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A simple implementation of the Arakawa and Schubert (1974) cumulus parameterization is presented. The major simplification made is to “relax”the state toward equilibrium each time the parameterization is invoked, rather than requiring that the final state be balanced, as in the original Arakawa-Schubert implementation. This relaxed Arakawa-Schubert (RAS) scheme is evaluated in off-line tests using the Global Atmospheric Research Programme (GARP) Atlantic Tropical Experiment (GATE) Phase III data. The results show that RAS is equivalent to the standard implementation of Arakawa-Schubert but is more economical and simpler to code. RAS also avoids the ill-posed problem that occurs in Arakawa-Schubert as a result of having to solve for a balanced state.
Moorthi et al. (Mon,) studied this question.