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OUTLINE

 1.  Highlights
 2.  Abstract
 3.  Keywords
 4.  1. Introduction
 5.  2. The century-old theory for underwater visibility
 6.  3. New theory for underwater visibility
 7.  4. Verification of the new model with independent measurements
 8.  5. Discussion and conclusions
 9.  Acknowledgments
 10. Appendix A. An illustration of the relationship between Kdpc and Kdtr
 11. References

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CITED BY (215)




FIGURES (7)

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TABLES (1)

 1. Table 1




REMOTE SENSING OF ENVIRONMENT

Volume 169, November 2015, Pages 139-149



SECCHI DISK DEPTH: A NEW THEORY AND MECHANISTIC MODEL FOR UNDERWATER VISIBILITY

Author links open overlay panelZhongPing Lee a, Shaoling Shang b, Chuanmin Hu c,
Keping Du d, Alan Weidemann e, Weilin Hou e, Junfang Lin a, Gong Lin b
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HIGHLIGHTS

 * •
   
   Caveats in the century-old underwater visibility theory are discussed.

 * •
   
   A new theory for underwater visibility is proposed.

 * •
   
   A new mechanistic model for Secchi disk depth is established.

 * •
   
   Results from the new model are verified with wide range of measurements.




ABSTRACT

Secchi disk depth (ZSD) is a measure of water transparency, whose interpretation
has wide applications from diver visibility to studies of climate change. This
transparency has been explained in the past 60 + years with the underwater
visibility theory, the branch of the general visibility theory for visual
ranging in water. However, through a thorough review of the physical processes
involved in visual ranging in water, we show that this theory may not exactly
represent the sighting of a Secchi disk by a human eye. Further, we update the
Law of Contrast Reduction, a key concept in visibility theory, and develop a new
theoretical model to interpret ZSD. Unlike the classical model that relies
strongly on the beam attenuation coefficient, the new model relies only on the
diffuse attenuation coefficient at a wavelength corresponding to the maximum
transparency for such interpretations. This model is subsequently validated
using a large (N = 338) dataset of independent measurements covering oceanic,
coastal, and lake waters, with results showing excellent agreement (~ 18%
average absolute difference, R2 = 0.96) between measured and theoretically
predicted ZSD ranging from < 1 m to > 30 m without regional tuning of any model
parameters. This study provides a more generalized view of visual ranging, and
the mechanistic model is expected to significantly improve the current capacity
in monitoring water transparency of the global aquatic environments via
satellite remote sensing.

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KEYWORDS

Secchi disk depth
Water transparency
Visibility theory
Remote sensing
Beam attenuation coefficient
Diffuse attenuation coefficient


1. INTRODUCTION

Secchi disk, a white or black-and-white disk with a diameter generally about
30 cm, is the oldest “optical instrument” used to measure transparency of ocean
and lake waters (see Tyler (1968), Wernand (2010), and Aas, Høkedal, and
Sørensen (2014) for a detailed review of the history of Secchi disk). The Secchi
disk depth (ZSD, m), a depth when a Secchi disk is no longer viewable by an
observer when it is lowered into the water, represents a quantitative measure of
the transparency of that water body, or the visibility in the vertical direction
(Duntley, 1952). Since the demonstration of transparency measurements with a
Secchi disk about 200 years ago (Aas et al., 2014, Wernand, 2010), due to its
low cost and easiness to operate, there have been millions of such measurements
(along with different sizes of disks) worldwide in the past century (Boyce,
Lewis, & Worm, 2012), with ZSD found in a range of a few centimeters for turbid
lakes to around 70 m for the clearest oceanic waters
(http://www.secchidipin.org/secchi_records.htm). Although more sophisticated
optical-electro systems are currently available to measure water quality
parameters, Secchi disks are still being widely and regularly used to measure
water transparency in both limnology and oceanography studies. Such data are
useful to describe the spatial variability of water properties (Arnone et al.,
1984, Binding et al., 2007, Carlson, 1977, Lewis et al., 1988, Megard and
Berman, 1989); to highlight the impact of light availability for the health of
substrates (Yentsch et al., 2002); and to show the changes of phytoplankton
concentration in the oceans in the past 100 + years (Boyce, Lewis, & Worm,
2010).

The theoretical interpretation of the Secchi disk depth falls into the visual
optics of natural waters (Preisendorfer, 1976, Preisendorfer, 1986) or the
underwater visibility theory (Duntley, 1952, Zaneveld and Pegau, 2003) — the
branch of the general visibility theory for visual ranging in water. Detailed
derivations (also see Section 2) to relate ZSD with water's optical properties
can be found in Duntley (1952), Preisendorfer, 1976, Preisendorfer, 1986,
Zaneveld and Pegau (2003), and Aas et al. (2014). A general conclusion from
these classical works is that ZSD is inversely proportional to the sum of Kd and
c within the visible domain, with Kd (m− 1) being the diffuse attenuation
coefficient of downwelling plane irradiance and c (m− 1) the beam attenuation
coefficient. c is an inherent optical property (IOP) (Preisendorfer, 1976) which
does not vary with the angular distribution of a light field, while Kd is an
apparent optical property (AOP) which does vary with the angular light
distribution (Preisendorfer, 1976). Because c is generally 2–5 times or more
greater than Kd for wavelengths in the visible domain, in essence ZSD is
primarily determined by c following the classical theory. But, numerous
measurements (Aas et al., 2014, Bukata et al., 1988, Davies-Colley and Vant,
1988, Effler, 1988, Holmes, 1970, Kratzer et al., 2003, Megard and Berman, 1989)
have found that: (1) there is no universal relationship between ZSD and c, and:
(2) the correlation between ZSD and Kd is typically similar or better than the
correlation between ZSD and c. Note that in general Kd and c are two independent
optical properties for aquatic environments. In addition, field measurements
(Verschuur, 1997) of ZSD show that it varies with sun angle by ~ 20% between the
Sun at zenith and the Sun at 60° from zenith. Such observations are
contradictory to the theoretical prediction based on the classical underwater
visibility theory. Furthermore, this theory could predict that a
half-black–half-white disk will be detectable regardless of its depth in water,
which is also contradictory to human experiences (see more detailed discussions
in Section 2.2).

These observations and results are quite puzzling, as the underwater visibility
theory and the associated models have been the rule in the past 60 + years to
theoretically interpret ZSD (Duntley, 1952, Preisendorfer, 1986). Here we
revisit the derivations, in particular the key assumptions, associated with the
classical visibility theory (CVT) and discuss the likely lapses in that theory
for the inconsistency between the theoretical predictions and observations. We
further propose a new theory and a mechanistic model to interpret and estimate
ZSD, which we subsequently verify with independent measurements from a wide
range of aquatic environments.


2. THE CENTURY-OLD THEORY FOR UNDERWATER VISIBILITY


2.1. THEORETICAL DERIVATIONS

Consider a Lambertian disk placed horizontally at a depth z in water which is
viewed by a snorkeler just below the surface (see Fig. 1). Following radiative
transfer theory, the radiance over the target (LT) propagating upward towards
the snorkeler can be expressed as (Aas et al., 2014, Duntley, 1952, Højerslev,
1986, Preisendorfer, 1986, Zaneveld and Pegau,
2003),(1)dLTzdz=−cLTz+∫4πL'Tzθφβθφdω,with L'T the radiance distribution in the
4π direction above the target and β the volume scattering function of water (see
Table 1 for notations; here the wavelength dependence is omitted for brevity).
Note that here we use radiometric rather than photometric quantities (Aas et
al., 2014, Duntley, 1952, Højerslev, 1986, Preisendorfer, 1986, Zaneveld and
Pegau, 2003) to discuss the concepts and assumptions taken by the CVT in
interpreting Secchi disk depth, as the concepts and assumptions remain the same
in both radiometric and photometric formulation.

 1. Download : Download high-res image (236KB)
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Fig. 1. A cartoon showing how the light over an underwater target and that of
the background are detected by a surface snorkeler.

Table 1. Notations.

SymbolDescriptionUnitβVolume scattering function of waterm− 1 sr− 1bfForward
scattering coefficientm− 1cBeam attenuation coefficientm− 1CaApparent
contrast–CanNew apparent contrastsr− 1CiInherent contrast–CinNew inherent
contrastsr− 1CtContrast threshold of human eye–CtrContrast threshold of human
eye in radiance reflectancesr− 1[Chl]Concentration of
chlorophyllmg/m3EdDownwelling irradianceW/m2/nmKdDiffuse attenuation coefficient
of downwelling plane irradiancem− 1KdpcDepth-averaged diffuse attenuation
coefficient of downwelling irradiance at the wavelength of perceived
colorm− 1KdtrDepth-averaged diffuse attenuation coefficient of downwelling
irradiance in the spectral transparent windowm− 1KTtrDepth-averaged diffuse
attenuation coefficient of radiance reflected by a target and in the spectral
transparent windowm− 1LwUpwelling radiance of adjacent water without a
diskW/m2/nm/srL'TRadiance distribution over the targetW/m2/nm/srL'wRadiance
distribution over the backgroundW/m2/nm/srLTUpwelling radiance over the area
with a targetW/m2/nm/srLTtr(0 −)Upwelling radiance just below the surface of the
target areaW/m2/nm/srLwtr(0 −)Upwelling radiance just below the surface of the
background areaW/m2/nm/srLCtrContrast in radiance between the disk and no-disk
areasW/m2/nm/srrTRadiance reflectance right above a targetsr− 1rwRadiance
reflectance of background (water)sr− 1VwVisibility in horizontal
directionmzWater depthmZSDSecchi disk depth or vertical visibilitym

Similarly the upward radiance of the adjacent water without the disk (Lw) is
given by(2)dLwzdz=−cLwz+∫4πL'wzθφβθφdω,with L'w the radiance distribution of the
background (reference) in the 4π direction. In all historical derivations (Aas
et al., 2014, Duntley, 1952, Preisendorfer, 1986, Zaneveld and Pegau, 2003), it
was assumed that(3)∫4πL'Tzθφβθφdω=∫4πL'wzθφβθφdω,and subtraction of Eqs. (1),
(2) resulted in(4)dLTz−Lwzdz=−cLTz−Lwz.

Assuming the water is homogeneous, integrating Eq. (4) from depth to surface
results in(5)LT0−Lw0=LTz−Lwze−cz.

Further, in the CVT, the apparent contrast (Ca) between the target and the
background (or reference) is defined as(6)Ca=LT0−Lw0Lw0.

The solar irradiance propagating from surface to depth generally follows an
exponential decline function (Gordon & Morel, 1983)(7)Edz=Ed0−e−Kdz.

Applying Eqs. (6), (7) to Eq. (5) leads to(8)Ca=Cie−Kd+cz,with the inherent
contrast, Ci, defined as (Aas et al., 2014, Duntley, 1952, Preisendorfer, 1986,
Zaneveld and Pegau, 2003)(9)Ci=rT−rwrw.

Here rT and rw are the reflectance of the target (measured right above it) and
the background, respectively. Eq. (8) forms the Law of Contrast Reduction
(Duntley, 1952, Preisendorfer, 1986), which is the core of the classical theory
for visibility in both air and water, and has been adopted by the research
community for more than 60 years to interpret underwater visibility. Such a Law
of Contrast Reduction is the same as that used for visual ranging in air
(Middleton, 1952).

When Ca matches the threshold of eye detection (Ct), the visibility in the
vertical direction (ZSD, or V− 90 in Duntley (1952)), is given
by(10)ZSD=1Kd+cln1CtrT−rwrw.

Further, if the target is black (rT = 0, i.e., negative contrast between the
target and the background) and viewed horizontally, the maximum horizontal
detectable distance is (Duntley, 1952, Preisendorfer, 1986, Zaneveld and Pegau,
2003)(11)Vw=−lnCtc.

As Duntley (1952) pointed out, Eq. (11) is in an identical form as the
Koschmieder theory established 90 years ago for visibility in the air
(Middleton, 1952). Furthermore, because c is an IOP, the predicted horizontal
visibility is independent of the azimuth viewing direction (or the background)
for a given threshold, which thus actually represents an easy-to-understand
index for the quality of atmosphere or water.

Eqs. (10), (11) become the key analytical models for visibility applications in
air and water in the past 60 + years. And, for the above derivations, Eq. (3) is
the critical assumption. The validity of this assumption, however, as discussed
in detail below, may not be assumed automatically for visual ranging.


2.2. CAVEATS IN THE CLASSICAL THEORY AND ASSOCIATED MODEL

2.2.1. THE ATTENUATION OF CONTRAST

The beam attenuation coefficient (c) is used in the CVT to propagate the
contrast of a finite-size target (Eqs. (5), (8)), where by definition c
represents the attenuation of a collimated light beam (Preisendorfer, 1976). In
the theoretical derivations to reach Eqs. (5), (8), there was no consideration
of the unique high-angular resolution of human eyes; and the relative size
between the target and the viewing distance (see Fig. 1) is ignored. Basically,
the target is treated as a small object, leading to the assumption that both
sides of Eq. (3) can be assumed to equal each other. This assumption is the key
for the resulted contrast propagation (Eq. (5)) and the Law of Contrast
Reduction for a vertically-viewed target (Eq. (8)). This assumption is generally
appropriate for the visibility theory in air where the maximum viewable distance
is often in the order of several tens of kilometers and the target (a finite
size black object) is in the order of meters (Middleton, 1952). For a target in
water (such as a Secchi disk or a diver, which is usually several tens of
centimeters or larger), because of the significantly higher absorption and
scattering coefficients of water constituents than that of air molecules (Kirk,
1994, Middleton, 1952), the maximum viewable distance is at most several tens of
meters, i.e., ~ 1/1000 of that in air, consequently the validity of Eq. (3) is
in question.

The “measurement” or detection of a target by the human eye is very different
from that by an eletro-optic sensor (Duntley, 1952), where the eye–brain system
is an optical imager with an array of millions of “tiny-sensors”. For a healthy
eye system, it can collect information simultaneously for targets in a range of
~ 160° × 175° (although the actual imaging region is smaller than this). Such a
unique combination enables simultaneous observations of the target and the
background (or reference), which is the key for target sighting under varying
environmental lighting. The angular resolution of the human eye is ~ 0.5 arcmin
(equivalent to a spatial resolution of ~ 0.2 mm from a distance of 1 m) (Clark,
1990, Curcio et al., 1990). This is equivalent to a digital camera with ~ 600
Megapixels, thus enables the collection of radiance at very fine resolutions,
which is why we can see fine details of a target and how we can read.

Due to this extremely fine resolution of the human eye, the relationship between
the pixel size of the collected image and the size of a target will depend on
the distance (z) and the size of the target (d, see Fig. 1). In the water ZSD is
often several tens of meters, resulting in a pixel size of several millimeters.
Thus, a Secchi disk is much larger than the pixel size and can no longer be
considered as a point source. Consequently, the radiance distribution over a
Secchi disk could be very different from that over the nearby background. This
unique feature and phenomenon are demonstrated in Fig. 2 for a black-and-white
disk in water pictured with a digital camera ~ 1 m above the disk. For a point
(B) over the disk and a point (A) in the adjacent water (both at same depth),
their surrounding light (represented by the brown dashed line above each letter
in the right side of Fig. 2) are L'T(z, B) and L'w(z, A), respectively. Because
the radiance distribution is generally not uniform at a given depth (especially
for depths closer to the target) due to the intrusion of this target, there is
in general:(12)L'TBz≠L'wAz.

 1. Download : Download high-res image (323KB)
 2. Download : Download full-size image

Fig. 2. (left) An alternating-black-and-white Secchi disk in blue water observed
vertically. (right) Variation of radiance (digital counts) for pixels on the
black lines of the Secchi disk image. Points A and B indicate likely locations
for judgment decisions on whether the disk is still discernable by a human eye,
with the brown dashed lines indicating the range of radiance that could be used
in Eq. (3) for integrations. Radiance within the green circles indicates those
outside of the overlap that are used in Eq. (3). Note that the digital camera
was saturated for radiance over the white portion of the disk, while the
radiance over the black portion of the disk increases towards the center due to
adjacent contributions from the white portion of the disk. Radiance at the
center of the disk is omitted due to interference of the holding string.

Therefore Eq. (3) is not always true for a Secchi disk or large objects,
especially for depths closer to the target (Aas et al., 2014). One exception is
when points A and B are two adjacent pixels (such as a point-source target, or
when B is at the edge of a finite-size target while A is an adjacent water
pixel), the two brown dashed lines will approach each other and the
approximation of Eq. (3) could then be valid. The sighting of a Secchi disk in
water, however, is generally not determined based on the contrast between its
edge and the adjacent water, but rather based on the detection of any portion of
the disk that has the highest contrast from the background. In general the
distance between points A and B is likely 10's to 100's of pixels. In these
cases, after subtracting the overlapping potions of L'T(z, B) and L'w(z, A), an
exact Eq. (4) in the above derivations for points A and B would
be:(13)dLTzB−LwzAdz=−cLTzB−LwzA+∫ζL'TzBζβζdω−∫ξL'wzAξβξdω,with [ζ] and [ξ]
representing the residual solid angles outside of the overlapping range between
points A and B, shown as the circled portions in the right side of Fig. 2. We
may further divide the radiances within [ζ] and [ξ] as the upward and downward
radiances following Zaneveld (1995). Because downward radiance is mainly
determined by incident light, L'T(z,B,ζd) is approximately L'w(z,A,ξd). For
upward radiance, L'T(z,B,ζu) and L'w(z,A,ξu) contribute to LT(z,B) and Lw(z,A),
respectively, through forward scattering (Zaneveld, 1995). Therefore, Eq. (13)
can be written as(14)dLTzB−LwzAdz=−cLTzB−LwzA+εbfLTzB−LwzA,which further leads
to a more generalized equation for contrast
propagation(15)LT0−Lw0=LTz−Lwze−c−εbfz.

The value of parameter ε depends on the distance (i.e. size of the target)
between points A and B. For a small target, ε approaches 0, and contrast
propagation follows the beam attenuation coefficient; for a large target,
because of contributions from forward scattering of adjacent pixels within the
target, ε is greater than 0 and the attenuation of contrast no longer follows
the beam attenuation coefficient. This dependence of attenuation on target sizes
is consistent with conclusions regarding image propagation through a media (Hou
et al., 2007, Wells, 1973a, Wells, 1973b), where the attenuation of
high-spatial-frequency images (small objects or narrow beam) follows c (which is
the sum of absorption and scattering coefficients) while the attenuation of
low-spatial-frequency images (large objects or broad beam) follows the sum of
absorption coefficient and a portion of the scattering coefficient (Wells,
1973a, Wells, 1973b). In short, for visual ranging of a target in water or air,
if the size of the target is much larger than the spatial resolution of a human
eye, Eq. (3) is not necessarily valid, the Law of Contrast Reduction (Eq. (8))
could not be derived, and then visibility models (Eqs. (10), (11)) based on this
theory may not be appropriate. Such a caveat associated with the CVT can also be
explained as follows. If Eq. (5) is valid, mathematically it will lead
to,(16)LT0−LTze−cz=Lw0−Lwze−cz.

For this to be satisfied for any c and z, the following relationships must be
true,(17a)LT0=LTze−cz+Xz,(17b)Lw0=Lwze−cz+Xz.

Here X(z) is a function of z (such as the path radiance between depth z and
surface) and becomes 0 when z is 0. Radiative transfer theory tells us that
Eq. (17a) is valid only for a point source or small target.

This caveat associated with the contrast attenuation of a Secchi disk in the CVT
could be the fundamental reason why many studies have shown that the estimated
ZSD based on the classical theory agree poorly with observations (Bowers et al.,
2000, Doron et al., 2011, Morel, Huot, et al., 2007, Zhang et al., 2014).
Instead of questioning the assumptions behind the theory, the discrepancies
between the modeled and observed ZSD were often implicitly attributed to
measurement errors or algorithms to estimate the IOPs.

In addition, there have been numerous reports showing c-based empirical models
of ZSD (Aas et al., 2014, Bukata et al., 1988, Davies-Colley and Vant, 1988,
Devlin et al., 2008, Gallegos et al., 2011, Holmes, 1970, Megard and Berman,
1989). Although strong correlations (R2 ~ 0.9 in general) were presented for
each dataset, the slopes between the modeled and measured ZSD show a rather wide
range of variations even for measurements of nearby lakes obtained by the same
researchers (e.g., Bukata et al. (1988)). Sometimes for data from the same
group, the measurements of ZSD < 2 m have to be excluded in order to obtain a
good fit with the c-based formula (Aas et al., 2014). These results indicate
further that there does not exist a single and globally applicable relationship
between ZSD and c (or c + Kd as c is ~ 2–5 times or more larger than Kd) for
global waters (Gordon, 1978). This non-uniformity, again, could be mainly due to
the assumption of Eq. (3).

The sighting of a black disk horizontally just below the surface may be a
special case (Davies-Colley and Vant, 1988, Zaneveld and Pegau, 2003). In this
scenario, while the distance between points A and B could still be relatively
wide (compared to eye resolution), the approximation of Eq. (3) might still be
valid. This may occur because most of the surrounding light over the target and
the background are strong radiances in the horizontal directions as demonstrated
with field observations (Zaneveld and Pegau, 2003).

2.2.2. CONTRAST FOR VISUAL JUDGMENT (CI AND CA)

In the CVT, the contrast for visual judgment (Ci and Ca) is defined as a
relative difference of radiance (or reflectance) between the target and the
background or reference (Eq. (6) or Eq. (9)) (Aas et al., 2014, Duntley, 1952,
Preisendorfer, 1986, Zaneveld and Pegau, 2003). This definition and application
of contrast provide a good measure of the sharpness of a picture, but is
subjective to the use of “background” or “reference” and may result in false
prediction of target sighting as the maximum Ci value is infinite. For instance,
for an alternating-black-and-white disk (usually used in limnology studies), the
Ci value approaches infinite when the black side is considered as the background
or reference. With this formulation for contrast the Secchi disk should be
detectable even at hundreds of meters deep as the calculated apparent contrast
(Eq. (8)) would still be greater than the eye threshold. Or, for a white cup
filled with black coffee, the white bottom of the cup should be always viewable
regardless of the cup's depth as Ci approaches infinite when the black coffee is
considered as the background.

Such contradictions can be further demonstrated with a hypothetical scenario.
Assuming a 90-m deep bottom under clear waters (e.g., those in the Caribbean)
and the bottom is sharply divided into two sides with different bottom types,
one side is black bottom (near 0 reflectivity) and the other side (the target)
is quartz sand bottom (50% reflectivity). The water has a chlorophyll
concentration ([Chl]) of 0.1 mg/m3 and all optical properties following the
Case-1 scheme (Morel & Maritorena, 2001). Fig. 3 shows the subsurface radiance
reflectance (r, sr− 1) of the two sides simulated by Hydrolight (Mobley &
Sundman, 2013), along with Ca calculated between the two sides following
Eq. (6). Value of Ca (see Fig. 3) in the spectral window around 490 nm is ~ 0.9%
(contrast becomes ~ 0.2% when using spectrally-integrated luminance), which
jumps to ~ 5.5% if the bottom is uplifted to 70 m (contrast becomes ~ 1.4% when
using spectrally-integrated luminance). These values are around or higher than
the 0.66% threshold for detection by the human eye as suggested for Secchi disk
sighting (Højerslev, 1986, Preisendorfer, 1986, Tyler, 1968). However, such
visual sightings have never been reported in the literature or news. In
contrast, reports for sighting bright bottoms in clear waters are in the range
of 20–30 m. In addition, these Ca values are much smaller than that would be
predicted by Eq. (8) as the inherent contrast between the two sides approach
infinite with the black side as the background.

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Fig. 3. An example showing how the contrast evaluation in classical underwater
visibility theory would result in likely false prediction of detecting a
half-bright–half-black bottom in deep clear waters. The y-axis to the left shows
the radiance reflectance of clear waters just below the surface (r(0 −), sr− 1)
with a highly reflecting quartz (solid circle) and black (open circle) bottom at
90 m depth. The y-axis to the right shows the apparent contrast (Eq. (6), square
symbol). Open square represents the apparent contrast if the quartz/black bottom
is uplifted to 70 m.

Fundamentally, target sighting by the eye-brain system depends on where there is
sufficient difference in the radiance (or brightness) between the target and the
background (reference) when there is no difference in color (Blackwell, 1946).
This difference in radiance changes with both the incident light and the
difference in reflectivity between the target and the background. On the other
hand, the sensitivity of the human eye also adapts to the intensity of the
ambient light. Therefore, what really matters for this judgment decision under
the photopic vision regime (i.e., light intensity is in a range of usual indoor
to outdoor light) is the difference in reflectivity between the target and the
background, or the so called “brightness constancy” concept of visual perception
(Bartleson and Breneman, 1967, Freeman, 1967). Specifically, it means “…
judgments of brightness have been shown to be dependent not on the quantity of
light entering the eye, but rather on the reflectance of the surface from which
luminous energy is reflected” (Freeman, 1967). This is why we perceive a
black–white checker board nearly the same under either sunshine or tree shadows.
The definition and application of relative difference in radiance or reflectance
as the contrast in the CVT, however, is not consistent with the “brightness
constancy” concept in visual perception. It is following this brightness
constancy concept that a new theory for underwater visibility is formulated.


3. NEW THEORY FOR UNDERWATER VISIBILITY

The ultimate goal of a generalized visibility theory is to express parameter ε
in Eq. (15) as a function of both target size and distance for any light
illumination conditions. This will require not only complex derivations based on
radiative transfer, but also sophisticated and carefully designed field
experiments for different objects under various conditions. Here the problem is
simplified to Secchi disks only and viewed vertically by a human eye in the
photopic vision regime. As discussed in details in Section 2, a regular Secchi
disk (~ 30 cm in diameter) in the viewable range in water is significantly
larger than the size of an image pixel of a human eye (generally d/Z > > angular
resolution and within the FOV of a human eye), thus we may consider this target
as a large bottom for the array of tiny sensors of a human eye when observed
vertically at surface (see Fig. 1). The upwelling radiance just below the
surface from pixels within such a target can then be considered to follow the
relationships established for optically shallow waters (Albert and Mobley, 2003,
Lee et al., 1998, Lyzenga, 1981, Philpot, 1989, Voss et al.,
2003)(18)LT0−=rwEd0−1−e−Kd+KTz+rTEd0−e−Kd+KTz.

Here LT(0 −) represents the radiance signal (after integration from the target
depth to surface) reaching the eye system, with Ed(0 −) the incident downwelling
irradiance just below the surface. rT and rw are the radiance reflectance of a
Secchi disk and background water, respectively. Kd (m− 1) is the depth-averaged
diffuse attenuation coefficient of plane downwelling irradiance, while KT (m− 1)
is the depth-averaged diffuse attenuation coefficient of the upwelling radiance
arising from the target reflection. Here wavelength dependence is omitted for
brevity unless it is necessary.

For adjacent water pixels (outside the glow of the disk where the adjacency
effect is minimal) that serve as the background, the total upwelling signal just
below the surface is(19)Lw0−=rwEd0−.

Because visual perception of a target by the human eye is based on the detection
of enough difference in brightness (radiance) and/or color between the target
and the reference (Blackwell, 1946), the contrast in radiance reaching a human
eye is calculated as(20)LC0−=LT0−−Lw0−.

Applying Eqs. (18), (19), Eq. (20) becomes(21)LC0−=rT−rwEd0−e−Kd+KTz.

This expression is conceptually consistent with Eq. (15) for contrast
attenuation as generally the diffuse attenuation coefficient is a function of
total absorption and backscattering coefficients (Gordon, 1989, Lee et al.,
2005). Similarly (c − ε bf) of Eq. (15) also represents a function of total
absorption and backscattering coefficients as ε approaches 1 for large targets
(Wells, 1973a, Wells, 1973b).


3.1. SECCHI DISK DETECTION BY A HUMAN EYE: SPECTRAL INFORMATION OF A TARGET

Detection of a target by the eye–brain system uses both intensity and color
contrast. In particular, a human eye can distinguish millions of colors in the
visible domain (Judd & Wyszecki, 1975), which translates to thousands of
spectral bands in the 400–700 nm range with each band at 1-nm bandwidth. For
sighting a target in air, while the relative contribution of light from the
target will decrease at each wavelength with the increase of distance, this
reduction is nearly the same across the visible domain, i.e. there will be
little change in the apparent color of the target at distance. In short, the
transmittance in air is spectrally neutral (except for the narrow absorption
bands of atmosphere gases or smokes) in general, and this spectral neutrality
remains nearly the same for different visibility ranges. Consequently
photometric (brightness) quantities are used for the evaluation of contrast for
a white or black target in air, and this approach was adopted in the classical
underwater visibility theory (Preisendorfer, 1986, Zaneveld and Pegau, 2003).

Because of the spectrally selective nature of the absorption and scattering
properties of water constituents (Kirk, 1994, Mobley, 1994), however, spectral
quality is no longer the same for observing a target in water. When a Secchi
disk is lowered in water and observed by a human eye at the surface, the
relative contribution of light from the Secchi disk will decrease with the
increase of depth. This reduction, however, is strongly spectrally dependent and
photons reflected by the Secchi disk that reach a human eye very quickly narrow
to waters' spectrally transparent window. In short, when a Secchi disk is
lowered deeper and deeper, there are changes in both brightness and color
between the area containing the Secchi disk and the adjacent water, and
eventually the difference in color diminishes (Aas et al., 2014) and the
contrast in brightness at this color (wavelength) becomes below the detection
threshold of a human eye. This phenomenon is illustrated in Fig. 4, where
Fig. 4a shows the change of spectral radiance with increasing Secchi disk depth
(simulated with Eq. (18)), while Fig. 4b shows the corresponding colors in CIE
chromaticity diagram (Mobley, 1994) perceived by a human eye and the dominant
wavelengths. For clear water ([Chl] = 0.1 mg/m3) with the disk 5 m below the
surface, there is not only a strong difference in radiance (brightness) between
the target and the background, but also a rather big difference in color, with
the target and the background centered at 486 nm and 478 nm, respectively. When
the disk gets to 40 m below the surface (a depth approaching the limitation of
detection), the difference in radiance (brightness) between the target and the
background is significantly reduced, and the color of the target (479 nm)
approaches that of the background (478 nm). It is therefore reasonable to
hypothesize that the detection of a Secchi disk in water by a human eye depends
on the contrast of brightness in the spectral window of the perceived water
color; whereas this spectral window changes significantly from water to water.
Experimental proof of this hypothesis is beyond the scope of the current work as
it would require sophisticated equipment and field-based measurements in
different water environments. However, such a hypothesis is supported by the
results shown later.

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Fig. 4. Illustration of changes of brightness (radiance) and color when a Secchi
disk is lowered in deep blue water, where the color difference between the two
disappears when the disk is approaching 40 m. (a) Spectral radiance (Lw) of the
water without the Secchi disk (“deep” in the legend, [Chl] = 0.1 mg/m3) and
spectral radiance of the water area containing a Secchi disk (with a reflectance
as 0.85) at different depths (modeled with Eq. (18)). All are under a clear sky
with the Sun at 30° from zenith. (b) The perceived colors by the human eyes and
their dominant wavelengths (annotated with circles) for the corresponding
radiance spectra on the left. Here the x- and y-axes represent the two
normalized values of the three tristimulus values. Note that when the disk is
40-m deep the wavelength (479 nm) corresponding to the human perceived color is
very close to the wavelength (478 nm) from the nearby waters (the background).
The background CIE chromaticity diagram is a courtesy of Wikipedia.

The contrast of brightness at the wavelength corresponding to the color
perceived by a human eye when the Secchi disk starts to disappear can be written
as(22)NCpc0−=rT−rwpcHdpc0−e−Kdpc+KTpcz.

Here NC represents the contrast in luminance recorded by a human eye, Hd is the
equivalent input illuminance, and the superscript “pc” stands for the perceived
color by a human eye and each color is associated with a specific wavelength
(see Fig. 4). Kdpc and KTpc in Eq. (22) are the depth-averaged diffuse
attenuation coefficients of the downwelling plane irradiance and upwelling
radiance arising from the target reflection at the wavelength of the perceived
color, respectively.

Because there have been no measurements or studies of Kd specifically for the
human eye perceived color, we rely on the modeling of Kdpc for waters with a
wide range of chlorophyll concentrations (see Appendix A for details of this
modeling). It is found that Kdpc can be well represented by the minimum Kd
within the visible domain (400–700 nm) (see Fig. 5), which is the attenuation
coefficient of the transparent window of the water column (Kdtr). We use this
diffuse attenuation coefficient to approximate Kdpc and KTpc, respectively, in
the following for easy computation, and rewrite Eq. (22)
as,(23)NCpc0−=rT−rwpcHdpc0−e−Kdtr+KTtrz,with Kdtr and KTtr the depth-averaged
diffuse attenuation coefficient of the downwelling irradiance and upwelling
radiance arising from the target reflection at the transparent window of the
water, respectively.

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Fig. 5. Relationship between diffuse attenuation coefficient at the wavelength
of the perceived color (Kdpc) and diffuse attenuation coefficient of the
transparent window (Kdtr) for waters with [Chl] as 0.03, 0.1, 0.3, 1, 3, 10, and
30 mg/m3. Details of the simulations are provided in Appendix A. These results
suggest that Kdpc can be approximated by Kdtr for the interpretation of Secchi
disk depth.


3.2. SECCHI DISK DETECTION BY A HUMAN EYE: CONTRAST FOR JUDGMENT DECISION

Detection of a target by a human eye requires that NC is greater than a
threshold. On the other hand, this threshold also varies with the intensity of
ambient light (Blackwell, 1946), thus a more applicable evaluation of the
contrast for the target detection is the ratio of NC to Hd. This is consistent
with the “brightness constancy” concept for visual perception under the photopic
vision regime (Bartleson and Breneman, 1967, Freeman, 1967). Therefore a new
apparent contrast (Can, sr− 1) is defined as(24)Can=NCpc0−Hdpc0−.

Applying Eq. (23) we obtain(25)Can0−=rT−rwpce−Kdtr+KTtrz.

This further leads to a new Law of Contrast Reduction for sighting a Secchi disk
as(26)Can=Cine−Kdtr+KTtrz,with Cin the new inherent contrast and defined
as(27)Cin=rT−rwpc.

Compared to the contrast evaluation in the CVT (Eq. (9)), now the contrast is
evaluated as the absolute difference in reflectance between the target and the
background (or reference). With such a formulation, the maximum value of Cin is
limited by the reflectance of the target or the background. For an
alternating-white–black disk as that usually used in limnology studies, the
inherent contrast will then become rT of the white side when the black side is
considered as the reference (assuming black side has a reflectance as 0). This
value is just slightly larger than the contrast between the white disk and the
water, which then explains why the observed ZSD were nearly the same between
using completely white disks and using alternating-white–black disks. In the
following, since reflectance in a narrow spectral band is the same for both
radiometric and photometric quantities, radiometric quantities are employed for
the derivation and discussion of Secchi disk depth.


3.3. NEW MECHANISTIC MODEL FOR SECCHI DISK DEPTH

When Can matches the contrast threshold (Ctr(0 −), sr− 1, i.e. measured in
sub-surface radiance reflectance) for target detection by the eye-imager, the
maximum detectable distance of this disk in the vertical direction or vertical
visibility (Duntley, 1952) becomes(28)ZSD=1Kdtr+KTtrlnrT−rwpcCtr0−.

The diffuse attenuation coefficient (Kd) is generally a function of IOPs and
solar elevation (Gordon, 1989, Lee et al., 2005). For easier data processing,
considering KTtr ≈ 1.5 Kdtr for the upwelling radiance arising from the
reflection by a Lambertian bottom and for the Sun high above the horizon (Kirk,
1991, Lee et al., 1994, Lee et al., 1998), Secchi disk depth described by
Eq. (28) can be approximated as(29)ZSD=12.5KdtrlnrT−rwpcCtr0−.

Eqs. (26), (27), (28) form the core of the new underwater visibility theory and
mechanistic models to interpret Secchi disk depth. Compared to the CVT, the new
visibility theory provides a mechanistic explanation for the numerous
observations over the past many decades that there is a strong inverse
relationship between ZSD and the diffuse attenuation coefficient (Holmes, 1970,
Kratzer et al., 2003, Megard and Berman, 1989, Padial and M.Thomaz, 2008). Also,
with the new visibility theory and model the bottom of a regular-size white cup
filled with black coffee or a 70-m deep half-bright–half-black bottom in clear
waters will not be detectable under the photopic vision regime (because the
inherent contrast is now limited), which is consistent with our observations.


4. VERIFICATION OF THE NEW MODEL WITH INDEPENDENT MEASUREMENTS

The establishment of the new visibility theory and its associate model
(Eqs. (28), (29)) is based entirely on radiative transfer theory. In addition to
the above theoretical arguments, their ultimate verification requires concurrent
measurements of visibilities and water optical properties (spectral rw, Kd and
KT) over a wide dynamic range of environments. This is a prerequisite rarely
met. However, by searching the SeaWiFS Bio-optical Archive and Storage System
(SeaBASS) database, a dataset with 144 measurements containing both ZSD and
Rrs(λ) was found for waters around the USA, with Rrs (sr− 1) being the
above-surface remote-sensing reflectance (Mobley, 1999). In addition, a total of
197 data points having both ZSD and Rrs were compiled from measurements of
oceanic and coastal waters off China (Shang et al., 2011). This combined dataset
covers oceanic, coastal, and lake waters (see Fig. 6a for locations), where ZSD
ranges between 0.1 and 30 m and Rrs values are provided at 412, 443, 488, 532,
555 and 665 nm, with measurements conducted independently by many research
groups.

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Fig. 6. (a) Locations of field measurements, with data obtained from NASA's
SeaBASS archive and measured in oceanic and coastal waters off China. (b)
Comparison between measured and predicted vertical visibility with the
mechanistic model (and its coefficients) developed following the new underwater
visibility theory. The three red points were considered as outliers (the
measured reflectance of these points are extremely different from those of
waters with identical or similar ZSD values) and were excluded in the model
verification. If included, the mean absolute percent difference increases from
18.2% to 19.3%.

Because Secchi disk depth was determined from viewers above the surface, the
radiance contrast in air (LCtr) must be used, which is written
as(30)LCtr0+=tn2LTtr0−+LT−skytr−tn2Lwtr0−+Lw−skytr.

Here t is the radiance transmittance across the water-air interface and n is the
refractive index of seawater; while LT − skytr and Lw − skytr are the
surface-reflected skylight of the target and the reference areas in the
transparent window of water, respectively. Assume LT − skytr and Lw − skytr are
the same during the observations, after converting the radiance contrast to
reflectance contrast (i.e., divided by Edtr(0 +), and note that
Edtr(0 −) = t Edtr(0 +)), there is(31)Can0+=t2n2rT−rwpce−Kdtr+KTtrz.

Lastly the visibility equivalent to Eq. (29) for an above-surface observer
is(32)ZSD=12.5Kdtrlnt2n2rT−rwpcCtr,with Ctr (sr− 1) the detection threshold of
the human eye in air.

To obtain the required Kd information for the estimation of ZSD, the Rrs values
were first fed to the latest version (http://www.ioccg.org/groups/software.html)
of the Quasi-Analytical Algorithm (Lee, Carder, & Arnone, 2002) to obtain total
absorption (a) and backscattering (bb) coefficients. Subsequently Kd at 443,
488, 532, 555 and 665 nm were derived from a and bb following the IOP-based
model (Lee et al., 2005, Lee et al., 2013) by assuming a nominal 30° for solar
zenith angle. The minimum Kd for wavelengths between 443 nm and 665 nm (the
visible domain) was used to represent Kdtr in Eq. (32). Further, rw can be
converted to Rrs following Lee et al. (2002), and Rrspc was taken as the Rrs
value corresponding to the wavelength with minimum Kd. Considering the disk is
white with RT = 0.85 (Preisendorfer, 1986, Tyler, 1968), rT is
RT/π ≈ 0.27 sr− 1. Also, t2/n2 approximates 0.54 for oceanic waters (Austin,
1974, Mobley, 1994), Eq. (32) then
becomes(33)ZSD=12.5MinKd443,488,532,555,665ln0.14−RrspcCtr.

The threshold contrast (Ctr) for sighting a white Secchi disk was determined
based on the measurements of Blackwell (1946). In that experiment, the
difference in brightness (radiance) between the target (BT) and the background
(B0) was calculated as(34)ΔB=BT−B0.

The threshold ΔB was determined at the point when 50% of participants reported
loss of sight of the target. Because the sensitivity of human eyes is adaptable
to ambient light, ΔB is not a constant but rather changes with the surrounding
light intensity. Following the “brightness constancy” concept (Freeman, 1967),
the threshold of contrast in reflectance can be calculated
as(35)Ctr=BT−B0Es,with Es representing the irradiance of surrounding light. In
the experiments, because a majority of the ambient light came from the
background screen (which occupies ~ 5° of the FOV of the human eye), the value
of Es approximated the value of B0 (where the difference between BT and B0 is
very small at the detection threshold) (Blackwell, 1946). The resultant Ctr
values are nearly the same for 3–4 orders of magnitude change in the ambient
light for a given target size under the photopic vision regime (see Table 8 of
Blackwell (1946)), which is consistent with the “brightness constancy” concept.
The replacement of Es by the values of B0 is appropriate for this experimental
setting (Blackwell, 1946), but may not be valid over all observations in the
field as ambient light does affect the adaptation of the human eye. The use of
B0 instead of Es by Blackwell (1946) may also be the reason why researchers
followed this approach to evaluate contrast for visual ranging (Eqs. (6), (9)).

For Secchi disk sighting, where at least a few pixels of the target are required
to make a judgment decision on detection, an average (0.013 sr− 1) was obtained
using the measured Ctr values for sizes between 3.6 and 9.68 arcmin and for
illumination between 10 and 1000 Footlambert (equivalent range is between 34 and
3400 Cd/m2, for the photopic vision regime). This average is then used for Ctr
in Eq. (33), and a comparison between the measured ZSD and the Eq. (33)
calculated ZSD is shown in Fig. 6b.

For this independent ZSD dataset where ZSD is in a range of ~ 0.1 to 30 m
(N = 338, 3 points were excluded as outliers, see Fig. 6b), the mean absolute
relative difference between the estimated and measured ZSD, defined as the
arithmetic average of 2*|ZSD-est − ZSD-mea|/(ZSD-est + ZSD-mea) from all data
pairs, is 18.2%. Linear regression yields a coefficient of determination (R2) of
0.96, with a slope of 1.04 and intercept of ~ 0.2 m (see Fig. 6b). Considering
that the 18.2% absolute relative difference includes both uncertainties in
field-measured ZSD (typically ~ 10% or more) and uncertainties in Kd derived
from non-perfect Rrs (Lee et al., 2013), this performance suggests that the new
model for ZSD (which includes approximations of Kdpc = Kdtr and KTtr = 1.5 Kdtr)
is excellent. In particular, in such a validation, the model and its
parameterization are completely independent from the measurements covering
different regions, thus the results indicate plausible interpretation and
estimation of Secchi disk depth and the model's applicability for global waters.
This agreement in ZSD also indirectly supports the hypothesis that due to the
spectrally-selective attenuation by the water body the eye–brain system likely
uses a narrow band associated with the maximum contrast for the detection of a
Secchi disk.

Furthermore, it is found that the logarithm term on the right side of Eq. (33)
is within a narrow range (2.38 ± 0.03) for such a wide range of waters, which
indicates that, as a rule of thumb, Secchi disk depth in water
approximates(36)ZSD~1Kdtr.

Interestingly, this is similar with the penetration depth for ocean color remote
sensing (Gordon & Mcluney, 1975).


5. DISCUSSION AND CONCLUSIONS

Given the excellent agreement between the model (together with its
parameterization) predictions from the new theory and the independent visibility
measurements from a wide range of environments, it is clear that the new
theoretical model regarding Secchi disk depth is plausible. This robust
performance is further supported through evaluating the diurnally varying ZSD
observed in the field (see Fig. 7). Because Kd varies with sun angle (Gordon,
1989, Kirk, 1984, Lee et al., 2005), the new model provides a consistent
explanation of diurnal changes in ZSD (assuming no change of water properties),
whereas the classical theory could not predict such a variation because c is an
IOP and c is significantly larger than Kd. However, it is desired and necessary
to carry out more, especially controlled, measurements of ZSD, IOPs, and Kd with
changing incident angles for such evaluations. In particular, narrow-band
filters should be used to evaluate the sensitivity of human eyes to contrasts in
different colors (i.e., wavelengths) in the real aquatic environments together
with these measurements.

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Fig. 7. Diurnal variation of Secchi disk depth. (Black) Ratio of ZSD(0°) to
ZSD(θ) for measurements made in Garner Lake, TN (Verschuur, 1997), with data
visually interpreted (average of five persons) from Fig. 3 of Verschuur (1997)
and ZSD(0°) extrapolated from observations around 10°–20°. (Blue) Predicted
ratio of ZSD(0°) to ZSD(θ) based on Eq. (10) (the classical theory), which is an
average (along with standard deviation) for chlorophyll-a concentration 0.5,
1.0, and 3.0 mg/m3, respectively. For each chlorophyll-a concentration, the IOPs
were simulated following the hyperspectral model of Lee et al. (1998), and a
backscattering efficiency of 0.015 was used to convert particle backscattering
coefficient to total scattering coefficient. (Green): Predicted ratio of ZSD(0°)
to ZSD(θ) based on Eq. (29) (the new model), also an average (along with
standard deviation) for chlorophyll-a concentration as 0.5, 1.0, and 3.0 mg/m3,
respectively. IOPs used in the new theory were the same as those for the
classical theory, and spectral Kd was modeled following Lee et al. (2013).

The new theoretical interpretation of Secchi disk depth provides a more
generalized view of visual ranging of “large” objects (but within the field-view
of a human eye), while the subsequent mechanistic model for ZSD will have
profound implications on remote sensing of water transparency and on studies of
aquatic environments. First, because ZSD is a function of Kd, analytical remote
sensing of water transparency on a global scale via ocean color remote sensing
is now possible because spectral Kd is a standard data product of satellite
ocean color missions. In contrast, ZSD mainly depends on c in the classical
theory, where c is impossible to be analytically derived from passive remote
sensing (Gordon, 1993) unless it is highly correlated with Kd. Note that water
transparency has direct impact on a wide range of biogeochemical processes
(e.g., photosynthesis, photo-oxidation, etc.) and bottom substrates such as
coral reefs and sea grasses (Chen et al., 2007, Letelier et al., 2004,
Sathyendranath and Platt, 1988, Vodacek et al., 1997, Weeks et al., 2012,
Yentsch et al., 2002, Zimmerman, 2006). In the past and present, usually this is
done via empirical tuning of regional ZSD algorithms (Chen et al., 2007,
Gallegos et al., 2011, Kratzer et al., 2003, Stock, 2015), but there is always a
challenge to define the spatial and temporal limitations of such local or
regional algorithms. Further, in the past when modern instruments were not
widely available for optical measurements of natural waters, ZSD was the
standard measurement for a wide range of waters, with a large volume of data
collected and archived (Boyce et al., 2012). The availability of such data and
the mechanistic model developed here make it possible to derive new and robust
remote sensing products to study global changes since the late 1970s. Such a
task has been notoriously difficult to accomplish with other data products
(e.g., chlorophyll-a concentration) due to the scarcity of measurements in the
1970s and 1980s, and contrary conclusions were sometimes reached from the same
satellite ocean color measurements (Antoine et al., 2005, Gregg et al., 2005).
Finally, there is a vast warehouse of in-situ data being collected through
Citizen Science Projects (e.g., the Secchi Dip-In,
http://www.secchidipin.org/index.php/monitoring-methods/; the Secchi APP,
http://www1.plymouth.ac.uk/marine/secchidisk/Pages/default.aspx), thus the
robust mechanistic model developed here provides a strong base to link these
measurements with satellite estimations and the ability to compare the quality
of various water bodies.

There have been numerous studies trying to link the attenuation coefficient of
the photosynthetically available radiation (KPAR, m− 1) with ZSD, from which a
wide range of empirical relationships have been reported (Bukata et al., 1988,
Effler, 1988, Hojerslev and Aarup, 2002, Holmes, 1970, Padial and M.Thomaz,
2008, Poole and Atkins, 1929, Tyler, 1968). This lack of algorithm uniformity
via KPAR is a result of two factors: (1) Visual ranging in water likely measures
light in the spectrally transparent window, where KPAR does not provide such
information. Actually the contribution of Kdtr to KPAR is secondary compared to
the contributions from other wavelengths that have higher attenuation
coefficients (e.g., 600–700 nm in oceanic waters; 400–500 nm for coastal turbid
waters), and; (2) because KPAR strongly depends on the depth range used for its
calculation (Lee, 2009, Megard and Berman, 1989, Morel, 1988), there are large
ambiguities in the measured and reported KPAR values. Therefore, to model ZSD of
global waters as a function of KPAR is not supported from the radiative transfer
point of view.

In conclusion, due to the neglect of the target size and the doubtful use of
contrast evaluation for visual judgment by the human eye, the century-old
classical underwater visibility theory is found questionable in interpreting
Secchi disk depth. The new theory tries to resolve both elements, resulting in a
new Law of Contrast Reduction and a new mechanistic model to explain and predict
Secchi disk depth, which is further validated and supported using data
independently collected from a wide range of aquatic environments. Although the
ultimate proof of the new theory regarding ranging of an under-water target by a
human eye would require carefully designed field experiments, the mechanistic
model developed here is expected to significantly improve the monitoring of
water transparency of global waters via ocean color remote sensing and the
findings here would expand our understanding of underwater visibility and visual
ranging in general.


ACKNOWLEDGMENTS

We are in debt to all scientists who provided the valuable field data for
community use. Financial support was provided by the National Natural Science
Foundation of China (No. 41376177, Shang; No. 41471284, Du) and Ministry of
Science and Technology of China (No. 2013BAB04B00, Shang), the National
Aeronautic and Space Administration (NASA) (NNX14AK08G, NNX14AQ47A, NNX14AM15G)
Ocean Biology and Biogeochemistry and Water and Energy Cycle Programs (Lee, Hu),
the National Oceanic and Atmospheric Administration (NOAA) (DG-133E-12-SE-1931)
JPSS VIIRS Ocean Color Cal/Val Project (Lee, Hu), Office of Naval Research (PE
0602435N, Hou, Weidemann), and the University of Massachusetts Boston
(P20120000019675). Comments and suggestions by Curt Mobley and Ron Zaneveld
greatly improved this manuscript.


APPENDIX A. AN ILLUSTRATION OF THE RELATIONSHIP BETWEEN KDPC AND KDTR

Following the radiative transfer theory, it has been found that the
depth-averaged diffuse attenuation coefficient of downwelling plane irradiance
can be expressed as (Gordon, 1989, Lee et al., 2005)(A1)Kdλ=faλ,bbλ,θSwith θS
being the solar zenith angle. a and bb are the absorption and backscattering
coefficients, respectively, and can be expressed as (Mobley,
1994)(A2)aλ=awλ+aphλ+adgλ,(A3)bbλ=bbwλ+bbpλ.

Here the subscripts “w, ph, dg” represent water molecules, phytoplankton
pigments, and the combination of detrital particles and gelbstoff, respectively;
and bbp represents backscattering coefficient of particulates. aw and bbw
spectra are known (Morel, 1974, Pope and Fry, 1997) and considered constants.
aph spectrum in the visible domain (5-nm resolution) can be modeled as a
function of aph(440) (Lee et al., 1998) while aph(440) can be modeled as a
function of [Chl] (Bricaud, Babin, Morel, & Claustre,
1995)(A4)aph440=0.05Chl0.65.

Spectral adg can be expressed as an exponential-decay function of wavelength
with a spectral slope as 0.015 nm− 1 (Bricaud et al., 1981, Carder et al., 1989)
and adg(440) was considered equal to aph(440) in the simulations (Morel,
Claustre, et al., 2007, Morel and Maritorena, 2001).

Spectral bbp can be modeled as (Gordon & Morel, 1983)(A5)bbpλ=bbp440440λ,and
bbp(440) was modeled as the following (Gordon and Morel, 1983, Loisel and Morel,
1998) after considering a 1.5% backscattering/scattering
ratio(A6)bbp440=0.006Chl0.6.a and bb spectra in the visible domain (5-nm
resolution) were then modeled following the above descriptions for [Chl] as
0.03, 0.1, 0.3, 1, 3, 10, and 30 mg/m3, respectively. We further obtained
spectral Kd for θS = 30° from zenith, and obtained Kdtr for each [Chl].

To obtain Kdpc for each [Chl], Lw spectrum was first calculated through
Hydrolight (Mobley & Sundman, 2013) for each pair of spectral a and bb along
with the Sun at 30° from zenith and a clear sky (with default atmospheric
properties in Hydrolight). The Lw spectrum was then converted to a CIE color
following the tristimulus calculations, and a corresponding wavelength was
determined for the perceived color in the CIE chromaticity diagram (see Fig. 4
for examples). The value of Kdpc was further sorted based on this wavelength
from the spectral Kd for each [Chl], and Fig. 5 shows the relationship between
Kdpc and Kdtr from these simulations.

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REFERENCES

 1.  Aas et al., 2014
     E. Aas, J. Høkedal, K. Sørensen
     Secchi depth in the Oslofjord–Skagerrak area: Theory, experiments and
     relationships to other quantities
     Ocean Sciences, 10 (2014), pp. 177-199
     
     CrossRefView in ScopusGoogle Scholar
 2.  Albert and Mobley, 2003
     A. Albert, C.D. Mobley
     An analytical model for subsurface irradiance and remote sensing
     reflectance in deep and shallow case-2 waters
     Optics Express, 11 (2003), pp. 2873-2890
     
     View in ScopusGoogle Scholar
 3.  Antoine et al., 2005
     D. Antoine, A. Morel, H.R. Gordon, V.F. Banzon, R.H. Evans
     Bridging ocean color observations of the 1980s and 2000s in search of
     long-term trends
     Journal of Geophysical Research, 110 (2005), Article C06009
     (doi:01029/02004JC002620)
     Google Scholar
 4.  Arnone et al., 1984
     R.A. Arnone, S.P. Tucker, F.A. Hilder
     Secchi depth atlas of the world coastlines
     Ocean Optics VII, Proc. SPIE 0489, The Society of Photo-Optical
     Instrumentation Engineers, Monterey, CA (1984), 10.1117/1112.943305
     
     Google Scholar
 5.  Austin, 1974
     R.W. Austin
     Inherent spectral radiance signatures of the ocean surface
     S.W. Duntley (Ed.), Ocean Color Analysis, Scripps Inst. Oceanogr, San Diego
     (1974), pp. 1-20
     
     View in ScopusGoogle Scholar
 6.  Bartleson and Breneman, 1967
     C.J. Bartleson, E.J. Breneman
     Brightness perception in complex fields
     Journal of the Optical Society of America, 57 (1967), pp. 953-957
     
     View in ScopusGoogle Scholar
 7.  Binding et al., 2007
     C.E. Binding, J.H. Jerome, R.P. Bukata, W.G. Booty
     Trends in water clarity of the lower great lakes from remotely sensed
     aquatic color
     Journal of Great Lakes Research, 33 (2007), pp. 828-841
     View PDFView articleCrossRefView in ScopusGoogle Scholar
 8.  Blackwell, 1946
     H.R. Blackwell
     Contrast thresholds of the human eye
     Journal of the Optical Society of America, 36 (1946), pp. 624-643
     
     View in ScopusGoogle Scholar
 9.  Bowers et al., 2000
     T.E. Bowers, L.A. Jugan, W.E. McBride, K. Davis-Lunde, A.D. Weidemann, K.
     Mahoney, E. Morgan
     Project GLOW: Results from in-situ validation of the US NAVY's algorithm to
     determine underwater horizontal visibility
     Ocean Optics XV (2000)
     (Monaco)
     Google Scholar
 10. Boyce et al., 2010
     D.G. Boyce, M.R. Lewis, B. Worm
     Global phytoplankton decline over the past century
     Nature, 466 (2010), pp. 591-596
     (doi:510.1038/nature09268)
     
     CrossRefView in ScopusGoogle Scholar
 11. Boyce et al., 2012
     D.G. Boyce, M. Lewis, B. Worm
     Integrating global chlorophyll data from 1890 to 2010
     Limnology and Oceanography: Methods, 10 (2012), pp. 840-852
     Google Scholar
 12. Bricaud et al., 1995
     A. Bricaud, M. Babin, A. Morel, H. Claustre
     Variability in the chlorophyll-specific absorption coefficients of natural
     phytoplankton: Analysis and parameterization
     Journal of Geophysical Research, 100 (1995), pp. 13321-13332
     Google Scholar
 13. Bricaud et al., 1981
     A. Bricaud, A. Morel, L. Prieur
     Absorption by dissolved organic matter of the sea (yellow substance) in the
     UV and visible domains
     Limnology and Oceanography, 26 (1981), pp. 43-53
     
     CrossRefView in ScopusGoogle Scholar
 14. Bukata et al., 1988
     R.P. Bukata, J.H. Jerome, J.E. Bruton
     Relationships among Secchi disk depth, beam attenuation coefficient, and
     irradiance attenuation coefficient for Great Lakes waters
     Journal of Great Lakes Research, 14 (1988), pp. 347-355
     View PDFView articleView in ScopusGoogle Scholar
 15. Carder et al., 1989
     K.L. Carder, R.G. Steward, G.R. Harvey, P.B. Ortner
     Marine humic and fulvic acids: Their effects on remote sensing of ocean
     chlorophyll
     Limnology and Oceanography, 34 (1989), pp. 68-81
     
     CrossRefView in ScopusGoogle Scholar
 16. Carlson, 1977
     R.E. Carlson
     A trophic state index for lakes
     Limnology and Oceanography, 22 (1977), pp. 361-369
     
     CrossRefView in ScopusGoogle Scholar
 17. Chen et al., 2007
     Z. Chen, F.E. Muller-Kargera, C. Hu
     Remote sensing of water clarity in Tampa Bay
     Remote Sensing of Environment, 109 (2007), pp. 249-259
     View PDFView articleView in ScopusGoogle Scholar
 18. Clark, 1990
     R.N. Clark
     Visual Astronomy of the Deep Sky
     Cambridge University Press and Sky Publishing, Cambridge (1990)
     Google Scholar
 19. Curcio et al., 1990
     C.A. Curcio, K.R. Sloan, R.E. Kalina, A.E. Hendrickson
     Human photoreceptor topography
     Journal of Comparative Neurology, 292 (1990), pp. 497-523
     
     CrossRefView in ScopusGoogle Scholar
 20. Davies-Colley and Vant, 1988
     R.J. Davies-Colley, W.N. Vant
     Estimation of optical properties of water from Secchi disk depths
     Water Resources Bulletin, 24 (1988), pp. 1329-1335
     
     CrossRefView in ScopusGoogle Scholar
 21. Devlin et al., 2008
     M.J. Devlin, J. Barry, D.K. Mills, R.J. Gowen, J. Foden, D. Sivyer, P. Tett
     Relationships between suspended particulate material, light attenuation and
     Secchi depth in UK marine waters
     Estuarine, Coastal and Shelf Science, 79 (2008), pp. 429-439
     View PDFView articleView in ScopusGoogle Scholar
 22. Doron et al., 2011
     M. Doron, M. Babin, O. Hembise, A. Mangin, P. Garnesson
     Ocean transparency from space: Validation of algorithms using MERIS, MODIS
     and SeaWiFS data
     Remote Sensing of Environment, 115 (2011), pp. 2986-3001
     View PDFView articleView in ScopusGoogle Scholar
 23. Duntley, 1952
     S.Q. Duntley
     The visibility of submerged objects
     Visibility Lab., Mass. Inst. Tech, Scripps Institution of Oceanography, San
     Diego (1952), p. 74
     Google Scholar
 24. Effler, 1988
     S. Effler
     Secchi disc transparency and turbidity
     Journal of Environmental Engineering, 114 (1988), pp. 1436-1447
     
     View in ScopusGoogle Scholar
 25. Freeman, 1967
     R.B. Freeman
     Contrast interpretation of brightness constancy
     Psychological Bulletin, 67 (1967), pp. 165-187
     
     CrossRefView in ScopusGoogle Scholar
 26. Gallegos et al., 2011
     C.L. Gallegos, P.J. Werdell, C.R. McClain
     Long-term changes in light scattering in Chesapeake Bay inferred from
     Secchi depth, light attenuation, and remote sensing measurements
     Journal of Geophysical Research, 116 (2011), 10.1029/2011JC007160
     
     Google Scholar
 27. Gordon, 1978
     H.R. Gordon
     Some relationships between Secchi depth and inherent optical properties of
     natural waters
     Applied Optics, 17 (1978), pp. 3341-3343
     
     View in ScopusGoogle Scholar
 28. Gordon, 1989
     H.R. Gordon
     Can the Lambert–Beer law be applied to the diffuse attenuation coefficient
     of ocean water?
     Limnology and Oceanography, 34 (1989), pp. 1389-1409
     
     CrossRefView in ScopusGoogle Scholar
 29. Gordon, 1993
     H.R. Gordon
     Sensitivity of radiative transfer to small-angle scattering in the ocean:
     Quantitative assessment
     Applied Optics, 32 (1993), pp. 7505-7511
     
     View in ScopusGoogle Scholar
 30. Gordon and Mcluney, 1975
     H.R. Gordon, W.R. Mcluney
     Estimation of the depth of sunlight penetration in the sea for remote
     sensing
     Applied Optics, 14 (1975), pp. 413-416
     
     View in ScopusGoogle Scholar
 31. Gordon and Morel, 1983
     H.R. Gordon, A. Morel
     Remote assessment of ocean color for interpretation of satellite visible
     imagery: A review
     Springer-Verlag, New York (1983)
     Google Scholar
 32. Gregg et al., 2005
     W.W. Gregg, N.W. Casey, C.R. McClain
     Recent trends in global ocean chlorophyll
     Geophysical Research Letters, 32 (2005), Article L03606
     (doi:03610.01029/02004GL021808)
     Google Scholar
 33. Højerslev, 1986
     N.K. Højerslev
     Visibility of the sea with special reference to the Secchi disc
     M.A. Blizard (Ed.), Ocean Optics VIII, SPIE 637 (1986), pp. 294-305
     
     CrossRefGoogle Scholar
 34. Hojerslev and Aarup, 2002
     N.K. Hojerslev, T. Aarup
     Optical measurements on the Louisiana Shelf off the Mississippi River
     Estuarine, Coastal and Shelf Science, 55 (2002), pp. 599-611
     View PDFView articleView in ScopusGoogle Scholar
 35. Holmes, 1970
     R.W. Holmes
     The Secchi disk in turbid coastal waters
     Limnology and Oceanography, 15 (1970), pp. 688-694
     
     CrossRefView in ScopusGoogle Scholar
 36. Hou et al., 2007
     W. Hou, Z.-P. Lee, A.D. Weidemann
     Why does the Secchi disk disappear? An imaging perspective
     Optics Express, 15 (2007), pp. 2791-2802
     
     View in ScopusGoogle Scholar
 37. Judd and Wyszecki, 1975
     D.B. Judd, G. Wyszecki
     Color in Business, Science and Industry
     Wiley-Interscience, New York (1975)
     Google Scholar
 38. Kirk, 1984
     J.T.O. Kirk
     Dependence of relationship between inherent and apparent optical properties
     of water on solar altitude
     Limnology and Oceanography, 29 (1984), pp. 350-356
     
     CrossRefView in ScopusGoogle Scholar
 39. Kirk, 1991
     J.T.O. Kirk
     Volume scattering function, average cosines, and the underwater light field
     Limnology and Oceanography, 36 (1991), pp. 455-467
     
     CrossRefView in ScopusGoogle Scholar
 40. Kirk, 1994
     J.T.O. Kirk
     Light & Photosynthesis in Aquatic Ecosystems
     University Press, Cambridge (1994)
     Google Scholar
 41. Kratzer et al., 2003
     S. Kratzer, B. Håkansson, C. Sahlin
     Assessing Secchi and photic zone depth in the Baltic Sea from satellite
     data
     Ambio, 32 (2003), pp. 577-585
     
     View in ScopusGoogle Scholar
 42. Lee, 2009
     Z.P. Lee
     KPAR: An optical property associated with ambiguous values
     Journal of Lake Science, 21 (2009), pp. 159-164
     
     CrossRefGoogle Scholar
 43. Lee et al., 2002
     Z.P. Lee, K.L. Carder, R. Arnone
     Deriving inherent optical properties from water color: A multi-band
     quasi-analytical algorithm for optically deep waters
     Applied Optics, 41 (2002), pp. 5755-5772
     
     View in ScopusGoogle Scholar
 44. Lee et al., 1994
     Z.P. Lee, K.L. Carder, S.K. Hawes, R.G. Steward, T.G. Peacock, C.O. Davis
     A model for interpretation of hyperspectral remote sensing reflectance
     Applied Optics, 33 (1994), pp. 5721-5732
     Google Scholar
 45. Lee et al., 1998
     Z.P. Lee, K.L. Carder, C.D. Mobley, R.G. Steward, J.S. Patch
     Hyperspectral remote sensing for shallow waters. 1. A semianalytical model
     Applied Optics, 37 (1998), pp. 6329-6338
     
     View in ScopusGoogle Scholar
 46. Lee et al., 2005
     Z.P. Lee, K.P. Du, R. Arnone
     A model for the diffuse attenuation coefficient of downwelling irradiance
     Journal of Geophysical Research, 110 (2005), 10.1029/2004JC002275
     
     Google Scholar
 47. Lee et al., 2013
     Z.P. Lee, C. Hu, S. Shang, K. Du, M. Lewis, R. Arnone, R. Brewin
     Penetration of UV – Visible solar light in the global oceans: Insights from
     ocean color remote sensing
     Journal of Geophysical Research, 118 (2013), pp. 4241-4255
     (doi:4210.1002/jgrc.20308)
     
     CrossRefView in ScopusGoogle Scholar
 48. Letelier et al., 2004
     R.M. Letelier, D.M. Karl, M.R. Abbott, R.R. Bidigare
     Light driven seasonal patterns of chlorophyll and nitrate in the lower
     euphotic zone of the North Pacific Subtropical Gyre
     Limnology and Oceanography, 49 (2004), pp. 508-519
     
     CrossRefView in ScopusGoogle Scholar
 49. Lewis et al., 1988
     M.R. Lewis, N. Kuring, C. Yentsch
     Global patterns of ocean transparency: Implications for the new production
     of the open ocean
     Journal of Geophysical Research, 93 (1988), pp. 6847-6856
     Google Scholar
 50. Loisel and Morel, 1998
     H. Loisel, A. Morel
     Light scattering and chlorophyll concentration in Case 1 waters: A
     reexamination
     Limnology and Oceanography, 43 (1998), pp. 847-858
     
     CrossRefView in ScopusGoogle Scholar
 51. Lyzenga, 1981
     D.R. Lyzenga
     Remote sensing of bottom reflectance and water attenuation parameters in
     shallow water using aircraft and Landsat data
     International Journal of Remote Sensing, 2 (1981), pp. 71-82
     
     CrossRefView in ScopusGoogle Scholar
 52. Megard and Berman, 1989
     R.O. Megard, T. Berman
     Effects of algae on the Secchi transparency of the southeastern
     Mediterranean Sea
     Limnology and Oceanography, 34 (1989), pp. 1640-1655
     
     CrossRefView in ScopusGoogle Scholar
 53. Middleton, 1952
     W.E.K. Middleton
     Vision Through the Atmosphere
     University of Toronto Press, Toronto (1952)
     Google Scholar
 54. Mobley, 1994
     C.D. Mobley
     Light and Water: Radiative Transfer in Natural Waters
     Academic Press, New York (1994)
     Google Scholar
 55. Mobley, 1999
     C.D. Mobley
     Estimation of the remote-sensing reflectance from above-surface
     measurements
     Applied Optics, 38 (1999), pp. 7442-7455
     
     View in ScopusGoogle Scholar
 56. Mobley and Sundman, 2013
     C.D. Mobley, L.K. Sundman
     HydroLight 5.2 User's Guide
     Sequoia Scientific, Inc., Bellevue, Washington (2013)
     Google Scholar
 57. Morel, 1974
     A. Morel
     Optical properties of pure water and pure sea water
     N.G. Jerlov, E.S. Nielsen (Eds.), Optical Aspects of Oceanography,
     Academic, New York (1974), pp. 1-24
     
     View in ScopusGoogle Scholar
 58. Morel, 1988
     A. Morel
     Optical modeling of the upper ocean in relation to its biogenous matter
     content (Case I waters)
     Journal of Geophysical Research, 93 (1988), pp. 10749-10768
     Google Scholar
 59. Morel, Claustre, et al., 2007
     A. Morel, H. Claustre, D. Antoine, B. Gentili
     Natural variability of bio-optical properties in Case 1 waters: attenuation
     and reflectance within the visible and near-UV spectral domains, as
     observed in South Pacific and Mediterranean waters
     Biogeosciences, 4 (2007), pp. 913-925
     
     CrossRefView in ScopusGoogle Scholar
 60. Morel, Huot, et al., 2007
     A. Morel, Y. Huot, B. Gentili, P.J. Werdell, S.B. Hooker, B.A. Franz
     Examining the consistency of products derived from various ocean color
     sensors in open ocean (Case 1) waters in the perspective of a multi-sensor
     approach
     Remote Sensing of Environment, 111 (2007), pp. 69-88
     View PDFView articleView in ScopusGoogle Scholar
 61. Morel and Maritorena, 2001
     A. Morel, S. Maritorena
     Bio-optical properties of oceanic waters: A reappraisal
     Journal of Geophysical Research, 106 (2001), pp. 7163-7180
     
     View in ScopusGoogle Scholar
 62. Padial and M.Thomaz, 2008
     A.A. Padial, S. M.Thomaz
     Prediction of the light attenuation coefficient through the Secchi disk
     depth: Empirical modeling in two large Neotropical ecosystems
     Limnology, 9 (2008), pp. 143-151
     
     CrossRefView in ScopusGoogle Scholar
 63. Philpot, 1989
     W.D. Philpot
     Bathymetric mapping with passive multispectral imagery
     Applied Optics, 28 (1989), pp. 1569-1578
     
     View in ScopusGoogle Scholar
 64. Poole and Atkins, 1929
     H.H. Poole, W.R.G. Atkins
     Photo-electric measurements of submarine illumination throughout the year
     Journal of the Marine Biological Association of the United Kingdom, 16
     (1929), pp. 297-324
     
     View in ScopusGoogle Scholar
 65. Pope and Fry, 1997
     R. Pope, E. Fry
     Absorption spectrum (380–700 nm) of pure waters: II. Integrating cavity
     measurements
     Applied Optics, 36 (1997), pp. 8710-8723
     
     View in ScopusGoogle Scholar
 66. Preisendorfer, 1976
     R.W. Preisendorfer
     Hydrologic Optics vol. 1: Introduction
     National Technical Information Service, Springfield (1976)
     (Also available on CD, Office of Naval Research)
     Google Scholar
 67. Preisendorfer, 1986
     R.W. Preisendorfer
     Secchi disk science: Visual optics of natural waters
     Limnology and Oceanography, 31 (1986), pp. 909-926
     
     CrossRefView in ScopusGoogle Scholar
 68. Sathyendranath and Platt, 1988
     S. Sathyendranath, T. Platt
     The spectral irradiance field at the surface and in the interior of the
     ocean: A model for applications in oceanography and remote sensing
     Journal of Geophysical Research, 93 (1988), pp. 9270-9280
     
     View in ScopusGoogle Scholar
 69. Shang et al., 2011
     S.L. Shang, Q. Dong, Z.P. Lee, Y. Li, Y.S. Xie, M.J. Behrenfeld
     MODIS observed phytoplankton dynamics in the Taiwan strait: An
     absorption-based analysis
     Biogeosciences, 8 (2011), pp. 841-850
     
     CrossRefView in ScopusGoogle Scholar
 70. Stock, 2015
     A. Stock
     Satellite mapping of Baltic Sea Secchi depth with multiple regressionmodels
     International Journal of Applied Earth Observation and Geoinformation, 40
     (2015), pp. 55-64
     View PDFView articleView in ScopusGoogle Scholar
 71. Tyler, 1968
     J.E. Tyler
     The Secchi disc
     Limnology and Oceanography, 13 (1968), pp. 1-6
     
     CrossRefView in ScopusGoogle Scholar
 72. Verschuur, 1997
     G.L. Verschuur
     Transparency measurements in Garner Lake, Tennessee: the relationship
     between Secchi depth and solar altitude and a suggestion for normalization
     of Secchi depth data
     Journal Lake and Reservoir Management, 13 (1997), pp. 142-153
     
     CrossRefView in ScopusGoogle Scholar
 73. Vodacek et al., 1997
     A. Vodacek, N. Blough, M. DeGrandpre, E. Peltzer, R. Nelson
     Seasonal variation of CDOM and DOC in the Middle Atlantic Bight:
     Terrestrial inputs and photooxidation
     Limnology and Oceanography, 42 (1997), pp. 674-686
     
     CrossRefView in ScopusGoogle Scholar
 74. Voss et al., 2003
     K.J. Voss, C.D. Mobley, L.K. Sundman, J.E. Ivey, C.H. Mazel
     The spectral upwelling radiance distribution in optically shallow waters
     Limnology and Oceanography, 48 (2003), pp. 364-373
     
     CrossRefView in ScopusGoogle Scholar
 75. Weeks et al., 2012
     S. Weeks, J. Werdell, B. Schaffelke, M. Canto, Z.-P. Lee, J. Wilding, G.
     Feldman
     Satellite-derived photic depth on the great barrier reef: Spatio-temporal
     patterns of water clarity
     Remote Sensing, 4 (2012), pp. 3781-3795
     (doi:3710.3390/rs4123781)
     
     CrossRefView in ScopusGoogle Scholar
 76. Wells, 1973a
     W.H. Wells
     Factors affecting long range vision
     P. Halley (Ed.), Optics of the Sea: Interface and In-water Transmission and
     Imaging, Technical Editing and Reproduction Ltd., London, UK (1973), pp.
     4.1.1-4.1.10
     Google Scholar
 77. Wells, 1973b
     W.H. Wells
     Theory of small angle scattering
     P. Halley (Ed.), Optics of the Sea: Interface and In-water Transmission and
     Imaging, Technical Editing and Reproduction Ltd., London, UK (1973), pp.
     3.3.1-3.3.17
     Google Scholar
 78. Wernand, 2010
     M.R. Wernand
     On the history of the Secchi disc
     Journal European Optical Society — Rapid Publications, 5 (2010), Article
     10013s
     
     View in ScopusGoogle Scholar
 79. Yentsch et al., 2002
     C.S. Yentsch, C.M. Yentsch, J.J. Cullen, B. Lapointe, D.A. Phinney, S.W.
     Yentsch
     Sunlight and water transparency: Cornerstones in coral research
     Journal of Experimental Marine Biology and Ecology, 268 (2002), pp. 171-183
     View PDFView articleView in ScopusGoogle Scholar
 80. Zaneveld, 1995
     J.R.V. Zaneveld
     A theoretical derivation of the dependence of the remotely sensed
     reflectance of the ocean on the inherent optical properties
     Journal of Geophysical Research, 100 (1995), pp. 13135-13142
     Google Scholar
 81. Zaneveld and Pegau, 2003
     J.R. Zaneveld, W.S. Pegau
     Robust underwater visibility parameter
     Optics Express, 11 (2003), pp. 2997-3009
     Google Scholar
 82. Zhang et al., 2014
     J.S. Zhang, G.M. Wei, G. Lin, S.L. Shang
     Evaluation of the applicability of an IOP-based algorithm to derive Secchi
     depth
     Journal of Xiamen University (Natural Science), 53 (2014),
     10.6043/j.issn.0438-0479.2014.6004.6001
     
     Google Scholar
 83. Zimmerman, 2006
     R.C. Zimmerman
     Light and photosynthesis in seagrass meadows
     A.W.D. Larkum, R.J. Orth, C.M. Duarte (Eds.), Seagrasses: Biology, Ecology
     and Conservation, Springer, Dordrechet, The Netherlands (2006), pp. 303-321
     
     View in ScopusGoogle Scholar


CITED BY (215)


 * TOWARDS GLOBAL LONG-TERM WATER TRANSPARENCY PRODUCTS FROM THE LANDSAT ARCHIVE
   
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   Water transparency, often quantified using the Secchi disk depth (Zsd), is a
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   linked to phytoplankton dynamics and climate change. In the coastal zones,
   the Zsd variability is attributed to various physical and environmental
   factors, including seasonal monsoons, river outflow, sediment resuspension,
   eutrophication, etc. Moreover, the climatological seasonal Zsd variations of
   22 typical ocean areas and the associated influencing factors are
   investigated on regional scales. The long-term trends of Zsd suggest the
   widespread expansion of oligotrophic waters within the North Pacific, North
   Atlantic, and South Indian Ocean gyres, indicating ongoing ocean
   desertification. The OC-CCI Zsd datasets can be used to build a merged
   centennial time series of Zsd in marine optics by linking to historical
   measurements. By relying on satellite-derived products, global and
   time-varying images offer a more comprehensive understanding of regional to
   global Zsd dynamics.


 * AN OPERATIONAL APPROACH FOR LARGE-SCALE MAPPING OF WATER CLARITY LEVELS IN
   INLAND LAKES USING LANDSAT IMAGES BASED ON OPTICAL CLASSIFICATION
   
   2023, Environmental Research
   Show abstract
   
   Water clarity is a critical parameter of water, it is typically measured
   using the setter disc depth (SDD). The accurate estimation of SDD for
   optically varying waters using remote sensing remains challenging. In this
   study, a water classification algorithm based on the Landsat 5 TM/Landsat 8
   OLI satellite was used to distinguish different water types, in which the
   waters were divided into two types by using the ad(443)/ap(443) ratio. Water
   type 1 refers to waters dominated by phytoplankton, while water type 2 refers
   to waters dominated by non-algal particles. For the different water types, a
   specific algorithm was developed based on 994 in situ water samples collected
   from Chinese inland lakes during 42 cruises. First, the Rrs(443)/Rrs(655)
   ratio was used for water type 1 SDD estimation, and the band combination of
   (Rrs(443)/Rrs(655) - Rrs(443)/Rrs(560)) was proposed for water type 2. The
   accuracy assessment based on an independent validation dataset proved that
   the proposed algorithm performed well, with an R2 of 0.85, mean absolute
   percentage error (MAPE) of 25.98%, and root mean square error (RMSE) of
   0.23 m. To demonstrate the applicability of the algorithm, it was extensively
   evaluated using data collected from Lake Erie and Lake Huron, and the
   estimation accuracy remained satisfactory (R2 = 0.87, MAPE = 28.04%,
   RMSE = 0.76 m). Furthermore, compared with existing empirical and
   semi-analytical SDD estimation algorithms, the algorithm proposed in this
   paper showed the best performance, and could be applied to other satellite
   sensors with similar band settings. Finally, this algorithm was successfully
   applied to map SDD levels of 107 lakes and reservoirs located in the
   Middle-Lower Yangtze Plain (MLYP) from 1984 to 2020 at a 30 m spatial
   resolution, and it was found that 53.27% of the lakes and reservoirs in the
   MLYP generally show an upward trend in SDD. This research provides a new
   technological approach for water environment monitoring in regional and even
   global lakes, and offers a scientific reference for water environment
   management of lakes in the MLYP.


 * A2DWQPE: ADAPTIVE AND AUTOMATED DATA-DRIVEN WATER QUALITY PARAMETER
   ESTIMATION
   
   2023, Journal of Hydrology
   Show abstract
   
   Accurate remote sensing estimation of inland water quality parameters (WQPs)
   plays a crucial role in guiding water resource management. To achieve this,
   researchers have explored various data-driven approaches utilizing machine
   learning (ML) techniques. However, there are two major challenges in WQPs
   estimation for inland waters. Firstly, current data-driven approaches focus
   on building a unified estimation model for an entire study area, which
   underestimates the complex dynamics of water constituents and optical
   properties. Secondly, ML models, particularly neural networks, require
   extensive hyperparameter tuning and are not user-friendly for researchers
   lacking relevant background and experience. In this paper, we propose an
   innovative method called adaptive and automated data-driven water quality
   parameter estimation (A2DWQPE) to address both challenges. Our method
   operates under the assumption that water bodies with similar spectral
   characteristics should share the same WQP estimation model. A2DWQPE is
   composed of three phases. Firstly, water types are automatedly classified by
   unsupervised hierarchical clustering according to spectral similarity. Then,
   optimal Deep Neural Network (DNN) models for estimating WQPs from
   multi-spectral satellite images are customized for each water type utilizing
   Bayesian optimization (BO). Finally, the target WQP is estimated based on the
   type-specific estimates and degree of membership of each water type. To
   evaluate the effectiveness of A2DWQPE, we applied it to estimate Secchi disk
   depth (SDD) in Lake Erie with in situ measurements and Moderate Resolution
   Imaging Spectroradiometer (MODIS) images. The results demonstrate that
   A2DWQPE outperforms the traditional approaches of developing a unified model
   for the entire study area. A2DWQPE achieved high accuracy with coefficient of
   determination (R2) over 0.72 and root mean square error (RMSE) below 1.4 m.
   Our method also outperforms the methods that applied Genetic Algorithm (GA)
   and Particle Swarm Optimization (PSO) instead of BO, and several traditional
   ML algorithms. We firmly believe that A2DWQPE holds great potential for
   accurate inland water quality estimation and will contribute significantly to
   various applications in water quality monitoring and pollution prevention.


 * RELATIVE IMPACT OF ENVIRONMENTAL VARIABLES ON THE LAKE TROPHIC STATE
   HIGHLIGHTS THE COMPLEXITY OF EUTROPHICATION CONTROLS
   
   2023, Journal of Environmental Management
   Show abstract
   
   For the effective management of lakes apart from defining and monitoring
   their current state it is crucial to identify environmental variables that
   are mostly responsible for the nutrient input. We used interpretative machine
   learning to investigate the environmental parameters that influence the
   lake's trophic state and recognize their patterns. We analysed the influence
   of the 25 environmental variables on the commonly used trophic state
   indicators values: total phosphorus (TP), Chlorophyll-a (Chl-a) and Secchi
   depth (SD) of 60 lakes located in the Central European Lowlands. We attempted
   to delineate the lakes into groups due to the influence of common prevailing
   environment variable/variables on the water trophic state reflected by each
   indicator. The results indicated that the relative impact of environmental
   variables on the lake trophic state has an individual hierarchy unique for
   each indicator. The most important are variables related to catchment impact
   on the lake, Ohle ratio (L. catchment area/L. area) for TP and Schindler
   ratio (L. area + L. catchment area)/L. volume for Chl-a and SD. There are
   also few variables strongly influential only for small sub-groups of lakes
   that stand out: lake maximum depth, catchment slope steepness expressed by
   the height standard deviation. The methods used in the study enabled the
   assessment of the character of the influence of the environmental variables
   on the indicator value and revealed that most essential variables (Ohle ratio
   for TP and Schindler ratio for Chl-a and SD) have bimodal distribution with a
   clear threshold value. These findings contribute to a better understanding of
   the drivers shaping the lake trophic status and have implication for planning
   effective management strategies.


 * MONITORING INLAND WATER VIA SENTINEL SATELLITE CONSTELLATION: A REVIEW AND
   PERSPECTIVE
   
   2023, ISPRS Journal of Photogrammetry and Remote Sensing
   Show abstract
   
   Clean Water and Sanitation, the sixth goal of Sustainable Development Goals
   (SDGs 6) is a call for action by the United Nations aiming at balancing the
   water cycle for sustainable life on the earth. For water security and
   regional sustainable development, the quantity and quality of inland waters
   are key variables. Over the past decades, satellite remote sensing offers
   global information about inland water dynamics in a real-time and low-cost
   way. Amongst, the Sentinel satellites designed by the European Space Agency
   can provide global monitoring with a spatial resolution of up to 10 m and
   several days of revisit time. Although Sentinel satellites have been explored
   in inland water monitoring for a long time period, a systematical review on
   the research progress and challenges of their applications has not been
   documented well. This review aims to present a comprehensive review of the
   Sentinel satellites (especially for Sentinel-1, Sentinel-2, and Sentinel-3)
   in monitoring inland water, both on the quantity and quality dimensions,
   including the water extent, level, depth, volume and water quality (e.g.,
   chlorophyll-a, phycocyanin, suspended particulate matter, colored dissolved
   organic matter, and Secchi disk depth). A total of 690 publications are
   involved and the bibliometric quantitative approach is used to analyze the
   areas in which Sentinel instrument excelled and their performance with
   different processing methods. The implications for virtual constellation
   construction using Sentinel satellites from different missions and the
   contribution of a virtual constellation in support of the SDG 6 are also
   discussed. According to the initial investigation and characteristics of
   various satellites, we have proposed several schemes for Sentinel virtual
   constellation toward different missions covering water quantity measurement
   and water quality monitoring, which can maximize the observation capability
   of the satellite. The optimal Sentinel virtual constellation constructing
   scheme theoretically enables a coverage of 10 m spatial resolution and less
   than 2 days temporal resolution for all-weather inland water monitoring.
   These solutions will significantly enhance the observational capacity to
   obtain high-quality, long-term water security parameters in supporting SDG 6.
   Nevertheless, there remains a scarcity of freely available Sentinel-derived
   products, widely applicable data processing algorithms, and unified platform,
   capable of supporting water security monitoring on a broad scale.

View all citing articles on Scopus
Copyright © 2015 Published by Elsevier Inc.


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