Phenomenology of convection-parameterization closure

Abstract. Closure is a problem of defining the convective intensity in a given parameterization. In spite of many years of efforts and progress, it is still considered an overall unresolved problem. The present article reviews this problem from phenomenological perspectives. The physical variables that may contribute in defining the convective intensity are listed, and their statistical significances identified by observational data analyses are reviewed. A possibility is discussed for identifying a correct closure hypothesis by performing a linear stability analysis of tropical convectively coupled waves with various different closure hypotheses. Various individual theoretical issues are considered from various different perspectives. The review also emphasizes that the dominant physical factors controlling convection differ between the tropics and extra-tropics, as well as between oceanic and land areas. Both observational as well as theoretical analyses, often focused on the tropics, do not necessarily lead to conclusions consistent with our operational experiences focused on midlatitudes. Though we emphasize the importance of the interplays between these observational, theoretical and operational perspectives, we also face challenges for establishing a solid research framework that is universally applicable. An energy cycle framework is suggested as such a candidate.