An Explicit One-Dimensional Time-Dependent Tilting Cloud Model

Abstract

Abstract An explicit one-dimensional time-dependent tilting cloud model has been developed for use in cumulus parameterizations. The tilting axis is not necessarily orthogonal to the (r, θ) plane, making the horizontal axisymmetric assumption more reasonable. This explicit time-dependent tilting model (ETTM) consists of an updraft and a downdraft, which are governed by the same dynamic and thermodynamic equations. The updraft is initiated by a moist thermal bubble, while the downdraft is consequently induced by evaporative cooling and the drag force of precipitation separating from the tilting updraft instead of being arbitrarily initialized. The updraft is capable of reproducing the major features of a deep cloud such as overshooting cooling above the cloud top, evaporative cooling near the surface, and drying in the lower atmosphere at dissipating stages. The entrainment–detrainment rate in this model is well defined, and its time variation is quite significant. Moreover, the vertical profile of the air inside the updraft does not follow the moist adiabat after deep convection. For the downdraft, the total precipitation and mass flux at low levels contributed from the downdraft cannot be neglected in this case study. In addition, the downdraft can bring dry air from middle levels to lower levels. Three sensitivity tests—the environmental sounding, the tilting angle, and the radius of the updraft–downdraft— have also been conducted. The cooling–warming of a downdraft near the surface is sensitive to the environmental sounding, consistent with results from Srivastava. The cloud life span, maximum vertical velocity, precipitation amount, and vertical mass flux are strongly influenced by the tilting angle and the radius of the cloud. The results from the ETTM simulation are quite reasonable and promising. However, some deficiencies of this model still exist, and more research will be conducted to improve its performance. The final goal is to implement this 1D model in a mesoscale model's cumulus parameterization scheme.