def nitrocon(z):
"""
Function for calculating the number concentration of
Nitrogen at a given altitude
Inputs:
z = altitude [m]
Outputs:
n_N2 = number concentration of Nitrogen [#/m^3]
"""
import numpy as np
import lidar_tools_v1 as ltools
#calculate temperature and pressure profiles using US Standard atmosphere
[T,P,d] = ltools.std_atm(z)
#determine backscatter and extinction coefficients as per Rayleigh scattering
#equations and constats from Kovalev pp 33-36
T_s = 288.15 #[K] reference temperature
P_s = 101325.0 #[Pa] reference pressure
N_s = 2.547e25 #[1/m^3] reference number concentration
gamma = 0.0279 #[unitless] depolarization factor (from Kovalev pg.35)
#convert air mass density to number density
N_a = 6.02214e23 #Avogadro's number [#/mol]
M_air = 0.028964 #molar density of air [kg/mol]
n_t = N_a*d/M_air
#assuming ideal gas, volume fraction of Nitrogen is mole fraction
c_N2 = 0.78084
n_N2 = n_t*c_N2
return n_N2
def nitrocon(z):
"""
Function for calculating the number concentration of
Nitrogen at a given altitude
Inputs:
z = altitude [m]
Outputs:
n_N2 = number concentration of Nitrogen [#/m^3]
"""
import numpy as np
import lidar_tools_v1 as ltools
#calculate temperature and pressure profiles using US Standard atmosphere
[T, P, d] = ltools.std_atm(z)
#determine backscatter and extinction coefficients as per Rayleigh scattering
#equations and constats from Kovalev pp 33-36
T_s = 288.15 #[K] reference temperature
P_s = 101325.0 #[Pa] reference pressure
N_s = 2.547e25 #[1/m^3] reference number concentration
gamma = 0.0279 #[unitless] depolarization factor (from Kovalev pg.35)
#convert air mass density to number density
N_a = 6.02214e23 #Avogadro's number [#/mol]
M_air = 0.028964 #molar density of air [kg/mol]
n_t = N_a * d / M_air
#assuming ideal gas, volume fraction of Nitrogen is mole fraction
c_N2 = 0.78084
n_N2 = n_t * c_N2
return n_N2
def raman_molecular(z, wave_0, wave_r):
"""
Function for generating molecular extinction coefficients at original and
Raman shifted wavelengths. Ozone absorption is ignored.
Inputs:
z = altitude [m]
wave_0 = original wavelength [nm]
wave_r = Raman-shifted wavelength [nm]
Outputs:
alpha_0 = extinction coefficient at original [1/m]
alpha_r = extinction at Raman
"""
import numpy as np
import lidar_tools_v1 as ltools
beta = np.empty_like(z)
alpha = np.empty_like(z)
#calculate temperature and pressure profiles using US Standard atmosphere
[T, P, d] = ltools.std_atm(z)
#determine backscatter and extinction coefficients as per Rayleigh scattering
#equations and constats from Kovalev pp 33-36
T_s = 288.15 #[K] reference temperature
P_s = 101325.0 #[Pa] reference pressure
N_s = 2.547e25 #[1/m^3] reference number concentration
gamma = 0.0279 #[unitless] depolarization factor (from Kovalev pg.35)
#calculate reference index of refraction using a polynomial approximation
nu_0 = 1000 / wave_0 #frequency in 1/um
m_s0 = 1 + 1e-8 * (8342.13 + (2406030 / (130 - nu_0**2)) +
(15997 / (38.9 - nu_0**2)))
#now calculate index of refraction at altitude as function of temperature and pressure
m_0 = 1 + (m_s0 - 1) * ((1 + 0.00367 * T_s) /
(1 + 0.00367 * T)) * (P / P_s)
#convert air mass density to number density
N_a = 6.02214e23 #Avogadro's number [#/mol]
M_air = 0.028964 #molar density of air [kg/mol]
N = N_a * d / M_air
#without absorption, extinction is equal to total scattering
alpha_0 = (8*np.pi**3*(m_0**2-1)**2*N/(3*N_s**2*(wave_0*1e-9)**4))*((6+3*gamma)/(6-7*gamma))* \
(P/P_s)*(T_s/T)
#repeat above steps for Raman shifted wavelength
nu_r = 1000 / wave_r #frequency in 1/um
m_sr = 1 + 1e-8 * (8342.13 + (2406030 / (130 - nu_r**2)) +
(15997 / (38.9 - nu_r**2)))
#now calculate index of refraction at altitude as function of temperature and pressure
m_r = 1 + (m_sr - 1) * ((1 + 0.00367 * T_s) /
(1 + 0.00367 * T)) * (P / P_s)
#without absorption, extinction is equal to total scattering
alpha_r = (8*np.pi**3*(m_r**2-1)**2*N/(3*N_s**2*(wave_r*1e-9)**4))*((6+3*gamma)/(6-7*gamma))* \
(P/P_s)*(T_s/T)
return T, P, d, alpha_0, alpha_r
def raman_molecular(z,wave_0,wave_r):
"""
Function for generating molecular extinction coefficients at original and
Raman shifted wavelengths. Ozone absorption is ignored.
Inputs:
z = altitude [m]
wave_0 = original wavelength [nm]
wave_r = Raman-shifted wavelength [nm]
Outputs:
alpha_0 = extinction coefficient at original [1/m]
alpha_r = extinction at Raman
"""
import numpy as np
import lidar_tools_v1 as ltools
beta = np.empty_like(z)
alpha = np.empty_like(z)
#calculate temperature and pressure profiles using US Standard atmosphere
[T,P,d] = ltools.std_atm(z)
#determine backscatter and extinction coefficients as per Rayleigh scattering
#equations and constats from Kovalev pp 33-36
T_s = 288.15 #[K] reference temperature
P_s = 101325.0 #[Pa] reference pressure
N_s = 2.547e25 #[1/m^3] reference number concentration
gamma = 0.0279 #[unitless] depolarization factor (from Kovalev pg.35)
#calculate reference index of refraction using a polynomial approximation
nu_0 = 1000/wave_0 #frequency in 1/um
m_s0 = 1 + 1e-8*(8342.13+(2406030/(130-nu_0**2))+(15997/(38.9-nu_0**2)))
#now calculate index of refraction at altitude as function of temperature and pressure
m_0 = 1+(m_s0-1)*((1+0.00367*T_s)/(1+0.00367*T))*(P/P_s)
#convert air mass density to number density
N_a = 6.02214e23 #Avogadro's number [#/mol]
M_air = 0.028964 #molar density of air [kg/mol]
N = N_a*d/M_air
#without absorption, extinction is equal to total scattering
alpha_0 = (8*np.pi**3*(m_0**2-1)**2*N/(3*N_s**2*(wave_0*1e-9)**4))*((6+3*gamma)/(6-7*gamma))* \
(P/P_s)*(T_s/T)
#repeat above steps for Raman shifted wavelength
nu_r = 1000/wave_r #frequency in 1/um
m_sr = 1 + 1e-8*(8342.13+(2406030/(130-nu_r**2))+(15997/(38.9-nu_r**2)))
#now calculate index of refraction at altitude as function of temperature and pressure
m_r = 1+(m_sr-1)*((1+0.00367*T_s)/(1+0.00367*T))*(P/P_s)
#without absorption, extinction is equal to total scattering
alpha_r = (8*np.pi**3*(m_r**2-1)**2*N/(3*N_s**2*(wave_r*1e-9)**4))*((6+3*gamma)/(6-7*gamma))* \
(P/P_s)*(T_s/T)
return T,P,d,alpha_0,alpha_r
