.. py:function:: 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 */m\ :sup:`2` units. :param fs: input fieldset :type fs: :class:`Fieldset` :param mode: specifies the computation mode (see below) :type mode: {"fdiff", "felem"}, default: "fdiff" :param poles_missing_values: puts missing values at the poles when ``mode`` is "felem". :type poles_missing_values: bool, default: False :rtype: :class:`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: .. math:: \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 * :math:`\phi` is the latitude * :math:`\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 :func:`regrid` with the nabla="scalar_gradient" option twice in a row .. note:: See also :func:`second_derivative_y`, :func:`first_derivative_x`, :func:`first_derivative_y` and :func:`gradient`.
.. mv-minigallery:: second_derivative_x