Several Unresolved Issues in Numerical Modelling of Geophysical Flows

This paper discusses several issues in the numerical modelling of atmospheric flow which have been left unresolved. These include the influence of partial model resolution of features that are represented in a model by only a few grid points and the implication of this inadequacy in terms of the parametrization of subgrid-scale processes. As a result of nonlinear interactions, this lack of resolution requires the introduction of new parametrization techniques such as "backscatter", as well as an assessment of the predictability and parametrizability of atmospheric flows as a result of the limited spatial resolution. Examples of these issues are presented in the paper. Among the conclusions is that for large eddy simulations a stochastic subgrid-scale parametrization is needed, while for well-defined surface forced mesoscale systems such as sea breezes, an ensemble-based subgrid-scale representation is adequate. Also introduced in this paper is an additional physical realism to atmospheric models (i.e., the compressibility effect) which provides an additional modelling degree of freedom to internal and externally imposed perturbations. RESUME On examine plusieurs problemes de modelisation numerique de l'ecoulement atmospherique qui sont encore sans solution. Parmi ceux-ci, I'influence de La resolution partielle par Ie modele d'entites representees par seulement quelques points de grille et la repercussion de celIe insuffisance en termes de parametrage des processus d'echelle inferieure a la maille. A cause des interactions non linea ires, ce manque de resolution demande I'introduction de nouvelles techniques de parametrage, la «retrodiffusion» p. ex., 558/ R.A. Pielke et al. ainsi qu 'une evaluation de la possibilite de prevision et de parametrage des ecoulements atmospheriques tenant compte de la resolution spatia Ie limitee. Dans cet article on expose des exemples de ces problemes. On trouve qu 'un parametrage stochastique de I' echelle inferieure il la maille est necessaire pour les simulations de grands tourbillons alors que pour des systemes bien definis de mesoechelle forces par la surface, leis que les brises de mer, une representation de l'echelle inferieure il la maille baste sur un ensemble est adequate. On introduit aussi un realisme physique supplementaire dans les modeles atmospheriques (p. ex., effet de compressibilite) qui fournit un degre de liberte supplementaire de modelisation pour les perturbations internes et celles imposees de l'exterieur.