pvtend.sh_ops.helmholtz_sh

pvtend.sh_ops.helmholtz_sh(u: ndarray, v: ndarray, lat: ndarray, lon: ndarray, R_earth: float = 6371000.0, return_harmonic: bool = True, sanity_tol: float = 0.001) → dict[source]

Spherical-harmonic Helmholtz decomposition.

On the full sphere a Helmholtz decomposition into rotational and divergent parts is exact, so the harmonic residual is zero up to floating-point error. We still report u_har / v_har for API parity with the FD path. NH-only inputs are mirrored with parity (u even, v odd) so the equator becomes a hard wall and the harmonic residual remains negligible inside the NH.

Parameters:

  • u – Zonal wind, shape (nlat, nlon).

  • v – Meridional wind, shape (nlat, nlon).

  • lat – Latitudes in degrees, ascending.

  • lon – Longitudes in degrees in [0, 360).

  • R_earth – Earth radius in metres.

  • return_harmonic – If True, also return the (numerical-residual) harmonic part.

  • sanity_tol – Warn if ‖u_har‖ / ‖u‖ > sanity_tol on a global input. Disabled for NH-only inputs (the equator wall generates an expected boundary residual).

Returns:

Dict with the same keys as pvtend.helmholtz.helmholtz_decomposition().