Figure 3. The rendered contour surfaces of hydro-meteor mixing ratio 0.1 gm-3 of the three simulated storms as viewed from top for t = 20 to 120 min. The horizontal ranges in both x and y-directions are 0—55 km.

Figure 3. The rendered contour surfaces of hydro-meteor mixing ratio 0.1 gm-3 of the three simulated storms as viewed from top for t = 20 to 120 min. The horizontal ranges in both x and y-directions are 0—55 km.

Figure 3 shows the same development history but viewed from the top. As is consistent with the descriptions above, the FPR storm evolves into a steady state supercell and hence maintains an extensive anvil. Both NLR and ELR storms dissipate after more than 90 min; the anvils break up and become disorganized. We are conducting a more thorough analysis of all three simulated storms and will report the results in a future paper.

Our conclusions here appear to be consistent with earlier findings using 2D model simulations on squall line systems, as mentioned at the beginning of Sec. 2, although the two situations are not identical. Thus the role of ice processes in the overall lifespan of thunderstorms seems to be valid for these different storm types.

3. Impacts of Ice Crystal Habit on Cirrus Development

Thin cirrus clouds are highly important to climate studies. In spite of their tenuous appearance, cirrus clouds have a pronounced influence on climate because of their effect on the radiation (Ramanathan et al., 1983). They are usually located high in the troposphere where the temperatures are cold. By virtue of their cold temperatures, they will interact strongly with the upwelling and downwelling infrared radiation in the atmosphere, as demanded by the Kirckhoff law. In addition, satellite observations indicate that cirrus clouds cover extensive areas of the Earth (e.g. Wylie and Menzel, 1989). These two factors together imply that cirrus clouds can significantly influence the radiative budget of the Earth-atmosphere system. The radiative effects of cirrus clouds can be highly variable because of the variability in thin radiative and micro-physical properties. Either cooling or warming can occur, depending on the cloud radiative properties, cloud height, and its thermal contrast with the surface (e.g. Manabe et al., 1965).

Randall et al. (1989) performed simulation studies using a general circulation model, and showed that upper tropospheric clouds have dramatic impacts on large-scale circulation in the tropics, with the attendant effects on precipitation and water vapor amounts. Ramaswamy and Ramanathan (1989) also performed GCM studies, and suggested that the discrepancies between the previous simulations and observed upper tropospheric temperature structure in the tropics and subtropics can be explained by the radiative heating effects of cirrus cloud systems. These studies point out that cirrus clouds are likely to have great impacts on the radiation, and hence the intensity of the general circulation.

At present, the cloud forcing in GCMs is a major uncertainty factor. Cess et al. (1989) compared the outputs of 14 GCMs simulating an equivalent climate change scenario, and found that the results of global temperature change in response to an imposed sea surface temperature change were relatively uniform when clear sky conditions were assumed for radiative computations. The results were very different when the radiative effects of clouds were included. They also found that the effect of cloud feedback was comparable in magnitude to that due to imposed forcing, i.e. the change in sea surface temperature, but the sign could be positive or negative, depending on the model chosen. Needless to say, this does not help to build confidence in the model predictions, and there is an urgent need to reduce the uncertainty in the cloud radiative forcing in GCM and climate models.

The radiative properties of cirrus clouds depend on their microphysical characteristics: ice crystal size, concentration, habit, spatial distribution, etc. The uncertainty about the radiative properties comes from our inadequate understanding of the cirrus microphysical behavior and associated subgrid (unresolved) dynamics in GCMs. One way to improve our understanding of cirrus microphysics is to perform model studies — provided, of course, that the model is adequately realistic.

In the following, we will briefly summarize our findings that are relevant to the impact of ice microphysics on cirrus clouds. The focus will be on the impacts of ice habit on the cirrus development. We have developed a cirrus model for this study, and performed various sensitivity studies using the model. The details of the physics and mathematics of the model can be found in Liu et al. (2003a,b). In the following subsections, the model will only be briefly described, and the main results relevant to the present article will be summarized.

3.1. The model physics

The basic idea of the cirrus model used for the present study was derived from an earlier work by Starr and Cox (1985), but the details differ significantly. In this subsection, the main elements of the model will be discussed. The three physical processes that have been identified to be essential for the development of cirrus clouds are the dynamical, microphysical and radiative processes. Cirrus clouds often form during the lifting of moist air associated with large-scale motions. Small ice crystals are formed in the updraft. If the upward motion persists long enough to cause further cooling of the layer, ice crystals will grow to sizes with substantial fall velocities, and precipitation will occur. As ice crystals grow larger, the radiative effect becomes more significant. The resulting radiative heating profile will change the temperature lapse rate, and thus the dynamics in the cloud will be different. A change in the cloud dynamics will affect the microphysical processes to alter the size distribution of ice crystals. This, in turn, will further modify the radiative heating profiles within the cloud. It is clear that these processes are interactive. None of the three processes should be ignored in developing a cirrus model.

The dynamics model is a modified version of the dynamics framework used in the WISCDYMM, as described in the previous section. The main modification is the use of the six-order Crowley scheme (see Tremback et al., 1987) to calculate the advection term for turbulent kinetic energy, water vapor and potential temperature. The numerical method used to calculate the advection of hydrometeors is the total variation diminishing (TVD) scheme, as described by Yee (1987).

The microphysical module focuses on the detailed ice microphysics. A double moment scheme is used to predict the evolution of the size distribution of ice crystals at each grid point. Both the mixing ratio and the number concentration of ice crystals are prognostic variables. The distribution mean diameter is then diagnosed from the mixing ratio and the number concentration. This is more realistic than predicting the mixing ratio only, as in most models with bulk microphysics. The growth rate of an ice crystal is explicitly calculated in this model. In the growth equation of ice crystals, both capacitance and ventilation coefficients are a function of ice crystal shape. Ventilation coefficients for different shapes of ice crystals that are commonly observed in cirrus are computed. The important microphy-sical process, homogeneous freezing nucleation, is included in our model since it has been recognized as a very effective source producing ice crystals in cirrus.

A radiation module is also implemented, as it is important to the development of cirrus clouds. Because we are examining optically thin cirrus clouds here, the mean free path for a photon colliding with a particle in cirrus is much larger than that in a typical stratocumulus; the radiative heating is distributed through the entire cirrus cloud body instead of being distributed like two Dirac functions with opposite signs at the cloud top and bottom as in a typical stratocumulus cloud (Ackerman et al., 1988). Moreover, the volume absorption coefficient and the volume extinction coefficient are very sensitive to the ice crystal size distribution. As the cloud evolves, the change in the ice crystal size distribution causes changes in the radiative heating rates not only in the interior, but also below and above the cloud deck. It is therefore important to correctly represent the ice crystal optical properties. For this purpose, a modified anomalous diffraction theory (MADT) proposed by Mitchell (1996) is employed. Its parametrization is based on the physics of how incident rays interact with a particle. By using anomalous diffraction theory, analytical expressions are developed describing the absorption and extinction coefficients and the single scattering albedo as functions of the size distribution parameter, ice crystal shape, wavelength and refractive index. Therefore, the optical properties calculated are not based on an effective radius that has little physical meaning. Another advantage of the MADT is that the scattering properties in the thermal infrared spectral range can be explicitly calculated, so that the scattering is not ignored. The radiative fluxes are calculated using a two-stream model. More details of the cloud microphysics and radiative modules are given in Liu et al. (2003a,b).

3.2. Model setup and initializations

The model domain illustrated in Fig. 4 represents a cross-section of cirrus advected by a nonsheared mean wind. The initial supersaturated layer is about 1 km thick. Temperature in the supersaturated layer is randomly perturbed between -0.02°C and 0.02°C to initialize the convective disturbance. The background vertical motion is set to 3 cm s_1, a typical value for large scale lifting, which is uniformly imposed throughout the model domain at all times.

The model domain is 20 km wide and 6 km deep, with respective spatial resolutions of 200 m and 100 m. When a test was conducted with the grid mesh reduced to 100 m in the horizontal and 50 m in the vertical, the results did

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