Weather models are routinely run at resolutions as fine as 1-3 km - fine enough that we do not parameterize things like convection and allow the model to resolv

Weather models are routinely run at resolutions as fine as 1-3 km - fine enough that we do not parameterize things like convection and allow the model to resolve these motions on its native grid. We typically do this over limited areas (e.g. domain the size of a continent), but plenty of groups have such simulations globally. It's just not practical (cost for compute and resulting data) to do this regularly, and it offers little by way of direct improvement in forecast quality. Furthermore, we don't have to necessarily measure the whole atmosphere in 3D; physical constraints arising from Navier-Stokes still apply, and we use them in conjunction with the data we _do_ have to estimate a full 3D atmospheric state complete with uncertainties.