My colleagues run the Advanced Research Weather Research & Forecasting (WRF) model in predictive mode, and then test the skill of the model anywhere from 12 - 84 hours out from the initialization time. The accuracy of the wind and the temperature profile are considered to be the most important indicators of the model's skill. An Eulerian grid model is then be used to represent air pollutant dispersion.
There have historically been discussions of problems with the model in places where there is complex terrain, and whether a finer-scale horizontal grid spacing would solve the issues (e.g. unable to capture local effects in the wind field or PBL). However, now there are models that are configured with the lowest recommended grid-spacing (1/3 km) and many more complex local weather patterns are being accurately modeled. I've been told that the models don't do well with grid-spacings any finer than 1/3 km. In fact, some people have said that the 4/3 km spacing can perform just as well, and that we've reached a point where Eulerian grid models don't gain much more by going to finer grids.
I know that for modeling pollutant dispersion at fine horizontal scales, Lagrangian methods have historically been used instead of Eulerian grid-cell methodology. However, with recent developments in computing, gridded modeling domains have been able to use much finer grid-spacings. What is the finest grid spacing that Eulerian dispersion grid-cell models should realistically use? Why?