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1. Reexamining the MJO Moisture Mode Theories with Normalized Phase Evolutions

   https://doi.org/10.1175/JCLI-D-20-0202.1  

   Wang, Lu; Li, Tim (October 2020, Journal of Climate)

   null (Ed.)

   Abstract A normalization method is applied to MJO-scale precipitation and column integrated moist static energy (MSE) anomalies to clearly illustrate the phase evolution of MJO. It is found that the MJO peak phases do not move smoothly, rather they jump from the original convective region to a new location to its east. Such a discontinuous phase evolution is related to the emerging and developing of new congestus convection to the east of the preexisting deep convection. While the characteristic length scale of the phase jump depends on a Kelvin wave response, the associated time scale represents the establishment of an unstable stratification in the front due to boundary layer moistening. The combined effect of the aforementioned characteristic length and time scales determines the observed slow eastward phase speed. Such a phase evolution characteristic seems to support the moisture mode theory of the second type that emphasizes the boundary layer moisture asymmetry, because the moisture mode theory of the first type, which emphasizes the moisture or MSE tendency asymmetry, might favor more “smooth” phase propagation. A longitudinal-location-dependent premoistening mechanism is found based on moisture budget analysis. For the MJO in the eastern Indian Ocean, the premoistening in front of the MJO convection arises from vertical advection, whereas for the MJO over the western Pacific Ocean, it is attributed to the surface evaporating process. 

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2. The Compressional Beta Effect: Analytical Solution, Numerical Benchmark, and Data Analysis

   https://doi.org/10.1175/JAS-D-20-0124.1  

   Ong, Hing; Roundy, Paul E. (November 2020, Journal of the Atmospheric Sciences)

   null (Ed.)

   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. 

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3. Slow Modes of the Equatorial Waveguide

   https://doi.org/10.1175/jas-d-19-0281.1  

   Emanuel, Kerry (May 2020, Journal of the Atmospheric Sciences)

   Abstract A recently developed linear model of eastward-propagating disturbances has two separate unstable modes: convectively coupled Kelvin waves destabilized by the wind dependence of the surface enthalpy flux, and slow, MJO-like modes destabilized by cloud–radiation interaction and driven eastward by surface enthalpy fluxes. This latter mode survives the weak temperature gradient (WTG) approximation and has a time scale dictated by the time it takes for surface fluxes to moisten tropospheric columns. Here we extend that model to include higher-order modes and show that planetary-scale low-frequency waves with more complex structures can also be amplified by cloud–radiation interactions. While most of these waves survive the WTG approximation, their frequencies and growth rates are seriously compromised by that approximation. Applying instead the assumption of zonal geostrophy results in a better approximation to the full spectrum of modes. For small cloud–radiation and surface flux feedbacks, Kelvin waves and equatorial Rossby waves are destabilized, but when these feedbacks are strong enough, the frequencies do not lie close to classical equatorial dispersion curves except in the case of higher-frequency Kelvin and Yanai waves. An eastward-propagating n = 1 mode, in particular, has a structure resembling the observed structure of the MJO. 

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4. Kelvin and Rossby Wave Contributions to the Mechanisms of the Madden–Julian Oscillation

   https://doi.org/10.3390/geosciences12090314  

   Haertel, Patrick (September 2022, Geosciences)

   The Madden–Julian Oscillation (MJO) is a large-scale tropical weather system that generates heavy rainfall over the equatorial Indian and western Pacific Oceans on a 40–50 day cycle. Its circulation propagates eastward around the entire world and impacts tropical cyclone genesis, monsoon onset, and mid-latitude flooding. This study examines the mechanism of the MJO in the Lagrangian atmospheric model (LAM), which has been shown to simulate the MJO accurately, and which predicts that MJO circulations will intensify as oceans warm. The LAM MJO’s first baroclinic circulation is projected onto a Kelvin wave leaving a residual that closely resembles a Rossby wave. The contribution of each wave type to moisture and moist enthalpy budgets is assessed. While the vertical advection of moisture by the Kelvin wave accounts for most of the MJO’s precipitation, this wave also exports a large amount of dry static energy, so that in total, it reduces the column integrated moist enthalpy during periods of heavy precipitation. In contrast, the Rossby wave’s horizontal circulation builds up moisture prior to the most intense convection, and its surface wind perturbations enhance evaporation near the center of MJO convection. Surface fluxes associated with the Kelvin wave help to maintain its circulation outside of the MJO’s convectively active region. 

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5. Moist Thermodynamics of Convectively Coupled Waves over the Western Hemisphere

   https://doi.org/10.1175/JCLI-D-22-0435.1  

   Mayta, Víctor C.; Adames, Ángel F. (May 2023, Journal of Climate)

   Abstract Convectively coupled waves (CCWs) over the Western Hemisphere are classified based on their governing thermodynamics. It is found that only the tropical depressions (TDs; TD waves) satisfy the criteria necessary to be considered a moisture mode, as in the Rossby-like wave found in an earlier study. In this wave, water vapor fluctuations play a much greater role in the thermodynamics than temperature fluctuations. Only in the eastward-propagating inertio-gravity (EIG) wave does temperature govern the thermodynamics. Temperature and moisture play comparable roles in all the other waves, including the Madden–Julian oscillation over the Western Hemisphere (MJO-W). The moist static energy (MSE) budget of CCWs is investigated by analyzing ERA5 data and data from the 2014/15 observations and modeling of the Green Ocean Amazon (GoAmazon 2014/15) field campaign. Results reveal that vertical advection of MSE acts as a primary driver of the propagation of column MSE in westward inertio-gravity (WIG) wave, Kelvin wave, and MJO-W, while horizontal advection plays a central role in the mixed Rossby gravity (MRG) and TD wave. Results also suggest that cloud radiative heating and the horizontal MSE advection govern the maintenance of most of the CCWs. Major disagreements are found between ERA5 and GoAmazon. In GoAmazon, convection is more tightly coupled to variations in column MSE, and vertical MSE advection plays a more prominent role in the MSE tendency. These results along with substantial budget residuals found in ERA5 data suggest that CCWs over the tropical Western Hemisphere are not represented adequately in the reanalysis. Significance StatementIn comparison to other regions of the globe, the weather systems that affect precipitation in the tropical Western Hemisphere have received little attention. In this study, we investigate the structure, propagation, and thermodynamics of convectively coupled waves that impact precipitation in this region. We found that slowly evolving tropical systems are “moisture modes,” i.e., moving regions of high humidity and precipitation that are maintained by interactions between clouds and radiation. The faster waves are systems that exhibit relatively larger fluctuations in temperature. Vertical motions are more important for the movement of rainfall in these waves. Last, we found that reanalysis and observations disagree over the importance of different processes in the waves that occurred over the Amazon region, hinting at potential deficiencies on how the reanalysis represents clouds in this region. 

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