.. py:function:: second_derivative_y(fs, mode="fdiff", poles_missing_values=False)
Computes the second meridional (from South to North) 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 y^2} = \frac{1}{R^2}\frac{\partial^2 f}{\partial \phi^2}
where:
* R is the radius of the Earth in m
* :math:`\phi` is the latitude
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_x`, :func:`first_derivative_x`, :func:`first_derivative_y` and :func:`gradient`.
.. mv-minigallery:: second_derivative_y