Roles of Drop Size Distribution and Turbulence in Autoconversion Based
on Lagrangian Cloud Model Simulations
Abstract
The roles of the drop size distribution (DSD) and turbulence in the
autoconversion rate A are investigated by analyzing Lagrangian cloud
model (LCM) data for shallow cumulus clouds. The correlations of DSD and
turbulence with other cloud parameters are estimated, and they are
applied to parameterize their effects on A. A new parameterization of A
is proposed based on it, as A = αqc7/3Nc-1/3H(Rc-Rc0) with α =
aNc-X(Rc-Rc0)(1+bε), where qc, Nc, and Rc are the mixing ratio, the
number concentration, and the volume mean radius of cloud droplets,
respectively. ε is the dissipation rate, Rc0 is the threshold value of
Rc, H is the Heaviside step function, and X, a, and b are constants.
Here, Nc-X(Rc-Rc0) represents the effect of DSD, via its correlation
with Nc and qc, while A ∝ qc7/3Nc-1/3 represents the effect of the
gravitational collisional growth for given DSD and turbulence. The
correlation between turbulence and DSD makes b larger than expected
based on turbulence-induced collision enhancement. The effects of DSD
and turbulence and their correlations with qc and Nc explain a wide
range of exponent values of qc and Nc in many existing parameterizations
of A. The new parameterization is compared with the LCM data and applied
to a bulk cloud model (BCM) while clarifying the difference between the
cloud droplet mixing processes of the LCM and BCM. The importance of DSD
and turbulence in the raindrop formation in shallow cumulus clouds are
shown by comparing the results from A with and without these effects.