def log_interpolate_1d(x, xp, *args, **kwargs):
'''
Interpolation on a logarithmic x-scale for interpolation values in pressure coordintates.
Parameters
----------
x : array-like
1-D array of desired interpolated values.
xp : array-like
The x-coordinates of the data points.
args : array-like
The data to be interpolated. Can be multiple arguments, all must be the same shape as
xp.
axis : int, optional
The axis to interpolate over. Defaults to 0.
Returns
-------
array-like
Interpolated values for each point with coordinates sorted in ascending order.
'''
# Log x and xp
log_x = np.log(x)
log_xp = np.log(xp)
return interpolate_1d(log_x, log_xp, *args, **kwargs)
def equivalent_potential_temperature(pressure, temperature, dewpoint):
r"""Calculate equivalent potential temperature.
This calculation must be given an air parcel's pressure, temperature, and dewpoint.
The implementation uses the formula outlined in [Bolton1980]_:
First, the LCL temperature is calculated:
.. math:: T_{L}=\frac{1}{\frac{1}{T_{D}-56}+\frac{ln(T_{K}/T_{D})}{800}}+56
Which is then used to calculate the potential temperature at the LCL:
.. math:: \theta_{DL}=T_{K}\left(\frac{1000}{p-e}\right)^k
\left(\frac{T_{K}}{T_{L}}\right)^{.28r}
Both of these are used to calculate the final equivalent potential temperature:
.. math:: \theta_{E}=\theta_{DL}\exp\left[\left(\frac{3036.}{T_{L}}
-1.78\right)*r(1+.448r)\right]
Parameters
----------
pressure: `pint.Quantity`
Total atmospheric pressure
temperature: `pint.Quantity`
Temperature of parcel
dewpoint: `pint.Quantity`
Dewpoint of parcel
Returns
-------
`pint.Quantity`
The equivalent potential temperature of the parcel
Notes
-----
[Bolton1980]_ formula for Theta-e is used, since according to
[DaviesJones2009]_ it is the most accurate non-iterative formulation
available.
"""
t = temperature
td = dewpoint
p = pressure
e = saturation_vapor_pressure(dewpoint)
r = saturation_mixing_ratio(pressure, dewpoint)
t_l = 56 + 1. / (1. / (td - 56) + np.log(t / td) / 800.)
th_l = t * (1000 / (p - e)) ** constants.kappa * (t / t_l) ** (0.28 * r)
th_e = th_l * np.exp((3036. / t_l - 1.78) * r * (1 + 0.448 * r))
return th_e
def dewpoint(e):
r"""Calculate the ambient dewpoint given the vapor pressure.
Parameters
----------
e : `pint.Quantity`
Water vapor partial pressure
Returns
-------
`pint.Quantity`
Dew point temperature
See Also
--------
dewpoint_rh, saturation_vapor_pressure, vapor_pressure
Notes
-----
This function inverts the [Bolton1980]_ formula for saturation vapor
pressure to instead calculate the temperature. This yield the following
formula for dewpoint in degrees Celsius:
.. math:: T = \frac{243.5 log(e / 6.112)}{17.67 - log(e / 6.112)}
"""
val = np.log(e / constants.sat_pressure_0c)
return 243.5 * val / (17.67 - val)
