Unified deep cumulus parameterization for numerical modeling of the atmosphere
Chien-Ming Wu
National Taiwan University 18 August, 10 am in 2890
Abstract:
A generalized framework for cumulus parameterization applicable to any
horizontal resolution between those typically used in general
circulation and cloud-resolving models is presented. It is pointed out
that the key parameter in the generalization is σ, which is the
fractional area covered by convective updrafts in the grid cell.
Practically all conventional cumulus parameterizations assume σ≪1, at
least implicitly, using the gridpoint values of the thermodynamic
variables to define the thermal structure of the cloud environment. The
proposed framework, called “unified parameterization,” eliminates this
assumption from the beginning, allowing a smooth transition to an
explicit simulation of cloud-scale processes as the resolution
increases. If clouds and the environment are horizontally homogeneous
with a top-hat profile, as is widely assumed in the conventional
parameterizations, it is shown that the σ dependence of the eddy
transport is through a simple quadratic function. Together with a
properly chosen closure, the unified parameterization determines σ for
each realization of grid-scale processes. The parameterization can also
provide a framework for including stochastic parameterization.
Additional analyzed fields include the vertical structure of the σ
dependence of vertical and horizontal eddy transports of moist static
energy and horizontal momentum and that of cloud microphysical sources.
For the momentum transport, the analysis results clearly show the
limits of the traditional approach of parameterization based on an
effectively one-dimensional model. For cloud microphysical conversions,
it is shown that those taking place primarily inside and outside the
updrafts are roughly proportional to σ and 1-σ, respectively