IEEE Geoscience and Remote Sensing Magazine - June 2019 - 41

[A(m) + B(m)] t b(m)
L backrad(m) =
+ L up(m).
1 - t b(m) S (m)

(8)

0.7
Soil
Water

0.6

Reflectance

0.5
0.4
0.3
0.2
0.1
0

0.5

1
1.5
Wavelength (µm)
(a)

2

0.7
Soil
Water

0.6
0.5
Reflectance

accurately models adjacency affects. It also retrieves column
water vapor, visibility, and a cloud mask, and it includes a polishing option and spectral recalibration options. A flowchart
illustrating the FLAASH algorithm is shown in Figure 9.
Water vapor is estimated based on a 2D lookup table
of water-column amount versus in-band and out-of-band
at-sensor radiances; the absorption band is user selectable.
Cirrus clouds are identified by examining the brightness
in one or two channels nearest 1,375 nm. To incorporate
adjacency effects into the aerosol retrieval and reflectance
calculation, the data are spatially convolved with the sum
of two radial exponential kernels (one for Rayleigh and
one for Mie scatter) to describe the atmospheric scattering of ground-reflected photons [61]. This results in a new
data cube of spatially averaged radiance, L backrad, which is
used in the final reflectance retrieval. Aerosol (visibility)
retrieval from either vegetation or water pixels is based on
empirical reflectance ratios for those materials, drawing on
earlier work with Moderate Resolution Imaging Spectroradiometer data [62], [63]. After the water vapor and visibility
are retrieved, there is sufficient information to compute the
average background reflectance t b(m) from the following
approximate expression:

0.4
0.3
0.2
0.1

The solution for t b(m) is then used in (2) to determine
the reflectance, t t (m).
FLAASH allows the adjacency averaging in t b(m) to be
turned off, thereby replicating the more approximate radiance equation used in ACORN, ATREM, and HATCH. The
effect is shown in Figure 10 for retrieved reflectance from
soil that is surrounded by vegetation in a hazy scene. The reflectance retrieval without rigorous adjacency compensation
(green line) shows a "red edge" artifact (a sharp rise in reflectance) associated with chlorophyll in
the nearby vegetation.
ATMOSPHERIC CORRECTION
ATCOR [64], [65] is another commercially available physics-based compensation model that uses the MODTRAN
RT code along with the HITRAN 2013
database. It was first released in the
early 1990s by the German Aerospace
Center, and it is now maintained by
the Swiss company ReSe Applications.
Like FLAASH, it makes use of the radiance equations (2) and (8) and, therefore, handles adjacency effects well,
although with a more approximate
averaging kernel.
ATCOR comes in three different
versions depending on the application. ATCOR2 is generally used for
JUNE 2019

Radiance Cube
Metadata (Lat./
Long., Date, etc.)
Base Atmospheric
Model
Visibility Retrieval
Bands
Reflectance Cutoff
Ratio
Input

0

0.5

1
1.5
Wavelength (µm)
(b)

2

FIGURE 8. An example of spectral polishing. The retrieved soil and

water reflectance spectra (a) before and (b) after spectral polishing. Data obtained from the AVIRIS sensor. (Source: M. Eisman;
used with permission.)
Water-Vapor
Estimation and
Spectral Calibration
Visibility Retrieval
Trial Visibility Loop
Trial Correction
Selected Dark Pixels

Refined
Water-Vapor Retrieval

Image Processing

Reflectance Error
Interpolated
Zero-Error Visibility

Reflectance Cube
Output

FIGURE 9. A general flowchart of the FLAASH atmospheric compensation algorithm. Visibility is defined in MODTRAN as VIS [km] = ln (50)/( Ext 550nm [km -1] + 0.01159 [km -1]) , where
Ext 550nm [km -1] is the surface aerosol extinction at 550 nm and 0.01159[km -1] is the surface
Rayleigh scattering coefficient at 550 nm. Lat: latitude; Long: longitude.

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IEEE Geoscience and Remote Sensing Magazine - June 2019

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