IEEE Geoscience and Remote Sensing Magazine - June 2019 - 87

PRESENT LIMITATIONS
The main limitations of AC algorithms are the assumptions
that perfect blackbodies are present in the scene and that
reflected downwelling effects can be ignored [33]. While
the algorithms that use this assumption are able to find
relatively accurate transmission and upwelling radiance
estimates for a scene with blackbody-like pixels, the emissivities of the blackbody-like pixels affect the transmission
and upwelling radiance estimates. When the blackbodylike pixels used by ISAC contain a single material, the shape
of the atmospheric estimate is affected by the shape of the
blackbody-like emissivity spectrum [48].
TES methods use the assumption that the ground
emissivity is smooth compared to the sharp atmospheric
features. The emissivity spectrum of a material is never
perfectly smooth, and there will be some amount of error
when a smoothing algorithm is applied to the emissivity
spectrum. This roughness in the true emissivity spectrum
introduces a bias smoothing error and under ideal conditions where all of the atmospheric parameters are known,
illustrates a fundamental limitation of TES algorithms in
finding the correct temperature and emissivity. The effect
of this emissivity smoothing bias error was studied and
explained under varying materials and atmospheric conditions in [49] and [50].
TES algorithms are mainly limited by the accuracy of
the estimated transmission, upwelling radiance, and
downwelling radiance. Errors in the transmission and
upwelling radiance introduce errors in AC, which are
introduced to the ground radiance and emissivity estimate. Even when the correct ground radiance is found,
errors in the downwelling radiance are transferred to the
emissivity [39]. Atmospheric errors are caused by using
an incorrect atmospheric model and/or band-averaging
the model to an incorrect sensor SRF. Slight atmospheric
mismatch errors caused by a wavelength calibration error
JUNE 2019

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

FUTURE CHALLENGES
Currently available TES algorithms make the assumption
that the materials within a pixel are at the same temperature. TES algorithms can find this temperature, and the
resulting emissivity estimate is a linear mixture based on
the relative abundances of the materials within the pixels.
When the materials in a pixel are at different temperatures,

1,000

At-Aperture Radiance

0.8

900

800

700

0.9

0.7

Emissivity
Algorithm 1
Algorithm 2
Truth
8

Emissivity

CHALLENGES
We have provided a high-level overview of algorithms
for LWIR AC and TES. The development of improved algorithms requires an understanding of the limitations of
current algorithms. We divide these issues into two parts.
The first describes challenges and limitations that have
been studied extensively in the literature, and the second
describes future challenges that have only recently begun
to be addressed.

prevent the complete removal of atmospheric features,
adding roughness to emissivity estimates. The effects of
varying wavelength calibration errors for different materials and temperatures were studied and explained in
[23] and [34].
AC and TES algorithms typically contain a wavelength
calibration correction that is done concurrently with the
model search [34], [47], which increases the difficulty of
finding the correct model.
More significant atmospheric
mismatch errors are caused
WHILE TEMPERATURE
by using an incorrect model.
IS NOT SIGNIFICANTLY
While rough atmospheric erIMPORTANT FOR MATERIAL
rors will add significant roughness to emissivity estimates
IDENTIFICATION, IT IS A
and can be easily eliminated,
KEY QUANTIFIER OF
mag nit u d e a n d s mo ot h CLIMATOLOGY STUDIES.
shape errors can still provide
smooth emissivity estimates.
Both types of errors affect the
temperature estimate, while only the atmospheric shape
errors affect the shape of the emissivity [51]. The possibility of several models providing smooth emissivity estimates
increases the difficulty of finding the correct atmospheric
model. Because the temperature errors can compensate for
atmospheric errors, it is increasingly important that the correct atmospheric model is chosen when the temperature is
the main quantity of interest. While temperature is not significantly important for material identification, it is a key
quantifier of climatology studies.

At-Aperture Radiance

where AC is combined with the emissivity estimate. The
model that provides the smoothest overall estimates for the
reflective pixels is chosen and then used to run AC and TES
on the rest of the scene.
Figure 13 shows emissivity estimates for the blue ataperture radiance spectrum using two AC and TES algorithms. The differences between the emissivity estimates
for each algorithm and the true emissivity in green are
caused by errors in the atmospheric estimates.

0.6
13

Wavelength (µm)
FIGURE 13. The emissivity estimates for an at-aperture radiance
spectrum using two AC and TES algorithms.

IEEE Geoscience and Remote Sensing Magazine - June 2019

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