Unified Spectrum of Tropical Rainfall and Waves in a Simple Stochastic Model

In the tropics, rainfall is coupled with atmospheric dynamics in ways that are not fully understood, and often different mechanisms are proposed to underlie different modes of variability. Here, it is shown that a unified model with a simple form can produce many different modes of variability. In particular, this includes the Madden--Julian oscillation and convectively coupled equatorial waves. The model predicts the length scales, time scales, structures, and spatiotemporal variability of these modes reasonably well for a simple model. Furthermore, the model produces a background spectrum of rainfall that resembles spatiotemporal red noise and is only weakly coupled with wave dynamics. The full spectrum is also shown to be shaped by antiresonance, whereby rainfall oscillations are prevented from occurring at the oscillation frequencies of dry waves. To produce all of these aspects simultaneously, a key factor is differing roles of lower and middle tropospheric water vapor.