Cumulus parameterization in numerical weather prediction models can significantly affect severe weather forecasts, such as hurricanes, flash floods, and winter storms. The role of convection is essential in stabilizing an unstable atmosphere through vertically transferring moisture, energy, chemical species and momentum. Cumulus parameterization schemes use simple one-dimensional convective cloud models to represent convection in the vertical direction. The cloud model is a fundamental determinant of vertical mass flux, heating and drying profiles, and precipitation rate.
The research presented in this paper is based on the cloud model developed by Chen and Sun (2004). This Explicit Time-dependent Tilting cloud Model (ETTM) features detailed processes for an updraft and a downdraft, both governed by the same dynamic and thermodynamic equations. The updraft is initiated with a thermal bubble, while the downdraft is maintained by evaporative cooling and the drag force of precipitation. Both up- and down-downdrafts employ non-hydrostatic pressure, entrainment, cloud microphysics, and lateral and vertical eddy mixing. A tilting angle for the cloud is specified to separate a portion of the downdraft from the updraft cell to account for vertical wind shear.
Since the ETTM described by Chen and Sun (2004) is not available as a community code, a slightly different algorithm was developed independently. The ETTM coordinate system is an axis-symmetric cylindrical with a constant radius mapped on where r is radius, ? is tangential angle, and Z is height in tilting coordinates. Prognosed variables are; vertical velocity, ice equivalent potential temperature, mixing ratios of water classes including cloud water, water vapor, ice water, rain water, snow and graupel.
The main purpose of this research is to examine the simulation of the development of a cumulus cloud by ETTM. An idealized sounding is used for environmental temperature, relative humidity and pressure. This sounding was measured on 20 May 1997 over Del City, Oklahoma during a storm. Time-stepping is determined according to Courant-Fredrich-Lewy (CFL) criteria, here we use 1s time-stepping. Vertical resolution is set to 500 m for each of the 34 vertical levels, placing the top of the domain at 17 km. The model is integrated for 70 minutes. ETTM also requires input for the radius and tilting angle of the up- and down-draft cells, these are based on the 3-D simulations with a mesoscale model simulation. The radius of the updraft and of the downdraft are set to 4000 and 1600 m respectively (radius of the downdraft being 40% of the updraft as described above). The tilting angle is set to 11.2?. In the model the effect of vertical diffusion and also non hydrostatic pressure gradient force are included. The governing equations of our model are exactly the same as those in Chen and Sun (2004). Results show that the ETTM is able to simulate a complete lifecycle for a cloud cell, featuring comparable zones of maximum vertical velocity, and overshooting layers on the cloud top and that this model can confidently be used in cumulus parameterization.