Colour Classification of 1486 Lakes across a Wide Range of Optical Water Types

Abstract

Remote sensing by satellite-borne sensors presents a significant opportunity to enhance the spatio-temporal coverage of environmental monitoring programmes for lakes, but the estimation of classic water quality attributes from inland water bodies has not reached operational status due to the difficulty of discerning the spectral signatures of optically active water constituents. Determination of water colour, as perceived by the human eye, does not require knowledge of inherent optical properties and therefore represents a generally applicable remotely-sensed water quality attribute. In this paper, we implemented a recent algorithm for the retrieval of colour parameters (hue angle, dominant wavelength) and derived a new correction for colour purity to account for the spectral bandpass of the Landsat 8 Operational Land Imager (OLI). We used this algorithm to calculate water colour on almost 45,000 observations over four years from 1486 lakes from a diverse range of optical water types in New Zealand. We show that the most prevalent lake colours are yellow-orange and blue, respectively, while green observations are comparatively rare. About 40% of the study lakes show transitions between colours at a range of time scales, including seasonal. A preliminary exploratory analysis suggests that both geo-physical and anthropogenic factors, such as catchment land use, provide environmental control of lake colour and are promising avenues for future analysis.

Full text

remote sensing
Article
Colour Classification of 1486 Lakes across a Wide
Range of Optical Water Types
Moritz K. Lehmann 1, *ID , Uyen Nguyen 1ID , Mathew Allan 1ID and
Hendrik Jan van der Woerd 2ID
1Environmental Research Institute, The University of Waikato, Private Bag 3105, Hamilton 3216,
New Zealand; unguyen@waikato.ac.nz (U.N.); mat.g.allan@gmail.com (M.A.)
2
Institute for Environmental Studies (IVM), Water & Climate Risk, VU University Amsterdam, De Boelelaan
1087, 1081HV Amsterdam, The Netherlands; h.j.vander.woerd@vu.nl
*Correspondence: mlehmann@waikato.ac.nz; Tel.: +64-07-858-5468
Received: 1 July 2018; Accepted: 9 August 2018; Published: 13 August 2018


Abstract:
Remote sensing by satellite-borne sensors presents a significant opportunity to enhance the
spatio-temporal coverage of environmental monitoring programmes for lakes, but the estimation of
classic water quality attributes from inland water bodies has not reached operational status due to the
difficulty of discerning the spectral signatures of optically active water constituents. Determination
of water colour, as perceived by the human eye, does not require knowledge of inherent optical
properties and therefore represents a generally applicable remotely-sensed water quality attribute.
In this paper, we implemented a recent algorithm for the retrieval of colour parameters (hue angle,
dominant wavelength) and derived a new correction for colour purity to account for the spectral
bandpass of the Landsat 8 Operational Land Imager (OLI). We used this algorithm to calculate
water colour on almost 45,000 observations over four years from 1486 lakes from a diverse range of
optical water types in New Zealand. We show that the most prevalent lake colours are yellow-orange
and blue, respectively, while green observations are comparatively rare. About 40% of the study
lakes show transitions between colours at a range of time scales, including seasonal. A preliminary
exploratory analysis suggests that both geo-physical and anthropogenic factors, such as catchment
land use, provide environmental control of lake colour and are promising avenues for future analysis.
Keywords: lakes; Landsat 8; Dominant Wavelength; colour; New Zealand; purity
1. Introduction
The colour of water as perceived by a human observer is intuitively associated with its suitability
for consumption, quality of food collection, fitness for recreation, and aesthetic value, making it
arguably one of the oldest water-quality attributes [
1
–
3
]. Water colour is integral to the concept of
optical water quality, which may be defined as “the extent to which the suitability of water for its
functional role in the biosphere or the human environment is determined by its optical properties” [
4
].
Perceived colour is the physiological sensation originating from the sensitivity of the human eye to
light in the spectral range of the primary colours red, blue, and green e.g., [
5
]. The standard colorimetric
system of the Commission Internationale de l’Éclairage (CIE) [
6
] defines colour mathematically by
weighting the light spectrum with the three mixing curves, or chromaticity curves, specifying the
respective sensitivity of the human eye to the primary colours. In the case of water, a medium that
is not self-luminous, the light perceived by an observer is sunlight scattered back from within the
water mass. This upwelling light is of a different colour than the incident solar radiation due to
wavelength-dependent absorption and scattering of light by water and its constituents [7].
Remote Sens. 2018,10, 1273; doi:10.3390/rs10081273 www.mdpi.com/journal/remotesensing

Remote Sens. 2018,10, 1273 2 of 22
The absorption spectrum of pure water has a minimum in the blue to green range of the visible
spectrum of light and it is much higher at red and near-infrared wavelengths. In addition, scattering
by water molecules is stronger at shorter wavelengths causing more of the incoming blue light to be
directed back at the observer [
8
]. Therefore, water that is characterised by the absence of absorbing and
scattering constituents is blue and is popularly perceived as ‘clean’—an often justifiable judgement.
The main constituents that give water a colour other than blue are phytoplankton pigments, such
as chlorophyll a(chl a), suspended particulate matter (SPM) and coloured dissolved organic matter
(CDOM) [
9
,
10
]. The perceived water colours in hues of green, yellow, and brown are thus generally
related to predominance of optical effects by phytoplankton, SPM, and CDOM, respectively (Figure 1).
In optically simple cases, i.e., when one of these constituents dominates the absorption and scattering
of light, water colour is related to the concentration of the dominant constituent and its inherent
optical properties (IOPs), but in complex mixtures, the spectral signatures are potentially not uniquely
separable [11,12].
Remote Sens. 2018, 10, x FOR PEER REVIEW 2 of 22
The absorption spectrum of pure water has a minimum in the blue to green range of the visible
spectrum of light and it is much higher at red and near-infrared wavelengths. In addition, scattering
by water molecules is stronger at shorter wavelengths causing more of the incoming blue light to be
directed back at the observer [8]. Therefore, water that is characterised by the absence of absorbing
and scattering constituents is blue and is popularly perceived as ‘clean’—an often justifiable
judgement. The main constituents that give water a colour other than blue are phytoplankton
pigments, such as chlorophyll a (chl a), suspended particulate matter (SPM) and coloured dissolved
organic matter (CDOM) [9,10]. The perceived water colours in hues of green, yellow, and brown are
thus generally related to predominance of optical effects by phytoplankton, SPM, and CDOM,
respectively (Figure 1). In optically simple cases, i.e., when one of these constituents dominates the
absorption and scattering of light, water colour is related to the concentration of the dominant
constituent and its inherent optical properties (IOPs), but in complex mixtures, the spectral signatures
are potentially not uniquely separable [11,12].
Figure 1. Chromaticity diagram showing the location of the white point (WP) and the x, chromaticity
coordinates of a range of water types modelled by adding optically active substances to pure water
according to a bio-optical model [13]. Dominant wavelength and distance to the white point (S) are
illustrated using the rightmost round data point. Purity (S*) is the distance S relative to the distance
of the white point to the horseshoe-shaped envelope. The units for the optically active substances are:
chl a (mg m−3), suspended particulate matter (SPM) (mg L−1), and coloured dissolved organic matter
(CDOM) (absorption at 440 nm m−1).
The derivation of concentrations of chl a, SPM and CDOM in inland waters from multispectral
observations such as those recorded by earth-orbiting satellites is an active area of research [7,14–16].
However, the wide range of concentrations of chl a, SPM, CDOM, and their independent variability
hinder efforts to develop general algorithms for the retrieval of these constituents that work across a
wide range of lake systems [17]. Therefore, studies reporting retrieval of inland water quality across
several lakes are tailored to lakes with comparable optical properties [18–20].
Algorithms have been developed for the retrieval of colour information from ocean-colour
sensors and a suite of medium resolution sensors [21,22]. This colour information is based only on
the remote sensing reflectance and can be retrieved accurately and consistently from sensors with
four or more spectral bands in the visual domain. Since colour estimation does not rely on knowledge
Pure water
Dominant wavelength
WP
S, S*
•Chl a: 0.5 –600
SPM: 0.5
CDOM: 0.01
+Chl a: 0.5
SPM: 0.5 –600
CDOM: 0.01
✕Chl a: 0.5
SPM: 0.5
CDOM: 0.01 –40
Figure 1.
Chromaticity diagram showing the location of the white point (WP) and the x, chromaticity
coordinates of a range of water types modelled by adding optically active substances to pure water
according to a bio-optical model [
13
]. Dominant wavelength and distance to the white point (S) are
illustrated using the rightmost round data point. Purity (S*) is the distance Srelative to the distance of
the white point to the horseshoe-shaped envelope. The units for the optically active substances are:
chl a(mg m
−3
), suspended particulate matter (SPM) (mg L
−1
), and coloured dissolved organic matter
(CDOM) (absorption at 440 nm m−1).
The derivation of concentrations of chl a, SPM and CDOM in inland waters from multispectral
observations such as those recorded by earth-orbiting satellites is an active area of research [
7
,
14
–
16
].
However, the wide range of concentrations of chl a, SPM, CDOM, and their independent variability
hinder efforts to develop general algorithms for the retrieval of these constituents that work across a
wide range of lake systems [
17
]. Therefore, studies reporting retrieval of inland water quality across
several lakes are tailored to lakes with comparable optical properties [18–20].
Algorithms have been developed for the retrieval of colour information from ocean-colour sensors
and a suite of medium resolution sensors [
21
,
22
]. This colour information is based only on the remote
sensing reflectance and can be retrieved accurately and consistently from sensors with four or more
spectral bands in the visual domain. Since colour estimation does not rely on knowledge of IOPs of

Remote Sens. 2018,10, 1273 3 of 22
optically active constituents in the water, it provides an objective water quality attribute across any
optical water type.
The goal of this study is to establish a methodology for satellite-based water colour assessment at
the national scale of New Zealand and to demonstrate its usefulness by relating it to geomorphology
and primary drivers of water quality. In New Zealand, versatile geology and climatic gradients have
produced a wide range of lake types [
23
], which, in combination with strong gradients of anthropogenic
pressures, produce a comprehensive range of optical water types [
24
–
26
]. The Freshwater Ecosystems
of New Zealand geodatabase (FENZ) [
27
,
28
] identifies 3820 lakes with a surface area greater than one
hectare (Figure 2), and obviously, traditional monitoring of water quality of a large number of lakes
represents considerable logistical and financial challenges. Data on water quality is available for less
than 2% of New Zealand’s lakes [29–31].
Remote Sens. 2018, 10, x FOR PEER REVIEW 3 of 22
of IOPs of optically active constituents in the water, it provides an objective water quality attribute
across any optical water type.
The goal of this study is to establish a methodology for satellite-based water colour assessment
at the national scale of New Zealand and to demonstrate its usefulness by relating it to
geomorphology and primary drivers of water quality. In New Zealand, versatile geology and climatic
gradients have produced a wide range of lake types [23], which, in combination with strong gradients
of anthropogenic pressures, produce a comprehensive range of optical water types [24–26]. The
Freshwater Ecosystems of New Zealand geodatabase (FENZ) [27,28] identifies 3820 lakes with a
surface area greater than one hectare (Figure 2), and obviously, traditional monitoring of water
quality of a large number of lakes represents considerable logistical and financial challenges. Data on
water quality is available for less than 2% of New Zealand’s lakes [29–31].
Figure 2. Map of New Zealand showing the locations of 3820 lakes according to the Freshwater
Ecosystems of New Zealand (FENZ) geodatabase [27]. The colour of the dots identifies the
geomorphic lake type as per the labels of the pie chart. The pie chart shows the relative distribution
of lake types.
Riverine
Glacial
other
Dam
Aeolian
Shoreline
Volcanic
Peat
Tectonic
Landslide
Geothermal
Figure 2.
Map of New Zealand showing the locations of 3820 lakes according to the Freshwater
Ecosystems of New Zealand (FENZ) geodatabase [
27
]. The colour of the dots identifies the geomorphic
lake type as per the labels of the pie chart. The pie chart shows the relative distribution of lake types.
Remote sensing has the potential to address this knowledge gap by providing current baseline
information and historic data for any lake large enough to be resolved by the footprint of satellite
sensors. Here, we derive water colour using the hue angle method of Woerd and Wernand [
22
]

Remote Sens. 2018,10, 1273 4 of 22
from over 1400 lakes across New Zealand using atmospherically corrected reflectance derived from
Landsat 8 OLI images that were captured between April 2013 and February 2018. We demonstrate the
monitoring capability of this product at the national scale by relating it to expected correlates of water
quality, such as lake depth, elevation, and land use.
2. Materials and Methods
2.1. Study Area
The study area includes the entire land mass of New Zealand (268,021 km
2
) comprised of
two major islands that are located in the southern hemisphere between 34.4
◦
S–46.7
◦
S, centred on
approximately 173
◦
E (Figure 2). This study considers 3820 freshwater bodies larger than 10,000 m
2
(one hectare) as delineated and classified as lakes in the Freshwater Ecosystems of New Zealand
geodatabase [
27
,
28
]. These water bodies were originally derived from the NZMS 260 1:50,000
topographic map series administered by Land Information New Zealand and include ephemeral
flooded areas, wetlands, stormwater retention ponds, and other water bodies, which may not strictly
fit definitions of lakes. We use these 3820 “lakes” as a starting set and derived the central point of each
lake using the Quantum GIS (QGIS) plugin “real centroid”, which forced the centroid to be inside the
lake outline (Figure 3). Subsequently, each centroid was expanded to a circle area of interest (AOI)
of 45 m radius and the AOI’s placement was inspected visually against aerial photos [
32
] to confirm
or adjust its location over a central region of the lake away from islands or obvious shallow regions.
2334 lakes were excluded from the analysis, because the AOI could not be placed in openwater or the
lakes were considered to be optically shallow, leaving a set of 1486 lakes.
Lake Rotokawau Lake Ngaroto Lake Wanaka
(a) (b) (c)
Figure 3.
Landsat 8 Operational Land Imager (OLI) images of three example lakes showing the 3-by-3
pixel area for which data was extracted. The outlines shown were taken from the FENZ geodatabase.
North is up in all images. (
a
) Lake Rotokawau (volcanic lake) on 3 March 2017; (
b
) Lake Ngaroto (peat
lake) on 2 March 2016; and, (c) Lake Wanaka (glacial lake) on 3 March 2017.
2.2. Satellite Imagery Acquisition and Processing
We chose Landsat 8 Operational Land Imager (OLI) data, because the 30-m pixel resolution allows
for the observation of lakes down to about 1 ha size. Furthermore, the Landsat series of satellites
provides the longest continuous time series of earth observations from space, allowing for retrospective
analysis of colour trends in future work. The OLI collects data in eight bands at 30 m resolution and
one panchromatic band at 15 m resolution [
33
]. 1521 OLI images that were captured along paths 71 to
75 and rows 84 through 93, between 12 April 2013, and 12 February 2018 from the Tier 1 collection
were downloaded from the USGS Earth Resources Observation and Science (EROS) Center Science
Processing Architecture (ESPA) on-demand interface.
The Tier 1 collection provides surface reflectance,
ρ
(sr
−1
), at each band.
ρ
is a level-2 product
resulting from atmospheric correction with the Landsat Surface Reflectance Code (LaSRC), which

Remote Sens. 2018,10, 1273 5 of 22
uses the coastal aerosol band and auxiliary climate data from MODIS with a radiative transfer model
designed for Landsat 8 [
34
,
35
]. We approximate surface remote sensing reflectance (R, sr
−1
) as
ρ
/
π
and note that this introduces some error as
ρ
includes contributions from specular reflectance at the
water surface (glint) [
36
] and from whitecaps [
37
]. However, as these contributions are spectrally flat,
they have an effect on purity, but not on dominant wavelength (see further down for definition of
these terms). Limitations of this approximation are presented in the Discussion. The Tier 1 collection
also includes quality attributes for each pixel determined using the CFMask algorithm, which we used
to exclude pixels with values indicating cloud, adjacent shadow, cloud shadow, and cirrus [
34
,
38
,
39
].
An additional NDWI [
40
] mask was applied to reduce the chance for data from optically shallow water.
Lake reflectance of each band was calculated by averaging R(
λ
) from 9 to 16 pixels, which intersected
the AOI of each lake. Pixels for which reflectance in any of the bands were negative or greater than
one were excluded from the averaging. This procedure generated a file with 44,947 observations for
1486 New Zealand lakes between 2013 and 2018.
The number of good observations, i.e., cloud-free with reflectance values between zero and
one, was recorded for each lake. In cases where there are duplicate observations from the zone of
row-overlap, only the data from the earlier scene was retained. We define the expected number of
observations per year by Landsat OLI for every lake by dividing the number of good observations by
4.08, which is the number of years in our data set.
2.3. Calculation of Chromaticity
Chromaticity analysis describes the colour of an object as perceived by the human eye using three
colour primaries X,Y, and Z, also known as tristimulus values [
12
]. The tristimulus values X,Y, and
Zare integrals of the weighted upwelling reflectance spectrum R(
λ
) within the region to which the
human eye is sensitive (390–740 nm). The weighting functions
x(λ)
,
y(λ)
and
z(λ)
are the colour
mixture values, which describe the wavelength dependence of human vision for red, green, and blue
light, respectively [6,12]:
X=Z740
390 R(λ)x(λ)d(λ)(1)
Y=Z740
390 R(λ)y(λ)d(λ)(2)
Z=Z740
390 R(λ)z(λ)d(λ)(3)
The chromaticity coordinates x,yand zare normalisations of the individual tristimulus values,
as follows:
x=X
X+Y+Z(4)
y=Y
X+Y+Z(5)
z=Z
X+Y+Z(6)
with x+y+z= 1.
Satellite remote sensing data from current satellite-borne sensors do not have full spectral coverage,
but provide remote sensing reflectance in a limited number of bands of 10 nm wavelength or wider.
Landsat 8 OLI has four bands in the visible part of the spectrum that are centred at 443 nm (narrow blue,
coastal/aerosol), 482 nm (blue), 562 nm (green), and 655 nm (red) [
41
,
42
], and therefore, the estimation
of the true colour of upwelling light requires assumptions about the full spectral distribution of remote
sensing reflectance. Early chromaticity mapping used radiances from the multispectral scanner carried
on Landsat missions 1 to 5 in spectral bands of 100 nm width in the green, red, and near infrared

Remote Sens. 2018,10, 1273 6 of 22
regions of the spectrum, and these radiances were assumed to be analogous to the tristimulus values
X,Y, and Z[12,43,44].
Van der Woerd and Wernand [
21
,
22
] describe that in first approximation the tristimulus values
can be reconstructed based on a linear weighted sum of the bands R, in this case, the four bands of OLI
X=11.053 R(443) + 6.950 R(482) + 51.135 R(561) + 34.457 R(655)(7)
Y=1.320 R(443) + 21.053 R(482) + 66.023 R(561) + 18.034 R(655)(8)
Z=58.038 R(443) + 34.931 R(482) + 2.606 R(561) + 0.016 R(655)(9)
Chromaticity coordinates are then calculated from the X,Y, and Zusing Equations (4)–(6); the
perceived colour of a given reflectance spectrum is defined by any pair of chromaticity coordinates and
can be plotted in a chromaticity diagram, e.g., xand y, as shown in Figure 1. The horseshoe-shaped
envelope (locus) is constructed from the xand yvalues calculated from monochromatic light at
each wavelength and therefore the space enclosed in it encompass all possible chromaticity values.
The centre of the chromaticity diagram is the “white point” at which x=y=z=
1/3
. Any pair of
x,ycoordinates of an upwelling radiance spectrum can be identified by the hue angle (
α
), which is
the angle of the line drawn from the white point to the x,ycoordinate and the x-axis of the plot in
anticlockwise direction. We calculate
α
using the four quadrant arctangent function atan2 in Matlab
(Equation (7) in [22]):
α= arctan(y−1/3, x−1/3) modulus 2π. (10)
As described in Van der Woerd and Wernand [
22
], the spectral bandpass of OLI causes an offset
between
−
5 and +20 degrees relative to the hyperspectral hue angle. The offset is not completely
random, and as a first approximation, the correction (
∆α
) can be described by a fifth order polynomial,
which is indicated by the grey line in Figure 4a. If ais the calculated hue angle divided by 100,
∆α
can
be approximated (for OLI) by:
∆α=−52.16a5+ 373.81a4−981.83a3+ 1134.19a2−533.61a+ 76.72 (11)
Remote Sens. 2018, 10, x FOR PEER REVIEW 6 of 22
distribution of remote sensing reflectance. Early chromaticity mapping used radiances from the
multispectral scanner carried on Landsat missions 1 to 5 in spectral bands of 100 nm width in the
green, red, and near infrared regions of the spectrum, and these radiances were assumed to be
analogous to the tristimulus values X, Y, and Z [12,43,44].
Van der Woerd and Wernand [21,22] describe that in first approximation the tristimulus values
can be reconstructed based on a linear weighted sum of the bands R, in this case, the four bands of
OLI
X = 11.053 𝑅(443)+6.950 𝑅(482)+51.135 𝑅(561)+34.457 𝑅(655)
(7)
𝑌 = 1.320 𝑅(443)+21.053 𝑅(482) +66.023 𝑅(561)+18.034 𝑅(655)
(8)
𝑍 = 58.038 𝑅(443)+34.931 𝑅(482) +2.606 𝑅(561)+0.016 𝑅(655)
(9)
Chromaticity coordinates are then calculated from the X, Y, and Z using Equations (4)–(6); the
perceived colour of a given reflectance spectrum is defined by any pair of chromaticity coordinates
and can be plotted in a chromaticity diagram, e.g., x and y, as shown in Figure 1. The horseshoe-
shaped envelope (locus) is constructed from the x and y values calculated from monochromatic light
at each wavelength and therefore the space enclosed in it encompass all possible chromaticity values.
The centre of the chromaticity diagram is the “white point” at which x = y = z = ⅓. Any pair of x, y
coordinates of an upwelling radiance spectrum can be identified by the hue angle (), which is the
angle of the line drawn from the white point to the x, y coordinate and the x-axis of the plot in
anticlockwise direction. We calculate  using the four quadrant arctangent function atan2 in Matlab
(Equation 7 in [22]):
 = arctan(y − 1/3, x −1/3) modulus 2
(10)
As described in Van der Woerd and Wernand [22], the spectral bandpass of OLI causes an offset
between −5 and +20 degrees relative to the hyperspectral hue angle. The offset is not completely
random, and as a first approximation, the correction (Δ) can be described by a fifth order
polynomial, which is indicated by the grey line in Figure 4a. If a is the calculated hue angle divided
by 100, Δ can be approximated (for OLI) by:
 = −52.16a5 + 373.81a4 − 981.83a3 + 1134.19a2 − 533.61a + 76.72
(11)
Figure 4. (a) Deviation in degrees from the hyperspectral hue angle for the OLI instrument. The
horizontal axis gives the hue angle based on the reconstructed spectra (scaled by 100 for practical
reasons). The drawn line is the fifth order polynomial fit to the data. (b) Deviation in distance (S) of
the hyperspectral distance from the universal white point.
 is based on calculations using semi-empirical model simulations published by the
International Ocean Colour Coordinating Group [9]. The above-water R(λ) is simulated using
Hydrolight [45] 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 [9] and the IOCCG website [46]. The 500 synthetic R spectra are provided every 10 nm
Figure 4.
(
a
) Deviation in degrees from the hyperspectral hue angle for the OLI instrument.
The horizontal axis gives the hue angle based on the reconstructed spectra (scaled by 100 for practical
reasons). The drawn line is the fifth order polynomial fit to the data. (
b
) Deviation in distance (S) of the
hyperspectral distance from the universal white point.
∆α
is based on calculations using semi-empirical model simulations published by the International
Ocean Colour Coordinating Group [9]. The above-water R(λ) is simulated using Hydrolight [45] 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 [
9
] and the IOCCG
website [
46
]. The 500 synthetic Rspectra are provided every 10 nm between 400–800 nm. In this paper,
we refer to the “hyperspectral” colour when these spectra are interpolated on a 1-nm grid and
α
is

Remote Sens. 2018,10, 1273 7 of 22
calculated based on Equations (1)–(6). The observations by OLI are simulated by folding the 1-nm
spectra with the detector efficiency for each band, as described by the spectral response function of the
OLI on Landsat 8 [47].
The distance (S) of a hyperspectral colour on the chromaticity diagram from the white point is
calculated by:
S=s(x−1
3)
2
+ (y−1
3)
2
(12)
We extend the work of van der Woerd and Wernand [
22
] by calculating
∆
S, a correction for the
spectral bandpass of OLI analogous to
∆α
, by calculating Sfrom x,ypairs derived for the hyperspectral
and 4-band OLI case, respectively. With increasing distance from the white point, the colour becomes
more intense, until it reaches the locus, the place in the chromaticity diagram for a monochromatic
reflection at a specific wavelength. This wavelength is called the dominant wavelength (
λd
, nm) and
the contribution of the dominant wavelength to an observed optical spectrum is termed purity (S*),
defined as the ratio of Sto the distance between the white point and the spectral locus of the dominant
wavelength [
12
]. We report lake colour in terms of
λd
instead of
α
, because it provides an intuitive and
illustrative amplification of the observed colour that is useful for plotting and interpretation purposes.
λd
is derived geometrically from
α
+
∆α
by determining the wavelength at the point of intersection
with the locus.
To investigate the lake colour characteristics with respect to landuse, we calculated the percentage
of land cover of high-producing exotic grassland (P) in each lake’s catchment from the New Zealand
Land Cover Database Version 4.1 [
48
]. This percentage was transformed using the logistic function
(log (P/(100-P)) where log is the natural logarithm. Moreover, each lake was assigned to one of eight
elevation-depth classes based on the elevation of the lake surface and the maximum depth as given
in [
29
]. The eight classes divide lowland and highland lakes (below and above 300 m above sea level,
respectively) and four depth ranges (0–5 m, 5–15 m, 15–50 m, >50 m), respectively.
3. Results
3.1. Observation Frequency of New Zealand Lakes
Landsat 8 data are acquired in 185 km swaths and segmented into 185 km
×
180 km scenes that
are defined in the second World-wide Reference System (WRS-2) of path (groundtrack parallel) and
row (latitude parallel) coordinates (Figure 5) [
33
]. Adjacent paths overlap by approximately 56 km
in the northern end of New Zealand and 76 km at the southern end. Every path is overpassed every
16 days and the path adjacent to it is overpassed seven days later. This means that repeat observations
of certain parts of the country are possible every eight days and every 16 days in the remaining regions.
Therefore, the maximum frequency of observations of any lake by Landsat 8 OLI is either 52 or 23 times
per year, depending on its location with respect to the groundtrack of the orbital paths.

Remote Sens. 2018,10, 1273 8 of 22
Remote Sens. 2018, 10, x FOR PEER REVIEW 8 of 22
Figure 5. 1486 lakes coloured by the average number of observations per year. The red rectangles
delineate the geographic locations of the Landsat 8 OLI path/row scene boundaries of the descending
(daytime) node in WRS-2 [49]. The boxes (a–d) show the locations of the closeup maps of Figure 6 and
Figure 9.
Successful imaging of aquatic ground targets by the OLI depends on cloudiness, and the quality
of retrieval data is dependant on atmospheric conditions, such as haze, and reflection from the target
surface, i.e., glint. Cloud cover varies greatly across New Zealand, with some areas of the country
showing almost half as many sunshine hours as other regions [50,51]. Cloud masking, as described
in the methods and removal of observations with reflectances outside the range between zero and
one, produced 44,947 spectra for 1486 lakes across the country. The lakes in our data set are observed
on average between once and 21 times per year. Lakes with four to six observations per year are most
common and on avearge lakes are observed 6.3 times (Figure 6a). The median number of observations
ranges between 600 and 1000 per month (Figure 6b). However, the interquartile range of the number
of monthly observations shows that the highest number of successful retrievals occurs in January,
February, August, and September, while April, May, June, and October can show the lowest number
of data points.
Figure 5.
1486 lakes coloured by the average number of observations per year. The red rectangles
delineate the geographic locations of the Landsat 8 OLI path/row scene boundaries of the descending
(daytime) node in WRS-2 [
49
]. The boxes (
a
–
d
) show the locations of the closeup maps of Figures 9
and 12.
Successful imaging of aquatic ground targets by the OLI depends on cloudiness, and the quality
of retrieval data is dependant on atmospheric conditions, such as haze, and reflection from the target
surface, i.e., glint. Cloud cover varies greatly across New Zealand, with some areas of the country
showing almost half as many sunshine hours as other regions [
50
,
51
]. Cloud masking, as described in
the methods and removal of observations with reflectances outside the range between zero and one,
produced 44,947 spectra for 1486 lakes across the country. The lakes in our data set are observed on
average between once and 21 times per year. Lakes with four to six observations per year are most
common and on avearge lakes are observed 6.3 times (Figure 6a). The median number of observations
ranges between 600 and 1000 per month (Figure 6b). However, the interquartile range of the number
of monthly observations shows that the highest number of successful retrievals occurs in January,
February, August, and September, while April, May, June, and October can show the lowest number of
data points.

Remote Sens. 2018,10, 1273 9 of 22
Remote Sens. 2018, 10, x FOR PEER REVIEW 9 of 22
(a)
(b)
Figure 6. (a) Frequency distribution of average number of observations per year for New Zealand
lakes. (b) Box plot of the average number of observations of New Zealand lakes by month. On each
box, the central mark indicates the median, and the bottom and top edges of the box indicate the 25th
and 75th percentiles, respectively. The whiskers extend to the most extreme data points.
The average annual number of images for each lake in the data set is shown on the map in Figure
5 (also available at lakes.takiwagis.co) along with the locations of the OLI ground paths. Lakes in
areas of overlapping paths systematically show higher frequency of observations relative to lakes in
non-overlapping areas, and variability in observation frequency within overlapping or non-
overlapping ground path areas is consistent with statistics of sunshine hours [50]. For example, a
small lake (lake ID 25550 in the FENZ geodatabase) near Nelson (41.27°S, 173.28°E), one of the
sunniest cities in New Zealand, was observed successfully 20 times per year. Lakes in Hawkes Bay
(39.49°S, 176.91°E) have high observation frequencies, as do lakes near Lake Tekapo (43.90°S,
170.53°E) in the central high country of the Canterbury region. Cloudiness is highest along the west
coast of New Zealand, especially in Fjordland at the south-westernmost end of the South Island,
which is being reflected by annual images fewer than four.
3.2. Correction for Purity
In Van der Woerd and Wernand [21,22], it was shown that in first approximation the hue angle
can be reconstructed using a linear weighted sum of the band R(λ), in this case the four bands of OLI
(see Equations (7)–(9)), and a correction Δ calculated by a fifth order polynomial (Figure 4a).
Likewise, we calculated the difference in distance (S) from the white point between the hyperspectral
and OLI results (ΔS). In Figure 4b, this difference is plotted as a function of the hue angle derived
from the OLI bands and is approximated by the following fifth-order polynomial:
ΔS = −0.0099a5 + 0.1199a4 – 0.4594a3 + 0.7515a2 – 0.5095a + 0.1222
(13)
This equation is used to reconstruct the distance S and purity S* for all OLI spectra.
3.3. Lake Colour and Purity Distribution
All 44,947 water colour observations from the study lakes, as derived by chromaticity analysis,
are shown in Figure 7. The observations form a teardrop-shaped point cloud occupying
predominantly orange-brown, yellow-green, and turquoise-blue areas of the colour space. The range
of dominant wavelengths extends from 475 nm at the blue end of the spectrum to 585 nm at the
yellow-orange end. Colour purity is strongest for observations in the orange-yellow part of the
Figure 6.
(
a
) Frequency distribution of average number of observations per year for New Zealand
lakes. (
b
) Box plot of the average number of observations of New Zealand lakes by month. On each
box, the central mark indicates the median, and the bottom and top edges of the box indicate the 25th
and 75th percentiles, respectively. The whiskers extend to the most extreme data points.
The average annual number of images for each lake in the data set is shown on the map in
Figure 5(also available at lakes.takiwagis.co) along with the locations of the OLI ground paths.
Lakes in areas of overlapping paths systematically show higher frequency of observations relative
to lakes in non-overlapping areas, and variability in observation frequency within overlapping or
non-overlapping ground path areas is consistent with statistics of sunshine hours [
50
]. For example, a
small lake (lake ID 25550 in the FENZ geodatabase) near Nelson (41.27
◦
S, 173.28
◦
E), one of the sunniest
cities in New Zealand, was observed successfully 20 times per year. Lakes in Hawkes Bay (39.49
◦
S,
176.91
◦
E) have high observation frequencies, as do lakes near Lake Tekapo (43.90
◦
S, 170.53
◦
E) in the
central high country of the Canterbury region. Cloudiness is highest along the west coast of New
Zealand, especially in Fjordland at the south-westernmost end of the South Island, which is being
reflected by annual images fewer than four.
3.2. Correction for Purity
In Van der Woerd and Wernand [
21
,
22
], it was shown that in first approximation the hue angle
can be reconstructed using a linear weighted sum of the band R(
λ
), in this case the four bands of
OLI (see Equations (7)–(9)), and a correction
∆α
calculated by a fifth order polynomial (Figure 4a).
Likewise, we calculated the difference in distance (S) from the white point between the hyperspectral
and OLI results (
∆
S). In Figure 4b, this difference is plotted as a function of the hue angle derived from
the OLI bands and is approximated by the following fifth-order polynomial:
∆S=−0.0099a5+ 0.1199a4- 0.4594a3+ 0.7515a2- 0.5095a+ 0.1222 (13)
This equation is used to reconstruct the distance Sand purity S* for all OLI spectra.
3.3. Lake Colour and Purity Distribution
All 44,947 water colour observations from the study lakes, as derived by chromaticity analysis, are
shown in Figure 7. The observations form a teardrop-shaped point cloud occupying predominantly

Remote Sens. 2018,10, 1273 10 of 22
orange-brown, yellow-green, and turquoise-blue areas of the colour space. The range of dominant
wavelengths extends from 475 nm at the blue end of the spectrum to 585 nm at the yellow-orange end.
Colour purity is strongest for observations in the orange-yellow part of the chromaticity diagram, as
indicated by points over half way from the white point (x=y= 1/3) towards the locus. Colour purity
of blue colours reaches 40% and blue-green to yellow-green colour purity is lower with a maximum
of 20%.
Remote Sens. 2018, 10, x FOR PEER REVIEW 10 of 22
chromaticity diagram, as indicated by points over half way from the white point (x = y = 1/3) towards
the locus. Colour purity of blue colours reaches 40% and blue-green to yellow-green colour purity is
lower with a maximum of 20%.
Figure 7. Chromaticity diagram showing the water colour of 44,947 lake observations determined
from Landsat 8 OLI data. The dashed lines from the white point (WP) to dominant wavelengths of
495 and 510 nm, respectively, indicate the nominal boundaries for colour classification into blue, green
and red bins.
Observations of dominant wavelength show a bi-modal frequency distribution with most
observations in the yellow-orange part of the spectrum, a secondary mode at the blue end and
relatively fewer green observations (Figure 8a). This frequency distribution is sensitive to the spatial
bias of observation frequency (Figure 5), and therefore it does not provide a representative summary
of lake colour in New Zealand in general. Lake-mean dominant wavelength is more uniformly
distributed (Figure 8b) than the individual observations, suggesting that colours are more or less
equally represented at the lake level. The geographic distribution of mean dominant wavelength
shows broad spatial patterns (Figure S1 in Supplementary Material; this dataset can also be explored
at lakes.takiwa.co). For example, lakes in Fjordland, in the western half of the South Island of New
Zealand tend to be blue to green (Figure 6c), while further north, in the Southern Alps, lakes are a
mixture of deep blue to orange colours (Figure 6d). The North Island has many green lakes in the
central volcanic plateau (southeastern corner of Figure 6a) and yellow to dark orange lakes in the
peat-dominated landscape about 100 km northwest (northwest corner of Figure 6a). Lakes on the
northern panhandle of the North Island are a diverse mix of blue to orange colours (Figure 6b).
Figure 7.
Chromaticity diagram showing the water colour of 44,947 lake observations determined from
Landsat 8 OLI data. The dashed lines from the white point (WP) to dominant wavelengths of 495 and
510 nm, respectively, indicate the nominal boundaries for colour classification into blue, green and
red bins.
Observations of dominant wavelength show a bi-modal frequency distribution with most
observations in the yellow-orange part of the spectrum, a secondary mode at the blue end and
relatively fewer green observations (Figure 8a). This frequency distribution is sensitive to the spatial
bias of observation frequency (Figure 5), and therefore it does not provide a representative summary
of lake colour in New Zealand in general. Lake-mean dominant wavelength is more uniformly
distributed (Figure 8b) than the individual observations, suggesting that colours are more or less
equally represented at the lake level. The geographic distribution of mean dominant wavelength
shows broad spatial patterns (Figure S1 in Supplementary Material; this dataset can also be explored
at lakes.takiwa.co). For example, lakes in Fjordland, in the western half of the South Island of New
Zealand tend to be blue to green (Figure 9c), while further north, in the Southern Alps, lakes are a
mixture of deep blue to orange colours (Figure 9d). The North Island has many green lakes in the
central volcanic plateau (southeastern corner of Figure 9a) and yellow to dark orange lakes in the
peat-dominated landscape about 100 km northwest (northwest corner of Figure 9a). Lakes on the
northern panhandle of the North Island are a diverse mix of blue to orange colours (Figure 9b).

Remote Sens. 2018,10, 1273 11 of 22
Figure 8.
(
a
) Frequency histogram of 44,947 observations of dominant wavelength. (
b
) Frequency
distribution of the mean dominant wavelength of 1486 lakes.
Remote Sens. 2018, 10, x FOR PEER REVIEW 11 of 22
Figure 8. (a) Frequency histogram of 44,947 observations of dominant wavelength. (b) Frequency
distribution of the mean dominant wavelength of 1486 lakes.
Figure 6. Geographic distribution of lakes coloured by mean dominant wavelength in four areas.
Placement of the areas shown in maps (a–d) are shown in Figure 5.
Figure 9.
Geographic distribution of lakes coloured by mean dominant wavelength in four areas.
Placement of the areas shown in maps (a–d) are shown in Figure 5.

Remote Sens. 2018,10, 1273 12 of 22
Inspection of the distribution of dominant wavelength observations within lakes revealed that a
large number of lakes are predominantly blue or predominantly yellow-orange, but there are no lakes
that are only green (Figure 10). Lakes that are green on average typically show observations across
the entire spectrum. For example, Lake Rotomanuka, a eutrophic peat lake of 8 m maximum depth in
an agricultural catchment [
52
], is persistently orange with a mean dominant wavelength of 575 nm
and purity from 13 to 80% (Figure 11). Lake Pukaki is a glacial lake fed by cold, short-transit-time
rivers with little interaction with vegetated terrain [
26
]. It is ultra-oligotrophic and famous for its
turquoise-blue water that is due to inputs of fine, highly scattering, and weakly absorbing glacial
‘flour’ [
1
]. The dominant wavelength of Lake Pukaki varies little (485–513 nm with a mean 494 nm) and
its purity ranges from 3 to 36% (mean 19%) (Figure 11). A lake with markedly variable colour is Lake
Rotoiti. This monomictic, eutrophic volcanic lake has a maximum depth of 124 m [
53
] and it shows
seasonal variability in the time series of dominant wavelength ranging from 490 to 571 nm (mean of
521 nm). Colour purity ranges from 5 to 46% with high values coinciding with maxima in dominant
wavelength (Figure 11). This pattern is likely caused by seasonal blooms of picocyanobacteria [
54
],
during which chl aconcentrations typically reach 10 mg m−3.
Remote Sens. 2018, 10, x FOR PEER REVIEW 12 of 22
Inspection of the distribution of dominant wavelength observations within lakes revealed that a
large number of lakes are predominantly blue or predominantly yellow-orange, but there are no lakes
that are only green (Figure 7). Lakes that are green on average typically show observations across the
entire spectrum. For example, Lake Rotomanuka, a eutrophic peat lake of 8 m maximum depth in an
agricultural catchment [52], is persistently orange with a mean dominant wavelength of 575 nm and
purity from 13 to 80% (Figure 8). Lake Pukaki is a glacial lake fed by cold, short-transit-time rivers
with little interaction with vegetated terrain [26]. It is ultra-oligotrophic and famous for its turquoise-
blue water that is due to inputs of fine, highly scattering, and weakly absorbing glacial ‘flour’ [1]. The
dominant wavelength of Lake Pukaki varies little (485–513 nm with a mean 494 nm) and its purity
ranges from 3 to 36% (mean 19%) (Figure 8). A lake with markedly variable colour is Lake Rotoiti.
This monomictic, eutrophic volcanic lake has a maximum depth of 124 m [53] and it shows seasonal
variability in the time series of dominant wavelength ranging from 490 to 571 nm (mean of 521 nm).
Colour purity ranges from 5 to 46% with high values coinciding with maxima in dominant
wavelength (Figure 8). This pattern is likely caused by seasonal blooms of picocyanobacteria [54],
during which chl a concentrations typically reach 10 mg m−3.
Figure 7. Box plot of the distribution of dominant wavelength in 1486 lakes ordered by median
dominant wavelength (black line). The bottom and top edges of each box indicate the 25th and 75th
percentiles, respectively; blue lines extend to the most extreme data points not considered outliers,
and outliers are shown as circles.
Figure 8. Three example time series of (a) dominant wavelength and (b) purity and the location of
each observation in a chromaticity diagram (c). The horizontal lines in (a) indicate the boundary
wavelengths between blue and green colour bins (495 nm) and green and yellow colour bins (560 nm).
•LakePukaki
△LakeRotomanuka
△LakeRotoiti
(a)
(b)
(c)
Figure 10.
Box plot of the distribution of dominant wavelength in 1486 lakes ordered by median
dominant wavelength (black line). The bottom and top edges of each box indicate the 25th and 75th
percentiles, respectively; blue lines extend to the most extreme data points not considered outliers, and
outliers are shown as circles.
Remote Sens. 2018, 10, x FOR PEER REVIEW 12 of 22
Inspection of the distribution of dominant wavelength observations within lakes revealed that a
large number of lakes are predominantly blue or predominantly yellow-orange, but there are no lakes
that are only green (Figure 7). Lakes that are green on average typically show observations across the
entire spectrum. For example, Lake Rotomanuka, a eutrophic peat lake of 8 m maximum depth in an
agricultural catchment [52], is persistently orange with a mean dominant wavelength of 575 nm and
purity from 13 to 80% (Figure 8). Lake Pukaki is a glacial lake fed by cold, short-transit-time rivers
with little interaction with vegetated terrain [26]. It is ultra-oligotrophic and famous for its turquoise-
blue water that is due to inputs of fine, highly scattering, and weakly absorbing glacial ‘flour’ [1]. The
dominant wavelength of Lake Pukaki varies little (485–513 nm with a mean 494 nm) and its purity
ranges from 3 to 36% (mean 19%) (Figure 8). A lake with markedly variable colour is Lake Rotoiti.
This monomictic, eutrophic volcanic lake has a maximum depth of 124 m [53] and it shows seasonal
variability in the time series of dominant wavelength ranging from 490 to 571 nm (mean of 521 nm).
Colour purity ranges from 5 to 46% with high values coinciding with maxima in dominant
wavelength (Figure 8). This pattern is likely caused by seasonal blooms of picocyanobacteria [54],
during which chl a concentrations typically reach 10 mg m−3.
Figure 7. Box plot of the distribution of dominant wavelength in 1486 lakes ordered by median
dominant wavelength (black line). The bottom and top edges of each box indicate the 25th and 75th
percentiles, respectively; blue lines extend to the most extreme data points not considered outliers,
and outliers are shown as circles.
Figure 8. Three example time series of (a) dominant wavelength and (b) purity and the location of
each observation in a chromaticity diagram (c). The horizontal lines in (a) indicate the boundary
wavelengths between blue and green colour bins (495 nm) and green and yellow colour bins (560 nm).
•LakePukaki
△LakeRotomanuka
△LakeRotoiti
(a)
(b)
(c)
Figure 11.
Three example time series of (
a
) dominant wavelength and (
b
) purity and the location
of each observation in a chromaticity diagram (
c
). The horizontal lines in (
a
) indicate the boundary
wavelengths between blue and green colour bins (495 nm) and green and yellow colour bins (560 nm).
Lake Pukaki (44.0542
◦
S, 170.1685
◦
E), Lake Rotomanuka (37.9257
◦
S, 175.3152
◦
E), and Lake Rotoiti
(38.0358◦S, 176.4174◦E).

Remote Sens. 2018,10, 1273 13 of 22
To facilitate a broad classification of the study lakes, the full spectrum of dominant wavelength
was divided into five colour bins: three solid colours (blue:
λd
< 495, green: 495
≤λd
< 560, and
yellow:
λd≥
560 nm) and three transient bins (blue-green, yellow-green, blue-yellow). Lakes were
assigned a solid colour if 60% or more observations of dominant wavelength were within the range of
a single solid colour. Lakes with bimodal distributions of dominant wavelength were identified as
transient based on the distribution of observations between solid colour ranges, as listed in Table 1.
Due to the relative sparseness of green observations, transient greenness required a minimum of 20%
of green observations only. The numbers of blue, blue-green, and green-yellow lakes are similar (16%,
19%, 21%, respectively) and only 8% of lakes are predominantly green. 15% of lakes do not fit into one
of those colour bins because their variability in dominant wavelength does not fit this categorisation.
Figure 12 shows the geographic distribution of lake colours by bins in regions, as identified in
Figure 5(Figure S2 in Supplementary Material shows the entire study area). The differences between
the lake-specific mean dominant wavelength (Figure 9) and the colour bin shows that the mean
statistic is a poor descriptor of lake colour over the observation period for about 40% of lakes due to
their bi-modal frequency distribution of dominant wavelength. Hence, more lakes have an average
dominant wavelength in the green part of the spectrum in Figure 9than expected from the minimum
of the frequency distribution of observations (Figure 8a), and Figure 12 shows that the green colour is
an artefact of averaging over observations in the blue and yellow range of the spectrum.
Remote Sens. 2018, 10, x FOR PEER REVIEW 14 of 22
Figure 9. Geographic distribution of lakes coloured by colour bins according to Table 1 in four areas.
Placement of the areas shown in maps (a–d) are shown in Figure 5.
Figure 10. Percentage distribution of lakes in colour bins according to Table 1 in elevation-depth
classes [29]. Lowland and highland lakes are where the lake surface is below 300 m and above 300 m,
respectively.
Blue
Green
Yellow
Blue-green
Green-yellow
Blue-yellow
Figure 12.
Geographic distribution of lakes coloured by colour bins according to Table 1in four areas.
Placement of the areas shown in maps (a–d) are shown in Figure 5.
Broad geographic patterns in lake colour-bin distribution exist (Figure 12), which are consistent
with geomorphic and land use characteristics. For example, blue lakes occur in the more sparsely
populated, mountainous, and forested regions along the west coast of the South Island (Figure 12c) and
in the eastern portion of the North Island (southeast corner of Figure 12a). Yellow and green-yellow

Remote Sens. 2018,10, 1273 14 of 22
lakes dominate in the agricultural areas in the central North Island and the southeast of the South
Island. A large number of yellow lakes also occur along the South Island’s west coast where there are
many lakes in forest catchments with high CDOM inputs. These geographical patterns can be partly
explained by elevation and lake depth. Figure 13 shows that systematic differences in lake colour
exist between eight classes of lowland and highland lakes of different depths. Approximately 85%
of shallow lakes (<5 m deep) in lowlands are yellow and about 10% are transient yellow-green lakes.
The fraction of blue and green lakes increases with lake depth in lowland lakes, and deep lakes (>50 m)
are often blue or blue-green transient. At higher elevations, the proportion of yellow lakes is smaller
than in lowland lakes, and the proportion of blue and blue-green lakes increases with lake depth.
Table 1.
Colour bins and numbers of lakes in each bin according to their dominant wavelength
distribution. Note that the percentages in the right-hand column add up to over 100% as some lakes fit
into more than one category.
Colour Bin 1Criterion Number of Lakes 2
Blue ≥60% blue 277 (18.6%)
Green ≥60% green 124 (8.3%)
Yellow ≥60% yellow 547 (36.8%)
Blue-green ≥40% blue
≥20% green 287 (19.3%)
Green-yellow ≥40% yellow
≥20% green 302 (20.3%)
Blue-yellow ≥40% blue
≥40% yellow 15 (1.0%)
Unassigned None of the above 195 (13.1%)
1
Wavelength ranges (in nm) for colour bins are as follows; blue:
λd
< 495, green: 495
≤λd
< 560, yellow:
λd≥
560.
2The percentage of lakes in a given colour bin is relative to the total number of lakes in this study (1486).
Remote Sens. 2018, 10, x FOR PEER REVIEW 14 of 22
Figure 9. Geographic distribution of lakes coloured by colour bins according to Table 1 in four areas.
Placement of the areas shown in maps (a–d) are shown in Figure 5.
Figure 10. Percentage distribution of lakes in colour bins according to Table 1 in elevation-depth
classes [29]. Lowland and highland lakes are where the lake surface is below 300 m and above 300 m,
respectively.
Blue
Green
Yellow
Blue-green
Green-yellow
Blue-yellow
Figure 13.
Percentage distribution of lakes in colour bins according to Table 1in elevation-depth
classes [
29
]. Lowland and highland lakes are where the lake surface is below 300 m and above
300 m, respectively.

Remote Sens. 2018,10, 1273 15 of 22
568 of our study lake catchments contain high-producing exotic grassland and percentage cover of
this land-use reaches over 90% for many lakes. The relationship between mean dominant wavelength
and the transformed percent cover forms a point cloud with a distinct boundary, showing that there are
no blue or blue-green lakes in catchments with over 25% (transformed value of
−
1.1) high-producing
exotic grassland (Figure 14). Yellow and green-yellow transient (see definitions in Table 1) lakes mostly
have catchments with this cover type making up more than 25%.
Remote Sens. 2018, 10, x FOR PEER REVIEW 15 of 22
568 of our study lake catchments contain high-producing exotic grassland and percentage cover
of this land-use reaches over 90% for many lakes. The relationship between mean dominant
wavelength and the transformed percent cover forms a point cloud with a distinct boundary,
showing that there are no blue or blue-green lakes in catchments with over 25% (transformed value
of −1.1) high-producing exotic grassland (Figure 11). Yellow and green-yellow transient (see
definitions in Table 1) lakes mostly have catchments with this cover type making up more than 25%.
Figure 11. Lake-mean dominant wavelength versus the percentage of land cover by high-producing
exotic grassland (P) in the lake catchment (after logistic transformation). Dots are colour-coded
according to colour bins (Table 1).
Table 1. Colour bins and numbers of lakes in each bin according to their dominant wavelength
distribution. Note that the percentages in the right-hand column add up to over 100% as some lakes
fit into more than one category.
Colour Bin 1
Criterion
Number of Lakes2
Blue
≥60% blue
277 (18.6%)
Green
≥60% green
124 (8.3%)
Yellow
≥60% yellow
547 (36.8%)
Blue-green
≥40% blue
≥20% green
287 (19.3%)
Green-yellow
≥40% yellow
≥20% green
302 (20.3%)
Blue-yellow
≥40% blue
≥40% yellow
15 (1.0%)
Unassigned
None of the above
195 (13.1%)
1 Wavelength ranges (in nm) for colour bins are as follows; blue:

d < 495, green: 495 ≤

d < 560, yellow:

d ≥ 560. 2 The percentage of lakes in a given colour bin is relative to the total number of lakes in this
study (1486).
4. Discussion
In this study, we determined the observation frequency by Landsat 8 OLI and the colour of 1486
lakes across New Zealand. Monitoring of the health and water quality of this resource falls to the
country’s sixteen local governments (i.e., regional councils) [55]. This involves in-situ sampling for a
base set of water quality attributes (chlorophyll a, total nitrogen, and total phosphorus) and
additional attributes, as decided by the regional councils [56]. A recent summary of council data
indicated that 63% of the monitored lakes are mesotrophic, eutrophic, or supertrophic and 36.7% of
Figure 14.
Lake-mean dominant wavelength versus the percentage of land cover by high-producing
exotic grassland (P) in the lake catchment (after logistic transformation). Dots are colour-coded
according to colour bins (Table 1).
4. Discussion
In this study, we determined the observation frequency by Landsat 8 OLI and the colour of
1486 lakes across New Zealand. Monitoring of the health and water quality of this resource falls to
the country’s sixteen local governments (i.e., regional councils) [
55
]. This involves in-situ sampling
for a base set of water quality attributes (chlorophyll a, total nitrogen, and total phosphorus) and
additional attributes, as decided by the regional councils [
56
]. A recent summary of council data
indicated that 63% of the monitored lakes are mesotrophic, eutrophic, or supertrophic and 36.7% of
lakes showed degrading trends. However, these assessments were limited to 72 lakes for state and even
fewer (18 lakes) for the trend analysis [
29
], and therefore, these results are hardly representative of the
nation’s lakes in general. We demonstrate that even with the requirement for clear skies and relatively
infrequent revisits (every eight or 16 days), Landsat 8 OLI can resolve 1486 lakes and over 50% of these
lakes are successfully observed four or more times per year. Higher observation frequencies should be
achieved by similar currently operational multispectral sensors with shorter revisit periods e.g., by
the Multispectral Instrument (MSI) on the tandem mission Sentinel-2 a and b of the European Space
Agency with a revisit period of three to four days [57].
Despite the advantages of enhanced spatio-temporal coverage of satellite observations of lakes,
remote sensing is unlikely to provide biogeochemical quantities for current regulatory monitoring
programmes, because prediction-precision residuals relative to in situ samples are relatively large.
These residuals are caused by the difficulty of retrieving concentrations of independently varying
optically active substances in inland waters and spatio-temporal variations of IOPs, which hamper
the application of algorithms across a wide range of optical water types such as those found in New
Zealand. Lake colour estimation from satellite imagery provides a reliable synoptic measurement of
an ecosystem attribute, as it does not suffer from our limited knowledge of IOPs of optically active
constituents in the water.
As we expected from our knowledge of New Zealand lakes, our dataset covers a large range
of natural water colours and we look forward to comparable large-scale studies to fully define the

Remote Sens. 2018,10, 1273 16 of 22
global boundaries of the point cloud in the chromaticity diagram (Figure 7). As an initial attempt to
handle the diversity of lake colour, we defined a simple heuristic classification of lakes into colour
bins (Table 1), which aimed to capture the mean properties and identify cases where mean properties
poorly represent lake state. With this approach we characterised both water type (colour of individual
observations) and lake type (i.e., colour bin membership). The colour of individual observations may
be useful for algorithm selection in multi-algorithm approaches to inland water applications [
58
] and
the colour-bin classification relates a lake to its environment, facilitating further ecological studies
of the drivers of lake water quality at a range of spatial scales. Other classifications of optical water
types were typically designed using in-situ hyperspectral data and in-situ optically active constituents
e.g., [
59
,
60
]. When applying these classifications to satellite data, misclassifications may occur due to
the reduced information content of multispectral data relative to the hyperspectral in-situ reflectances.
Our approach is solely based on multispectral satellite data and quantifying the limitations that this
imposes on algorithm selection and water quality monitoring is the goal of ongoing validation of
remotely sensed water colour with in-situ hyperspectral and water quality data.
The colour of water is directly linked to the spectral quality of the underwater light field
and therefore the light available for photosynthesis by aquatic plants and visibility for the aquatic
fauna [
4
,
61
]. The relationship between water colour and inherent optical properties of water quality
constituents should allow for colour to be used as proxy for concentrations of chl a, CDOM, or SPM in
well-characterised systems. This provides an opportunity for efficient monitoring using stationary or
remote radiometers, as well as for community involvement in science, e.g., through the measurement
of colour by smartphone cameras [
62
]. In addition, the perceived colour has been directly linked to
recreational use and the desirability of freshwater systems [
2
,
3
] affecting the social and economic
value of lakes and rivers [
63
]. This makes perceived colour a useful measurement in the context of
optical water quality [
1
,
4
] and led to its recent inclusion in the New Zealand national environmental
monitoring standards for lakes [
64
]. One example application is the protection of visual characteristics
of the unique and iconic natural character of lakes, such as Tekapo and Pukaki of the Canterbury
region, which have low clarity and distinctive milky-blue hues. To this end, water colour monitoring
based on the Munsell colour scale [
65
] has been part of regional water quality objectives [
66
]. However,
only 41 of the region’s 464 lakes that are greater than 1 ha are monitored and the high country lakes,
including the aforementioned optically unique lakes, are sampled by helicopter, prohibiting visual
Munsell colour matching. Our dataset includes 157 Canterbury lakes and immediately offers four
years of data that can be used to set targets for water colour and assess departures from baseline values
and trends. The relationships that we described between lake colour and catchment land use, lake
elevation, and depth suggest that colour can be predicted from a suitable set of driver variables and
future effort will be devoted to finding these relationships.
A previous multivariate analysis identified percentage land cover by high-producing exotic
grassland as the strongest predictor whether a lake shifted from clear to turbid states [
67
] and we
therefore chose this variable for a first investigation into potential correlates of lake water colour.
High-producing exotic grassland identifies pasture used for intensive dairy, beef, and sheep grazing,
which is the mainstay of New Zealand’s primary industry. Covering almost 9 mil ha, it made up 33% of
New Zealand’s land area in 2012 and it had the second highest increase in areal coverage between 2008
and 2012 after harvested forest [
48
,
68
]. Nitrogen and phosphorus runoff from fertiliser application
and animal excretion has been identified as a leading cause for the degradation in New Zealand’s
inland waters [
69
,
70
]. Our results show that lakes with a higher proportion of high-producing exotic
grassland are more green to orange, rather than blue and blue-green (Figure 14). If lake colour is
taken as a proxy for chl aand SPM, this relationship supports the causal link suggested between
dairy production and environmental impacts [
68
]. However, blue lakes also tend to be deep, which
makes them less vulnerable to eutrophication and at high elevation (Figure 13), i.e., in landscapes
potentially less suitable for intensive-pasture farming. The observed correlation must therefore be