earthkit.meteo.thermo.array.saturation_specific_humidity_slope
==============================================================

.. py:function:: earthkit.meteo.thermo.array.saturation_specific_humidity_slope(t, p, es=None, es_slope=None, phase='mixed', eps=0.0001)

   Compute the slope of saturation specific humidity with respect to temperature.

   :param t: Temperature (K)
   :type t: :class:`array-like`
   :param p: Pressure (Pa)
   :type p: :class:`array-like`
   :param es: :func:`saturation_vapour_pressure` pre-computed for the given ``phase`` (Pa)
   :type es: :class:`array-like` or :obj:`None`, *optional*
   :param es_slope: :func:`saturation_vapour_pressure_slope` pre-computed for the given ``phase`` (Pa/K)
   :type es_slope: :class:`array-like` or :obj:`None`, *optional*
   :param phase: Define the phase with respect to the computation will be performed.
                 It is either “water”, “ice” or “mixed”. See :func:`saturation_vapour_pressure`
                 for details.
   :type phase: :class:`str`, *optional*
   :param eps: Where p - es < ``eps`` nan is returned.
   :type eps: :class:`number`

   :returns: Slope of saturation specific humidity (:math:`kg kg^{-1} K^{-1}`)
   :rtype: :class:`array-like`

   The computation is based on the following formula:

   .. math::

       \frac{\partial q_{s}}{\partial t} =
       \frac{\epsilon\; p}{(p+e_{s}(\epsilon - 1))^{2}} \frac{d e_{s}}{d t}

   where

       * :math:`\epsilon = R_{d}/R_{v}` (see :data:`earthkit.meteo.constants.epsilon`).
       * :math:`e_{s}` is the :func:`saturation_vapour_pressure` for the given ``phase``