IEEE Geoscience and Remote Sensing Magazine - June 2019 - 86

METHODS EXPLOITING THE EFFECT OF DOWNWELLING
RADIANCE ON GROUND RADIANCE ROUGHNESS
These methods work on the ground radiance spectrum
and assume that all of its roughness is from the reflected
downwelling component. The only rough atmospheric
component of the ground radiance in (4) is L d (m k). The
height of the reflected downwelling features is directly related to its emissivity. Figure 12 shows how features become pronounced as the emissivity decreases for ground
radiance spectra of varying constant emissivities and the
same temperature. Optimization can be done with respect
to the emissivity over key atmospheric features and is assumed to be constant across the feature. An emissivity for
the feature is found in a step-wise manner by subtracting
the reflected feature component for the current emissivity
and finding the emissivity that produces the smoothest
ground-emitted radiance. The smoothness is measured by
the peak height relative to a linearly interpolated version
across the estimated ground-emitted radiance. The temperature is found from the emissivity estimate that provides the smoothest ground-emitted radiance using
L g (m f ) - [1 - et (m f )] L d (m f )
n,
Tt g = B -1 d m f ;
et (m f )

(21)

where m f is the peak feature band and et (m f ) is the emissivity estimate for the peak feature band. The average temperature can be found for several features and used to calculate
the whole emissivity spectrum [42].
An emissivity estimate can also be determined directly
from the heights of the reflected features. The height of reflected features can be compared to the height of the same
feature in the downwelling radiance. The peak feature
heights are measured relative to a linear interpolation across
the feature, as shown in Figure 12 for the water feature between 12.2-12.7 µm. The emissivity at a feature band can be
estimated by comparing the height of a reflected feature in

Radiance (µ-Flicks)

1,000

P(λk) = 1, B (λk; 295 K)

800

Interpolation
Hg

P(λk) = 0.9
P(λk) = 0.7

600

Hd
P(λk) = 0, Ld (λk)

400

200

8

9

10

11

12

λf 13

Wavelength (µm)
FIGURE 12. The measured height of the reflected L d (m k) features

in L g (m k) spectra with various constant emissivity spectra.
86

the ground radiance, H g, to a reference height of the same
feature from an accurate estimate of the downwelling radiance H d [43]. Knowing that the height of the downwelling
radiance occurs at an emissivity of 1, the ratio of the two
heights can be used to estimate the emissivity at the feature
band m f using
Hg
et (m f ) = 1 - H .
d

(22)

Intuitively, if H g = H d, then et (m f ) = 0, and if H g = 0,
then et (m f ) = 1. The estimated emissivity is then used to
estimate the ground temperature using (21), which is then
used to calculate the entire emissivity spectrum.
TEMPERATURE-EMISSIVITY SEPARATION FOR
MULTISPECTRAL DATA
TES is possible with multispectral LWIR sensors; however,
a sensor with higher spectral resolution is required to estimate atmospheric parameters for AC. Multispectral sensors
do not have sufficient spectral resolution to determine the
fine atmospheric features needed for AC. More rigorous assumptions of the emissivity spectrum are made to reduce
the number of unknowns and make emissivity retrieval a
tractable problem. Multiple measurements of a pixel can be
retrieved at several temperatures, thus doubling the number of ground radiance measurements while increasing the
number of unknowns by only a single temperature [44]. The
emissivity spectrum of a gray body material can be assumed
to be constant over at least two bands, thereby reducing the
number of emissivity unknowns [45]. The TES method used
by the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) relies on an empirical relationship between spectral contrast and minimum emissivity, as
determined from laboratory and field measurements [46].
While emissivity spectra can be retrieved with multispectral
sensors, their reduced spectral resolution will make it difficult to identify materials with sharp spectral features.
INTEGRATED ATMOSPHERIC COMPENSATION
AND TEMPERATURE-EMISSIVITY
SEPARATION ALGORITHMS
Determining the downwelling radiance and the other
atmospheric parameters when blackbody-like pixels are
not available requires knowledge of the ground emissivity. Because the ground emissivities are unknown, the
atmospheric parameters and emissivities are typically determined concurrently with TES on reflective pixels. Algorithms such as the Automatic Retrieval of Temperature
and Emissivity using Spectral Smoothness [34], [38] and
Fast Line-of-Sight Atmospheric Analysis of Spectral Hypercubes IR [47] use an LUT of atmospheric models and
estimate the temperature and emissivity of reflective pixels for each model using
et (m k) =

L m (m k) - Lt u (m k) - Lt dx (m k)
,
B (m k; Tt g) xt a (m k) - Lt dx (m k)

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