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The IFS uses a spectral transform method to solve numerically the equations governing the spatial and temporal evolution of the atmosphere. The idea is to fit a discrete representation of a field on a grid by a continuous function. This is achieved by expressing the function as a truncated series of spherical harmonics:
where θ the latitude of the grid point, T is the spectral truncation number and Y_{ lm }are the spherical harmonic functions which are products of the associated Legendre polynomials,
and the Fourier functions,
The spectral coefficients - a Fast Fourier Transform in the zonal direction followed by
- a slow/fast Legendre transform in the meridional direction.
At each time step in the IFS: - derivatives, semi-implicit correction and horizontal diffusion are computed in spectral space;
- explicit dynamics, semi-Lagrangian advection and physical parametrizations are computed in grid point space.
The representation in grid point space is on the |