earthkit.meteo.thermo.array.saturation_vapour_pressure
======================================================

.. py:function:: earthkit.meteo.thermo.array.saturation_vapour_pressure(t, phase='mixed')

   Compute the saturation vapour pressure from temperature with respect to a phase.

   :param t: Temperature (K)
   :type t: :class:`array-like`
   :param phase: Define the phase with respect to the saturation vapour pressure is computed.
                 It is either “water”, “ice” or “mixed”.
   :type phase: :class:`str`, *optional*

   :returns: Saturation vapour pressure (Pa)
   :rtype: :class:`array-like`

   The algorithm was taken from the IFS model [IFS-CY47R3-PhysicalProcesses]_ (see Chapter 12).
   It uses the following formula when ``phase`` is "water" or "ice":

   .. math::

       e_{sat} = a_{1}\;exp \left(a_{3}\frac{t-273.16}{t-a_{4}}\right)

   where the parameters are set as follows:

   * ``phase`` = "water": :math:`a_{1}` =611.21 Pa, :math:`a_{3}` =17.502 and :math:`a_{4}` =32.19 K
   * ``phase`` = "ice": :math:`a_{1}` =611.21 Pa, :math:`a_{3}` =22.587 and :math:`a_{4}` =-0.7 K

   When ``phase`` is "mixed" the formula is based on the value of ``t``:

   * if :math:`t <= t_{i}`: the formula for ``phase`` = "ice" is used (:math:`t_{i} = 250.16 K`)
   * if :math:`t >= t_{0}`: the formula for ``phase`` = "water" is used (:math:`t_{0} = 273.16 K`)
   * for the range :math:`t_{i} < t < t_{0}` an interpolation is used between the "ice" and "water" phases:

   .. math::

       \alpha(t) e_{wsat}(t) + (1 - \alpha(t)) e_{isat}(t)

   with :math:`\alpha(t) = (\frac{t-t_{i}}{t_{0}-t_{i}})^2`.