Overview

windspharm is designed to simplify the computation of quantities that are composed of derivatives/integrals of a vector wind field defined on a sphere. windspharm works by expressing the vector field in the form of spherical harmonics. In the spherical harmonic basis many operations that are hard to compute in the spatial representation, such as the Laplacian operator, become trivial. This allows one to compute such quantities both quickly and accurately.

The down-side of using a spherical harmonic representation is that the input and output fields must all be defined over the whole globe. The spherical harmonic representation is simply not defined for non-global fields.

Computations with windspharm

windspharm uses VectorWind objects to do computations. A VectorWind object is an object that is initialized with the components of a global vector wind field (eastward and northward components), that provides many methods for returning quantities of interest. The typical usage pattern for windspharm is:

1. Import the appropriate VectorWind object for the type of data being worked with.

2. Create a VectorWind instance using eastward and northward wind components.

3. Call methods of the VectorWind instance to compute and return quantities of interest.

The following table describes the methods that are common to the VectorWind objects in all interfaces:

Method	Description
magnitude	Magnitude of the vector wind (the wind speed).
vrtdiv	Relative vorticity and divergence.
vorticity	Relative vorticity.
divergence	Divergence.
planetaryvorticity	Planetary vorticity (Coriolis parameter).
absolutevorticity	Absolute (planetary + relative) vorticity.
sfvp	Streamfunction and velocity potential.
streamfunction	Streamfunction.
velocitypotential	Velocity potential.
helmholtz	Helmholtz decomposition, irrotational and non-divergent components of the vector wind.
irrotationalcomponent	Irrotational component of the vector wind (the component associated with divergence/velocity potential.
nondivergentcomponent	Non-divergent component of the vector wind (the component associated with vorticity/streamfunction).
gradient	The vector components of the gradient of a scalar field.
truncate	Apply triangular truncation to a scalar field.