def _(temperature):
if temperature > constants.triple_point_water:
return typ.e_eq_water_mk(temperature)
elif temperature < (constants.triple_point_water - 23.0):
return typ.e_eq_ice_mk(temperature)
else:
e_eq_ice = typ.e_eq_ice_mk(temperature)
return (
e_eq_ice +
(typ.e_eq_water_mk(temperature) - typ.e_eq_ice_mk(temperature)) *
((temperature - constants.triple_point_water + 23) / 23)**2)
def test_e_eq_mixed_mk(self):
"""Test calculation of vapor pressure with respect to mixed phase."""
assert np.allclose(physics.e_eq_ice_mk(240),
physics.e_eq_mixed_mk(240))
assert np.allclose(physics.e_eq_water_mk(290),
physics.e_eq_mixed_mk(290))
assert (physics.e_eq_ice_mk(263)
< physics.e_eq_mixed_mk(263)
< physics.e_eq_water_mk(263))
def saturation_pressure(temperature):
r"""Return equilibrium pressure of water with respect to the mixed-phase.
The equilibrium pressure over water is taken for temperatures above the
triple point :math:`T_t` the value over ice is taken for temperatures
below :math:`T_t–23\,\mathrm{K}`. For intermediate temperatures the
equilibrium pressure is computed as a combination
of the values over water and ice according to the IFS documentation:
.. math::
e_\mathrm{s} = \begin{cases}
T > T_t, & e_\mathrm{liq} \\
T < T_t - 23\,\mathrm{K}, & e_\mathrm{ice} \\
else, & e_\mathrm{ice}
+ (e_\mathrm{liq} - e_\mathrm{ice})
\cdot \left(\frac{T - T_t - 23}{23}\right)^2
\end{cases}
References:
IFS Documentation – Cy45r1,
Operational implementation 5 June 2018,
Part IV: Physical Processes, Chapter 12, Eq. 12.13,
https://www.ecmwf.int/node/18714
Parameters:
temperature (float or ndarray): Temperature [K].
See also:
:func:`~typhon.physics.e_eq_ice_mk`
Equilibrium pressure of water over ice.
:func:`~typhon.physics.e_eq_water_mk`
Equilibrium pressure of water over liquid water.
Returns:
float or ndarray: Equilibrium pressure [Pa].
"""
# Keep track of input type to match the return type.
is_float_input = isinstance(temperature, Number)
if is_float_input:
# Convert float input to ndarray to allow indexing.
temperature = np.asarray([temperature])
e_eq_water = typ.e_eq_water_mk(temperature)
e_eq_ice = typ.e_eq_ice_mk(temperature)
is_water = temperature > constants.triple_point_water
is_ice = temperature < (constants.triple_point_water - 23.)
e_eq = (e_eq_ice + (e_eq_water - e_eq_ice) *
((temperature - constants.triple_point_water + 23) / 23)**2)
e_eq[is_ice] = e_eq_ice[is_ice]
e_eq[is_water] = e_eq_water[is_water]
return float(e_eq) if is_float_input else e_eq
def test_e_eq_ice_mk(self):
"""Test calculation of equilibrium water vapor pressure over ice."""
x = physics.e_eq_ice_mk(260)
assert np.allclose(x, 195.81934571953161)