It seems like FastEddy mostly replaces WRF-LES, which is used for high-resolution localized modeling.
The errors in the weather forecast are not the result of chaos: they are the result of the errors in the measurements (recorded in the observation covariance) and the sparsity of the measurements themselves vs the size of Earth, for example, and limitations in model resolution (consider a FEM grid over the entire surface of Earth). The effect of chaos just compounds these errors near bifurcations around fixed points.
Perturbations are not used in the way you think; think of Taylor series approximations around specific points of interest.
Anyway, I work on compilers/auto-vectorization now (lol), so I'll defer to The Expert, if such person wants to chime in.
The data itself is noisy. Bad readings aren’t uncommon. Common hygrometers (humidity sensors) have hysteresis, wind is turbulent, radiosondes stop transmitting in midair. Some data is really weird, like GPS occultation data, which gives temperature mixed with humidity along a 200km long cylinder. Suffice to say that while higher order approximations in modeling have helped, DA is super important because measurements are both sparse and flaky.
But that’s why I asked: numerical errors are typically dwarfed by measurement errors. So it shouldn’t be worse than a member of an ensemble model, right?
If so, wouldn't it be relatively simple to swap-in a CUDA implementation of this solver?
> The Navier–Stokes equations are nonlinear partial differential equations in the general case and so remain in almost every real situation. In some cases, such as one-dimensional flow and Stokes flow (or creeping flow), the equations can be simplified to linear equations. The nonlinearity makes most problems difficult or impossible to solve and is the main contributor to the turbulence that the equations model.