120
Y. Fouquart and M. Vesperini
In the infrared, classical sensors are using filters whose spectral width t:>v is very large with
respect to absorption lines. In this case, the gradient ~ is not as sharp as for a single line since
for each of the lines contained in t:>v, the variation in absorption (through pressure and temperature dependence) does not occur at the same level z. Consequently, the weighting function is
broader. New generation sensors (spectrometers or interferometers) provide measurements in
much narrower spectral bands and the related weighting function are much sharper.
Inversion of radiance measurements
The computation of radiance knowing the profiles of atmospheric temperature, humidity and
other gases, constitutes the direct problem, whereas inversion consists in extracting information
on the atmosphere from the observed radiance. An ideal system for vertical profile inversion
would have narrow weighting functions which do not overlap each other, so that radiance could
be interpreted as a function of temperature in a single layer. As seen previously, the actual
weighting functions are quite broad and overlap each other and this is a limitation to the vertical
resolution of the set of sensors.
a) Information content
The expression for the weighting function
1 JZT kabs(ZI)p(ZI)dz l
Wv(z, ZT, 0) = ~k~bs(z) p(z) e --,; z v
(5.102)
shows that the weighting function is dependent of
1. k~bs(z): the spectroscopic properties of each gas which has significant absorption at this
wavelength. These are functions of pressure (hence altitude) and to a minor extent of
temperature.
2. p(z) vertical profile (density) of these gases
Among the main absorbers, gases such as CO2 and N20 are uniformly distributed along the
vertical and with no significant variations with time. They provide quite steady weighting
functions for temperature sounding. For example the TOVS-HIRS (High-resolution Infrared
Radiation Sounder) channels 1 to 5 are located on the same edge of the CO2 absorption band
between 14 and 15 flm, but with different absorption efficiencies which yield Wv(z) peaking in
different layers of the atmosphere. In H20 absorption bands (e.g. channels HIRS 10, 11, and
12 of TOVS), the weighting function is much more variable since it changes with water vapour
content so with meteorological situation. Note that when H2 0 content increases, absorption is
stronger so that the weighting function peaks higher in the atmosphere.
b) Temperature inversion
From equation (5.101), we understand that inversion of temperature profiles is easier than
that of atmospheric constituents, since the atmospheric term of the RTE is the product of
temperature profile (through Bv(T(z))) and of a weighting profile Wv(z) that should strictly
be called the "temperature weighting function".
With a set of measurements (subscript n) made at different wavelengths, whose Wv(z) peak in
different layers (subscript p), each measurement Ln can be expressed as a linear combination
Ln = cnBn,o + L Bn(Tp)Wn,p(Tp,p,p)
(5.103)
p
Y. Fouquart and M. Vesperini
In the infrared, classical sensors are using filters whose spectral width t:>v is very large with
respect to absorption lines. In this case, the gradient ~ is not as sharp as for a single line since
for each of the lines contained in t:>v, the variation in absorption (through pressure and temperature dependence) does not occur at the same level z. Consequently, the weighting function is
broader. New generation sensors (spectrometers or interferometers) provide measurements in
much narrower spectral bands and the related weighting function are much sharper.
Inversion of radiance measurements
The computation of radiance knowing the profiles of atmospheric temperature, humidity and
other gases, constitutes the direct problem, whereas inversion consists in extracting information
on the atmosphere from the observed radiance. An ideal system for vertical profile inversion
would have narrow weighting functions which do not overlap each other, so that radiance could
be interpreted as a function of temperature in a single layer. As seen previously, the actual
weighting functions are quite broad and overlap each other and this is a limitation to the vertical
resolution of the set of sensors.
a) Information content
The expression for the weighting function
1 JZT kabs(ZI)p(ZI)dz l
Wv(z, ZT, 0) = ~k~bs(z) p(z) e --,; z v
(5.102)
shows that the weighting function is dependent of
1. k~bs(z): the spectroscopic properties of each gas which has significant absorption at this
wavelength. These are functions of pressure (hence altitude) and to a minor extent of
temperature.
2. p(z) vertical profile (density) of these gases
Among the main absorbers, gases such as CO2 and N20 are uniformly distributed along the
vertical and with no significant variations with time. They provide quite steady weighting
functions for temperature sounding. For example the TOVS-HIRS (High-resolution Infrared
Radiation Sounder) channels 1 to 5 are located on the same edge of the CO2 absorption band
between 14 and 15 flm, but with different absorption efficiencies which yield Wv(z) peaking in
different layers of the atmosphere. In H20 absorption bands (e.g. channels HIRS 10, 11, and
12 of TOVS), the weighting function is much more variable since it changes with water vapour
content so with meteorological situation. Note that when H2 0 content increases, absorption is
stronger so that the weighting function peaks higher in the atmosphere.
b) Temperature inversion
From equation (5.101), we understand that inversion of temperature profiles is easier than
that of atmospheric constituents, since the atmospheric term of the RTE is the product of
temperature profile (through Bv(T(z))) and of a weighting profile Wv(z) that should strictly
be called the "temperature weighting function".
With a set of measurements (subscript n) made at different wavelengths, whose Wv(z) peak in
different layers (subscript p), each measurement Ln can be expressed as a linear combination
Ln = cnBn,o + L Bn(Tp)Wn,p(Tp,p,p)
(5.103)
p