Wavelet-Compressed Representation of Deep Moist Convection

Abstract

The capacity of wavelets to effectively represent atmospheric processes under compression is tested by a dataset generated by a cloud-resolving model simulation of deep convective events observed during the Tropical Ocean Global Atmosphere Coupled Ocean?Atmosphere Response Experiment (TOGA COARE). Generally, more than 90% of the total variance is reproduced by retaining only the top 10% of the modes. The compressed data does not drastically deteriorate for graphic purposes, even when only the top 1% of modes are retained. The performance of compression is overall comparable for all the wavelets considered and also does not strongly depend on the type of physical variables. Conventional quantitative measures do not distinguish the compression errors arising from different characters of individual wavelets well, although different wavelet modes filter out different structures as ?noises? depending on their characteristics. The importance of choosing wavelets that represent the shape of signals physically expected is emphasized. Analytical discontinuities of wavelets are not necessarily undesirable for all the purposes, but must be consistent with our physical picture for the system. For this reason, the Haar wavelet may be acceptable because of its piecewise-constant structure, whereas the Daubechies wavelets of lower degrees are less appropriate because of their highly irregular structures. Some preliminary analyses are performed for assessing the capacity of wavelets to represent the full physics of meteorological systems. It is suggested that the loss of magnitudes in vertical fluxes under high compression can be recovered by a kind of ?renormalization? to a good extent. The mass continuity is found to be reasonably satisfied under the proposed compression method, although the latter is not explicitly constrained by the former.