys. Res.,116, D06118, doi:10.1029/2010JD015016.
Yanai, M., and T. Maruyama, 1966: Stratospheric wave disturbances propagation over the equatorial Pacific. J. Meteor. Soc. Japan, 44, 291–294.