| The present talk does not seek an answer on a pattern formation, but
it proposes an approach for representing the subgrid-scale processes
assuming coherent pattern structures.
Due to a limit of spatial resolution in geophysical modelling, the
information on the processes of the scales less than the model
resolution is not readily available. The problem of inferring
information on these subgrid-scale processes may be collectively
called the subgrid-scale representation problem.
Traditionally, the subgrid-scale representation problem is separated
into two completely separate problems. The first is an issue of
inferring the subgrid-scale information directly (e.g., subgrid-scale
spatial pattern of a variable), called "downscaling". The second is an
issue of inferring the feedbacks of these subgrid-scale processes onto
the resolved scales, called "parameterization". The proposed
pattern-based subgrid-scale representation approach enables to deal
with these two problems simultaneously.
We specifically pay an attention to the fact that these subgrid-scale
pattern structures represents a scaling law associated with isolated
coherent structures. Thus, the multiresolutional analysis techniques
such as wavelet can efficiently represent these patterns with a heavy
truncation of the modes in phase space, or compression. Such a
compression provides a parameterization. Then the decompression of the
phase space information back to the real space provides a
downscaling.
However, a minor twist is required for this general strategy, because
most of the physical processes can efficiently be calculated only in the
real space, thus the phase-space transformation makes the model
description rather awkward. Here, the idea of multiresolutional
approach is replaced by a finite volume approach, but keeping the
basic spirit of the former approach. That leads to a highly-flexible
time-dependent mesh-refinement model.
An atmospheric demonstration of this approach will be presented. |