Modulating synoptic scale convective activity and boundary layer dissipation in the IPESD models of the Madden–Julian oscillation

A self-contained derivation of the IPESD models [Majda, A.J., Klein, R., 2003. Systematic multi-scale models for the tropics. J. Atmos. Sci. 60, 393–408] governing synoptic and planetary scale tropical flows is provided. This derivation demonstrates the analytic tractability of the model and the effect of zonally and meridionally tilted synoptic scale heating on the forcing of planetary scale flows through upscale momentum and temperature fluxes. Exploiting the analytic tractability of the models, different aspects of the planetary scale forcing are traced to meridional and vertical tilts in the synoptic scale heating profile. Variants of the archetypal IPESD models for the Madden–Julian oscillation (MJO) presented in Majda and Biello [Majda, A.J., Biello, J.A., 2004. A multi-scale model for tropical intraseasonal oscillations. Proc. Natl. Acad. Sci. 101, 4736–4741; Biello, J.A., Majda, A.J., 2005. A new multi-scale model for the Madden–Julian oscillation. J. Atmos. Sci. 62, 1694–1721] are studied. In addition to vertically tilted synoptic scale heating, the models discussed herein incorporate upscale zonal momentum flux due to meridional flux convergence arising from meridionally tilted heating. The effect of a boundary layer momentum drag at the base of the free troposphere is also systematically incorporated into the IPESD models. Both meridional tilts and lower boundary layer drag are shown to meridionally confine the MJO westerly wind burst and drive a planetary scale barotropic flow. Meridionally tilted heating can also greatly strengthen the wind burst at the base of the troposphere and modify its vertical profile. The competing effects of meridionally tilted, and off-equatorial heating can also significantly weaken the MJO winds. Appendices are provided which discuss generalizations and a solution algorithm for the IPESD models.