“Renormalization” Approach for Subgrid-Scale Representations

Abstract

Physical processes in numerical modeling are currently handled by a dichotomy of either an explicit or a parameterization approach. Herein, an alternative approach is proposed, in which degrading explicit physics with decreasing resolutions are compensated by a ?renormalization.? More specifically, a ?renormalization? factor depending on the model resolution is multiplied on explicit evaluations so that the subgrid-scale contributions to a given grid scale are approximately recovered without a parameterization. The approach is analogous to the renormalization approach in statistical physics, but without rigorously relying on its mathematical basis. For this reason, this name is evoked with a quotation. In order to demonstrate this idea, the domain-mean vertical fluxes of heat, moisture, and momentum from cloud-resolving model experiments, corresponding to the grid-box averages in the large-scale modeling, are examined. In order to mimic the effects of degrading horizontal resolution, data are filtered in wavelet space. The ?renormalization? factors that recover the full vertical fluxes are found to be relatively stable with time, and the associated errors by ?renormalization? are overall less than the order of the vertical variance of the fluxes, indicating a potential usefulness of this approach. An analogous approach is found to work more effectively using data compression by wavelets.