earthkit.meteo.vertical.array.pressure_at_model_levels
======================================================

.. py:function:: earthkit.meteo.vertical.array.pressure_at_model_levels(A, B, sp, alpha_top = 'ifs')

   Compute pressure at model full- and half-levels.

   :param A: A-coefficients defining the model levels. See [IFS-CY47R3-Dynamics]_
             (page 6) for details.
   :type A: :class:`ndarray`
   :param B: B-coefficients defining the model levels. See [IFS-CY47R3-Dynamics]_
             (page 6) for details.
   :type B: :class:`ndarray`
   :param sp: Surface pressure (Pa)
   :type sp: :class:`number` or :class:`ndarray`
   :param alpha_top: Option to initialise alpha on the top of the model atmosphere (first half-level in vertical coordinate system). The possible values are:

                     - "ifs": alpha is set to log(2). See [IFS-CY47R3-Dynamics]_ (page 7) for details.
                     - "arpege": alpha is set to 1.0
   :type alpha_top: :class:`str`, *optional*

   :returns: * :class:`ndarray` -- Pressure at model full-levels
             * :class:`ndarray` -- Pressure at model half-levels
             * :class:`ndarray` -- Delta at full-levels
             * :class:`ndarray` -- Alpha at full levels

   .. rubric:: Notes

   ``A`` and ``B`` must contain the same model half-levels in ascending order with
   respect to the model level number. The model level range must be contiguous and
   must include the bottom-most model half-level (surface), but not all the levels
   must be present. E.g. if the vertical coordinate system has 137 model levels using
   only a subset of levels between e.g. 137-96 is allowed.

   For details on the returned parameters see [IFS-CY47R3-Dynamics]_ (page 7-8).

   The pressure on the model-levels is calculated as:

   .. math::

       p_{k+1/2} = A_{k+1/2} + p_{s}\; B_{k+1/2}

       p_{k} = \frac{1}{2}\; (p_{k-1/2} + p_{k+1/2})

   where

       - :math:`p_{s}` is the surface pressure
       - :math:`p_{k+1/2}` is the pressure at the half-levels
       - :math:`p_{k}` is the pressure at the full-levels
       - :math:`A_{k+1/2}` and :math:`B_{k+1/2}` are the A- and B-coefficients defining
         the model levels.

   .. seealso:: :obj:`pressure_at_height_levels`, :obj:`relative_geopotential_thickness`