On the Relationship between the Streamfunction and Velocity Potential of the Madden–Julian Oscillation

Abstract

The streamfunction and velocity potential variances associated with the Madden?Julian oscillation are explained substantially by their zonal wavenumber-1 components, which are used to measure quantitatively the phase relationship between the two variables. There exists a quarter-cycle phase difference between them. A simplified streamfunction budget equation was used to demonstrate analytically that this spatial quadrature relationship is maintained through the counteraction between streamfunction tendencies induced by the horizontal advection of planetary vorticity and the divergence of planetary vorticity flux.