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Abstract Two analytical models with different starting points of convective parameterizations, the Fuchs and Raymond model on one hand and the Khairoutdinov and Emanuel model on the other, are used to develop “minimal difference” models for the MJO. The main physical mechanisms that drive the MJO in both models are wind-induced surface heat exchange (WISHE) and cloud–radiation interactions (CRI). The dispersion curves for the modeled eastward-propagating mode, the MJO mode, are presented for an idealized case with zero meridional wind and for the realistic cases with higher meridional numbers. In both cases, the two models produce eastward-propagating modes with the growth rate greatest at the largest wavelengths despite having different representations of cumulus convection. We show that the relative contributions of WISHE and CRI are sensitive to how the convection and entropy/moisture budgets are represented in models like these. Significance StatementThe Madden–Julian oscillation is the largest weather disturbance on our planet. It propagates eastward encompassing the whole tropical belt. It influences weather all around the globe by modulating hurricanes, atmospheric rivers, and other phenomena. Numerical models that forecast the Madden–Julian oscillation need improvement. Here we explore the physics behind the Madden–Julian oscillation using simple analytical models. Our models are based on the assumption that surface enthalpy fluxes and cloud–radiation interactions are responsible for the Madden–Julian oscillation but it should be borne in mind that other physical mechanisms have been proposed for the MJO. The impact of this research is to better understand the Madden–Julian oscillation mechanism.
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Slow Modes of the Equatorial Waveguide
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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- Award ID(s):
- 1906768
- PAR ID:
- 10167488
- Date Published:
- Journal Name:
- Journal of the Atmospheric Sciences
- Volume:
- 77
- Issue:
- 5
- ISSN:
- 0022-4928
- Page Range / eLocation ID:
- 1575 to 1582
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract In theoretical models of tropical dynamics, the effects of both surface friction and upward wave radiation through interaction with the stratosphere are oft-ignored, as they greatly complicate mathematical analysis. In this study, we relax the rigid-lid assumption and impose surface drag, which allows the barotropic mode to be excited in equatorial waves. In particular, a previously developed set of linear, strict quasi-equilibrium tropospheric equations is coupled with a dry, passive stratosphere, and surface drag is added to the troposphere momentum equations. Theoretical and numerical model analysis is performed on the model in the limits of an inviscid surface coupled to a stratosphere, as well as a frictional surface under a rigid lid. This study confirms and extends previous research that shows the presence of a stratosphere strongly shifts the growth rates of fast-propagating equatorial waves to larger scales, reddening the equatorial power spectrum. The growth rates of modes that are slowly propagating and highly interactive with cloud radiation are shown to be negligibly affected by the presence of a stratosphere. Surface friction in this model framework acts as purely a damping mechanism and couples the baroclinic mode to the barotropic mode, increasing the poleward extent of the equatorial waves. Numerical solutions of the coupled troposphere–stratosphere model with surface friction show that the stratosphere stratification controls the extent of tropospheric trapping of the barotropic mode, and thus the poleward extent of the wave. The superposition of phase-shifted barotropic and first baroclinic modes is also shown to lead to an eastward vertical tilt in the dynamical fields of Kelvin wave–like modes.more » « less
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Abstract Westerly wind bursts (WWBs) are brief, anomalously westerly winds in the tropical Pacific that play a role in the dynamics of ENSO through their forcing of ocean Kelvin waves. They have been associated with atmospheric phenomena such as tropical cyclones, the MJO, and convectively coupled Rossby waves, yet their basic mechanism is not yet well understood. We study WWBs using an aquaplanet general circulation model, and find that eastward-propagating convective heating plays a key role in the generation of model WWBs, consistent with previous studies. Furthermore, wind-induced surface heat exchange (WISHE) acts on a short time scale of about two days to dramatically amplify the model WWB winds near the peak of the event. On the other hand, it is found that radiation feedbacks (i.e., changes in the net radiative anomalies accompanying westerly wind bursts) are not essential for the development of WWBs, and act as a weak negative feedback on WWBs and their associated convection. Similarly, sensible surface heat flux anomalies are not found to have an effect on the development of model WWBs.more » « less
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Abstract Linearized wave solutions on the equatorial beta plane are examined in the presence of a background meridional moisture gradient. Of interest is a slow, eastward-propagating n = 1 mode that is unstable at planetary scales and only exists for a small range of zonal wavenumbers ( ). The mode dispersion curve appears as an eastward extension of the westward-propagating equatorial Rossby wave solution. This mode is therefore termed the eastward-propagating equatorial Rossby wave (ERW). The zonal wavenumber-2 ERW horizontal structure consists of a low-level equatorial convergence center flanked by quadrupole off-equatorial gyres, and resembles the horizontal structure of the observed MJO. An analytic, leading-order dispersion relationship for the ERW shows that meridional moisture advection imparts eastward propagation, and that the smallness of a gross moist stability–like parameter contributes to the slow phase speed. The ERW is unstable near planetary scales when low-level easterlies moisten the column. This moistening could come from either zonal moisture advection or surface fluxes or a combination thereof. When westerlies instead moisten the column, the ERW is damped and the westward-propagating long Rossby wave is unstable. The ERW does not exist when the meridional moisture gradient is too weak. A moist static energy budget analysis shows that the ERW scale selection is partly due to finite-time-scale convective adjustment and less effective zonal wind–induced moistening at smaller scales. Similarities in the phase speed, preferred scale, and horizontal structure suggest that the ERW is a beta-plane analog of the MJO.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1175/jas-d-19-0281.1
