A prognostic cumulus parameterization with cloud-updraft interaction

Convective parameterizations used in atmospheric models to represent the effects of unresolved shallow and deep convection on the large-scale flow are traditionally formulated in a diagnostic manner that assumes an instantaneous adjustment of convection to the resolved-scale environment. Prognostic parameterizations, on the other hand, can represent the time evolution and memory of moist atmospheric convection, leading to more realistic interactions between convection and large-scale atmospheric circulation, especially if far from convective quasi-equilibrium. Several such prognostic formulations for the mass flux have been proposed by relaxing the quasi-equilibrium assumption introduced by Arakawa and Schubert [1], based on assumed relations between the convective mass flux and the convective kinetic energy [2,3]. In this work, we develop a new prognostic formulation for shallow and deep convection with cloud cover and convective velocity both being treated as prognostic variables. Interactions between shallow and deep convection are represented in our formulation due to their differing effects on the large-scale environment, but also due to direct cloud-updraft interactions. In radiative-convective equilibrium (RCE), our model predicts that the cumulus cloud cover is proportional to the radiative cooling rate and that the convective velocity depends only on the relative humidity and the tropospheric depth, in agreement with numerical experiments. In addition, our model predicts that convective available potential energy decreases in RCE with the increase of the radiative cooling rate due to the cloud-updraft interaction. Moreover, we show that the inclusion of the cloud-updraft interaction and the cold pools feedback is required for a realistic representation of the diurnal cycle of shallow and deep convection.

 

[1] Arakawa, A., & Schubert, W. H. (1974). Interaction of a cumulus cloud ensemble with the large-scale environment, Part I. Journal of Atmospheric Sciences, 31(3), 674-701.

[2] Pan, D. M., & Randall, D. D. (1998). A cumulus parameterization with a prognostic closure. Quarterly Journal of the Royal Meteorological Society, 124(547), 949-981.

[3] Yano, J. I., & Plant, R. (2012). Finite departure from convective quasi‐equilibrium: Periodic cycle and discharge–recharge mechanism. Quarterly Journal of the Royal Meteorological Society, 138(664), 626-637.