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Hue-Angle Product for Low to Medium Spatial Resolution Optical Satellite Sensors

Authors:
  • Royal Netherlands Institute for Sea Research - Royal NIOZ

Abstract and Figures

In the European Citclops project, with a prime aim of developing new tools to involve citizens in the water quality monitoring of natural waters, colour was identified as a simple property that can be measured via a smartphone app and by dedicated low-cost instruments. In a recent paper, we demonstrated that colour, as expressed mainly by the hue angle (α), can also be derived accurately and consistently from the ocean colour satellite instruments that have observed the Earth since 1997. These instruments provide superior temporal coverage of natural waters, albeit at a reduced spatial resolution of 300 m at best. In this paper, the list of algorithms is extended to the very first ocean colour instrument, and the Moderate Resolution Imaging Spectroradiometer (MODIS) 500-m resolution product. In addition, we explore the potential of the hue angle derivation from multispectral imaging instruments with a higher spatial resolution but reduced spectral resolution: the European Space Agency (ESA) multispectral imager (MSI) on Sentinel-2 A,B, the Operational Land Imager (OLI) on the National Aeronautics and Space Administration (NASA) Landsat-8, and its precursor, the Enhanced Thematic Mapper Plus (ETM+) on Landsat-7. These medium-resolution imagers might play a role in an upscaling from point measurements to the typical 1-km pixel size from ocean colour instruments. As the parameter α (the colour hue angle) is fairly new to the community of water remote sensing scientists, we present examples of how colour can help in the image analysis in terms of water-quality products.
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remote sensing
Article
Hue-Angle Product for Low to Medium Spatial
Resolution Optical Satellite Sensors
Hendrik Jan van der Woerd 1,*ID and Marcel Robert Wernand 2ID
1Institute for Environmental Studies (IVM), Water & Climate Risk, VU University Amsterdam,
De Boelelaan 1087, Amsterdam 1081HV, The Netherlands
2Royal Netherlands Institute for Sea Research, Coastal Systems, Marine Optics & Remote Sensing,
P.O. Box 59, Den Burg 1790AB, Texel, The Netherlands; marcel.wernand@nioz.nl
*Correspondence: h.j.vander.woerd@vu.nl; Tel.: +31-020-598-9555
Received: 15 November 2017; Accepted: 24 January 2018; Published: 26 January 2018
Abstract:
In the European Citclops project, with a prime aim of developing new tools to involve
citizens in the water quality monitoring of natural waters, colour was identified as a simple property
that can be measured via a smartphone app and by dedicated low-cost instruments. In a recent paper,
we demonstrated that colour, as expressed mainly by the hue angle (
α
), can also be derived accurately
and consistently from the ocean colour satellite instruments that have observed the Earth since
1997. These instruments provide superior temporal coverage of natural waters, albeit at a reduced
spatial resolution of 300 m at best. In this paper, the list of algorithms is extended to the very
first ocean colour instrument, and the Moderate Resolution Imaging Spectroradiometer (MODIS)
500-m resolution product. In addition, we explore the potential of the hue angle derivation from
multispectral imaging instruments with a higher spatial resolution but reduced spectral resolution:
the European Space Agency (ESA) multispectral imager (MSI) on Sentinel-2 A,B, the Operational
Land Imager (OLI) on the National Aeronautics and Space Administration (NASA) Landsat-8, and its
precursor, the Enhanced Thematic Mapper Plus (ETM+) on Landsat-7. These medium-resolution
imagers might play a role in an upscaling from point measurements to the typical 1-km pixel size from
ocean colour instruments. As the parameter
α
(the colour hue angle) is fairly new to the community
of water remote sensing scientists, we present examples of how colour can help in the image analysis
in terms of water-quality products.
Keywords: hue; colour; CZCS; Landsat-7 and Landsat-8; MERIS; MODIS; MSI; OLCI; SeaWiFS
1. Introduction
Although ocean colour satellite sensors only measure the visual radiation in a limited number of
narrow spectral bands, they are perfectly capable of measuring the colour of natural waters [
1
]. Colour
is a sensation that originates in the human perception of radiation between the wavelengths of 380–720
nm. Since the beginning of the 20th century, the science of human colour perception has been well
studied [
2
,
3
]. Since that time, colour has become more and more important in societal communication,
as is evident from the development in colour printing, colour screens (television, computer monitors,
tablets), digital cameras, and smartphones. Therefore, colour was chosen in the European Citclops
(Citizens’ observatories for coast and ocean optical monitoring) project [
4
] as a primary parameter
to involve citizens in the monitoring of natural waters [
5
]. Involvement of the general public in
the collection of observations of the environment has gained momentum under the term “citizen
science”. These observations might help scientists in their understanding of local processes, and create
awareness and commitment in the environmental stewardship of the general public [68].
At the end of the 19th century, protocols were developed to provide consistent measures of
“water colour” by using human perception to compare colours of natural waters to a predefined
Remote Sens. 2018,10, 180; doi:10.3390/rs10020180 www.mdpi.com/journal/remotesensing
Remote Sens. 2018,10, 180 2 of 18
scale of colours [
9
]. One of these colour comparators is the Forel–Ule (FU) scale, a historical standard
that has recently been recalibrated [
10
,
11
], and is still used to this day [
12
]. This colour-comparator
scale was developed because of technological limitations that existed at the end of the 19th century.
However, new initiatives in participatory science, such as those within the European Union (EU)
Citclops project, indicate that the colour comparison methodology can be transferred to nowadays
measuring techniques using smartphones [
13
], and made fully operational in the EyeOnWater colour
application and supporting website (www.eyeonwater.org/color).
In Citclops, it was considered beneficial for multiple end-users to validate and compare the
localised in-situ data collected with the Eye-On-Water App (EOW) with recent and historical
maps of water composition and colour of a larger region, which are mainly based on satellite
observations. A recent article by Busch et al. provided a demonstration of this integration for
the Ebro Delta. [
14
]. Since no water colour product is offered by the standard processing from
ESA and NASA, Van der Woerd and Wernand [
1
] published algorithms to derive the colour hue
angle (
α
) and FU-scale number accurately and consistently from four spaceborne instruments:
the Moderate Resolution Imaging Spectroradiometer (MODIS), the Sea-viewing Wide Field-of-view
Sensor (SeaWiFS), Medium Resolution Imaging Spectrometer (MERIS), and the Ocean and Land
Colour Instrument (OLCI) on the Sentinel-3 platform. The algorithms are now publicly available and
implemented in the ESA Sentinel Application Platform (SNAP) open software [15].
Ocean colour measurements from space are well suited to assess dynamics in water composition
over a broad range of spatial scales, from global ocean composites down to the basic pixel size,
which is 300 m in the case of MERIS Full Resolution (FR) data. The colour of the open ocean
varies mainly with the chlorophyll-aconcentration (CHL) in phytoplankton [
9
,
16
]. However, most
EOW colour observations are collected close to the shore, where other components contribute to or
dominate the colour of the water column, such as absorption by plant degradation products (Coloured
Dissolved Organic Matter, or CDOM) and Suspended Particulate Matter concentration (SPM), which is
an indicator of turbidity, coastal erosion, riverine flux, and wind or current generated resuspension [
17
].
Busch et al. [
14
] demonstrated that far from the shore in complex coastal waters (such as the
Ebro Delta in northwest Spain), the derived colour of the MERIS FR (300 m) agreed well with the
colour derived from hyperspectral data in optically deep waters. However, MERIS FR data were not
of good quality closer to the shore, where the EoW App might provide the most abundant information.
The degradation of satellite data near shore can be the result of influences by land reflection on
atmospheric correction, sea-bottom reflection, and subscale variability in one pixel. Large gradients
in water composition and a land-sea boundary in one pixel can contribute to the uncertainty in the
retrieval process. Wang et al. [
18
] came up with another solution to the large pixel problem by using
the 500-m resolution product from MODIS, which was initially developed for land applications. It uses
the bands at 466 nm, 553 nm, and 647 nm (No. 3, 4, and 1, respectively), instead of the MODIS bands
8–14 that are measured at a smaller spatial resolution (1 km).
Maybe a different type of sensor can play a role here: the classical land-oriented imagers such as
Landsat observe the Earth with a spatial resolution in the order of 30 m. These instruments have less
spectral resolution than the ocean colour instruments (see Figure 1); the number of bands in the visual
domain is limited (3–5); and also, each band covers a wide range of wavelengths, much wider than the
characteristic 10-nm Full Width at Half Maximum (FWHM) of instruments such as MERIS, MODIS,
and OLCI. Nevertheless, these imagers have been used in many studies of inland and coastal waters,
some with success [1922].
The aim of this paper is to extent the hue angle (
α
) algorithms for 10 spaceborne instruments that
monitor or have monitored the natural waters on Earth. In Van der Woerd and Wernand [
1
], it was
already demonstrated that (α) can be derived consistently form SeaWiFS, MODIS, MERIS, and OLCI,
facilitating the future consistent merging of these four sensors to a global monitoring of colour from
1997 to the present (see also Van der Woerd et al. [
23
]). In this paper, we present results for two
other ocean colour sensors: the MODIS 500-m product, and the observations by the Coastal Zone
Remote Sens. 2018,10, 180 3 of 18
Color Scanner (CZCS), allowing the analysis of measurements over the years 1979–1986 [
24
]. In this
paper, we also investigate the accuracy of the hue angle retrieval from two present medium-resolution
imagers: the multispectral imager (MSI) on Sentinel-2 A,B [
25
], and the Operational Land Imager (OLI)
on Landsat-8 [
26
]. In order to allow a coupling to historical data, the Landsat-8 precursors Landsat-7
ETM is also analysed. Finally, in order to demonstrate and discuss the merit of the true colour products
from these 10 satellites, some general coupling of (
α
) to CHL and the absorption at 440 nm is presented.
Remote Sens. 2018, 10, x FOR PEER REVIEW 3 of 18
Color Scanner (CZCS), allowing the analysis of measurements over the years 1979–1986 [24]. In this
paper, we also investigate the accuracy of the hue angle retrieval from two present medium-
resolution imagers: the multispectral imager (MSI) on Sentinel-2 A,B [25], and the Operational Land
Imager (OLI) on Landsat-8 [26]. In order to allow a coupling to historical data, the Landsat-8
precursors Landsat-7 ETM is also analysed. Finally, in order to demonstrate and discuss the merit of
the true colour products from these 10 satellites, some general coupling of (α) to CHL and the
absorption at 440 nm is presented.
Figure 1. Plot of the available spectral bands in the visual range (400–710 nm) as function of spatial
resolution for seven types of sensors. The multispectral imager (MSI) provides three different
resolution modes, Landsat 8 has one band more than Landsat 7 at 30-m resolution. The Medium
Resolution Imaging Spectrometer (MERIS), Moderate Resolution Imaging Spectroradiometer
(MODIS) and Ocean and Land Colour Instrument (OLCI) provide products at two resolutions.
2. Materials and Methods
2.1. Satellite Colourimetry
The derivation of the colour of natural waters is based on the calculation of the so-called
“Tristimulus” values of the three primaries (X, Y, Z) that specify the colour stimulus of the human eye [4].
We start with the satellite remote sensing reflectance (Rrs), which is often derived from standard
image processing. Rrs is a function of wavelength (λ), and already corrected for atmospheric
influences, the air–water interface, and illumination conditions; it is a quasi-inherent optical property
[27]. The tristimulus values are defined by (example given for red):
()
λλλ
=dxRrsX)(
(1)
The standard colourimetry two degree Colour Matching Functions (CMFs) are represented by
x (red), y (green), and z (blue) (see Figure 2). The CMFs serve as weighting functions for the
determination of the tristimulus values [3]. As ocean colour satellites do not provide hyperspectral
coverage, the full spectrum should be first reconstructed, for example by linear interpolation, based
on the Rrs measured at the spectral bands available. It was shown in Van der Woerd and Wernand
[1] that for ocean-colour instruments, for example MERIS with nine bands, Equation (1) can be
approximated by Equation (2).
=
=
=
9
1
)()(
i
i
iRrsiMX
(2)
Figure 1.
Plot of the available spectral bands in the visual range (400–710 nm) as function of spatial
resolution for seven types of sensors. The multispectral imager (MSI) provides three different resolution
modes, Landsat 8 has one band more than Landsat 7 at 30-m resolution. The Medium Resolution
Imaging Spectrometer (MERIS), Moderate Resolution Imaging Spectroradiometer (MODIS) and Ocean
and Land Colour Instrument (OLCI) provide products at two resolutions.
2. Materials and Methods
2.1. Satellite Colourimetry
The derivation of the colour of natural waters is based on the calculation of the so-called
“Tristimulus” values of the three primaries (X,Y,Z) that specify the colour stimulus of the human
eye [
4
]. We start with the satellite remote sensing reflectance (Rrs), which is often derived from standard
image processing. Rrs is a function of wavelength (
λ
), and already corrected for atmospheric influences,
the air–water interface, and illumination conditions; it is a quasi-inherent optical property [
27
].
The tristimulus values are defined by (example given for red):
X=ZRrs(λ)x(λ)dλ(1)
The standard colourimetry two degree Colour Matching Functions (CMFs) are represented by
x
(red), y(green), and
z
(blue) (see Figure 2). The CMFs serve as weighting functions for the determination
of the tristimulus values [
3
]. As ocean colour satellites do not provide hyperspectral coverage, the full
spectrum should be first reconstructed, for example by linear interpolation, based on the Rrs measured
at the spectral bands available. It was shown in Van der Woerd and Wernand [
1
] that for ocean-colour
instruments, for example MERIS with nine bands, Equation (1) can be approximated by Equation (2).
X=i=9
i=1M(i)Rrs(i)(2)
Remote Sens. 2018,10, 180 4 of 18
This implies that each stimulus value can be calculated as a linear weighted sum of the band
information. M(i) are the linear coefficients that are precalculated for each of the three stimulus values
and each instrument. Basically, M(i) is the integral between band (i
1) and (i+ 1) of the tristimulus
values times the weight (w), which we assume is a linear function of the wavelength between the band
considered (w= 1) and the previous or next band (w= 0). Suppose we want to calculate the integral of
Equation (1) between band 1 at λ1and band 2 at λ2, we can approach the integral by the summation
X=
λ2
λ1
Rrs(λ)x(λ)dλ(3)
The next step is that we approach the Rrs(
λ
) with (
λ1λλ2
) by linear interpolation, such that
Rrs(λ) = Rrs(λ1)×(λλ2)/(λ1λ2)Rrs(λ2)×(λλ1)/(λ1λ2) (4)
Now, if we combine Equations (3) and (4), we see that the summation is split in two components:
X=Rrs(λ1)
λ2
λ1
x(λ)(λλ2)
(λ1λ2)dλRrs(λ2)
λ2
λ1
x(λ)(λλ1)
(λ1λ2)dλ(5)
Since we know the CMF, the summation can be made once we know which two bands to choose.
In this example, the total weight at band 2 (M(2)) consists of the summation in Equation (5) with the
previous band at a shorter wavelength (λ1), and the next band at a larger wavelength (λ3).
Once the tristimulus values (X,Y,Z) have been calculated, the three values are normalised,
and the colour is expressed in the chromaticity coordinates (x,y):
x=X
X+Y+Zy=Y
X+Y+Z(6)
The white point has the coordinates x
w
=y
w
= 1/3. In the (x,y) chromaticity plane, the coordinates
are transformed to polar coordinates with respect to the white point, and the hue angle is derived.
The hue angle (
α
) lies between the vector to a point with coordinates (x
x
w
,y
y
w
) and the positive
x-axis (at y
y
w
= 0), giving higher angles in an anti-clockwise direction (see Figure 2in Van der
Woerd and Wernand [1]). Note that the definition of (α) is different in Wang et al. [18].
α=arctan(yyW,xxW)modulus 2π(7)
Finally, each (
α
) is corrected by a small number (
) to get the best linear relation between the
calculated hyperspectral hue angle and the ocean colour instrument hue angle. This correction
(
) compensates for the spectra of natural waters deviating from the linear interpolation between
detector bands. This is illustrated in Figure 2, which compares the hyperspectral Rrs spectrum and
reconstructed spectrum for open ocean water (CHL = 0.015 mgm
3
), based on the MERIS information
in nine spectral bands.
Remote Sens. 2018,10, 180 5 of 18
Remote Sens. 2018, 10, x FOR PEER REVIEW 5 of 18
Figure 2. Original hyperspectral data plus red squares at the position of MERIS bands (a); the
reconstructed spectrum from Rrs at nine MERIS spectral bands (b); a comparison of the two (c); and
Colour Matching Function (CMF) curves for red, green, and blue that weight the spectral information
to derive the hue angle (d).
2.2. Synthetic and Field Spectra
As a benchmark for algorithm development, we use the synthetic remote sensing reflectance
data from the International Ocean Colour Coordinating Group (IOCCG) in this study [17]. The above
water Rrs is simulated using Hydrolight [28] and a set of inherent optical properties derived from
field measurements, representing a wide range of compositions that occur in natural waters. Details
on this data set can be found in Lee et al. [17] and the IOCCG website [29]. The 500 synthetic Rrs
spectra are provided every 10 nm between 400–800 nm. In this paper, we refer to the “true” or
“hyperspectral” colour when these spectra are interpolated on a 1-nm grid and the hue angle (α) is
calculated based on Equations (1) and (3).
Validation of the algorithms is carried out by analysis of a new hyperspectral Rrs in-situ data
set, based on field measurements collected during the EU Citclops project [4]. Validation is carried
out by comparing the hyperspectral hue angle to the sensor hue angle. The sensor hue angle is
calculated from the extraction of Rrs at the spectral band positions of each sensor. A total of 603
spectra were accumulated in 2013 at 43 sampling stations at the North Sea and Dutch coastal and
inland water bodies. The concentrations of the water quality indicators varied considerably among
the 43 stations, reflecting the widely different water body types that were sampled: clear North Sea
(CHL <0.5 mgm3), turbid coastal North Sea (SPM up to 24 gm3), rivers, eutrophic lakes (CHL up to
55 mgm3), and even peat lakes with extreme CDOM values (g440 up to 3.1 m1). More information
can be found in Novoa et al. [13]. At each station, hyperspectral measurements were carried out using
TriOS-RAMSES hyperspectral radiometers following the NASA protocols [30]. The measurements
included sky radiance (Lsky), upwelling radiance (Lsfc), and incident spectral irradiance (Es). The
radiometers cover the spectral range 320–950 nm, with a spectral resolution of 3.3 nm (Full Width at
Half Maximum, or FWHM) and an accuracy of 0.3 nm. The water-leaving radiance Lw (λ, 0+) at
wavelength (λ) just above the surface (0+) is derived from Equation (8):
LW (λ, 0+) = Lsfc (λ, 0+) ρ × Lsky (λ) (8)
The reflectance factor ρ is a correction factor to compensate for Fresnel reflectance at the
air/water boundary [30], which is defined as the fraction of skylight actually reflected from the wave
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
400 45 0 500 550 60 0 650 70 0 750
Sensitivit y
Wavelength (nm)
R
G
B
d
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
400 45 0 500 55 0 600 650 700 75 0
Rrs
Wavelength (nm)
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
400450500550600650700750
Rrs
Wavelength (nm)
b
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
400 45 0 500 550 60 0 650 70 0 750
Rrs
Wavelength (nm)
c
a
Figure 2.
Original hyperspectral data plus red squares at the position of MERIS bands (
a
);
the reconstructed spectrum from Rrs at nine MERIS spectral bands (
b
); a comparison of the two
(
c
); and Colour Matching Function (CMF) curves for red, green, and blue that weight the spectral
information to derive the hue angle (d).
2.2. Synthetic and Field Spectra
As a benchmark for algorithm development, we use the synthetic remote sensing reflectance
data from the International Ocean Colour Coordinating Group (IOCCG) in this study [
17
]. The above
water Rrs is simulated using Hydrolight [
28
] and a set of inherent optical properties derived from field
measurements, representing a wide range of compositions that occur in natural waters. Details on this
data set can be found in Lee et al. [
17
] and the IOCCG website [
29
]. The 500 synthetic Rrs spectra are
provided every 10 nm between 400–800 nm. In this paper, we refer to the “true” or “hyperspectral”
colour when these spectra are interpolated on a 1-nm grid and the hue angle (
α
) is calculated based on
Equations (1) and (3).
Validation of the algorithms is carried out by analysis of a new hyperspectral Rrs in-situ data set,
based on field measurements collected during the EU Citclops project [
4
]. Validation is carried out by
comparing the hyperspectral hue angle to the sensor hue angle. The sensor hue angle is calculated
from the extraction of Rrs at the spectral band positions of each sensor. A total of 603 spectra were
accumulated in 2013 at 43 sampling stations at the North Sea and Dutch coastal and inland water bodies.
The concentrations of the water quality indicators varied considerably among the 43 stations, reflecting
the widely different water body types that were sampled: clear North Sea (CHL < 0.5 mgm
3
), turbid
coastal North Sea (SPM up to 24 gm
3
), rivers, eutrophic lakes (CHL up to 55 mgm
3
), and even
peat lakes with extreme CDOM values (g440 up to 3.1 m
1
). More information can be found in
Novoa et al. [
13
]. At each station, hyperspectral measurements were carried out using TriOS-RAMSES
hyperspectral radiometers following the NASA protocols [
30
]. The measurements included sky
radiance (L
sky
), upwelling radiance (L
sfc
), and incident spectral irradiance (E
s
). The radiometers cover
the spectral range 320–950 nm, with a spectral resolution of 3.3 nm (Full Width at Half Maximum,
Remote Sens. 2018,10, 180 6 of 18
or FWHM) and an accuracy of 0.3 nm. The water-leaving radiance
Lw(λ, 0+)
at wavelength (
λ
) just
above the surface (0+) is derived from Equation (8):
LW(λ, 0+) = Lsfc (λ, 0+) ρ×Lsky (λ) (8)
The reflectance factor
ρ
is a correction factor to compensate for Fresnel reflectance at the air/water
boundary [
30
], which is defined as the fraction of skylight actually reflected from the wave roughened
(water) surface. In this study, we simply calculated
ρ
by demanding that the water-leaving radiance
at 360 nm equals zero. The intrinsic colour of the water is given by the spectral distribution of the
remote-sensing reflectance Rrs (
λ
, 0+) that is calculated as the ratio of water-leaving radiance
LW(λ, 0+)
over downwelling irradiance ES(λ, 0+):
Rrs = LW(λ, 0+)/ES(λ, 0+) (9)
Again, the intrinsic or true colour was calculated by conversion of the TriOS data to a 1-nm grid,
and calculation of the hyperspectral hue angle by Equations (1), (6), and (7).
2.3. Satellite Simulated Spectra
In Van der Woerd and Wernand [
1
], the hue-angle algorithm was based on the 500 simulated
Rrs spectra for SeaWiFS, MODIS, MERIS, and OLCI. First, the weights M(i) of Equation (2) were
precalculated based on CMFs and the central wavelengths of the bands of each sensor. We refer to
Van der Woerd
and Wernand [
1
] for details. It was essential that these sensors have 10-nm narrow
bands, making sure that each band reliably measures the actual Rrs at that wavelength, since the
variations of Rrs within the band are small. Subsequently, the offset (
) for all of the hue angles
in the interval 30–230 degrees is determined by comparison of the reconstructed sensor spectrum
(Equation (2)) to the original hyperspectral spectrum (Equation (1)).
In this paper, we extend the list of imaging sensors with instruments that all have broad spectral
bands with a radiation detection efficiency that is not uniform within each band. This detection
efficiency is described by the Spectral Response Function (SRF). For example, Figure 3shows the SRF
for the five bands from the MSI sensor on Sentinel-2 [
31
]. Similar functions were used for Landsat-8 [
32
]
and Landsat-7 ETM+ [
32
]. The MODIS 500-m product uses only three wide spectral bands [
33
], which
are different from the standard MODIS band setting that is used for ocean-colour imaging, but prove to
be useful for analysing smaller waters (Wang et al., 2015). The CZCS is the predecessor of the present
ocean-colour instruments, and has a limited set of four narrow spectral bands, plus a broad band in
the Near-Infrared (NIR) [34].
Remote Sens. 2018, 10, x FOR PEER REVIEW 6 of 18
roughened (water) surface. In this study, we simply calculated ρ by demanding that the water-
leaving radiance at 360 nm equals zero. The intrinsic colour of the water is given by the spectral
distribution of the remote-sensing reflectance Rrs (λ, 0+) that is calculated as the ratio of water-leaving
radiance LW (λ, 0+) over downwelling irradiance ES (λ, 0+):
Rrs = LW (λ, 0+)/ES (λ, 0+) (9)
Again, the intrinsic or true colour was calculated by conversion of the TriOS data to a 1-nm grid,
and calculation of the hyperspectral hue angle by Equations (1), (6), and (7).
2.3. Satellite Simulated Spectra
In Van der Woerd and Wernand [1], the hue-angle algorithm was based on the 500 simulated
Rrs spectra for SeaWiFS, MODIS, MERIS, and OLCI. First, the weights M(i) of Equation (2) were
precalculated based on CMFs and the central wavelengths of the bands of each sensor. We refer to
Van der Woerd and Wernand [1] for details. It was essential that these sensors have 10-nm narrow
bands, making sure that each band reliably measures the actual Rrs at that wavelength, since the
variations of Rrs within the band are small. Subsequently, the offset (Δ) for all of the hue angles in
the interval 30–230 degrees is determined by comparison of the reconstructed sensor spectrum
(Equation (2)) to the original hyperspectral spectrum (Equation (1)).
In this paper, we extend the list of imaging sensors with instruments that all have broad spectral
bands with a radiation detection efficiency that is not uniform within each band. This detection
efficiency is described by the Spectral Response Function (SRF). For example, Figure 3 shows the SRF
for the five bands from the MSI sensor on Sentinel-2 [31]. Similar functions were used for Landsat-8
[32] and Landsat-7 ETM+ [32]. The MODIS 500-m product uses only three wide spectral bands [33],
which are different from the standard MODIS band setting that is used for ocean-colour imaging, but
prove to be useful for analysing smaller waters (Wang et al., 2015). The CZCS is the predecessor of
the present ocean-colour instruments, and has a limited set of four narrow spectral bands, plus a
broad band in the Near-Infrared (NIR) [34].
Figure 3. Original hyperspectral data plus green squares at the central positions of MSI bands (a); MSI
measures the visual spectrum in only five wide bands (b); and the reconstructed spectrum will start
to deviate from the original spectrum, especially at green and red wavelengths (c,d).
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
400 45 0 500 55 0 600 65 0 700 750
Sensitivity
Wavelength (nm)
R
G
B
d
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
400 45 0 500 55 0 600 65 0 700 75 0
Rrs
Wavelength (nm)
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
400 45 0 500 55 0 600 65 0 700 75 0
Rrs
Wavelength (nm)
0
0.2
0.4
0.6
0.8
1
1.2
400 45 0 500 55 0 600 650 70 0 750
Normalised response
Wavelength (nm)
MSI SRF
b
ac
Figure 3. Cont.
Remote Sens. 2018,10, 180 7 of 18
Remote Sens. 2018, 10, x FOR PEER REVIEW 6 of 18
roughened (water) surface. In this study, we simply calculated ρ by demanding that the water-
leaving radiance at 360 nm equals zero. The intrinsic colour of the water is given by the spectral
distribution of the remote-sensing reflectance Rrs (λ, 0+) that is calculated as the ratio of water-leaving
radiance LW (λ, 0+) over downwelling irradiance ES (λ, 0+):
Rrs = LW (λ, 0+)/ES (λ, 0+) (9)
Again, the intrinsic or true colour was calculated by conversion of the TriOS data to a 1-nm grid,
and calculation of the hyperspectral hue angle by Equations (1), (6), and (7).
2.3. Satellite Simulated Spectra
In Van der Woerd and Wernand [1], the hue-angle algorithm was based on the 500 simulated
Rrs spectra for SeaWiFS, MODIS, MERIS, and OLCI. First, the weights M(i) of Equation (2) were
precalculated based on CMFs and the central wavelengths of the bands of each sensor. We refer to
Van der Woerd and Wernand [1] for details. It was essential that these sensors have 10-nm narrow
bands, making sure that each band reliably measures the actual Rrs at that wavelength, since the
variations of Rrs within the band are small. Subsequently, the offset (Δ) for all of the hue angles in
the interval 30–230 degrees is determined by comparison of the reconstructed sensor spectrum
(Equation (2)) to the original hyperspectral spectrum (Equation (1)).
In this paper, we extend the list of imaging sensors with instruments that all have broad spectral
bands with a radiation detection efficiency that is not uniform within each band. This detection
efficiency is described by the Spectral Response Function (SRF). For example, Figure 3 shows the SRF
for the five bands from the MSI sensor on Sentinel-2 [31]. Similar functions were used for Landsat-8
[32] and Landsat-7 ETM+ [32]. The MODIS 500-m product uses only three wide spectral bands [33],
which are different from the standard MODIS band setting that is used for ocean-colour imaging, but
prove to be useful for analysing smaller waters (Wang et al., 2015). The CZCS is the predecessor of
the present ocean-colour instruments, and has a limited set of four narrow spectral bands, plus a
broad band in the Near-Infrared (NIR) [34].
Figure 3. Original hyperspectral data plus green squares at the central positions of MSI bands (a); MSI
measures the visual spectrum in only five wide bands (b); and the reconstructed spectrum will start
to deviate from the original spectrum, especially at green and red wavelengths (c,d).
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
400 45 0 500 55 0 600 65 0 700 750
Sensitivity
Wavelength (nm)
R
G
B
d
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
400 45 0 500 55 0 600 65 0 700 75 0
Rrs
Wavelength (nm)
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
400 45 0 500 55 0 600 65 0 700 75 0
Rrs
Wavelength (nm)
0
0.2
0.4
0.6
0.8
1
1.2
400 45 0 500 55 0 600 650 70 0 750
Normalised response
Wavelength (nm)
MSI SRF
b
ac
Figure 3.
Original hyperspectral data plus green squares at the central positions of MSI bands (
a
); MSI
measures the visual spectrum in only five wide bands (
b
); and the reconstructed spectrum will start to
deviate from the original spectrum, especially at green and red wavelengths (c,d).
In case of the ocean-colour instruments, such as MERIS, the number of bands, the bandwidth,
and band positions are such that the full spectrum is reasonably well reconstructed. Therefore,
the weighting with the CMF curves is accurate enough to derive the hue angle (
α
) over the entire range
of natural water colours (see Figure 4). However, in the case of a limited set of broad bands (Figure 3),
it is not possible to reconstruct the underlying Rrs spectrum with high accuracy. In other words,
the band averaging of radiation introduces a larger uncertainty in the folding with the CMF curves. We
have approached this problem as follows: the weights M(see Equation (2)) were precalculated based
on the mean wavelength of each band, i.e., a linear interpolation between the centres of the broad
bands. All of the 500 IOCCG spectra and fields spectra were folded with the SRF of the sensor bands to
derive the Rrs that is measured at each band, and the hue angle is derived from Equations (2) and (3).
The results are compared with the hue angle of the original hyperspectral data.
3. Results
3.1. Sensor Algorithms
The coefficients M(i) of eight sensor configurations are given in Table 1. The entries for MERIS,
MODIS, SeaWiFS, and OLCI on Sentinel-3 have already been published in Van der Woerd and
Wernand [
1
], and the MERIS result serves here as a benchmark for the new calculations. Each
entry is composed as follows: the columns are identified by the central wavelength of each band
in nm (R400, R412,
. . .
). In the second row, the band number is provided, as given in the product
documentation of each instrument. The next three rows contain the coefficients for red (X), green (Y),
and blue (Z). Note that all of the instruments start with R400 and end with R710, because these are the
end points of the spectrum reconstruction. Outside this visual interval, the CMF values are near to
zero. The entries at R400 and R710 do give relevant information, because they complete the picture of
how well the sensor bands are able to measure the three primary colours. For example, MERIS has
bands at 413 nm and 708 nm, and therefore covers all of the colours very well. The R400 and R710
values are less than 1% of the total information in X,Y, and Z. However, if we consider the blue (Z)
R400 value of the CZCS, it becomes clear that a large amount (10.745) is not detected by the CZCS,
which has a first blue band at 443 nm. The importance of this number depends on the underlying
spectrum, for if its radiation at 400 nm is zero, there is no effect. However, if the radiation at 400 nm is
relatively high, we can expect that the CZCS has problems in retrieving the proper hue angle. For all
of the instruments, the weights are such that in case the Rrs is constant, (wavelength-independent
or white) the sum of all of the weights is (106.665; 106.824, 106.335), and the (x,y) values are (0.3335;
0.3340) close to the theoretical white point of (1/3, 1/3).
Figure 4shows the results of the hue angle calculations for six sensors. At the horizontal axis,
this sensor hue angle is plotted, as derived from Equations (2), (6), and (7)). At the vertical axis, the
Remote Sens. 2018,10, 180 8 of 18
deviation from the hyperspectral hue angle (Equations (1), (6), and (7)) is provided. This
is defined
as the hyperspectral (
α
)-sensor (
α
), and is expressed in degrees (
). The shape of the offset (
) is more
or less similar in for all of the sensors: a bell-shaped curve that has the largest offset in the green part of
the spectra around (
α
) 125 degrees. On the one hand, it is expected that the sensors with a limited set of
bands show larger offsets than an instruments such as MERIS, with nine bands situated at well-chosen
wavelengths to cover the dynamics in water-leaving spectra. On the other hand, the offset is not
completely random, and as a first approximation, the correction (
) can be described by a fifth order
polynomial, which is indicated by the drawn blue line. If (a) is the calculated hue angle divided by 100,
can be approximated (for MERIS) by:
=12.05a5+ 88.93a4244.70a3+ 305.241a2164.70a + 28.53 (10)
Remote Sens. 2018, 10, x FOR PEER REVIEW 8 of 18
Figure 4. Deviation in degrees from the hyperspectral hue angle for six instruments. The horizontal
axis gives the hue angle based on the reconstructed spectra (scaled by 100 for practical reasons). Note
that, although the shape follows the same pattern for all of the instruments, the vertical scale is very
different. The drawn line is the fifth order polynomial fit to the data.
The best approximation of the true colour of water is reached by adding this Δ correction to the
results of Equations (2) and (3). In Table 2, the polynomial coefficients are given for all of the
instrument configurations.
-15
-10
-5
0
5
10
15
20
25
30
35
00.511.522.5
hue (°)
Sensor hue (α
S
) / 100
CZCS
-5
-4
-3
-2
-1
0
1
2
3
4
5
00.511.522.5
hue (°)
Sensor hue (α
S
) / 100
MERIS
-20
-10
0
10
20
30
40
50
60
0 0.5 1 1.5 2 2 .5
hue (°)
Sensor hue (α
S
) / 100
MODIS-500
-15
-10
-5
0
5
10
15
20
25
30
0 0.5 1 1.5 2 2 .5
hue (°)
Sensor hue (α
S
) / 100
Sentinel 2 60m
-15
-10
-5
0
5
10
15
20
25
30
00.511.522.5
hue (°)
Sensor hue (α
S
) / 100
Landsat 8 OLI
-20
-10
0
10
20
30
40
50
60
00.511.522.5
hue (°)
Sensor hue (α
S
) / 100
Landsat 7 ETM
Figure 4.
Deviation in degrees from the hyperspectral hue angle for six instruments. The horizontal
axis gives the hue angle based on the reconstructed spectra (scaled by 100 for practical reasons). Note
that, although the shape follows the same pattern for all of the instruments, the vertical scale is very
different. The drawn line is the fifth order polynomial fit to the data.
The best approximation of the true colour of water is reached by adding this
correction to
the results of Equations (2) and (3). In Table 2, the polynomial coefficients are given for all of the
instrument configurations.
Remote Sens. 2018,10, 180 9 of 18
Table 1. Linear coefficients to calculate the chromaticity values (X,Y,Z) for eight sensor configurations.
Sensor and Resolution Weights to Calculate the Three Primaries
MERIS FR and RR λ(nm) R400 R413 R443 R490 R510 R560 R620 R665 R681 R708 R710
Band 1 2 3 4 5 6 7 8 9
X0.154 2.957 10.861 3.744 3.750 34.687 41.853 7.619 0.844 0.189 0.006
Y0.004 0.112 1.711 5.672 23.263 48.791 23.949 2.944 0.307 0.068 0.002
Z0.731 14.354 58.356 28.227 4.022 0.618 0.026 0.000 0.000 0.000 0.000
CZCS λ(nm) R400 R443 R520 R550 R670 R710
Band 1 2 3 4
X2.217 13.237 5.195 50.856 34.797 0.364
Y0.082 4.825 25.217 56.997 19.571 0.132
Z10.745 74.083 21.023 0.462 0.022 0.000
MODIS-500 λ(nm) R400 R466 R553 R647 R710
Band 3 4 1
X5.3754 13.3280 46.3789 40.2774 1.3053
Y0.337 15.756 67.793 22.459 0.478
Z26.827 73.374 6.111 0.024 0.000
S2 MSI-10 m λ(nm) R400 R490 R560 R665 R710
Band 2 3 4
X8.356 12.040 53.696 32.087 0.487
Y0.993 23.122 65.702 16.830 0.177
Z43.487 61.055 1.778 0.015 0.000
S2 MSI-20 m λ(nm) R400 R490 R560 R665 R705 R710
Band 2 3 4 5
X8.356 12.040 53.696 32.028 0.529 0.016
Y0.993 23.122 65.702 16.808 0.192 0.006
Z43.487 61.055 1.778 0.015 0.000 0.000
S2 MSI-60 m λ(nm) R440 R443 R490 R560 R665 R705 R710
Band 1 2 3 4 5
X2.217 11.756 6.423 53.696 32.028 0.529 0.016
Y0.082 1.744 22.289 65.702 16.808 0.192 0.006
Z10.745 62.696 31.101 1.778 0.015 0.000 0.000
Remote Sens. 2018,10, 180 10 of 18
Table 1. Cont.
Sensor and Resolution Weights to Calculate the Three Primaries
Landsat 8 OLI λ(nm) R400 R443 R482 R561 R655 R710
Band 1 2 3 4
X2.217 11.053 6.950 51.135 34.457 0.852
Y0.082 1.320 21.053 66.023 18.034 0.311
Z10.745 58.038 34.931 2.606 0.016 0.000
Landsat 7 ETM+ λ(nm) R400 R485 R565 R660 R710
Band 1 2 3
X7.8195 13.104 53.791 31.304 0.6463
Y0.807 24.097 65.801 15.883 0.235
Z40.336 63.845 2.142 0.013 0.000
Table 2. Polynomial coefficients to calculate the hue-angle offset () for each instrument.
Sensor Resolution (m) Polynomial Coefficients Constant
a5a4a3a2a
MERIS FR and RR 300 and 1200 12.05 88.93 244.70 305.24 164.70 28.53
CZCS 1100 65.95 510.37 1475.80 1927.61 1078.62 202.25
MODIS-500 500 68.36 534.04 1552.76 2042.42 1157.00 223.04
S2 MSI-10 m 10 164.83 1139.90 3006.04 3677.75 1979.71 371.38
S2 MSI-20 m 20 161.23 1117.08 2950.14 3612.17 1943.57 364.28
S2 MSI-60 m 60 65.74 477.16 1279.99 1524.96 751.59 116.56
Landsat 8 OLI 30 52.16 373.81 981.83 1134.19 533.61 76.72
Landsat 7 ETM+ 30 84.94 594.17 1559.86 1852.50 918.11 151.49
Remote Sens. 2018,10, 180 11 of 18
3.2. Algorithm Validation
The set of Rrs spectra from the central North Sea and Dutch coastal and inland waters were used
to validate the hue-angle algorithms. As these hyperspectral data are real measurements, it is expected
that measurement errors and variation in water types within the sample will produce larger errors as
compared to the modelled IOCCG dataset. Again, the hyperspectral hue angle was calculated and
compared with the calculated sensor hue angle. Note that also for these spectra, the SRF of all of the
bands was first folded with the spectrum before Equations (2) and (3) were applied, and corrected with
the sensor-specific
-polynomial. Figure 5shows that this algorithm is able to derive the true colour in
a consistent manner over the full range of potential angles. The slope is close to 1.00, and the offset
remains small. However, what is different is that the scatter around the 1:1 line increases significantly
for sensors such as MODIS-500 and the land imagers Landsat 7 and 8, notably in the green region
(70
–130
). This demonstrates that variations in the underlying hyperspectral distribution have a much
larger effect on the hue angle retrieval for sensors with limited and wide bands.
3.3. Accuracy
In this study, we have two datasets available that can be used to characterise the accuracy of (
α
)
retrieval; the 500 IOCCG spectra, and the 603 field spectra. Figures 4and 5show that the accuracy is
mainly a function of (
α
) itself. Each sensor has intervals in (
α
) that can be covered perfectly with that
particular band setting (such as blue waters in Sentinel 2 MSI), or can only be poorly covered (such
as green waters with Landsat-7 ETM). Therefore, we present in Figure 6the standard deviation in
both datasets in intervals of 30 degrees. The standard deviation is defined for the parameter (sensor-
α
minus hyperspectral-
α
). Note that the results are provided for the interval 37
–230
degrees where the
fifth order polynomial was fitted.
From Figure 6, it can be concluded that MERIS and OLCI perform well over the entire range,
with an average standard deviation for the IOCCG data of around one degree. The other classic
ocean colour sensors—CZCS, SeaWiFS, and MODIS—perform almost as well in the extreme blue
waters (
α
>170
), but have a standard deviation around two degrees for the green–brown colours
(
α
< 140
). The MODIS-500 and Landsat ETM sensors, both three-band instruments, have problems
in covering the whole colour scale. Already, when (
α
> 110
), the band information plus the large
polynomial correction (in the order of 40 degrees) introduce large errors in the hue-angle calculation.
As stated above, field data contain multiple error sources (clouds, sky correction, waves), and indeed
the lower panel in Figure 6shows larger standard deviations than the IOCCG data. First of all, we
must emphasise that the two intervals (170
–200
and 200
–230
) are not representative because of
the limited number of spectra. This number (N=) is given below the interval. However, the field data
contain a wealth of information at all other hue-angle intervals. The hue-angle dependent standard
deviation of the instruments MERIS, OLCI, MODIS, and SeaWiFS follows similar patterns as for the
modelled data, but scaled up by a factor of two. Also, the CZCS, OLI, and MSI do very well, and
have an average standard deviation of 4to 5. The three-band instruments again show larger errors
with increasing hue angles, and seem to be quite inaccurate for all ocean-type waters. However, more
and better data of these blue waters should be used to test the performance of these two sensors in
that range.
Remote Sens. 2018,10, 180 12 of 18
Remote Sens. 2018, 10, x FOR PEER REVIEW 12 of 18
Figure 5. Validation of the hue angle reconstruction for six instruments.
y = 0.9962x + 1.9675
R² = 0.9972
0
50
100
150
200
250
0 50 100 150 200 250
Se nsor hue angle
Hyperspectral hue angle
MERIS
y = 0.9921x + 1.09
R² = 0.9778
0
50
100
150
200
250
0 50 100 150 200 250
Sensor hue angle
Hyperspectral hue angle
CZCS
y = 0.9373x + 1.6507
R² = 0.9462
0
50
100
150
200
250
0 50 100 150 200 250
Sensor hue angle
Hyperspectral hue angle
MODIS-500
y = 0.9842x + 1. 8458
R² = 0.9806
0
50
100
150
200
250
0 50 100 150 200 250
Se nsor hue a ngle
Hyperspectral hue angle
Sentinel 2 60m
y = 0.9638x + 4.1577
R² = 0.9831
0
50
100
150
200
250
0 50 100 150 200 250
Sensor hue angle
Hyperspectral hue angle
Landsat 8 OLI
y = 0.7935x + 11.536
R² = 0.919
0
50
100
150
200
250
0 50 100 150 200 250
Se nsor hue a ngle
Hyperspectral hue angle
Landsat 7 ETM
Figure 5. Validation of the hue angle reconstruction for six instruments.
Remote Sens. 2018,10, 180 13 of 18
Remote Sens. 2018, 10, x FOR PEER REVIEW 13 of 18
Figure 6. Plot of the standard deviation in the parameter (α-sensor minus α-hyperspectral) for nine
sensors. On the horizontal axis, the hyperspectral hue interval is given in degrees, together with the
number of spectra (N) that were used to calculate the standard deviation. The upper panel (a) is based
on the International Ocean Colour Coordinating Group (IOCCG) data, and the lower panel (b) is
based on the field data.
3.4. The Use of Hue
After the retrieval potential of the hue angle by medium-resolution imaging instruments is
presented and characterised, it is important to introduce the value of this parameter, and how it can
be used in the study of biology and ecology of oceans, lakes, and estuaries. First of all, it is a parameter
that can be monitored over time to describe daily to seasonal changes and trends [9]. In Wernand et
al. [9], it was already demonstrated that for open ocean waters (FU number 1 to 9), the colour is
related to the CHL concentration. In the open ocean, CDOM co-varies with CHL, and therefore, the CHL–
(α) relation holds [16]. In Figure 7, the relation between CHL and (α) is presented for the full range of
angles, based on the simulations as described by the IOOCG [17]. Most prominent in the colouration
of natural waters is the combined CHL and CDOM absorption of blue light, plus disturbance by
0
2
4
6
8
37-50
(N=35)
50-80
(N=123)
80-110
(N=64)
110-140
(N=42)
140-170
(N=32)
170-200
(N=44)
200-230
(N=160)
Standard De viation in degrees
MERI S MODIS OLCI Se aWiFS CZCS MODIS -500 MS I OLI ETM
a
0
4
8
12
16
20
37-50
(N=27)
50-80
(N=140)
80-110
(N=171 )
110-140
(N=113)
140-170
(N=144)
170-200
(N=3)
200-230
(N=5)
Standard De viation in degrees
MERI S MODIS OLCI Se aWiFS CZCS MODIS -500 MS I OLI ETM
b
Figure 6.
Plot of the standard deviation in the parameter (
α
-sensor minus
α
-hyperspectral) for nine
sensors. On the horizontal axis, the hyperspectral hue interval is given in degrees, together with the
number of spectra (N) that were used to calculate the standard deviation. The upper panel (
a
) is based
on the International Ocean Colour Coordinating Group (IOCCG) data, and the lower panel (
b
) is based
on the field data.
3.4. The Use of Hue
After the retrieval potential of the hue angle by medium-resolution imaging instruments is
presented and characterised, it is important to introduce the value of this parameter, and how it can be
used in the study of biology and ecology of oceans, lakes, and estuaries. First of all, it is a parameter that
can be monitored over time to describe daily to seasonal changes and trends [
9
]. In
Wernand et al. [9]
,
it was already demonstrated that for open ocean waters (FU number 1 to 9), the colour is related to the
CHL concentration. In the open ocean, CDOM co-varies with CHL, and therefore, the CHL–(
α
) relation
holds [
16
]. In Figure 7, the relation between CHL and (
α
) is presented for the full range of angles, based
on the simulations as described by the IOOCG [
17
]. Most prominent in the colouration of natural
waters is the combined CHL and CDOM absorption of blue light, plus disturbance by absorption and
scattering of SPM. The data in Figure 7have been split into eight classes of CDOM concentration. This
helps in the interpretation of the CHL–(α) relationship for natural waters.
Remote Sens. 2018,10, 180 14 of 18
CDOM consists of very stable molecules that only degrade slowly in the natural environment [
35
].
This makes it a rather well kept quantity that varies little in oceans, seas, and estuaries. For example,
the North Sea CDOM varies between 0.2 and 0.5 m
1
at 440 nm, and we expect that the CHL–(
α
)
relation for that continental shelf sea follows the orange dots in Figure 7. The scatter in this relation is
due to CDOM variations in the interval, plus SPM variations. The second major indicator of ecosystem
health is the indication of light attenuation in the water. Figure 8gives a quick impression of the
relation between total absorption at 440 nm and (
α
). Although the vertical scale is logarithmic and
the scatter is large, the underlying pattern in clearly visible. In order to get a much more detailed
derivation of light attenuation, the underlying absorption and scattering properties must first be
derived from the spectrum [36].
Remote Sens. 2018, 10, x FOR PEER REVIEW 14 of 18
absorption and scattering of SPM. The data in Figure 7 have been split into eight classes of CDOM
concentration. This helps in the interpretation of the CHL–(α) relationship for natural waters.
CDOM consists of very stable molecules that only degrade slowly in the natural environment [35].
This makes it a rather well kept quantity that varies little in oceans, seas, and estuaries. For example,
the North Sea CDOM varies between 0.2 and 0.5 m
1
at 440 nm, and we expect that the CHL–(α)
relation for that continental shelf sea follows the orange dots in Figure 7. The scatter in this relation
is due to CDOM variations in the interval, plus SPM variations. The second major indicator of
ecosystem health is the indication of light attenuation in the water. Figure 8 gives a quick impression
of the relation between total absorption at 440 nm and (α). Although the vertical scale is logarithmic
and the scatter is large, the underlying pattern in clearly visible. In order to get a much more detailed
derivation of light attenuation, the underlying absorption and scattering properties must first be
derived from the spectrum [36].
Figure 7. Relation between the hue angle and chlorophyll-a concentration (CHL) for eight classes of
Coloured Dissolved Organic Matter (CDOM) concentration. The first four classes (0.001 < g440 < 0.1)
can be found in the open ocean, while the next two (0.1 < g440 < 0.5) represent regional seas and
coastal waters. The very CDOM-rich waters (0.5 < g440 < 2.5) can be found in rivers and lakes.
Figure 8. Relation between the hue angle and the absorption (a) of radiation at 440 nm.
Figure 7.
Relation between the hue angle and chlorophyll-aconcentration (CHL) for eight classes of
Coloured Dissolved Organic Matter (CDOM) concentration. The first four classes (0.001 < g440 < 0.1)
can be found in the open ocean, while the next two (0.1 < g440 < 0.5) represent regional seas and coastal
waters. The very CDOM-rich waters (0.5 < g440 < 2.5) can be found in rivers and lakes.
1
Figure 8. Relation between the hue angle and the absorption (a) of radiation at 440 nm.
Remote Sens. 2018,10, 180 15 of 18
4. Discussion
The information provided in Figures 46provide a first impression of the potential for hue-angle
retrieval from a range of optical satellite sensors. Although long underestimated, the CZCS sensor
proved to be a worthy predecessor of the present ocean colour instruments. Although it was limited
to only four narrow bands in the visual, and a wide band in the NIR, the ability to retrieve the hue
angle was surprisingly good for most angles. In a sense, the CZCS is very similar in its optical band
setting to SeaWiFS, but has limited information in the NIR, a region so important for atmospheric
correction. Therefore, the CZCS has had limited success above turbid coastal and inland waters, but is
important for the history of colour [
9
] and trend detection [
24
]. The error analysis presented in Figure 6
shows that the ESA (MERIS and OLCI) and NASA (SeaWiFS and MODIS) remain different in their
accuracy to retrieve the hue for all of the waters with a hue of less than 150 degrees, corresponding
with FU = 7 [10].
Wang et al. [
18
] made the innovative move to use the 500-m resolution product from MODIS
(MOD09 and MYD09 formats) that is derived from three broad bands in the visual (No. 3, 4, and 1).
Many arguments and calculations presented in Wang et al. [
18
] are very similar to the algorithms
presented here. There are some differences that should be pointed out: first of all, the hue angle in this
paper referenced the y= 1/3 line in the xy-chromaticity diagram, while Wang et al. (2015) take the
x= 1/3
axis as zero (
α
= 0
). Second, they refer to the dominant wavelength (see their Figure 4or any
reference book). Third, do they analyse spectra with a dominant wavelength in the interval 555–575 nm,
which is equivalent to our definition of (45
<
α
< 75
). Fourth, they use a linear combination of bands
to calculate the hue angle, plus a small correction that is very similar in magnitude to our
-correction
(See Figure 4). We therefore seem to confirm their results, but also found that for waters with
(α> 110)
,
the limitations of the band setting will introduce large errors; see Figures 46.
The Landsat 7 ETM+ sensor is designed to optimise the observation of land use and land cover,
although recent studies [
37
] reveal that it also performs well in the monitoring of permanent and
temporal variation in the surface of water bodies. In this paper, we have shown that its capacity to
observe the composition in the water is clearly worse than all of the other sensors. Some reconstruction
of (
α
) is possible, but the errors are large (Figures 46). This instrument does have a good track record
on the observation of SPM [
38
], but this based on the absolute Rrs value of the green band around
565 nm, not the radiation distribution. Van Hellemont and Ruddick [
21
] showed that OLI on Landsat
8 is even better suited to observe the SPM patterns in the coastal zone. In this paper, we have also
shown that it performs well in
α
-reconstruction. Both Landsat-7 and Landsat-8 miss the ocean colour
band setting to retrieve separately the concentration of CDOM, CHL, and SPM in the water at 30-m
resolution. However, the hue angle opens the opportunity to study the patterns and evolution of the
hue angle. A combination with the in-situ measurements of these constituents might provide a first
rough estimate of CHL patterns, as was shown in Figure 7.
In a way, the MSI on Sentinel-2 A,B is rather similar to OLI in its ability to retrieve the hue
angle. Figures 46show a remarkably good linear behaviour and low error budget for most natural
waters. What is interesting is that three types of band settings are available that come at different
spatial resolutions. In this paper, we have only presented the five-band results that formally come at
a resolution of 60 m. However, some basic results are given in Table 2for if a different band setting is
tested at higher spatial resolution. In the operational ESA software SNAP, it is possible to interpolate
the observation at a resolution higher than 60 m. The algorithm presented here is implemented in the
latest version of the SNAP (V6.0) [15].
Now that we have linked the remote sensing reflectance to colour by means of the hue angle,
we can ask ourselves: “what is the potential of this parameter?” The hue angle is an addition to
the large suite of parameters that is presently retrieved from the reflection spectra of natural waters.
Figures 7and 8show that, if we have some extra information on the CDOM concentrations of
the water under study, some basic relations between hue and CHL can be used for converting
optical imaging spectrometer data to images of the CHL distribution of lakes and seas. Especially,
Remote Sens. 2018,10, 180 16 of 18
the medium-resolution images such as MSI on Sentinel-2 could in principle use this hue angle to
derive CHL products. However, maybe the value of hue is more related to the quality control of the
processing, the atmospheric correction in particular. Van der Woerd et al. [
23
] showed that errors in the
atmospheric correction of a MERIS scene of the North Sea were easily detected in the hue map. This
information can help to detect errors and identify the impact on the other satellite products, such as the
algal-1 and algal-2 products in MERIS. We are looking forward to a hue-angle analysis of the images
collected by all of the sensors that have been presented in this paper. Overall, when we think of climate
change, and its possible influence on the colour of natural waters, we can now connect the present
with the past through the calculation of the hue angle and FU number from the youngest to the oldest
satellite colour sensor, and even back to the early 1900s.
5. Conclusions
The derivation of the hue angle of natural waters from satellite data is based on the assumption
that the spectral shape of the remote sensing reflectance falls in a group of curves that is described by the
set of 500 IOCCG synthetic spectra. Validation by a set of over 600 spectra from North Sea and Dutch
inland waters confirmed this point, and the hue angles could be well reconstructed from a limited set
of narrow spectral bands, mimicking the band setting of MERIS, MODIS, SeaWiFS, and OLCI. In this
paper, we have extended the analysis to instruments that have fewer and wider spectral bands in
the visual domain (400–710 nm). Again, we see that the hue colour can be derived, but not all of the
colours can be derived with the same accuracy. This is mainly due to the band setting, and not so
much the width of the bands. In simulations that involved only the mean wavelength of each band
(not including the detailed SRF), more or less similar results were obtained (results not shown). This
study started with the requirements that were defined by citizen science for natural waters. The freely
available EyeOnWater Colour app provides point measurements of the colour that could very well be
integrated with the high-temporal ocean-colour sensor data. Indeed,
Busch et al. [14]
made a test for
the Ebro Delta, and they showed that such an integration is possible. However, in that same article,
it also became clear that there is still a (spatial) gap to fill between the position of most app users (more
than 90% of the received data are situated within 1 km from the shoreline), and the first valid pixel
from the shoreline from these ocean-colour sensors. This paper shows that there is great potential to
fill this gap with the new medium-resolution sensors Sentinel-2 MSI and Landsat 8 OLI. Of course,
this study is based on model simulations and ground-truth spectra. The next step is the testing of the
hue-angle derivation in actual satellite observations over a large range of natural waters, from the blue
oligotrophic ocean waters to the brown peat lakes. A start has been made in the analysis of MERIS and
MODIS products from the North Sea in the SNAP environment [
23
]. It is our hope and expectation
that the hue angle parameter will find a place in both ocean-colour science and in citizen science.
Acknowledgments:
The research described in this paper was partly funded by the European project Citclops
under Grant FP7-ENV-308469. The authors acknowledge the stimulating and fruitful cooperation with all scientists
in this wonderful project. We like to thank Marco Peters and Carsten Brockmann from Brockmann Consult for
their initiative to convert the hue colour algorithms into a processor in the SNAP software. H.J. van der Woerd
acknowledges A. Dekker for a visitors grant to CSIRO in Canberra, Australia. The opinions expressed in this paper
are those of the authors and are not necessarily those of Citclops projects partners or the European Commission.
Author Contributions:
M.R. Wernand invented the satellite colour concept and did the handling and quality
control of in-situ data. H.J. van der Woerd develop the algorithms for all sensors. H.J. van der Woerd and
M.R. Wernand wrote the manuscript.
Conflicts of Interest: The authors declare no conflict of interest.
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