gradient

gradient(fs, mode='fdiff', poles_missing_values=False, vector=False)

Computes the horizontal gradient of each field in a Fieldset in */m units.

Parameters

  • fs (Fieldset) – input fieldset

  • mode ({"fdiff", "felem"}, default: "fdiff") – specifies the computation mode (see below)

  • poles_missing_values (bool, default: False) – puts missing values at the poles when mode is “felem”.

  • vector (bool, default: False) – indicates if fs is a vector field when mode is “felem”

Return type

Fieldset

The numerical method to compute the gradient is based on the value of mode.

When mode is “fdiff”:

  • a second order finite-difference approximation is used

  • the output fields contain missing values at the poles

  • only works for regular latitude-longitude grids

When mode is “felem”:

  • a finite-element technique is used

  • works with (regular and reduced) latitude-longitude and Gaussian grids

  • no missing values are allowed in fs!

  • the computations are performed by using regrid() with the nabla option. If vector is False regrid() is invoked with nabla=”scalar_gradient” otherwise nabla=”uv_gradient” is used.

The resulting fieldset contains two fields for each input field: the zonal derivative followed by the meridional derivative.

The computations for a field f are based on the following formula:

\[\nabla f = (\frac {\partial f}{\partial x}, \frac {\partial f}{\partial y}) = (\frac{1}{R \ cos\phi}\frac{\partial f}{\partial \lambda}, \frac{1}{R}\frac{\partial f}{\partial \phi} )\]

where:

  • R is the radius of the Earth (in m)

  • \(\phi\) is the latitude

  • \(\lambda\) is the longitude.

Note

See also first_derivative_x(), first_derivative_y(), second_derivative_x() and second_derivative_y().