4.11.1.6. refractiveIndex.water

refractive.ice module.

Copyright (C) 2017 - 2018 Davide Ori dori@uni-koeln.de Institute for Geophysics and Meteorology - University of Cologne

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

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This module provides a list of water refractive index models to compute the dielectric properties of water according to the requested frequency and temeperatures. The module can be also used as a standalone python script.

Example

The python script is callable as

$ python water.py temperature frequency

and returns the complex refractive index of water at the requested Temperature [Kelvin] and Frequency [Hz]

Notes

It is possible to call the functions implemented in this module using nd-arrays. The function arguments must either have exactly the same shape allowing element-wise application of the functions or one of the two must be a scalar which will be spread across the nd computations

Temperature should be provided in Kelvin and frequency in Hz The specific called algorithm check for arguments values to be within the limits of validity of the dielectric model and raises ValueError in case they are not respected

4.11.1.6.1. Module Contents

4.11.1.6.1.1. Functions

turner_kneifel_cadeddu(temperature, frequency)	The "Turner-Kneifel-Cadeddu" liquid water absorption model (JTECH 2016).
ellison(temperature, frequency)	Water complex relative dielectric constant according to Ellison (2005)
pamtra_water(temperature, frequency)
eps(temperature, frequency, model='Ellison')	Water complex relative dielectric constant according to the requested model
n(temperature, frequency, model='Ellison')	Water complex refractive index according to the requested model

turner_kneifel_cadeddu(temperature, frequency)

The “Turner-Kneifel-Cadeddu” liquid water absorption model (JTECH 2016).

SPECIAL MODEL FOR SUPERCOOLED LIQUID WATER

It was built using both laboratory observations (primarily at warm temperature) and field data observed by MWRs at multiple frequency at supercool temperature. The field data were published in Kneifel et al. JAMC 2014. The strength of the TKC model is the use of an optimal estimation framework to determine the empirical coefficients of the double-Debye model. A full description of this model is given in

Turner, D.D., S. Kneifel, and M.P. Cadeddu, 2016: An improved liquid water absorption model in the microwave for supercooled liquid clouds. J. Atmos. Oceanic Technol., 33(1), pp.33-44, doi:10.1175/JTECH-D-15-0074.1.

Note that the model is designed to operate over the frequency range from 0.5 to 500

GHz, and temperature from -40 degC to +50 degC; only for freshwater (no salinity)

Parameters

• temperature (array_like) – nd array of temperature [Kelvin]

• frequency (array_like) – nd array of frequency [Hz]

Returns

Relative dielectric constant of ice at the requested frequency and temperature

Return type

nd - complex

Raises

• ValueError – If a negative frequency or temperature is passed as an argument

• ValueError – If frequency or temperature out of the limits of validity of the model is passed as an argument

ellison(temperature, frequency)

Water complex relative dielectric constant according to Ellison (2005) “…” TODO: put the extensive correct reference here

Parameters

• temperature (array_like) – nd array of temperature [Kelvin]

• frequency (array_like) – nd array of frequency [Hz]

Returns

Relative dielectric constant of ice at the requested frequency and temperature

Return type

nd - complex

Raises

• ValueError – If a negative frequency or temperature is passed as an argument

• ValueError – If frequency or temperature out of the limits of validity of the model is passed as an argument

pamtra_water(temperature, frequency)

eps(temperature, frequency, model='Ellison')

Water complex relative dielectric constant according to the requested model

Parameters

• temperature (array_like) – nd array of temperature [Kelvin]

• frequency (array_like) – nd array of frequency [Hz]

• model (string) – dielectric model name default to Ellison (2005)

Returns

Relative dielectric constant of water for the requested frequency and temperature

Return type

nd - complex

Raises

ValueError – If a negative frequency or temperature is passed as an argument

n(temperature, frequency, model='Ellison')

Water complex refractive index according to the requested model

Parameters

• temperature (array_like) – nd array of temperature [Kelvin]

• frequency (array_like) – nd array of frequency [Hz]

• model (string) – dielectric model name default to Ellison (2005)

Returns

Refractive index of water for the requested frequency and temperature

Return type

nd - complex

Raises

ValueError – If a negative frequency or temperature is passed as an argument