Retrieval of Precipitation from Satellites
251
11.3 Interaction between atmospheric hydrometeors
and radiation
The earth atmosphere is roughly a mixture of gases, aerosols, and hydrometeors, which differ by
size, shape, and substance. The naturally occuring interaction processes between atmospheric
constituents and electromagnetic radiation are absorption due to resonance effects caused by
changes of the electronic, vibrational, and rotational states of molecules and emission, absorption, and scattering caused by inhomogeneities of the complex refractive index m (or dielectric
constant E) of the atmosphere. For scattering to be efficient, these inhomogeneities must occur
in a spatial scale comparable to the wavelength. Thus, the non-dimensional Mie-parameter x,
defined as being proportional to the ratio between the spatial dimension of the inhomogeneity,
i.e. the radius of the particle 1', and the wavelength>. of the electromagnetic radiation
27fT
X = -
>.
(11.1)
serves as one measure of the importance and indicates the type of scattering effects (Fig.
11.2). At very low values of X scattering is negligible. With increasing X scattering becomes
increasingly important and can be described by Rayleigh scattering. Maximum scattering
effects are observed for X around 3 to 10 (i.e. particle size is in the range of the wavelength) and
for homogeneous spherical particles Mie-theory serves as an appropiate quantitative description.
Far more complicated treatment is necessary and is still not at hand, when the non-spherical
irregular particles are considered. For large X (particle size much larger than the wavelength)
scattering decreases again approaching the geometrical optics limit, which can be adequately
modelled by ray-tracing techniques.
It follows that scattering at molecules and aerosols is an important process in the solar spectral
range but at longer wavelengths scattering is mainly caused by atmospheric hydrometeors, namely cloud and rain particles. Cloud and rain particles, however, interact with electromagnetic
radiation of almost the whole spectrum significantly via scattering processes. This leads to
multiple scattering effects, which renders the relation between cloud and rain particles and radiances outside the cloud highly non-linear. This non-linear relation causes additional problems
when - typical for satellite measurements - retrieval must be performed on spatial averages
of radiances (beam-filling problem).
Beside the spatial dimensions of the inhomogeneities in the atmosphere caused by the hydrometeors, the value of the complex index of refraction m = m' + im" compared to its value for
the gaseous atmosphere must be considered. The larger the difference, the larger the scattering
effects will be. The value of the real part m' determines the scattering efficiency and the value of
the imaginary part mil is responsible for absorption within the hydrometeors. Due to multiple
scattering both effects cannot be estimated separately, because every scattering event can give
rise to another absorption event which increases the overall absorption within an ensemble of
hydrometeors.
For water and ice both parts of the refractive index are quite complicated and irregular functions
of wavelength and temperature. Some values for water are given in Tab. 11.1. The real part
of m starts at values around 1.3 in the visible range, goes through a minimum of about 1.1 in
the thermal window around 10 /lm, and increases towards the microwave frequencies to almost
10. The imaginary part starts at very low values in the visible, increases steeply to about 0.4
in the thermal infrared, then more slowly up to around 3 in the mid-microwaves from where
it decreases again. Except in the very long microwaves, where m decreases with temperature,
both parts of the refractive index increase somewhat with temperature. Values for ice are of
251
11.3 Interaction between atmospheric hydrometeors
and radiation
The earth atmosphere is roughly a mixture of gases, aerosols, and hydrometeors, which differ by
size, shape, and substance. The naturally occuring interaction processes between atmospheric
constituents and electromagnetic radiation are absorption due to resonance effects caused by
changes of the electronic, vibrational, and rotational states of molecules and emission, absorption, and scattering caused by inhomogeneities of the complex refractive index m (or dielectric
constant E) of the atmosphere. For scattering to be efficient, these inhomogeneities must occur
in a spatial scale comparable to the wavelength. Thus, the non-dimensional Mie-parameter x,
defined as being proportional to the ratio between the spatial dimension of the inhomogeneity,
i.e. the radius of the particle 1', and the wavelength>. of the electromagnetic radiation
27fT
X = -
>.
(11.1)
serves as one measure of the importance and indicates the type of scattering effects (Fig.
11.2). At very low values of X scattering is negligible. With increasing X scattering becomes
increasingly important and can be described by Rayleigh scattering. Maximum scattering
effects are observed for X around 3 to 10 (i.e. particle size is in the range of the wavelength) and
for homogeneous spherical particles Mie-theory serves as an appropiate quantitative description.
Far more complicated treatment is necessary and is still not at hand, when the non-spherical
irregular particles are considered. For large X (particle size much larger than the wavelength)
scattering decreases again approaching the geometrical optics limit, which can be adequately
modelled by ray-tracing techniques.
It follows that scattering at molecules and aerosols is an important process in the solar spectral
range but at longer wavelengths scattering is mainly caused by atmospheric hydrometeors, namely cloud and rain particles. Cloud and rain particles, however, interact with electromagnetic
radiation of almost the whole spectrum significantly via scattering processes. This leads to
multiple scattering effects, which renders the relation between cloud and rain particles and radiances outside the cloud highly non-linear. This non-linear relation causes additional problems
when - typical for satellite measurements - retrieval must be performed on spatial averages
of radiances (beam-filling problem).
Beside the spatial dimensions of the inhomogeneities in the atmosphere caused by the hydrometeors, the value of the complex index of refraction m = m' + im" compared to its value for
the gaseous atmosphere must be considered. The larger the difference, the larger the scattering
effects will be. The value of the real part m' determines the scattering efficiency and the value of
the imaginary part mil is responsible for absorption within the hydrometeors. Due to multiple
scattering both effects cannot be estimated separately, because every scattering event can give
rise to another absorption event which increases the overall absorption within an ensemble of
hydrometeors.
For water and ice both parts of the refractive index are quite complicated and irregular functions
of wavelength and temperature. Some values for water are given in Tab. 11.1. The real part
of m starts at values around 1.3 in the visible range, goes through a minimum of about 1.1 in
the thermal window around 10 /lm, and increases towards the microwave frequencies to almost
10. The imaginary part starts at very low values in the visible, increases steeply to about 0.4
in the thermal infrared, then more slowly up to around 3 in the mid-microwaves from where
it decreases again. Except in the very long microwaves, where m decreases with temperature,
both parts of the refractive index increase somewhat with temperature. Values for ice are of