Description:
AbstractWe present a linear equation for the Walker circulation streamfunction and find its analytic solutions given specified convective heating. In a linear Boussinesq fluid with Rayleigh damping and Newtonian cooling, the streamfunction obeys a Poisson’s equation, forced by gradients in the meridionally averaged diabatic heating and Coriolis force. For an idealized convective heating distribution, analytic solutions for the streamfunction can be found through an analogy with electrostatics. We use these solutions to study the response of the Walker circulation strength (mass transport) to changes in the vertical and zonal scales of convective heating. Robust responses are obtained that depend on how the total convective heating of the atmosphere responds to changing scale. If the total heating remains unchanged, increasing the zonal scale or the vertical scale always leads to a weaker circulation. Conversely, if the total heating grows in proportion to the spatial scale, the circulation becomes stronger with increasing scale. These conclusions are shown to be consistent with a three-dimensional numerical model. Moreover, they are useful in describing the observed seasonal and interannual (ENSO) variability of the Indo-Pacific Walker circulation. On both time scales, the overturning becomes weaker with increasing zonal scale of the convective region, reminiscent of our solutions where we do not vary the total convective heating. Reanalysis data also indicate that the zonal circulation is quite strongly damped, thus yielding a result that the circulation strength is directly proportional to the warm-pool spatial-mean precipitation.