A theory of the MJO horizontal scale

Here we ask, what controls the horizontal scale of the Madden-Julian Oscillation, i.e., what controls its zonal wave number k? We present a new one-dimensional (1D) β-plane model that successfully simulates the MJO 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 ~ (S_(c)/c)^(1/2), where S_c 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