IEEE Geoscience and Remote Sensing Magazine - June 2019 - 83

Meteorological station and radiosonde data can be used
to determine the surface conditions and the relative humidity and temperature in the lowest part of the atmosphere. Automated solar radiometer measurements can
also be used to determine the total water column and
the aerosol optical depth. Additionally, global models
of the vertical structure of the atmosphere are available
from the National Oceanic and Atmospheric Administration's National Center for Environmental Prediction.
Large water targets have been used extensively because
they are uniform in composition with high emissivity.
The skin temperature determines the radiance that is remotely sensed, and it is quantified based upon measurements below the surface and radiometer measurements
of the surface-leaving radiance because the bulk and surface temperatures are slightly different. This combination
of measurements is used to develop a radiative transfer
model of the at-aperture radiance [30]. The uncertainty in
terms of temperature from the method is approximately
0.5 K for the Landsat series [31].
CHALLENGES
The characterization of LWIR imaging spectrometers is well
understood and mature for the typical user. High-quality
blackbodies are available and traceable to national metrology laboratory standards. The spectral calibration is more
challenging for dispersive systems if the instrumental profile is to be measured for each spatial-spectral pixel. Vicarious techniques are also mature. The requirements for
future science missions are considerably more challenging
because of the National Research Council's decadal survey
requirement for the accuracy of the measurement of spectrally resolved IR radiance over the 200-2,000-cm−1 range,
emitted to space to be 0.065 K at a 95% confidence level.
This will require a highly stable and well-characterized imaging spectrometer with a suite of internal sources traceable
to radiance and spectral standards at a national metrology
laboratory [32].
EMISSIVITY RETRIEVAL
The at-aperture radiance data obtained after radiometric
calibration can be used with a model described by (3) and
(4) to retrieve the emissivity of each pixel. Emissivity retrieval involves two stages:
1) Atmospheric compensation: In this stage, the ground radiance is retrieved from the at-aperture radiance spectrum
by removing the effects of atmospheric transmission
loses and emissions.
2) Temperature-emissivity separation: In this stage, ground
temperature and emissivity are concurrently determined from the ground radiance and the reflected
downwelling radiance.
For tutorial purposes, we first discuss the general processes of AC and TES separately. We then discuss how the
two processes are interwoven in practical emissivity-retrieval algorithms.
JUNE 2019

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

ATMOSPHERIC COMPENSATION
Rearranging (3) and (4), we recover the ground radiance as
L g (m k) =

L m (m k) - L u (m k)
, k = 1, 2, f, K,
x a (m k)

(12)

if we have estimates of the upwelling radiance and transmission function, where K is the number of sensor bands
and k is the band index. The main difficulty of AC lies in
the accurate estimation of the scene's atmospheric parameters. Typically, AC algorithms assume the ground scene
area is small enough to ensure that the atmosphere is
horizontally homogeneous across the scene. The AC algorithm then determines a single set of functions, L u (m k) and
x a (m k), for the entire scene; these are then used to convert
the at-aperture radiance spectra of each pixel to ground
radiance using (12). The accuracy of the final ground radiance estimates is determined by the accuracy of the atmospheric parameter estimates. We next discuss two families
of AC methods.
IN-SCENE ATMOSPHERIC COMPENSATION METHODS
These methods assume that there are pixels within the
scene containing materials that closely resemble blackbodies, i.e., e (m k) . 1. These pixels of interest usually contain
water or vegetation. When a pixel contains a blackbody-like
material, its at-aperture radiance (3) can be simplified to
L m (m k) . B (m k; Tg) x a (m k) + L u (m k), if e (m k) . 1.

(13)

This equation shows that there is a linear relationship between the emitted ground radiance of a blackbody B (m k; Tg)
and the at-aperture radiance; note that x a (m k) is the slope
and L u (m k) is the intercept of the regression line.
To fit this linear model, we need an estimate of the
ground temperature Tg to evaluate B (m k; Tg) for each pixel.
This is accomplished by choosing a reference channel m R
that is known to be "clear" [x a (m R) . 1 and L u (m R) . 0],
and approximately m R = 10.1 nm. Because the at-aperture
radiance for a blackbody at m R can be simplified to
L m (m R) . B (m R; Tg) if x a (m k) . 1,

(14)

the ground temperature can be estimated using the brightness temperature. The brightness temperature, defined as the
inverse of the Planck function
TB (m k; L S (m k)) = B -1 (m, L m (m k)),
=

C2
,
m k ln (C 1 /(m 5 L m (m k)) + 1)

(15a)
(15b)

is the temperature required for a blackbody to emit the radiance observed at a specific wavelength. The approximate
ground temperature for each blackbody-like pixel,
Tt g = B -1 (m R; L m (m R)),

(16)
83
IEEE Geoscience and Remote Sensing Magazine - June 2019

Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - June 2019
