RADAR Models

class pyrism.models.Rayleigh(frequency, particle_size, diel_constant_p, diel_constant_b=(1+1j))[source]

Bases: pyrism.core._core.Scattering

Calculate the extinction coefficients in terms of Rayleigh scattering ([UL15a] and [UL15b]).

Parameters:
  • frequency (int or float) – Frequency (GHz)
  • particle_size (int, float or array) – Particle size a [m].
  • diel_constant_p (complex) – Dielectric constant of the medium.
  • diel_constant_b (complex) – Dielectric constant of the background.
Returns:

  • All returns are attributes!
  • self.ke (int, float or array_like) – Extinction coefficient.
  • self.ks (int, float or array_like) – Scattering coefficient.
  • self.ka (int, float or array_like) – Absorption coefficient.
  • self.om (int, float or array_like) – Omega.
  • self.s0 (int, float or array_like) – Backscatter coefficient sigma 0.

class pyrism.models.Mie(frequency, particle_size, diel_constant_p, diel_constant_b=(1+1j))[source]

Bases: pyrism.core._core.Scattering

Calculate the extinction coefficients in terms of Mie scattering ([UL15a] and [UL15b]).

Parameters:
  • frequency (int or float) – Frequency (GHz)
  • particle_size (int, float or array) – Particle size a [m].
  • diel_constant_p (complex) – Dielectric constant of the medium.
  • diel_constant_b (complex) – Dielectric constant of the background.
Returns:

  • All returns are attributes!
  • self.ke (int, float or array_like) – Extinction coefficient.
  • self.ks (int, float or array_like) – Scattering coefficient.
  • self.ka (int, float or array_like) – Absorption coefficient.
  • self.om (int, float or array_like) – Omega.
  • self.s0 (int, float or array_like) – Backscatter coefficient sigma 0.

class pyrism.models.DielConstant[source]

Class to calculate the Dielectric Constant of different objects ([UL15a] and [UL15b]).

See also

DielConstant.pureWater, DielConstant.salineWater, DielConstant.soil, DielConstant.vegetation, DielConstant.combine

static combine(mg, temp, S, C, mv, rho_b=1.7)[source]

Combine the Relative Dielectric Constant of Vegetation with Soil. Computes the real and imaginary parts of the relative dielectric constant of vegetation material, such as corn leaves, in the microwave region.

Computes the real and imaginary parts of the relative dielectric constant of soil at a given temperature 0<t<40C, frequency, volumetric moisture content, soil bulk density, sand and clay fractions.

Parameters:
  • frequency (int, float or array_like) – Frequency (GHz).
  • mg (int or float) – Gravimetric moisture content (0<mg< 1).
  • temp (int, float or array) – Temperature in C° (0 - 30).
  • S (int or float) – Sand fraction in %.
  • C (int or float) – Clay fraction in %.
  • mv (int or float) – Volumetric Water Content (0<mv<1)
  • rho_b (int or float (default = 1.7)) – Bulk density in g/cm3 (typical value is 1.7 g/cm3).
static saline_water(temp, salinity)[source]

Relative Dielectric Constant of Saline Water. Computes the real and imaginary parts of the relative dielectric constant of water at any temperature 0<t<30, Salinity 0<Salinity<40 0/00, and frequency 0<f<1000GHz

Parameters:
  • frequency (int, float or array_like) – Frequency (GHz).
  • temp (int, float or array) – Temperature in C° (0 - 30).
  • salinity (int, float or array) – Salinity in parts per thousand.
Returns:

Dielectric Constant

Return type:

complex

static soil(temp, S, C, mv, rho_b=1.7)[source]

Relative Dielectric Constant of soil. Computes the real and imaginary parts of the relative dielectric constant of soil at a given temperature 0<t<40C, frequency, volumetric moisture content, soil bulk density, sand and clay fractions.

Parameters:
  • frequency (int, float or array_like) – Frequency (GHz).
  • temp (int, float or array) – Temperature in C° (0 - 30).
  • S (int or float) – Sand fraction in %.
  • C (int or float) – Clay fraction in %.
  • mv (int or float) – Volumetric Water Content (0<mv<1)
  • rho_b (int or float (default = 1.7)) – Bulk density in g/cm3 (typical value is 1.7 g/cm3).
Returns:

Dielectric Constant

Return type:

complex

static vegetation(mg)[source]

Relative Dielectric Constant of Vegetation. Computes the real and imaginary parts of the relative dielectric constant of vegetation material, such as corn leaves, in the microwave region.

Parameters:
  • frequency (int, float or array_like) – Frequency (GHz).
  • mg (int or float) – Gravimetric moisture content (0<mg< 1).
Returns:

Dielectric Constant

Return type:

complex

static water(temp)[source]

Relative Dielectric Constant of Pure Water. Computes the real and imaginary parts of the relative dielectric constant of water at any temperature 0<t<30 and frequency 0<f<1000 GHz. Uses the double-Debye model.

Parameters:
  • frequency (int, float or array_like) – Frequency (GHz).
  • temp (int, float or array) – Temperature in C° (0 - 30).
Returns:

Dielectric Constant

Return type:

complex

class pyrism.models.I2EM(iza, vza, raa, normalize=True, nbar=0.0, angle_unit='DEG', frequency=None, diel_constant=None, corrlength=None, sigma=None, n=10, corrfunc='exponential')[source]

Bases: pyrism.core._core.Kernel

RADAR Surface Scatter Based Kernel (I2EM). Compute BSC VV and BSC HH and the emissivity for single-scale random surface for Bi and Mono-static acquisitions ([UL15a] and [UL15b]).

Parameters:
  • vza, raa (iza,) – Incidence (iza) and scattering (vza) zenith angle, as well as relative azimuth (raa) angle.
  • normalize (boolean, optional) – Set to ‘True’ to make kernels 0 at nadir view illumination. Since all implemented kernels are normalized the default value is False.
  • nbar (float, optional) – The sun or incidence zenith angle at which the isotropic term is set to if normalize is True. The default value is 0.0.
  • angle_unit ({'DEG', 'RAD'}, optional) –
    • ‘DEG’: All input angles (iza, vza, raa) are in [DEG] (default).
    • ’RAD’: All input angles (iza, vza, raa) are in [RAD].
  • frequency (int or float) – RADAR Frequency (GHz).
  • diel_constant (int or float) – Complex dielectric constant of soil.
  • corrlength (int or float) – Correlation length (cm).
  • sigma (int or float) – RMS Height (cm)
  • n (int (default = 10), optinal) – Coefficient needed for x-power and x-exponential correlation function.
  • corrfunc ({'exponential', 'gaussian', 'xpower', 'mixed'}, optional) – Correlation distribution functions. The mixed correlation function is the result of the division of gaussian correlation function with exponential correlation function. Default is ‘exponential’.
Returns:

Return type:

For more attributes see also pyrism.core.Kernel and pyrism.core.ReflectanceResult.

Note

The model is constrained to realistic surfaces with (rms height / correlation length) ≤ 0.25. Hot spot direction is vza == iza and raa = 0.0

class Emissivity(iza, vza, raa, normalize=False, nbar=0.0, angle_unit='DEG', frequency=1.26, diel_constant=(10+1j), corrlength=10, sigma=0.3, corrfunc='exponential')[source]

Bases: pyrism.core._core.Kernel

This Class calculates the emission from rough surfaces using the I2EM Model.

Parameters:
  • vza, raa (iza,) – Incidence (iza) and scattering (vza) zenith angle, as well as relative azimuth (raa) angle.
  • normalize (boolean, optional) – Set to ‘True’ to make kernels 0 at nadir view illumination. Since all implemented kernels are normalized the default value is False.
  • nbar (float, optional) – The sun or incidence zenith angle at which the isotropic term is set to if normalize is True. The default value is 0.0.
  • angle_unit ({'DEG', 'RAD'}, optional) –
    • ‘DEG’: All input angles (iza, vza, raa) are in [DEG] (default).
    • ’RAD’: All input angles (iza, vza, raa) are in [RAD].
  • frequency (int or float) – RADAR Frequency (GHz).
  • diel_constant (int or float) – Complex dielectric constant of soil.
  • corrlength (int or float) – Correlation length (cm).
  • sigma (int or float) – RMS Height (cm)
  • corrfunc ({'exponential', 'gaussian', 'mixed'}, optional) – Correlation distribution functions. The mixed correlation function is the result of the division of gaussian correlation function with exponential correlation function. Default is ‘exponential’.
Returns:

Return type:

For attributes see also core.Kernel and core.EmissivityResult.

emsv_integralfunc(x, y)[source]

References

[Bar]Frederic Baret. The specific absorption coefficient corresponding to brown pigment. emmah, inra avignon.
[Cam86]G. S. Campbell. Extinction coefficients for radiation in plant canopies calculated using an ellipsoidal inclination angle distribution. Agricultural and Forest Meteorology, 36(4):317–321, 1986. doi:10.1016/0168-1923(86)90010-9.
[Cam90]G.S Campbell. Derivation of an angle density function for canopies with ellipsoidal leaf angle distributions. Agricultural and Forest Meteorology, 49(3):173–176, 1990. doi:10.1016/0168-1923(90)90030-A.
[FFranccoisA+08]Jean-Baptiste Feret, Christophe François, Gregory P. Asner, Anatoly A. Gitelson, Roberta E. Martin, Luc P.R. Bidel, Susan L. Ustin, Guerric Le Maire, and Stéphane Jacquemoud. Prospect-4 and 5: advances in the leaf optical properties model separating photosynthetic pigments. Remote Sensing of Environment, 112(6):3030–3043, 2008. doi:10.1016/j.rse.2008.02.012.
[GomezD18]José Gómez-Dans. Prosail implementation for python. 2018. URL: https://github.com/jgomezdans/prosail.
[JB90]S. Jacquemoud and F. Baret. Prospect: a model of leaf optical properties spectra. Remote Sensing of Environment, 34(2):75–91, 1990. doi:10.1016/0034-4257(90)90100-Z.
[NK89]Tiit Nilson and Andres Kuusk. A reflectance model for the homogeneous plant canopy and its inversion. Remote Sensing of Environment, 27(2):157–167, 1989. doi:10.1016/0034-4257(89)90015-1.
[UL15a](1, 2, 3, 4) Fawwaz T. Ulaby and David G. Long. Microwave Radar and Radiometric Remote Sensing. Artech House, Norwood, 2015. ISBN 978-0-472-11935-6. URL: http://gbv.eblib.com/patron/FullRecord.aspx?p=4537961.
[UL15b](1, 2, 3, 4) Fawwaz T. Ulaby and David G. Long. Microwave radar and radiometric remote sensing: remote sensing computer codes. 2015. URL: http://mrs.eecs.umich.edu/microwave_remote_sensing_computer_codes.html.
[VMB98]W. Verhoef, M. Molenaar, and N.J.J Bunnik. Theory of radiative transfer models applied in optical remote sensing of vegetation canopies. Landbouwuniversiteit Wageningen (LUW), Wageningen, 1998. ISBN 9054858044.