Sometimes these smaller perturbations are called "sub-grid phenomena". I think practitioners think of them as, say, pressure waves or flows which average to zero when observed on a 10km x 10km grid. But it is possible that their ultimate origin is on a much finer grid ;-)
Another problem, separate from these effects, is getting closure on the variables in the model. Things like evaporation from soils and vegetation, for example, which ECMWF is trying to include in their models. You put them in the weather model to improve accuracy, and all the sudden you need a time-dependent model for soil and vegetation water content. And also, sensors to satisfy the boundary conditions for your model (e.g., to estimate plant vegetation type).
Another problem, separate from these effects, is getting closure on the variables in the model. Things like evaporation from soils and vegetation, for example, which ECMWF is trying to include in their models. You put them in the weather model to improve accuracy, and all the sudden you need a time-dependent model for soil and vegetation water content. And also, sensors to satisfy the boundary conditions for your model (e.g., to estimate plant vegetation type).