## 4.2 Analysis of model results

Figure 6 shows the time-longitude maps of the 30-60d components of mean zonal winds at 200 and 850 hPa in the Indo-western tropical Pacific during September-November 2004 simulated by experiment Ndg_q. Comparing the results before and after the nudging of experiment CPS3, it can be seen that CPS3 does not simulate the eastward propagation characteristics of the MJO at 200 and 850 hPa (Fig. 3d, Fig. 4d), but after nudging of the water-vapor field, the results of Ndg_q show a significant improvement in terms of the eastward propagation of the MJO; the time-longitude correlation coefficients are 0.81 and 0.96 between simulations (Fig. 6a, Fig. 6b) and observations (Fig. 3a, Fig. 4a), respectively, which simulates better than experiment CPS5 for the MJO. The importance of the water vapor field in influencing the eastward propagation of the MJO zonal wind field is further explored below by comparing the evolution of the vertical profiles of the 30-60d component zonal wind, temperature, and specific humidity fields.

Figures 3a and 4a show the eastward propagation characteristics of the mean zonal winds at 850 hPa in the Indo-western Pacific region from 15 September to 15 October 2004. The period from 15 September to 15 October 2004 is thus chosen as the study period, and the altitude-longitude maps of the 30-60d components of the observed, CPS3, CPS5 and Ndg_q zonal winds, temperature and specific humidity are plotted every five days (Figs. 7, 8 and 9) to examine the phase evolution characteristics of each variable.

As seen in Fig. 7, due to the inappropriate cumulus parameterization scheme adopted in experiment CPS3, the simulated 30-60d component of the zonal wind at five-day interval shows different distribution characteristics throughout the troposphere from the observations; it not only fails to simulate the normal eastward propagation of the MJO, but even shows the westward propagation characteristics (the first and second columns of Fig. 7). Experiment Ndg_q, on the other hand, ensures that after the water-vapor distribution is assimilated, the atmospheric thermodynamic and dynamic adjustment processes make the 30-60d component of the zonal wind very similar to the observation (the last column of Fig. 7). The correlation coefficients of the 30-60d zonal wind component between the simulation and observation reach 0.52, 0.59, 0.47, 0.38, 0.54, 0.61, and 0.53 for these maps at 5-day interval, with a mean value of 0.52, while the corresponding correlation coefficients for experiment CPS5 (the third column of Fig. 7) are 0.44, 0.52, 0.42, 0.24, 0.41, 0.55, and 0.50, with a mean value of 0.44, which is smaller than the correlation coefficient values for experiment Ndg_q.

Figure 8 shows the height-longitude maps of the mean specific humidity 30-60d component corresponding to Fig. 7. It can be seen that the observations show the obvious eastward propagation of the MJO (the first column of Fig. 8). Since the water-vapor field is continuously nudged toward the observed field during the assimilation, experiment Ndg_q is able to simulate the eastward propagation of the specific humidity 30-60d component relatively well (the last column of Fig. 8), and experiment CPS5 is also able to simulate the eastward propagation of the specific humidity 30-60d component relatively well (the third column of Fig. 8), only that the simulation intensity too strong. However, experiment CPS3 gives completely inconsistent results, except that the simulated low-frequency disturbances are basically stationary most of the time, and their wavelength is only about 1/3 of the actual MJO wavelength (the second column of Fig. 8).

Comparing Figs. 7 and 8, we can see that the low-frequency propagation characteristics of water vapor and zonal wind are very similar, and the phases of both fields are basically the same: the positive perturbation zonal-wind region is accompanied by the positive perturbation water-vapor region. This is similar to the conclusion that the positive water-vapor anomaly in the mid troposphere has approximately the same phase as the MJO convection by Sperber (2003). However, the low-frequency perturbation of water vapor is 5–8 days ahead of the low-frequency perturbation of zonal wind; therefore, having sufficient water vapor in the eastward propagation of the low-frequency perturbation of zonal wind to produce wet convection to match the eastward propagation of the low-frequency perturbation of zonal wind may be a factor for the eastward propagation of the low-frequency perturbation of zonal wind. Li (1985) first introduced the conditional instability of the second kind (CISK) theory into the study of atmospheric low-frequency oscillations, and proposed a cumulus convective heating feedback mechanism for tropical atmospheric low-frequency oscillations. Lau and Peng (1987) introduced mobile wave-CISK as the generation mechanism of tropical low-frequency oscillations, which can better explain the slow eastward propagation of tropical atmospheric MJO along the equator. All these theoretical works clarify the role of tropical wet convection in the generation and propagation of the MJO, and the sensitivity experiments in this paper provide verification for these theories. In addition, the presence of a westerly dip of the low-frequency components of water vapor and zonal winds throughout the troposphere, that is, the zonal asymmetric distribution with respect to the tilting axis, confirms that a suitable water-vapor distribution is a key factor to ensure the observed eastward propagation of the tropical atmospheric MJO, as pointed out by Hsu and Li (2012).

Figure 9 shows the height-longitude maps of mean temperature 30-60d component, corresponding to Fig. 7. Although Fig. 9 also presents the observed eastward propagation characteristics of the low-frequency temperature perturbation (the first column of Fig. 9), its spatial structure is relatively complex compared to the eastward propagation characteristics of the zonal wind (the first column of Fig. 7) and specific humidity (the first column of Fig. 8) low-frequency perturbations; and the intensity of the perturbation shows irregular variation in both horizontal and vertical directions. Similarly, both experiments CPS5 (the third column of Fig. 9) and Ndg_q (the last column of Fig. 9) can simulate the eastward propagation of low-frequency temperature perturbations, but the average correlation coefficients of the simulated and observed intensity distributions of temperature low-frequency perturbations on the altitude-longitude maps at different moments are only 0.14 and 0.28, respectively, much smaller than the corresponding correlations coefficients of specific humidity and zonal winds. In contrast, experiment CPS3 (the second column of Fig. 9) does not simulate the eastward propagation characteristics of the temperature low-frequency disturbance as observed.

In addition, similar to experiment Ndg_q that nudges only specific humidity, temperature is also nudged in experiment CPS3, but the analysis of the results shows that the temperature nudging assimilation only improves the low-frequency propagation characteristics of temperature to a large extent, and the effects on the low-frequency zonal wind and low-frequency specific humidity in terms of eastward propagation characteristics do not improve significantly (figure omitted). Therefore, temperature distribution is not a key factor to control the low-frequency MJO eastward propagation compared to humidity distribution.

## 4.3 Mechanism analysis

From Fig. 8, it can be seen that there is a zonal asymmetry in the specific humidity field relative to the tilting axis during the evolution from 15 September to 15 October. To demonstrate the importance of atmospheric stability in the propagation of the MJO, we investigate the role of water vapor in influencing the propagation of the MJO via affecting atmospheric stability by examining the evolution of equivalent potential temperature .

is determined by both temperature and humidity. If the atmosphere is initially moist but unsaturated and , the atmosphere is potentially unstable. If such atmosphere reaches saturation by sufficient lifting, the entire atmosphere column becomes unstable (Li and Wang 1994). Figure 10 shows the height-longitude maps of the 30-60d component of corresponding to Fig. 7. It shows that both observations and simulations are similar to water vapor in terms of the low-frequency characteristics (Fig. 8), and differ significantly from the low-frequency characteristics of temperature (Fig. 9). The difference of the 30-60d component of variation with height from 925 to 775 hPa is defined as the 30-60d component of the convective instability parameter at 850 hPa. The time-longitude maps of the observation and experiments CPS3, CPS5 and Ndg_q of the tropical mean convective instability parameter in the Indo-western Pacific region during September-November 2004 are plotted (Fig. 11). The convective instability parameter (Fig. 11a) shows eastward propagation, but compared to the 850 hPa zonal wind (Fig. 1b), the propagation is not continuous and there are some westward propagation periods. Experiment CPS3 (Fig. 11b) shows westward propagation contrary to the observation. Experiment CPS5 (Fig. 11c) simulates part of the eastward propagation, but the simulation degrades to the east of 80°E. Experiment Ndg_q (Fig. 11d) can basically simulate the eastward propagation of the low-frequency convective instability parameter at 850 hPa, but the simulated intensity is weak in some periods. These experimental results indicate that the water-vapor field can maintain the MJO propagation by affecting the atmospheric stability, while the temperature field has little effect on the MJO eastward propagation, so enhancing the model's simulation effect on atmospheric stability plays an important role in improving the simulation of MJO eastward propagation.

The convective instability parameter at 850 hPa (Fig. 11a) and the time-longitude map of zonal wind (Fig. 1b) show that the low-frequency propagation characteristics of both are similar, but there is a lead-lag relation in time. Figure 12 shows the time-lag correlation coefficients between the four mean convective instability parameters given in Fig. 11 and the 30-60d component time-longitude maps of the observed zonal wind (Fig. 1b). The correlation coefficient is the largest when the observed convective instability parameter is ahead of the zonal wind by 6–7 days (Fig. 12a), which is consistent with the water-vapor low-frequency disturbance estimated from Figs. 7 and 8 being ahead of the zonal wind low-frequency disturbance by 5–8 days, again demonstrating that the water-vapor field can contribute to the propagation of the MJO by affecting the atmospheric stability and that the tropical wet convection located east of the MJO disturbance plays a key role. The simulated results of experiment Ndg_q are the closest to the observations, but the correlation coefficient between the two is the greatest when the convective instability parameter is ahead of the zonal wind by about 10 days (Fig. 12d). Although the simulated results of experiment CPS5 are better than those of experiment CPS3, the simulated results of CPS5 also do not portray the evolution of the convective instability parameter well. The convective instability parameter is ahead of the zonal wind by about 18 days (Fig. 12c), while the simulated convective instability parameter of experiment CPS3 even lags behind the zonal wind by 3–4 days (Fig. 12b). Figure 12a also shows that the correlation coefficient is the greatest when the convective instability parameter overtakes the zonal wind by 6–7 days, while the negative correlation is the greatest when it lags the zonal wind by 13–14 days, that is, convective instability exists in the lower troposphere 6–7 days before the occurrence of the low-level easterly anomaly and 13–14 days after the occurrence of the westerly anomaly. This confirms the finding of Maloney (2009), that is, column-integrated MSE accumulates before intraseasonal precipitation prior to the onset of low-level easterly anomalies, while MSE releases energy during and after precipitation during the onset of westerly anomalies.