import numpy as np
[docs]def LR_W(bp, por, ap, sp, wp, clay):
"""
Calculate the soil bulk real relative dielectric permittivity using the Lichtenecker and Rother model modified by Wunderlich and return
This function computes the volumetric water content of a soil
mixture using the volumetric mixing model of Lichtenecker and Rother [1], and Wunderlich [2] alpha correction model (LR_W).
The model incorporates the bulk dielectric permittivity, bulk and particle densities, and
permittivities of air, solid, and water, as well as the soil clay content.
Parameters
----------
bp : array_like
Soil bulk real relative dielectric permittivity [-]
por: array_like
Soil porosity [m**3/m**3].
ap : array_like
Soil air real relative dielectric permittivity phase [-].
sp : array_like
Soil solid real relative dielectric permittivity phase [-].
wp : array_like
Soil water phase real dielectric permittivity [-].
clay : array_like
Soil clay content [g/g]*100
Returns
-------
array_like
Soil volumetric water content [m**3/m**3].
References
----------
.. [1] Lichtenecker, K., and K. Rother. 1931.
Die Herleitung des logarithmischen Mischungsgesetzes aus allgemeinen Prinzipien der staionären Strömung.
Phys. Z. 32:255-260.
.. [2] Tina Wunderlich, Hauke Petersen, Said Attia al Hagrey, Wolfgang Rabbel;
Pedophysical Models for Resistivity and Permittivity of Partially Water-Saturated Soils.
Vadose Zone Journal 2013;; 12 (4): vzj2013.01.0023. doi: https://doi.org/10.2136/vzj2013.01.0023
Example
-------
>>> LR_W(10, 1.3, 2.65, 1, 4, 80, 20)
0.177
"""
alpha = -0.46*(clay/100)+0.71
water = (bp**alpha - (1-por)*sp**alpha - por*ap**alpha) / (wp**alpha - ap**alpha)
return water
[docs]def LR(bp, por, ap, sp, wp, alpha):
"""
Calculate the soil volumetric water content using the Lichtenecker and Rother model.
This function computes the volumetric water content of a soil
mixture using the volumetric mixing model of Lichtenecker and Rother [1] (LR).
The model incorporates the bulk dielectric permittivity, bulk and particle densities, and
permittivities of air, solid, and water.
Parameters
----------
bp : array_like
Soil bulk real relative dielectric permittivity [-]
por: array_like
Soil porosity [m**3/m**3].
ap : array_like
Soil air real relative dielectric permittivity phase [-].
sp : array_like
Soil solid real relative dielectric permittivity phase [-].
wp : array_like
Soil water phase real dielectric permittivity [-].
alpha : float
Soil alpha exponent as defined in volumetric mixing theory [-].
Returns
-------
array_like
Soil volumetric water content [m**3/m**3].
References
----------
.. [1] Lichtenecker, K., and K. Rother. 1931.
Die Herleitung des logarithmischen Mischungsgesetzes aus allgemeinen Prinzipien der staionären Strömung.
Phys. Z. 32:255-260.
Example
-------
>>> LR(10, 1.3, 2.65, 1, 4, 80, 0.5)
0.210
"""
if not isinstance(alpha, np.floating):
alpha = alpha[0]
if np.isnan(alpha):
alpha = 0.5
water = (bp**alpha - (1-por)*sp**alpha - por*ap**alpha) / (wp**alpha - ap**alpha)
return water
[docs]def LR_MV(bp, por, ap, sp, wp, CEC):
"""
Calculate the soil volumetric water content using the Lichtenecker and Rother model modified by Mendoza-Veirana and return
This function computes the volumetric water content of a soil
mixture using the volumetric mixing model of Lichtenecker and Rother [1], and Mendoza Veirana [2] alpha correction model (LR_MV).
The model incorporates the bulk dielectric permittivity, bulk and particle densities, and
permittivities of air, solid, and water, as well as the soil cation exchange capacity. Reported R2 = 0.94
Parameters
----------
bp : array_like
Soil bulk real relative dielectric permittivity [-]
por: array_like
Soil porosity [m**3/m**3].
ap : array_like
Soil air real relative dielectric permittivity phase [-].
sp : array_like
Soil solid real relative dielectric permittivity phase [-].
wp : array_like
Soil water phase real dielectric permittivity [-].
CEC : array_like
Soil cation exchange capacity [meq/100g].
Returns
-------
array_like
Soil volumetric water content [m**3/m**3].
References
----------
.. [1] Lichtenecker, K., and K. Rother. 1931.
Die Herleitung des logarithmischen Mischungsgesetzes aus allgemeinen Prinzipien der staionären Strömung.
Phys. Z. 32:255-260.
.. [2] Gaston Mendoza Veirana, Jeroen Verhegge, Wim Cornelis, Philippe De Smedt,
Soil dielectric permittivity modelling for 50-MHz instrumentation,
Geoderma, Volume 438, 2023, 116624, ISSN 0016-7061,
https://doi.org/10.1016/j.geoderma.2023.116624.
Example
-------
>>> LR_MV(10, 1.3, 2.65, 1, 4, 80, 20)
0.078
"""
alpha = 0.248*np.log(CEC) + 0.366
water = (bp**alpha - (1-por)*sp**alpha - por*ap**alpha) / (wp**alpha - ap**alpha)
return water