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  • View in gallery

    Zonal-mean zonal wind (shaded), domain-averaged 1-day precipitation (light gray lines), and smoothed precipitation (thick blue lines) of model-top experiments. The horizontal dashed cyan lines indicate the bottom of the Rayleigh damping layer.

  • View in gallery

    (a),(c) Amplitudes and (b),(d) phases of the QBO-like oscillation of (a),(b) model-top experiments and (c),(d) low-level nudging experiments. The downward phase propagation of the oscillation is represented by the descent of the 0 m s−1 line of the zonal-mean zonal wind at the bottom of the Rayleigh damping layer. The cross symbol on each line marks the half-oscillation period and indicates the switching time when the opposite phase begins from the bottom of the Rayleigh damping layer. See the text for more details of how these plots are constructed.

  • View in gallery

    (a),(c) Statistical properties of 1-day smoothed precipitation. The inner boxes indicate the first, second, and third quartiles; the blue and red crosses indicate the 10th and 90th percentiles; and the whiskers indicate minimum and maximum values. (b),(d) Differences of the absolute value of vertical shear of the zonal-mean zonal wind between days with smoothed precipitation greater than the 90th-percentile values and less than the 10th-percentile values. Red filled circles, red open circles, small red circles, and blue circles indicate the values that are significant at greater than the 99%, 95%, 90%, and <90% levels, respectively. (a),(b) Model-top experiments; (c),(d) low-level nudging experiments.

  • View in gallery

    Smoothed precipitation (gray lines) and absolute vertical shear of the zonal-mean zonal wind at z = 1 (green lines) and 8 km (yellow lines), plotted in a normalized time with a reference level of 8 km for model-top experiments. See the text for the descriptions of the normalized time.

  • View in gallery

    As in Fig. 1, but for low-level nudging experiments. The horizontal dashed gray line in each panel indicates the upper nudging level [z2 in Eq. (4)].

  • View in gallery

    As in Fig. 4, but for low-level nudging experiments. In this case, the reference level of 18 km is chosen instead of that of 8 km.

  • View in gallery

    (a),(c) Zonal-mean zonal wind (shaded and black contour lines; m s−1) and its vertical shear (red and blue dashed contour lines; ×10−3 s−1). (b),(d) Domain-averaged 1-day precipitation (green bars) and smoothed precipitation (gray line with circles). Smoothed precipitation that is over the 90th (under 10th) percentiles is colored red (blue). The red (blue) rectangles indicate time windows in (b) and (d) that will be used for composite calculation of heavy (light) precipitation conditions. The symbol on the top of each window indicates if the fields are horizontally flipped (minus sign) or not (plus sign). See the text for the description of the composite analysis procedure.

  • View in gallery

    (a),(b),(e),(f) Hovmöller diagrams and (c),(d),(g),(h) time series of domain-averaged 5-min precipitation of some notable examples of composite windows indicated by the red and blue boxes in Figs. 7a and 7c.

  • View in gallery

    Hovmöller diagram of composite 5-min precipitation (white contour; mm) and 250-m temperature (shaded; °C) for the (a),(c) light and (b),(d) heavy precipitation conditions of the (a),(b) Control and (c),(d) Nudge7_10 experiments. The dotted white lines indicate the averaged propagation speed of precipitation systems.

  • View in gallery

    (a),(e) Zonal-mean profiles at the key time of zonal wind, (b),(f) vertical shear of zonal wind, (c),(g) temperature anomaly, and (d),(h) static stability for the (a)–(d) Control and (e)–(h) Nudge7_10 experiments. Red lines are for the heavy precipitation condition, and blue lines are for the light precipitation condition. The vertical red and blue dashed lines in (a) mark the averaged propagation speed of precipitation systems for heavy and light conditions, respectively.

  • View in gallery

    (a),(b),(e),(f) Cross section of composite vertical speed (rainbow contours; m s−1) and streamline of zonal wind relative to the propagation speed. (c),(d),(g),(h) Cross sections of composite water cloud (gray shades; ×10−2 g kg−1), ice cloud (blue shades; ×10−2 g kg−1), rainwater (red contours; ×10−1 g kg−1), and potential temperature (orange contours; K).

  • View in gallery

    (a),(d) Composite mixing ratio of rainwater (red lines; 5 × 10−1 g kg−1), cloud water (black lines; ×10−2 g kg−1), and cloud ice (blue lines 5 × 10−2 g kg−2) at the cloud and precipitation center; (b),(e) composite temperature anomaly (°C) at center of the cloud (magenta lines) and rain (cyan lines); (c),(f) composite vertical velocity (m s−1) at center of the cloud (magenta lines) and rain (cyan lines). In all panels, heavy precipitation composite conditions are denoted by thick lines, and light precipitation conditions are denoted by thin lines.

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Downward Influence of QBO-Like Oscillation on Moist Convection in a Two-Dimensional Minimal Model Framework

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  • 1 Department of Geophysics, Kyoto University, Kyoto, Japan, and Vietnam National University of Science, Hanoi, Vietnam
  • | 2 Department of Geophysics, Kyoto University, Kyoto, Japan
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Abstract

The influence of the quasi-biennial oscillation (QBO)-like oscillation on moist convection is examined using the two-dimensional minimal model framework of Yoden et al. with two series of parameter sweep experiments: model-top experiments with varying model height and low-level nudging experiments with reduced zonal-mean zonal wind toward zero from the surface to a certain level. The QBO-like oscillation in the mean zonal wind is a robust feature obtained in all the experiments, including low-top cases in which only the tropospheric portion is retained. The zonal-mean precipitation is modulated with a half period of the mean zonal wind oscillation in the model-top experiments, and a positive correlation exists between the precipitation intensity and the vertical shear of the mean zonal wind near the surface. The precipitation modulation is weakened with a nudging of the low-level mean zonal wind but appears again in the cases with the low-level nudging in the middle and lower troposphere. There is a negative correlation between the precipitation intensity and the vertical shear of the mean zonal wind in the upper troposphere. These results suggest that the QBO-like oscillation modulates the moist convection via two mechanisms related to the vertical shear. Large values of the shear near the surface enhance the longevity and intensity of the moist convective systems by separating the updraft and downdraft. On the other hand, large values of shear near the cloud top tend to disrupt the convective structure and lead to weakening moist convection, although this mechanism seems to be secondary.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Hoang-Hai Bui, haibh@vnu.edu.vn

Abstract

The influence of the quasi-biennial oscillation (QBO)-like oscillation on moist convection is examined using the two-dimensional minimal model framework of Yoden et al. with two series of parameter sweep experiments: model-top experiments with varying model height and low-level nudging experiments with reduced zonal-mean zonal wind toward zero from the surface to a certain level. The QBO-like oscillation in the mean zonal wind is a robust feature obtained in all the experiments, including low-top cases in which only the tropospheric portion is retained. The zonal-mean precipitation is modulated with a half period of the mean zonal wind oscillation in the model-top experiments, and a positive correlation exists between the precipitation intensity and the vertical shear of the mean zonal wind near the surface. The precipitation modulation is weakened with a nudging of the low-level mean zonal wind but appears again in the cases with the low-level nudging in the middle and lower troposphere. There is a negative correlation between the precipitation intensity and the vertical shear of the mean zonal wind in the upper troposphere. These results suggest that the QBO-like oscillation modulates the moist convection via two mechanisms related to the vertical shear. Large values of the shear near the surface enhance the longevity and intensity of the moist convective systems by separating the updraft and downdraft. On the other hand, large values of shear near the cloud top tend to disrupt the convective structure and lead to weakening moist convection, although this mechanism seems to be secondary.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Hoang-Hai Bui, haibh@vnu.edu.vn

1. Introduction

The stratospheric quasi-biennial oscillation (QBO) is the prominent variability of the equatorial stratospheric zonal wind between westerly and easterly regimes with a period of approximately 28 months (Baldwin et al. 2001). Although the QBO is essentially a stratospheric phenomenon, observational studies show that the QBO may influence tropical moist convection (e.g., Collimore et al. 2003; Liess and Geller 2012). The connection between the QBO and moist convection is thought to be the key link between the QBO and other phenomena such as ENSO (Gray et al. 1992; Huang et al. 2012; Hansen et al. 2016), monsoon (Giorgetta et al. 1999), and MJO (Yoo and Son 2016; Nishimoto and Yoden 2017).

Some early observational studies also found the relation between the QBO and tropical cyclones (TCs), which is a mesoscale organization of convective systems in low latitudes. For example, Gray (1984) found that TC activity in the Atlantic was greater in the westerly phase of the QBO (W-QBO) than that in the easterly phase of the QBO (E-QBO), although such a statistically significant relationship was not obtained for a longer dataset including the period of 1983–2008 (Camargo and Sobel 2010). Even though these are controversial results, we have some recent studies on possible relationship between the QBO and TCs; Ho et al. (2009) reported the QBO influence on TC tracks in the western North Pacific, and Fadnavis et al. (2014) reported that over the Bay of Bengal region. Recent studies also show the stratospheric temperature trend near the tropopause may have influenced TC activity in the tropical North Atlantic basin (Emanuel et al. 2013; Vecchi et al. 2013).

There are some possible processes that could account for the influence of the QBO on tropical deep moist convection. The QBO-associated meridional circulations and temperature anomalies (Plumb and Bell 1982) change the dynamic and/or thermodynamic condition in the lower stratosphere and the upper troposphere that may influence the convection activity. The positive anomaly of the tropopause height in the E-QBO favors stronger convection because of the stronger upper-level divergence and deeper convective clouds (Gray et al. 1992; Collimore et al. 2003). A colder tropopause in the E-QBO may lead to a destabilized troposphere (lower static stability) and a stronger convection condition (Giorgetta et al. 1999; Garfinkel and Hartmann 2011). Recently, Nie and Sobel (2015) suggested that in the colder tropopause of E-QBO, the convection may be enhanced at upper levels but decreased below, which may lead to a complicated relationship between the QBO and precipitation over warm pool regions; the equilibrium precipitation rate shows slight increases in response to an E-QBO temperature perturbation and small SST anomalies but strong decreases over large SST anomalies.

The QBO-induced vertical shear of the zonal-mean zonal wind between the lower stratosphere and upper troposphere (i.e., cross-tropopause shear) itself may play a role in the modulation of moist convection. The strong cross-tropopause shear in the W-QBO may disrupt the heating effect of the convective cloud to the lower stratosphere (Gray et al. 1992), “shear off” the top of deep convective clouds (Collimore et al. 2003), and weaken the feedback mechanism of moist convection. Gray et al. (1992) suggested that the QBO may also influence moist convection in off-equator regions where the cross-tropopause shear is weak during the W-QBO. Collimore et al. (2003) showed that the convective signals as indicated by the outgoing longwave radiation (OLR) and high reflective cloud (HRC) indices are physically consistent with the QBO variations of the cross-troposphere zonal wind shear in some parts of the tropics while in other parts they are not.

Held et al. (1993) obtained an internally generated zonal-mean zonal wind oscillation that is qualitatively similar to the QBO with a two-dimensional cloud-resolving model for a total integration period of 107 s (about 116 days). This QBO-like oscillation was reconfirmed by Yoden et al. (2014, hereafter YBN14) in a similar two-dimensional minimal model framework with a longer integration period of 2 years, and the robustness of the oscillation was proved to be insensitive to the model configurations and experiment settings. The oscillation is analogous to the QBO as it is the result of the interaction between the zonal-mean zonal wind and gravity waves (Nishimoto et al. 2016).

One important finding of YBN14 is that the zonal-mean precipitation also varies periodically in accordance with the QBO-like oscillation. Unlike studies that rely on integration periods of several days, YBN14 took an approach that employed a long integration period in order to ensure a quasi-equilibrium state after the initial transition. The modulation of precipitation by the QBO-like oscillation may provide some hints to the influence of the QBO on tropical deep moist convection as reviewed above. A high temporal output from YBN14’s framework was analyzed by Nishimoto et al. (2016), and it was revealed that the precipitation modulation is associated with the alternate appearance of precipitation patterns of back-building type (a new convective system emerges at the rear side of the previous one) and squall-line type (a new convective system emerges at the front side of the old one). This modulation of precipitation depends on magnitudes of the vertical shear of zonal-mean zonal wind near the surface.

In this study, we continue using the minimal model framework of YBN14 to further investigate the downward influence of the internally generated QBO-like oscillation to deep moist convection under quasi-equilibrium states obtained by a long time integration over 2 years by carrying out two series of parameter sweep experiments. The first one, model-top experiments, investigates the effect of the model height to the precipitation modulation. The second one, low-level nudging experiments, examines the precipitation modulation when the low-level zonal-mean zonal wind is nudged toward zero from the surface to a certain level. This second series of experiments is carried out to eliminate the effects of the vertical shear of low-level zonal-mean zonal wind. It is also noted that this nonrotation framework without the Coriolis effects also eliminates the dynamical constraints of the thermal wind relationship and the tropopause height/temperature variations associated with the QBO. Thus, the effects of vertical shear of high-level zonal-mean zonal wind can be isolated.

The rest of this paper is organized as follows. The model descriptions, nudging methods and detailed experimental designs are described in section 2. Section 3 gives results on the obtained properties of the QBO-like oscillation and its relation with the precipitation. In section 4, a composite analysis is performed on two prominent examples with a high temporal output resolution of 5 min to have a look at the detailed structures of the deep moist convective systems in different precipitation conditions. The role of vertical shear of zonal-mean zonal wind on moist convection and its relevance with the equatorial QBO are discussed in section 5, and conclusions are given in section 6.

2. Model descriptions and experiment design

a. Model descriptions

Similar to YBN14, the model used here is version 3.4 of the Advanced Research of the Weather Research and Forecasting Model (ARW) (Skamarock et al. 2008). The model is configured to run in a two-dimensional framework in a periodic domain of 640-km width and 5-km horizontal resolution. The initial domain top of the Control experiment is 40-km height with 200 vertical levels. Lower model-top cases have fewer vertical levels so that the vertical resolution is kept at 200 m on average. The diurnal and seasonal variations of solar radiation are removed by setting the solar declination to the equinox condition and the solar insolation to the daily averaged value (436 W m−2). The Coriolis parameter is set to zero, and the sea surface temperature is fixed to 27°C throughout the integration. In the model, convective parameterization is turned off and moist convection is represented explicitly. For cloud microphysics, the WRF single-moment 6-class microphysics scheme (WSM6) is used. Other physics options include the Rapid Radiative Transfer Model (RRTM) longwave radiation, MM5 (Dudhia) shortwave radiation, Yonsei University (YSU) PBL, Monin–Obukhov similarity theory surface layer, and the 1.5-order prognostic TKE closure option for the eddy viscosities.

The initial state is constructed by using the climatological profiles of equatorial temperature and moisture from the ERA-Interim dataset (Dee et al. 2011) with an initial perturbation of a small warm bubble in the middle of the domain as described in YBN14. The initial zonal wind is slightly greater than zero in a thin horizontal band in the stratosphere or in the middle of the domain in case of lower model top. The purpose of this is to break up the zonally symmetric condition and to speed up the initial transition time.

There is a traditional Rayleigh damping layer in the top 5 km of the model to absorb gravity waves and to nudge the top conditions to the reference states (Skamarock et al. 2008). This scheme simply adds an additional linear relaxation term to the tendency equations in the form
e1
where φ represents zonal wind u, vertical wind w, or potential temperature θ. The variable represents the reference states, which is zero for , , and the climatological vertical profile for . The coefficient that defines the vertical structure of the Rayleigh damping layer has the form
e2
where the damping coefficient in this study takes the value 3 × 10−3 s−1, is the height of the model, and is the depth of the Rayleigh damping layer with the value of 5 km.

b. A low-level nudging method

In our minimal framework of QBO-like oscillation, as shown in YBN14 and in the next section, the oscillation of the zonal-mean zonal wind penetrates into the troposphere and modulates the vertical shear of the zonal-mean zonal wind in the troposphere. In this study, we introduce a simple nudging scheme to reduce the vertical shear of the zonal-mean zonal wind near the surface to zero. Similar to the Rayleigh damper described above, the nudging scheme applies a linear relaxation term to the zonal wind tendency equation. The difference of this nudging scheme compared with the Rayleigh damper is that it only reduces the zonal-mean zonal wind to zero, while it retains horizontal convergence or divergence. The additional tendency term has the form
e3
where the overbar means the zonal averaging operator and represents the vertical structure of the nudging strength that takes the form
e4
where is equal to the prescribed coefficient from the surface to , from where it gradually decreases to zero at . In this study, a weak value of is chosen for after some initial trial-and-error tests. With this value, the zonal-mean zonal wind is mildly nudged toward zero, but some small perturbations are allowed. It is possible to specify below the surface (negative value). In this case, the maximum value of is located at the surface and smaller than .

c. Experimental design

Two series of parameter sweep experiments are performed in this study to investigate the downward influence of QBO-like oscillation to activities of moist convection. The first series, model-top experiments, changes the height of the model domain from 40 (Control) to 15 km to examine the robustness of the precipitation modulation with the choice of model height. The 12 experiments are denoted as TopXX, where XX denotes the initial height of the domain: Top40 (=Control), Top38, Top36, Top34, Top32, Top30, Top28, Top26, Top24, Top22, Top20, and Top15.

In the second series, low-level nudging experiments, the zonal-mean zonal wind is nudged toward zero by changing the depth of the nudging levels from 2 to 14 km with the same transition depth z2z1 = 3 km. The purpose of this series is to isolate the effect of the zonal-mean state around the tropopause by removing the effect of low-level shear of the zonal-mean zonal wind. The eight experiments are denoted as NudgeYY_ZZ, where YY and ZZ denote and in Eq. (4), respectively: Nudge0_0 (=Control), Nudge–1_2, Nudge1_4, Nudge3_6, Nudge5_8, Nudge7_10, Nudge9_12, and Nudge11_14.

All experiments have integration periods of 2 years (730 days) with a time step of 10 s. The outputs are produced every 24 h and interpolated into a height coordinate of 500 m for further analysis. The first 100 days are considered the spinup transition and are not included in the analysis. To make a detailed analysis of convective systems, two important experiments of Control and Nudge7_10 are rerun for 148 days from day 150 to produce high-frequency outputs of every 5 min.

3. The QBO-like oscillation and the precipitation modulation

a. Model-top experiments

Figure 1 shows the time–height section of the zonal-mean zonal wind and the time series of 1-day domain-averaged precipitation (hereafter unsmoothed precipitation) and those of 15-day running mean of 1-day domain-averaged precipitation (hereafter smoothed precipitation) of model-top experiments from day 100. All the experiments exhibit a clear QBO-like oscillation of the zonal-mean zonal wind that propagates downward from the bottom of the Rayleigh damping layer to the lower troposphere. There is a kink of the oscillation amplitudes near the tropopause, and in the troposphere, the oscillation strengthens and continues propagating down to near the surface. Even in the experiments in which no stratosphere portion is represented (Top15 and Top20), the oscillations of the zonal-mean zonal wind still exist with shorter periods and weaker amplitudes. There is a clear modulation of smoothed precipitation in all experiments with a half period of the zonal wind oscillation in most of the cases. The modulation is not so clear in Top24. In high-top experiments (from Control to Top26), large values of smoothed precipitation are clearly associated with larger variations of unsmoothed precipitation. This relationship may exist, but it is not so clear in the lower-top cases.

Fig. 1.
Fig. 1.

Zonal-mean zonal wind (shaded), domain-averaged 1-day precipitation (light gray lines), and smoothed precipitation (thick blue lines) of model-top experiments. The horizontal dashed cyan lines indicate the bottom of the Rayleigh damping layer.

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-17-0095.1

Figure 2a shows the oscillation amplitudes as a function of height for model-top experiments. For cases with high model top (from Control to Top30), there are two peaks of the amplitudes: a larger one in the stratosphere and another smaller one around the tropopause. The first peak in the stratosphere weakens as the model top is lowered and disappears in Top28.

Fig. 2.
Fig. 2.

(a),(c) Amplitudes and (b),(d) phases of the QBO-like oscillation of (a),(b) model-top experiments and (c),(d) low-level nudging experiments. The downward phase propagation of the oscillation is represented by the descent of the 0 m s−1 line of the zonal-mean zonal wind at the bottom of the Rayleigh damping layer. The cross symbol on each line marks the half-oscillation period and indicates the switching time when the opposite phase begins from the bottom of the Rayleigh damping layer. See the text for more details of how these plots are constructed.

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-17-0095.1

Figure 2b shows the composite zero line of the zonal-mean zonal wind to represent the downward propagation of a particular phase of the QBO-like oscillation. To construct this zero line, first, the downward speed is computed for each height level when there is a change of sign in the zonal-mean zonal wind. The composite of this downward speed is then integrated with time to obtain the downward propagation of the zero line from the bottom of the Rayleigh damping layer. The time of the zero line at the bottom of the Rayleigh damping layer is set to be t = 0 days. The estimated downward speed is not reliable or meaningful when the vertical shear of the zonal-mean zonal wind is not so large. When the value of the vertical shear is below an ad hoc threshold value of 3 × 10−3 s−1, the lines are marked as dashed lines to indicate this unreliability. In general, the phase of oscillation propagates downward fastest (i.e., steepest zero lines) in the upper stratosphere, then it slows down as it reaches the tropopause before it becomes faster again when the phase of oscillation penetrates into the troposphere.

From the illustration of the zero line, the switching level and the switching time of the oscillation can be defined as a point (height, time) on the zero line when the opposite oscillation phase appears at the bottom of the Rayleigh damping layer. Because of the symmetric oscillation, the switching time is equal to the half period of the oscillation. The switching level and switching time for model-top experiments are marked as plus signs in Fig. 2b. It can be seen that the switching level is getting lower with lower model-top runs. The result shows a nonmonotonic relation of oscillation period with model height. The oscillation half period is about 47 days for Control, Top38, and Top36. After that, it increases to about 72 days in Top30 and Top28. As the model top goes lower, the half period decreases and becomes shortest at about 31 days for Top15.

Figure 3a shows some statistical properties of smoothed precipitation. Almost all the experiments show similar mean values of smoothed precipitation of about 2.6 mm day−1 except for Top15, where the value is apparently smaller. For each of the experiments, the 90th percentiles and 10th percentiles of smoothed precipitation are calculated and marked as red and blue crosses, respectively. The mean differences of the absolute vertical shear of the zonal-mean zonal wind (; hereafter absolute shear) between the days when the smoothed precipitation is greater than (hereafter heavy precipitation) and the days when the smoothed precipitation is less than (hereafter light precipitation) are shown in Fig. 3b. In this plot, the statistical significance of the mean difference is determined by a two-sided Student’s t test. Except for Top24, there is a large positive and significant (over 99% confidence level) difference of the absolute shear at z = 1 km between the heavy precipitation period and the light precipitation period, which implies a positive correlation of the low-level shear with the precipitation. The exception of Top24 may result from the fact that the precipitation modulation of this case is not as clear as the others, as shown in Fig. 1. There are also significant differences of the absolute shear between heavy and light precipitation periods at higher levels, but the signs are not consistent among the different experiments. This suggests that the differences at upper levels may partly result from the lag correlation of the vertical shear at 1 km and higher levels. This lag correlation, in turn, results from the downward propagation of zonal-mean zonal wind as shown in Fig. 2b.

Fig. 3.
Fig. 3.

(a),(c) Statistical properties of 1-day smoothed precipitation. The inner boxes indicate the first, second, and third quartiles; the blue and red crosses indicate the 10th and 90th percentiles; and the whiskers indicate minimum and maximum values. (b),(d) Differences of the absolute value of vertical shear of the zonal-mean zonal wind between days with smoothed precipitation greater than the 90th-percentile values and less than the 10th-percentile values. Red filled circles, red open circles, small red circles, and blue circles indicate the values that are significant at greater than the 99%, 95%, 90%, and <90% levels, respectively. (a),(b) Model-top experiments; (c),(d) low-level nudging experiments.

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-17-0095.1

Figure 4 shows composite plots of smoothed precipitation and the absolute shears at z = 1 and 8 km in a nondimensional normalized time coordinate for model-top experiments. The normalized time is based on a half period of the zonal-mean zonal wind oscillation. Each half period is defined by two successive changes of zonal-mean zonal wind direction from westerly to easterly or vice versa at a prescribed reference level. The chosen reference level for model-top experiments is 8 km to ensure a clear signal of the zonal-mean zonal wind oscillation for all cases. These half periods are linearly mapped to the normalized time ranged from 0 to 1. The heavy (light) precipitation periods are represented by clusters of red (blue) circles, which indicate the days that have smoothed precipitation greater than (less than ).

Fig. 4.
Fig. 4.

Smoothed precipitation (gray lines) and absolute vertical shear of the zonal-mean zonal wind at z = 1 (green lines) and 8 km (yellow lines), plotted in a normalized time with a reference level of 8 km for model-top experiments. See the text for the descriptions of the normalized time.

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-17-0095.1

There is one clear heavy precipitation period for most of the cases except Top24. It can be seen that for all experiments, the absolute shear at 1 km is closely related to the heavy precipitation clusters, while the relation of absolute shear at 8 km with the smoothed precipitation is not so consistent among the experiments. For light precipitation periods, there is one clear cluster for cases with model top higher than 34 km or lower than 26 km. The cases in between Top34 and Top26 have two distinguishable light precipitation clusters, and there seems to be a systematic redistribution between these two clusters as the model top changes.

b. Low-level nudging experiments

This series of experiments is carried out in order to examine the effect of the zonal-mean state around the tropopause on moist convection. The low-level shear of the zonal-mean zonal wind is reduced by the nudging scheme from the surface to a nudging level . Similar to Fig. 1, Fig. 5 shows the time–height section of the zonal-mean zonal wind and the time series of unsmoothed and smoothed precipitation for low-level nudging experiments. As the nudging is applied from the surface to , with a gradual transition from to , the QBO-like oscillation efficiently disappears from the surface to near . On the other hand, above , the oscillation still exists with similar properties to the nonnudging Control case.

Fig. 5.
Fig. 5.

As in Fig. 1, but for low-level nudging experiments. The horizontal dashed gray line in each panel indicates the upper nudging level [z2 in Eq. (4)].

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-17-0095.1

For the cases with z2 > 10 km, the amplitude of the oscillation is reduced substantially. When the low-level zonal-mean zonal wind (and hence, low-level vertical shear) weakens, the modulation of smoothed precipitation also weaken until Nudge3_6. Intriguingly, the modulation reappears with higher nudging levels and becomes maximum at Nudge7_10 before it weakens again.

Figure 2c shows that higher nudging levels lead to smaller oscillation amplitude in the stratosphere. This systematic variation suggests the modification of characteristics of generated gravity waves in the troposphere (i.e., reduction of the maximum phase speed). However, the descent rates of the zero line of the zonal-mean zonal wind in the stratosphere and the oscillation periods are similar for all cases as shown in Fig. 2d. The switching times (half periods) and switching levels of the oscillations are also similar among all experiments, unlike the large variation of the model-top experiments, insensitive to the choice of the height of nudging levels.

Figure 3c shows some statistical properties of smoothed precipitation for low-level nudging experiments. It can be seen that the variation is largest in Nudge7_10, in agreement with the clear modulation of smoothed precipitation in Fig. 5. The median of the smoothed precipitation first decreases in Nudge1_4 and Nudge3_6 and increases with higher nudging levels.

Figure 3d shows the mean difference and statistical significance of absolute shear between the heavy and light precipitation days. It can be seen that the positive difference of vertical shear at 1 km systematically reduces with higher nudging levels to Nudge3_6, and the difference in the upper troposphere becomes negative. In the clearest oscillation of the smoothed precipitation in Nudge7_10, the difference is not significant at lower levels and reaches its largest negative value in the upper troposphere at levels from 8 to 9 km. This implies a negative correlation of high-level vertical shear with the smoothed precipitation. In other words, larger vertical shear at high levels leads to less precipitation. This relation also exists in Nudge5_8 and Nudge9_12 with weaker magnitudes and disappears with higher nudging levels.

The above remarks can also be revealed in the composite plots of smoothed precipitation and absolute shear at z = 1 and 8 km in Fig. 6. It can be seen that the absolute vertical shear at 8 km has a negative correlation with smoothed precipitation without significant variation of the absolute shear at 1 km for cases with high nudging levels (from Nudge5_8 to Nudge9_12). When the nudging level is low (Nudge–1_2) or no nudging is presented (Control), the periods with large values of absolute shear at 8 km, which tend to reduce the precipitation, coincide with the periods with large values of that at 1 km, which tend to enhance the precipitation. It is likely that the effect of low-level shear is dominated and overwhelms the effect of high-level shear. When the low-level shear is weakened to a degree, the two opposite effects cancel each other and result in a small modulation of precipitation (Nudge1_4). When the vertical shear of the zonal-mean zonal wind throughout the troposphere is eliminated, the modulation of precipitation disappears (Nudge11_14 and Nudge13_16).

Fig. 6.
Fig. 6.

As in Fig. 4, but for low-level nudging experiments. In this case, the reference level of 18 km is chosen instead of that of 8 km.

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-17-0095.1

4. Composite analysis of convective systems

a. High-frequency output reruns and analysis procedure

As shown from the previous section, there seem to be two opposite effects of vertical shear of the zonal-mean zonal wind at low levels near the surface (around 1 km) and high levels in the upper troposphere (around 8 km). Because the two series of experiments do not have frequent temporal output (once a day), it is difficult to diagnose detailed structures and evolutions of the convective systems. Thus, we select two notable representatives of the two effects, Control and Nudge7_10, to set up a rerun with higher-frequency temporal output of 5 min. Each rerun lasts from day 150 through day 298, which covers about 1.5 oscillation periods in both cases.

Figure 7 shows the height–time section of the zonal-mean zonal wind, its vertical shear, and 1-day unsmoothed and smoothed 15-day running-mean precipitation for the reruns of Control and Nudge7_10. Once again, it can be seen that the heavy precipitation periods of Control coincide with the periods when bands of large vertical shear (indicated by the contours for 5 × 10−3 and −5 × 10−3 s−1) reach down near the surface. For Nudge7_10, on the other hand, the heavy precipitation periods occur when the vertical shear in the upper troposphere around 8 km is small.

Fig. 7.
Fig. 7.

(a),(c) Zonal-mean zonal wind (shaded and black contour lines; m s−1) and its vertical shear (red and blue dashed contour lines; ×10−3 s−1). (b),(d) Domain-averaged 1-day precipitation (green bars) and smoothed precipitation (gray line with circles). Smoothed precipitation that is over the 90th (under 10th) percentiles is colored red (blue). The red (blue) rectangles indicate time windows in (b) and (d) that will be used for composite calculation of heavy (light) precipitation conditions. The symbol on the top of each window indicates if the fields are horizontally flipped (minus sign) or not (plus sign). See the text for the description of the composite analysis procedure.

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-17-0095.1

Based on the smoothed precipitation variations, we subjectively choose three 10-day subperiods of light and heavy precipitation for each experiment for composite analysis. The light precipitation subperiods are shown by blue rectangles in Figs. 7b and 7d: days 178–188, 220–230, and 268–278 in Control and days 156–166, 200–210, and 248–258 in Nudge7_10. Similarly, the heavy precipitation subperiods are shown by red rectangles: days 196–206, 238–248, and 286–296 in Control and days 176–186, 226–236, and 268–278 in Nudge7_10.

Hovmöller diagrams of 5-min precipitation and time series of domain-averaged 5-min precipitation are shown in Fig. 8 for a light and heavy precipitation subperiod in Control and Nudge7_10. These subperiods are marked as blue and red rectangles in Figs. 7a and 7c.

Fig. 8.
Fig. 8.

(a),(b),(e),(f) Hovmöller diagrams and (c),(d),(g),(h) time series of domain-averaged 5-min precipitation of some notable examples of composite windows indicated by the red and blue boxes in Figs. 7a and 7c.

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-17-0095.1

For Control, there is a clear contrast of precipitation patterns between the two subperiods. The light precipitation subperiod is characterized by short-lived, back-building-type precipitation systems, whereas the heavy precipitation subperiod is featured by long-lived, front-building squall-line-type precipitation systems. In the heavy precipitation subperiod, the time series of domain-averaged 5-min precipitation is featured with a more intermittent pattern. Heavy precipitation durations and intervals of no precipitation alternately appear with the durations of about 1 day or so. Alternate appearance of back-building-type and squall-line-type precipitation patterns associated with temporal variations of the vertical shear of the zonal-mean zonal wind near the surface was already reported in Nishimoto et al. (2016), whereas this is the first description of the modulation of the precipitation and its intermittent characteristics between the two types of precipitation patterns in the subperiods of the QBO-like oscillations.

For Nudge7_10, on the other hand, the light and heavy precipitation subperiods have similar appearances in the domain-averaged 5-min precipitation patterns except for a slower drift of precipitation clusters in the heavy precipitation subperiod. The time series for the light and heavy precipitation subperiods also have nonintermittent appearances similar to each other with shorter intervals of no precipitation, although there is a slightly larger magnitude for the heavy precipitation subperiod.

To get detailed structures of the convective systems for light and heavy precipitation conditions, a composite analysis is carried out as follows.

First, all the precipitation centers, defined by local maxima of 5-min precipitation, are identified for all time steps of the chosen subperiods (in total 30 days for each condition). The total number of precipitation centers of about 20 000 for each condition (20 162 for Control, light; 17 545 for Control, heavy; 21 445 for Nudge7_10, light; and 23 741 for Nudge7_10, heavy). By choosing the 99th percentile of each condition as the threshold for the composite calculation, we have four sets of composite centers of about 200 each.

After the composite centers are obtained, a time-lagged compositing is carried out after translating the composite centers to the center of the domain. Because of the zonally periodic boundary, the translated domains still have the original size of 640 km with continuous fields. Because the zonal-mean zonal wind oscillates alternately but only one-half period is considered into the composite calculation, all the dependent variables are also flipped horizontally with respect to the composite context, and the zonal wind takes opposite sign for the second composite subperiod of each precipitation condition (denoted by the minus sign at the top of each subperiod box in Figs. 7b and 7d).

b. Control experiment

Figures 9a and 9b show the Hovmöller diagram of composite 5-min precipitation and near-surface temperature at z = 250 m of the light and heavy precipitation conditions, respectively, for Control. The precipitation systems in both conditions propagate westward with comparable speed of 11 and 13 m s−1, respectively. There is a contrast between the light and the heavy conditions in term of the longevity of the precipitation systems. The systems (here defined by the 0.5-mm contours of 5-min precipitation) have an average lifetime of about 1.5 h for the light precipitation condition but 3 h in the heavy precipitation condition. The lower near-surface temperature after the occurrence of the precipitation suggests that it is a cold pool associated with the precipitation-induced downdraft. It is colder, propagates farther, and persists longer in the heavy precipitation condition. In the light precipitation condition, there is a signal of cold pools centered around (−15 km, −2 h) with the yellow tone before the main precipitation system appears around (+30 km, −0.6 h). This feature suggests a hint of back-building-type precipitation systems still remains in the composite average; the current system is triggered by the propagation of the cold pool from the previous one. In the heavy precipitation condition, there is no signal of such back-building-type systems, whereas the main convective system lives longer as the associated cold pool extends in space and time.

Fig. 9.
Fig. 9.

Hovmöller diagram of composite 5-min precipitation (white contour; mm) and 250-m temperature (shaded; °C) for the (a),(c) light and (b),(d) heavy precipitation conditions of the (a),(b) Control and (c),(d) Nudge7_10 experiments. The dotted white lines indicate the averaged propagation speed of precipitation systems.

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-17-0095.1

Figures 10a–d show the composite profiles of the zonal mean of zonal wind, its vertical shear, temperature anomaly from the time average over the whole rerun period of 148 days, and the static stability of the Control experiment. It can be seen that the propagation speed of heavy (light) precipitation systems is approximately equal to the zonal-mean zonal wind at about 2.5 or 4.5 km (3 or 9 km). The steering levels for the precipitation systems seem to be the lower levels (2.5–3 km) rather than higher levels (4.5 or 9 km), because, for example, the composite zonal wind at 9 km for heavy condition is eastward, totally opposite the propagation direction of the precipitation systems.

Fig. 10.
Fig. 10.

(a),(e) Zonal-mean profiles at the key time of zonal wind, (b),(f) vertical shear of zonal wind, (c),(g) temperature anomaly, and (d),(h) static stability for the (a)–(d) Control and (e)–(h) Nudge7_10 experiments. Red lines are for the heavy precipitation condition, and blue lines are for the light precipitation condition. The vertical red and blue dashed lines in (a) mark the averaged propagation speed of precipitation systems for heavy and light conditions, respectively.

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-17-0095.1

In the heavy precipitation condition, the vertical shear of the zonal-mean zonal wind has the maximum at a level of about 1 km and is still large below (about 3 × 10−3 s−1 in magnitude at z = 250 m). On the other hand, in the light precipitation condition, the vertical shear has the maximum at about 2.5 km but reduces to nearly zero at z = 250 m. The environmental temperature of the light precipitation condition is negative anomaly throughout the troposphere, whereas that of the heavy precipitation condition is large positive anomaly with a maximum of about 1 K around z = 4 km but nearly zero in the upper troposphere. These differences result in differences in the static stability; the static stability of the heavy precipitation condition is slightly smaller above z = 10 km compared to the light precipitation condition.

Figures 11a and 11b show the composite vertical velocity and streamlines of the relative velocity, in which the propagation speed of the precipitation system is subtracted from the zonal wind speed. In the heavy precipitation condition, the updraft is strong and maximum at z = 4 km, and the downdraft is also strong at z = 2 km and located adjacent to the right side of the updraft. This separation of the updraft and downdraft and its relation to the longevity of the convective systems were pointed out in classic theories of squall lines (e.g., Rotunno et al. 1988). In the light precipitation condition, on the other hand, the updraft and downdraft are weaker and there is no such separation because the downdraft is located nearly under the bottom of the updraft. The updraft in the heavy precipitation condition is more intensive and narrower and starts nearer to the surface than that in the light precipitation condition.

Fig. 11.
Fig. 11.

(a),(b),(e),(f) Cross section of composite vertical speed (rainbow contours; m s−1) and streamline of zonal wind relative to the propagation speed. (c),(d),(g),(h) Cross sections of composite water cloud (gray shades; ×10−2 g kg−1), ice cloud (blue shades; ×10−2 g kg−1), rainwater (red contours; ×10−1 g kg−1), and potential temperature (orange contours; K).

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-17-0095.1

Figures 11c and 11d show the composite cross section at the key time of potential temperature and mixing ratios of water cloud, ice cloud, and precipitation of the heavy and light precipitation conditions, respectively, for Control. In both conditions, there is a warm-core structure in the cloud above the precipitation center, whereas the temperature at the precipitation center just above the surface is colder than the environment because of the evaporation of rainwater. A clear contrast in moist convection structures of the two conditions is that the heavy precipitation condition has a large tilt to the right with height, consistent with the upper-level shear above z = 3 km, that is, a downshear tilt to the upper-level shear following the terminology of Weisman (1992; see his Fig. 2), whereas it has an upshear tilt against the low-level shear below z = 3 km. The light precipitation system has a slight upshear tilt against the upper-level shear above z = 6 km.

Figure 12a shows the mixing ratio of rainwater (red lines) at the rain center and those of cloud water (black lines) and cloud ice (blue lines) at the cloud center for the light precipitation (thin lines) and heavy precipitation (thick lines) conditions. Here, the rain center on each level is defined as the grid point that has the maximum value of horizontally. Similarly, the cloud center is defined as the maximum location for . The precipitation starts at z = 4 km and increases downward until the maximum at z = 2 km, then it decreases slightly as a result of evaporation in the downdraft. It is clear that the rainwater amount is larger in the heavy precipitation condition. The cloud water is a maximum at about z = 3.5 km, and the amount in the heavy precipitation condition is double of that in the light precipitation condition. The cloud ice is a maximum at a level of about z = 9 km. There is a smaller amount of ice cloud at the cloud center in the heavy precipitation condition than in the light precipitation condition.

Fig. 12.
Fig. 12.

(a),(d) Composite mixing ratio of rainwater (red lines; 5 × 10−1 g kg−1), cloud water (black lines; ×10−2 g kg−1), and cloud ice (blue lines 5 × 10−2 g kg−2) at the cloud and precipitation center; (b),(e) composite temperature anomaly (°C) at center of the cloud (magenta lines) and rain (cyan lines); (c),(f) composite vertical velocity (m s−1) at center of the cloud (magenta lines) and rain (cyan lines). In all panels, heavy precipitation composite conditions are denoted by thick lines, and light precipitation conditions are denoted by thin lines.

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-17-0095.1

Figure 12b shows the temperature anomaly at the cloud and rain centers from the zonal average for the light and heavy precipitation conditions. The temperature anomaly is positive from z ≈ 3 to 11 km in the light condition and to 12 km in the heavy condition. Below 3 km, the temperature anomaly is negative because of the evaporation of rainwater. In the heavy precipitation condition, the temperature anomaly at the cloud center is higher than that at the rain center because there is a separation between the centers of cloud (updraft) rain (downdraft) as seen in Fig. 11d. In the light precipitation condition, on the other hand, there is no difference between the anomalies at the cloud and rain centers because there is no such separation.

Figure 12c shows the vertical velocity at the cloud and rain centers in the light and heavy precipitation conditions. Again, in the heavy precipitation condition, there is a contrast of the vertical velocity at the cloud and rain centers below z ≈ 3 km because of the separation of the updraft and the downdraft. The downdraft magnitude is nearly 1 m s−1 at the rain center and z ≈ 1 km. There is almost no difference in the rain and cloud centers for the light precipitation condition. The updraft at the cloud center is stronger in the heavy precipitation case compared with the light precipitation condition below 6 km and weaker above 6 km. This difference may be related to the difference in the distributions of water cloud and ice cloud as described in Figs. 11c, 11d, and 12a.

c. Nudge7_10 experiment

Figures 9c and 9d show the Hovmöller diagram of composite 5-min precipitation and near-surface temperature (z = 250 m) of the light and heavy precipitation conditions, respectively, for Nudge7_10. Unlike the Control experiment, the composite precipitation systems in both conditions are stationary. The lifetimes of both systems are similar to each other of about 1.5 h. The cold pool of the light precipitation systems spreads out nearly symmetrically in both directions, whereas that of the heavy precipitation system has asymmetry with predominance of westward propagation. A hint of westward propagation of cold pool in the previous system, which appears around (40 km, −2.4 h), is detectable.

Figures 10e–h show the profiles of composite zonal-mean zonal wind, its vertical wind, temperature anomaly, and the static stability of Nudge7_10 experiment. It can be seen that the zonal-mean zonal wind in both light and heavy precipitation conditions is reduced to nearly zero below z = 6 km because of the nudging term. Around 8–9 km, the vertical shear is largely negative in the light precipitation condition of about −6.5 × 10−3 s−1 while nearly zero for the heavy precipitation condition. The environmental temperature of precipitation light condition is negative anomaly throughout the troposphere above 3 km. The temperature anomaly of heavy precipitation condition is positive and larger than the light precipitation condition from the surface to about 13 km. The static stability of the heavy precipitation condition is slightly smaller compared to the light precipitation condition above 8 km.

Figures 11e and 11f show the cross sections of the composite vertical velocity and streamlines of the relative velocity for the Nudge7_10 experiment. Again, in the lower part of the convective systems, the updraft and downdraft just near the precipitation center are similar for both light and heavy precipitation conditions. The downdrafts are located at the bottom of the updraft because of the precipitation. Because the low-level shear is nudged, there is no mechanism to separate the location of the updraft and the downdraft in zonal direction for both precipitation conditions. As a convective system develops, the precipitation-induced downdraft eventually causes the dissipation of the system. There is a contrast in upper-level structure of the systems; in the light precipitation condition, the vertical shear of the zonal-mean zonal wind makes the updraft broader, weaker, and shorter, while in the heavy condition, the updraft is narrower, stronger, and taller.

Figures 11g and 11h show the composite cross section at the key time of potential temperature and mixing ratios of water cloud, ice cloud, and precipitation of the light and heavy precipitation conditions, respectively, for the Nudge7_10 experiment. Unlike the Control experiment, the structures of rainwater and water cloud are similar for both conditions. However, there are differences in the upper structure of the ice cloud. The composite ice cloud of the light precipitation condition has a slight tilt to the left, whereas in the heavy precipitation condition, the cloud is nearly symmetric around the center. The tilt of the ice cloud is downshear because of the large upper-level shear around z = 9 km as shown in Fig. 10f.

Figure 12d shows the composite mixing ratio of rainwater at the rain center and those of cloud water and cloud ice at the cloud center for the light precipitation and heavy precipitation conditions. Similar to the Control experiment, the rainwater profile is slightly larger for the heavy precipitation condition compared to the light precipitation one. However, the contrasts in the cloud water and cloud ice between the light and heavy precipitation condition are not as large as those of the Control experiment. The profiles for both cloud water and cloud ice of the heavy precipitation condition extend about 0.5 km higher than those of the light precipitation one. For the composite temperature anomaly at the cloud and rain centers, both light and heavy precipitation conditions are also similar as shown in Fig. 12e. For composite vertical velocity at the cloud center, however, there is a large difference between the heavy and light precipitation conditions as shown in Fig. 12f. From z = 4 to 14 km, the vertical velocity of the heavy precipitation condition is noticeably larger than that of the light one.

5. Discussion

From Fig. 4, the smoothed precipitation is clearly larger when the low-level shear at z = 1 km (green lines) is large, as shown by red circles for the upper 90th percentile of daily zonal-mean precipitation. On the other hand, the relation between the small precipitation time (denoted by blue circles for the lower 10th percentile) and the low-level shear is not clear. In Top34 to Top26, two clusters of the lighter precipitation periods exist for different normalized time periods, most of which do not coincide with any particular condition of the low-level shear. The relation of high-level shear at z = 8 km with the smoothed precipitation is also not so systematic among the experiments. The heavy precipitation periods might coincide with the larger high-level shear in some cases (e.g., Top28) or with smaller high-level shear in other cases (e.g., Top15).

This complication may be due to a speculation that the effect of low-level shear is so dominant that it overwhelms the effect of the high-level shear. When the effect of low-level shear is removed in low-level nudging experiments, especially Nudge7_10, the role of high-level shear at z = 8 km is revealed to be negatively correlated with smoothed precipitation as shown in Fig. 5. With this interpretation, the above complication of model-top experiments is somewhat explainable as the combination of the effects of the low-level shear and the high-level shear. For example, the first small smoothed precipitation period in case Top32 can be associated with the small low-level shear and a medium value of high-level shear, while the second one can be associated with a medium value of low-level shear and a medium value of high-level shear.

The detailed structure of the composite convective system in the heavy precipitation condition of Control, as shown in Figs. 11b and 11d, is a confirmation of the classic theory of the strong and long-lived squall-line-type convective systems (Rotunno et al. 1988) in our minimal framework of self-sustained QBO-like oscillations with associated modulation of moist convection. On the other hand, for Nudge7_10, without the effect of the low-level shear, the high-level shear makes the updraft broader and weaker, and cloud top becomes lower as shown in Figs. 11g, 11h, and 12d, and leads to the smaller amount of precipitation. These findings qualitatively agree with the proposed mechanism of the influence of the QBO-induced variation of cross-tropopause shear on tropical deep convection in some previous studies (Gray et al. 1992; Collimore et al. 2003).

In the classic theory of the QBO (Lindzen and Holton 1968; Holton and Lindzen 1972), the downward propagation of the shear zone of zonal-mean zonal wind results from the interaction between the zonal-mean zonal wind and the atmospheric waves that propagate from the troposphere into the stratosphere. The theory can explain most of the prominent features about the QBO, but the timing of the switch between the westerly and easterly phases is one of the unexplained features of the QBO. As shown in Fig. 2d, the timing of the switch to the opposite phase at the bottom of the Rayleigh damping layer and the half period of the QBO-like oscillation are not sensitive to the choice of the height of the low-level nudging layer. In model-top experiments, on the other hand, the timing of the switch and the half period of oscillation as well as the switching level to start the other phase of oscillation largely depend on the choice of the height of the model top as shown in Fig. 2b. These experimental results would give a fundamental dataset to consider the switching mechanism of the QBO-like oscillation.

In an idealized framework by Plumb (1977) that two internal waves interact with the mean zonal flow to produce a QBO-like oscillation and in its laboratory analog experiment done by Plumb and McEwan (1978), the vertical diffusion of the zonal momentum at the bottom of the domain reduces the zonal-mean zonal wind when the shear zone approaches the bottom boundary, and the next phase of the oscillation can be started aloft. As a result, the switching time to the opposite sign of the mean zonal wind aloft at the top of the interaction domain coincides with the time when the zero line of the mean zonal wind reaches to the bottom of the domain. The switching to the opposite phase at the model top (bottom of the Rayleigh damping layer) inferred from such idealized framework does not take place when the zero line of the zonal-mean zonal wind reaches the tropopause or any specific level (as shown in Fig. 2). An explanation for the switching time might have to take the wide range of atmospheric waves with different phase speeds into the account.

The domain in Plumb (1977)’s framework can be regarded as the stratosphere, while the bottom of domain can be regarded as the tropopause, below which deep convection produces vertically propagating gravity waves above the clouds. However, there is no clear separation between the source of waves (the troposphere) and the propagation media (the stratosphere) in the real atmosphere as well as in our idealized minimal framework. In the real atmosphere, the mixing mechanisms due to convection and the interactions with the surface might be the main reasons that the QBO almost disappears in the troposphere. In our framework, the zonal-mean zonal wind oscillation continues to penetrate into the troposphere despite the fact that these mentioned dissipation processes exist. In our minimal framework, the dissipation mechanisms might not be strong enough to damp the zonal-mean zonal wind effectively because of the two-dimensional nature of the model and/or its much shorter periods compared to the QBO.

6. Conclusions

The downward influence of the QBO-like oscillation on deep moist convection was further investigated using the two-dimensional minimal model framework of Yoden et al. (2014) with two series of parameter sweep experiments.

In the first series of model-top experiments, the height of the model domain was changed from 40 to 15 km to examine the robustness of the QBO-like oscillation and the associated modulation of precipitation with the choice of model height. The QBO-like oscillation in the zonal-mean zonal wind is a robust feature that was obtained in all the experiments (Fig. 1), including low-top cases in which only the tropospheric portion is presented. As the model top is lowered, the peak of the oscillation amplitude in the stratosphere has a smaller value and disappears in the cases of top height being 28 km or below. The period of the oscillation also varies substantially and has a maximum value of 144 days in the cases of top height being 30 or 28 km (Figs. 2a,b). There is a modulation of smoothed precipitation with a half period of zonal wind oscillation in all the cases, and a positive correlation exists between the smoothed precipitation and the vertical shear of the zonal-mean zonal wind near the surface (Figs. 3a,b and 4).

In the second series of low-level nudging experiments, the zonal-mean zonal wind was nudged toward zero in a certain height ranged from the surface to remove the effect of vertical shear of the low-level mean zonal wind. Again, the QBO-like oscillations were robustly obtained in all the experiments, even in the case in which the whole troposphere was nudged (Fig. 5). The higher nudging level leads to a smaller oscillation amplitude in the stratosphere, although the oscillation period and the descent rate of its phase are similar for all cases, insensitive to the choice of the height of nudging levels (Figs. 2c,d). When the low-level shear is nudged to zero in a certain height from the surface, the smoothed precipitation modulation weakens for shallow-nudging-layer cases but appears again, comparable to the Control case, in the cases with the low-level nudging in the middle and lower troposphere and then weakens again and disappears for higher nudging levels (Figs. 3c,d and 6). There is a negative correlation between the smoothed precipitation and high-level vertical shear around the cloud-top height, and the relation is clearest in case Nudge7_10 (Fig. 6).

These results obtained in the two series of parameter sweep experiments suggest that the QBO-like oscillation modulates deep moist convection via two mechanisms related to the vertical shear of the zonal-mean zonal wind. The two prominent cases of Control and Nudge7_10 were chosen for further composite analysis to reveal the modulation of convective structures associated with the mean zonal wind oscillation in a heavy or light precipitation condition (Fig. 7).

First, in the Control case that is a typical one in the first series of experiments, stronger low-level shear leads to a heavier and intermittent precipitation with a squall-line-type organization of precipitation pattern (Figs. 8b,d and 9b). In the heavy precipitation condition, a large value of low-level shear (red lines in Figs. 10a and 10b) results in an upshear tilt of the updraft and a clear separation of the updraft and downdraft in the lower troposphere (Figs. 11b,d). On the other hand, in a condition of small value of low-level shear (blue lines in Figs. 10a and 10b) for a back-building-type organization of precipitation pattern (Figs. 8a,c and 9a), the development of the downdraft eventually makes the convective cloud weaken and dissipates in a time scale of 1–2 h without large tilts of the convective system (Figs. 11a,c). This well-discussed mechanism in the classic theory of two-dimensional squall lines (e.g., Rotunno et al. 1988) was analyzed and described in the composites of extreme events of heavy and light precipitation conditions that were obtained in a long enough dataset of self-sustained QBO-like oscillations.

The second mechanism is related to the vertical shear of the zonal-mean zonal wind in the upper troposphere near the cloud tops and was investigated in detail for Nudge7_10 in low-level nudging experiments (Figs. 7c,d), because the negative correlation between the smoothed precipitation and upper-level vertical shear around the cloud-top height is clearest (Fig. 6). In the heavy precipitation condition, the upper-level vertical shear is nearly zero (red lines in Figs. 10e and 10f), whereas it is largely negative in the light precipitation condition (blue lines in Figs. 10e and 10f). In the light precipitation condition, the vertical shear of the zonal-mean zonal wind makes the updraft broader, weaker, and shorter in the upper troposphere (Figs. 11e,g), whereas in the heavy precipitation condition, the updraft is narrower, stronger, and taller (Figs. 11f,h). As a result, the cloud top becomes higher in the heavy precipitation condition, which finally leads to the larger amount of precipitation (Fig. 12d). This effect seems to be secondary if compared to the first mechanism as summarized above, because it can only be well revealed when the low-level shear is reduced by our newly introduced nudging method. If compared to the low-level shear mechanism, the vertical shear near the cloud top produces an opposite effect on moist convective systems. Large values of upper-level vertical shear weaken the updraft and reduce precipitation intensity. This is a qualitative demonstration of the modulation of convection by the QBO-induced variation of cross-tropopause shear proposed by some previous studies (Gray et al. 1992; Collimore et al. 2003).

Acknowledgments

The authors thank two anonymous reviewers for their constructive comments. This work was supported by JSPS KAKENHI Grants JP24224011 and JP17H01159, and JSPS Core-to-Core Program, B. Asia-Africa Science Platforms.

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