Cloud Microphysics Parameterization in Shallow Cumulus Clouds Simulated by a Largrangian Cloud Model

Lagrangian cloud model (LCM) is a fundamentally new approach of cloud simulation, in which the flow field is simulated by LES and droplets are treated as Lagrangian particles undergoing cloud microphysics (Riechelmann et al. 2012; Hoffmann et al. 2017). LCM enables us to investigate raindrop formation and examine the parameterization of cloud microphysics directly by tracking the history of individual Lagrangian droplets simulated by LCM. In the present work the autoconversion and accretion rates are calculated directly by capturing the moment of the conversion of individual Lagrangian droplets from cloud droplets to raindrops. Analysis reproduces the formulae for autoconversion and accretion for the first time. The comparison of the autoconversion rate A and the accretion rate C with various parameterizations shows the closest agreement with Tripoli and Cotton (1980); that is, A = a q_c^7/3 N_c^-1/3 H(R - R_T) and C = βq_cq_r. where q_c and q_r are the mixing ratio of cloud droplets and raindrops, N_c is the number concentration of cloud droplets, α and β are the proportional constant, and R_T is the threshold radius (Fig. 1). Furthermore, the effects of turbulence (ε) through collision enhancement and the dispersion of drop size distribution (σ) on autoconversion are clarified. a increases linearly with ε and σ, but R_T decreases rapidly with σ, while disappearing at σ > 3.5 μm. The LCM also shows that ε and σ increase with time in shallow cumulus clouds, and it helps resolve the problem associated with the too early production of rain water too low in the cloud, which is common in many parameterizations. Finally, accretion is found to depend mainly on the raindrop size distribution, which results from the accumulated collisional growth.

References

Hoffmann, F., Y. Noh, and S. Raasch, 2017: The route to raindrop formation in a shallow cumulus cloud simulated by a Langrangian cloud model. J. Atmos. Sci., 74, 2125-2142.

Riechelmann, T., Y. Noh, and S. Raasch, 2012: A new method for large-eddy simulations of clouds with Lagrangian droplets including the effects of turbulent collision. New J. Phys., 14, 065008.

Tripoli, G. J. and W. R. Cotton, 1980: A numerical investigation of several factors contributing to the observed variable intensity of deep convection over South Florida, J. Atmos. Sci., 19, 1037-1063.