second_derivative_x

second_derivative_x(fs, mode='fdiff', poles_missing_values=False)

Computes the second zonal (from West to East) partial derivative of each field in fs in */m2 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”.

Return type

Fieldset

The numerical method to compute the derivative 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

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

    \[\frac {\partial^2 f}{\partial x^2} = \frac{1}{R^2 \ cos^2\phi}\frac{\partial^2 f}{\partial \lambda^2}\]

    where:

    • R is the radius of the Earth in m

    • \(\phi\) is the latitude

    • \(\lambda\) is the longitude.

When mode is “felem”:

  • a finite-element technique is used, and the first derivative operator is invoked twice

  • 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=”scalar_gradient” option twice in a row

Note

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