Atmospheric-correction for airborne sensors: comment on a scheme
used for CASI
Chuanmin Hu, Kendall L. Carder
College of Marine Science, University of South Florida
140 Seventh Ave. S., St. Petersburg, FL 33701
Phone: (727)553-1186
Fax: (727)553-1103
Email: hu@seas.marine.usf.edu
Revision. Original version submitted in October 2000.
Abstract
In a recent work (Gould and Arnone, 1997) the compact airborne spectrographic imager
(CASI) was used to map the absorption and scattering properties of a coastal environment. The
methodology used in this work is also cited in a number of more recent studies. The authors
found large discrepancies between the parameters estimated from measurements (AC9) and from
a bio-optical model (Carder et al., 1999). As a result, they adjusted the backscattering efficiency
parameter of the model. We found, however, that the discrepancies may actually be due, at least
in part, to an erroneous atmospheric correction used for the airborne data. Because the removal
of the surface-reflected sky radiance was neglected, the estimated water-leaving radiance was
erroneously augmented and used as the input of the bio-optical model. This caused a scattering
overestimate and an absorption underestimate. It is suggested that the surface reflection, unlike
for land applications, should always be removed to obtain the water signal for use with such biooptical models.
Keyword: Atmospheric correction, CASI, absorption, scattering, water-leaving radiance.
Introduction
Airborne sensors, such as CASI, have been frequently used in aquatic environments for
estimates of various water constituents, including phytoplankton, colored dissolved organic
matter (CDOM, or Gelbstoff), and resuspended sediments (e.g., see Gould and Arnone (1997)
and Jorgensen and Edelvang (2000)). The sensors are particularly useful for mapping coastal
areas where spectral and spatial resolutions are more demanding than satellite sensors. For
example, CASI data, used with concurrent ship and mooring measurements, were used to map
the absorption and scattering properties of a coastal environment (Gould and Arnone, 1997). The
general methodology in Gould and Arnone (1997) is useful for deriving water-leaving radiance
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over turbid, coastal waters. However, due to a fundamental weakness, the method should be
revised in future work.
Atmospheric correction of airborne sensors
A critical step to interpret the sensor radiance (Lt) in terms of predicting the optical properties
of the water column is the removal of the atmospheric path radiance (Lpath). The purpose is to
obtain water-leaving radiance (radiance exiting from below the surface as viewed by a
downward-looking sensor just above the surface), Lw:
Lt = Lpath + t  Lw,
(1)
where t is the diffuse transmittance for propagation of Lw from the surface to the sensor. For
simplicity the wavelength dependency of each term is suppressed here. The assumption for Eq.
(1) is that the ocean can be de-coupled from the atmosphere because Lw is generally much
smaller than Lpath. Note that by using Eq. (1) which follows the terminology of Gordon and coworkers (see Gordon, 1997 for review), Lpath (i.e., the LA term in Eq. (1) of Gould and Arnone
(1997)), as shown below, implicitly includes the surface (Fresnel) reflected sky radiance because
the information below the surface is carried by Lw only. This is different from land applications
where Lpath does not contain surface reflection. For example, in their atmospheric-correction
work for land Liang et al. (1997) explicitly stated that “L0 is the upward radiance of the
atmosphere for zero surface reflectance, often called path radiance”. Note that Eq. (1) can be
written in a similar way to Eq. (1) of Liang et al. (1997), such as Eq. (1) of Gordon (1978).
However, Gordon (1978) explicitly stated that I1 in his Eq. (1) (corresponding to the “path
radiance” term in Eq. (1) of Liang et al. (1997)) contained surface reflection (p1633 of Gordon
(1978)). In other words, the so called “path radiance” has a different meaning for the ocean than
for the land.
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Although simple in meaning, Lw can never be measured directly. Instead it can only be
derived using measurements from either under- or above-water instruments (see Mueller and
Austin, 1995 and references therein). An above-water sensor will not only detect Lw, but also the
sky radiance reflected by the surface into the field of view of the sensor.
For an optically thin atmosphere (optical thickness,  < 0.1) and moderate solar and sensor
zenith angles, Lpath can usually be approximated (assuming a two-layer system) as Lr + La where
Lr and La are the radiances caused by Rayleigh scattering and aerosol scattering in the absence of
each other, respectively. Lr and La can be derived using single-scattering approximations, i.e.,
each photon, if scattered (assuming a non-absorbing atmosphere), will be scattered only once.
Figure 1 describes the three processes that contribute to the sensor signal.
Lr and La are each composed of the three parts: photons scattered to the sensor before
reaching the surface (Fig. 1a), photons specularly reflected by the surface and then scattered to
the sensor (Fig. 1b), and photons scattered to the surface and then specularly reflected by the
surface to reach the sensor (Fig. 1c). Note that process (c) describes the reflected sky
contribution (In contrast, “path radiance” for land application does not include either (b) or (c)).
Using radiative transfer equations (RTEs, Gordon, 1997 and references therein), it is easy to
show that L(a) = F0P(180o-0)z, L(b) = F0P(0)(0)z, and L(c) = F0P(0)(0o) where F0 is the
solar constant, P(0) is the scattering phase function (normalized to 1) at scattering angle 0, and
(0) is the Fresnel reflectance at incident angle 0.  is the total atmospheric optical thickness
due to either Rayleigh or aerosol scattering, and z is the optical thickness between the surface
and the sensor altitude (z). Here the observation nadir angle is 0o. Note that process (c) is
proportional to  instead of z (Fig. 1). Therefore, we have
Lpath(z) = Lr(z) + La(z) = (Lr(a) + Lr(b) + Lr(c)) + (La(a) + La(b) + La(c))
= F0[Pr(180o- 0) + Pr(0)(0)]rz + F0Pr(0)(0o)r
+ F0[Pa(180o- 0) + Pa(0)(0)]az + F0Pa(0)(0o)a,
(2)
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Lpath(0+) = Lr(c) + La(c)= F0Pr(0)(0o)r + F0Pa(0)(0o)a,
(3)
where 0+ means just above the surface, and the subscripts "r" and "a" indicate Rayleigh and
aerosol scattering, respectively. The results show that (1) the surface reflection (process (c)) is
included in the path radiance, and therefore (2) no matter how close the sensor is to the surface
(even for the above-water measurement from a ship), Lpath is never nil. Indeed L(c) in the singlescattering approximation is a constant regardless of the sensor altitude. This is because that there
is no transmission loss during propagation of surface-reflected skylight to the airborne sensor
(the photons have already been scattered because they come from skylight, therefore they will no
longer be scattered, for otherwise it is a violation of the single-scattering assumption). At 0+,
because t = 1, Eq. (1) becomes
Lt(0+) = F0Pr(0)(0o)r + F0Pa(0)(0o)a + Lw.
(4)
To estimate the atmospheric effect, Gould and Arnone (1997) used Lt(z) measured at three
altitudes, and extrapolated to the surface to obtain "LT(surface)" (i.e., Lt(0+) in Eq. (4)). They
further assumed that LT(surface) was Lw. This makes sense only if [F0Pr(0)(0o)r +
F0Pa(0)(0o)a] is much smaller than Lw, which is not true for either the visible or the near-IR
bands. Indeed the near-IR Lw is often assumed less than one digital count (i.e., negligible) for
clear open ocean waters, which is the basis for atmospheric-correction of satellite ocean-color
sensors (Gordon, 1997). Thus, the surface-reflection term, [F0Pr(0)(0o)r + F0Pa(0)(0o)a], is
likely to dominate the extrapolated LT(surface) in Figure 1 of Gould of Arnone (1997) (i.e., the
extrapolated LT(surface) at 865 nm is virtually reflected sky radiance), and the "atmospheric
effect" in their Figure 1 is underestimated because reflected sky radiance is not included. Note
that the "LT(surface)" term in their Figure 1 is not the "LT(surface)" term in their Eq. (11) because
the latter is indeed Lw while the former includes additional reflected sky radiance. Thus, applying
the "atmospheric effect" derived from a deep-water site to the shallow-water pixels will likely
overestimate the shallow-water Lw. Note that Eq. (1) of Gould and Arnone (1997) does not
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contain an explicit term for reflected skylight, nor is it suggested that it is implicitly included in
LA as it is in Gordon (1997).
The actual atmospheric effect is much more complicated than shown above due to multiplescattering and gaseous absorption effects. The surface reflection term is also much more
complicated due to solar/viewing geometry and surface roughness (Mobley, 1999). But the
concept remains the same: surface-reflected skylight should always be subtracted from Lt(0+) to
obtain Lw. Otherwise, severely overestimated Lw values, especially at the near-IR wavelengths,
are encountered. For example, for a clear atmosphere in mid-latitude fall, the near-nadir sky
radiance was measured as ~7 W/cm2/nm/sr at 555 nm (data collected at ~11 am on 5 October
1998 over Tampa Bay water, Florida, 27oN, unpublished). Assuming a 2% surface Fresnel
reflectance (the real reflectance is usually larger than 2%, see Mobley, 1999), the contribution to
Lt(0+) will be 0.14 W/cm2/nm/sr, corresponding to ~30% of the extrapolated "water-leaving
radiance" at 555 nm in Figure 2 of Gould and Arnone (1997) (~0.45 W/cm2/nm/sr. Note that
this “water-leaving radiance” has the 0.14 surface reflection included). This is corresponding to
an error of 0.14/(0.45-0.14)  45% in Lw(555) for this clear-water site. Note that by assuming
0.14 as the surface reflection contribution, Lw(555) for this clear-water site is ~0.45-0.14 = 0.31
W/cm2/nm/sr, not significantly different from the well established clear-water value, 0.28
W/cm2/nm/sr (e.g., Gordon and Clark, 1981. Note that 0.28 is for water-leaving radiance result
from a nadir sun without the atmospheric interference). However, this error estimate is certainly
not rigorous, as the sky measurement was conducted at a different time and at a different location
than in the Gould and Arnone study. Also, for turbid, shallow waters (the focus of Gould and
Arnone (1997)) the relative error will be smaller than shown here because of enhanced Lw values
due to both high backscattering and bottom reflection. Nevertheless, neglecting of removal of the
surface-reflected skylight will have Lw overestimated for both clear, offshore and turbid, shallow
waters.
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The erroneously augmented "Lw" data, if used as input to the bio-optical model (Carder et al.,
1999), will certainly provide absorption coefficients that are underestimated and scattering
coefficients that are overestimated because Lw  Edbb/(a+bb) where Ed is the surface
downwelling irradiance, and a and bb are absorption and backscattering coefficients,
respectively. This is also clearly evidenced in the Gould and Arnone results using the
"unmodified" bio-optical model. Eventually they adjusted the parameters in the bio-optical
model to "force" the model results to agree with the in situ (AC9) measurements, rather than by
correcting for the reflected skylight (a bias), but by changing the parameter X for backscattering
by particles (Carder et al., 1999). It would be interesting to see how the bio-optical algorithm
performs with unbiased (i.e., surface reflection subtracted) Lw values, and how much the X
parameter actually needs to be adjusted to have the model results agreed with the AC9
measurements for this environment.
Hence, reflected skylight should always be considered when removing the path radiance of
airborne sensors for aquatic applications. If a sky measurement is not available, at least models
should be used to estimate this quantity, just as Ed was estimated using Gregg and Carder (1990)
by Gould and Arnone (1997) when a measurement was not available. Indeed, the surface
reflection, as shown in Fig. 1c, is part of the Rayleigh or aerosol scattering because the source
light, i.e., sky light, is actually the result of Rayleigh or aerosol scattering. Therefore the so
called “path radiance”, “Rayleigh radiance”, and “aerosol radiance” for aquatic applications,
following Gordon and co-workers (Gordon, 1997 and references therein), should naturally
include the surface reflected sky radiance. However, these terms can certainly be defined not to
include the surface reflection, provided a separate surface term used in the equation, such as Eq.
(1) of Jorgensen and Edelvang (2000), Eq. (69) of Mueller and Austin (1995), and Eq. (1) of
Fraser et al. (1997). No matter what terminology is used, it is the signal below the surface (waterleaving radiance) that carries the information of the water column.
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On the other hand, since Lt(0+) can be extrapolated using Lt(z) at different altitudes, the
Gould and Arnone technique provides an alternative way to estimate Lw if a concurrent sky
measurement is available from a ship or an airborne sky-viewing sensor. Note that this
extrapolation technique does not depend on atmospheric models as do many other studies (e.g.,
MODTRAN used in Jorgensen and Edelvang, 2000), therefore it eliminates possible error
sources in the model assumptions such as the aerosol type and optical thickness. This is
particularly useful for turbid, coastal waters where accurate estimates of the near-IR Lw are
crucial for atmospheric correction of Case II waters for remote-sensing ocean-color sensors (e.g.,
Hu et al., 2000). These estimates, however, are notoriously difficult to obtain using conventional
means due to, for example, the self-shading problem of under-water instruments, and stray-light
problem of above-water instruments (Mueller and Austin, 1995).
Concluding remarks
The meaning of atmospheric path radiance for oceanic applications is different than for land
applications because the former implicitly contains the surface reflected light, which generally
does not contain the optical information of the water column. This signal, as in the conventional
atmospheric-correction scheme for ocean-color satellite sensors (Gordon, 1997 and references
therein), should always be removed for any above-water sensors (including the airborne sensors)
to obtain the useful water-leaving radiance data for estimating the optical properties of the water
column. Otherwise, the data will cause bio-optical models to perform poorly by yielding
erroneous optical data.
Acknowledgements
This work was supported by NASA contracts NAS5-31716, NAS5-97137, NAG-3446, and
ONR contract N0014-96-I-5013.
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Figures
Figure 1. Schematic of single-scattering processes that contribute to the nadir-viewing airborne
sensor signal at z.  is the total atmospheric optical thickness due to either Rayleigh or aerosol
scattering, and z is the optical thickness between the surface and the sensor altitude (z).
10
0

z
(a)
(b)
(c)
Figure 1
11