26
H. Rott
where fs is the surface emissivity, Ts is the surface temperature, and Tc is
the brightness temperature of the cosmic background (2.7 K). Whereas the
infrared emissivity of most natural materials is 0.9 ~ fIR < 1.0, fs in the
microwave region is much more variable, as explained in Sect. 2.4. Because of
the linear temperature-radiance relationship (Eq. 2.4), t.he radiative transfer
calculations can be carried out in terms ofTB. The upward T1 and downward
T~ radiating brightness temperatures of the atmosphe~e can be calculated
from the atmospheric temperature profile and the vertical derivative of the
transmissivity in analogy to Eq. 2.20. Thus
T1 = t=oo T(z) at(z, 00) dz
Jz=o
az
(2.22)
Atmospheric emission and scattering at frequencies between 18 and 40 GHz
and in the 80-100 GHz window are the basis for estimating precipitation rates
from satellite radiometric measurements.
2.4 Reflection and Emission Characteristics of Natural
Media
When an electromagnetic wave hits the interface between two media with
different dielectric properties, it is partly reflected back into medium 1 and
partly refracted and proceeding into medium 2. The penetrating component
may be partly or completely absorbed and scattered. Part of the scattered
radiation passes back through the interface into medium 1. The reflection
coefficients depend on the polarization of the incident wave, which means
that the polarization state of a reflected wave is changed.
The percentages of reflection and penetration at a given incidence angle
can be calculated from the dielectric properties of the two media using the
Fresnel equations (Schanda, 1986). For a homogeneous lossy material the
dielectric properties can be described by the complex dielectric constant
(2.23)
The real part, c~, corresponds to the dielectric constant for a loss less medium,
the imaginary part, c;, accounts for the losses. Here the dielectric constant,
Cn refers to the permittivity relative to vacuum. In the optical region the
refractive index, n, is commonly used, the two parameters are related by
n=..ft;.
Reflectivity in the Visible and Infrared. In the visible and infrared the
penetration into solid materials is in most cases limited to a very thin layer
at the surface. Among the exceptions are snow with a typical penetration of
several centimeters and ice with penetration of several meters in the visible.
H. Rott
where fs is the surface emissivity, Ts is the surface temperature, and Tc is
the brightness temperature of the cosmic background (2.7 K). Whereas the
infrared emissivity of most natural materials is 0.9 ~ fIR < 1.0, fs in the
microwave region is much more variable, as explained in Sect. 2.4. Because of
the linear temperature-radiance relationship (Eq. 2.4), t.he radiative transfer
calculations can be carried out in terms ofTB. The upward T1 and downward
T~ radiating brightness temperatures of the atmosphe~e can be calculated
from the atmospheric temperature profile and the vertical derivative of the
transmissivity in analogy to Eq. 2.20. Thus
T1 = t=oo T(z) at(z, 00) dz
Jz=o
az
(2.22)
Atmospheric emission and scattering at frequencies between 18 and 40 GHz
and in the 80-100 GHz window are the basis for estimating precipitation rates
from satellite radiometric measurements.
2.4 Reflection and Emission Characteristics of Natural
Media
When an electromagnetic wave hits the interface between two media with
different dielectric properties, it is partly reflected back into medium 1 and
partly refracted and proceeding into medium 2. The penetrating component
may be partly or completely absorbed and scattered. Part of the scattered
radiation passes back through the interface into medium 1. The reflection
coefficients depend on the polarization of the incident wave, which means
that the polarization state of a reflected wave is changed.
The percentages of reflection and penetration at a given incidence angle
can be calculated from the dielectric properties of the two media using the
Fresnel equations (Schanda, 1986). For a homogeneous lossy material the
dielectric properties can be described by the complex dielectric constant
(2.23)
The real part, c~, corresponds to the dielectric constant for a loss less medium,
the imaginary part, c;, accounts for the losses. Here the dielectric constant,
Cn refers to the permittivity relative to vacuum. In the optical region the
refractive index, n, is commonly used, the two parameters are related by
n=..ft;.
Reflectivity in the Visible and Infrared. In the visible and infrared the
penetration into solid materials is in most cases limited to a very thin layer
at the surface. Among the exceptions are snow with a typical penetration of
several centimeters and ice with penetration of several meters in the visible.