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Figure 176: Brightness temperature also called apparent temperature that represents atmospheric
radiation downwelling at angle θ measured by a radiometer
The integral Eq. (341) expresses the well known forward (or direct) problem: for a given
weightingfunctionW(ν,z,θ).Bytheatmospherictemperature’sprofileT(z),wecancompute
a measured ground level brightness temperature Tb(ν,θ) using this equation.
However, in remote-sensing applications, we are concerned with the inverse problem in
which Tb(ν,θ) is generally measured by a radiometer at a discrete number of elevation angle
θ i (or at a discrete frequency ν i or both) and the objective is to infer the atmospheric
properties or simply to find a unknown function T(z i ) that, when substituted in Eq. (340),
will yield values of Tb(ν i ,θ i ) approximately equal to the measured values. This is also known
as the inverse problem and generally is more difficult to solve. A logic scheme of the two
different procedures (direct and inverse) is shown in Figure 177.
Currently, there are three main absorption models that are widely used in these problems
by the microwave propagation communities inside the recalled weighting function W(ν,z,θ).
A computer code has been developed and distributed of the microwave propagation model
(MPM). More recently, Rosenkranz (1992) developed an improved absorption model that
also is frequently used in the microwave propagation community. Another model that is used
extensively in the US climate research community is the line by line radiative transfer model.
14.4 Upward-looking angular scanning microwave radiometry
The spectrum of received radiation depends on a variety of atmospheric variables including
temperature, water vapor concentration, and liquid water (i.e. rain, clouds and fog). Through
the measure of the received brightness temperature, it is possible to infer the atmospheric
temperature profile T(z) with a resolution that depends on the atmospheric absorption at
the chosen frequencies. Therefore, the temperature weighting functions of upward-looking
profiling radiometers above introduced in Eq. (341) have narrow peaks near the surface which
decrease with altitude (see Figures 178(a) and (b)). In addition, sensitivity to oxygen is not
degraded by radiation from the terrestrial surface. This allows accurate temperature profile
retrievals with relatively high resolution in the lower troposphere’s layer, typically until 2 km
of height.
The retrieval of atmospheric temperature’s profile by passive measurement of brightness
attenuated by a factor exp(−τν(z,θ)) (by the intervening medium as it travels toward the point of measurement),
weighted by αν(z)/cosθ. It is of fundamental importance to notice the difference between this
Tb(ν,θ), also called apparent temperature TAP (shown in Fig. 176) sensed at ground level and a thermodynamic
temperature profile T(z) which remotely has originated it
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