Comprehensive Quantification of Height Dependence of 1 Entrainment-Mixing between Stratiform Cloud Top and 2 Environment

. Different entrainment-mixing processes of turbulence are crucial to processes related to clouds; however, only a few 14 qualitative studies have been concentrated on the vertical distributions of entrainment-mixing mechanisms with low vertical 15 resolutions. To quantitatively study vertical profiles of entrainment-mixing mechanisms with a high resolution, the stratiform 16 clouds observed in the Physics of Stratocumulus Top (POST) project are examined. The unique sawtooth flight pattern allows 17 for an examination of the vertical distributions of entrainment-mixing mechanisms with a 5 m vertical resolution. Relative 18 standard deviation of volume mean radius divided by relative standard deviation of liquid water content is introduced to be a 19 new estimation of microphysical homogeneous mixing degree, to overcome difficulties of determining the adiabatic 20 microphysical properties required in existing measures. The vertical profile of this new measure indicates that entrainment- 21 mixing mechanisms become more homogeneous with decreasing altitudes and are consistent with the dynamical measures of 22 Damkohler number and transition scale number. Further analysis shows that the vertical variation of entrainment-mixing 23 mechanisms with decreasing altitudes is due to the increases of turbulent dissipation rate in cloud and relative humidity in 24 droplet-free air, and the decrease of size of droplet-free air. The results offer insights into the theoretical understanding and 25 parameterizations of vertical variation of entrainment-mixing mechanisms. adjacent to 45 entrained air would evaporate completely to saturate the air, while the other droplets are not affected by the entrainment. In this scenario, number concentration decreases but droplet size remains unchanged. Some observational studies support the 47 extreme IM concept (Burnet and Brenguier, 2007; Lu et al., 2011; Freud et al., 2011; Pawlowska et al., 2000; Haman et al., 48 2007; Freud et al., 2008); while some others indicate that the HM mixing dominates (Gerber et al., 2008; Lu et al., 2013c; 49 Burnet and Brenguier, 2007; Jensen et al., 1985), and still some others find intermediate features fall in between the HM IM mixing (Lehmann et al., 2009; Lu et al., 2014a; Kumar et The variation of entrainment-mixing mechanisms is less studied. For cumulus, Jarecka found that a trend existed of entrainment-mixing to be more HM in cloud top, resulted from increasing of cloud droplet radius and turbulence with increasing altitudes. In stratiform clouds, Yum et Wang positive correlation at of no correlation at top droplet suggested that entrainment mixing at cloud top region was indeed IM, while during the descent of vertical circulation, the cloud droplets in more diluted parcels would evaporate faster, and observe the generally HM feature at a relatively long depth vertical variation entrained air RH plays a significant part in determining the entrainment-mixing mechanisms. In former literatures et al., 2017; Lu et al., 2018), RH is commonly assumed to be constant across multiple different 290 altitudes when calculating τ evap using S 0 = RH - 1. In fact, RH should not be a constant. We determine RH as the mean RH of 291 droplet-free air in each level. Figures 10 (c), (f), (i) and (l) show that RH increases with decreasing altitudes due to droplet 292 evaporation. According to the definition of Da , Da decreases with the increase of τ evap , and thus decreases with the increase of 293 RH (equation (7) and (10)). Equations (10), (11) and (12) show that N L increases with increasing RH. Both Da and N L indicate 294 more HM mixing at a lower altitude. These results suggest that the increases of ε and RH and the decrease of L with decreasing 295 altitudes are in keeping with the variation of entrainment-mixing processes, together playing the primary role in determining 296 the vertical distribution of HMD observed. microphysical properties needed in the traditional approaches. This new method can be applied to other 346 datasets since the new definition is based on theoretical understanding of entrainment-mixing mechanisms, which is not limited 347 to the dataset used here. It would be interesting to apply this method to other stratocumulus and cumulus observations in 348 different climate zones.

Entrainment-mixing processes are considered to occur primarily near the stratiform cloud top and entrainment-mixing around 35 the stratiform cloud sides is negligible (Wood, 2012;Xu and Xue, 2015).

37
The question about how entrained air affects cloud microphysics has been debated for a long time. Several conceptual models 38 have been established to study the different entrainment-mixing processes, e.g., entity-type entrainment-mixing (Telford, 1996; 39 Telford and Chai, 1980), vertical circulation entrainment-mixing (Yeom et (Baker et al., 1980;Baker et al., 1984). The last one is the most 41 used and studied. During the HM mixing, the time scale for droplets to evaporate completely is larger than the time scale for 42 mixing between entrained air and cloudy air. All droplets are exposed to the same unsaturated state and evaporate concurrently.

43
In this scenario, all droplets' sizes decrease simultaneously, and number concentration also decreases due to the dilution effect 44 of entrained air. While in the IM mixing, mixing time scale is larger than evaporation time scale. Some droplets adjacent to 45 entrained air would evaporate completely to saturate the air, while the other droplets are not affected by the entrainment. In 46 this scenario, number concentration decreases but droplet size remains unchanged. Some observational studies support the

142
The dynamical aspect, i.e., the mixing process between cloud and environment air vs. the evaporation process of cloud droplets, 143 is important to distinguish different entrainment-mixing mechanisms (Baker et al., 1980;Baker and Latham, 1979). The mixing used as a proxy for the entrained air parcels' size. In equation (7), the time scale for a droplet of radius rva to completely 162 evaporate (evaporate time) is given by: 164 where S0 is the supersaturation of the droplet-free air at the corresponding altitude (Yau and Rogers, 1996); A is a affected by 165 air temperature and pressure (see Appendix B for details). (12) 172 In equation (11), η is the Kolmogorov length scale (Wyngaard, 2010), which is given by: 174 where v is the kinematic viscosity (Wyngaard, 2010). A higher probability of HM mixing corresponds to a larger value of NL.  (Table 1) at each level near the stratiform cloud tops for the data collected during the four flights. Only the results

191
for the first microphysical measure are shown in Figure 3; the other results are shown in the Supporting Information. In Figure   192 3, LWCa is based on the adiabatic growth from cloud base, the maximum number concentration at each level is assumed as na,

193
and rva is calculated from LWCa and na. In Figure S1, LWCa is based on the adiabatic growth from cloud base, the maximum 194 volume mean radius at each level is assumed as rva, and na is calculated from LWCa and rva. In Figure S2, the maximum liquid 195 water content at each level is assumed as LWCa, the maximum number concentration at each level is assumed as na, and rva is 196 calculated from LWCa and na. In Figure S3, the maximum liquid water content at each level is assumed as LWCa, the maximum   (Panofsky, 1984). DNN is the local spatial structure function using three wind components and is defined 367 as: The parameter A in equation (10) is