A theory of the MJO horizontal scale

Herewe ask, what controls the horizontal scale of theMadden-Julian Oscillation, i.e., what controls its zonal wave number k?We present a new one-dimensional (1D) β-planemodel that successfully simulates theMJO with the same governing mechanism as the 2D shallow water model of Yang and Ingersoll (2013). Convection is parameterized as a short-duration localized mass source that is triggered when the layer thickness falls below a critical value. Radiation is parameterized as a steady uniform mass sink. Both models tend toward a statistically steady state—a state of radiative-convective equilibrium, not just on a global scale but also on the scale of each MJO event. This gives k~ (Sc/c) , where Sc is the spatial-temporal frequency of convection events and c is the Kelvin wave speed. We offer this scaling as a prediction of how the MJO would respond to climate change.