first_derivative_y
======================

.. py:function:: first_derivative_y(fs, mode="fdiff",  poles_missing_values=False)

   Computes the meridional (from South to North) partial derivative of each field in ``fs`` in */m 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

   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 :func:`regrid` with the nabla="scalar_gradient" option to compute the gradient and taking the meridional component of it

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

   .. math::

      \frac {\partial f}{\partial y} = \frac{1}{R}\frac{\partial f}{\partial \phi} 
   
   where:
   
   * R is the radius of the Earth
   * :math:`\phi` is the latitude
   * :math:`\lambda` is the longitude.

   .. note::
      See also :func:`first_derivative_x`, :func:`second_derivative_x`, :func:`second_derivative_y` and :func:`gradient`.

.. mv-minigallery:: first_derivative_y