J.-I. Yano (1), J.-L. Redelsperger (1), P. Bechtold (2) and F. Guichard (1)
(1) CNRM–GAME, Météo-France and CNRS, 31057 Toulouse Cedex,
France
(2) ECMWF, Shinfield Park, Reading, RG2 9AX, UK
Q. J. R. Meteorol. Soc., 2005, vol 131, pp. 2313-2336 [doi: 10.1256/qj.04.44]
Summary : Mode decomposition is proposed as a methodology for
developing subgrid-scale physical representations in global models by a
systematic reduction of an originally full system such as a cloud-resolving
model (CRM). A general formulation is presented, and also discussed are
mathematical requirements that make this procedure possible. Features of
this general methodology are further elucidated by the two specific examples:
mass fluxes and wavelets.
The traditional mass-flux formulation for convective parametrizations
is derived as a special case from this general formulation. It is based
on the decomposition of a horizontal domain into an approximate sum of
piecewise-constant segments. Thus, a decomposition of CRM outputs on this
basis is crucial for their direct verification. However, this decomposition
is mathematically not well-posed nor unique due to the lack of admissibility.
A classification into cloud types, primarily based on precipitation characteristics
of the atmospheric columns, that has been used as its substitute, does
not necessarily provide a good approximation for a piecewiseconstant segment
decomposition. This difficulty with mass-flux decomposition makes a verification
of the formulational details of parametrizations based on mass fluxes by
a CRM inherently difficult.
The wavelet decomposition is an alternative possibility that can more
systematically decompose the convective system. Its completeness and orthogonality
also allow a prognostic description of a CRM system in wavelet space in
the same manner as is done in Fourier space. The wavelets can, furthermore,
efficiently represent the
various convective coherencies by a limited number of modes due to
their spatial localizations. Thus, the degree of complexity of the wavelet-based
prognostic representation of a CRM can be extensively reduced. Such an
extensive reduction may allow its use in place of current cumulus parametrizations.
This wavelet-based scheme can easily be verified from the full original
system due to its direct reduction from the latter. It also fully takes
into account the multi-scale nonlinear interactions, unlike the traditional
mass-flux-based schemes.
keywords : cloud-resolving model - cumulus parametrization -
mass flux - wavelets