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PUBLICATIONS Journal of Advances in Modeling Earth Systems RESEARCH ARTICLE 10.1002/2016MS000824 Key Points: Realistic IGW parameterization based on the radiosondes data A systematic discussion of parameterized IGW effects on QBO features The simulated QBO-like oscillation agrees better with observation than before

Correspondence to: X. Xue, [email protected]

Citation: Yu, C., X. Xue, J. Wu, T. Chen, and H. Li (2017), Sensitivity of the quasi-biennial oscillation simulated in WACCM to the phase speed spectrum and the settings in an inertial gravity wave parameterization, J. Adv. Model. Earth Syst., 9, 389–403, doi:10.1002/ 2016MS000824. Received 30 SEP 2016 Accepted 12 JAN 2017 Accepted article online 20 JAN 2017 Published online 10 FEB 2017

Sensitivity of the quasi-biennial oscillation simulated in WACCM to the phase speed spectrum and the settings in an inertial gravity wave parameterization Chao Yu1

, Xianghui Xue1,2

, Jianfei Wu1

, Tingdi Chen1,3, and Huimin Li1

1

CAS Key Laboratory of Geospace Environment, Department of Geophysics and Planetary Sciences, University of Science and Technology of China, Hefei, China, 2Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, China, 3Collaborative Innovation Center of Astronautical Science and Technology, Hefei, Anhui, China

Abstract The application of inertial gravity wave parameterization has allowed for the spontaneous generation of quasi-biennial oscillation (QBO) in the Whole Atmosphere Community Climate Model (WACCM), although there is some mismatch when comparing with observations. The parameterization is based on Lindzen’s linear saturation theory, modified to describe inertia-gravity waves (IGW) by considering the Coriolis effect. In this work, we improve the parameterization by importing a more realistic IGW phase speed spectrum that exhibits a double peak Gaussian distribution calculated from tropical radiosonde observations. A series of numeric simulations are performed to test the sensitivity of QBO-like oscillation features to the phase speed spectrum and the settings of parameterized IGW. All these simulations are capable of generating equatorial wind oscillations in the stratosphere based on standard spatial resolution settings. Central phase speeds of the ‘‘double-Gaussian parameterization’’ affect QBO magnitudes and periods, and the momentum flux of IGW determines the acceleration rate of zonal wind. Furthermore, stronger IGW forcing can lead to a propagation of the QBO-like oscillation to lower altitude. The intermittency factor of the parameterization also prominently affects the QBO period. Stratospheric QBO-like oscillation with obvious improvements is generated using the new IGW parameterization in a long-time simulation.

1. Introduction The quasi-biennial oscillation (QBO) is a prominent feature of zonal-mean zonal winds, which alternate over a period of approximately 28 months from eastward to westward in the equatorial stratosphere. The oscillation can be clearly identified over the tropical stratosphere from the ERA-interim data set [Solomon et al., 2014] and from tropical radiosonde data [Baldwin et al., 2001]. Figure 1 shows the monthly mean zonalmean zonal wind pattern averaged between 2.58N and 2.58S for the ERA-interim data set for 1998–2011. Zonal winds are characterized by an alternating eastward and westward phase between 5 and 100 hPa with an average downward propagation rate of approximately 1 km/month.

C 2017. The Authors. V

This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

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It is well known that the QBO arises as a result of wave mean-flow interactions and is mainly driven by the momentum deposited in shear zones from vertically propagating waves in the troposphere [Alexander, 1998; Alexander and Pfister, 1995]. Many previous studies have confirmed that mixed Rossby gravity waves (MRGs) are the primary resolved drivers of the westward phase of the QBO, and Kelvin waves constitute a major source of momentum to the eastward phase [Maruyama, 1994; Wallace and Kousky, 1968]. In addition to these two waves, recent studies have confirmed that inertial and mesoscale gravity waves also contribute to the formation of the QBO in numerical models [Kim and Chun, 2015a; Krismer and Giorgetta, 2014]. It is now generally accepted that momentum flux carried by Kelvin and MRG forces is not sufficient to drive the oscillation and that a variety of wave sources are required. It is difficult to resolve all waves of different scales that contribute to QBO formation in global general circulation models (GCMs). The most effective way to generate QBO involves using gravity wave parameterizations to consider gravity wave contributions. One widely used GCM is the Whole Atmosphere Community Climate Model (WACCM), which was developed by the National Center for Atmospheric Research (NCAR)

PARAMETERIZATION AND MODELING THE QBO

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and can simulate the QBO internally with parameterized IGW [Xue et al., 2012]. Since this IGW parameterization is an artificial box-shaped idealized phase speed spectrum, it is necessary to find observational support. Globally distributed radiosondes can be used to study latitudinal gravity wave activities in the troposphere and lower stratosphere (TLS) [Allen and Vincent, 1995; Vincent and Alexander, 2000; Zink and Vincent, 2001]. Many parameters of gravity waves can be calculated, such as the intrinsic frequency, horizontal wavelength, momentum, and quasi-monochromatic GW phase speed [Zhang and Yi, 2005]. Then the phase speed spectrum of GWs within equatorial region can be investigated. In this study, we develop an observationally supported IGW parameterization and systematically analyze the IGW parameterization method to generate a QBO-like oscillation in WACCM 4.0. The manuscript is organized as follows. Section 2 describes the radiosonde data, method and results. Section 3 provides a brief description of the WACCM model. Section 4 describes the setting of the parameterized IGW. In section 5, we present a quantitative discussion of the effects of parameterized IGW on QBO-like oscillation. Section 6 provides discussion of the intermittency factor. Section 7 mainly concentrates on a long-term simulation. Finally, section 8 concludes with a summary.

2. Radiosonde Data, Method, and Statistical Results We used high-resolution United States radiosonde data for 1998–2008 from the National Oceanic and Atmospheric Administration (NOAA) National Climatic Data Center. Ninety-three stations are distributed across the Earth’s surface, but only a few are positioned close to the equator. The specific coordinates of the five stations selected are [9.488N, 138.088E], [7.338N, 134.488E], [6.978N, 158.228E], [7.478N, 151.858E], and [7.088N, 171.388E], with latitudes ranging between 108N and 08. Radiosonde observations of the five stations are typically launched twice daily at 00:00 and 12:00 UT. The parameters studied, including pressure, temperature, and horizontal winds, are collected at irregular height resolutions ranging from the ground to the low stratosphere. 2.1. Extraction of Quasi-Monochromatic GWs Background winds and temperatures should be removed when performing a quasi-monochromatic approximation of gravity waves. By fitting a three-order polynomial to vertical profiles of horizontal winds and temperature [U, V, T], we remove the background [U0 ; V0 ; T0 ] [Zhang and Yi, 2005], then fluctuation components [U0 ; V 0 ; T 0 ] can be derived. Since the major upward GWs that can provide momentum flux to drive QBO always generate in the troposphere, we mainly focus on wave features below the tropopause. From the least-square harmonic fittings of these three parameters, amplitude, phase, and vertical wavelength distributions are estimated. Waves with maximum amplitudes in U0 , V0 , and T0 , are deemed as quasimonochromatic gravity waves. As dominant vertical wavelengths for U0 ; V 0 ; and T 0 may be different, the dominant wavelengths in U0 , V0 , and T0 is used: a unique quasi-monochromatic gravity wave is considered to be observed when the relative difference between these three dominant wavelengths in U0 , V0 , and T0 is limited within 20%. Then we re-take the harmonic fitting using the specified vertical wavelength to determine amplitudes and phases of the quasi-monochromatic wave.

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2.2. Statistical Results and Fitting The horizontal propagation runs along the major axis of the horizontal wind vector hodograph. Upara and Uperp , which represent horizontal perturbation velocities parallel and perpendicular to the major axis, respectively, adhere to the following equation [Eckermann, 1996; Tsuda et al., 1990]: Uperp f 52i ^ Upara x

(1)

^ and f denote the intrinsic frequency of the gravity wave and local Coriolis frequency, respectively. where x ^ to f can create uncertainties [Vincent and Alexander, 2000]. After However, an excessively large ratio of x setting 10 as the maximum ratio, roughly 3500 quasi-monochromatic gravity waves are extracted from nearly 42,000 radiosonde records. The horizontal wavenumber can be deduced from the following simplified dispersion equation [Fritts, 2003]:

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2 2 ^ 2f m2 x ; N2

(2)

where k, m, and N are the horizontal wavenumber, vertical wavenumber, and buoyancy frequency, respectively. Figure 2 shows histograms of vertical and horizontal wavelengths. Vertical wavelengths in the troposphere varied from 5 to 8 km with a dominant wavelength of 7.3 km. The horizontal wavelength parameter ranges from 250 km to 3000 km, peaks at approximately 500 km and averages at 970 km, reflecting the results of a previous work by Ern et al. [2014]. The horizontal wavelengths are much larger than the vertical wavelengths, suggesting that gravity waves are propagating at very shallow angles to the horizontal direction. ^ horizontal wavenumber (k) and background wind (U) are known, we can estiAs the intrinsic frequency (x), ^ mate the GW horizontal phase speed (c5x=k1U). Figure 3a shows the distribution of zonal and meridional phase speeds at 200 hPa (the launch level of IGW in WACCM), illustrating that most gravity waves have a zonal/meridional speed that ranges from 10 to 40 m/s. For the GW parametrization scheme currently used in WACCM, a GW phase-speed spectrum is induced in the direction of the background horizontal wind at the wave launch level, i.e., 200 hPa, and it can affect both zonal and meridional mean flow by deposit its momentum flux as the background condition changes [Garcia et al., 2007]. As indicated by the statistical distribution from radiosondes observations, the

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Figure 2. Histograms of gravity wave wavelengths. (a) and (b) are the vertical and horizontal wavelengths of the quasi-monochromatic GWs, respectively. The solid lines denote the occurrence rates of gravity waves with different wavelengths from the selected radiosonde data.

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zonal background wind is dominant at 200 hPa (figure not shown). Then, for simplification, we use the zonal GW phase-speed spectrum in Figure 3b as a reference to the IGW spectrum at launch level in WACCM. The parameterized IGW has the effect on the zonal as well as the meridional directions in our simulation. Black lines in Figure 3b shows the zonal IGW phase-speed spectrum has an approximate double peak Gaussian distribution (It is also true for the meridional IGW phase-speed spectrum). Then we use the following equation to fit the occurrence rate GðcÞ along with IGW phase speed (c): ! 8 2 > > A exp 2 ðc2l2 Þ ; c < 0 > > 2 > 2r2 2 < (3) GðcÞ5 ! > > ðc2l1 Þ2 > > > ; c0 : A1 exp 2 2r 2 1 where the ‘‘2’’means the negative part of the IGW phase-speed spectrum (c < 0), and ‘‘1’’ means the positive part of the IGW phase-speed spectrum (c 0); A2=1 ; l2=1 ; and r2=1 are the amplitude of the occurrence rate, the central phase speed, and standard deviation of the Gaussian distribution of negative/positive phasespeed spectrum as shown in Figure 3b, respectively. Parameters of the Gaussian fitting in Figure 3b are estimated as follows: A2 53:5%, A1 53:1%, l2 52 20:1m=s, l1 57:9m=s, r2 55:9; and r1 56:1.

3. WACCM Model Description

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WACCM cannot produce a QBO spontaneously, likely causing by weak resolved equatorial waves and other gravity waves sources [Richter et al., 2008]. A QBO imposed by nudging tropical winds to the observations [Balachandran and Rind, 1995] was imported into the WACCM as a default. As noted earlier, Xue et al. [2012] introduced an IGW parameterization to spontaneously generate the QBO in WACCM. A QBO-like oscillation can be successfully generated in the stratospheric region over the Equator with a latitudinal span of 208 (the westward phase is maximized at 30 m/s and the eastward phase is maximized at 15 m/s). There are still some discrepancies, such as the eastward phase does not

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extend to lower altitudes than 40 hPa, and a much longer eastward phase of approximately 18 months appears at 10 hPa.

4. The Parameterized IGW Settings We started the numerical experiment using IGW parameterization method according to Lindzen’s saturation formulation [Lindzen, 1981] considering the Coriolis effect [Xue et al., 2012]. The dispersion relation for vertically propagating IGW is as follows:

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(4)

where m, N, c, U, f, and k are the vertical wavenumber of the GW, the buoyancy frequency, the gravity wave phase speed, the background wind, the local Coriolis frequency (f 52X sin/, X is the Earth’s rotation and / is the latitude), and the horizontal wavenumber, respectively. The equation (4) shows that when ðc2UÞ2 2f 2 =k 2 50, the vertical wavelength of the IGW will tend to zero. Therefore, the critical level is: c5U6jf j=k

(5)

The GW amplitude grows exponentially until the wave becomes unstable. At that point, the wave is said to be ‘‘saturated.’’ The IGW momentum flux at saturation level is given in [Xue et al., 2012]: s 5

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0 is atmospheric density. An IGW can have multiple saturation layers until the critical level, where where q the wave momentum flux is absolutely dissipated. The acceleration rate for a saturated region is then obtained [Garcia et al., 2007; Xue et al., 2012]: h i1=2 k ðc2UÞ2 2f 2 =k 2 ðc2UÞ2 @U 1 @s 5 52 0 @Z 2NH @t q

(7)

where represents the intermittency of wave sources. To compare effects of our simulation, we first run a 5 year simulation using the standard WACCM without the imposed QBO. Figure 4 presents a time-height cross section of zonal-mean zonal winds (2.58N–2.58S), from which we can identify the followings: (1), semiannual oscillation (SAO) occurs in the mesosphere; (2), background zonal winds are westward in the stratosphere; and (3) slight annual oscillation (AO) occurs but no obvious long-term oscillation patterns occur in the stratosphere. In standard WACCM 4.0, parameterized GWs spectrum is employed with the conventional Lindzen’s scheme [Garcia et al., 2007], in which parameterized GWs are mesoscale waves with a horizontal wavelength of approximately 100 km that mostly break in the mesosphere and lower-thermosphere (MLT). Another simulation to test whether the GWs of horizontal wavelength 100 km would break in the MLT region is run with all settings the same to the five-year simulation in Figure 4, except for a great reduce of mesoscale wave parameterizations (not shown). According to linear theory [Holton, 1982], the breaking altitude of gravity waves is zb / 2Hlnð2p=kh AÞ, where zb , H, kh , and A denote the breaking level, scale height, horizontal wavelength, and vertical wind amplitude at the launching altitude, respectively. An order of magnitude increase in horizontal wavelength, from 100 km to 1000 km, will lead to a decrease of zb by 4.6H (32 km). As zb of the mesoscale waves is in the MLT region, a decrease of 32 km will reduce the breaking altitude to the stratosphere, meaning that GWs with horizontal wavelength 1000 km will likely break in the stratosphere. This theoretical horizontal wavelength corresponds well with radiosonde observations

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shown in Figure 2b. Then in Figure 5, a new IGW phase speed spectrum is used to replace the idealized box-shaped one used by Xue et al. [2012]. The shape of new parameterization follows equation (3), in which three factors largely determine the features: (1) the central phase speed (l2 , l1 ); (2) amplitudes of the phase speed spectrum (A2 , A1 ); and (3) r2 and r1 . Parameters r2 and r1 are set to average values ( 6.0 m/s) since they are very similar. The new IGW parameterization is launched at a model level of 200 hPa from 308N to 308S with a horizontal wavelength of kh 51000 km for each spectral element. Wave components are then specified from 2C0 to C0 (cutoff phase velocity) with a spacing of 1 m/s, such as [2C0 , , l2 -1, l2 , , l1 , l1 11, , C0 ]. In all of our simulations, we set C0 as 40 m/s. When A2 or A1 equals to 1.0, we define this wave at phase speed l2 or l1 carrying a momentum of s50:001 Pa at the launch level of 200 hPa. In addition, the intermittency factor affects the zonal wind oscillation period. Generally speaking, the value 1.0 for is the largest value of physical significance in numerical modeling. Larger value for can make the QBO period shorter, then reduce the simulation time to obtain enough QBO periods. This is very meaningful since we must run tens of cases. Also, a series of cases in which equals 1.0, 0.5, 0.25, and 0.125 are also carried out to examine the effects of . From here we define the IGW phase speed parameterization following distribution in equation (3) and settings above as ‘‘double-Gaussian parameterization.’’

Momentum Flux (10−3Pa)

Major parameters of all ten cases are listed in Table 1. All these cases can reproduce a stratospheric QBO-like zonal wind oscillation with various characteristics. The maximum eastward/westward wind amplitude and the dominant period of the wind oscillation at 30 hPa are also listed. Zonal-mean zonal winds at 30 hPa for Cases a–g and associated Lomb-Scarge periodograms are shown in 1.0 Figure 6. The effects of our parameter settings on the QBO-like oscillation will be discussed in the following section. 0.5

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Figure 5. Momentum flux carried by IGW parameterization for Case j (red) and simulation by Xue et al. [2012] (blue). The phase speeds are all in a uniform spacing of 1 m/s. The dotted lines indicate the momentum flux of 0.001 Pa, phase speed at 216 and 8 m/s, respectively.

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5. Effects of the IGW Parameters on QBO-Like Oscillation Features 5.1. Central Phase Speeds of ‘‘Double-Gaussian Parameterization’’ We first investigate the effects of l2 and l1 , which denote IGW central

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Table 1. Summary of WACCM 4.0 Simulationsa (a) Case a b c d (b) Case a e f g (c) Case c h i j

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a l2 and l1 are the negative/positive central phase speeds of the ‘‘double-Gaussian parameterization,’’ A2 and A1 denote the phase speed amplitudes, respectively. AMP is the westward/eastward amplitude of QBO-like oscillation, and s is the period. show the intermittency factor.

phase speeds on the negative and positive direction of horizontal background wind, respectively. All parameters of Cases a–d (cases in Table 1a) are the same except for Case a with l2 5216 m=s and l1 516 m=s; Case b with l2 528 m=s and l1 58 m=s; Case c with l2 5216 m=s and l1 58 m=s; and Case d with l2 528 m=s and l1 516 m=s. In Case a and b, the QBO westward amplitude at 30 hPa changes from 242.5 to 229.7 m/s, and the eastward amplitude changes from 40.3 to 29.8 m/s. Amplitudes are reduced by approximately 10 m/s from Case a to Case b, reflecting the decline of l2 and l1 (8 m/s). In Case a to d, A2 , A1 and are the same, meaning that the momentum flux of the IGW remains unchanged. When QBO are driven to higher amplitude with larger IGW phase speeds, its period will become longer since the driving forces (A2 and A1 ) are the same. In Case a, the effective range of positive phase speeds is approximately 4–28 m/s (l1 21.96r, l1 11.96r), accounting for 95% of the momentum flux. Compared to Case b, the maximum effective phase speed change from 28 m/s (Case a) to 20 m/s (Case b), which decrease by nearly 30%. As this result corresponds well with period variation (175 days of Case a and 130 days of Case b, decrease about 26%), there should be a positive correlation between the IGW maximum effective phase speed and the QBO period. In Case c and d, the QBO eastward amplitudes are 31.1 and 40.3 m/s, and the westward amplitudes are 239.2 and 231.0 m/s, respectively. The variation in westward/eastward amplitudes is sensitive to changes in l2 and l1 , respectively. The period of Cases c and d are between that of Case a and b, denoting mixed effects of l2 and l1 on the QBO period. 5.2. Parameter of IGW Momentum Flux IGW phase speed spectrum amplitude, A2 and A1 , allow for the magnitude of momentum flux carried by IGW with negative and positive phase speeds, respectively. Cases a, e, f, and g (cases in Table 1b) are used to investigate effects of momentum flux on stratospheric zonal winds. As l2 and l1 are equal, the QBO amplitude for Cases a, e, f, and g should not change considerably. For example, A2 and A1 of Case e are twice that of Case a, but the QBO amplitudes remain almost the same (240.1 m/s westward and 45.3 m/s eastward). However, the period of Case e (100 days) is nearly half that of Case a (175 days), showing a negative relationship between QBO period and IGW momentum flux. For Cases f and g, we triple A2 and A1 , respectively. Therefore, the periods last for approximately 90 days. Acceleration rates of the zonal wind increase when the momentum flux provided by the IGW parameterization increases. To quantitatively analyze the magnitude of the momentum flux drag, we determine c as follows:

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Case (a): µ−=−16ms−1, µ+= 16ms−1, A−=1.0, A+=1.0, Period ~175days

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The altitude for c is 30 hPa, where QBOs are most apparent in our simulation. c denotes the rate of eastward acceleration to westward acceleration. In Cases a, e, f, and g, c values are 0.86, 0.77, 0.63, and 0.94, respectively. When c increases (0.86–0.94 for Case a and g), due to high eastward IGW drag forcing, eastward acceleration increases. Similarly, when c decreases (0.86–0.63 for Cases a and f), stronger westward drag occurs. Figure 7 shows acceleration rates of the zonal wind oscillation for Cases f and g, it is easy to investigate that QBO westward phase of Case f with A2 triple of A1 , can extend to slightly lower than 100 hPa. In Case g, A1 triple A2 , the eastward phase extends to nearly 100 hPa. Excessive momentum flux can easily drag the wind oscillation to a lower altitude. However, acceleration and deceleration processes show no necessary effect on the duration of eastward and westward oscillation. In all these cases, the duration time of the westward phase accounts for 34%–47% of the entire simulation time regardless of parameter variations, but it accounts for approximately 55% in Figure 1.

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Figure 7. Time-height cross section of the zonal-mean zonal winds and the accelerated rate averaged from 2.58N to 2.58S for a 1 year run of Case f (Figure 7a) and Case g (Figure 7b). Winds are plotted in intervals of 20 m/s. Red and blue colors depict eastward and westward acceleration, respectively.

The main effects of the IGW parameters on the QBO-like oscillation are as follows: (1) the central phase speeds l2 and l1 (determine the maximum effective phase speeds) are positively correlated with the QBO amplitude and period; (2) phase speed spectrum amplitudes A2 and A1 are negatively related to the period and are unrelated to the amplitude of the QBO-like oscillation; and (3) stronger westward/eastward IGW forcing drags the corresponding oscillation phase to a lower altitude.

6. Intermittency Factor Effects Now we should choose a proper case from Case a–Case g to generate a QBO similar to the observation after we set the factor to a normal value. There are two reasons for us to choose Case c: (1), the asymmetry of westward/eastward QBO amplitudes with westward 10 m/s larger, is similar to the observation; (2), the setting of ‘‘double-Gaussian parameterization’’ corresponds well with the radiosondes data in Figure 3b. In Table 1c, all IGW parameters are the same as those of Case c (l2 5216 m=s, l1 58 m=s, A2 5A1 51) with the exception of the intermittency factor . In cases h, i, and j, equal to 0.5, 0.25, and 0.125, respectively. Simulation time of these three cases is longer than 10 years to accurately evaluate the main QBO-like oscillation period. Figure 8 shows the wavelet power spectra of zonal-mean zonal winds at 30 hPa for Cases c, h, i, and j. The main period ranges are as follows: Case c, 100–200 days; Case h, 250–450 days; Case i, 350–450 days; and Case j, 700–950 days. Figure 8 clearly shows a linear tendency toward period variation with an exception of period shown in Figure 8c. In cases h and i, changes from 0.5 to 0.25, but the period does not vary considerably. As we discussed above, the standard WACCM without imposed QBO includes strong SAO and weak AO oscillations in the stratosphere in Figure 4. Drag forcing from the IGW parameterization becomes weak with a decrease , and background oscillation increasingly comes into effect to modulate the QBO-like oscillation period. The following are the two major causes of the phenomenon shown in Figure 8c: (1) the QBO-like oscillation period multiplies the SAO period in the stratosphere; (2) the drag forcing from our IGW parameterization is not strong enough to disregard other processes. In Cases a–g, factor (1.0) values effectively prevent effects of other oscillations, thus guaranteeing the reliability of section 5. When decreases to a normal range of less than 0.6, the period is signally modulated by the SAO, the main oscillation near the QBO region. In general, factor of the parameterization almost exhibits an inverse ratio to the QBO-like oscillation period.

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7. Long-Term Realistic Simulation and Discussion Case j uses a IGW parameterization with the following parameters: l2 5216 m=s; l1 58 m=s; A2 5A1 51:0; r2 5r1 56:0; and 50:125. In Figure 8d, the average period of zonal-mean zonal wind in Case j is approximately 28 months, reflecting the observed QBO. Figure 9a shows the time-height cross section of zonal-mean zonal wind for Case j with westward and eastward amplitudes of 229.5 m/s and 19.3 m/s (30 – 35 m/s westward and 15 – 20 m/s eastward according to the observations). Alternating winds are most apparent from 1 hPa to 100 hPa, but the westward amplitude is deeper than the eastward amplitude. The eastward amplitudes always extend to an altitude of 60 hPa. The zonal momentum flux carried and released by IGW parameterizations is shown in Figure 9b, reaching a maximum value of roughly 60.002 Pa at 30 hPa. When zonal winds in the stratosphere are directed westward, only the eastward momentum flux can spread to the upper atmosphere. The same applies to the westward momentum flux. Figure 9c compares acceleration rates resulting from the resolved waves (divergence of the Eliassen-Palm flux, red lines) and parameterized IGW (shown in Figure 9b, blue lines). For the other parameterized mesoscale GW drag forcings, deep convections and fronts are normally one order of magnitude lower than equatorial waves and IGW in the stratosphere (not shown). At 30 hPa, the forcing by IGW approximately ranges from 20:7 to 0:5 m=s=day, and the forcing by resolved waves ranges from approximately 20.1 to 0:2 m=s=day. Acceleration rates due to resolved waves are much lower than those of the IGW and particularly for the westward tendency, meaning that the IGW parameterization provides necessary drag forcing for the oscillation. Figure 10 presents a composite contour of equatorial zonal wind based on the ERA-Interim data for 1998–2011, the WACCM with a box-shaped IGW phase speed spectrum developed by Xue et al. [2012], and Case j, respectively. We carried this procedure out according to the eastward-westward QBO transition moment at 30 hPa. When this transition occurred, we overlaid the next period over the previous one and obtained the composite contour of zonal winds. There are two major improvements when we compare QBO features by Xue et al. [2012] in Figure 10b and Case j in Figure 10c: (1) in Figure 10b, the QBO period averages at 24 months, while period of Case j averages at 28 months. The QBO period of case j corresponds better with the ERA-Interim QBO period in Figure 10a (28 months); (2) the eastward phase of Case j can reach the lowest region of approximately 60 hPa, which is much deeper than that 40 hPa shown in Figure 10b. To assess the characteristics of equatorial waves and our parameterized IGW when propagating upward, three space-time analyses outlined by Wheeler and Kiladis [1999] were performed on daily 30 hPa zonal

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winds between 108S and 108N for 5 years data (2002–2006). The three analyses focus on ERA-Interim data, the standard WACCM with imposed QBO, and Case j, respectively. Figures 11a, 11c, and 11e present the power spectra of symmetric waves (mainly Kelvin waves), and power spectra of antisymmetric waves (mainly mixed Rossby gravity waves) are shown in Figures 11b, 11d, and 11f. Figure 12 is similar to Figure 11 but at 100hPa. Our parameterized IGW always break in the stratosphere, as a result, the power spectra in Figure 12 is mainly caused by the equatorial waves such as Kelvin waves and MRGs. The power spectra in Figure 11 can be regarded as a mixed effect of equatorial waves and parameterized IGW. In Figures 11a, 11c, and 11e, power spectra of ERA-Interim data, standard WACCM, and Case j are similar, with prominent Kelvin wave power between equivalent depths of 250 and 50 m, except for a weaker westward wave component of Case j. The dispersion relation of symmetric waves at 100 hPa in Figures 12a, 12c, and 12e, is similar to that at 30 hPa. Our IGW parameterization does not affect the symmetric wave spectra too much, since there is no significant difference between the power spectra at different altitudes. In Figure 11b, the power spectra of ERA-Interim data are evident between 250 and 50 m equivalent depth curves of the MRGs with major zonal wavenumbers of 24 to 1 and periods of 2–3 days, and in Figure 11d, power spectra of MRGs in standard WACCM are weaker. As to Figure 11f, the antisymmetric power spectra are significantly strong since additional waves with great power appears near to the 250 m equivalent depth curves of MRGs with major zonal wavenumbers 28 to 24 and periods 2–6 days. As these waves do not exist in Figure 12f which show the pure power spectra of equatorial resolved waves, it is convinced that our

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IGW parameterization is the source of these waves, providing enough westward momentum flux absent in standard WACCM to generate the QBO-like oscillation. Longwave radiative wave damping is the dominant damping mechanism for large-scale equatorial waves, contributing 40%–50% of the total resolved wave forcing in the Max Planck Institute Earth System model (MPI-ESM); the horizontal diffusion of the zonal wind disturbance also dissipates waves with zonal wavenumbers of larger than 10 and at frequencies exceeding 0.5 cpd. These two mechanisms reflect the EP flux and wave-induced zonal wind tendencies in the tropical stratosphere [Krismer and Giorgetta, 2014]. Equatorial waves with rapid dissipation do not generate enough momentum flux to drag the QBO, and other sources such as small-scale GWs are necessary. In the work by Kim and Chun [2015b], after considering reference data corrections, the net GW forcing of QBO eastward shear is lower than the Kelvin wave forcing, whereas in the QBO westward shear, GW forcing is the more dominant forcing term than the MRGs. This conclusion corresponds well with results presented in Figure 11f, in which our IGW parameterization presents the main QBO westward forcing mechanism.

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In addition to the most frequently used IGW parameterization, several other methods generate QBO-like oscillation Figure 10. Time-height cross section of composite contour of the QBO period at 30 hPa averaged from 2.58N to 2.58S for (a) ERA-Interim data; (b) 10 years of simuin numerical models. Another efficient lation by Xue et al. [2012]; (c) Case j. The transition month was chosen as the first approach involves improving the modmonth when eastward wind is present at 30 hPa. The time axis extends from the el resolution. According to Richter et al. west-east transition until 28 months afterward. The red and blue lines show the pressure level of 30 and 50 hPa. [2014], high vertical resolution (500 m) and parameterized gravity wave drag are needed to generate a realistic QBO in the CAM5. However, the westward phase of the QBO becomes too weak when the eastward phase is enhanced in their best simulation (60LcamGW). This echoes the disadvantages of wind phases found in our simulated Case j, which are likely caused by coarse vertical resolutions as the authors discussed. In addition, the generation of QBO-like oscillations is also successful when using two GISS models (GCMAM III and Model E2) based on parameterized gravity waves and a finer vertical resolution [Rind et al., 2014]. In their work, the modeled QBO shared numerous features with the observations, but eastward winds were also enhanced in the midstratosphere. The relationship between the QBO period and the magnitude of parameterized momentum flux has also been investigated. While QBO-like oscillations are generated through numerous numerical models, additional work must be conducted to identify perfect simulations that reflect observations.

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Figure 11. (a), (c), and (e) show symmetric/background Wheeler’s wavenumber-frequency spectra of zonal-mean zonal wind for ERA-Interim data, the standard WACCM run with imposed QBO and Case j, respectively. (b), (d), and (f) denote their anti-symmetric/background features. All of these values are calculated between 108S and 108N at 30 hPa. Analytical dispersion relations are plotted at equivalent depths of 250, 50, and 10 m (black lines, from left to right).

8. Summary QBO is a dominant dynamic process in the stratospheric atmosphere, it is necessary to better simulate it in our numerical model. WACCM 4.0 model cannot generate QBO-like oscillation spontaneously using standard model settings. In this manuscript, we use a new ‘‘double-Gaussian parameterization’’ which based on radiosonde data to replace the box-shaped IGW parameterization previously used by Xue et al. [2012]. We then systematically study effects of IGW parameters and the intermittency factor on the features of QBOlike oscillations. We presented several configurations of the ‘‘double-Gaussian parameterization’’ through WACCM4.0, and we examined how their differences affect models that reproduce QBO-like oscillation. Our main conclusions are as follows. (1) Central phase speeds of the ‘‘double-Gaussian parameterization’’ in the positive and negative direction, determine the amplitude of the QBO-like oscillation. The maximum effective phase speeds of parameterized IGW are positively correlated with the oscillation period. (2) The amplitude of IGW phase speed spectrum is negatively related to the QBO period but unrelated to its amplitude. (3) Stronger IGW forcing can drag the apparent amplitude of the QBO-like oscillation to a lower altitude (100 hPa). (4) The IGW parameterization and other oscillations such as the SAO in the lower mesosphere modulate QBO, and generally speaking, the intermittency factor is negatively related to the period of QBO-like oscillation. (5) The IGW parameterization do not have obvious effects on the duration time of QBO westward and eastward phase. The ratio of the westward phase duration to the entire simulation period ranges from 34% to 47% at 30 hPa. Meanwhile, the ratio of ERA-Interim data shown in Figure 1 is valued at roughly 55%. This is proven insoluble using the current parameterization method after conducting various long-term simulations in WACCM 4.0.

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Figure 12. The same as Figure 11 but at 100 hPa.

Acknowledgments This work is supported by the National Natural Science Foundation of China (41322029, 41474129, 41421063, 41404119), the Project of Chinese Academy of Sciences (KJCX2-EW-J01), Youth Innovation Promotion Association of the Chinese Academy of Sciences (2011324), and the Fundamental Research Funds for the Central Universities. We wish to thank the United States SPARC date center for the free radiosonde data (http:// www.sparc.sunysb.edu/), and ECMWF for providing the ERA-Interim data set (http://www.ecmwf.int/). We also sincerely thank the National Center for Atmospheric Research (NCAR) for providing the Whole Atmosphere Community Climate Model (WACCM) source code which can be freely modified and run. Our WACCM simulations have been carried out at the supercomputing platform of geospace of the University of Science and Technology of China. All codes of this work are available through this email: [email protected].

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The simulated QBO of Case j complements the observations in more respects: (1) the IGW parameterization is based on observational data, making the parameterization and QBO-like oscillation more convinced; (2) the QBO-like oscillation period last for approximately 28 months, reflecting the observations; and (3) the eastward phase of the QBO can extend to a lower altitude and it damps near 60 hPa, which is deeper than that recorded before (40 hPa). This work had the following two objectives: (1) providing a quantitative and systematic discussion of parameterized IGW effects on QBO features in the stratosphere and (2) providing a realistic source of parameterized IGW to improve the credibility of the physical parameterization in WACCM. This parameterization renders the QBO more realistic for proper periods and amplitudes. In this systematic work, we used parameterization methods to generate QBO-like oscillation in the WACCM model, and the corresponding results can serve as a reference when parameterizing other gravity waves. Until now, it has been difficult to perform long-tern climate simulations at hyperfine spatial resolutions. To better simulate QBO-like oscillation, it is necessary to ensure the contributions of equatorial waves and parameterized gravity waves; in turn, parameterization methods could continue to be used in climate research for a long time.

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