def test_integrate_column(self):
"""Test numerical intergration of array elements.
As no coordinates are given, the function is expected to integrate
along the indices.
"""
t = math.integrate_column(np.arange(5))
assert (np.isclose(t, 8))
def integrate_water_vapor(vmr, p, T=None, z=None, axis=0):
r"""Calculate the integrated water vapor (IWV).
The basic implementation of the function assumes the atmosphere
to be in hydrostatic equilibrium. The IWV is calculated as follows:
.. math::
\mathrm{IWV} = -\frac{1}{g} \int q(p)\,\mathrm{d}p
For non-hydrostatic atmospheres, additional information
on temperature and height are needed:
.. math::
\mathrm{IWV} = \int \rho_v(z)\,\mathrm{d}z
Parameters:
vmr (float or ndarray): Volume mixing ratio,
p (float or ndarray): Pressue [Pa].
T (float or ndarray): Temperature [K] (see ``z``).
z (float or ndarray): Height [m]. For non-hydrostatic calculation
both ``T`` and ``z`` have to be passed.
axis (int): Axis to integrate along.
Returns:
float: Integrated water vapor [kg/m**2].
"""
if T is None and z is None:
# Calculate IWV assuming hydrostatic equilibrium.
q = thermodynamics.vmr2specific_humidity(vmr)
g = constants.earth_standard_gravity
return -math.integrate_column(q, p, axis=axis) / g
elif T is None or z is None:
raise ValueError(
'Pass both `T` and `z` for non-hydrostatic calculation of the IWV.'
)
else:
# Integrate the water vapor mass density for non-hydrostatic cases.
R_v = constants.gas_constant_water_vapor
rho = thermodynamics.density(p, T, R=R_v) # Water vapor density.
return math.integrate_column(vmr * rho, z, axis=axis)
def integrate_water_vapor(vmr, p, T, z, axis=0):
"""Calculate the integrated water vapor (IWV).
Parameters:
vmr (float or ndarray): Volume mixing ratio,
p (float or ndarray): Pressue [Pa].
T (float or ndarray): Temperature [K].
z (ndarray): Height [m]. Size must match vmr.
axis (int): Axis to intergrate along.
Returns:
float: Integrated water vapor [kg/m**2].
"""
R_v = constants.gas_constant_water_vapor
rho = thermodynamics.density(p, T, R=R_v) # Water vapor density.
return math.integrate_column(vmr * rho, z, axis=axis)
def test_integrate_column_coordinates(self):
"""Test numerical intergration of array elements along coordinates."""
x = np.linspace(0, 1, 5)
t = math.integrate_column(np.arange(5), x)
assert (np.isclose(t, 2))