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Abstract The variability of the phase speed of the Madden–Julian oscillation (MJO) is poorly understood. The authors assess how the phase speed of the convective signal of the MJO associates with the background states over eastern Africa and the Indian Ocean. Relaxation of the coupling between tropical modes and their circulation has been previously linked to faster propagation; for example, the MJO speeds up over the eastern Pacific where its convective signal decouples from the circulation. In contrast, our results show that fast MJO events happen to exist during periods of wetter background states (>90 days) from East Africa across the Indian Ocean, whereas slow MJO is associated with dry background states. We found that fast MJO exhibits strong active and inactive phases with a structure suggesting more hierarchical convection. Results indicate that the association of the phase speed of the MJO as seen in the integrated filtered moist static energy with its tendency is stronger than the association of the phase speed as observed in the dry static energy with its tendency which is consistent with the acceleration of the MJO during wet background states. Also, our results indicate that the MJO may be faster during periods of enhanced low-level moisture because these periods have anomalously weak upper-tropospheric easterly background winds, which reduce the westward advection of the MJO by the background easterly wind, resulting in higher eastward phase speed of the MJO. The acceleration of the MJO by the background zonal wind overwhelms the deceleration associated with the moist-wave dynamics. Significance StatementThis study shows that the Madden–Julian oscillation (MJO), which is the dominant subseasonal weather signal in the tropics, moves eastward more quickly across eastern Africa and the Indian Ocean when the region is abnormally moist. The faster propagation does not appear to result from the higher moisture but instead from encountering weaker-than-normal upper-air winds from the east that tend to occur during moist periods. 

Abstract Qualities of the meridional movements of geopotential height anomalies in the upper troposphere of the subtropics are analysed via wavelet analysis using a meridional–temporal partial Morlet wavelet. Results show that power, which represents increased presence or amplitude of waves with direct meridional movement, is increased in regions where the corresponding equatorial winds in the upper troposphere are westerly or weakly easterly. Furthermore, equatorward power is enhanced near subtropical jet exit regions whereas poleward power is enhanced in jet entrance regions. Regressions of upper‐tropospheric winds, geopotential height, and outgoing long‐wave radiation (OLR) against the wavelet transforms demonstrate that the wavelets are identifying signals with tropical–extratropical interactions that are connected to organized convection in the tropics. The relationship of power with background‐state flow characteristics, including the horizontal winds and shear, are evaluated. Instead of the zonal wind and meridional shear of the zonal wind (du/dy), both the meridional wind and the zonal shear of the meridional wind (dv/dx) appear to have a clearer relationship with the power. Power is favoured for waves whose movement is aligned in the same direction as the meridional wind, and reduced in the opposite direction. Additionally, power increases with increasing zonal shear of the meridional wind in the Northern Hemisphere and with decreasing zonal shear of the meridional wind in the Southern Hemisphere. Power in the equatorward direction is stronger than in the poleward direction and more heavily influenced by background flow characteristics. Furthermore, power for wavelets with smaller meridional and temporal scales tends to have a higher sensitivity to the background horizontal flow as compared to larger meridional and temporal scales. 

Abstract Wave‐number‐frequency power spectrum analysis has been used as a primary tool to detect the ranges of wave numbers and frequencies about which observed convectively coupled equatorial waves are active. Previous works have suggested that activity in these waves clusters between roughly 12 and 60 m equivalent depths because spectral peaks normalized by dividing by a smoothed spectral background follow those ranges. Through a combination of wave‐number‐frequency power spectrum analysis, filtering and linear regression, this work shows that the traditional approach generates confusion because it conflates different, sometimes conflicting, signals from around the world that contribute to the same parts of the spectrum. Results also suggest that the traditional method leads us to ignore substantial power associated with variability structurally consistent with observed Kelvin waves but that occurs at lower frequencies. Wave signals at these frequencies are stronger than but similar to Kelvin wave signals coincident with the Kelvin peak in the normalized spectrum. Results suggest that the wave signal itself has red properties, possibly because more strongly convectively coupled waves propagate more slowly. The slower, more intense wave signals outside of the standard band would impact tangible weather signals and should not be ignored in operations. Instead, results support the view that disturbances labelled as Kelvin waves form a continuum with the Madden–Julian Oscillation (MJO) and suggest that the whole region of the spectrum from the broadly recognized Kelvin band to the MJO should be considered together. 

Previous research has shown that the equatorial upper tropospheric circulation signal associated with the Madden Julian Oscillation (MJO) over the Indian Ocean behaves like a Kelvin wave, with the eastward-propagation of the associated zonal wind anomaly caused by acceleration by the geopotential gradient force in quadrature with the wind anomaly, with the resultant signal amplified or decayed as the MJO wind advects background zonal wind in regions of background confluent or diffluent flow, with its phase speed adjusted by Doppler shifting by background zonal wind. This paper assesses these previously diagnosed mechanisms in the GEFS V12 forecast model, showing that similar mechanisms occur with the model MJO, but weaker and less organized. Results suggest that, relative to the validation data, the model stalls the MJO upper tropospheric zonal wind anomaly during diffluent background conditions near the Maritime Continent and weakens its amplitude more rapidly than validation data. The stalled propagation leads the model MJO to persist the signals of advection of and by the background wind, but at a reduced rate as the scale of the model MJO wind anomaly diminishes. Results show that beyond the stronger Doppler effect in the model, stalling the model MJO results from filling of the relative geopotential trough collocated with the MJO easterly wind anomaly, leading to breakdown of the geopotential gradient force term that is responsible for propagation of the wind anomaly. Thus, when the Maritime Continent region experiences zonally diffluent flow, the reason for the stronger Maritime Continent barrier effect in the model is that the model does not persist the Kelvin wave propagation mechanism that continues the eastward movement of the easterly wind anomaly in observations. 

Abstract A robust linear regression algorithm is applied to estimate 95% confidence intervals on the background wind associated with Madden–Julian oscillation (MJO) upper-tropospheric atmospheric circulation signals characterized by different phase speeds. Data reconstructed from the ERA5 to represent advection by the upper-tropospheric background flow and MJO-associated zonal wind anomalies, together with satellite outgoing longwave radiation anomalies, all in the equatorial plane, are regressed against advection data filtered for zonal wavenumber 2 and phase speeds of 3, 4, 5, and 7 m s −1 . The regressed advection by the background flow is then divided by the negative of the zonal gradient of regressed zonal wind across the central Indian Ocean base longitude at 80°E to estimate the associated background wind that leads to the given advection. The median estimates of background wind associated with these phase speeds are 13.4, 11.2, 10.5, and 10.3 m s −1 easterly. The differences between estimated values at neighboring speeds suggests that advection acts most strongly in slow MJO events, indicating that the slowest events happen to be slow because they experience stronger easterly advection by the upper-tropospheric background wind. Significance Statement The Madden–Julian oscillation (MJO) is the dominant subseasonal rainfall signal of the tropical atmosphere. This project shows that the background wind of the tropical atmosphere most especially slows down the slowest MJO events. Understanding what controls its speed might help scientists better predict events. 

Abstract This study derives a complete set of equatorially confined wave solutions from an anelastic equation set with the complete Coriolis terms, which include both the vertical and meridional planetary vorticity. The propagation mechanism can change with the effective static stability. When the effective static stability reduces to neutral, buoyancy ceases, but the role of buoyancy as an eastward-propagation mechanism is replaced by the compressional beta effect (i.e., vertical density-weighted advection of the meridional planetary vorticity). For example, the Kelvin mode becomes a compressional Rossby mode. Compressional Rossby waves are meridional vorticity disturbances that propagate eastward owing to the compressional beta effect. The compressional Rossby wave solutions can serve as a benchmark to validate the implementation of the nontraditional Coriolis terms (NCTs) in numerical models; with an effectively neutral condition and initial large-scale disturbances given a half vertical wavelength spanning the troposphere on Earth, compressional Rossby waves are expected to propagate eastward at a phase speed of 0.24 m s −1 . The phase speed increases with the planetary rotation rate and the vertical wavelength and also changes with the density scale height. Besides, the compressional beta effect and the meridional vorticity tendency are reconstructed using reanalysis data and regressed upon tropical precipitation filtered for the Madden–Julian oscillation (MJO). The results suggest that the compressional beta effect contributes 10.8% of the meridional vorticity tendency associated with the MJO in terms of the ratio of the minimum values.