ISPRS Journal of Photogrammetry and Remote Sensing

ISPRS Journal of Photogrammetry and Remote Sensing 182 (2021) 134–152
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ISPRS Journal of Photogrammetry and Remote Sensing

journal homepage: www.elsevier.com/locate/isprsjprs
Water clarity in Brazilian water assessed using Sentinel-2 and machine

learning methods
Daniel Andrade Maciel *, Claudio Clemente Faria Barbosa, Evlyn Márcia Leão de Moraes Novo,
Rogério Flores Júnior, Felipe Nincao Begliomini
Instrumentation Lab for Aquatic Systems (LabISA), Earth Observation Coordination of National In-stitute for Space Research (INPE), São José dos Campos, SP, Brazil
Earth Observation and Geoinformatics Division, National Institute for Space Research (INPE), São José dos Campos, SP 12227-010, Brazil
A R T I C L E I N F O A B S T R A C T
Keywords: Secchi Disk Depth (Zsd) is one of the widely used water quality measurements. Controlled by variations in
Secchi disk depth Optically Active Constituents, it is a key index of overall water quality. In-situ measurements of Zsd lacks
Atmospheric correction spatiotemporal coverage which could be solved using remote sensing data, such as from the Sentinel-2/MSI.
Water quality
However, inland waters have highly variable optical properties, and that is still a challenge for the state-of-art
Google earth engine
algorithms of Zsd retrieval. One of the most promising approaches for dealing with this challenge is the use of
Remote sensing
Water transparency Machine Learning methods. Moreover, predicting Zsd for large areas using high-resolution remote sensing im
agery requires a high computational effort, which could be solved using Cloud-Computing platforms. Therefore,
this study evaluates the use of Machine Learning (Random Forest, Extreme Gradient Boosting, and Support
Vector Machines) and Semi-Analytical algorithms (SAA) for Zsd retrieval focused on Sentinel-2 imageries
available in the Google Earth Engine platform to assess the clarity of the Brazilian inland waters. Machine
Learning methods were calibrated and validated using a comprehensive dataset (N = 1492) collected in the last
20 years in Brazil. The results were compared with semi-analytical approaches. After evaluation with in-situ data,
the best algorithm was implemented in the Google Earth Engine platform to generate Zsd maps. The calibration
with in-situ data demonstrated that the Machine Learning methods outperform the SAA, with the Random Forest
presenting the best results (errors lower than 22%). The results showed that when SAA were applied to the
environment in which they were calibrated, the results were closer to that of machine learning methods, indi
cating that SAA could also be used for Zsd retrieval. The application of Random Forest to the Sentinel-2 atmo
spherically corrected imagery had errors of 28%, demonstrating the feasibility of the algorithm and atmospheric
correction methods for predicting Zsd.
1. Introduction light field as their concentration and covariance are modified. Those
changes in OACs affect water transparency, making this parameter a key
Water clarity has been studied in several science fields such as index of the overall water quality (Luis et al., 2019). Thus, it could be
limnology, oceanography, biology, and physics since the late 19th used as a proxy for the trophic state (Lisi and Hein, 2019), primary
century (Cialdi, 1866; Kirk, 2010; Lee et al., 2015; Mobley, 1994; Tyler, productivity (Behrenfeld and Falkowski, 1997), and phytoplankton
1968). The first instrument for quantifying water clarity was the Secchi functional groups biodiversity (Buchanan, 2020; Kraus et al., 2019).
Disk, in which transparency is measured considering the depth at which The Secchi Disk is a white or black-white disk, usually with a 30 cm
the Secchi Disk is no longer visible by the observer. Being first reported diameter. Each Zsd measurement is carried out by lowering the disk into
between 1864 and 1866, Secchi Disk Depth (Zsd) has become one of the the water column until the depth at which the disk is no longer visible
most traditional measurements for water clarity monitoring (Wernand, from the water surface (Tyler, 1968). Despite its simplicity, Zsd mea
2010). The water clarity is controlled by the Optically Active Constitu surements are widely used due to their practicality, without expert
ents (OACs) in the water column (e.g., suspended sediments, colored knowledge requirements, and low cost (Aas et al., 2014). Moreover, Zsd
dissolved organic matter, chlorophyll-a), which change the underwater measurements were essential to observe long-term trends in water
* Corresponding author at: Remote Sensing Program, Graduate Division, National Institute for Space Research (INPE), São José dos Campos, SP 12227-010, Brazil.
E-mail addresses: daniel.maciel@inpe.br, damaciel_maciel@hotmail.com (D.A. Maciel).
https://doi.org/10.1016/j.isprsjprs.2021.10.009
Received 24 June 2021; Received in revised form 12 October 2021; Accepted 23 October 2021
Available online 30 October 2021
0924-2716/© 2021 International Society for Photogrammetry and Remote Sensing, Inc. (ISPRS). Published by Elsevier B.V. All rights reserved.
D.A. Maciel et al. ISPRS Journal of Photogrammetry and Remote Sensing 182 (2021) 134–152
clarity because this method has been used since the beginning of the provides a petabyte-scale satellite imagery freely and of easy access to
20th century (Borkman and Smayda, 1998; Sandén and Håkansson, the research community (Gorelick et al., 2017). In the GEE platform, the
1996). However, even being a simple and low-cost measurement, it fails entire catalog of Sentinel-2/MSI Top-Of-Atmosphere reflectance data is
in providing knowledge on spatial and temporal changes, requiring a available. Moreover, GEE also has a catalog with surface reflectance
significant sample size to characterize large areas with statistical sig data, atmospherically corrected using the Sen2Cor processor. However,
nificance. Moreover, remote areas are another limitation to in-situ pe for South America, this data is available only after 2019, limiting the
riodic measurement of Zsd, preventing the characterization of large/ applicability of time series using Sentinel-2 imagery. To overcome this
isolated regions, such as the Amazonian floodplain lakes. To overcome issue, some researchers have implemented customized atmospheric
this problem, remote sensing data have been widely used to estimate Zsd, correction in the GEE platform, such as the Sensor Invariant Atmo
providing a synoptic view with a temporal resolution otherwise spheric Correction (SIAC) (Song et al., 2020; Yin et al., 2019).
impossible using only in-situ measurements (Bai et al., 2020; Feng et al., This study has evaluated the performance of Machine Learning
2019; Lee et al., 2015; Liu et al., 2020; Rodrigues et al., 2017). methods (XGBoost, Random Forest, Support Vector Machine) and semi-
The remote estimates of Zsd can be performed using empirical and analytical algorithms to estimate Zsd in Brazilian inland waters, focusing
semi-analytical algorithms (SAA). SAA are based on physical methods, on Sentinel-2/MSI data available in the Google Earth Engine platform.
such as the underwater visibility theory and the Law of Contrast Machine Learning methods were trained and validated using the in-situ
Reduction, and provide a sharper mechanistic approach based on the data, and the results were compared to the estimates from semi-
radiative transfer equations (Lee et al., 2015). These algorithms for Zsd analytical algorithms previously calibrated for Brazilian waters. More
retrieval rely on the relationship between the Diffuse Attenuation Co over, the accuracy of atmospheric correction for Sentinel-2/MSI prod
efficient of Downwelling Irradiance (Kd), at a wavelength of maximum ucts available in GEE platform was assessed. The best algorithm was
transparency, and Zsd. It links the Apparent Optical Proprieties (AOPs) implemented and validated in the GEE platform to provide Zsd maps for
(i.e., Rrs and Kd) and Inherent Optical Proprieties (IOPs) (absorption and Brazilian waters.
backscattering coefficients) for semi-analytically deriving Kd in the
visible domain (400–700 nm) and uses Law of Contrast Reduction for 2. Material and methods
retrieving Zsd. However, SAA still relies on in-situ IOPs data collection to
calibrate the physical assumptions inherent to those algorithms. In 2.1. Study area
highly diverse environments and territories, such as Brazil, uncertainties
regarding IOPs inversion methods to different optical water types are The available dataset for this study encompasses 22 water bodies in
expected (da Silva et al., 2020; Silva et al., 2021). In addition, IOPs data Brazil from three different Brazilian biomes: Amazon Forest (Floresta
were not always available for algorithm calibration in most southern Amazônica), Savanna (Cerrado), and Atlantic Forest (Mata Atlântica)
hemisphere waterbodies due to the high cost of equipment, mainte (Fig. 1). For Amazon Forest, most of the data are located at the lower
nance, and logistics. Finally, uncertainties in measurement correction Amazon River floodplain. This region is characterized by shallow and
(Sander de Carvalho et al., 2015) and difficult assess to remote areas large lakes, whose depths vary along the hydrological year of the
decrease the availability of in-situ IOPs. Amazon River and can reach a high concentration of suspended sedi
On the other hand, empirical approaches are based on statistical ments (up to 1000 mgL-1) (Barbosa et al., 2010). The data for this biome
methods by either carrying out regression analysis or using machine also includes the Mamiraua Sustainable Development Reserve (MSDR),
learning methods to retrieve Zsd.. Recent works take advantage of a floodplain area located in the confluence of Solimões and Japurá
comprehensive datasets to calibrate empirical algorithms to retrieve Zsd Rivers, and floodplain lakes of the Juruá River, a right margin affluent of
using satellite data (Alikas and Kratzer, 2017; Ren et al., 2018; Wang Solimões River. These waters are characterized by optical complexity,
et al., 2020; Wu et al., 2008; Zhang et al., 2021). These empirical al presenting a high variability of the OACs in a spatiotemporal scale
gorithms can be based on band ratios (Alikas and Kratzer, 2017; Rotta (Barbosa et al., 2010; Maciel et al., 2020a). At the Savanna biome, in-situ
et al., 2016; Zhang et al., 2021), chromaticity parameters (i.e., hue angle data are represented by two field campaigns in the Três Marias Reser
and Forel-Ule Index) (Wang et al., 2020), bands combinations (Wu et al., voir, an oligotrophic reservoir in the central region of Minas Gerais (MG)
2008), and machine learning (Rubin et al., 2021). Unlike empirical al state (Curtarelli et al., 2020). For the Atlantic Forest biome, there are
gorithms constructed based on linear or multivariate regression, most tree eutrophic aquatic systems (Funil, Billings and Ibitinga reservoirs
machine learning applications do not require assumptions about the (Rio de Janeiro (RJ) and São Paulo (SP) states) (Augusto-Silva et al.,
data, such as the homoscedasticity or independence of variables used for 2014; Cairo et al., 2020), and other two oligotrophic: Itaipu (Paraná
the algorithm construction. However, the performance of Machine (PR) state), and Nova Avanhandava (SP).
Learning methods relies on the comprehensiveness of the dataset used
for algorithm calibration, which could be an issue if large datasets are 2.2. In-situ data collection
not available (Sagan et al., 2020). In recent years, cloud computing
systems are becoming abundant, allowing an individual researcher to 2.2.1. Secchi disk depth and OACs measurements
process a huge amount of data. With the recent advance in computa The dataset comprises 1492 measurements of Secchi Disk Depth (Zsd)
tional power and the availability of large datasets, remote sensing acquired between 2003 and 2021 in the Brazilian territory. For Zsd
communities are evaluating Machine Learning methods as a feasible measurements, a circular 30 cm diameter black-and-white disk (Secchi
option for estimating water bodies’ optical proprieties (Cao et al., 2020; Disk) was used at the boat’s shady side, lowered into the water column
Liu et al., 2021; Sagan et al., 2020; Smith et al., 2021). Recent examples up to its complete disappearance. All samples were collected between
of application are for estimating Particulate Organic Carbon (POC) (Liu 10:00 to 14:00 to avoid the effects of low sun-zenith angles. Along with
et al., 2021), Chlorophyll-a concentration (Cao et al., 2020; Pahlevan Zsd measurements, information about AOC’s were also available for part
et al., 2019; Smith et al., 2021), suspended sediments (Balasubramanian of the sampling stations (Total Suspended Sediments (n = 860), Chl-a (n
et al., 2020; Peterson et al., 2018), and water clarity (Rubin et al., 2021) = 926), and aCDOM(4 4 0) (n = 383)). For OACs determination, water
The advance of computational power has gained an impulse with the samples were collected at the subsurface (~30 cm depth) using opaque
cloud computing services dedicated to process remote sensing data, such sampling bottles and stored in ice until filtration. Total Suspended
as Amazon AWS (Ferreira et al., 2020), Microsoft Planetary Computer Sediment (TSS), Total Suspended Inorganic Sediments (TSI), and Total
(Microsoft, 2021), and Google Earth Engine (GEE) (Gorelick et al., Suspended Organic Sediments (TSO) were measured using the protocols
2017). From the available cloud-computing system focused on Remote of Wetzel and Likens (2013). The Chl-a concentration was determined
Sensing data, the Google Earth Engine outperforms. GEE platform based on Nush (1980) procedure. More information about these
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Fig. 1. Study Area in Brazil. Labels in each figure represent each location: A) Juruá River Floodplain; B) Mamiruá Sustainable Development Reserve; C) Tucurui
Reservoir; D) Lower Amazon Floodplain Lakes; E) Billings Reservoir; F) Funil Reservoir; G) Nova Avanhandava Reservoir; H) Ibitinga Reservoir; I) Três Marias
Reservoir; J) Itaipu Reservoir. Red points denote each field station. (For interpretation of the references to color in this figure legend, the reader is referred to the web
version of this article.)
protocols is available in Maciel et al. (2020). Water samples for were positioned 2 m above the water surface to prevent shadows and
aCDOM(4 4 0) determination (n = 383) were filtered through a nylon filter vessel reflections. Therefore, Remote Sensing Reflectance was calculated
membrane with 0.22 µm pore size, which was kept cool until analysis using Equation (1).
and then measured at room temperature using a 10 cm quartz cuvette in
LT (θ, ∅, λ) − ρ(θ, ∅)LSKY (θ’’ , ∅, λ) − 1
a single beam mode of a 2600 UV–VIS spectrophotometer (Shimadzu, Rrs (θ, ∅, λ) = (sr ) (1)
Kyoto, Japan). Es (λ)
Where ρ(θ ∅) is air–water interface reflectance and was obtained
2.2.2. In-situ reflectance and remote Sensing reflectance measurements from the Look-Up-Table of Mobley (Mobley, 2015), based on sensor
The Remote Sensing Reflectance (Rrs) spectra were acquired geometry settings (sun zenith and azimuth angles) and wind speed. At
concomitant with Zsd measurements. The data for Amazon Basin (earlier each sampling station, around 150 measurements of Lt, Lsky, and Es were
2011), and Ibitinga Reservoir (2005), were collected using the Spectron acquired in approximately 20 min. The Rrs spectrum was post-processed,
SE-590. The data for Amazon Basin between 2011 and 2013, were with outliers removed by visual analysis. From that filtered dataset, the
collected using HandHeld-2 FieldSpec, and the remaining data were Rrs was calculated based on the median spectrum, following the pro
collected using three intercalibrated TriOS-RAMSES radiometers oper cedure described in Maciel et al. (2019).
ating in the 350–950 nm spectral range. Each TriOS instrument For Amazon campaigns before 2011, and Ibitinga campaign of 2005,
measured, simultaneously, the downwelling irradiance above the water the bidirectional reflectance spectra were obtained using a Spectron SE-
surface (Es(λ, θ, ∅)), total water-leaving radiance (Lt(λ, θ, ∅)), – with a 590 spectroradiometer, operating in the range of 400–1000 nm. For
nadir angle (θ) of 45◦ and an azimuthal angle (∅) of 135◦ from the sun, Amazon Campaigns after 2011 and before 2013, the HandHeld-2
and the sky radiance (Lsky(λ, θ“, ∅)) with a zenithal angle (θ”) of 45◦ and FieldSpec operating in the range of 400–1000 nm were used. For both
an azimuthal angle of 135◦ from the sun. The measurements followed equipment, the spectra of a Lambertian Spectralon target and water
the protocols proposed by Mobley (1999) to avoid sunglint effects (i.e., surface were obtained. Water surface measurements were taken within
the geometric position of sensors). Moreover, the spectroradiometers 45◦ of zenith angle and 135◦ azimuth angle to the sun. The reflectance
136
factor was calculated as the ratio of Water Surface Reflectance to the It is important to highlight the differences between protocols for the
Labertian Spectralon target. Ten measurements were obtained for each radiometric instruments used in this study. First, while TriOS-RAMSES
field station, and the representative spectral were calculated as the sensors measured the Es, Lsky, and Lt, Spectron SE-590 and HandHeld-
geometric mean of all samples after outlier removal. Finally, to convert 2 FieldSpec measured the reflectance factor without Lsky measure
the data to Remote Sensing Reflectance, the reflectance factor was ments, which does not allow the use of Mobley (1999)’s glint correction
divided by π. method. Moreover, the Spectron SE-590 and HandHeld-2 view angles
Fig. 2. Framework proposed for Zsd algorithms training, validation, and application to Sentinel-2 imagery in Google Earth Engine platform.
137
are manually operated, increasing the uncertainties in those measure 2.3.1.1. Prediction variables and hyperparameters tunning. All algorithms
ments. Therefore, considering the difference in the protocols for each used the same input data for prediction. The features consists of: In-situ
database, and the possible impacts of glint correction in the Rrs mea Remote Sensing Reflectance data for MSI bands 2–6 (490, 560, 660, 705,
surements, an exercise were performed to evaluate the impacts of a re and 740 nm), the Normalized Difference Chlorophyll Index (NDCI)
sidual glint correction method (Cairo et al., 2020; Jiang et al., 2020) in (Mishra and Mishra, 2012), which has a high correlation with Chl-a
the accuracy of the algorithms. The results did not indicate a significa concentration, and band ratios: i) Rrs(5 6 0)/Rrs(4 9 0), to highlight ef
tive difference in the algorithms accuracy after the glint correction. The fects of CDOM absorption (Da Silva et al., 2020), and ii) Rrs(5 6 0)/
result of this exercise is presented in Supplementary Files 1. To reduce Rrs(6 6 5), and iii) Rrs(5 6 0)/Rrs(7 4 0) to highlight effects of sediment
the uncertainties in Spectron SE-590 data, the data from this instrument concentration (Doxaran et al., 2002). As the algorithms were calibrated
were manually filtered to exclude outliers or glint-contaminated spectra. using in-situ data, the Sentinel-2 bands at 780, 840, and 860 nm were
Finally, the Rrs spectra were used to simulate the spectral bands of the excluded from the algorithm training due to uncertainties in atmo
Sentinel-2/MSI sensor, using their respective spectral response function spheric correction (Bernardo et al., 2017; Curtarelli et al., 2020; Maciel
(SRF). et al., 2019; Pahlevan et al., 2021).
For hyperparameters tuning, the R package caret was employed
(Kuhn, 2020). The tuning consists in varying the hyperparameters of
2.3. Secchi disk depth estimates from Rrs each algorithm using a K-Fold cross-validation technique. In this study
we used 5-fold cross-validation (K = 5). Therefore, the dataset was
The approach adopted for estimating the Secchi Depth from Rrs divided into train (4 datasets) and validation (1 dataset). The process is
(Fig. 2) is described in the next topics and consisted of running several repeated until all folds were used in the tuning process. For each fold,
semi-analytical and machine learning algorithms through a Monte Carlo the hyperparameters of each algorithm were randomly varied 100 times.
calibration, validation, and model selection scheme and, then in the The best hyperparameters were, therefore, mean values of these folds
application of the best model to the Sentinel 2 MSI time series. (Xiong et al., 2020). Therefore, for all algorithms, the tunning was
carried out using all data (N = 1492). For Random Forest algorithm, the
2.3.1. Machine learning approaches hyperparameters tunned in this study were the Number of Trees (ntree
In this study, we selected three Machine Learning algorithms to = 62) and the number of variables in each split (mtry = 6). For the SVM
evaluate their potential in estimating Zsd for Brazilian waters: i) Random algorithm, the kernel function radial was adopted with a cost function
Forest Regression; ii) XGBoost, iii) Support Vector Machine. These equal to 4. Finally, for XGBoost algorithm, the number of trees was 20
methods were selected considering the Machine Learning methods (nrouds = 20), maximum depth of each tree was set as 10 (max.depth =
available in GEE platform, and because they have been successfully 10), learning rate was set as 1 (eta = 1), gamma was set as 0.3 (gamma =
applied in water quality studies (Liu et al., 2021; Rubin et al., 2021). 0.3), and minimum leaf weight was set as 1 (min_child_weigth = 1).
The Random Forest algorithm is an ensemble learning algorithm that After the training process of the Machine Learning algorithms, we
deals with regression and classification problems (Breiman, 2001). assessed the variable importance to observe which variables better
Random Forest algorithm operates by generating several decision trees explained the Zsd variation. Variable importance will explain what input
based on training datasets using a bagging technique. For each tree, a data have the highest predictive power in the developed model (Liaw
prediction is generated considering a random sample of the training and Wiener, 2002). For example, in Random Forest Regression the
dataset. From these several decision trees, the final value is calculated variable importance could be assessed using the Increment in Mean
based on the mean values of all decision trees. The Random Forest al Square Error (IncMSE), which is the error in each tree whenever a given
gorithm has been widely used by the remote sensing community in land variable is permuted between trees. As the error increase, the more
use/land cover classification (Diniz et al., 2020; Uehara et al., 2020; important the variable is to explain the variability in Zsd (Genuer et al.,
Zurqani et al., 2018). However, it was only recently applied for water 2010). For XGBoost, one of the widely used metrics is the Gain, which
quality studies (DeLuca et al., 2018; Larson et al., 2021; Rubin et al., measures the relative contribution of a given variable in each of the
2021). algorithm’s tree. Similar to IncMSE, the higher Gain indicates higher
Support Vector Machine (SVM) is a kernel-based supervised method importance (Chen and Guestrin, 2016)
developed by Cortes and Vanik (1995) for binary classification and then
expanded to other classifications and regression problems. In this study, 2.3.2. Semi-analytical approaches
we used the SVM for regression, considering the explicative variable the To assess the reliability of Machine Learning methods for Zsd
Zsd. SVM relies on a non-parametric approach based on the theory of retrieval, we compared their results with those of the three semi-
structural risk minimization. Thus, SVM looks into an optimal separa analytical algorithms recalibrated for Brazilian Inland Waters. The
tion between the training data by maximizing the margin between semi-analytical algorithm was initially proposed by Lee et al. (2015) and
extreme points. These points are the support vectors, and the middle of is based on three main steps: 1) retrieval of absorption and backscat
both points is the hyperplane. For SVM regression, the best fit line is tering coefficient using an inversion method; 2) calculation of Diffuse
considered by the hyperplane that presents the highest number of Attenuation Coefficient of Downwelling Irradiance (Kd); 3) calculating
points. SVM has been successfully applied for water quality studies the Zsd from Kd and Rrs data. These steps will be briefly explained below.
(Deng et al., 2019; Larson et al., 2021; Peterson et al., 2018; Sun et al., The retrieval of total absorption (at(λ)) and backscattering (bbp(λ))
2014; Zhao et al., 2018). coefficients are needed as input to the Kd algorithm (Equation (2)).
The Extreme Gradient Boosting (XGBoost) is a recent implementa However, the accurate modeling of at(λ) and bbp(λ) in optically complex
tion of the Gradient Boosting algorithm (Chen and Guestrin, 2016). It inland waters is challenging. Besides, environments with different op
has a similar principle to the Random Forest algorithm, being an tical water types may require different algorithms for inversion of Rrs
ensemble learning algorithm based on decision trees. However, differ and retrieval of IOPs. In the last years, several efforts have been con
ently from Random Forest, XGBoost uses an additive training strategy ducted in Brazil for retrieving both apparent and inherent water optical
that follows a loss function to boost its ensemble learning process. proprieties (Curtarelli et al., 2020; da Silva et al., 2020; Jorge et al.,
XGBoost algorithm will use the errors of the previous trees to minimize 2017; Maciel et al., 2020a; Rodrigues et al., 2017; Rotta et al., 2021,
the bias in the following ones and the final prediction will be the mean 2019; Sander de Carvalho et al., 2015; Watanabe et al., 2016). There
values of each decision tree. Despite its novelty, some studies demon fore, this study takes advantage of recently published approaches for
strated the potential of XGBoost for water quality estimates (Liu et al., IOPs retrieval in Brazilian environments to evaluate its applicability in
2021; Smith et al., 2021). the Zsd SAA scheme and compare it with Machine Learning methods. We
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selected three algorithms for IOPs retrieval based on the environments methods were those obtained as described in Section 2.3.1.1. At each
in which they were developed: i) SAA recalibrated for Amazon Flood round of Monte Carlo simulation, the Mean Absolute Percentage Error
plain Lakes (Maciel et al., 2020); ii) SAA recalibrated for Três Marias (MAPE) (Equation (5)), Root Mean Squared Error (RMSE) (Equation
Reservoir (Curtarelli et al., 2020), and; iii) SAA recalibrated for Lower (6)), BIAS (Equation (7)), Median Absolute Error (mAE) (Equation (8)),
Tiete River Basin (Watanabe et al., 2016). Therefore, these algorithms and Pearson Correlation Coefficient were calculated. Note that BIAS and
were used for IOPs retrieval to be applied in the next steps of the Zsd mAE are calculated in the multiplicative space (log-scale), and therefore,
SAA. are dimensionless (Seegers et al., 2018). A BIAS of 1.1 indicates that
( ) predicted Zsd is 10% greater on average than the in-situ measured Zsd,
bbw (λ) ( )
Kd− Lee (λ)=(1+m0 θ0 )*at (λ)+ 1− γ* *m1 * 1− m2 *e− m3 *at (λ) *bb (λ) and mAE values of 1.1 indicates a median relative error of 10%.
bb (λ)
Differently from that performed with the Machine Learning methods,
(2) SAA were not calibrated using the in-situ data, as previously recalibrated
Where the parameters γ and m0-3 were obtained from Hydrolight algorithms for Brazilian inland waters were adopted. Two assessment
simulations and are spectrally constant and do not vary with water methods were used to compare SAA with Machine Learning algorithms:
properties (Lee et al., 2013, 2005), θ0 is the solar zenith angle (degrees), 1) At each round of Monte Carlo simulation, the SAA algorithms were
and bbw (λ) is the pure water backscattering coefficient (Zhang and Hu, applied to the same validation dataset (N = 453) used for ML methods
2009). After obtaining Kd, Zsd is semi-analytically derived using the new validation (resulting in a “global” validation), and; 2) At each round of
underwater visibility theory, proposed by Lee et al. (2015) in an update Monte Carlo simulation, the validation dataset was grouped by lakes/
of drawbacks in the classical theory presented by Duntley (1952). Ac reservoirs with more than ten validation samples (Curuai, Mamirauá,
cording to the new underwater visibility theory, Zsd is inversely pro Billings, Ibitinga, and Três Marias) (resulting in a “lake/reservoir”
portional to the Kd and Rrs in the visible domain (i.e., from 400 to 700 validation). Therefore, the statistics for both methods (ML and SAA)
nm) (Equation (3)). The KTR d and Rrs refers to the Kd and Rrs in the
TR were computed for each environment, making it possible to compare
transparent window (i.e., wavelength with the minimum value of Kd in SAA performance for the environment to which each algorithm was
the visible domain). This wavelength was automatically selected based calibrated. After the Monte Carlo process, the algorithm (e.g., Random
on Kd calculated for each station using Equation (2). Forest, SVM) that presented the better statistics results was selected and
⃒ ⃒ implemented in the Google Earth Engine platform. Please, note that the
⃒0.14 − RTR ⃒
Zsd =
1
*ln( rs
) (3) for the algorithm implementation in GEE platform, the whole samples
(1 + KKt )*Min(KdTR )
d
0.013 (N = 1492) were used to be applied in the Sentinel-2 MSI imagery.
Where Kt
Kd
is the relationship between the upwelling radiance diffuse ∑ n
|esti − measi |
MAPE = 100* (5)
attenuation coefficient (Kt) and Kd. In Lee et al. (2015), this ratio was i=1
measi
empirically obtained and is equal to 1.5. However, this assumption
√̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
could be a source of uncertainties in waters baring widely different √ n
√∑
optical proprieties as values of KKdt may vary between 0.5 to up to 2 (Jiang RMSE = √ (measi − esti )2 (6)
et al. 2019). To overcome those uncertainties, Jiang et al. (2019) i=1
employed an update of the algorithm proposed by Lee et al. (2015) to ∑n log10 (esti )− log10 (measi )
account for the variability in KKdt according to different optical water BIAS = 10 i=1 n (7)
types. Based on simplifications of the radiative transfer theory, Jiang
et al. (2019) obtained an Equation to express the relationship between Kt mAE = 10median(|log10 esti − log10 measi | )
(8)
and Kd (Equation (4)). Where esti represented the Zsd estimated for each field station i, and
Kt 1.04(1 + 5.4*u)0.5 measi, represents each measured Zsd for station i.
= (4)
Kd ( 1 )0.5
1−
sin2 (θ) 2.5. Satellite data
RI 2
Where RI is the water refractive index (1.34) (Mobley, 1994), θ is the Sentinel-2A and 2B satellites were launched in 2015 and 2017 by the
sun zenith angle, and u is the ratio between the backscattering coeffi European Space Agency. The sensor aboard those satellites (MSI –
cient to its sum with the absorption coefficient (bb/(bb + a)). Thus, Zsd is MultiSpectral Instruments) provides 13 spectral bands, ranging from the
calculated using the updated algorithm. Considering the explained blue to the shortwave infrared, with a spatial resolution of 10–60 m.
above, the Jiang et al. (2019) SAA for Zsd were employed to retrieve Zsd, Moreover, when both satellites were considered, it provides five days of
with Kd semi-analytically derived using three IOP inversion methods: temporal resolution, enabling to detect small-scale hydrological process.
Maciel et al. (2020a) (For turbid waters of Amazon Floodplain Lakes); Its temporal resolution increases the possibility of cloud-free scene
Curtarelli et al. (2020) for clear waters; and Watanabe et al. (2016) for acquisition, mainly in tropical regions subjected to high cloud cover,
eutrophic waters. such as Amazon Basin (Asner, 2001; Martins et al., 2018). The correct
application of any Remote Sensing algorithm requires an accurate and
robust atmospheric correction method to retrieve the truly Remote
2.4. Machine Learning algorithm validation and performance evaluation Sensing Reflectance. As water bodies generally have low reflectance
values, this correction is important to avoid aerosol scattering and at
The validation of Machine Learning algorithms was performed using mospheric gas absorption (Martins et al., 2017).
Monte Carlo simulation. Monte Carlo simulation is a bootstrapping In this study, the Sentinel-2 imageries were acquired and processed
procedure that randomly selects a given percentage of the dataset for using the GEE platform, with 20 m of spatial resolution. The Surface
calibration and the remaining for validation of determined algorithm Reflectance data for Sentinel-2/MSI image collection available in GEE is
(Liu et al., 2021; Maciel et al., 2019). This operation is repeated several delivered using the Sen2Cor processor. However, for Brazilian territory,
times, allowing the construction of confidence intervals. This study Surface Reflectance data were available only for images acquired after
conducted 1000 rounds of Monte Carlo simulation, with 70% of the 2019. Therefore, if the user needs surface reflectance for dates before
dataset (N = 1043) for algorithm calibration and 30% (N = 449) for 2019, an atmospheric correction should be performed. To keep the
algorithm validation. The hyperparameters of the Machine Learning process in the GEE platform, we adopted the Sensor Invariant
139
Atmospheric Correction (SIAC) (Song et al., 2020; Yin et al., 2019) Sentinel-2 data from seven different dates and locations (Table 1) were
method for images before 2019. used to validate atmosphere correction methods (SIAC and Sen2Cor)
Sen2Cor is a scene-based method that uses the Dark Dense Vegeta and the Zsd algorithm. These images were selected based on available
tion algorithm to retrieve visibility and aerosol type. The water vapor for match-ups with cloud-free data. Note that for Sen2Cor validation, only
land areas is retrieved using the Atmospheric Pre-corrected Differential dates after 2019 were used. For the match-ups, only images with ± 2
Absorption algorithm based on bands 8A and 9. When the atmosphere days of difference between satellite overpass and in-situ measurements
parameters are known, the atmospheric correction is performed using a were selected.
set of Look-Up Tables generated using libRadtran (Louis et al., 2016).
Sen2Cor has been used for water applications in previous studies and 3. Results
presented reasonable results (Maciel et al., 2019; Martins et al., 2017;
Pereira-Sandoval et al., 2019). On the other hand, the SIAC method uses 3.1. In-situ data variability
the coarse-resolution spectral Bidirectional Reflectance Directional
Function (BRDF) derived from MODIS MCD43A3 datasets (500 m) to The water quality parameters (TSS, TSI, TSO, Chl-a, aCDOM, and Zsd)
describe surface anisotropy and the Copernicus Atmospheric Monitoring observed from the dataset used in this study indicate the high variability
Service (CAMS) as a prior estimative of atmospheric composition, which in Brazilian territory (Fig. 3). The Zsd data presented the lowest median
will be used to solve an inversion problem. Therefore, the MODIS data is values for the Amazon Basin (AMZ) dataset (median Zsd of 0.4 m), fol
mapped to Top-Of-Atmosphere (TOA) using the radiative transfer model lowed by São Paulo (SP) (0.98 m), Paraná (PR) (1.4 m), Rio de Janeiro
to be compared with higher spatial resolution data, and CAMS data were (RJ) (1.4 m), and Minas Gerais (MG) (2.12 m) data. However, it is
used to solve the inversion problem. The atmospheric correction was important to observe that |Zsd values for the Amazon Basin dataset had
divided by π to be converted to Remote Sensing Reflectance (Rrs). More remarkable variations, with values ranging from 0.05 m in Curuai Lake
detailed information about SIAC could be obtained in Yin et al. (2019) to up to 4.6 m in the clear waters of Tucurui Reservoir. The patterns of
and Song et al. (2020), and more details about Sen2Cor could be ob Zsd are a consequence of the concentrations of the optically active
tained in Louis et al. (2016). The code used for running SIAC could be constituents, whose variability depends on the region. For example, in
obtained in https://github.com/MarcYin/SIAC_GEE. the Amazon Basin (AMZ), suspended sediments presented the highest
After the atmospheric correction process, a glint correction based on median values (TSS = 22.7 mgL-1), with maximum values of 1138 mgL-1,
subtraction of NIR (Band 08 – 850 nm) or SWIR band (Band 11 – 1600 according to the hydrological and sedimentological variation of TSS in
nm) was performed (Wang and Shi, 2007). To switch between using NIR this region (Barbosa et al., 2010). On the other hand, Chlorophyll-a
or SWIR band for glint correction, we adopted a threshold based on concentration was higher in SP, comprised of eutrophic environments
Sentinel-2 Band 06 (740 nm). If Rrs (7 4 0) is higher than 0.003 sr-1, the such as Billings and Ibitinga Reservoirs, with a maximum Chl-a con
SWIR method is used. This threshold was based on in-situ Rrs data, which centration of 1410 μgL-1. Regarding aCDOM(4 4 0), the values were
indicated that when Rrs(7 4 0) is < 0.003, TSS concentration is < 5 mgL-1 higher in the AMZ, followed by MG, SP, and RJ states.
preventing the backscattering coefficient from exceeding the NIR ab The variability in the OACs is reflected in the observed in-situ Rrs
sorption (Vanhellemont, 2019). This method assumes that the remain values (Fig. 4). For SP region, the occurrence of algae blooms is frequent.
ing signal in the NIR or SWIR band is related to the specular reflectance Therefore, some spectra presented a clear effect of high Chl-a concen
in the air–water interface, as the signal of water itself should be negli tration, with Rrs in wavelengths longer than 700 nm higher than those of
gible at this band due to extremely high absorption by pure water the VIS bands. For example, for Ibitinga reservoir, Rrs in ~ 740 nm
(Knaeps et al., 2015). Therefore, subtracting this signal should remove reached values up to 0.28 sr-1 in an extreme bloom event (Chl-a con
the glint effects. This method was previously evaluated in several Bra centration > 1000 µgL-1). The higher values of Rrs in VIS bands were
zilian water studies using Landsat-8 and Sentinel-2 data and presented observed for Curuai Lake, in locations with up to 1000 mgL-1 of TSI, and
satisfactory results (Cairo et al., 2020; Lobo et al., 2015; Maciel et al., for Amazon River, with TSS of approximately 250 mgL-1. For the MG
2020a). dataset, the spectra presented expected shape and intensity of clear
For cloud, cloud-shadow and land-pixels masking, we adopted the water. The dataset for PR, in Itaipu Reservoir also showed a clear water
following procedure: First, the Pekel et al. (2016) JRC Global Surface behavior, with Rrs values slightly higher than those for MG.
Water Mapping Layers v1.3 was used to exclude areas with water
occurrence lower than 60%. This threshold was used to select locations
3.2. Assessment of Secchi disc depth algorithm performance
in the Amazon Floodplains that naturally transits between water and
land along the hydrological year (Bourgoin et al., 2007). After applying
The global performance of Machine Learning (ML) methods and SAA
Pekel’s water mask, the Sentinel-2 Cloud Probability Product was used
assessed from Monte Carlo simulation is shown in Table 2. The Monte
to select only pixels with up to 10% of cloud probability. Finally, the
Carlo simulation results for the three ML methods demonstrate their
Modified Normalized Water Index (mNDWI) (Xu, 2006) was calculated
potential for estimating Zsd. The Random Forest (RF) algorithm out
to exclude the possibility of inclusion of non-water pixels in the previous
performed the other two ML (SVM and XGBoost) and SAA in almost all
masks. In this study, we calculated the mNDWI using the normalized
statistical metrics. Mean MAPE for RF was 21.29%, followed by XGBoost
difference between green and SWIR1 bands, with a threshold of 0.1.
(26.87%) and SVM (29.39%). The mAE value was 1.12 for RF, followed
Table 1
Sentinel-2/MSI Images used for atmospheric correction and algorithm validation. SZA and SAzA refer to Sun Zenith Angle and Sun Azimuth Angle in degrees.
Tile Number Date Location Acquisition Time SZA (◦ ) SAzA (◦ ) Cloud Cover (%) Number of Valid Samples
(UTC – 3)
21MXT Aug/28/2019 Curuai 10:10:49 26.60 58.68 14.92 15

21MXT Aug/08/2017 Curuai 10:13:29 29.70 51.22 15.22 12
21MZT Jul/14/2016 Curuai 10:13:06 33.30 43.05 18.96 16
21MZT Aug/15/2017 Monte Alegre 10:05:31 28.86 55.24 31.89 6
23KLP Nov/06/2020 Billings Reservoir 10:17:04 22.45 74.75 13.69 35
23KLP Aug/09/2021 Billings Reservoir 10:12:51 48.21 37.70 0.27 41
22KGA Aug/08/2018 Ibitinga Reservoir 10:31:46 45.65 38.88 0 8
23KMV Jul/01/2019 Três Marias Reservoir 10:12:47 49.33 33.41 01.49 19
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Fig. 3. Variation of in-situ water quality parameters for the dataset used in this study. Chl-a unit is in µgL-1. TSS, TSI, and TSO units are in mgL-1. aCDOM unit is in
meters− 1, and Zsd unit is in meters.
Fig. 4. Variability of in-situ Rrs spectra in the selected regions and locations. Color refers to each location. Please, note that y-axis of each figure is in different scale.
141
Table 2 SAA approaches accuracy improved considering the reduced dataset, the
Results of the Monte Carlo simulation for the Machine Learning and the Semi- ML methods still outperform. For Curuai Lake, MAPE of 20.38% was
Analytical approaches considering the complete dataset. obtained for RF compared to 39.30% for the best-performed SAA
Machine Learning Algorithms Semi-Analytical Algorithms (Maciel20). However, for the Três Marias reservoir, the SAA developed
Statistic RF SVM XGBoost Maciel Curtarelli Watanabe
by Curtarelli et al. (2020) presented similar results compared to the ML
et al. et al. et al. approaches (18.02% for Curtarelli20 against 17.58% for SVM). These
(2020a) (2020) (2016) results indicate what is expected: SAA performs well for the environ
BIAS 1.05 0.94 1± 0.92 ± 0.93 ± 1.23 ± ment in which they were calibrated and did not perform well in other
± 0.02 ± 0.02 0.02 0.02 0.03 environments. ML approaches are, therefore, a feasible solution when
0.05 dealing with data from different sources and locations. In this compar
MAPE 21.29 29.39 26.87 ± 44.23 50.31 ± 108 ± 5.2 ison, RF performed better in almost all scenarios, following what was
(%) ± 2.07 3.32 ± 1.14 2.13
observed for the complete dataset.
±
2.86
mAE 1.13 1.19 1.16 ± 1.45 ± 1.39 ± 1.69 ± To illustrate the performance of both methods for Zsd retrieval, a
± 0.01 ± 0.01 0.04 0.03 0.02 scatterplot of in-situ measured Zsd versus Zsd estimated are presented in
0.01 Fig. 5. This scatterplot is for the 50th iteration of the Monte Carlo
Pearson 0.94 0.93 0.91 ± 0.71 ± 0.87 ± 0.53 ±
simulation (from the 1000). Note that the statistics of this iteration are
R ± 0.02 ± 0.02 0.02 0.02 0.03
0.01 close to the Monte Carlo simulation results provided in Table 1. From
RMSE 0.27 0.29 0.34 ± 1.17 ± 0.45 ± 0.7 ± 0.03 Fig. 5, we can observe that RF provides more realistic estimates of Zsd for
± 0.03 ± 0.04 0.08 0.03 a wide range of values (0 to up to 4 m).
0.03 Fig. 6 demonstrates the variable importance for RF and XGBoost
algorithm when all samples are used (n = 1485), as these algorithms
by 1.16 and 1.19 for XGBoost and SVM, respectively. For BIAS, XGBoost presented the best results. For RF, the most important variables
performed better than RF, with a mean value of 1, indicating that, on (measured by the Increment in Mean Square Error (MSE)) were B3/B4
average, the model neither underestimates nor overestimates Zsd. The ratio, NDCI, and Rrs(7 0 5). Therefore, if those variables were removed
BIAS for RF was 1.05, indicating a slight overestimation of Zsd values from the algorithm, the error would increase. This endorses that these
(5%). RMSE values were lower for the RF method (0.27 m). The corre variables give the model high explanatory power regarding Zsd varia
lation (Pearson R coefficient) between predicted and measured Zsd was tion. Regarding XGBoost, Rrs(7 0 5) and B3/B4 were the most important
higher for RF (0.94), followed by SVM (0.93) and XGBoost (0.91). When variables.
the ML approaches were compared to SAA algorithms considering the
full dataset, they outperform SAA, which is expected since the optical 3.3. Atmospheric correction evaluation
water types used in this study are highly variable. Moreover, each SAA
was calibrated in a specific environment, restricting the global appli For atmospheric correction validation, we assessed the accuracy for
cation of those algorithms. all bands used in this study (Bands 2–6) (Fig. 7). As the data available
After comparing SAA and ML approaches using the Global Valida using Sen2Cor and SIAC were not the same, the sample size was not the
tion, we assessed the performance of both methods using the Local same (See Table 1). There were 105 match-ups for the Sen2Cor, while
Validation approach (See in Fig. 2 and Section 2.4). For that analysis, for the SIAC 153 match-ups were available. Fig. 7 presented the results
each round of Monte Carlo simulation results was grouped by each lake for SIAC considering i) same match-ups of Sen2Cor, and ii) all available
with N > 10, and the statistical metrics calculated (Table 3). Although match-ups. For the Blue Band (B2), SIAC (MAPE = 20.14%, mAE = 1.2,
Table 3
Results of the Monte Carlo simulation for Machine Learning and Semi-Analytical approaches considering only lakes with N > 10 for the validation dataset.
Location Statistc RF SVM XGB Maciel20 Curtarelli20 Watanabe16
Billings MAPE 21.39 19.42 27.32 47.56 26.55 35.27

R 0.66 0.74 0.54 0.51 0.54 0.023
BIAS 10.7 10.6 10.3 0.99 0.83 0.79
mAE 1.08 1.09 1.1 1.43 1.24 1.28
RMSE 0.18 0.15 0.25 0.53 0.23 0.29
Curuai MAPE 20.38 33.04 25.86 39.30 63.25 154.11

R 0.92 0.92 0.84 0.89 0.86 0.76
BIAS 1.07 0.91 1.01 1.04 1.19 1.94
mAE 1.11 1.23 1.15 1.42 1.40 1.78
RMSE 0.10 0.10 0.14 0.15 0.14 0.23
Ibitinga MAPE 32.79 46.25 44.81 56.55 45.75 62.31

R 0.93 0.91 0.81 0.77 0.88 0.53
BIAS 0.92 0.94 0.88 0.39 0.57 0.61
mAE 1.23 1.26 1.32 2.46 1.78 1.96
RMSE 0.36 0.43 0.52 0.88 0.84 1.04
Mamiraua MAPE 23.88 20.20 28.77 34.41 17.03 37.13

R 0.81 0.87 0.63 0.70 0.81 0.12
BIAS 1.11 1.09 1.04 0.63 0.92 1.04
mAE 1.21 1.15 1.26 1.54 1.15 1.39
RMSE 0.24 0.23 0.34 0.49 0.28 0.44
Três Marias MAPE 18.09 17.58 24.03 195.89 18.02 70.70

R 0.85 0.74 0.72 0.5 0.81 0.68
BIAS 1.02 0.94 0.98 2.70 0.85 0.28
mAE 1.12 1.14 1.16 3.08 1.19 3.54
RMSE 0.51 0.67 0.71 4.75 0.7 2.28
142
Fig. 5. Scatterplots of Zsd retrieved using Machine Learning (Random Forest, XGBoost, SVM), and SAA (Maciel20, Curtarelli20, Watanabe16) methods and in-situ
measured Zsd.
Fig. 6. Variable importance employing Increment in Mean Square Error (Random Forest) and Gain (XGBoost).
BIAS = 0.9) presented best results than Sen2Cor (MAPE = 28.3%, mAE 20.16% for SIAC and Sen2Cor, respectively). Moreover, SIAC full dataset
= 1.33, and BIAS = 0.85) in the comparison with the same match-ups. also presented a stable behavior, with MAPE of 18.77%, mAE of 1.17
The errors remain almost the same when all possible (Full) match-ups and BIAS of 0.97. For the remaining bands evaluated in this study (B4-
for SIAC were compared in the blue band (e.g. mAE = 1.21, BIAS = B6), Sen2Cor presented better results. Considering the bands B4 and B5,
0.93, and MAPE = 21.2%), indicating an stability in the validation MAPE values for Sen2Cor were lower than 24%, with BIAS between 0.77
dataset and in the atmospheric correction method. For Band 3, SIAC still and 0.86, mAE between 1.26 and 1.22, and Pearson R higher than 0.9.
presented slightly better results than Sen2Cor (MAPE = 19.5% and For the comparison between the same match-ups with SIAC, the later
143
Fig. 7. Validation of atmospheric correction for Sen2Cor and SIAC methods with the same match-ups and validation of SIAC with all dataset. Colors in each plot refer
to the location of each field station and is summarized in the top-left box of the first figure.
presented MAPE lower than 42%, with mAE between 1.17and 1.22,
BIAS between 1.11 and 1.2, and Pearson R higher than 0.9. The higher
errors for both methods occurred in the Band 6, centered at 740 nm. For
Sen2Cor, MAPE was 68.19%, mAE was 1.3, BIAS 0.95, and Pearson R
was 0.81. Errors increased for SIAC, with MAPE of 222.06% and mAE of
1.54 for the dataset with the same match-ups. It is important to highlight
in this comparison that, although the differences between the MAPE
values, the other statistical metrics remained reasonable. Moreover, for
skewed distributions, small deviations for low Rrs increase MAPE values,
demanding metrics calculated in the logarithmic scale, such as BIAS and
mAE (Seegers et al., 2018). These metrics, therefore, demonstrate the
reasonability of both methods for retrieving Rrs (490–740). An addi
tional evaluation was performed comparing the Rrs obtained with SIAC
and Sen2Cor for both methods in Billings Reservoir and in Curuai Lake
(Images from 2019, and 2021). The comparison (not showed here)
presented mAE values between 1.03 and 1.46, with a maximum RMSE of
0.005 sr-1, indicating a reasonable agreement between both methods.
Fig. 8. Validation of Zsd from Random Forest algorithm. Sampling point shape
refer to each atmospheric correction method (Sen2Cor or SIAC).
144
3.4. Application of Zsd Random Forest algorithm to Sentinel-2 imagery 3.5. Spatiotemporal patterns of Zsd in selected regions
The application of the Random Forest algorithm to Sentinel-2 im To illustrate the application of the developed algorithm and to un
agery to estimate Zsd was performed at the locations having match-ups derstand the Zsd spatiotemporal variability along hydrological years,
for validating the calibrated algorithm (Fig. 8). For dates before 2019, average monthly time series of Zsd were generated for two environ
SIAC atmospheric correction method was used, and after that, the at ments: Lower Amazon Floodplain Lakes; and for Billings Reservoir,
mospheric correction was performed using Sen2Cor. The validation considering Sentinel-2 data available between 2015 and 2020. Both
dataset comprises Zsd ranging from almost 0 up to 4.3 m. The results locations have different variability in the OACs: Amazon Floodplain
presented MAPE values of 27.95%, with BIAS of 1.12, similar to the lakes are characterized by their optical complexity and high concen
observed using in-situ Rrs. mAE results were also accurate, with values of tration of inorganic sediments, while Billings Reservoir is characterized
1.25. Moreover, Pearson R was 0.94. It is important to observe that by frequent algae blooms and, therefore, high Chl-a concentrations.
Pearson R could be misleading due to the two data groups (Zsd < 2 m and
Zsd > 2 m). Nevertheless, the other statistical metrics demonstrated the 3.5.1. Curuai lake and lower amazon floodplains
feasibility of the proposed algorithm. These results indicate that the The Zsd variability based on Sentinel-2 in Curuai Lake presented a
Random Forest Regression implemented in GEE, aligned with both at pattern related to the hydrological phase in the region (Fig. 10). The
mospheric correction algorithms, can estimate Zsd with reasonable ac water level of the Amazon River controls inorganic and organic sedi
curacy and suggest that the results were not highly biased regarding the ments input and output to the floodplain lakes. As the OACs presented
variability of the Optical Water Types used in this study. variability, Zsd follows this pattern. The water level at Óbidos station
The proposed algorithm was then applied to Sentinel-2/MSI images varies almost 5 m during the hydrological year. Following this pattern,
for an area in the Amazon Basin region for July/2019 to observe the the temporal variation of Zsd in the Amazon River is regulated by the
spatial patterns of Zsd and to demonstrate the applicability in a basin rain and thaw processes that occur in the Andes region between
scale. For those dates, we can observe that the Zsd values were lower at December-March (the rainy period at the top of the basin). In the
Madeira, Solimões, and Amazon River (Fig. 9A), in response to their floodplain lakes, the higher values of Zsd occur between May-July, when
sediment-rich characteristic. Higher values of Zsd were observed for the Amazon River is in the high-water period. Tapajós River presented a
Negro, Tapajós, and Xingu Rivers, which was also expected due to their slightly different behavior, with the higher Zsd values for August and the
lower sediment concentration. The algorithm also captured the different lowest values in January.
Zsd values at the confluence of different rivers of the Amazon Basin, as it
is possible to observe in the confluence of Solimões and Japurá (Fig. 9B), 3.5.2. Billings reservoir
Solimões and Negro (Fig. 9C), and Negro and Branco Rivers (Fig. 9D). The variability in Zsd was also evaluated for Billings Reservoirs (São
Paulo) (Fig. 11). The analysis revealed a high degree of spatial and
temporal heterogeneity in the analyzed parameter along the reservoir.
The highest Zsd values were mostly observed in the northeast arm (Rio
Fig. 9. Zsd variation for a subset area in the Amazon River basin considering cloud-free pixels for July/2019. The boxes B-F refers to the zoomed red box in A main
box. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
145
Fig. 10. Spatiotemporal variation of Zsd in Lower Amazon Floodplain lakes.
Grande), while the lowest frequently occurred in the northwest arm applications. It is free for the research community and has made avail
(Central Body). Despite recording the lowest values of Zsd from the time able a large amount of data, including the full catalog of surface
series, the Central Body presented an alternation of the water clarity reflectance data for the Landsat-like family. However, for the Sentinel-
state depending on the evaluated period. The same pattern was observed 2/MSI, there is still a lack of atmospherically corrected data for South
in the southwest arm (Taquacetuba) and, although in lower intensity, in America countries, to which GEE provides surface reflectance data only
the south arm (Capivari). The Rio Grande and the Rio Pequeno (east for 2019 and onwards. Although GEE allows the development of ap
arm) have the most time stable Zsd measures for the studied period, plications using Python programming language through its API, it is still
indicating lower variation in those arms’ water quality during the year. limited in its web interface to scripts created by the GEE community, not
allowing, for example, the use of recent machine learning methods
4. Discussion available in Python or R languages. Considering this fact, adding a new
processing chain to GEE is not an easy task and prevents users from
This study investigates the performance of three widely used Ma implementing their atmospheric correction method (e.g. ACOLITE). The
chine Learning methods (Random Forest, Support Vector Machine, and Python interface has enabled the possibility of using physical methods
XGBoost) to estimate water clarity in Brazilian inland waters. Moreover, such as the 6S. However, users still are not able to implement it in the
these algorithms were compared to state-of-art semi-analytical Zsd al web application.
gorithm. For semi-analytically derive Zsd, three reparametrized Quasi- To overcome that, Yin et al. (Yin et al., 2019) developed and
Analytical Algorithms for Brazilian waters were used for IOPs implemented the SIAC atmospheric correction, enabling surface reflec
retrieval. We observed that the Random Forest algorithm outperformed tance products for users who has limited Sen2Cor atmospherically cor
the other models, with percent errors lower than 22% based on a vali rected time-series. The results observed in this study for both methods
dation dataset for all environments considered in this study. Moreover, (Sen2Cor and SIAC) demonstrated that both atmospheric correction
even when the validation data were split according to the aquatic sys algorithms have a reasonable accuracy (MAPE < 80%, RMSE < 0.005 sr-
1
tems where SAA were calibrated, the Random Forest outperformed or , Pearson R > 0.93) for retrieving Rrs in the wavelengths of the visible
presented similar results. Therefore, RF Zsd algorithm was implemented domain and the red edge (<740 nm). Despite the high MAPE values, the
in the GEE platform for Zsd retrieval. The validation results with match- remaining statistical metrics’ values show reasonable accuracy. The
ups of measured Zsd and estimated with MSI data presented errors of Pearson Correlation Coefficient for these bands was higher than 0.93,
27.95%, demonstrating the applicability of the proposed algorithm. indicating that the satellite data presented a linear relationship despite
the offset. The mAE suggests that both methods present median errors
lower than 28%, and BIAS indicates an overestimation of Rrs Sen2Cor
4.1. Atmospheric correction uncertainties for Zsd retrieval in Google Earth
and SIAC, with the latter more evidenced (BIAS = 1.41).
Engine
The uncertainties, however, varied with the study site. In Table 4 we
provide a comparison between MAPE values for 1) Três Marias Reser
One of the key advances in the last decade for the remote sensing
voir, for the 2019 campaign 2) Curuai Lake, for the 2019 campaign, and
community is the Cloud Services, which allows processing a large
3) Billings Reservoir for 2020 and 2021 campaigns, for both atmospheric
amount of data. Google Earth Engine (GEE) is one of the most successful
146
Fig. 11. Spatiotemporal variation of Zsd in Billings Reservoir.
6S atmosphere correction for Três Marias reservoir and observed MAPE

Table 4
varying between 11.89 to up to 64%, for wavelengths between 490 and
MAPE (%) values for each band and atmospheric correction method for Três
705 nm. The low-reflectance environment of Três Marias makes the
Marias, Billings, and Curuai for the 2019, 2020, and 2019 campaigns of each
location. Please, refer to the images used in Table 1.
correct retrieval of Rrs in NIR bands a challenge (Bernardo et al., 2017;
Doxani et al., 2018; Maciel et al., 2020b; Pahlevan et al., 2021; Rotta
Três Marias Billings Curuai
et al., 2016). Despite higher errors at Três Marias, MAPE values at
SIAC Sen2Cor SIAC Sen2Cor SIAC Sen2Cor Billings and Curuai lake are lower than 49%. In Billings Reservoir, the
Band 2 12.23 11.66 23.54 34.8 16.46 22.6 eutrophic environment could be a challenge for using in-situ data for Rrs
Band 3 24.87 6.40 18 25.22 17.57 16.3 validation (Lobo et al., 2021). For a recent study in lower Amazon
Band 4 121.05 11.84 16.06 27.69 18.7 17.61 Floodplain Lakes, Maciel et al. (2020) observed MAPE values up to
Band 5 151.43 28.01 18.54 26.12 11.55 10.71
34.52% for Sentinel-2 data validation, being band 6 (740 nm), that with
Band 6 1006.16 260.12 49.28 30.3 47.31 16.68
the highest errors. Maciel et al. (2020) results were close to those of both
methods evaluated in this study for the Curuai Lake, indicating the
correction methods and the same points. For Três Marias reservoir, the suitability of using the available surface reflectance data in Google Earth
atmospheric correction errors for Band 6 bands are very high (MAPE > Engine platform for studying Brazilian aquatic systems.
260, disregarding the methods). For Band 5, MAPE values regarding
SIAC method were 151.43%, and 28.01% for Sen2Cor. These errors were
relatively close to that of Curtarelli et al.’s (2020). The authors applied
147
4.2. Application of Machine Learning methods to estimate Zsd and et al. (2015b), in which the authors obtained errors lower than 30%
comparison with SAA approaches from global ocean to coastal waters (Kd(4 9 0) < 5 m− 1).
Moreover, Chen et al. (2015a) developed a Machine Learning algo
The use of Machine Learning (ML) approaches is gaining space into rithm to retrieve absorption coefficients for the ocean and coastal wa
remote sensing of aquatic ecosystem to estimate optical proprieties of ters, which performed better than QAA in turbid regions. For TSS
water bodies (Balasubramanian et al., 2020; Chen et al., 2014; Jamet estimates, a new approach that combines the use of semi-analytical and
et al., 2012; Liu et al., 2021; Peterson et al., 2018; Sagan et al., 2020; Sun machine learning approaches was developed by Balasubramanian et al.
et al., 2014). These techniques, aligned with the increase of computa (2020) to take advantage of the use of both applications. The authors
tional power and the number of in-situ data available for algorithm pointed out the benefit of this method for TSS estimates in a wide range
calibration, can be an alternative approach for predicting these optical of concentrations (0.1 – 2628.8 mgL-1) compared to other empirical and
proprieties in regional-to-global scales (Balasubramanian et al., 2020; semi-analytical approaches, obtaining errors of 48.94% for a global al
Liu et al., 2021; Rubin et al., 2021; Sagan et al., 2020). However, one of gorithm. Application of Machine Learning methods for Chlorophyll-a
the main challenges of using ML methods for water quality monitoring is retrieval in optically complex inland waters was also successfully
that these methods rely on the sample size used for algorithm calibra applied by Pahlevan et al. (2020) using Sentinel-2/MSI and Sentinel-3/
tion. ML approaches require a sizeable data set to correctly model the OLCI imagery. The authors evaluated the use of Mixture Density Net
environmental phenomena and stabilize the relationships between the works (MDN). They observed that the algorithm performed well (BIAS
training data’s parameters. Achieving suitable sample data is particu = 1.34, mAE = 1.86) for a large range of variability in Chl-a concen
larly difficult in emergent countries without a collaboration network or tration (from 0.2 to 1209 ugL-1).
long-term funding projects. Even with this limitation, this study took Moreover, Smith et al. (2021) used the same algorithm (MDN) to
advantage of a large in-situ dataset (N > 1500) of Rrs data collected over estimate Chl-a using Landsat-8/OLI sensor, demonstrating a reasonable
the last 20 years in Brazilian territory to develop an application of a accuracy (49% in median) for the pigment retrieval, although the lack of
Machine Learning algorithm to retrieve water clarity in these waters. Chl-a specific bands in OLI sensor. Applications of Machine Learning for
In this study, a comparison between machine learning and semi- Chl-a estimation using Landsat-8/OLI were also provided by Cao et al.
analytical algorithms was carried out to evaluate their performance (2020), in which authors used XGBoost and obtained an accuracy of
regarding Zsd estimates. ML methods presented superior results on both 24%. However, the algorithm was judged as appropriate only for a range
approaches considered: global and grouped by lakes. ML methods su of conditions in which the algorithm is trained. This is a limitation of
periority was higher when we compared the global dataset, as the SAA some Machine Learning approaches, such as Random Forest, as the al
approaches were not fully developed to cover the IOPs variability in gorithm will never extrapolate the results beyond its training data set
those environments. However, when SAA approaches were applied to (Hengl et al., 2018).
the environment for which they were calibrated, the results were The extrapolation problem of some Machine Learning methods could
proximal to those of ML. At Curuai Lake, the best results for the SAA be reduced by using a comprehensive dataset representing the natural
approaches were Maciel et al. (2020) IOP inversion algorithm, which variability of the environment. This study used a dataset with>1500
was calibrated for Amazon Lakes floodplain areas. For Três Marias samples for Brazilian inland waters in a range of Zsd values between ~
reservoir, the accuracy of both Random Forest and the algorithm of 0 to up to 5 m. Although it does not represent all water bodies and
Curtarelli et al. (2020) was close to 20%. These results demonstrate that conditions, it could be treated as a representative sample, as OACs were
both types of algorithms could be used for Zsd estimates. One of the highly variable: Chl-a: from 0 to up to 800 μgL-1; TSS: from 0 to up to
advantages of SAA approaches against Machine Learning methods is 1500 mgL-1; aCDOM: from 0 to up to 6 m− 1. The accuracy assessment
that it does not require a large sample size to model the water optical based on our validation process (i.e. Monte Carlo simulation) demon
proprieties correctly. It requires, of course, in-situ IOPs data necessary strates the ML methods’ applicability for Zsd retrieval on the considered
for algorithm recalibration (Curtarelli et al., 2020). interval. For example, the Random Forest algorithm results presented a
Moreover, SAA approaches have an easier implementation. It only good performance concerning the mean values of statistical metrics
requires mathematical expressions and could easily extrapolate the obtained from Monte Carlo simulation (e.g. MAPE < 22%, R > 0.9).
predicted values beyond the range of the training data set, as the algo Moreover, low values of standard deviation for these metrics indicate no
rithm is based on physical relationships (Hengl et al., 2018; Lee et al., high divergence from the mean (i.e. low coefficient of variation).
2015). Despite these advantages, the semi-analytical methods did not
outperform ML approaches in this study, which could be related to the 4.3. The applicability of the proposed algorithm to estimate Zsd: The
high variability in the OACs, making its use only feasible at local to example of lower Amazon floodplain lakes and Billings reservoir
regional scale and in optically homogeneous waters. To achieve a higher
performance of the SAA, a previous reparameterization of the algo The Zsd is an important measurement of water quality because it
rithms based on Optical Water Types classification (Cherukuru et al., gives an integrated idea of the light availability in the water column, key
2021; da Silva et al., 2020) or in single thresholds (Jiang et al., 2019; Lee information for monitoring aquatic ecosystems. Zsd accounts for the
et al., 2016) could be performed to avoid these uncertainties. light attenuated in the water column and, therefore, the increase/
The accuracy of ML methods for predicting water quality parameters decrease of the OACs concentration (Mobley, 1994). Moreover, the light
has been explored mainly in the last decade. Recently, Rubin et al. availability in the water column is an important variable that is related
(2021) reviewed several empirical algorithms for Zsd estimates focusing to primary productivity (Behrenfeld and Falkowski, 1997), euphotic
on Landsat data and observed that the Random Forest algorithm out zone depth (Lee et al., 2007), and the diversity of phytoplankton species
performs the other 14 empirical models. Random Forest algorithm has (Bomfim et al., 2019; Buchanan, 2020; Kraus et al., 2019).
been used for multi-depth TSS estimates in the Maumee River (Ohio, With the calibrated algorithm, we can map Zsd values on a large scale
US). The authors compared the RF approach with SVM, least-squares using the Google Earth Engine cloud computing services. In Fig. 9, we
regression, and Model Averaged Neural Network and concluded that provided Zsd map for a selected area in the Amazon Basin using Sentinel-
the RF method presented the best results (R2 = 0.89). Focusing on water 2 imagery from July/2019. With this image, the spatial patterns of water
clarity estimates through Kd, Jamet et al. (2012) used Multi-Layer Per clarity in this basin could be observed. As expected, sediment-rich rivers
ceptron (MPL) Neural Networks (NN) to estimate Kd(4 9 0) for the clear such as Solimões, and Amazon River presented the lowest values of Zsd.
ocean to turbid waters (Kd(5 1 0) up to 12.41 m− 1). They observed that The connection between black and white waters in the confluence of
the MPL performed better than other semi-analytical or empirical al Negro and Solimões River are also highlighted. Considering the lower
gorithms. The use of NN for Kd estimates was also presented by Chen Amazon Region, the spatiotemporal variability of Zsd is related to the
148
water inputs from the Amazon River in the rising and high-water season satellite data were in according to in-situ (MAPE = 27.95%). Moreover,
and sediment-resuspension and algae bloom that occur in the receding we observed errors lower than 80% for Rrs retrieval using SIAC and
and low water period (Barbosa et al., 2010). The spatiotemporal pattern, Sen2Cor methods. With the proposed algorithm, we could obtain maps
controlled by the Amazon Basin hydrology and observed in Fig. 10 in of Zsd in Brazil Regions, such as lower Amazon Floodplain lakes, and
dicates that for low water season (October and November), Zsd values observe the spatiotemporal pattern of the data. Therefore, this study
were lower than 0.5 m in most of the floodplains (e.g., Curuai Lake), presents a simple methodology to estimate Zsd using cloud-computing
indicating less light availability. The Zsd values start to increase by services (GEE), enabling near-real-time monitoring of water trans
January in the floodplain lakes due to the water fluxes increasing from parency in Brazilian Waters. The GEE App developed in this study is
Amazon and other rivers into the floodplain lakes. freely available here: https://daniellookorox.users.earthengine.
Unlike the Amazon floodplain, where the Zsd variation is ruled app/view/waterclaritybrazil. The code could also be accessed here:
mainly by temporal patterns, the Billings Reservoir also showed strong https://code.earthengine.google.com/393c66ede90e5d928a65ea7dc
spatial dependence for the evaluated parameter (Fig. 11). The spatial 0d18e79.
heterogeneity of Billings’ water quality is related to the influence of the
São Paulo Metropolitan Region (SPMR), one of the most populated areas
in the world (Braga et al., 2006). Due to the anthropogenic pressures Declaration of Competing Interest
derived from SPMR, the reservoir is subjected to a high degree of
eutrophication, which culminates in frequent cyanobacteria blooms The authors declare that they have no known competing financial
(Carvalho et al., 2007; Gemelgo et al., 2008; Lobo et al., 2021). There interests or personal relationships that could have appeared to influence
fore, most of the Zsd estimative variation is attributed to changes in the the work reported in this paper.
phytoplankton community, which controls the water body’s optical
properties. Besides the influence from the SPMR, the seasonality of the Acknowledgments
phytoplankton blooms seems to follow the regional precipitation
pattern, with the strongest events occurring in the rainiest months This research is funded through the 2017-2018 Belmont Forum and
(October-March). During the rainy period, a great volume of polluted BiodivERsA joint call for research proposals, under the BiodivScen ERA-
water from the Tietê River is transposed to Billings reservoir for flood Net COFUND programme, and with the funding organizations French
control, which is frequent during the rainy season (Oct-Mar). The National Research Agency (ANR), São Paulo Research Foundation and
polluted runoff from SPRM also reaches its maximum volume in those National Science Foundation (NSF), the Research Council of Norway and
months with the greatest accumulated precipitation, contributing to the German Federal Ministry of Education and Research (BMBF). This
Billings’ eutrophication (Morihama et al., 2012). The most impacted study was financed in part by the Coordenação de Aperfeiçoamento de
area is the Billings’ Central Body, where the Tietê’s transposed waters Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001. This
are launched. Moreover, this region are densely covered by urban areas. study was funded in part by São Paulo Research Foundation (FAPESP-
Those conditions allowed intense algae growth and consequent Zsd Grants 2019/15984-2, 2018/12083-1, 2014/23903-9, 2013/09045-7,
reduction, especially in the rainy season (Lobo et al., 2021). The Billings’ 2012/19821-1, 2011/23594-8; 2011/19523-8, 2008/56252-0, and
dendritic shape and high hydraulic residence time (392 days) reduce the 2003/06999-8) and MSA-BNDES (Grant 1022114003005). The study
water circulation and also contribute to the water quality’s spatial was also funded in part by National Counsel of Technological and Sci
variation (Wengrat and Bicudo, 2011). The lowest values of Zsd observe entific Development (CNPq 552490/2011-3; 471223/2011-5), and Na
in this study corroborates with a recent study that demonstrates that the tional Institute of Science and Technology (INCT) on Climate Change
Central Body of Billings Reservoir, aligned with the Taquacetuba Arm, (CNPq-PROCAD grant 573797/2008-0). Authors would like to thank
are the ones with the highest Chlorophyll-a concentration, and more Gustavo Nagel and Felipe Lobo for help with Google Earth Engine. Au
occurrence of blooms (Lobo et al., 2021). thors are in debt with Caroline Cairo, Edson Silva, Lino Sander de Car
Another interesting pattern revealed by the analysis is the temporal valho, Victor Curtarelli, Rejane Paulino, and Waterloo Pereira-Filho, for
stability of the Zsd in the Rio Grande arm. This reservoir’s arm is isolated providing in-situ water quality data.
from the rest through the Anchieta Dam. The dam was constructed to
prevent the contamination of the Rio Grande, which is used for sup
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ISPRS Journal of Photogrammetry and Remote Sensing

Water clarity in Brazilian water assessed using Sentinel-2 and machine

21MXT Aug/28/2019 Curuai 10:10:49 26.60 58.68 14.92 15

Billings MAPE 21.39 19.42 27.32 47.56 26.55 35.27

Curuai MAPE 20.38 33.04 25.86 39.30 63.25 154.11

Ibitinga MAPE 32.79 46.25 44.81 56.55 45.75 62.31

Mamiraua MAPE 23.88 20.20 28.77 34.41 17.03 37.13

Três Marias MAPE 18.09 17.58 24.03 195.89 18.02 70.70

Fig. 10. Spatiotemporal variation of Zsd in Lower Amazon Floodplain lakes.

Fig. 11. Spatiotemporal variation of Zsd in Billings Reservoir.

6S atmosphere correction for Três Marias reservoir and observed MAPE

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