Improved mixing representation in Emanuel's convection scheme

Recent empirical and modelling studies suggest that mid-tropospheric relative humidity (RH) is an important controlling factor of deep atmospheric convection, which appears to be underestimated in present cumulus parametrizations. This indicates the possible presence of shortcomings in the way that entrainment is represented in such parametrizations. This matter was explored in the European Cloud Systems project (EUROCS) by means of an idealized humidity experiment in which the main controlling parameter is RH. In the latter study, cloud-resolving model (CRM) experiments suggested that a shallow/deep convection transition occurs when RH crosses a threshold value that ranges from about RH = 50% to RH = 60%. In this paper, we seek to increase the responsiveness of Emanuel's convection scheme to RH, and to reproduce the threshold behaviour of the idealized humidity case, by replacing the original uniform probability density function (PDF) for mixing fractions by a more flexible two-parameter bell-shaped function that allows a wider range of behaviour. The main result is that the parameters of this PDF can be tuned to allow a regime transition to occur near a threshold value of RH approximate to 55%. In contrast to CRM results, however, this transition is between two different regimes of deep convection rather than between a shallow and deep regime. Possible ways to obtain a shallow-to-deep transition with Emanuel's scheme are discussed.