Residual cumulus parametrization

A novel approach to the parametrization of convective heating‐moistening is proposed. It is observationally known that convective heating is balanced overall by adiabatic cooling due to the resolved‐scale upward motion (large‐scale forcing) during the convective situations, with a corresponding balance also found in the moisture budget. A parametrization may be tuned to satisfy this first‐order balance. However, a small difference between these two terms defines the actual temporal evolution of the temperature and the moisture fields. Hence, the errors due to the cumulus parametrization are often the same order of magnitude as the temporal change itself, in spite of this first‐order tuning. In the present paper, it is proposed that this small ‘residual’ difference be directly represented by a cumulus parametrization. This idea is pursued by adopting a simple Newtonian relaxation formulation in the same spirit as the Betts‐Miller cumulus parametrization. Both the relaxation time‐scale and the reference profile are defined by the optimal fitting of convective‐forcing data diagnosed over the Intensive Flux Array domain during the TOGA‐COARE period for both the total and the residual convective heating parametrizations. Performance of these two types of parametrizations under this optimization is compared using single‐column model experiments.