Before exploring the MJO features of the model, it is important to verify the model climate in order to determine if the MJO signal simulated by MM5 develops in a realistic background state. Figure 1 shows the 2-year mean (from 1 August 1990 to 31 July 1992) of 850-hPa winds and the annual mean precipitation. Contrary to Gustafson and Weare (2004) where the model introduces an easterly wind bias of approximately 2 m s−1 at 850-hPa, this simulation presents a 1 m s−1 westerly bias over the whole domain. The model and the observed wind patterns agree well over most of the domain, with stronger winds away from the Equator, westerlies over the Indian Ocean north of the equator, and easterlies elsewhere. Yet, the model shows westerlies over the southern and eastern Pacific Ocean, near the boundaries, where the observations present strong easterly winds. Overall these differences are small since they are within the 2–4 m s−1 differences between the NRA and ERA re-analyses (Annamalai et al. 1999). The model output and the observations show maxima in precipitation over the Indian Ocean and Pacific Ocean with a local minimum near the equator in the Pacific, which is associated with of a double intertropical convergence zone (ITCZ). The model precipitation is too weak over the Indian Ocean and over the northern branch of the ITCZ in the Pacific but too strong over the southern branch. These errors are within the range of errors exhibited by the general circulation model (GCM) simulations presented in the latest Intergovernmental Panel on Climate Change (IPCC) report (Randall et al. 2007). Notwithstanding, a major difference between the model output and the observations is the absence of precipitation over the islands of Indonesia and Papua New Guinea in the MM5 model. This result is quite different from the IPCC report where GCMs show a wet bias in annual-mean precipitation over Indonesia and Papua New Guinea (Randall et al. 2007). Overall, the model errors are within the differences between the various available observational datasets and the average GCM simulation in the IPCC comparison.
The space–time power spectra of 20°S–20°N averaged U850 and OLR are presented in Fig. 2. The main features of the observations are very similar to those shown by Salby and Hendon (1994). However, it is important to note that the ratios of eastward to westward power shown in Table 1 are much greater than that shown in Zhang et al. (2006). This is easily explained by the data reconstruction methodology used here since it emphasizes the power of the Eastern Hemisphere where the MJO signal is the strongest. The MJO characteristics in the zonal winds are well reproduced by the model, especially the stronger eastward propagating power and the intraseasonal frequency band well separated from the lower frequencies. However, the model output zonal winds display a weaker ratio of eastward to westward power (Table 1) and a slightly more dominant wavenumber 1 (Fig. 2) than for the observations. In addition, Table 1 shows that the model OLR, 850-hPa specific humidity (Q850) and precipitation (P) do not demonstrate any obvious eastward propagation. Thus this analysis reveals that an intraseasonal planetary-scale eastward propagating signal is present in the model upper- and lower-level zonal winds, but is not present in the OLR, precipitation and in the free atmosphere lower-level moisture. Yet, there seems to be a clear eastward propagating signal in the boundary layer moisture field (Q1000) and moist static energy (MSE1000), suggesting that moisture processes in the boundary layer and the free atmosphere have very different mechanisms. Similarly to Kemball-Cook and Weare (2001), a moist static energy instability index (MSEII) is constructed by taking MSE(1,000-hPa) minus MSE(300-hPa). This index measures the tropospheric instability and can be useful to assess the instability as a control mechanism for the MJO propagation characteristics. Indeed, the space–time power spectral analysis of the MSEII demonstrates that the model reproduces very well the intraseasonal eastward propagation of the instability that is present in the observations. In addition, the ratios of eastward to westward power for the meridional lateral boundaries show that the eastward propagating signals are weaker at the boundaries than within the model domain in all variables but the MSEII. This is especially true in the zonal winds which present very little eastward propagating signal.
Extraction of the leading modes
Figure 3 presents the zonal structure of the first two EOFs of combined bandpass filtered U850 and U200, and OLR, averaged over 20°S–20°N. For the observations, the leading pair of combined EOFs explains more than 60% of the total explained variance, making them well separated from the remaining EOFs based on the criteria of North et al. (1982) (the third EOF explains only 8.7% of the variance) and they are similar to the analysis of Wheeler and Hendon (2004). The corresponding principal components (PCs) are in quadrature and the first PC leads the second one by 11 days with a correlation of 84.0%. This implies a periodicity of 44 days, consistent with the theory. Thus the leading EOF pair represents the main structure and eastward propagation of the MJO. Furthermore, the PCs associated with the leading modes exhibit moderate active MJO events during the fall 1990, spring 1991 and strong events during winter and spring 1992. These two PCs are used to construct an MJO index. Weare (2006) warns about doing composite analysis using a reference dataset which focuses on convection centered over the Maritime Continent. The composites would then present an amalgam of the different properties of the MJO over the Indian and Pacific Oceans. Since the index is associated with a pattern of convection similar to that of the first EOF, centered east of the Maritime Continent, this issue should be avoided.
Like the observations, the model output has a dominant pair of leading EOFs, explaining approximately 50% of the explained variance (while the third EOF accounts for just 10% of the variance). These leading modes display wind patterns consistent with the observations. However, the associated enhanced convective center is not reproduced. Nonetheless the correlations between the first pairs of PCs of the observations and the model are high, 87.9% for the first PC and 92.1% for the second. This implies strong similarities in the MJO circulation and its propagation between the ERA-40 re-analysis and the model. In addition, the model output PCs show a maximum correlation (81.8%) for a lag of 12 days.
The phase speed and the eastward propagation of the MJO signal are investigated through lag-correlations, at all longitudes, of the equatorially averaged U850, U200, Q850, OLR and MSEII upon the MJO index (Fig. 4). The observations show a coherent organization and consistent eastward propagation in all fields with a characteristic phase speed around 8 m s−1, typical of the MJO (Hendon and Salby 1996; Lin et al. 2006). It is worthy of note that the phase speeds of the NOAA OLR and the CPC precipitation (not shown) display good agreement with the ERA-40, thus demonstrating consistency in the observational datasets used in this study.
The model output shows very good agreement with the ERA-40 re-analysis in the eastward propagation of the zonal winds, both at upper- and lower-levels. The propagation is smooth and well organized with a realistic MJO phase speed over the whole domain. However, as expected from the previous results, the MM5 model output lacks a clear organization and a realistic eastward propagation in Q850 and OLR. While there are indications of eastward propagation in the OLR, it does not have a realistic MJO phase speed and it is too intermittent. Yet, the MSEII in the model displays a clear eastward propagation with a realistic phase speed, especially over the Indian Ocean. Like for the observations, the MSEII does not propagate as smoothly as the zonal wind and exhibits some discontinuity between the Maritime Continent and the western Pacific Ocean. Overall, only the model output winds and stability index show a clear and realistic MJO propagation.
The analysis of the meridional boundaries reveals the absence of coherent eastward propagation in phase with the propagation seen in the zonal winds for both the observations and the model output. Moreover, the absence of propagation is similar in the lower-level moisture and OLR. Only the MSEII presents a realistic propagation speed around 8 m s−1 over the whole latitudinal domain. This result strongly suggests that the realistic aspects of the MJO in this model are not dictated by the meridional boundary input data.
Horizontal and vertical structure
The horizontal and vertical structure of the MJO signal are investigated using composites of various MJO variables associated with the MJO index for a lag of −10 days in order to center the various MJO features within the domain. The horizontal composites (Fig. 5) describe the latitudinal distribution of the signal, especially the discrepancies between the Equator and the regions closer to the boundaries, while the vertical composites (Fig. 6) provide insight into the differences in the vertical structure of the MJO as it evolves. The horizontal and vertical structure of the simulated MJO winds agree well with the observations. The MJO winds exhibit the first baroclinic mode in the troposphere as well as a distinct zonal asymmetry, with lower-level convergence and upper-level divergence. However, the convective center, diagnosed from the OLR, located slightly to the west of the upper-level divergence, seen in the observations (Sperber 2003; Kiladis et al. 2005), is not reproduced in the model. Instead some deep convection is evident around the dateline and away from the Equator, far east of the upper-level divergence. Figures 5 and 6 also display a fundamental large-scale feature observed in the MJO: positive moisture anomalies are present near and to the east of the convective center while a rapid drying, associated with negative moisture anomalies, occurs immediately to the west (Weare 2003). This dry/moist pattern is partly reproduced by the model in the boundary layer, but it is weak and noisy in the free troposphere. In addition, the moisture signal above 500-hPa in the model is very insubstantial, except around the dateline where positive moisture anomalies coincide with the simulated convective center and where the observations show weak negative anomalies. This suggests that the inability of the model to reproduce the correct location of the deep convection is a result of a poor simulation of the upper-level moisture. Furthermore, the vertical structure of the observed MJO MSE is similar to that of the observed MJO specific humidity, indicating that the MSE is strongly dominated by the moisture term. On the other hand, the model output MJO MSE composite displays a similar pattern to its observational counterpart, though weaker and noisier. Overall, the moist static energy shows lower-level positive anomalies building upward in the troposphere ahead of the convective center and sharp negative anomalies just west of the convection. The associated composites of MJO MSEII for the observations and the model output agree well with each other. They feature positive and negative anomalies, respectively to the east and west of the lower-level convergence, representing an unstable atmosphere ahead of the convective center and a stable troposphere after the convection has passed.
Finally, the vertical structure of the MJO signal on the meridional boundaries reveals that the zonal winds lack the first baroclinic mode, which is an essential feature of the MJO. The MJO signal in the moisture and deep convection are both noisy and lack the zonal wavenumber 1 structure. The moisture also lacks a consistent lower-level moistening building upward into the troposphere ahead of the convection. Meanwhile, the MSE vertical structure shows a signal above 500-hPa, which seems to be solely responsible for the strong signal in the MSEII. The MSE signal is noisy and inconsistent in the boundary layer. Overall, a realistic and coherent MJO signal is absent from the meridional boundaries in the winds, moisture and MSE, especially at lower-levels.
Spatial and temporal distribution
Figure 7 shows Hovmöller diagrams of the equatorially averaged bandpass filtered 200-hPa zonal winds. It reveals that the observations and model output are very similar, with the same relative strength and a strong seasonal variability. MJO events are clearly identifiable during the boreal fall of 1990, the spring and early summer of 1991 and the winter and spring of 1992. Outside these time periods, the organization, the power and the propagation of the signals are weak or non-existent. Longitudinal correlations at all times and temporal correlations at all longitudes between Hovmöller diagrams of the model output and the observations for U200, U850, Q850, OLR and MSEII are presented in Fig. 8. This analysis reveals high correlations for U200 and U850 with a mean temporal correlation over all longitudes of 85.4 and 77.1% respectively, and a mean longitudinal correlation over all times of 79.2 and 64.8% respectively. As expected, the correlations are weaker over the Maritime Continent than over the Indian and Pacific Oceans. They are also weaker during inactive MJO events than during strong MJO events. The OLR and Q850 present poor overall correlations, with mean temporal and longitudinal correlations close to zero for OLR and close to 15% for Q850. It should be noted that the temporal correlations of the free atmosphere lower-level moisture are significantly higher west of the Maritime Continent (42% as a mean) than to the east of the Indian Ocean (close to zero). This demonstrates the significant impact of the Maritime Continent on the simulation of the MJO signal, especially in the moisture field. In addition, the correlations of the OLR and Q850 are clearly higher over the African Continent, which is most likely due to the limited influence of the West boundary condition. Finally, correlations for MSEII are higher than for OLR and Q850 but weaker than for the winds (mean temporal and longitudinal correlations of 55.5 and 35.0% respectively). This analysis indicates that the model is able to reproduce the conditional instability over the whole domain better than the moisture field or the deep convection.