Sensitivity Experiments on the Role of Water Vapor in the Eastward Propagation of MJO

In this study, we employed the nudging assimilation of the Weather Research and Forecasting (WRF) model to conduct a set of sensitivity experiments on the role of water vapor in the Madden-Julian Oscillation (MJO) eastward propagation, focusing on the eastward propagating 30-60d low-frequency component in the tropical atmosphere from the Indian Ocean to the western Pacic Ocean during September-November 2004. Using 11 different cumulus parameterization schemes, the simulation results show that the ability of the regional climate model in simulating the MJO eastward propagation is sensitive to the cumulus scheme: A suitable scheme can well reproduce the MJO eastward propagation characteristics, while most schemes show no skill for the MJO eastward propagation. When the water vapor in the model domain was assimilated using reanalysis data with nudging technique, we found that the low-frequency evolution of the tropical zonal wind exhibits MJO features well, and the low-frequency phase of water vapor is ahead of the zonal wind by about 6-7 days, which suggests that the atmospheric water-vapor distribution is the key factor for the eastward propagation of the MJO, and the effect of water-vapor eld via affecting the atmospheric stability. When the atmospheric temperature assimilation was conducted, there was almost no improvement in the skill of MJO simulation.


Introduction
The Madden-Julian Oscillation (MJO) is the dominant intra-seasonal oscillation mode in the tropics (Madden and Julian 1972), which has a planetary-scale spatial structure dominated by zonal wavenumbers 1-3, eastward propagation, exhibiting a broad-band oscillation cycle of 30-60d (Li et al. 2007). A lot of previous studies have shown that similar low-frequency oscillations are found everywhere in the world, and they can propagate in different directions (Li and Li 1997;Chen et al. 2001;Li 2014). The activity and anomalies of the MJO affect regional weather and climate. For example, the convergence of the southward propagating MJO in the mid and high latitudes of East Asia and the northward propagating MJO in the Yangtze and Huai river basins of China will produce persistent precipitation in the Yangtze River basin and North China in summer; and these regions are more prone to ooding in years of strong MJO activity (Yang and Li 2003). In addition, the intensity of precipitation in East China varies with the propagation of the MJO. When the tropical MJO travels eastward to the Indian Ocean, precipitation in East China increases; whereas the MJO travels to the western Paci c, precipitation in East China decreases. Meanwhile, there are seasonal differences in MJO's effects on precipitation (Jia et al. 2011). Therefore, it is important to study the propagation mechanism of the MJO for better precipitation prediction in East China.
Simulation studies on intra-seasonal oscillations in the tropical atmosphere have shown that numerical models have di culty in capturing the characteristics of MJO activities; and none of the models participating in the Atmospheric Model Intercomparison Project (AMIP) can accurately characterize the main features of the MJO (Slingo et al. 1996). At present, most models produce short intra-seasonal oscillation periods and weak oscillation intensity, and are unable to describe the seasonal differences of the MJO, and even its continuous eastward propagation characteristics (Kim et al. 2009).
Various theories have been proposed to explain the MJO eastward propagation. The theoretical model proposed by Emanuel (1987) and Neelin (1987) emphasizes the effect of east-west asymmetry of surface heat ux on the generation and eastward propagation of the MJO. However, this theory assumes that surface mean winds are easterly winds of a certain strength, but observations show that surface easterly winds are prevalent only over the central-eastern Paci c and Atlantic Ocean; thus, it cannot explain the generation and propagation of the MJO throughout the tropics ). Based on a series of assumptions,  considered the MJO as a convection-coupled Kelvin wave, and numerical experimental simulations yielded mostly unstable modes with short wavelengths and too fast eastward propagation. Wang and Li (1994) considered the MJO as a Kelvin-Rossby wave coupled with convection and boundary-layer friction effects . More recent theories emphasized the role of sea-air interactions (Wang and Xie 1998) and water-vapor distribution (Maloney 2009; Hsu and Li 2011; Sobel and Maloney 2013).
Regional climate models (RCMs) are an effective tool for obtaining high-resolution regional information on weather-climate evolution (Xu et al. 2019). The nudging method used in the process of dynamic downscaling numerical simulations using RCMs is a way to maintain small-and medium-scale dynamic characteristics in RCMs while preserving large-scale features, so that the model simulation results approximate the real conditions (Wang and Kotamarthi 2013). Sperber (2003) found that in the speci c humidity and vertical velocity elds of the MJO, speci c humidity pro le and vertical motion pro le are similar, both tilting westward with height, that is, there is a zonal asymmetry with respect to the tilt axis. Maloney (2009) showed that before the occurrence of lower-level easterly wind anomalies, the columnintegrated moist static energy (MSE) accumulates prior to precipitation, and with the occurrence of westerly wind anomalies, MSE discharges during and after precipitation. The MSE anomalies occurred in the lower troposphere are mainly regulated by speci c humidity anomaly. Hsu and Li (2012) demonstrated that the distinct zonal asymmetric distribution of the water-vapor eld in the boundary layer with respect to the convective center is the key to the maintenance of the MJO eastward propagation. In the model simulation, however, different cumulus parameterization schemes have different effects on the simulation of the water vapor eld. It is shown that the model's lack of ability to simulate the MJO is largely in uenced by the model's cumulus parametrization scheme (Duvel et al. 2013). In this paper, we use different cumulus parameterization schemes to numerically simulate an individual case of MJO eastward propagation to verify the sensitivity of the Weather Research and Forecasting (WRF) model to cumulus parameterization schemes in simulating the effect of MJO eastward propagation, and then use the nudging assimilation of the WRF model to investigate the effects of different spatial distributions of atmospheric variable elds on the simulated MJO eastward propagation process.
The article is organized as follows. In Sect. 2, we present the model, datasets and method used. In Sect. 3, we analyze the simulation results of different cumulus parameterization schemes. In Sect. 4, we describe the nudging simulation and analyze the simulation results. Conclusions are presented in Sect. 5.

Model
The WRF model is a fully compressible non-hydrostatic model with a vertical coordinate system that follows the hydrostatic coordinate system of the terrain, and uses an interleaved grid of the Arakawa C grid, which is bene cial for improving accuracy in high-resolution simulations. In this study, WRF V4.0 model is used.

Datasets
The data used in this paper include daily reanalysis products from the National Centers for Environmental Prediction and National Center for Atmospheric Research (NCEP-NCAR), with a resolution of 2.5° × 2.5°( referred to as Re1) for the period from 1 January 1985 to 31

Bandpass ltering
Bandpass ltering is often used for extracting low-frequency signals. It was pointed out that for longer time series, the Lanczos lter has the distinct advantage of effectively suppressing spurious Gibbs waves due to nite truncation and having narrow transition bands (Duchon 1979). Therefore, we used a 100point Lanczos lter to extract the 30-60d component of atmospheric variables.

Correlation coe cient
The correlation coe cient between two elds is calculated as follows,

Case selection and nudging simulation
The MJO has a planetary-scale spatial structure dominated by zonal wave numbers 1-3 and eastward propagation. To study the eastward propagation characteristics of the MJO, we select a typical 30-60d propagation process in the tropics (10°S-10°N) from the Indian Ocean to the western Paci c Ocean (30°-130°E) in the autumn (September-November) of 2004 as the study object based on 30-60d ltered time-longitude maps of tropical (10°S-10°N) mean zonal winds at 200 and 850 hPa from 1985 to 2019 of the Re1 data (not shown). Figure 1 shows the time-longitude maps of the tropical mean zonal winds at 200 and 850 hPa from the Indian Ocean to the western Paci c Ocean in September-November 2004. We can see that the 30-60d low-frequency components of the zonal winds at both 200 hPa (Fig. 1a) and 850 hPa ( Fig. 1b) have obvious eastward propagation characteristics, and the amplitude of zonal winds at 200 hPa is stronger than that at 850 hPa, but the continuous eastward propagation characteristics of the zonal winds at 850 hPa are more obvious. So, the results of the 30-60d low-frequency component of the zonal winds at 850 hPa will be our focus in the subsequent analysis.
Nudging assimilation is an option in the WRF model to assimilate the simulated variables to the largescale driving eld during the simulation, and different variables can be selected. When using the reanalysis data as the driving force for WRF model simulation, the variables selected to be nudged in the model domain will be assimilated toward the reanalysis data, ensuring that there will be no large The physical parameterizations used in this study include the WSM6 microphysics scheme (Hong and Lim 2006), the Rapid Radiative Transfer Model (RRTM) (Mlawer et al. 1997) for longwave radiation calculation, the Dudhia scheme (Dudhia 1989) for shortwave radiation calculation, the Eta similarity scheme (Monin and Obukhov 1954;Janjić 1994Janjić , 1996Janjić , 2002, the ve-layer thermal diffusion scheme (Dudhia 1996) for land surface processes, and the Mellor-Yamada-Janjić boundary layer scheme (Mesinger 1993;Janjić 1994). Eleven cumulus parameterization schemes are selected for the simulations (Tab. 1). More details of the physical parameterizations are described in the WRF user's guide (Skamarock 2019). 2004 are determined by calculating the correlation coe cients of the 30-60d component amplitude distributions on these maps from simulations and observations. According to Hsu and Li (2012), the asymmetric water-vapor distribution between the east and west sides of the maximum amplitude of the MJO is a necessary condition for its eastward propagation. The water vapor is assimilated in the worst cumulus parameterization scheme for simulating the eastward propagation of the MJO, that is, the simulated water-vapor mixing ratio is nudged to the observed value (reanalysis eld, hereafter) during the simulation, and the improvement of the model for the eastward propagation of the MJO is examined.

Experimental design
The nudging assimilation used in this paper works as follows: during the simulation, the simulated eld in the model region is assimilated using the reanalysis eld. The parameterization schemes of the physical process for the nudging simulation are the same as those used in Sect. 2.3.3, and the analysis eld for nudging is also updated every six hours. Since experiments using different nudging coe cients show that the simulation results are not sensitive to the nudging coe cients, the nudging assimilation for CPS3 takes the default value of the model nudging coe cient 0.0003 for the analysis nudging simulation of the water-vapor eld (Ndg_q).  (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 eld in in uencing the eastward propagation of the MJO zonal wind eld is further explored below by comparing the evolution of the vertical pro les of the 30-60d component zonal wind, temperature, and speci c humidity elds. 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 ve-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 rst 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  Figure 8 shows the height-longitude maps of the mean speci c humidity 30-60d component corresponding to Fig. 7. It can be seen that the observations show the obvious eastward propagation of the MJO (the rst column of Fig. 8). Since the water-vapor eld is continuously nudged toward the observed eld during the assimilation, experiment Ndg_q is able to simulate the eastward propagation of the speci c humidity 30-60d component relatively well (the last column of Fig. 8), and experiment CPS5

Analysis of model results
is also able to simulate the eastward propagation of the speci c 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 elds 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 su cient 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) rst 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 veri cation 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, con rms 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 rst column of Fig. 9), its spatial structure is relatively complex compared to the eastward propagation characteristics of the zonal wind (the rst column of Fig. 7) and speci c humidity (the rst 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 coe cients 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 coe cients of speci c humidity and zonal winds. In contrast, experiment CPS3 (the second column of Fig. 9) does not simulate the eastward propagation characteristics of the temperature lowfrequency disturbance as observed.
In addition, similar to experiment Ndg_q that nudges only speci c 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 speci c humidity in terms of eastward propagation characteristics do not improve signi cantly ( gure omitted). Therefore, temperature distribution is not a key factor to control the low-frequency MJO eastward propagation compared to humidity distribution.

Mechanism analysis
From Fig. 8, it can be seen that there is a zonal asymmetry in the speci c humidity eld 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 in uencing 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 su cient lifting, the entire atmosphere column becomes unstable . 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 signi cantly from the low-frequency characteristics of temperature (Fig. 9). The  (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 eld can maintain the MJO propagation by affecting the atmospheric stability, while the temperature eld 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 coe cients 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 coe cient 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 eld 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 coe cient 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 coe cient 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 con rms the nding 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.

Conclusions
In this study, we focus on the eastward propagation of the MJO in the tropical atmosphere from the Indian Ocean to the western Paci c Ocean in the autumn of 2004 (September-November). The nudging assimilation of the WRF model is used to conduct sensitive tests of the role of water vapor in the eastward propagation of the MJO. The role of water-vapor disturbance in the eastward propagation of the MJO is revealed by comparing the simulation results with observations. The following conclusions are obtained.
The regional climate model is sensitive to the cumulus parameterization scheme to simulate the eastward propagation of the MJO. An unsuitable scheme will not simulate the eastward propagation of the MJO at all. For the individual cases of MJO eastward propagation studied here, the Tiedtke scheme can simulate the MJO eastward propagation well, while the Grell-Freitas scheme nearly has no skill.
When using the Grell-Freitas scheme and the water-vapor eld in the model is simulated by assimilating the observation, the model will be able to describe the eastward propagation of MJO better. Moreover, the low-frequency water-vapor phase is ahead of the zonal-wind phase. In contrast, nudging simulations of temperature in the model cannot reasonably produce the eastward propagation of the MJO, which con rms that only the tropical atmospheric water-vapor distribution is the main factor determining the eastward propagation of the MJO.
The evolution characteristics of equivalent potential temperature and speci c humidity during the MJO propagation are basically consistent, and both show a westerly dip, that is, a zonal asymmetry with respect to the tilting axis, while there are large differences with the evolution characteristics of the temperature eld. After nudging the water-vapor eld in the model domain, the simulated effect of the convective instability parameter on the MJO at 850 hPa is enhanced, and it is 6-7 days ahead of the zonal wind. Therefore, the water-vapor eld affects the propagation of the MJO by in uencing the atmospheric stability, while temperature has little effect on the eastward propagation of the MJO. Time lag correlation coe cients of observation (a) and simulated results by CPS3 (b), CPS5 (c) and Ndg_q (d) between time-longitude maps of 30-60d components of observed zonal winds (Fig. 1b) and