Project Report—A Simple 2-D Cloud Model with a Parameterized Ice-Phase Microphysics

Summary:

   The simulation results of the tropical convection are reported by a simple 2-D cloud model with a Parameterized Ice-Phase Microphysics.

The growing and mature stages of the convection can be seen from the simulation results. As a comparison, the moist convection is also modeled using liquid water only microphysical parameterizations. For the simulation with ice microphysics, the kinetic energy is a little bigger than that without ice, to due the latent heating by melting of ice hydrometeors. However, the vertical velocity fields, perturbation of potential temperature fields and the non-dimensional perturbation pressure fields are very similar for the simulations with and without ice microphysical processes.  

Model

    The model is based on the quasi-compressible outflow model (QCOM) described in Droegemeier and Wilhelmson (1987). Ice or water only microphysical processes are added by following Lord et al (1984). The model predicts the horizontal velocity (v), the vertical velocity (w), the potential temperature () and the non-dimensional perturbation pressure (). The equations in Cartesian coordinates (y,z) are:

                                                                                                       (1)

                                                                            (2)

                                                                                                                         (3)

                                                                                                      (4)

                                               (5)

   where in Eq.(4) is the constant sound speed. In Eq.(5), q is mixing ratio, the subscript x denotes water vapor, cloud water, rain, cloud ice, snow and graupel.  is the height-dependent basic-state density of air. U is the mass-weighted fall speed (U>=0) for precipitating particles, P the net production rate due to the bulk-parameterized microphysical processes, C the source or sink of cloud water and cloud ice due to condensation, deposition, evaporation and sublimation, and D is eddy diffusion. (For the details of the microphysical processes in the model, see Lord et al. 1984)  

   The simple eddy viscosity approach is used for turbulence closure. The lower and upper boundaries are both rigid and free slip. The lateral boundary conditions are periodic. The domain extends 30 km horizontally and 15 km vertically. The vertical resolution is 100 m, the horizontal resolution is 200 m. Time step is 0.1 s.

   The GATE mean sounding (Fig. 1) is used as the background sounding. For initializing convection, a warm bubble (Fig. 2) is added.

Results: (at 6000s simulation)

a.       Simulation of a tropical convection with ice-microphysics processes: (with ice, including cloud water, rain water, cloud ice, snow, and graupel)

Animation1: Time series of the contours of hydrometeor mixing ratios

Animation2: Time series of the contours of vertical velocity

Animation3: Time series of the contours of potential temperature perturbation and the non-dimensional perturbation pressure.

b.       Simulation of a tropical convection with ice-microphysics processes (without ice, including cloud water and rain water):

 Animation4: Time series of the contours of hydrometeor mixing ratios

 Animation5: Time series of the contours of vertical velocity

       Animation6: Time series of the contours of potential temperature perturbation and the non-dimensional perturbation pressure.

c.       Comparison of the results with ice and without ice: 

 Fig3(jpg) or (PDF) :  The kinetic energy with and without ice vs. time.

 Fig4:  Time series of domain average mixing ratios of each hydrometeor species for the simulation with ice (a) and without ice (c).

                    Time and horizontally averaged mixing ratio profiles of each hydrometeor species with ice (b) and without ice (d).

            Fig5: Time series of maximum mixing ratios for each hydrometeor species for the simulation with ice.

            Fig6: Time series of maximum mixing ratios for each hydrometeor species for the simulation without ice.

            Fig7: Time series of maximum and minimum of perturbation of  , perturbation of , vertical velocity, and horizontal velocity for the       

                     simulation with ice.

            Fig8: Time series of maximum and minimum of perturbation of  , perturbation of , vertical velocity, and horizontal velocity for the       

                     simulation with ice.

Possible future simulation:

        To simulate a squall line by adding a wind shear at initial conditions.