Supported by the National Natural Science Foundation of China (41975090 and 42075077) and Natural Science Foundation of Hunan Province, China (2022JJ20043).
In this study, driven by ERA5 reanalysis data, the Weather Research and Forecasting (WRF) version 4.0 was used to investigate the eastward propagation of the Madden–Julian oscillation (MJO) in the tropical atmosphere during December–February (DJF) of 2007/2008. The experiment with 11 cumulus parameterization schemes respectively shows that the Grell 3D scheme is one of several worse ones in describing MJO activities. In addition, still by use of the Grell 3D scheme, four nudging assimilation experiments for water vapor in all model vertical layers (Ndg_all), lower layers (Ndg_low), middle layers (Ndg_mid), and upper layers (Ndg_upp) were conducted. It is found that when the water vapor in the model approaches to the observed value, the model performance for MJO activities is improved greatly. Among the four nudging simulations, Ndg_all certainly performs best. Although Ndg_mid is important for the MJO-filtered profiles related to moisture, Ndg_low and Ndg_upp exhibit superiority to Ndg_mid in simulating MJO eastward propagation. Ndg_low has advantages when MJO features are represented by zonal wind at 850 hPa and precipitation because the lower-level MJO-filtered moisture is conducive to the existence of lower-level condensational heating to the east of the MJO convective center. Ndg_upp performs better when describing the MJO eastward propagation features by outgoing longwave radiation (OLR) since it can capture the moisture and cloud top temperature of deep convection associated with MJO, as well as front Walker cell. These results suggest that the lower-level moisture is more important in regulating the MJO eastward propagation, and the observed maximum MJO-filtered moisture in the middle troposphere might be a phenomenon accompanying the MJO deep convection, but not a factor controlling its eastward propagation.
Numerical models are essential tools for forecasting weather and climate, but current state-of-the-art models, such as the general circulation models (GCMs) and the newly released Coupled Model Intercomparison Project Phase 6 (CMIP6) models, have limited skills in simulating MJO behaviors (Slingo et al., 1996; Kim et al., 2009; Jiang et al., 2015; Le et al., 2021). Besides, based on the primary goals for filling the gap between subseasonal and seasonal time ranges, the subseasonal to seasonal (S2S) prediction research project was established jointly by the World Weather Research Programme (WWRP) and World Climate Research Programme (WCRP) (Wheeler and Hendon, 2004; Gottschalck et al., 2010; Rashid et al., 2011). The S2S database is an important resource for predicting MJO, but most S2S models for MJO prediction still have systematic errors when capturing the key dynamic features of MJO, such as its growth rate and propagation speed (Vitart, 2014; Vitart et al., 2017; Lim et al., 2018; Wu and Jin, 2021). The model deficiencies in capturing MJO characteristics suggest that the description of the MJO mechanism within the models is incomplete.
Progress has been made recently in theoretical research on the MJO (Jiang et al., 2020; Zhang et al., 2020) and various theories have been proposed to explain the eastward propagation of the MJO. In particular, the moisture mode theory has been a focus, which provides critical insights into key processes regulating MJO variability (Liu et al., 2009; Maloney, 2009; Jiang et al., 2011; Del Genio et al., 2012; Hsu and Li, 2012; Sobel and Maloney, 2013; Adames and Kim, 2016; Wang et al., 2017; Li and Hu, 2019; Maloney et al., 2019; Rushley et al., 2019; Wang and Li, 2020). Some studies have emphasized that MJO development and propagation are regulated by a recharge–discharge cycle, namely, increased lower-level moisture destabilizes the atmosphere before the moisture initiates MJO deep convection, and moisture is discharged during and after convection (Kiladis et al., 2005; Benedict and Randall, 2007). Thus, shallow convection (moisture in the lower troposphere) motivates deep convection (moisture in the upper troposphere). Besides, diagnostic analysis with reanalysis data by Hsu and Li (2012) revealed the importance of the zonal asymmetry of the moisture relative to the MJO convection below 700 hPa on the MJO eastward propagation, and numerical experiments have been conducted to confirm this (Hsu et al., 2014). Additionally, Gonzalez and Jiang (2017) showed that the mean moisture pattern in the lower troposphere is important for MJO propagation. In addition, it has been found that the maximum MJO-filtered moisture locates in the middle troposphere (Hsu and Li, 2012) and is important for convection (Holloway and Neelin, 2007, 2009). These findings illustrate that moisture at different altitudes are all likely to play a role during the eastward propagation of the MJO, but previous observational studies can not indicate which altitude is the most important. Therefore, it is necessary to explore the effect of MJO-filtered moisture in different layers of the troposphere.
Regional Climate Models (RCMs) require less computational resource to run at higher horizontal resolutions, and the complex topography and land–sea mask can be better represented in RCMs (Laprise, 2008; Weng et al., 2009; Tan et al., 2020). Therefore, as a commonly used RCM, the Weather Research and Forecasting (WRF) model is used in this study. In RCMs, the nudging method is an effective dynamic downscaling tool used to retain small- and medium-scale signals so that the model can obtain high resolution regional information despite being constrained by large-scale features and coarser input data (Wang and Kotamarthi, 2013; Xu et al., 2019). The purpose of the nudging applications is to narrow the gap between the simulated results and the forcing data and then to compare the assimilation effect between variables (Stauffer and Seaman, 1994; Liu et al., 2008; Bowden et al., 2012). Besides, because the ability of numerical models to simulate MJO eastward propagation is largely influenced by cumulus parameterization schemes (Duvel et al., 2013; Zhu et al., 2022), using the nudging method with a worse cumulus parameterization scheme can more directly evaluate the influence of the actual atmospheric variables. In this study, the nudging assimilation technique was employed to investigate the effects of moisture in different altitude layers in the WRF model with lower horizontal resolutions, which is expected to be useful for improving the models that are part of the S2S project.
This article is organized as follows. In Section 2, the model, datasets, and methods are presented. The simulation results with different cumulus parameterization schemes are analyzed in Section 3. Section 4 discusses the results of nudging assimilation experiments for moisture. Section 5 reveals the relationship between MJO eastward propagation and the moisture profile. The conclusions are presented in Section 6.
2.
Model, datasets, and methods
2.1
Model
The model configuration is similar to our previous work (Zhu et al., 2022). The model adopted here is version 4.0 of the WRF Model (Skamarock et al., 2019), which was developed by NCAR. To test the simulation performance of the MJO eastward propagation characteristics in the tropics, the Mercator projection is adopted in this study with the center located at 120°E on the equator. The number of horizontal grid points is 420 (west–east) × 200 (south–north) with a grid spacing of 50 km. Despite that the gray-zone resolution (5–9 km) was suggested to be used for MJO, monsoon, and regional climate simulations (Zhang et al., 2017; Chen et al., 2018a, b; Taraphdar and Pauluis, 2021; Taraphdar et al., 2021), the lower resolution (50 km) is still employed in this study, as we focus on the features of cumulus parameterization schemes in the S2S models mostly with lower resolution.
Figure 1 shows the model domain. The model has 45 vertical layers, and the pressure at the top of the model is 10 hPa. The sea surface temperature (SST) is updated every 6 h in the simulation. The model is initialized at 0000 UTC 1 July 2007 and ends at 0000 UTC 30 June 2008, for a total of 365 simulation days. The time step is 180 s, and the model outputs are stored daily.
The physical parameterizations used in this study include the WRF single-moment 6-class (WSM6) microphysics scheme (Hong and Lim, 2006), the Rapid Radiative Transfer Model for GCMs (RRTMG) scheme (Iacono et al., 2008) for longwave and shortwave radiation calculations, the Eta similarity scheme (Monin and Obukhov, 1954; Janjić, 1994, 2002; Janjic, 1996), the unified Noah land-surface model (Tewari et al., 2004) for land surface processes, and the Yonsei University Scheme (YSU) boundary layer scheme (Hong et al., 2006). Moreover, 11 cumulus parameterization schemes are selected for the simulations, respectively (Table 1). More details of the physical parameterizations are described in the WRF user’s guide (Skamarock et al., 2019).
Table
1.
Names of the 11 experiments and their cumulus parameterization schemes
The initial and lateral boundary conditions used for driving the WRF model come from the fifth generation ECMWF reanalysis (ERA5; Hersbach et al., 2023), with a horizontal resolution of 0.5° × 0.5° and 6-h temporal resolution from 0000 UTC 1 July 2007 to 0000 UTC 30 June 2008, and they are also used as the observations to compare the simulation effects. The moisture data are key to this study and constrained by satellite observations in ERA5 (Kim et al., 2014). The ERA5 reanalysis data are available at https://cds.climate.copernicus.eu/cdsapp#!/search?type=dataset&text=ERA5.
To investigate the effect of moisture on the eastward propagation of MJO, a typical MJO case was selected in the winter (December–February, DJF) of 2007/2008, which was determined based on the eastward propagation feature of MJO-filtered time–longitude cross-sections in terms of the tropical mean OLR and zonal wind at 850 hPa from 1985 to 2022 (figures omitted). In addition, for consistent comparison, daily precipitation and OLR as well as model outputs are stored by using daily means and a horizontal resolution of 0.5° × 0.5° prior to analysis.
2.3
Methods
2.3.1
Filtering
For longer time series, the Lanczos filter is a better bandpass filtering method to effectively suppress spurious Gibbs waves; therefore, it is often used for extracting low frequency signals (Duchon, 1979). In this study, a 100-point Lanczos filter was employed to extract the 30–100-day component of atmospheric variables (Wheeler and Kiladis, 1999).
2.3.2
Selection of the maximum MJO convective activity center
To examine the effect of moisture on the MJO eastward propagation, it is necessary to locate the center of maximum MJO convective activity. Figure 2 shows the distribution of the standard deviation of the MJO-filtered OLR, which implies that the large standard deviation locates in the south to equator (15°–7.5°S). In this study, the maximum standard deviation area in the north to Australia (MSDA1) was studied as the MJO convective activity center, and the area over the Indian Ocean (MSDA2) was used for verification and for increasing the sample size (Fig. 2).
Fig
2.
Spatial distribution of the standard deviation of MJO-filtered OLR (shading; W m−2) from December to February (DJF) of 2007/2008, where the green rectangle north to Australia represents the MSDA1 (15°–7.5°S, 130°–140°E) and the green rectangle over the Indian Ocean represents the MSDA2 (15°–7.5°S, 72°–82°E).
In addition, to obtain the MJO active and suppressed phases during DJF of 2007/2008, a reference time series was computed by a box-averaged MJO-filtered OLR. The MJO active phases are extracted from the series when the averaged MJO-filtered OLR is less than a standard deviation of −1, while suppressed phases are those exceeding a standard deviation of 1. Based on this criterion, 12 days are selected from the MSDA1 (from 25 December 2007 to 5 January 2008) and the MSDA2 (from 26 January to 6 February 2008) for the MJO active phase, and 15 days are selected from the MSDA1 (from 16 to 30 January 2008) and the MSDA2 (from 29 December 2007 to 12 January 2008) for the MJO suppressed phase. Because the MJO active and suppressed phases have opposite signs, only the MJO active phase is shown in the subsequent study below.
2.3.3
Nudging simulation
Nudging assimilation is an option in the WRF model, and the analysis nudging technique is chosen in this study. Three different variables (u and v wind components, temperature, and water vapor) can be selected during the analysis nudging period. With the aforementioned model configuration and forcing data, analysis nudging for water vapor is employed for the entire simulation period and the nudging coefficient is set to the default value of 0.0003 s−1 (Mölg and Kaser, 2011; Zhu et al., 2022). A poor cumulus parameterization scheme is used to best show how the moisture distribution can improve the model performance.
In the WRF model, analysis nudging can be selected and restricted to above the specific model vertical layer, below the layer, or even between two model layers. To analyze the effect of moisture in different altitude layers on the eastward propagation of the MJO, it is important to make a reasonable division of the model atmosphere into lower, middle, and upper layers. Hsu and Li (2012) emphasized the importance of the zonal asymmetry of the moisture relative to the MJO convection below 700 hPa on the MJO eastward propagation. Gonzalez and Jiang (2017) suggested that the mean moisture pattern in the lower troposphere (650–900 hPa) can serve as an important diagnostic metric for MJO propagation. Therefore, in this study, the boundary between the lower and middle layers is set to approximately 700 hPa, while the boundary between the middle and upper layers is set to approximately 500 hPa so that the maximum MJO-filtered moisture in the vertical direction is in the middle layer.
The vertical layers are unevenly set in the WRF model, so we choose the nearest layers of 700 and 500 hPa as the boundaries for the lower, middle, and upper layers. The pressure distribution in the vertical layers of the model illustrates that the pressure field is relatively uniform over the ocean (figures omitted). The average pressure in MSDA1 at the 12th and 17th layers, corresponding to model vertical coordinates η = 0.74 and 0.51, is approximately 718 and 488 hPa, respectively. To investigate the effect of moisture in different altitude layers in the troposphere, four additional analysis nudging assimilation experiments for water vapor are conducted. Ndg_all refers to an experiment in which the analysis nudging is carried out in all model layers, whereas Ndg_low refers to the nudging assimilation implemented below the 12th model layer, Ndg_upp indicates nudging above the 17th model layer, and Ndg_mid refers to nudging between the 12th and 17th model layers.
3.
Experiments with different cumulus parameterization schemes
Similar to our previous work (Zhu et al., 2022), Fig. 3 shows the observed and simulated time–longitude cross-sections of the meridionally averaged MJO-filtered OLR in the tropical Indo–Pacific from 1 December 2007 to 29 February 2008. Figure 3a shows that the observed MJO-filtered OLR has obvious eastward propagation characteristics, with an average phase speed of approximately 4 m s−1. Comparisons with observations suggest that none of the 11 experiments with different cumulus parameterization schemes can accurately characterize the main features of the MJO, especially the eastward propagation and intensity, as noted by Slingo et al. (1996). Experimental schemes CPS3, CPS4, and CPS8 do not simulate the eastward propagation characteristics; experiments CPS1, CPS2, CPS6, CPS9, and CPS10 simulate a weak intensity, while CPS5, CPS7, and CPS11 exhibit better eastward propagation performances. In addition, both the observed time–longitude cross-sections of the meridional-averaged MJO-filtered zonal wind at 850 hPa, and precipitation display the MJO eastward propagation characteristics, and the simulation results also show model deficiencies in capturing the characteristics of MJO activities (figures omitted).
Fig
3.
Time–longitude cross-sections of observed and simulated meridional-averaged (15°–7.5°S) MJO-filtered OLR (W m−2) in the Indo–Pacific (30°E–150°W) from 1 December 2007 to 29 February 2008. (a) Observation, (b) CPS1, (c) CPS2, (d) CPS3, (e) CPS4, (f) CPS5, (g) CPS6, (h) CPS7, (i) CPS8, (j) CPS9, (k) CPS10, and (l) CPS11.
Figure 4 shows the pattern correlation coefficients between the observed time–longitude cross-sections of MJO-filtered OLR, zonal wind at 850 hPa as well as precipitation and the simulated ones with 11 cumulus parameterization schemes, respectively. The simulations with different cumulus parameterization schemes exhibit diverse performances among the three selected MJO variables (e.g., OLR, zonal wind at 850 hPa, and precipitation), and most of the 11 experiments can not adequately characterize the eastward propagation of MJO. The pattern correlation coefficient of MJO-filtered zonal wind at 850 hPa is the largest among the three MJO variables with the same cumulus parameterization scheme, and the model simulates the eastward propagation of the MJO-filtered OLR better than precipitation except for CPS3. By comprehensively considering the pattern correlation coefficients for all three MJO variables, CPS4 with Grell 3D scheme (Grell, 1993; Grell and Dévényi, 2002) is recognized as one of several worse simulations for the eastward propagation of the MJO in the selected case, and the pattern correlation coefficients between the CPS4 and the observations reach 0.37 (OLR), 0.44 (zonal wind at 850 hPa), and 0.25 (precipitation), respectively.
Fig
4.
Pattern correlation coefficients between observed and simulated MJO-filtered time–longitude cross-sections of OLR (blue), zonal wind at 850 hPa (green), and precipitation (grey) with 11 cumulus parameterization schemes (CPS1–CPS11).
4.
Nudging assimilation experiments for moisture
In this section, four experiments (Ndg_all, Ndg_low, Ndg_mid, and Ndg_upp) are presented to examine the effect of moisture in different altitude layers. These experiments are intended to improve the model performance for MJO eastward propagation when the nudging assimilation for water vapor is integrated into the model for one of several worse simulations, CPS4 with Grell 3D scheme (Grell, 1993; Grell and Dévényi, 2002).
Similar to Fig. 3, Fig. 5 shows the simulated MJO-filtered OLR of the nudging assimilation experiments. Ndg_all (Fig. 5b) can reproduce the MJO eastward propagation perfectly, despite that the Grell 3D scheme is still employed. Therefore, the moisture profile does play a very important role in maintaining MJO activities (Maloney, 2009; Hsu and Li, 2012; Wang et al., 2017; Zhu et al., 2022). In addition, Ndg_low (Fig. 5c) and Ndg_upp (Fig. 5e) can also reproduce basic features of the eastward propagating MJO, whereas Ndg_mid (Fig. 5d) does not improve much compared to CPS4 (Fig. 3e). Ndg_upp appears to simulate MJO-filtered OLR better because it can significantly improve the moisture processes associated with deep convection as well as the temperature at the cloud top in the upper atmosphere. Furthermore, when nudging assimilation for water vapor is applied, there are also improvements when the MJO eastward propagation features are described by zonal wind at 850 hPa and by precipitation (figures omitted).
Fig
5.
As in Fig. 3, but for simulations of the nudging assimilation experiments. (a) Observation, (b) Ndg_all, (c) Ndg_low, (d) Ndg_mid, and (e) Ndg_upp.
Figure 6 shows the pattern correlation coefficients between the simulated (CPS4, Ndg_all, Ndg_low, Ndg_mid, and Ndg_upp) and observed time–longitude cross-sections of MJO-filtered OLR, zonal wind at 850 hPa, and precipitation. It is clearly shown that nudging assimilation can significantly improve the model performance when simulating MJO activities; that is, in terms of MJO eastward propagation features, the pattern correlation coefficients of all variables are substantially improved compared to the original simulation. Ndg_all performs best in describing the MJO eastward propagation features by OLR (also see Fig. 5), zonal wind at 850 hPa and precipitation, while the other three experiments (Ndg_low, Ndg_mid, and Ndg_upp) show different improvements after conducting nudging assimilation of moisture in different altitude layers. Comparatively, Ndg_low exhibits a better ability than Ndg_mid and Ndg_upp in the simulation of zonal wind at 850 hPa and precipitation. Ndg_upp performs better when describing the MJO eastward propagation features by OLR, because assimilation of the water vapor in the upper troposphere actually improves the response of the OLR-related convective clouds at those layers, with a pattern correlation coefficient of 0.91 compared to the observations.
Fig
6.
Pattern correlation coefficients between observations and CPS4 (blue), Ndg_all (green), Ndg_low (grey), Ndg_mid (orange), and Ndg_upp (yellow) on MJO-filtered time–longitude cross-sections of OLR, zonal wind at 850 hPa, and precipitation, respectively.
Fig
7.
Height–longitude cross-sections of meridional-averaged (15°–7.5°S) MJO-filtered specific humidity (contour; 10−4 kg kg−1) and specific humidity tendency (shading; 10−10 kg kg−1 s−1) during the active phase of MJO over the MSDA1. (a) Observation, (b) CPS4, (c) Ndg_all, (d) Ndg_low, (e) Ndg_mid, and (f) Ndg_upp.
Previous studies have shown that the zonal asymmetry of the moisture in the lower troposphere is important for MJO eastward propagation (Hsu and Li, 2012; Hsu et al., 2014); moreover, the effect of lower-level MJO-filtered moisture itself was also confirmed (Gonzalez and Jiang, 2017). In our sensitivity experiments, Ndg_low exhibits better performance for MJO activities by zonal wind at 850 hPa and precipitation, which further verifies that the moisture in the lower troposphere plays an important role in simulating MJO activities. Additionally, this confirms the proposed theory that the intraseasonal wind speed field is observed to have a positive covariance with the intraseasonal precipitation field (Raymond et al., 2003).
5.
Relationship between MJO eastward propagation and moisture profile
In this section, the active phase (from 25 December 2007 to 5 January 2008) of MSDA1 (15°–7.5°S, 130°–140°E) is presented to investigate the relationship betw-een MJO eastward propagation and moisture profile.
Figure 7 shows the height–longitude cross-sections of meridional-averaged MJO-filtered specific humidity and specific humidity tendency during the MJO active phase over MSDA1. For the specific humidity (contour in Fig. 7), the observed maximum MJO-filtered moisture is in the middle troposphere (approximately 600 hPa), at 135°E where the MJO convective center is basically located (Fig. 7a). In addition, the maximum moisture content line tilts westward, as shown in the previous study (Sperber, 2003). CPS4 itself can not capture the maximum MJO-filtered moisture in the middle troposphere, and the horizontal scale is considerably shortened (Fig. 7b). Once the nudging assimilation is performed, all four experiments (Ndg_all, Ndg_low, Ndg_mid, and Ndg_upp) exhibit improvements in simulating the moisture field to some extent. Ndg_all almost perfectly recreates the observed moisture profile (Fig. 7c). When the nudging assimilation is conducted in the lower troposphere, Ndg_low simulates a wider range of positive MJO-filtered moisture than CPS4, but the maximum MJO-filtered moisture is still located lower than the observation and there is another maximum center at 700 hPa at 105°E (Fig. 7d). Ndg_mid reproduces the maximum MJO-filtered moisture in the middle troposphere but it also simulates other centers with large values (Fig. 7e). Ndg_upp simulates a narrower range of positive MJO-filtered moisture than the observations in the lower troposphere (Fig. 7f). Ndg_mid and Ndg_upp simulate better than that of Ndg_low, and the pattern correlation coefficients for height–longitude cross-sections of MJO-filtered specific humidity between Ndg_mid and Ndg_upp with observations are 0.80 and 0.79.
For the specific humidity tendency (shading in Fig. 7), observations show that the positive specific humidity tendency center is mainly located on the east side of the MJO convective center (135°E), while the negative center is almost located on the west side, and the boundary between the positive and negative ones also tilts westward from the lower to the upper troposphere (Fig. 7a). Therefore, the MJO-filtered moisture is enhanced to the east of the MJO convection cell, which may be a reason for MJO eastward propagation. The CPS4 shows almost no skill in simulating the specific humidity tendency (Fig. 7b), but there are some improvements after nudging water vapor. Ndg_all demonstrates a clear boundary between positive and negative values just as the observations (Fig. 7c). When the nudging assimilation is conducted in the lower troposphere, Ndg_low provides better simulations in the lower troposphere, but the positive specific humidity tendency is located to the west of the MJO convective center in the middle troposphere (Fig. 7d). Ndg_mid and Ndg_upp produce better simulations than Ndg_low, and Ndg_mid has the highest pattern correlation coefficient with observations among the three nudging assimilation simulations in different altitude layers.
The equivalent potential temperature (θe) is a physical variable integrating moisture and temperature. A layer of atmosphere is considered potentially unstable when the air mass in this layer is initially moist but unsaturated, and ∂θe/∂z<0 within the layer (Holton, 1992; Emanuel, 1994). Here, ∂θe/∂p is an atmospheric stability parameter, and ∂θe/∂p>0 is used to represent a potentially unstable atmosphere. To demonstrate the effect of moisture in different altitude layers on MJO eastward propagation through atmospheric stabilization, corresponding to the phase shown in Fig. 7, the vertical profile of the MJO-filtered equivalent potential temperature (θe′) and its vertical differential (∂θ′e/∂p) are examined (Fig. 8). Both the observed and simulated height–longitude cross-sections for MJO-filtered equivalent potential temperature (contour in Fig. 8) are similar to those for MJO-filtered specific humidity (contour in Fig. 7). Specifically, the positive regions of the MJO-filtered equivalent potential temperature correspond to those of the MJO-filtered specific humidity, and the centers of maximum values are located in almost the same areas (Zhu et al. 2022).
Fig
8.
As in Fig. 7, but for MJO-filtered equivalent potential temperature (contour; K) and its vertical differential (shading; K Pa−1).
At the center of MJO convective activity, the observed vertical differential of MJO-filtered equivalent potential temperature (∂θ′e/∂p) shows that the atmosphere is potentially stable in the lower troposphere, and it becomes progressively unstable above 500 hPa (shading in Fig. 8a). Contrary to the observations, CPS4 can not simulate the characteristics of atmospheric instability (Fig. 8b). After performing the nudging assimilation, Ndg_all simulates the general feature of the observed ∂θ′e/∂p (Fig. 8c). Ndg_low can not adequately reproduce the observed pattern (Fig. 8d), whereas Ndg_mid and Ndg_upp exhibit better performances for the overall atmospheric instability characteristics (Figs. 8e, f).
Figure 9 shows the pattern correlation coefficients between observations and simulations (CPS4, Ndg_all, Ndg_low, Ndg_mid, and Ndg_upp) on height–longitude cross-sections over MSDA1 for q′, ∂q′/∂t, θ′e, and ∂θ′e/∂p. In the nudging experiment, the simulated moisture approaches to the observations and ensures that there is no large deviation between the simulation and the observations; therefore, as expected, Ndg_all can correctly simulate the MJO-filtered profiles for q′, ∂q′/∂t, θ′e, and ∂θ′e/∂p. As the observed maximum MJO-filtered specific humidity, specific humidity tendency, and equivalent potential temperature are mainly distributed in the middle troposphere (Figs. 7a, 8a), Ndg_mid gives the best performance for q′, ∂q′/∂t, and θ′e among Ndg_low, Ndg_mid, and Ndg_upp. For the atmospheric stability parameter (∂θ′e/∂p), Ndg_mid also produces a good simulation. It should be noted that all of these characteristics about MJO-filtered profiles for q′, ∂q′/∂t, θ′e, and ∂θ′e/∂p are also true in MSDA2 (figures omitted), suggesting that the simulated features have regional consistency.
Fig
9.
Pattern correlation coefficients of MJO-filtered specific humidity (q′), specific humidity tendency (∂q′/∂t), equivalent potential temperature (θ′e), and its vertical differential (∂θ′e/∂p) over MSDA1 on height–longitude cross-sections between observations and simulations of CPS4 (blue), Ndg_all (green), Ndg_low (grey), Ndg_mid (orange) and Ndg_upp (yellow), respectively.
The vertical circulation and thermodynamic structure are shown in Fig. 10. Figure 10a shows that the MJO-filtered ascending air flow roughly ranges from 100° to 150°E, and the maximum value occurs at approximately 135°E, where the center of MJO convective activity is located. Besides, there exists vertically overturning circulation to the east of the MJO convective center (also called “front Walker cell”) in observations, which could favor the eastward propagation of the MJO (Chen and Wang, 2018). Consistent with Fig. 7b, CPS4 also simulates a narrower range of ascending air flow with a width of only 15° longitude and does not simulate the front Walker cell as observations (Fig. 10b). After performing the nudging assimilation, Ndg_all almost simulates the vertical structure of the MJO circulation as observed (Fig. 10c). Among the other three experiments (Ndg_low, Ndg_mid, and Ndg_upp), only Ndg_upp simulates the front Walker cell (Fig. 10f).
Fig
10.
Height–longitude cross-sections of meridional-averaged (15°–7.5°S) MJO-filtered moisture sink (shading; J kg−1 s−1), and vertical structure of circulation (vectors; m s−1 for zonal wind and 0.01 Pa s−1 for vertical pressure velocity) during the active phase of MJO over the MSDA1. (a) Observation, (b) CPS4, (c) Ndg_all, (d) Ndg_low, (e) Ndg_mid, and (f) Ndg_upp.
The unstable thermodynamic structure east of the convection also favors the MJO eastward propagation. The shading in Fig. 10 stands for the MJO-filtered moisture sink (Yanai et al., 1973), which to some extent represents the condensational heating. The large value center of MJO-filtered moisture sink simulated by all experiments is roughly consistent with the MJO convective center, and only Ndg_all (Fig. 10c) and Ndg_low (Fig. 10d) simulate the condensational heating existing to the east of MJO convective center.
In brief, the lower-level MJO-filtered moisture is conducive to the existence of lower-level condensational heating to the east of MJO convective center (Fig. 10); the middle-level MJO-filtered moisture is important for the MJO-filtered profiles related to moisture (specific humidity and its tendency, equivalent potential temperature and its vertical differential; Fig. 9); and the upper-level MJO-filtered moisture benefits the simulation of moisture associated with MJO deep convection as well as front Walker cell (Fig. 10).
Here, we will disclose the relationship between the model skill in representing the MJO-filtered moisture in different altitude layers and that in simulating MJO eastward propagation across different experiments (CPS4, Ndg_all, Ndg_low, Ndg_mid, Ndg_upp, and other CPSs). The model skill for the MJO-filtered moisture in each experiment is defined by the pattern correlation coefficient between the simulated and observed height–longitude cross-section of meridional-averaged moisture from 1000 to 300 (the whole troposphere), 1000 to 718 (lower troposphere), 718 to 488 (middle troposphere), and 488 to 300 hPa (upper troposphere). According to Gonzalez and Jiang (2017), the skill for MJO propagation is determined by the pattern correlation coefficient between simulated time–longitude cross-section of MJO-filtered precipitation and that of the TRMM precipitation products (treated as observations). To increase the sample size, calculations were performed in both MSDA1 and MSDA2.
Figure 11 shows the scatterplots of model skill in representing the averaged MJO-filtered specific humidity in different altitude layers over MSDA1/MSDA2 versus MJO propagation skill for different simulations, and the corresponding linear best fit regression line. The regression line for MSDA1 (dotted blue line) is almost always above that for MSDA2 (dotted purple line), indicating that the model skill for the MJO-filtered moisture in different altitude layers over MSDA1 is a little better than that over MSDA2, however, there is no essential difference between them, suggesting consistency in both areas. In addition, the calculated correlation coefficient for the scatters of both MSDA1 and MSDA2 between the model skill for lower-level moisture and that for MJO propagation across different simulations is 0.58 (above the 99% confidence level), strongly suggesting a high correlation between MJO propagation and MJO-filtered moisture in the lower troposphere (Fig. 11b). However, the model skill for middle-level moisture and that for MJO propagation across different simulations has the lowest correlation coefficient of 0.27, indicating that moisture in the middle troposphere can not be the key factor for the MJO eastward propagation though the maximum MJO-filtered moisture is mainly distributed there (Fig. 11c).
Fig
11.
Scatterplots of model skill in representing the meridional-averaged MJO-filtered specific humidity in different altitude layers. (a) All-level, (b) lower-level, (c) middle-level, and (d) upper-level over MSDA1 (solid dots) and MSDA2 (hollow triangles) versus MJO propagation skill across different simulations (CPS4: yellow, Ndg_all: red, Ndg_low: green, Ndg_mid: blue, Ndg_upp: brown, and other CPSs: black). The dotted blue line, dotted purple line, and solid black line represent the linear best fit regression lines for scatters over MSDA1, MSDA2, and both MSDA1 and MSDA2, respectively, and the corresponding linear regression equation is shown on the left of the lines in black. The calculated correlation coefficient for scatters of both MSDA1 and MSDA2 in each plot is shown in the top left corner.
Figure 12 shows the observed and simulated height–time cross-sections of box-averaged MJO-filtered specific humidity over the MSDA1 from 1 December 2007 to 29 February 2008. It clearly demonstrates that the maximum MJO-filtered moisture is located in the middle troposphere (Fig. 12a), which is consistent with the distribution shown in Fig. 7a. Again, CPS4 cannot adequately reproduce the MJO-filtered moisture (Fig. 12b), and Ndg_all captures almost all features after assimilating the water vaper in the whole troposphere (Fig. 12c). In addition, although Ndg_mid (Fig. 12e) and Ndg_upp (Fig. 12f) give better performances for the box-averaged moisture in the whole troposphere than Ndg_low (Fig. 12d) with the pattern correlation coefficients of 0.72 (Ndg_low), 0.92 (Ndg_mid), and 0.86 (Ndg_upp), respectively, Ndg_low reproduces the lower-level moisture pattern as well as Ndg_all with the pattern correlation coefficient of 0.98, while the corresponding values are 0.87 (Ndg_mid) and 0.64 (Ndg_upp). These features suggest that even if Ndg_low can not reproduce moisture profile in the middle and upper troposphere as well as the other nudging simulations, the moisture profile in the lower troposphere is simulated perfectly, which is the most important factor ensuring MJO eastward propagation.
Fig
12.
Height–time cross-sections of observed and simulated box-averaged (15°–7.5°S, 130°–140°E) MJO-filtered specific humidity (10−4 kg kg−1) over MSDA1 from 1 December 2007 to 29 February 2008. (a) Observation, (b) CPS4, (c) Ndg_all, (d) Ndg_low, (e) Ndg_mid, and (f) Ndg_upp.
6.
Conclusions
In this study, we focus on the WRF model’s ability in reproducing the MJO eastward propagation in the tropical atmosphere during DJF of 2007/2008. By use of WRF version 4.0, it is found that none of the sensitivity experiments with 11 cumulus parameterization schemes can perfectly describe the features of the MJO activities for DJF 2007/2008 case, especially its eastward propagation and intensity. Relatively, for the features of MJO eastward propagation, the model performs better when MJO is represented by zonal wind at 850 hPa than by OLR or precipitation. Moreover, the simulation with Grell 3D (CPS4) is one of several worse ones among the 11 experiments. Furthermore, four nudging assimilation experiments for water vapor were conducted in all model layers (Ndg_all), lower layers (Ndg_low), middle layers (Ndg_mid), and upper layers (Ndg_upp), respectively, while the Grell 3D scheme was still employed. Then, the nudging assimilation experiments were used to disclose the relationship between moisture in different altitude layers and the eastward propagation of the MJO. The main conclusions are as follows.
When the model performance for MJO eastward propagation is evaluated by pattern correlation coefficients between MJO-filtered observations and simulations on the time–longitude cross-sections, among the four nudging assimilation simulations, Ndg_all performs best for the features of MJO eastward propagation represented by all three commonly used variables (e.g., zonal wind at 850 hPa, precipitation, and OLR) as expected. Whereas Ndg_low simulates the features of the MJO eastward propagation well for zonal wind at 850 hPa and precipitation, presenting more advantages than Ndg_mid, and Ndg_upp performs better when describing the MJO eastward propagation features by OLR because it can significantly improve the moisture associated with deep convection as well as the temperature at the cloud top in the upper troposphere. Therefore, the moisture in the lower troposphere is more important for maintaining MJO eastward propagation, as revealed in terms of diagnostic analysis with reanalysis data by Maloney (2009) and Hsu and Li (2012). Also, the simulation for the 2012/2013 winter case is conducted (figures omitted), and it gives exactly the same results as the 2007/2008 winter case, which shows the generality of the results for different MJO cases.
To understand the relationship between MJO eastward propagation and moisture profile, the MJO active phase (from 25 December 2007 to 5 January 2008) over the MSDA1 (15°–7.5°S, 130°–140°E) is presented for this study. For the model simulation, CPS4 has almost no skill in reproducing moisture profile; however, when the nudging assimilation for water vapor is integrated in the model, though the Grell 3D scheme (CPS4) is still used, all four experiments (Ndg_all, Ndg_low, Ndg_mid, and Ndg_upp) show some degrees of improvements in simulating the profiles of atmospheric variables. In the height–longitude cross-sections, Ndg_mid exhibits superiority to Ndg_low and Ndg_upp in simulating the MJO-filtered profiles for q′, ∂q′/∂t, θe′, and ∂θ′e/∂p, because the maximum MJO-filtered moisture is mainly distributed in the middle troposphere (Hsu and Li, 2012). The lower-level MJO-filtered moisture is conducive to the existence of lower-level condensational heating to the east of MJO convective center, and the upper-level MJO-filtered moisture benefits the simulation of moisture associated with MJO deep convection as well as front Walker cell.
The examination of the correlation coefficient between model skill in representing the MJO-filtered moisture in different altitude layers and that in simulating MJO eastward propagation across different experiments shows that, there is a high (low) correlation between the simulated MJO-filtered lower-level (middle-level) moisture and MJO eastward propagation. Therefore, it is quite certain that the lower-level moisture is more important than the middle-level moisture in regulating the MJO eastward propagation despite that the maximum MJO-filtered moisture is in the middle troposphere. This finding indicates that the observed maximum MJO-filtered moisture in the middle troposphere might be a phenomenon accompanying the MJO deep convection, but not a factor controlling its eastward propagation.
Acknowledgments
The authors are grateful to the anonymous reviewers and editor for their valuable and constructive comments.
Fig.
12.
Height–time cross-sections of observed and simulated box-averaged (15°–7.5°S, 130°–140°E) MJO-filtered specific humidity (10−4 kg kg−1) over MSDA1 from 1 December 2007 to 29 February 2008. (a) Observation, (b) CPS4, (c) Ndg_all, (d) Ndg_low, (e) Ndg_mid, and (f) Ndg_upp.
Fig.
2.
Spatial distribution of the standard deviation of MJO-filtered OLR (shading; W m−2) from December to February (DJF) of 2007/2008, where the green rectangle north to Australia represents the MSDA1 (15°–7.5°S, 130°–140°E) and the green rectangle over the Indian Ocean represents the MSDA2 (15°–7.5°S, 72°–82°E).
Fig.
4.
Pattern correlation coefficients between observed and simulated MJO-filtered time–longitude cross-sections of OLR (blue), zonal wind at 850 hPa (green), and precipitation (grey) with 11 cumulus parameterization schemes (CPS1–CPS11).
Fig.
5.
As in Fig. 3, but for simulations of the nudging assimilation experiments. (a) Observation, (b) Ndg_all, (c) Ndg_low, (d) Ndg_mid, and (e) Ndg_upp.
Fig.
6.
Pattern correlation coefficients between observations and CPS4 (blue), Ndg_all (green), Ndg_low (grey), Ndg_mid (orange), and Ndg_upp (yellow) on MJO-filtered time–longitude cross-sections of OLR, zonal wind at 850 hPa, and precipitation, respectively.
Fig.
7.
Height–longitude cross-sections of meridional-averaged (15°–7.5°S) MJO-filtered specific humidity (contour; 10−4 kg kg−1) and specific humidity tendency (shading; 10−10 kg kg−1 s−1) during the active phase of MJO over the MSDA1. (a) Observation, (b) CPS4, (c) Ndg_all, (d) Ndg_low, (e) Ndg_mid, and (f) Ndg_upp.
Fig.
9.
Pattern correlation coefficients of MJO-filtered specific humidity (q′), specific humidity tendency (∂q′/∂t), equivalent potential temperature (θ′e), and its vertical differential (∂θ′e/∂p) over MSDA1 on height–longitude cross-sections between observations and simulations of CPS4 (blue), Ndg_all (green), Ndg_low (grey), Ndg_mid (orange) and Ndg_upp (yellow), respectively.
Fig.
10.
Height–longitude cross-sections of meridional-averaged (15°–7.5°S) MJO-filtered moisture sink (shading; J kg−1 s−1), and vertical structure of circulation (vectors; m s−1 for zonal wind and 0.01 Pa s−1 for vertical pressure velocity) during the active phase of MJO over the MSDA1. (a) Observation, (b) CPS4, (c) Ndg_all, (d) Ndg_low, (e) Ndg_mid, and (f) Ndg_upp.
Fig.
11.
Scatterplots of model skill in representing the meridional-averaged MJO-filtered specific humidity in different altitude layers. (a) All-level, (b) lower-level, (c) middle-level, and (d) upper-level over MSDA1 (solid dots) and MSDA2 (hollow triangles) versus MJO propagation skill across different simulations (CPS4: yellow, Ndg_all: red, Ndg_low: green, Ndg_mid: blue, Ndg_upp: brown, and other CPSs: black). The dotted blue line, dotted purple line, and solid black line represent the linear best fit regression lines for scatters over MSDA1, MSDA2, and both MSDA1 and MSDA2, respectively, and the corresponding linear regression equation is shown on the left of the lines in black. The calculated correlation coefficient for scatters of both MSDA1 and MSDA2 in each plot is shown in the top left corner.
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DOI:10.1007/s00376-024-4082-1
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Zhu, X. Y., Z. Zhong, Y. M. Zhu, et al., 2024: The effect of moisture in different altitude layers on the eastward propagation of MJO. J. Meteor. Res., 38(3), 437–452, doi: 10.1007/s13351-024-3168-0.
Zhu, X. Y., Z. Zhong, Y. M. Zhu, et al., 2024: The effect of moisture in different altitude layers on the eastward propagation of MJO. J. Meteor. Res., 38(3), 437–452, doi: 10.1007/s13351-024-3168-0.
Zhu, X. Y., Z. Zhong, Y. M. Zhu, et al., 2024: The effect of moisture in different altitude layers on the eastward propagation of MJO. J. Meteor. Res., 38(3), 437–452, doi: 10.1007/s13351-024-3168-0.
Citation:
Zhu, X. Y., Z. Zhong, Y. M. Zhu, et al., 2024: The effect of moisture in different altitude layers on the eastward propagation of MJO. J. Meteor. Res., 38(3), 437–452, doi: 10.1007/s13351-024-3168-0.
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Manuscript History
Received: 05 October 2023
Revised: 03 December 2023
Accepted: 04 December 2023
Available online: 05 December 2023
Final form: 12 December 2023
Typeset Proofs: 25 December 2023
Issue in Progress: 30 April 2024
Published online: 27 June 2024
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Abstract
摘要
1.
Introduction
2.
Model, datasets, and methods
2.1
Model
2.2
Datasets
2.3
Methods
3.
Experiments with different cumulus parameterization schemes
4.
Nudging assimilation experiments for moisture
5.
Relationship between MJO eastward propagation and moisture profile
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