The WBF efficiency and liquid persistence

Sustaining liquid is the other key part of phase inversion in ASC. After the first ice nucleation (see §.4.2.1.1), the depositional growth of ice would occur, which would consume water vapor and hinder the generation of the liquid layer afterward. Fortunately, the environment is suitable for updrafts (Figure 31) and helps to form liquid afterward (see §2.3) and the amount of dust to serve as IN is not very high. After liquid formation, the WBF growth of ice would consume liquid. Therefore, the strength of the WBF process affects the persistence of liquid, which would be discussed in this section.

.4.2.2.1 WBF characteristic time

The intensity of the WBF process can be evaluated by the WBF characteristic time τ that contained in the following equation (Morrison and Gettelman 2008):

dq_i

dt = ∫ Crni(S_i− 1)dr =^qv_Γ^−qsi

pτ , ( 3 )

where ^dqi

dt is the depositional growth rate of ice, C is an environment parameter associated with heat conductance and vapor diffusivity, r is the radius of ice particles, n_i is the number concentration of ice particles, S_i is the ice saturation ratio, q_v is the in-cloud water vapor mixing ratio, qsi is the ice-saturation mixing ratio, and Γp is a correction accounting for the drop surface heating due to latent heat release (Morrison and Gettelman 2008). This formula means that the depositional growth of ice is proportional to the water vapor difference between the in-cloud environment and that

τ is inversely

proportional to the summation of r and ni, which is the first moment of ice. The shorter the τ is, the faster the cloud liquid evaporates to supply water vapor for ice growth, which represents a stronger ice WBF growth.

In CTL, the profiles of τ (Figure 32a) and ice number concentration (Figure 32b) show two things. One is that τ is more or less layered in the cloud deck, being mostly longer than 1 day at the upper levels and shorter than 1 day below. As the drop size does not differ much, the longer τ tends to be associated with a lower number of ice particles.

Indeed, the results show more ice in the lower levels and revealed the phase inversion structure. The other is that the mixed-phase layer has rather long τ (generally longer than 6 hours, also can be seen in Figure 33), mainly because relatively few ice particles (around 500 m^-3) are present in this area. In the mixed-phase layer, IN in ice can be removed by gravitational sedimentation (with fall speed about 30 cm s^-1 in Figure 17a) to maintain low number concentrations of dust and ice, which leads to a weak WBF process. Such removal of IN is generally not considered in the empirical nucleation approach but is explicitly treated in this study. Thus, τ at the upper part of the cloud is longer than the lifetime of liquid (about 3.5 hours as indicated in Figure 15b), which means that the ice WBF growth will not use up all the liquid. The persistent droplets have time to capture more dust particles by Brownian diffusion and gravitational collection, and further weakens the nucleation ability of dust due to the lower immersion freezing rate and the loss of effective dust in the air. Also, lower number concentration means lower competition, such that ice can grow larger and settle faster gravitationally. All these help to sustain the liquid layer. In summary, the low concentration of ice particles in the mixed-phase layer results in a weak WBF process and assists the persistence of liquid in CTL.

Therefore, the number of dust particles is crucial to liquid persistence by regulating the number of nucleated ice particles.

.4.2.2.2 Sensitivity of dust number concentration

To know how dust number concentration N₀ affects the liquid persistence and the phase inversion structure, sensitivity tests of changing dust number concentration are designed. Figure 34 and Figure 35 show that when N₀ is increased by 10 times (N10), there is essentially no liquid left and the cloud is all ice phase. When N₀ is reduced by 10 times (N0.1), the amount of ice significantly reduces while that of liquid becomes ampler as reflected in the time series of average IWP and LWP in domain 3 (Figure 36).

When N₀ is further reduced by 100 times compared to CTL (N0.01), ice still can be nucleated but the amount is too low such that the cloud condensates are mostly water (Figure 34d, Figure 35d, & Figure 36).

N₀ influences the amount of nucleated ice. From the profiles of the ice number concentration (Figure 38), ice particles can be more than 1000 m^-3 in the N10 run, while reduces to about 50 to 250 m^-3 in N0.1. As discussed in §.4.2.2.1, the number of nucleated ice particles strongly affects the WBF process and liquid persistence. From Figure 37, one can see that τ is mainly shorter than 6 hours in N10, while longer than 1 day in N0.1 and N0.01. Figure 39 shows that the predominant value of τ becomes larger as N0

reduces, being 1 to 3 hours in N10 and more than 1 day in N0.1. The characteristic time of 1 hour in N10 is much shorter than the liquid-cloud lifetime such that the liquid is hard to maintain under the strong WBF process; whereas of 1 day in N0.1 and N0.01 is much longer than the lifetime of the cloud so that the liquid can persist and maintain the phase inversion structure under sustained frontal vertical lifting.

Figure 40 and Figure 41 show the liquid mass fraction and cross-section area ratio profiles averaged within 5x5 grids centered at Barrow for N0.1 and N0.01 runs. One can

see that the liquid-dominant layer becomes thicker when N0 is reduced. Too few dust particles result in a nearly all liquid cloud such that phase inversion can hardly be observed. Therefore, N₀ affects the amount of ice and liquid and changes the phase inversion structure. If the environment has too many or too few dust particles, the phase inversion structure cannot be found. Only with just about the right amount of dust can phase inversion be formed.