WISHE‐Moisture Mode in a Vertically Resolved Model

Abstract

Abstract The Madden‐Julian oscillation is a global phenomenon, a wave with the wavelength of the circumference of the Earth. A theoretical model presented by Fuchs and Raymond (2007, https://doi.org/10.1111/j.1600-0870.2007.00230.x) obtained a mode called the eastward propagating wind‐induced surface heat exchange (WISHE)‐moisture mode that had its largest instability for the longest wavelengths. That model imposed the first baroclinic mode vertical structure. This paper expands the Fuchs and Raymond model by developing a vertically resolved model, a model in which all the variables except the heating vertical profile are calculated. The heating profile is assumed to have a vertical structure of the first baroclinic mode. The model uses the upper boundary radiation condition and thus includes the effects of the stratosphere. The convective parametrization includes wind‐induced surface heat exchange, cloud‐radiation interactions, and moisture closure. The vertically resolved model produces one unstable mode whose dispersion relation characteristics closely resemble the eastward propagating WISHE‐moisture mode. For the longest wavelengths it is more unstable and its phase speed is slightly larger than in the Fuchs and Raymond model. The calculated vertical structure reveals a similar vertical structure to the first baroclinic mode with small differences that to some extent agree with observations.

Keywords

• MJO
• WISHE‐moisture mode
• vertically resolved model
• global disturbance
• CRI
• stratosphere