1. Introduction
The quasi-biennial oscillation (QBO) is one of the most dominant, periodic, and therefore predictable modes in the tropical stratosphere on interannual time scales (Scaife et al. 2014), with alternate easterlies and westerlies descending from the equatorial upper stratosphere to the tropopause every 21–32 (~28 on average) months (Baldwin et al. 2001 and references therein). The QBO is driven by various waves propagating upward that deposit westerly and easterly momentum in the stratosphere (Lindzen and Holton 1968; Andrews and McIntyre 1976). Specifically, QBO westerlies are mainly associated with eastward propagating Kelvin waves (Wallace and Kousky 1968; Maruyama 1994; Canziani and Holton 1998), whereas internal gravity waves excited by convection and frontal systems are more important for the formation of the QBO easterlies (Holt et al. 2016). Although the equatorial easterlies usually follow westerlies in a complete QBO cycle, occasionally a sudden easterly zone can form and disrupt the usual progress of westerlies, for example, in the early months of 2016 and 2020 (Newman et al. 2016; Osprey et al. 2016; Watanabe et al. 2018; also see the QBO time series: https://www.geo.fu-berlin.de/en/met/ag/strat/produkte/qbo/index.html).
The influence of the QBO on the Northern Hemisphere winter surface climate was reviewed by Baldwin et al. (2001) and Anstey and Shepherd (2014). The QBO appears to impact the near surface climate through exciting teleconnections to the troposphere either directly (Garfinkel and Hartmann 2011a,b; Hendon and Abhik 2018) or via the response of the stratospheric polar vortex as a bridge linking the QBO with the troposphere (Holton and Tan 1980; Anstey and Shepherd 2014; Andrews et al. 2019). The weakening and strengthening of the northern winter stratospheric polar vortex during the easterly and westerly QBO phases, respectively, was first reported by Holton and Tan (1980), who hypothesized that they are due to the respective poleward or equatorward shift (i.e., latitudinal variation) of the stratospheric zero-wind line. This latitudinal variation of the zero-wind line changes the region in which tropospheric planetary waves propagate upward and equatorward, modulating the interaction with the stratospheric polar vortex. In the literature, the Holton–Tan (HT) relationship refers to this statistical linkage between the stratospheric polar vortex and the QBO. In this study the HT mechanism is used to describe the mechanism they hypothesized to occur.
The anomalous QBO winds can also arch downward into the subtropical troposphere in a horseshoe-shaped pattern (Crooks and Gray 2005; Haigh et al. 2005). The meridional circulation response associated with the QBO may help to explain the downward arching zonal winds (Garfinkel and Hartmann 2011a,b; Garfinkel et al. 2012; Seo et al. 2013; White et al. 2015). The vertical shear of the QBO wind is thermally balanced by the temperature anomalies of opposite signs above and below the peak QBO winds. By using models with different complexities, Garfinkel and Hartmann (2011a,b) demonstrated that such a temperature anomaly pattern must include a meridional circulation cell that redistributes the zonal wind anomalies that extend from the equatorial stratosphere into the subtropical troposphere. In the presence of extratropical eddies, the zonal wind anomalies are intensified and extend downward to the troposphere.
Given the apparent influence of the QBO in the variation and prediction of the tropospheric circulation, an increasing number of models are now capable of spontaneously simulating QBO-like phenomena in the equatorial stratosphere. For example, it is reported that the QBO spontaneously appears in two GISS coupled models by introducing gravity wave parameterization associated with tropical convection and improving the vertical resolution (Rind et al. 2014; Geller et al. 2016). Richter et al. (2014) performed similar exploration by using a vertical resolution of 500 m and adequate gravity wave drag in the CAM5 model to simulate a realistic QBO. More recently, several metrics of the QBO in Chemistry-Climate Model Validation-2 (CCMVal2) models and models in phase 5 of the Coupled Model Intercomparison Project (CMIP5) were assessed, including the squared amplitude and the period (Schenzinger et al. 2017; Butchart et al. 2018). Naoe and Yoshida (2019) also find the QBO winds arch downward and an Eliassen–Palm (E-P) flux divergence/convergence dipole forms between the mid- and high latitudes in a CMIP6 model (MRI-ESM2.0). Andrews et al. (2019) show that the observed AO response to the QBO is also identified in another CMIP6 model (HadGEM3). Richter et al. (2020) show that CMIP5/6 models simulate the QBO period and latitudinal extent reasonably, but the QBO amplitude at all levels below 20 hPa is underestimated. Of the five subseasonal forecasting models considered by Garfinkel et al. (2018), only one maintained a QBO of similar strength to that observed, but even some of the other models were able to simulate an HT relationship (albeit one weaker than that observed). The HT relationship and impacts of the QBO on the extratropical circulation via other pathways were recently evaluated for 16 CMIP5/6 models (Rao et al. 2020a,b). All of those studies show that very few models can simulate all aspects of the QBO, and most models can only capture one or two facets of the QBO.
The maximum near surface impact of the QBO on average appears in different winter months for different regions. For example, the HT relationship is strongest in midwinter (Anstey and Shepherd 2014), and Gray et al. (2018) find the HT relationship leads to a maximum North Atlantic Oscillation (NAO)-like response in January in the Atlantic–European sector. Because of the limited observational record, it remains unclear to what extent the observed seasonal synchronization of the QBO impact is forced or is a reflection of the short observations. Namely, in contrast to ENSO or the solar cycle where the peak response in high latitudes is seen in the second half of winter, the response to the QBO seems to peak earlier in winter. Does the extratropical circulation respond identically to the same QBO wind relaxation but in different months?
Although the HT relationship has been widely explored in literature by using observations, reanalyses, and outputs from the state-of-the-art complex models, we still do not clearly know how this relationship is established. Is the HT mechanism enough to explain the extratropical circulation response to the QBO? Two modeling studies that addressed this question [HadGEM2-CCS by Watson and Gray (2014) vs WACCM3 by Garfinkel et al. (2012)] reached opposite conclusions, but it is not clear why the responses in their respective models differed. The models used in these studies differed in a number of respects, for example, resolution (WACCM3: 4° latitude × 5° longitude, L66; HadGEM2-CCS: 1.25° latitude × 1.875° longitude, L60), ability to spontaneously simulate a QBO (no QBO appears in the WACCM3 free run, but the QBO appears in the HadGEM2-CCS free run), and magnitude of the anomalous QBO winds [nudged maximum easterlies around 30–50 hPa in the sensitivity experiment: 22 m s−1 or triple in Garfinkel et al. (2012) vs 70 m s−1 in Watson and Gray (2014)]. It is not clear if these factors are important.
Here, we utilize an idealized model that is capable of spontaneously simulating the QBO to better understand the establishment of the QBO teleconnection in the extratropics by relaxing to an imposed QBO wind profile. In this manner, interference of other influences with the QBO teleconnection is excluded. Namely, confounding interactions between the extratropical response to other forcing and the response to the QBO can be minimized, as compared with observations and complex coupled model outputs.
The structure of this paper is as follows. Following the introduction, section 2 presents the idealized model used, experimental designs, datasets, and methods employed in this study. The simulated QBO and the HT relationship in this idealized model is assessed in section 3 against reanalyses and the state-of-the-art models with a spontaneous QBO. The excitation and evolution of the stratospheric polar vortex response is shown in section 4. Section 5 presents a summary and discussion.
2. Model, experimental designs, datasets, and methods
a. MiMA, version 2
In this study the Model of an Idealized Moist Atmosphere (MiMA; Jucker and Gerber 2017), version 2 (Garfinkel et al. 2020), is utilized. MiMA is an intermediate-complexity atmospheric model with a spectral dynamical core and a variety of physical processes. MiMA is based on the aquaplanet model by Frierson et al. (2006, 2007) and Merlis et al. (2013). The physical processes include large-scale moisture transport (and the related latent heat release), a mixed-layer ocean, a subgrid-scale convection scheme (Betts 1986; Betts and Miller 1986), and a Monin–Obukhov similarity boundary layer scheme. Different from the dry dynamical core in some idealized models, MiMA includes an explicit treatment of moisture and radiation. To incorporate the interaction of shortwave radiation with ozone and water vapor, MiMA uses the Rapid Radiative Transfer Model (RRTM) radiation scheme (Mlawer et al. 1997; Iacono et al. 2000), allowing the representation of a realistic stratosphere. Following Alexander and Dunkerton (1999) and Cohen et al. (2013), a parameterization of gravity waves has been added to the model; this allows for the spontaneous generation of a QBO. A companion paper will describe the sensitivities of the QBO to the settings of the gravity wave scheme. As in Garfinkel et al. (2020), three forcing mechanisms of stationary waves are added to a moist aquaplanet model without zonally asymmetric forcings: land–sea contrast (i.e., the difference in heat capacity, surface friction, and moisture availability between oceans and continents), climatological ocean horizontal heat fluxes (to generate zonal asymmetries in sea surface temperatures), and realistic topography. We refer readers to Jucker and Gerber (2017), Garfinkel et al. (2020), and White et al. (2020) for more details on the model configuration.
b. Experimental designs
A series of experiments (Table 1) are performed using MiMA with a T42 horizontal resolution (i.e., 2.8° latitude × 2.8° longitude) and with 40 vertical levels spanning from the surface to ~0.01 hPa (11 levels between 100 and 10 hPa and 9 levels between 10 and 1 hPa). All of the parameters use the same values as in Garfinkel et al. (2020) with all of the three forcing mechanisms of stationary waves (i.e., land–sea contrast, net surface energy flux in the warm pools, and topography). The solar radiation, ozone, and greenhouse gases are kept constant in the experiments. The first experiment is a free run of 65 years (termed “Control” herein; see Fig. 1). On the first day of every year in the free Control run, a restart file is generated. Discarding the spinup of the Control run in its first 5 years, restart files for the remaining 60 years are saved for the branch runs. The metrics of the QBO and its teleconnections in MiMA are based on the Control experiment, in which the QBO is generated by MiMA spontaneously.
Experiment designs in this study. Note that the MiMA configuration used in this paper includes a “360-day” calendar, so the Control experiment runs 65 years in total.
(left three columns) Monthly and (right column) seasonal climatology of the zonal-mean zonal winds (contours; m s−1, with interval of 5 m s−1) in the boreal winter from different datasets. (a)–(d) The ERA-Interim reanalysis (nearly identical to ERA5 and JRA-55, which are not shown for brevity). (e)–(h) The free Control run by MiMA. (i)–(l) The climate branch runs in December–February and their mean. The color shading in (a)–(d) shows zonal-mean temperature in ERA-Interim (K). The color shadings in (e)–(h) and (i)–(l) show the temperature differences between the Control run and ERA-Interim, and between the climate branch runs and the Control run, respectively. Stippled regions in (e)–(l) mark the temperature difference between two datasets at the 95% confidence level.
Citation: Journal of Climate 34, 17; 10.1175/JCLI-D-20-0960.1
To mimic the westerly and easterly phases of the QBO and to reveal the transient response of the extratropics to the QBO, a variety of branch runs are performed. The zonal mean zonal winds from 6°S to 6°N and from around 100 to 10 hPa are relaxed toward the specified profile (see section 4) in the branch runs with a 10-day time scale. Away from the equator from 6° to 22°N and from 6° to 22°S, the linear relaxation time scale increases as τ(φ) = 10 exp[(1/2)(φ/10)2], where φ is latitude and τ is the relaxation time scale (τ = 10 at the equator). Zonal winds evolve freely poleward of the 22° latitudes in both hemispheres. In this manner, the QBO wind is relaxed toward its easterly or westerly phase. More details can also be found in Garfinkel and Hartmann (2011a,b) and Garfinkel et al. (2012).
The annual cycle of incoming solar radiation is included in three seasonal runs. These runs are forced by an equatorial stratospheric zonal wind profile around 100–10 hPa to reflect the climatology, the easterly QBO phase, and the westerly QBO, respectively. The three seasonal branch runs are termed as Sea_climate, Sea_EQBO, and Sea_WQBO, respectively. Each experiment ensemble has 60 members initialized from the 1 January conditions for each year in the control simulation. The Sea_EQBO minus Sea_climate composite is fairly similar to the Sea_EQBO minus Sea_WQBO composite but with the zonal mean zonal wind amplitude nearly doubled for the latter. For brevity, we mainly analyze the difference between Sea_EQBO and Sea_WQBO.
The seasonal locking of the extratropical response to the QBO is another focus of this study (i.e., why does the observed extratropical response achieves its maximum in mid-to-late winter?). This question is tackled using additional branch experiments with incoming solar radiation fixed to that in different winter months (perpetual November, perpetual December, perpetual January, and perpetual February). Take the November branch runs as an example, we branch alternately with climatological equatorial winds, easterly QBO (EQBO) winds, or westerly QBO (WQBO) winds (Nov_climate, Nov_EQBO, and Nov_WQBO, respectively). The three experiments are similar to the three seasonal branch runs, but the calendar date is fixed in mid-November to remove the annual cycle. The aim of these branch runs is to explore the extratropical response to the QBO in different months and to consider the possible impact of seasonal synchronization on the QBO teleconnection. Similarly, the branch runs in other fixed months (December, January, and February) are also performed (see Table 1).
c. Reanalyses and CMIP5/6 historical outputs
To validate the general performance of MiMA in simulating the QBO and the HT relationship, three modern reanalyses are also used as a reference. They are European Centre for Medium-Range Weather Forecasts (ECMWF) Interim Reanalysis (ERA-Interim; Dee et al. 2011), ECMWF fifth major global reanalysis (ERA5; Hersbach et al. 2020), and Japanese 55-year Reanalysis (JRA-55; Kobayashi et al. 2015). The three reanalyses have a well-resolved stratosphere, and the composite zonal-mean response to the QBO is nearly identical in these three reanalyses. For brevity, only one reanalysis is shown unless stated otherwise. The composite QBO period and amplitude are also extracted from reanalyses as a reference for MiMA.
To get a general view of the QBO simulation between MiMA and some state-of-the-art global climate models, historical runs from 27 CMIP5/6 models are also used in this study. There are 7 CMIP5 models with a QBO in the historical simulation (from CESM1-WACCM to MPI-ESM-MR in Fig. 2). The HT relationship simulated in those models has been assessed in Rao et al. (2020a). We also use historical simulations from 20 CMIP6 models with a spontaneous QBO [from ACCESS-CM2 to the U.K. Earth System Model, version 1 (UKESM1.0-LL) in Fig. 2]. For more details about these models in terms of resolutions, vertical levels, model tops, and references, readers can refer to Rao et al. (2020a,b). The QBO metrics and the QBO teleconnections in these CMIP5/6 models are not the focus of this study, but they provide an opportunity to evaluate the general performance of MiMA in reproducing the QBO.
(a) Mean period of the QBO at 30 hPa from different datasets in comparison with MiMA, including three modern reanalyses (ERA5, ERA-Interim, and JRA-55), seven CMIP5 models (from CESM1-WACCM to MPI-ESM-MR), 20 CMIP6 models (from ACCESS-CM2 to UKESM1.0-LL), and the CMIP5/6 MME. The error bar shows the standard deviation of the mean period. The horizontal reference line shows the mean of the three modern reanalyses as a baseline. (b) As in (a), but for the mean amplitude and its standard deviation of the QBO at 30 hPa.
Citation: Journal of Climate 34, 17; 10.1175/JCLI-D-20-0960.1
d. Methods
Since the QBO amplitude is too weak in the equatorial lower stratosphere in most models, and even disappears in some (see the introduction), we define QBO phases using the zonal-mean zonal winds at the equator (5°S–5°N) at 30 hPa. The QBO time series are smoothed using a five-month running mean, so the intraseasonal variability is removed. Using the smoothed QBO time series, every pair of westerly and easterly peaks (AW and AE) is selected from CMIP5/6 and MiMA Control simulations. The QBO amplitude is estimated as (AW − AE)/2 in each complete QBO cycle, constructing a nonuniform discrete series. The composite QBO amplitude is the mean of this discrete time series at unequal intervals. The number of the QBO cycles is written out for future use, and the average period of the QBO is the ratio between the time length in months of the QBO series and the number of the QBO cycles (excluding the incomplete ending points). The other method of quantifying the QBO amplitude is 21/2 times the standard deviation of the smoothed monthly QBO index (i.e., 21/2σ; not shown), showing similar results to those estimated by (AW − AE)/2.
Considering the asymmetry between QBO westerlies and easterlies (i.e., QBO easterlies are stronger than QBO westerlies in observations), the QBO index at 30 hPa is deseasonalized to better reveal the HT relationship in different datasets. A winter is composited as westerly QBO winter if the winter-mean (December–February) deseasonalized QBO index exceeds 5 m s−1 for each model, and as easterly QBO if the winter-mean deseasonalized QBO index falls below −5 m s−1. The sensitivity of the composite HT pattern to a smaller threshold has been tested, but the composite pattern is nearly unchanged. Other diagnostic tools used in this study also include the E-P flux (Fy, Fz) and its divergence, residual circulation in the transformed Euler framework (
3. Assessment of the QBO simulation in MiMA
a. The zonal-mean climatology
The zonal-mean zonal wind and temperature in December–February are shown in Fig. 1 for ERA-Interim (nearly identical to ERA5 and JRA-55, not shown), the MiMA Control runs, and three branch runs with relaxed climatological equatorial zonal winds. In the reanalysis data, the northern winter stratosphere is characterized by a strong polar vortex encircled by the polar westerly jet centered around 60°N in the stratosphere, accompanied by a cold center over Arctic at 50–30 hPa (Figs. 1a–d). The stratospheric polar vortex is stronger in December and January than February. The stratospheric polar vortex is well simulated in December and January by MiMA although its intensity is overestimated in January and February (Figs. 1e–h). The Arctic stratosphere is colder in MiMA than the reanalysis, denoted by the cold bias in Figs. 1e–h. The winter-mean lowest temperature of the Arctic stratosphere is ~205 K in the reanalysis, whereas it is ~195 K in MiMA (see the temperature bias, ~10 K). Actually, the too-cold Arctic stratosphere is a common bias in models (e.g., Charlton et al. 2007; Rao et al. 2015). A strong westerly bias throughout the equatorial stratosphere is present in MiMA, though the bias is reduced if the resolution is increased to T85 (not shown). In contrast, the Northern Hemisphere tropospheric subtropical jet (centered around 30°N and 200 hPa) is well simulated: It is observed to gradually intensify from December to February in the reanalysis, which is well simulated by MiMA. The reproducibility of the mean flow is important for the tropospheric response to QBO, as Garfinkel and Hartmann (2011a) show that the tropospheric circulation response to the QBO is sensitive to the central latitudinal position of the subtropical jet.
When the tropical stratospheric zonal winds are relaxed toward the climatology in the branch runs (Figs. 1i–l), the extratropical stratosphere is better simulated than the free Control runs. The stratospheric polar jet intensity is reasonably reproduced in the branch runs (central magnitude: ~35 m s−1 in the December and January perpetual runs and ~30 m s−1 in the February perpetual run). The Arctic stratospheric cold bias in the free Control run is also improved in the branch runs with the stratospheric equatorial zonal winds relaxed (see the Arctic stratospheric temperature improvement in the branch run over the Control run, >8 K). The strong westerly bias in the equatorial stratosphere simulated by the free Control run is also removed as the stratospheric winds are relaxed toward the reanalysis.
b. A brief assessment of the QBO in MiMA
The composite mean period and amplitude of the QBO at 30 hPa and their standard deviation are shown in Fig. 2 for three reanalyses, 27 CMIP5/6 models, and MiMA. The horizontal line shows the ensemble mean of the three reanalyses, as a reference for models. The QBO period is ~28 months in all three reanalyses (Fig. 2a). CMIP5 and especially CMIP6 models show a wide intermodel spread for the QBO period, but the multimodel ensemble (MME) for these 27 CMIP5/6 models shows a high skill in reproducing the QBO cycle (~27 months) also with a small standard deviation, generally consistent with the reanalyses. In contrast, the period of the QBO in MiMA is ~32 months, longer than the reanalyses and CMIP5/6 MME. However, the simulated QBO cycle in MiMA still falls in the upper range of the CMIP6 models, although some CMIP5/6 models have a varying period. For example, the standard deviation of the QBO period in AWI-CM-1.1-MR (i.e., the Alfred Wegener Institute Climate Model) and GFDL-ESM4 (σ = 8 and 16 months, respectively) is much more uncertain than in the reanalysis (σ = 4 months). A follow-up paper will consider the sensitivity of the period of the QBO in MiMA to resolution and settings of the gravity wave drag parameterization.
The composite QBO amplitude at 30 hPa is consistently around 20 m s−1 in the three reanalyses and their mean (Fig. 2b). The QBO amplitude and cycle in CESM1-WACCM is nearly identical to the reanalyses, because the QBO in this model is not a spontaneous phenomenon but a relaxed forcing based on the observations (Marsh et al. 2013; Rao et al. 2020c). Most models underestimate the amplitude of the QBO, so an improvement in the QBO amplitude is still a challenge for model developers in the near future. The composite QBO intensity is ~16 m s−1 in the CMIP5/6 MME, and MiMA better simulates the QBO intensity (~19 m s−1) than the CMIP5/6 MME, although the QBO intensity in MiMA fall within the intermodel spread of CMIP5/6 models.
To better characterize the underestimated QBO amplitude in models, Fig. 3 displays the vertical profile of the standard deviation of the monthly zonal-mean zonal winds at the equator (5°S–5°N) for reanalyses and models. Based on the reanalyses, the maximum variability of zonal-mean zonal winds is situated around 20 hPa. The variability of the zonal winds increases with height between 100 and 20 hPa, whereas the variability in most models (including MiMA and the CMIP5/6 MME) increases monotonically even above 20 hPa. The variability of zonal winds in the stratosphere below 20 hPa is also smaller in the CMIP5/6 MME, most CMIP5/6 models, and MiMA than the reanalyses. The underestimated variation of zonal winds at equator is consistent with the weaker QBO for models.
Vertical profiles of the standard deviation of monthly zonal-mean zonal winds (m s−1) near the equator (5°S–5°N) from three reanalyses (blue for ERA5, green for ERA-Interim, and red for JRA-55), 27 CMIP5/6 models (grays), and MiMA (brown). The dashed vertical profile shows the CMIP5/6 MME. The bar plot embedded also presents the mean frequency of major sudden stratospheric warming events for the reanalysis (with a horizontal dashed reference line), CMIP5, CMIP6, and MiMA. An SSW is defined if the zonal-mean zonal winds at 10 hPa and 60°N reverse from westerlies to easterlies.
Citation: Journal of Climate 34, 17; 10.1175/JCLI-D-20-0960.1
Another concern is on the simulation of sudden stratospheric warming (SSW) events by MiMA as compared with other models (for more details, see Rao and Garfinkel 2021), also shown in Fig. 3. On average, five or six SSWs happen per decade in the reanalyses, and the CMIP5 MME simulates many fewer SSWs. In contrast, the CMIP6 MME reproduces the SSW frequency in the reanalysis. The general skill of MiMA for the SSW simulation falls between CMIP5 and CMIP6. The downward response to SSWs is also similar in MiMA to observations (White et al. 2020). This validates the usage of MiMA for understanding the extratropical response to the QBO.
c. Reproducibility of the HT relationship and surface response by MiMA
The composite difference in zonal-mean zonal winds, scaled E-P flux, and E-P flux divergence (Andrews et al. 1987) between easterly QBO and westerly QBO during boreal winter (December–February) is shown in Figs. 4a–4c. During easterly QBO winters as compared with westerly QBO winters, the stratospheric polar vortex is weakened, manifested by the easterly anomalies in the circumpolar region. The HT mechanism attributes the weakening of the polar night jet to fewer waves propagating into the EQBO region due to the shift in the location of the zero-wind line. Such a mechanism is not enough to fully understand the polar stratospheric response to the QBO, as there is actually anomalous wave propagation into the EQBO region near 50 hPa and 30°N, opposite to what might be expected if waves are reflected or refracted away from the zero-wind line. The climatological equatorward propagation of waves around 50 hPa and 40°N increases due to the local westerlies and enhanced refractive index (not shown; see Fig. 1 in Garfinkel et al. 2012). Rather, the polar vortex weakening is associated with an anomalous E-P flux divergence dipole between 20° and 80°N in the upper stratosphere, and specifically with the anomalous poleward propagation of waves emitting from the Northern Hemisphere extratropics (Fig. 4a). The CMIP5/6 MME tends to underestimate the HT relationship (the composite also varies with the model; see Rao et al. 2020a,b), and the easterly response is much weaker than the reanalysis (Figs. 4a,b). Some CMIP5/6 models have a relatively higher skill in simulating the HT relationship than others (Rao et al. 2020a), although the response in the MME is too weak. In contrast, MiMA better simulates the response in the extratropical stratosphere to the QBO, and both the upward propagations of waves in the lower stratosphere around 50°–70°N and the anomalous E-P flux divergence dipole in the middle stratosphere between 20° and 80°N is well reproduced in MIMA (Fig. 4c). Difference between ERA-Interim and MiMA is also evident: the anomalous E-P flux is poleward in the reanalysis but equatorward in MiMA in the stratosphere at 20°N, which might be related to the different mean states in the two datasets (i.e., a strong westerly bias is present in the MiMA control run in Fig. 1). Similarly, the E-P flux anomalies at 40°–60°N in the troposphere are also different among datasets due to their various mean states.
(a)–(c) Composite differences in the zonal-mean zonal wind (contours; m s−1), in the scaled E-P flux (Fy/ρ0, 50 × Fz/ρ0; vectors; m3 s−2), and in the E-P flux divergence (shading; m s−1 day−1) in the boreal winter (December–February) between the easterly QBO and westerly QBO phases. The blue contours mark the wind differences at the 95% confidence level according to the two-sided Student’s t test. The contour interval is 5 m s−1 in the tropical stratosphere (inside the gray-outlined box) but 0.5 m s−1 elsewhere (outside the gray-outlined box). The zero contours are skipped for clarity. The purple contours (starting from 25 m s−1, with an interval of 5 m s−1) show the subtropical jet with the jet center at each pressure level from 1000 to 10 hPa marked by the asterisks. (d)–(f) Composite differences in the zonal-mean temperature (shading; °C) and in the scaled residual velocity (
Citation: Journal of Climate 34, 17; 10.1175/JCLI-D-20-0960.1
The composite difference in zonal-mean temperature and the residual velocity (
The composite sea level pressure difference in late winter (January–March) between the easterly QBO and westerly QBO is shown in Figs. 4g–4i. As the stratospheric polar vortex weakens during easterly QBO in the reanalysis (Fig. 4g), a dipole sea level pressure pattern forms in the Atlantic–Europe sector, which highly resembles the negative NAO (Baldwin et al. 2001; Gray et al. 2018). The NAO-like response pattern is not simulated by the CMIP5/6 MME due to the underestimation of the HT relationship (Fig. 4h), and the pressure pattern is even opposite sign to that in reanalysis (Rao et al. 2020b). In contrast, MiMA well simulates the near surface response in the Atlantic–Europe sector, with the pressure rising around Iceland and decreasing in midlatitudes (Fig. 4i).
4. Establishment of the polar vortex response to QBO
To delineate the establishment of the polar vortex response to the QBO, we have performed branch runs from the Control experiment. Some studies emphasize the seasonal synchronization of the QBO on the timing of the strongest HT relationship (Anstey et al. 2010; Garfinkel and Hartmann 2011a,b; Anstey and Shepherd 2014). A comparison between the HT relationship in seasonal branch runs and perpetual branch runs with fixed incoming solar radiation might provide a better understanding of the timing of QBO teleconnections. The fixed profile of equatorial zonal-mean zonal winds between 100 and 10 hPa is shown in Fig. 5 for all easterly and westerly QBO branch runs, which come from the raw (i.e., not anomalous) zonal wind composite of the reanalysis. Although the relaxed wind profiles are the same for perpetual (November–February) and seasonal branch runs (black), the modified winds are somewhat different in the first 20 days in those runs (colors in Figs. 5a,e). In the second 20 days, the equatorial zonal winds have finished relaxing to the fixed profile in all branch runs (Figs. 5b,f), and the relaxed profile is nearly constant in the remaining days in those branch runs (Figs. 5c,d,g,h). We leave for future work an exploration of the extratropical stratospheric response to other QBO phases, such as the QBO maximized at 50 hPa.
Vertical profiles of the nudged (fixed, interpolated to MiMA pressure levels) zonal winds near the equator (5°S–5°N) and the equatorial zonal wind response to the nudging in different runs: shown are the means from days (left) 1–20, (left center) 21–40, (right center) 41–70, and (right) 71–100 for zonal-mean zonal winds in (a)–(d) easterly and (e)–(h) westerly QBO runs. The black line shows the nudged equatorial zonal winds (m s−1), and colored lines show the adjustment of the equatorial zonal winds to the fixed nudging (purple: November runs; red: December runs; orange: January runs; navy blue: February runs; blue: seasonal runs).
Citation: Journal of Climate 34, 17; 10.1175/JCLI-D-20-0960.1
a. Seasonal experiments by MiMA
The composite difference between the easterly and westerly QBO seasonal branch runs is shown in Figs. 6a–6d for the E-P flux (scaled to show the stratospheric response) and its divergence for branch runs initialized on 1 January (note that these runs include the seasonal cycle). The extratropical response to QBO first appears during days 1–20: large-scaled E-P flux anomalies first appear in the upper stratosphere, and the E-P flux divergence/convergence anomalies in the upper stratosphere is much larger than in the troposphere (Fig. 6a). This is different from the HT mechanism, which emphasizes the upward and poleward propagation of waves in the lower stratosphere. The E-P flux divergence dipole anomaly further strengthens with fewer waves converging in the subtropical upper stratosphere rather than in the polar upper and midstratosphere (Fig. 6b). The E-P flux divergence dipole response matures during days 41–70 and begins to decay during days 71–100, although the QBO forcing is still present in the tropical stratosphere (Figs. 6c,d). Namely, without a weakening of the QBO forcing, the extratropical response to QBO reaches a statistically steady state within ~2.5 months.
Composite differences in the scaled E-P flux (Fy/ρ0, 100 × Fz/ρ0; vectors; m3 s−2) and in the E-P flux divergence (shading; m s−1 day−1) between the seasonal runs with easterly QBO nudging and those with westerly QBO nudging in days (a) 1–20, (b) 21–40, (c) 41–70, and (d) 71–100 relative to the initial time. (e)–(h) As in (a)–(d) but for composite differences in the zonal-mean temperature (shading; °C) and in the scaled residual velocity (
Citation: Journal of Climate 34, 17; 10.1175/JCLI-D-20-0960.1
Similarly, the composite difference in the zonal-mean temperature and residual velocity between the easterly and westerly QBO seasonal branch runs is shown in Figs. 6e–6h. The direct response of the temperature in the tropical stratosphere occurs within the first 20 days after the QBO forcing is turned on (Fig. 6e). The meridional cells directly associated with the QBO temperature anomaly is excited between the equator and 30°N. The downwelling in the Arctic stratosphere well explains the local warm anomalies (albeit insignificant) via the adiabatic heating. The Arctic warm anomaly center gradually descends in the following periods (Figs. 6f–h), but the magnitude diminishes little with a constant QBO forcing. During days 71–100, the Arctic downwelling response weakens, possibly as a result of the reduced wave propagation into the weakened vortex in days 71–100.
The stratospheric polar vortex is a key medium bridging the QBO and the circulation in the North Atlantic–Europe sector. Variations in the stratospheric polar vortex project onto the annular mode, which propagates downward to change the phase of the North Atlantic Oscillation (NAO) (Baldwin et al. 2001; Cao et al. 2019). The composite surface pressure difference between the Sea_EQBO and Sea_WQBO runs is shown in Figs. 6i–6l. A negative NAO-like response is modeled 20 days after the QBO forcing is turned on, and the midlatitude negative pressure response gradually intensifies. Although a positive pressure response center forms finally near Iceland, the composite-mean anomaly is not significant at the 90% confident level. In contrast, the midlatitude negative pressure response center near the Azores during days 21–40 and afterward is robustly present (Figs. 6k,l). In summary, a time lag exists between the polar vortex signal and the near-surface response, and the NAO-like response to the QBO reaches the maximum ~40 days after QBO winds are imposed and changes little afterward.
b. A parallel comparison between perpetual branch runs
In observations the QBO phase with peak anomalies in the lower stratosphere can begin in any month of the year, but the composite HT relationship is largest in early to midwinter and the near-surface response is strongest in mid-to-late winter (e.g., Garfinkel et al. 2012; Gray et al. 2018). Is this a random phenomenon or a subseasonal locking of the QBO’s impact? Rao et al. (2020b) emphasize the vital importance of the QBO phase in CMIP5/6 models, although most models still struggle to model a reasonable surface response following the QBO. The composite scaled E-P flux and its divergence are shown in Fig. 7 for perpetual runs for 4 months (November–February). In all four perpetual runs, an E-P flux divergence dipole already appears in days 1–20 and includes less wave convergence in the subtropical upper stratosphere but more convergence near the polar upper stratosphere (first column in Fig. 7). In contrast, a tendency for less wave propagation into the equatorial lower stratosphere during EQBO (i.e., the HT mechanism with poleward directed arrows in the EQBO minus WQBO difference) does not appears until days 21–40 for January and February branches [Figs. 7b(3),b(4)], and days 41–70 for November and December [Figs. 7c(1),c(2)].
Composite differences (i.e., easterly QBO minus westerly QBO composite) in the scaled E-P flux (Fy/ρ0, 100 × Fz/ρ0; vectors; m3 s−2) and in the E-P flux divergence (shading; m s−1 day−1) between the month-perpetual runs with easterly QBO nudging and those with westerly QBO nudging in days (a) 1–20, (b) 21–40, (c) 41–70, and (d) 71–100 relative to the initial time for differences for the (top) November, (top middle) December, (bottom middle) January, and (bottom) February runs.
Citation: Journal of Climate 34, 17; 10.1175/JCLI-D-20-0960.1
The time scale of the E-P flux divergence anomaly in the polar stratosphere also differs among the different branch dates: it moves poleward and fades quickly for the November run, fades after 40 days for the December and January runs, but persists throughout the 120-day integration in February runs. While this delayed response for the February runs is not immediately relevant to observations as in reality the final warming would have already occurred at such a long time lag, these results highlight why the observed HT relationship appears stronger in January and February than in November. Namely, there is a difference in the formation and persistence of upward wave flux associated with QBO among the different calendar months, even as the EP flux dipole in the subtropical upper stratosphere in the first 20 days is similar in all four perpetual runs.
The composite difference in the evolution of temperature and residual velocity is shown in Fig. 8 for perpetual runs. The most prominent feature in this figure is the gradual poleward expansion of the meridional circulation in the upper stratosphere. As a consequence, the extratropical cold anomalies in the upper stratosphere intensify and even cover the Arctic in days 41–100 for midwinter perpetual runs as the initial warming of the vortex propagates downward (December and January; second and third rows in Fig. 8). Consistent with the upward-propagating wave response in Fig. 7, the Arctic downwelling ends at different periods: the sign changes during days 71–100 for November runs (first row), and the ending time is earlier for December and January runs (second and third rows), but it is persistent throughout the February run (fourth row).
As in Fig. 7, but for the zonal-mean temperature (shading; °C) and the scaled residual velocity (
Citation: Journal of Climate 34, 17; 10.1175/JCLI-D-20-0960.1
It is suggested the extratropical response to the QBO has different evolutions in different background states. The modeled early winter response appears quickly at high latitudes in the November perpetual run, but the quick response is weaker in amplitude than the midwinter perpetual runs. The response under the midwinter perpetual condition is faster, and the response to an early winter QBO forcing is relatively slow. This difference pace in the reaction of the extratropical circulation to the QBO might explain the composite response in the stratosphere maximized in midwinter: early winter forcing has a slower evolution of extratropical wave response, favoring the maximum response in midwinter; in contrast, midwinter forcing has a near-instantaneous wave response with the maximum also falling in midwinter.
How long does it take for the near-surface response to develop? Recall that the surface response is strongest in January and later (Gray et al. 2018). Figure 9 presents the composite surface pressure difference between EQBO and WQBO branch runs. During the first 20 days after the QBO is relaxed (note that the relaxation time scale is 10 days), no significant surface response appears in any of the perpetual runs (Fig. 9a). The most striking feature is the contrast in the timing of the significant low anomaly center over the midlatitude Atlantic. An NAO-like pattern does not appear for the November runs consistent with the relatively weak polar lower stratospheric response (first row in Fig. 9), and the pressure anomaly sign does not change from the midlatitude Atlantic to the Arctic. A negative NAO-like response does appear after 21 days for the other three runs with the Arctic pressure rising and/or midlatitude Atlantic pressure decreasing (second–fourth rows in Fig. 9). Despite no evident high anomaly center over the Arctic (not significant at the 90% and 95% confidence levels), the low anomaly band across midlatitude Atlantic is mainly projected to the negative phase of NAO during days 21–40 and 41–70 (second row in Fig. 9) for December perpetual runs. The high center over Iceland forms in the second 20 days after the QBO forcing is relaxed in January and February perpetuals runs (third and fourth rows in Fig. 9). The negative NAO-like response also decays earlier in midwinter perpetual runs. The Arctic surface high pressure anomaly center gradually diminishes during days 71–100 for December and January perpetual runs, and it still persists in the February perpetual run (Fig. 9d).
Composite differences in the surface pressure (contours; Pa, with interval of 100 Pa) between the month-perpetual runs with easterly QBO nudging and those with westerly QBO nudging in days (a) 1–20, (b) 21–40, (c) 41–70, and (d) 71–100 relative to the initial time for the (top) November, (top middle) December, (bottom middle) January, and (bottom) February runs. The zero contours are skipped for clarity. The light and dark shadings show the pressure anomalies at the 90% and 95% confidence levels, respectively.
Citation: Journal of Climate 34, 17; 10.1175/JCLI-D-20-0960.1
5. Summary and discussion
a. Summary
Recent studies have revisited the HT relationship based on observations and assessed its reproducibility in the state-of-the-art complex models. However, the mechanism whereby the extratropical response to the QBO becomes established is not clearly known. The sensitivity of the HT relationship and the extratropical QBO signal in the troposphere to the mean state in different months is explored in this study using an idealized model with equatorial zonal winds relaxed toward the easterly and westerly QBO, respectively.
As a moderate-complexity model, MiMA can generate a QBO albeit with a westerly bias in the tropical stratosphere. The simulated QBO amplitude and cycle by MiMA are comparable to most comprehensive CMIP5/6 models. Based on three modern reanalyses (ERA5, ERA-Interim, and JRA-55), the QBO has a mean period of ~28 months and a mean magnitude of ~20 m s−1. Most CMIP5/6 models tend to simulate a shorter QBO cycle and a smaller QBO magnitude below 20 hPa estimated by the variability of the equatorial zonal winds. MiMA reasonably simulates the amplitude and period of the QBO, falling within the intermodel spread of CMIP5/6. The polar vortex variability measured by the frequency of SSWs is also evaluated for MiMA (e.g., White et al. 2020). On average, five or six SSWs occur every decade in the reanalysis, which is underestimated somewhat in MiMA. MiMA reproduces a much better SSW frequency (~0.5 yr−1) than does the CMIP5 MME (~0.3 yr−1), although it does not do as well as CMIP6 MME (~0.6 yr−1).
The HT relationship is also well simulated by MiMA: the composite warm anomalies in the Arctic stratosphere and easterly anomalies in the circumpolar region are realistically produced by MiMA. As in the reanalysis, the upward and poleward propagation of waves is enhanced from the midlatitude tropopause to the stratosphere in the MiMA free run (Control) during the easterly QBO winter as compared with westerly QBO. MiMA seems to show a higher skill of reproducing the polar vortex response to the QBO than most CMIP5/6 models (Rao et al. 2020a). The two corresponding meridional cells above and below the QBO center spanning from tropics to midlatitudes, as a direct response to the QBO, are captured by MiMA. The magnitude of the composite downwelling (EQBO minus WQBO) in the Arctic stratosphere, as well as the local warm temperature response, is more realistically simulated by MiMA than the CMIP5/6 MME. The ability of MiMA to reproduce the stratospheric response associated with the QBO confirms the validation and usefulness of this model in our study.
The extratropical instantaneous response to the QBO is first simulated in seasonal runs (Sea_EQBO minus Sea_WQBO), and the relative importance of the E-P divergence dipole in the upper stratosphere and the HT mechanism is tested. In the tropics, the direct response of the meridional cells and temperature forms instantly with the constant QBO wind forcing. In contrast to the HT mechanism, which emphasizes changes in the propagation of waves near the zero wind line in the lower stratosphere, an E-P flux divergence/convergence dipole forms rapidly in the upper stratosphere between 20° and 80°N with anomalous dissipation in the circumpolar region and less convergence in the subtropics in the upper stratosphere. The wave dissipation in the subpolar region seems to develop faster than the HT effect at the early stage of the QBO forcing [in agreement with Garfinkel et al. (2012) but contrary to Watson and Gray (2014)]. Specifically, in the first 20 days after the QBO relaxation in the equatorial stratosphere is switched on, changes in midlatitude tropospheric waves or subtropical lower stratospheric waves are relatively weak. Namely, the HT mechanism is not significant in the first 20 days. After the polar vortex begins to weaken due to changes in wave propagation in the upper stratosphere, tropospheric wave feedbacks become active to affect the polar vortex. Although the QBO is relaxed constantly, warm anomalies in the Arctic stratosphere still descend gradually. An NAO-like response forms 40–71 days after the QBO relaxation is switched on in the seasonal branch runs.
The sensitivity of the formation time and persistence of the HT relationship to the month is also tested by performing perpetual branch run with the date of the year fixed in mid-November, December, January, and February, respectively. Therefore, the modulation of the QBO’s effect by the mean state (i.e., the mean state varies with month) can be explored. All branch runs show a nearly instantaneous response of the E-P flux divergence dipole between 20° and 80°N in the upper stratosphere, and a simultaneous response of meridional circulation cells and temperature in the tropical stratosphere. The HT relationship begins at different times in branch runs for the four months: It appears during days 41–70 in November and December branch runs, earlier (days 1–40) in mid-to-late winter branch runs, and throughout the whole relaxation time in February runs. Without an annual cycle, the Arctic warm anomaly associated with the QBO also descends in perpetual runs, but the maximum signal appears just before the anomalous upward propagation of waves stops (i.e., later in November and December runs, and earlier in mid-to-late winter runs). As a consequence, the mature NAO-like response in the Atlantic sector forms later in December runs (the NAO-like response in November run is not evident) but earlier in mid-to-late winter runs (days 21–40). The near-surface high pressure anomaly in the Arctic and/or low pressure anomaly in midlatitude Atlantic during EQBO diminishes more rapidly in December and January perpetual runs than the February perpetual runs.
b. Discussion
Previous studies have emphasized the seasonal synchronization of the QBO phase to explain the seasonality of the strongest HT relationship in midwinter (e.g., Anstey et al. 2010; Rajendran et al. 2016, 2018). Christiansen (2010) suggests that the seasonality of the QBO phase might be a random process associated with the annual sampling of the QBO. However, CMIP5/6 models show a relatively even seasonal distribution of the QBO phases, and the HT relationship in those models is more dependent on the QBO phase than the month (Rao et al. 2020a). Rao et al. (2020a) calculated the probability density of the QBO phases, which is more uniform in models than the reanalyses. In this study, the QBO relaxation and the initial EP flux divergence dipole in the upper stratosphere is similar in all months. However, the subsequent feedback by waves in the troposphere and lower stratosphere to the QBO differs among the months, with a vortex response simulated only for December–February. Another recent study using this model but focusing on the solar cycle also found that the midwinter vortex responds more quickly to an external forcing than the November vortex (Givon et al. 2021).
Our results from the branch runs forced by an observed QBO profile are generally consistent with Garfinkel et al. (2012), and they emphasize the direct mean meridional circulation response to the easterly QBO, which also creates a barrier to planetary wave equatorward propagation in the middle and upper stratosphere. Changes in the subtropical critical line emphasized in the HT mechanism is not as evident as the direct effect of the mean meridional circulation. Our study further reveals that the direct response of the mean meridional circulation is also much stronger than the HT mechanism on shorter time scale, inconsistent with Watson and Gray (2014). Watson and Gray (2014) find that the transient vortex response to the QBO on the shorter time scale is consistent with the HT mechanism, but the HT mechanism works much later than the direct meridional circulation response in our experiments.
Our study might suggest that the direct responses to the QBO develops fast, and they are more related to the QBO phase than the specific month of the year. Branch runs in October and March were also performed with MiMA but not shown for brevity, and the direct response is nearly identical to branch runs in November–February. Specifically, the equatorial stratospheric temperature anomaly dipole forced by the QBO wind center via the thermal wind balance and the meridional circulation cells are established soon after the QBO winds are relaxed. Associated with the meridional cells, an anomalous upwelling is produced in the extratropical upper stratosphere for an easterly QBO relaxation instantly, accounting for the local cold anomalies. Conversely, warm anomalies develop fast in the midlatitude lower stratosphere associated with the local downwelling. In addition, the E-P flux divergence dipole develops nearly at the same pace in all branch runs.
In contrast, the wave response in the lower stratosphere evolves differently in perpetual branch runs. The HT mechanism emphasizes the upward propagation of waves, but this effect depends on the initial month and the mean state. The tropospheric jet gradually strengthens from November to February in both the reanalysis and MiMA (Fig. 1; November not shown). It is evident that the tropospheric (indirect) response to the QBO is faster in mid-to-late winter runs than November runs. This study might suggest that the QBO’s influence is also sensitive to the intensity of the tropospheric jet. The upward propagation of waves also reacts at different time to the QBO relaxation in branch runs of the four months. Accordingly, in the Atlantic sector, the NAO-like response matures mainly in midwinter branch runs but not November runs.
In short, we do not deny the role of the specific QBO phase and the seasonal synchronization of the QBO for the tropospheric response. However, this study provides us a new perspective into the observed seasonal locking of the tropospheric response to the QBO related to the reaction time since the QBO is relaxed (slow in early winter and fast in midwinter). The initial fields of all branch runs are from the restart files on 1 January of the free Control run, which has been hypothesized not to speed the establishment of the HT relationship in the January branch run. The QBO profile for the branch runs is maximized around 30 hPa in this study; sensitivity experiments forced by evolving QBO with a realistic cycle of 28 months and by the QBO maximized at 50 hPa and other neighboring levels should be conducted in future work.
Acknowledgments
Author Rao was funded by the National Natural Science Foundation of China (Grants 42030605 and 41705024). Authors Garfinkel and White are funded by the ISF-NSFC joint research program (3259/19) and the European Research Council starting grant under the European Union’s Horizon 2020 research and innovation program (677756). All data used in this study are publicly available. The CMIP5/6 simulations are available through the ESGF (https://esgf-node.llnl.gov/projects/esgf-llnl/). Our experiments are performed using the Model of an Idealized Moist Atmosphere (MiMA), version 2, which is updated by Garfinkel (https://zenodo.org/record/3984605#.X2kPoJMzZsN). We also acknowledge the ECMWF and JMA for providing three modern reanalyses (ERA-Interim, ERA5, and JRA-55). ERA-Interim is available from https://apps.ecmwf.int/, ERA5 is available from https://cds.climate.copernicus.eu/, and JRA-55 is available from https://jra.kishou.go.jp/JRA-55/index_en.html.
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