I have been watching the hurricane forecasting for Hurricane Henri, and it made me think about the accuracy of the forecasting for hurricane tracks. While I don't know much about meteorology, it seems that hurricane models are likely based on large systems of hyperbolic PDEs. My question is, what methods are used to solve these PDEs or whatever models, such that it allows weather forecasters to predict the flow of the system over hundreds of miles?
There are many different methods for solving hyperbolic pdes, finite elements, finite volume methods, etc., symplectic integrators for the timestepping. But I did not think that these types of methods would guarantee accuracy over such a long long time domain and spatial domain.
I was hoping someone might know what techniques are used to solve these hurricane models, that enable such a high level of accuracy over hundreds of miles.
It's not just the choice of pde models and of numerical solvers that makes modern numerical weather prediction (NWP) so successful. The availability of data (weather stations, radio sondes, satellites etc.), international cooperation, new techniques such as ensemble forecasting and data assimilation, and improved physical models for atmospheric phenomena and for ocean-atmosphere interaction all have contributed.
For a thorough discussion of the progress of NWP during the last 100 years, take a look at the linked article.