A Test of the Strict Quasi-Equilibrium Theory on Long Time and Space Scales

Quasi-equilibrium convective parameterizations share the common assumption that in regions of sustained deep convection rates of change in convective available potential energy (CAPE) are small compared to the magnitude of the large-scale and boundary layer forcings that act to modify CAPE. The more restrictive strict quasi-equilibrium hypothesis (SQE) is that changes in CAPE are dynamically negligible. Under this assumption, tropospheric temperature and thickness variations largely follow a moist adiabat associated with variations in the boundary layer θe. SQE is an attractive simplification for theories of large-scale circulation in the Tropics but has been inadequately tested to date. In this paper, we test the SQE hypothesis over convecting regions of the tropical oceans using microwave sounding unit tropospheric temperature and precipitation fields, along with COADS surface data, on timescales of a month and longer and on space scales ranging upward from O(300 km). One prediction of SQE, that θe and vertically averaged temperature (〈T 〉) are positively correlated in space and time, is found to hold for month-to-month, seasonal, and interannual timescales, but the proportionality coefficient between 〈T 〉 and θe is at most half as large as predicted. This is associated with variations of mean CAPE of as much as 25% over even the largest time and space scales examined.