Mapes, B. E., 1998: The large-scale part of tropical mesoscale convective system circulations: a linear vertical spectral band model. J. Meteor. Soc. Japan, 76, 29-55.
The linear response of the tropical troposphere to a heat source resembling a moderately large mesoscale convective system (MCS) is modeled. The spectral representation of vertical structure, with and without rigid lids atop the atmosphere, is illustrated graphically and discussed physically. The spectrum characterizing a mean radar-observed MCS heating profile in an unbounded, realistically stratified atmosphere can be well approximated with just two spectral bands. The equations governing the wind and height amplitudes of each spectral band are linear shallow-water equations, combined with a time-dependent spatial smoothing that accounts for the finite spectral widths of the bands. This spectral band smoothing mimics the tropospheric smoothing effects of the preferential upward propagation of high horizontal wavenumber components. During the period from 0-72 hours after the MCS, the flow evolves from initially circular expanding wavelike rings, toward the planetary-wave patterns studied by Matsuno, Gill, and others. This size expansion is not truly an "up-scale" evolution: the red horizontal spectrum of scales excited by a meso-sized heat source merely undergoes phase evolution with time. Small scales do preferentially propagate upward, however. An interesting feature strongly excited by an equatorial MCS is a zonally elongated inertio-gravity motion along the equator, which cools the troposphere 48 hours after a brief heating event. This oscillation has a large zonally-symmetric component. The linear solutions developed here are superposed to obtain estimates of the wind and temperature changes forced by satellite-observed ensembles of MCSs. Low-level winds comparable to observed Australian monsoon winds spin up from rest in just 2-3 days, while some of the monsoon convective heating escapes into the equatorial waveguide as downwelling Kelvin and mixed Rossby-gravity waves. Synthetic data constructed from model fields illustrate how observing systems experience the effects of MCS heating events. Deep vertical motion on tropical rawinsonde-array scales responds rapidly to convective heating, with a response time (1-2 h) small compared to the observed lifetime of MCSs (6-12 h). These results indicate that rawinsonde array observations of a "quasi-equilibrium" between large-scale vertical motion and convection may be due to the rapid response of the former to the latter, not vice versa as has sometimes been supposed.