def impure_ice_permittivity_maetzler06(frequency, temperature, salinity):
""" Computes permittivity of impure ice from Maetzler 2006 - Thermal Microwave Radiation: Applications for Remote Sensing.
Model developed for salinity around 0.013 PSU. The extrapolation is based on linear assumption to salinity, so it is not recommended for much higher salinity.
:param temperature: ice temperature in K
:param salinity: salinity of ice in kg/kg (see PSU constant in smrt module)
**Usage example**::
from smrt.permittivity.saline_ice import impure_ice_permittivity_maetzler06
eps_ice = impure_ice_permittivity_maetzler06(frequency=18e9, temperature=270, salinity=0.013)
"""
# Issue warning if salinity > 0.013 PSU
if salinity > 0.013e-3:
warnings.warn(
"This permittivity model was developed for saline impurities of around 0.013 10^-3 kg/kg (or 0.013 PSU)")
# Modify imaginary component calculated for pure ice
pure_ice_permittivity = ice_permittivity_maetzler06(frequency, temperature)
# Equation 5.37 from Maetzler 2006: Thermal Microwave Radiation: Applications for Remote Sensing
freqGHz = frequency / GHz
g0 = 1866 * np.exp(-0.317 * freqGHz)
g1 = 72.2 + 6.02 * freqGHz
# Equation 5.36
delta_Eimag = 1. / (g0 + g1 * (FREEZING_POINT - temperature))
# Equation 5.38
S0 = 0.013 # CURRENT UNITS ARE PSU
# print (pure_ice_permittivity, delta_Eimag * salinity * 1e3 / S0)
# print (pure_ice_permittivity + 1j * delta_Eimag * salinity * 1e3 / S0)
return pure_ice_permittivity + 1j * delta_Eimag * salinity * 1e3 / S0
def test_impure_ice_freezing_point_0p013psu_10GHz():
delta_epsimag = 1. / (1866 * np.exp(-3.17))
test_eps = ice_permittivity_maetzler06(10e9, FREEZING_POINT) + delta_epsimag
impure = impure_ice_permittivity_maetzler06(10e9, FREEZING_POINT, 0.013*PSU)
def test_saline_permittivity_same_as_pure_for_zero_salinity():
pure = ice_permittivity_maetzler06(18e9, 265)
impure = saline_ice_permittivity_pvs_mixing(18e9,265,0)
assert abs(pure.real - impure.real) < 1e-4
assert abs(pure.imag- impure.imag) < 1e-7
def test_real_ice_permittivity_output_maetzler87_temp_268():
eps87 = ice_permittivity_maetzler87(10e9, 268.15)
eps06 = ice_permittivity_maetzler06(10e9, 268.15)
assert eps87.real == eps06.real
def test_imaginary_ice_permittivity_output_matzler_temp_250_freq_40GHz():
eps = ice_permittivity_maetzler06(40e9, 250)
np.testing.assert_allclose(eps.imag, 0.0023952, atol=1e-4)
def test_imaginary_ice_permittivity_output_matzler_temp_270_freq_30GHz():
eps = ice_permittivity_maetzler06(30e9, 270)
np.testing.assert_allclose(eps.imag, 0.0025971, atol=1e-4)
def test_ice_permittivity_output_matzler_temp_250():
eps = ice_permittivity_maetzler06(10e9, 250)
print(eps)
np.testing.assert_allclose(eps.real, 3.1675, atol=1e-3)
np.testing.assert_allclose(eps.imag, 6.0571e-4, atol=1e-4)
def test_ice_permittivity_output_matzler_temp_270():
eps = ice_permittivity_maetzler06(10e9, 270)
print(eps)
np.testing.assert_allclose(eps.real, 3.18567, atol=1e-3)
np.testing.assert_allclose(eps.imag, 9.093e-04, atol=1e-4)