from __future__ import annotations
import numpy as np
from sasktran2.optical import pressure_temperature_to_numberdensity
from sasktran2.units import celsius_to_kelvin
def _o2_refrac_bates(wavelengths_um: np.array) -> np.array:
"""
Calculates the O2 refractive index using the parameterization suggested by Bates.
Parameters
----------
wavelengths_nm : np.array
Wavelengths in [nm]
Returns
-------
np.array
O2 Refractive index, (n-1) * 10**8
"""
coeff_ranges = [
{"coeff": [23796.7, 168988.4], "range": [0, 0.221]},
{"coeff": [22120.4, 203187.6], "range": [0.221, 0.288]},
{"coeff": [20564.8, 248089.9], "range": [0.288, 0.546]},
{"coeff": [21351.1, 218567.0], "range": [0.546, np.inf]},
]
result = np.zeros_like(wavelengths_um)
for ele in coeff_ranges:
good = (wavelengths_um > ele["range"][0]) & (wavelengths_um <= ele["range"][1])
result[good] = ele["coeff"][0] + ele["coeff"][1] / (
40.9 - wavelengths_um[good] ** (-2)
)
return result
def _n2_refrac_bates(wavelengths_um: np.array) -> np.array:
"""
Calculates the N2 refractive index using the parameterization suggested by Bates.
Parameters
----------
wavelengths_nm : np.array
Wavelengths in [nm]
Returns
-------
np.array
N2 Refractive index, (n-1) * 10**8
"""
coeff_ranges = [
{"coeff": [6998.749, 3233582.0], "range": [0, 0.254]},
{"coeff": [5989.242, 3363266.3], "range": [0.254, 0.468]},
{"coeff": [6855.200, 3243157.0], "range": [0.468, np.inf]},
]
result = np.zeros_like(wavelengths_um)
for ele in coeff_ranges:
good = (wavelengths_um > ele["range"][0]) & (wavelengths_um <= ele["range"][1])
delta_lambda = 0.468 - wavelengths_um[good]
result[good] = (
ele["coeff"][0]
+ ele["coeff"][1] / (144 - wavelengths_um[good] ** (-2))
+ 2.27684009 * np.sign(delta_lambda) * np.exp(-np.abs(delta_lambda) / 0.003)
)
return result
def _ar_refrac_bates(wavelengths_um: np.array) -> np.array:
"""
Calculates the Ar refractive index using the parameterization suggested by Bates.
Parameters
----------
wavelengths_nm : np.array
Wavelengths in [nm]
Returns
-------
np.array
Ar Refractive index, (n-1) * 10**8
"""
nsq_m_1 = 5.547e-4 * (
1 + 5.15e-3 * wavelengths_um ** (-2) + 4.19e-5 * wavelengths_um ** (-4)
)
return (np.sqrt(nsq_m_1 + 1) - 1) * 1e8
def _co2_refrac_bates(wavelengths_um: np.array) -> np.array:
"""
Calculates the CO2 refractive index using the parameterization suggested by Bates.
Parameters
----------
wavelengths_nm : np.array
Wavelengths in [nm]
Returns
-------
np.array
CO2 Refractive index, (n-1) * 10**8
"""
return (
22822.1
+ 117.8 * wavelengths_um ** (-2)
+ 2406030 / (130 - wavelengths_um ** (-2))
+ 15997 / (38.9 - wavelengths_um ** (-2))
)
def _o2_king_bates(wavelengths_um: np.array) -> np.array:
"""
Calculates the O2 King factor using the parameterization suggested by Bates.
Parameters
----------
wavelengths_nm : np.array
Wavelengths in [nm]
Returns
-------
np.array
O2 King factor
"""
return 1.096 + 1.385e-3 * wavelengths_um ** (-2) + 1.448e-4 * wavelengths_um ** (-4)
def _n2_king_bates(wavelengths_um: np.array) -> np.array:
"""
Calculates the N2 King factor using the parameterization suggested by Bates.
Parameters
----------
wavelengths_nm : np.array
Wavelengths in [nm]
Returns
-------
np.array
N2 King factor
"""
return 1.034 + 3.17e-4 * wavelengths_um ** (-2)
def _ar_king_bates(wavelengths_um: np.array) -> np.array:
"""
Calculates the Ar King factor using the parameterization suggested by Bates.
Parameters
----------
wavelengths_nm : np.array
Wavelengths in [nm]
Returns
-------
np.array
Ar King factor
"""
return np.ones_like(wavelengths_um)
def _co2_king_bates(wavelengths_um: np.array) -> np.array:
"""
Calculates the CO2 King factor using the parameterization suggested by Bates.
Parameters
----------
wavelengths_nm : np.array
Wavelengths in [nm]
Returns
-------
np.array
CO2 King factor
"""
return np.ones_like(wavelengths_um) * 1.15
[docs]
def rayleigh_cross_section_bates(
wavelengths_um: np.array,
n2_percentage: float = 78.084,
o2_percentage: float = 20.946,
ar_percentage: float = 0.934,
co2_percentage: float = 0.036,
) -> np.array:
"""
Calculates the Rayleigh scattering cross section in units of [m**2] for a given refractive index according to the Bates
approximation. Cross section is returned back at (0C, 1013.25 hPa)
Parameters
----------
wavelengths_um : np.array
Wavelengths in [um]
n2_percentage : float, Optional
Percentage of N2, default 78.084%
o2_percentage : float, Optional
Percentage of O2, default 20.946%
ar_percentage : float, Optional
Percentage of Ar, default 0.934%
co2_percentage : float, Optional
Percentaage of CO2, default 0.036%
Returns
-------
np.array
The rayleigh scattering cross section in units [m**2]
np.array
The effective King factor [unitless]
"""
lorenz_factors = (
o2_percentage
/ 100
* _o2_refrac_bates(wavelengths_um) ** 2
* _o2_king_bates(wavelengths_um)
+ n2_percentage
/ 100
* _n2_refrac_bates(wavelengths_um) ** 2
* _n2_king_bates(wavelengths_um)
+ ar_percentage
/ 100
* _ar_refrac_bates(wavelengths_um) ** 2
* _ar_king_bates(wavelengths_um)
+ co2_percentage
/ 100
* _co2_refrac_bates(wavelengths_um) ** 2
* _co2_king_bates(wavelengths_um)
)
eff_king = (
o2_percentage / 100 * _o2_king_bates(wavelengths_um)
+ n2_percentage / 100 * _n2_king_bates(wavelengths_um)
+ ar_percentage / 100 * _ar_king_bates(wavelengths_um)
+ co2_percentage / 100 * _co2_king_bates(wavelengths_um)
)
num_dens = pressure_temperature_to_numberdensity(
1013.25 * 100, celsius_to_kelvin(0)
)
return (
32 * np.pi**3 / (3 * num_dens**2 * wavelengths_um**4) * (lorenz_factors) * 1e8,
eff_king,
)
