Inclusion
of rainwater budget and convective downdrafts in the Arakawa-Schubert cumulus
parameterization
M. -D. Cheng and A. Arakawa, 1997
(J. Atmos. Sci., 54, 1359-1378)
ABSTRACT
A combined updraft-downdraft model that includes the mass, rainwater and vertical
momentum budget equations for both updrafts and downdrafts is incorporated into
the Arakawa-Schubert cumulus parameterization. The model assumes that the rainwater
generated in an updraft falls partly inside and partly outside the updraft.
Two types of stationary solutions are identified for the coupled rainwater budget
and vertical momentum equations: solutions for small tilting angles and solutions
for large tilting angles. The balance of terms in the rainwater budget equation
is quite different between these solutions, and solutions for small tilting
angles are unstable while solutions for large tilting angles are stable. The
cause of the instability is interpreted considering the effect of rain-drag
on the vertical transport of rainwater. The motivation for an optimum choice
of the tilting angle for use in the revised parameterization is discussed. The
results of semi-prognostic and single-column prognostic tests of the revised
A-S parameterization using the GATE Phase III data show drastic improvement
in predicting the humidity field through the inclusion of downdraft effects.
An updraft model with a simplified rainwater budget equation, which is used
in our current GCM applications of the revised parameterization, is also presented.