remote sensing
ArticleImproved Perceptron of Subsurface Chlorophyll Maxima by a
Deep Neural Network: A Case Study with BGC-Argo Float Datain the Northwestern Pacific Ocean
Jianqiang Chen 1 , Xun Gong 2,3 , Xinyu Guo 4 , Xiaogang Xing 5 , Keyu Lu 3 , Huiwang Gao 6,7
and Xiang Gong 1, *
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5

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Citation: Chen, J.; Gong, X.; Guo, X.;
Xing, X.; Lu, K.; Gao, H.; Gong, X.
Improved Perceptron of Subsurface
Chlorophyll Maxima by a Deep
Neural Network: A Case Study with
BGC-Argo Float Data in the
Northwestern Pacific Ocean. Remote
Sens. 2022, 14, 632. https://doi.org/
10.3390/rs14030632
Academic Editors: Xiao-Hai Yan,
William Llovel, Hua Su, Wei Zhuang
and Andrew Clive Banks
Received: 5 October 2021
Accepted: 24 January 2022
Published: 28 January 2022
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims inpublished maps and institutional affiliations.

*

School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China;
angyi_jq@163.com
Hubei Key Laboratory of Marine Geological Resources, China University of Geosciences,
Wuhan 430074, China; gongxun@cug.edu.cn
Shandong Provincial Key Laboratory of Computer Networks,
Qilu University of Technology (Shandong Academy of Sciences), Jinan 250101, China; ucfalux@ucl.ac.uk
Center for Marine Environmental Study, Ehime University, 2-5 Bunkyo-cho, Matsuyama 790-8577, Japan;
guoxinyu@sci.ehime-u.ac.jp
State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography,
Ministry of Natural Resources, Hangzhou 310012, China; xing@sio.org.cn
Qingdao National Laboratory for Marine Science and Technology, Qingdao 266237, China; hwgao@ouc.edu.cn
Key Laboratory of Marine Environment and Ecology, Ministry of Education of China,
Ocean University of China, Qingdao 266071, China
Correspondence: gongxiang@qust.edu.cn

Abstract: Subsurface chlorophyll maxima (SCMs), commonly occurring beneath the surface mixed
layer in coastal seas and open oceans, account for main changes in depth-integrated primary production and hence significantly contribute to the global carbon cycle. To fill the gap of previous
methods (in situ measurement, remote sensing, and the extrapolating function based on surface-oceandata) for obtaining SCM characteristics (intensity, depth, and thickness), we developed an improved
deep neural network (IDNN) model using a Gaussian radial basis activation function to retrieve
the vertical profile of chlorophyll a concentration (Chl a) and associated SCM characteristics fromsurface-ocean data. The annually averaged SCM depth was further incorporated into the bias term
and the Gaussian activation function to improve the estimation accuracy of the IDNN model. Basedon the Biogeochemical-Argo (BGC-Argo) data acquired for three regions in the northwestern Pacific
Ocean, vertical Chl a profiles produced by our improved DNN model using sea surface Chl a and sea
surface temperature (SST) were in good agreement with the observations, especially in regions withlow surface Chl a. Compared to other neural-network-based models with one hidden layer and asigmoid activation function, the IDNN model retrieved vertical Chl a profiles well in more eutrophic
subpolar regions. Furthermore, the application of the IDNN model to infer vertical Chl a profiles
from remote-sensing information was validated in the northwestern Pacific Ocean.
Keywords: subsurface chlorophyll maximum; deep neural network; Gaussian radial basis activation
function; BGC-Argo; northwestern Pacific Ocean

Copyright: © 2022 by the authors.

1. Introduction

Licensee MDPI, Basel, Switzerland.

The ocean plays an important role in the global carbon cycle, with marine phytoplankton accounting for ~50% of the global primary production [1]. In particular, the subsurface
chlorophyll maximum (SCM) layer contributes up to 75% of the depth-integrated primary
production in open oceans and coastal seas [2–4]. Moreover, the phytoplankton carbon
content in the SCM layer is positively correlated with the downward flux of particulateorganic carbon (POC) to the deep sea [5]. Over the period of a year, 59–73% of the ocean isThis article is an open access article
distributed under the terms andconditions of the Creative Commons
Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

Remote Sens. 2022, 14, 632. https://doi.org/10.3390/rs14030632

https://www.mdpi.com/journal/remotesensing

Remote Sens. 2022, 14, 632

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expected to have the SCM layers with vertical scales from a few meters to tens of meters,
where chlorophyll a concentration (Chl a) presents a peak value [6–8]. Therefore, characterizing SCM (intensity, depth, and thickness) is important for understanding marine primary
production, the carbon cycle, and ongoing global warming trends.
Since the 1950s, based on in situ measurements, SCM characteristics have been examined from vertical distributions of Chl a concentration, which are either measured indiscrete samples typically taken at standard depths or estimated continuously using in vivo
fluorometry [9–12]. Cullen [7] summarized the observation of SCM characteristics since the1940s based on the benchmark studies by Riley and Steele [13–15]. Anderson [9] reported
that the high values of Chl a measured by in vivo fluorometry are typically confined to alayer between 55 and 65 m, with a peak value at 60 m in the northeast Pacific Ocean. In
comparison, a prominent SCM between 65 and 150 m was found during two cruises in thewestern Pacific Ocean [16]. Taking the above as examples, SCM characteristics show spatial
heterogeneity. However, not all in situ measurements capture SCM characteristics continuously and they depend on cruise lines or float trajectories, thus limiting the knowledge of
SCM complexity in global oceans.
Since the late 1980s, efforts have been made to statistically extrapolate SCM characteristics from surface-ocean data, which can be detected by satellite. Morel and Berthon applieda shifted Gaussian function to categorize ~4000 vertical profiles of pigments to define seven
Chl a hierarchies in open oceans and examine the associated SCM characteristics [17,18].
Uitz [19] upgraded the shifted Gaussian function for two ocean conditions that represent
vertically stratified and mixed cases. Focusing on coastal seas, Richardson et al. [20] established a generalised linear model as a function of surface Chl a concentrations and surface
water temperatures to estimate SCM characteristics in the southern Benguela upwellingsystems. Xiu et al. [21] applied a blue-to-green band ratio algorithm and successfully retrieved SCM intensity from remote-sensing reflectance in the Bohai Sea of China. Although
the retrieving functions based on surface-ocean data can provide Chl a concentration datafor vast and continuous ocean areas, they show limitations in characterizing the SCM
complexity due to the inadequacy of statistical adaptability at finer temporal resolutions(seasonal, daily, and smaller spatio-temporal scales).
Recently, neural-network-based algorithms have been regularly used to calculate
SCM from surface-ocean data [22–24]. An advantage of neural networks is that they
provide a near-real-time depiction of the SCM characteristics from remote-sensing data.
For instance, Sammartino et al. [24] trained an artificial neural network (ANN) model with
one hidden layer (also known as a shallow ANN) to infer Chl a vertical profiles in the
Mediterranean Sea via in situ measurements together with remote-sensing data (Chl aand temperature). The shallow ANN model works well in the regions with low surface
Chl a concentrations, but its performance decreases for the area with high Chl a surface
concentrations [23,24]. It is known that the number of hidden layers in neural-networkbased algorithms are one important factor controlling the estimation accuracy [24–26].
More importantly, a neural-network-based algorithms’ estimation accuracy depends on
the the type of activation function [26,27]. Compared with the logistic (sigmoid) activation
function, a radial basis activation function is likely to produce better solutions for nonlinear
problems [26]. Generally speaking, the previous neural-network-based models work betterin retrieving SCMs than the traditional statistics-based models did. However, because
previous neural-network-based models used only one genu in the hidden layer with thesigmoid activation function, their accuracy needs to improve for the vertical Chl a profiles.
In this study, we develop a deep neural network (DNN) model to retrieve the verticalprofiles of Chl a from surface-ocean data which are equivalent to the average value within
the first 20 m water depth [4]. Our DNN model has at least three hidden layers in thealgorithm. Compared to the shallow ANN, such an improvement theoretically helps to improve performance for prediction capability [28]. Rather than using the sigmoid activation
function, we use a Gaussian radial basis activation function in the DNN model, which isone of the most frequently used radial functions in the literature [26]. We train the DNN

Remote Sens. 2021, 13, x FOR PEER REVIEW

Remote Sens. 2022, 14, 632

3 of 20

improve performance for prediction capability [28]. Rather than using the sigmoid activation function, we use a Gaussian radial basis activation function in the DNN model, which
3 of 19
is one of the most frequently used radial functions in the literature [26]. We train the DNN
model by inputting sea surface temperature (SST) and surface Chl a from BiogeochemicalArgo (BGC-Argo) floats. We apply the DNN model to the northwestern Pacific Ocean andmodel
by theinputtingsea surface
surfaceSCM
Chl acharacteristics
from Biogeochemicalcompare
estimatedvertical temperature
Chl a profiles(SST)
and andassociatedwith obArgo(BGC-Argo)
floats.
We
apply
the
DNN
model
to
the
northwestern
Pacific
Ocean
servations in different regions and seasons. Finally, we examine the prediction
capability
andcomparetheestimatedverticalChlaprofilesandassociatedSCM
characteristics
of our DNN model in retrieving vertical Chl a profiles from remote-sensing data inwith
theobservations
different
regions and seasons. Finally, we examine the prediction capability
northwesterninPacific
Ocean.
of our DNN model in retrieving vertical Chl a profiles from remote-sensing data in thenorthwestern
Pacific Ocean.
2. Data and Methods
2.1.
Improved
DNN model
2.
Dataand Methods
The DNNmodel
is an extension of a conventional ANN, with at least two hidden
2.1. Improved
DNN
Model
layersbetweenthe input
andoutput layers.
Because eachANN,
node inthe athiddenlayerhidden
makes
The
DNN model
is anextensionof a conventional
withleast twoboth associations
gradesof the input
toBecausedetermine
thenodeoutput,stacking
theselayersbetween theandinput
and output
layers.
eachin thehiddenmore
layerofmakes
layers
upon
each
other
benefits
morefrommultiple
hiddenlayers.
Generally,therunningboth associations and grades of the input to determine the output, stacking more of theseof a DNN
includestwo moresteps:fromerrormultiple
forwardhidden
and error
backward
propagation.
Forlayers
uponmodel
each otherbenefits
layers.
Generally,
the runningofward
propagationreferstotheDNN
receiving
signals
from
the
input
layer
and
then
a DNN model includes two steps: error forward and error backward propagation. Forward
passes the signals
layer (Figure1).from
Aftertheprocessing
theandsignals
the neupropagationrefers to the hidden
DNN receiving
signals
input layer
thenbypassestherons in tothethehiddenlayer,
DNN 1).
passesto the output
layer.byThen,by comparing
signals
hiddenlayerthe(FigureAfterthemprocessing
the signals
the neurons
in theand calculating
outputerror
withtheoutput
target,layer.
backward
usedto adjusthiddenlayer, the theDNNpassesthemto theThen, propagationby comparingisandcalculating
the output
weight errorof signals
thehiddenlayers andfurther reduce
theto
error
using
optimithewith inthetarget,backward
propagation
is usedadjustthetheweightofzation algorithm.
signalsin the hidden layers and further reduce the error using the optimization algorithm.

Figure 1.
1. Structure
Structure ofof thethe deep
deep neuralneural network
network (DNN).
(DNN). The
The input
input elements
elements ofof DNNDNN areare longitude,
longitude,
Figurelatitude, time,
time, sea
Chl
a, a,
water
depth.
TheTheoutputis thelatitude,sea surface
surfacetemperaturetemperature(SST),(SST),seaseasurface
surfaceChlwater
depth.
outputis verthetical distribution of Chl a concentration over the water depth of 0–300 m. b is the bias term in thevertical distribution of Chl a concentration over the water depth of 0–300 m. b is the bias term in thehidden layer. The prior information of nonlinear activation function (f) connects the hidden layers
hidden layer. The prior information of nonlinear activation function (f ) connects the hidden layers toto the output.
the output.

In the calculation of SCM characteristics, we improved the existing DNN model inIn the calculation of SCM characteristics, we improved the existing DNN model inthefollowing
two aspects.
aspects. First,
First, we
we improve
improve thethe capability
capability ofof modelmodel forfor thethe calculation
calculation ofofthe following two
SCM depth
depthbybyreplaced
replacedthe
thebiasbiasterm
termb 𝒃(thatintercept
term)
from
randomvaluesSCM(thatis,is,
thetheintercept
term)
from
randomvaluestotoannualmeanofSCM
depths(Equation(1)).
annual mean of SCM depths (Equation (1)).
avg ( zmax(z)max )bSCM= = avg,bSCM
max(maxz ) (z) ,(1)(1)

where z is the water depth, max(z) is set to 300 m by assuming that there is no Chl a below
300 m depth, and avg(zmax ) is the annual mean of SCM depth (zmax ).
In the second aspect, we improve the calculation accuracy of the model for the SCM
intensity and thickness. Considering the unimodal chlorophyll profiles, a Gaussian radialwhere z is the water depth, max ( z ) is set to 300 m by assuming that there is no Chl a
Remote Sens. 2022, 14, 632

below 300 m depth, and avg ( zmax ) is the annual mean of SCM depth ( zmax ).

4 of 19

In the second aspect, we improve the calculation accuracy of the model for the SCM
intensity and thickness. Considering the unimodal chlorophyll profiles, a Gaussian radialbasis function is substituted for the sigmoid function as a nonlinear activation function (f,basis function
is substituted
for model
the sigmoid
functionas a nonlinear
activation
function
Equation(2)) in theoriginal DNN
to amplify
the signals
within the
SCM layer.
The(f,Equation
(2))
in
the
original
DNN
model
to
amplifythesignals
withinthe
SCM
layer.
advantage of Gaussian radial basis activation function is that it is similar to quadraticTheadvantageofGaussianradialbasis
activation
function
is
that
it
is
similartoquadratic
function for the center values of input variables, while the sigmoid activation function isfunctionfor thefunction
center values
variables,whilesimilarto linearabout oftheinputmoderate
inputs[26].the sigmoid activation function issimilar to linear function about the moderate inputs [26].
−π ( X −b)2(2)
f = e j SCM ,2
f = e−π (X j −bSCM ) ,(2)
where X j is the X value of the jth output in the hidden layer, and bSCM is the bias term
where X is the X value of the jth output in the hidden layer, and bSCM is the bias termcomputedj by the annual mean of SCM depth (Equation (1)). The Gaussianradial basis
computed by the annual mean of SCM depth (Equation (1)). The Gaussian radial basis
activation function helps to absorb the information of the annually averaged SCM depth
activation function helps to absorb the information of the annually averaged SCM depth
and, hence, further extract the SCM features.
and, hence, further extract the SCM features.
Consequently, a DNN model with at least two hidden layers was applied due to its
Consequently, a DNN model with at least two hidden layers was applied due to its
availability in capturing the nonlinear relationships, and the annual averaged SCM depth
availability in capturing the nonlinear relationships, and the annual averaged SCM depth
is incorporated into both the bias term and the Gaussian radial basis activation function
is incorporated into both the bias term and the Gaussian radial basis activation function
to improve the capability in retrieving the SCM characteristics. We name this improved
to improve the capability in retrieving the SCM characteristics. We name this improved
model the IDNN model.
model the IDNN model.
2.2.
theIDNN
IDNNModel
Model
2.2.BGC-Argo
BGC-ArgoData
Data forfor theThe
for thethe IDNN
IDNNmodel
modelwere
werecollected
from
16 BGC-Argo
profiling
Theininsitu
situ data
data forcollected
from
16 BGC-Argo
profilingfloatsfloatsthe northwestern
Pacific
Ocean(https://biogeochemical-argo.org/,
accessed19
in theinnorthwestern
Pacific
Ocean(https://biogeochemical-argo.org/,
accessedon 19onApril
◦ E,
April
2021).
Figure2 plotted
the trajectories
ofBGC-Argo
the 14 BGC-Argofloatswithin2021).
Figure2 plotted
the trajectoriesof the 14
profilingprofiling
floats within
123–180◦
123–180
°E,
12–48
°N,
where
a
SCM
featurewasobserved.
FigureA1
showedthelocations
12–48 N, where a SCM feature was observed. Figure A1 showed the locations of verticalofChl
vertical
Chl aobserved
profiles observed
from 16 BGC-Argoin the absenceof Thea SCM.
Thea profiles
from 16 BGC-Argofloats in floats
the absenceof a SCM.
acquiredacquired2409 vertical
Chl a profiles,
covering
four seasonsthe period
from2017
Julyto2409 vertical
Chl a profiles,
covering
four seasons
during during
the period
from July2017
to 2021,
Aprilwere2021,usedwereinusedin ourafter
study
after control
quality tocontrol
to aberrant
remove aberrant
databyApril
our study
qualityremovedata caused
causedby electronic
electronicnoise [29].noise [29].

Figure2.2.Locations
Locationsandmeasuring
measuringmonthsBGC-Argoprofiles
profileswith
witha asubsurface
subsurfacechlorophyll
chlorophyll
Figureandmonthsofof1414BGC-Argo
maximum(SCM)
featureinthenorthwestern
Pacific
Ocean.
maximum (SCM) feature in the northwestern Pacific Ocean.

Most vertical profiles of Chl a showed a unimodal distribution, while the remaining
minors showed either increasing or decreasing Chl a with depth. Here, focusing on the
SCM patterns, we structure each BGC-Argo vertical profile based on a Gaussian function
assumption [30] (Equation (3)).
Chl (z) = Ae)
− (z−zmax
2
2σ

2

(3)

minors showed either increasing or decreasing Chl a with depth. Here, focusing on the
SCM patterns, we structure each BGC-Argo vertical profile based on a Gaussian function
assumption [30] (Equation (3)).

Remote Sens. 2022, 14, 632

Chl ( z ) = Ae−

( z − zmax )2
2σ 2

,

(3)
5 of 19

where 𝝈 is its standard deviation, A is the amplitude of the Gaussian curve, and zmax isthe location of the amplitude. To quantify the vertical scale of the SCM layer, 2σ was used
where
σ is its thestandard
deviation,[2,31].
A is theamplitudeof the layer
Gaussiantheto represent
SCM thickness
Becausethe upperof thecurve,
SCMand( zmaxzmax− σ )ismust
location of the amplitude. To quantify the vertical scale of the SCM layer, 2σ was used to
be inside the water, it is set as a nonnegative value. That is, if z max − σ < 0 , the upper layer
represent the SCM thickness [2,31]. Because the upper layer of the
SCM (zmax − σ) must beof the theSCM
is setitto(0 m).value.
In addition,
intensity refers to the peakinsidewater,
is theset seaas asurface
nonnegativeThat is,theif zSCMmax − σ < 0, the upper layer ofvalueof Chlconcentration(A).(0 m). In addition, the SCM intensity refers to the peaktheSCM
is seta to
the sea surface
valuesof the Gaussian
value Theof Chla concentration(A). parameters (𝝈, A, and zmax) were obtained by fitting all
observedverticalChlaprofiles(Figure 3), which
can beused
to filterout Chla profiles
The values of the Gaussian parameters(σ, A, andzmax) wereobtainedby fitting
all
with
no
significant
SCM
characteristics
via
thefollowing
three
steps.
First,
profileswithobserved vertical Chl a profiles (Figure 3), which can be used to filter out Chl a profiles
the valuesof parameter𝝈 ranging fromthefollowing
lower limitof thedatavalue
to half
of thethewithno significant
SCM characteristics
via thethree
steps.
First,
profiles
with
upper
limit
(0–48
m)
(Figure
3a),
are
kept,
therebyleaving1676
profiles.
Second,paramevalues of parameter σ ranging from the lower limit of the data value to half of the upper
ter A(0–48(the peakvalues3a),of Chla obtainedfromGaussianfitting) was
assumedto be atlimitm) (Figure
are kept,
therebyleaving
1676 profiles.
Second,parameter
A least(thetwicevalues
the surface
a concentrations.
Meanwhile,larger thanlimit the(2.2
peakof ChlChl
a obtained
from Gaussian
fitting)values
was assumed
to betheat upperleast twice
mg m−3Chl) wereneglected as outliers(Figure3b).larger
This step
surfacea concentrations.
Meanwhile,
valuesthan excluded
the upper328
limitprofiles.
(2.2 mgThird,m−3 )𝒛𝒎𝒂𝒙 neglectedvalues areaslimited
depths3b).
above
Finally, 328
afterprofiles.
visuallyThird,
reviewing
all thewere
outliersto(Figure
This200
stepm.excluded
zmax values
filtered
profiles,
1342
out
of
the
total
2409
profileswereretainedinthefollowing
analysis.
are limited to depths above 200 m. Finally, after visually reviewing all the filtered profiles,
Consequently,
the remaining
verticala profiles
significant
SCM
characteris1342
out of the total
2409 profiles
wereChlretainedin thepresent
following
analysis.
Consequently,
tics.remaining vertical Chl a profiles present significant SCM characteristics.
theFigure3.3.Boxplot
Boxplotof
ofthreethreeparametersparameters(standard(standarddeviation
deviation(a);(a);amplitude
amplitudeof
ofthe
theGaussian
Gaussiancurve
curve(b);(b);
Figurelocationofofthe
theamplitude
amplitude(c))
Gaussianfunctionin thenorthwestern
Pacific
Ocean.
In box,each
location(c))
in inthetheGaussianfunctionin thenorthwestern
Pacific
Ocean.
In eachbox,
the orange
horizontal
line represents
the median.
The upper
and lowerhorizontalthetheorangehorizontal
line represents
the median.
The upper
and lowerhorizontal
lines linesof theofbox
box represent the 75th and 25th percentiles (Q3 and Q1), respectively. The upper and lower horizontal
represent the 75th and 25th percentiles (Q3 and Q1), respectively. The upper and lower horizontal
whiskers lines are the upper limit (U) and lower limit (L) of the data, respectively; the circles reprewhiskers lines are the upper limit (U) and lower limit (L) of the data, respectively; the circles represent
sent the outliers.
the outliers.

The remaining 1342 profiles with SCM covered four seasons from February 2018 to
The remaining 1342 profiles with SCM covered four seasons from February 2018
April 2021 (Table 1, Figure 2), while those profiles that are excluded in the initial quality
to April 2021 (Table 1, Figure 2), while those profiles that are excluded in the initial
controlcontrol
are mostly
characterized
by the absenceof SCMofduring
the winterseason season(Figurequality
are mostly
characterized
by the absence
SCM during
the winter
S1).
In
general,verticalChlaprofileswithaSCM
accompany
higher
SSTs
and
lower
sur(Figure A1). In general, vertical Chl a profiles with a SCM accompany higher SSTs andlower surface Chl a concentrations in subtropical and subpolar areas, compared to the
profiles without SCM. For example, in subtropical area (BOX2 in Figure 2), for the profiles
with SCM, the average surface Chl a concentration is about 0.14 mg m−3 , and the average
SST is about 24.3 ◦ C; for the profiles without SCM, the average surface Chl a and SST is
0.72 mg m−3 and 19.6 ◦ C, respectively. In tropical area (BOX1 in Figure 2), no significant
difference between profiles with and without SCM was found from averaged surface Chl aconcentration and SST.

Remote Sens. 2022, 14, 632

6 of 19

Table 1. Averaged intensity and depth of SCM in BGC-Argo database used (Year/Month/Day).
RegionFloat No.
(Number of Profiles)

Data Duration

SCM Intensity(mg m−3 )SCM Depth(m)BOX1(12–24◦ N, 123–156◦ E)

2902753 (118)2902756 (184)2902762 (82)2902822 (37)2902823 (30)2902824 (30)2019/3/30–2019/12/8
2019/3/25–2020/12/2
2020/8/16–2021/4/18
2021/1/12–2021/4/17
2021/1/17–2021/4/17
2021/1/20–2021/4/16

0.57 (0.37–0.85)
0.67 (0.34–0.73)
0.43 (0.29–0.77)
0.43 (0.29–0.53)
0.41 (0.19–0.55)
0.47 (0.39–0.55)

117 (88–166)
115 (88–150)
139 (90–175)
127 (97–149)
147 (129–183)
153 (127–176)

0.44, 0.59, 0.58, 0.57

134, 124, 109, 128

1.23 (0.55–3.54)
1.07 (0.61–2.18)
0.85 (0.44–1.67)
1.1 (0.32–6.65)
0.65 (0.58–1.17)
0.91 (0.91–0.91)
0.79 (0.45–6.12)

76 (30–117)
79 (40–108)
89 (29–118)
76 (23–135)
40 (18–62)
68 (68–68)
65 (28–100)

0.62, 1.18, 1.49, 0.91

74, 69, 74, 83

1.92 (0.50–5.70)
2.5 (0.24–7.07)

41 (12–96)
28 (6–49)

1.09, 1.60, 2.40, 2.00

59, 39, 33, 40

1.14 (0.20–7.07)

85 (6–183)

0.52, 0.88, 1.57, 1.17

115, 101, 72, 75

Seasonal average (Winter, Spring, Summer, Autumn)

BOX2(26–38◦ N, 132–173◦ E)

2902748 (199)2902749 (28)2902750 (108)2902754 (147)2902755 (9)2903213 (1)2903394 (78)2018/5/31–2021/4/17
2018/5/31–2018/9/8
2018/9/13–2019/5/31
2018/8/30–2021/4/16
2019/10/19–2019/11/28
2018/2/22–2018/2/22
2019/5/26–2020/12/8

Seasonal average (Winter, Spring, Summer, Autumn)
BOX3(38–48◦ N, 145–180◦ E)

2902755 (204)2903354 (87)2018/9/3–2021/4/16
2018/7/25–2019/9/4

Seasonal average (Winter, Spring, Summer, Autumn)
Total area

(1342)

2018/2/22–2021/4/18

Seasonal average (Winter, Spring, Summer, Autumn)

The average value of SCM depth and its intensity in each BGC-Argo float is shown in
Table 1. The averaged SCM intensity from profiles of each BGC-Argo float in tropical area
(12–24◦ N) has ranges between 0.41–0.67 mg m−3 over depths of 115–153 m; the averaged
SCM intensity in subtropical (26◦ N–38◦ N) is about 0.65–1.2 mg m−3 with shallower SCM
depths over 40–89 m. At high latitudes (38–48◦ N), the SCM exists at a depth <50 m with thelargest intensity larger than 1.5 mg m−3 . Table 1 also presents the seasonal averaged SCM
depth and intensity. Compared with summer and autumn, the SCMs get deeper and weakerin winter and spring, which is probably due to increased vertical mixing in winter andspring. This indicates that physical entrainment may extract some of phytoplankton fromthe SCM layer to the surface layer and thereby reduce the SCM intensity [2,32]. Generally,
the SCM characteristics differ among the three regions that range from tropical area tosubtropical area and then to subpolar area, with a weaker seasonal variation. Therefore,
based on spatial variations of SCM characteristics in the northwestern Pacific Ocean, theremained 1342 vertical profiles of Chl a are classified into three BOXes (Table 1). In BOX1,
6 BGC-Argo floats contained 481 profiles span in the tropical Pacific. 570 profiles from
7 BGC-Argo floats near 30◦ N belong to BOX2 in subtropical area, and the remaining
291 profiles from 2 BGC-Argo floats locate at BOX3 in subpolar Pacific.
2.3. Satellite Data for the IDNN Model
To evaluate the performance of IDNN reconstruction using remote-sensing data, the
MODIS Level 3 standard mapped image monthly Chl a and SST database with a 9 km
spatial resolution were downloaded from Asia-Pacific Data-Research Center (ARDRC, http://apdrc.soest.hawaii.edu/dods/public_data/satellite_product/MODIS_Aqua/, accessedon 19 April 2021) and used to extract the input values for the IDNN model.
Each profile of the BGC-Argo database remained above was then matched up withsatellite data of surface Chl a and SST using the bilinear interpolation method [33]. This
matchup process led to keeping a number of 985 BGC-Argo profiles from 2017 to 2021. The
matchup file includes both training and test points.

Remote Sens. 2022, 14, 632

7 of 19

Before the training, SST and Chl a data from BGC-Argo profiles and satellite werestandardized to make them dimensionless and have the same order of magnitude. Thus,
for each point, all data are clustered around 0 with a variance of 1.
2.4. Training Process
In our IDNN model, SST, sea surface Chl a, associated geo-location (latitude, longitude)
and observation time, and water depth were selected as input variables (Figure 1), which
are similar to the study by Sammartino et al. [24]. The reason for choosing geo-locationand observation time is that the SCM characteristics varied with seasonality and spatiality(Table 1). SST is related with vertical stratification of the water column, influencing SCM
characteristics. Moreover, the choice is supported by the potential capability of the network
to find the nonlinear relationship between the input variables and Chl a concentration at
different depths of the water column.
The IDNN model was trained in each BOX, respectively. Seventy-five percent of the
input data and vertical profiles of Chl a from BGC-Argo floats in each BOX (Table 1) weresegmented and fed into the IDNN model as the training set, which was selected randomly.
We conducted 10 experiments by selecting 75% of the input data randomly in each BOX.
The RMSEs ranged between 0.0033–0.0038 mg m−3 in BOX1, 0.036–0.044 mg m−3 in BOX2,
and 0.25–0.36 mg m−3 in BOX3. The results indicate the stability by randomly selecting
training data. Gradient descent was applied to reverse propagation of the IDNN model,
which was trained using an Adam optimizer. Moreover, to avoid over-fitting, we applied
the dropout technique to discard some neurons. During the training process, 15% of the
training set was randomly selected as a validation set to verify whether the IDNN model
was over-fitted. According to the performance of the validation set, the parameters of the
IDNN model were determined using a grid search. Overall, after stable network training,
three IDNN model frames were determined for each BOX region (Table 2). Based on thebest calculation performance, the parameters in BOX1 and BOX2 are equivalent to eachother, but differ from those in BOX3.
Table 2. Parameters of the IDNN model in three BOXes.
Parameters
Network Parameter
Hidden layer depth
Number of hidden neurons
Momentum
Epoch
Learning rate
Dropout rate

BOX1

BOX2

BOX3

3
64, 64, 64
0.9
115
0.01
0.1

3
64, 64, 64
0.9
115
0.01
0.1

4
64, 128, 128, 64
0.9
150
0.01
0.1

To evaluate the errors between the IDNN output and the observed value, the determination coefficient (R2 ), correlation coefficient (ρ), root mean square error (RMSE), mean
absolute percentage error (MAPE), and mean bias error (MBE) are introduced as evaluation
indicators. Their formulas are shown in Table A1. The R2 and RMSE values were used as
performance indicators to evaluate the effectiveness of the developed models. MAPE andMBE capture the average difference between the estimated and observed values.
3. Results and Discussion
3.1. IDNN-Retrieved Vertical Chl a Profiles
After evaluating the IDNN performance on a training set, we applied the IDNN model
to a test set. Here, the test set contains 25% of the total BGC-Argo surface Chl a and SST
datasets. In the testing phase of the IDNN model, a trained network was used for forward
estimation. The data on the test set are normalized in a similar manner to that in the
training set, with the network output being inversely normalized to the original unit.

Remote Sens. 2022, 14, 632

the training set, with the network output being inversely normalized to the original unit.
As shown in Figure 4 a–c, the modeled Chl a concentrations from the test set areclosely comparable with the observed values for the upper 300 m in each BOX. Most of
the data are close to the bisector (the black dashed line in Figure 4 a–c), especially for Chl
a concentration of ~0.1 mg m−3. Owing to the high noise/signal ratio, the low Chl a8conof 19
centration shows a relatively higher offset [25]. Compared with the BGC-Argo profiles of
Chl a in each BOX, our IDNN modeling results show smaller fluctuations in the surface
and SCMlayers,inexcept
thetheplace
close tothea SCM
depth in the
BOX3
where
standAs shown
Figurefor
4a–c,modeledChlconcentrations
fromthe test
set theare closelyardvariances
of
the
model
resultsarelarger
than
those
from
observations(Figure4d–f).
comparable with the observed values for the upper 300 m in each BOX. Most of the dataareThevariability
intheshapesofverticalChlaprofilesbetween0–50
meters
in
the
in
situ
close to the bisector (the black dashed line in Figure 4a–c), especially for Chl a concentration
observationsof3 .BOX2(greenFigure 4e) ismainlytwo out of 16 profiles,of ~0.1 mg m−
Owing
to theshadehigh innoise/signal
ratio,
the caused
low Chlbya concentrationshows a−3. After removing
which
present
theoffset
SCM depth
above 50 mwith
withthetheBGC-Argointensity over
4 mgofmChl
relatively
higher[25]. Compared
profilesa in each BOX,these
two profiles,
greenshow
shadedregions
betweenin0–50
meters andin BOX2
our IDNN
modelingthe
results
smallerfluctuations
the surface
SCMshow
layers,smaller
exceptfluctuations(FigureA2).
This
resultsuggests
that,
even
with
some
episodicsignals,thefor the place close to the SCM depth in the BOX3 where the standard variances of the model
network
model
has
good
robustness
and
can
infer
the
shapesofverticalChlaprofilesresults are larger than those from observations (Figure 4d–f). The variability in the shapes
fromsurfacedataonly. between 0–50 meters in the in situ observations of BOX2 (greenof verticalChla profiles
Statistically,
theisrelative
show
that out
maximalbias (8–10%)
occursat about
10–
shade
in Figure 4e)
mainlybiases
causedby twoof 16 profiles,
which
present
the SCM−3 . BOX2,
20m shallower
thanthe
depthoverin BOX1
andwhile in BOX3
there
are large
depth
above 50 m
with
theSCM
intensity
4 mg mAfter removing
these two
profiles,therelativebiasesregions(about between±10%) at0–50
the meters
SCM depth
andshowabout
20 m fluctuations
above (Figure4g). The
green shadedin BOX2
smaller(FigureA2).
relativebiasesin BOX1
and
BOX2
retrievedby signals,
smaller thevaluescompared
thoseinThis result
suggeststhat,evenwitharesome
episodic
networkmodeltohas
good
BOX3,
indicatingthat
theperformance
of
the
IDNN
model
is
better
for
BOX1
and
BOX2.
robustness and can infer the shapes of vertical Chl a profiles from surface data only.

FigureScatter plot
plot ofofobserved
observedChl
Chla aconcentration
concentration(x-axis)andestimated
a value(yFigure 4.
4. (a–c)(a–c) Scatter(x-axis)andestimated
ChlChla value(y-axis)axis)
in
BGC-Argo
test
set
in
BOXes
1–3.
The
black
dashedline
isthebisector
of
the
first
quadrant,in BGC-Argo test set in BOXes 1–3. The black dashed line is the bisector of the first quadrant, i.e.,y = x. (d–f) The mean of observed value (blue line) and the mean of IDNN predicted values (orangeline) in each BOX. The pink and green shades are the standard variance of the model results andobservations, respectively, which overlap and form the brown shade. (g) The mean relative bias as afunction of the adjusted depth between observed and the IDNN predicted Chl a in the test set for thethree BOXes. The adjusted depth is defined as the difference between the observed SCM depth andthe modeled one.

Statistically, the relative biases show that maximal bias (8–10%) occurs at about
10–20 m shallower than the SCM depth in BOX1 and BOX2, while in BOX3 there arelarge relative biases (about ±10%) at the SCM depth and about 20 m above (Figure 4g). The
relative biases in BOX1 and BOX2 are retrieved by smaller values compared to those inBOX3, indicating that the performance of the IDNN model is better for BOX1 and BOX2.
The statistical indices calculated for the IDNN assessment from the test set are listed
in Table 3. For all three BOXes, high R2 values suggest that input variables (the surface
Chl a, SST, acquisition date and geo-location) can explain over 71% of Chl a variability
at different depths. Here, the calculated R2 values are consistent with those reported bySammartino et al. [24], owing to similar input variables. Moreover, the high correlation
coefficient (ρ > 0.87) suggests the goodness of IDNN model performance, with a slightunderestimation of the observed Chl a in BOX3. Statistically, RMSEs less than 0.11 mg m−3

Remote Sens. 2022, 14, 632

9 of 19and MAPEs from 0.036 to 0.13 in three BOXes reveal a small divergence between thepredicted values and observed values. The statistical results indicate a robust prediction
capability of the IDNN in three BOXes.
Table 3. Statistical results of the comparison between the observed Chl a values and the predicted
Chl a concentration by the IDNN models using BGC-Argo data. R2 refers to the Determination
Coefficient, ρ to the Pearson’s correlation coefficient, RMSE denotes the root mean square error, and
MAPE represent the mean absolute percentage error.
Region
Index
R2
ρ
RMSE
MAPE

BOX1

BOX2

BOX3

0.77
0.89
0.0040
0.036

0.72
0.88
0.025
0.073

0.71
0.87
0.11
0.13

3.2. IDNN-Retrieved SCM Characteristics
We apply the IDNN model to calculate the seasonality of SCM characteristics. As
shown in Figure 5, the regionally averaged Chl a profile predicted by the IDNN modelfrom surface data is comparable to the observations for four seasons. In general, thepredicted Chl a concentrations fluctuated within the observation variances. Moreover, the
IDNN retrieves the vertical Chl a profile with better performance for the area with low
surface Chl a values than the area with high surface Chl a values. For instance, the IDNN
presents the best estimation for spring to autumn in BOX1 (Figure 5c). In Figure 5f–g,
large standard variances of observed profiles occurred between 0–50 m (green shades),which is similar to those in Figure 4e. Therefore, we removed the two profiles with an
episodically stronger SCM within 0–50 m in BOX2 during summer and autumn, and then
the two variance spikes in 0–50 m disappear (Figure A2). These results highlight thecapability of a deep neural algorithm to extend the surface-ocean information to SCM layer
with seasonal variation. For the non-standard bell-shape of vertical Chl a profiles withhigher surface Chl a values (Figure 5h–k), the IDNN predictions close to SCM depths areslightly overestimated or underestimated with respect to the observed values, especiallyin BOX2 Winter and in BOX3 Spring. The high variance in surface Chl a (e.g., the green
shaded area in Figure 5h–k) is related to dissimilar shapes of vertical Chl a profiles, andthus reduce the network prediction accuracy on SCM characteristics. However, beyond theSCM layer, the two lines (red and blue) coincide during four seasons, especially in summer
and autumn (Figure 5h–k). Here, we attribute the relatively high estimation offset for thearea with high surface Chl a values to a non-standard bell-shape of vertical Chl a profiles
and seasonal inconsistency.
As shown in Table 4, the seasonally averaged SCM characteristics from the test set
agree well with the observations in each BOX. The SCM thickness can be estimated by fitting
vertical Chl a profiles using the generalized Gaussian function (Equation (3)). Since recent
studies have developed the curve fitting of vertical Chl a profiles by superimposing thegeneralized Gaussian function onto a linearly [19] or exponentially decreasing background
Chl a concentration [34], we compared the curve-fitting performance of the three approaches
in three BOXes. The results show that the generalized Gaussian function has a higher
goodness of fit than other two functions. For example, for the non-standard bell-shape ofvertical Chl a profiles in BOX3 (Figure 5i–k), the generalized Gaussian function has the
goodness of fit of 90%, following by the function combined an exponentially decreasing
background (88%) and the function combined a linearly decreasing background (about 76%).
Based on our statistical results, we estimate the SCM thickness by using the generalized
Gaussian function (Equation (3)).

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13, 632x FOR PEER REVIEW
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20
10 of
of 19

Figure 5.
5. AggregatedAggregated chlorophyll
chlorophyllverticalverticalprofiles
profilesfrom
fromthethetesttestsetset
terms
seasons
BOX1
(a–
inin
terms
of of
seasonsin inBOX1(a–d),d),inBOX2(e–h),
andinBOX3(i–k).
The
blue
and
red
solid
lines
represent
the
mean
of
observed
in BOX2 (e–h), and in BOX3 (i–k). The blue and red solid lines represent the mean of observed
value andpredicted
ChlChla, respectively.
The Thepinkpink
and green
shadesshades
are theare
standvalue
and thethemeanmeanofofIDNN
IDNN
predicted
a, respectively.
and greentheard variance of the model results and observations, respectively, which overlap and form the brownstandard variance of the model results and observations, respectively, which overlap and form theshade.
brown shade.

As shown MAPEs
in Table of4, allthethreeseasonallyaveraged SCM
characteristics
from antheaverage
test set
Generally,
SCM parameters
are lessthan 35%, with
agree
well
with
the
observations
in
each
BOX.
The
SCM
thicknesscanbeestimatedbyvalue of 21%; MAPE of the SCM depth was the smallest (18% on average), which was
fitting vertical
Chlof
a profiles
using thegeneralized(Equation
Since
followedby that
SCM intensity
andthicknessGaussian(Table 4).function
In addition,the (3)).
averagedrecentstudieshavedeveloped
thecurvefittingofverticalChlaprofilesbysuperimposing
absolute relative bias is small in BOX1 (18%) and BOX2 (22%) but slightly larger in BOX3

Remote Sens. 2022, 14, 632

11 of 19(25%) due to the differences in SCM intensity during spring and SCM thickness in summer.
Overall, these results indicate that our model captures the SCM characteristics well.
Table 4. Comparison of seasonal averaged SCM characteristics of three BOXes from test set withobservations. Winter is defined as from December to February, and so on.
SCM Intensity (mg m−3 )SCM Depth (m)RegionSeasonSCM Thickness (m)

Obs.

Model

MAPE

Obs.

Model

MAPE

Obs.

Model

MAPE

BOX1

WinterSpringSummerAutumn

136
126
120
110

136
126
125
115

9%
10%
19%
8%

0.45
0.59
0.62
0.58

0.37
0.52
0.50
0.47

20%
19%
21%
19%

70
75
75
75

73
85
78
80

21%
25%
31%
15%

BOX2

WinterSpringSummerAutumn

76
69
71
80

75
73
75
82

14%
25%
16%
12%

0.62
1.04
1.13
0.94

0.54
0.78
1.01
0.65

21%
21%
28%
27%

80
65
43
54

76
70
56
64

21%
32%
22%
26%

BOX3

SpringSummerAutumn

40
34
42

35
32
44

35%
21%
24%

1.80
2.48
2.12

1.70
2.49
1.80

30%
29%
15%

69
43
39

56
42
41

20%
31%
22%

In addition to the seasonally averaged SCM characteristics in a region, our IDNN
also successfully retrieved pixel-by-pixel variations along with the trajectory of a BGCArgo float (Figure 6). The reconstructions of SCM characteristics in the test set show highconsistency with the in situ observations along the BGC-Argo float No. 2902756 in BOX1,
except for the SCM depth upwards during July and August 2020 (Figure 6a). In BOX2,
the modeled SCM depth and thickness agree with observations along BGC-Argo float No.
2902748, while the SCM intensity was slightly overestimated during summer in 2018 and2019 (Figure 6b). Similar to BOX2, the IDNN estimation shows relatively higher summer
SCM intensities in BOX3 (e.g., BGC-Argo float No. 2902755) compared to the observations(Figure 6c).
3.3. Role of the Gaussian Activation Function in Enhancing Estimation Accuracy
As explained in Section 2.1, our IDNN model has two improvements compared toprevious DNN model: the bias term and the Gaussian activation function. To anatomicallydetermine the contribution of each modification in our IDNN model, we conducted two
additional experiments with each stand-alone improvement.
(i)
(ii)

DNN model using a sigmoid activation function with bias improvement by incorporating SCM depth (Equation (1)) (hereafter, referred to as DNN-b);
DNN model using random bias values with a Gaussian activation function, rather
than a sigmoid function (Equation (4)) (hereafter, referred to as DNN-G).
2

f = e−π ( X j −b) ;(4)

where X j is the X value of the jth output in the hidden layer, b is the bias term withrandom values.
As shown in Figure 7, the DNN-b failed to reproduce the SCM characteristics, especially in BOX2. Compared to the observations, the SCM intensities predicted by the DNN-b
in BOX1 and BOX3 were smaller, and the SCM depth in BOX3 was shallower. The DNN-G
applied the Gaussian activation function to retrieve the SCM characteristics successfully,
although the estimated SCM depth in BOX3 was slightly shallower than the observed
one (Figure 7). Thus, we deduce that the application of the Gaussian activation function,rather than the sigmoid function, significantly improves the capability of the DNN modelin estimating SCM characteristics.

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Furthermore, towards BOX3 in the subpolar areas with high surface Chl a concentration, we conducted two other experiments to explore the role of the Gaussian activation
function in learning the SCM characteristics in based on:(iii) DNN-G model in which the bias term b was set as 0 (Equation (5)) (hereafter, referred
to as DNN-G-b0),

f =e−π X j 2;(5)(iv) DNN-G model in which the bias term b was set as 1 (Equation (6)) (hereafter, referred
to as DNN-G-b1),

f =e

(

)

− π X j −1

2

(6)

.

The predicted chlorophyll values in DNN-G-b0 and DNN-G-b1 were similar to the
IDNN results, especially for BOX1 and BOX2 (Figure 7a,b). In BOX3, the SCM intensity
captured by these two experiments varied slightly from the values of bias, while the SCM
depthsremained
generally
constant(Figure7c). Our
results
indicatethat
theFigureComparison
SCM
characteristics(depth,intensity,
thickness)
obtainedfrom
Figure6.6. Comparison
of of
SCM
characteristics(depth,intensity,
andandthickness)
obtainedfromtheimprovementin
model
learning
using
different
bias
valuesbasedontheGaussian
activation
functhe IDNN
resultsin testthe settestandset observationand observation
profilestrajectoriesof three
BGC-Argo
IDNN
resultsin theprofilesalongalong
trajectoriesof three
BGC-Argo(No.
tion
gentle.
2902756(a),isNo.
(b), and(c) in (c)BOX1–BOX3,
respectively).
(No. 2902756(a),2902748
No. 2902748(b),No.
and2902755
No. 2902755
in BOX1–BOX3,
respectively).
3.3. Role of the Gaussian Activation Function in Enhancing Estimation Accuracy
As explained in Section 2.1, our IDNN model has two improvements compared toprevious DNN model: the bias term and the Gaussian activation function. To anatomicallydetermine the contribution of each modification in our IDNN model, we conducted two
additional experiments with each stand-alone improvement.
(i)

DNN model using a sigmoid activation function with bias improvement by incorporating SCM depth (Equation (1)) (hereafter, referred to as DNN-b);(ii) DNN model using random bias values with a Gaussian activation function, rather
than a sigmoid function (Equation (4)) (hereafter, referred to as DNN-G).

f =e− π ( X j − b )2;

(4)

where X j is the X value of the jth output in the hidden layer, b is the bias term withrandom values.
As shown in Figure 7, the DNN-b failed to reproduce the SCM characteristics, especially in BOX2. Compared to the observations, the SCM intensities predicted by the DNNb in BOX1 and BOX3 were smaller, and the SCM depth in BOX3 was shallower. The DNNG applied the Gaussian activation function to retrieve the SCM characteristics successfully, although the estimated SCM depth in BOX3 was slightly shallower than the observed one (Figure 7). Thus, we deduce that the application of the Gaussian activation
function,rather than
the sigmoid
function,
capabilityinof
theFigure 7. Aggregatedchlorophyll
verticalprofiles significantly
from the test setimproves
in differentthe
experiments
BOXes
Figure 7. Aggregated chlorophyll vertical profiles from the test set in different experiments in
DNN
model
in
estimating
SCM
characteristics.
1–3 (a–c).
BOXes 1–3 (a–c).

3.4. Comparison with Shallow ANNs

Studies have used shallow ANN models to estimate the vertical distribution of Chl ain open oceans and coastal seas [22,23,24]. The shallow ANN model is a multi-layer perceptron (MLP), which consists of input layers, output layers, and one hidden layer be-Remote Sens. 2022, 14, 632

13 of 19

Furthermore, towards BOX3 in the subpolar areas with high surface Chl a concentration, we conducted two other experiments to explore the role of the Gaussian activation
function in learning the SCM characteristics in based on:(iii) DNN-G model in which the bias term b was set as 0 (Equation (5)) (hereafter, referred
to as DNN-G-b0 ),2
f = e−πX j ;(5)(iv) DNN-G model in which the bias term b was set as 1 (Equation (6)) (hereafter, referred
to as DNN-G-b1 ),2

f = e − π ( X j −1) .

(6)

The predicted chlorophyll values in DNN-G-b0 and DNN-G-b1 were similar to the
IDNN results, especially for BOX1 and BOX2 (Figure 7a,b). In BOX3, the SCM intensity
captured by these two experiments varied slightly from the values of bias, while the SCM
depths remained generally constant (Figure 7c). Our results indicate that the improvement
in model learning using different bias values based on the Gaussian activation function
is gentle.
3.4. Comparison with Shallow ANNs
Studies have used shallow ANN models to estimate the vertical distribution of Chl a inopen oceans and coastal seas [22–24]. The shallow ANN model is a multi-layer perceptron(MLP), which consists of input layers, output layers, and one hidden layer between them.
In the northwestern Pacific Ocean around Japan, Osawa et al. [22] applied a shallow
ANN model with six input variables (SST, surface Chl a, mixed layer depth, geo-location,
and Julian days), 50 nodes in the hidden layer to output four Gaussian parameters for
estimating vertical profiles of Chl a. In the Mediterranean Sea, Sammartino et al. [24]reconstructed vertical profiles of Chl a by employing a shallow ANN model in which input
variables included SST, surface Chl a, geo-location, and day of the year. The shallow ANN
model works well in the regions with low surface Chl a concentrations but its performancedecreases for the area with high Chl a surface concentrations [23,24].
To test the advantages of including more hidden layers, we perform calculations by
two ANN models with one hidden layer (MLP-1 thereafter) and three hidden layers (MLP-3
thereafter), respectively. Both MLP models are input the same data. Moreover, the MLP
models were trained using the same training and test sets that were employed to train the
IDNN model. The comparison was carried out on the test sets.
The relative deviation between MLP models and the IDNN model were plotted side
by side in Figure 8. Compared to our IDNN model results, the mean value of R2 and ρ
obtained by the MLP-1 and MLP-3 decrease in all three BOXes, while RMSE and MAPD
increase significantly in BOX2 and BOX3 (>55%), especially obtained by the MLP-1 model(86–196%). This suggests that the IDNN model exhibited a better performance, and the
MLP-3 model has a similar capability with the IDNN model in the tropical sea area (BOX1).
In terms of SCM intensity and thickness, the MLP-3 model performed better than the
MLP-1, although the mean values were underestimated by the MLP models in BOX1 andBOX2 (Figure 9a,b). While in the BOX3, both the MLP-1 and MLP-3 models failed to reveal
the presence of SCM in the vertical Chl a profiles (Figure 9c). Therefore, the MLP-3 model
is more capable of predicting SCM characteristics than the MLP-1 model; however, both
MLP models are not adapted to the subpolar sea areas.
3.5. Application of the IDNN Model to Satellite Data
To evaluate the IDNN prediction capability using remote-sensing data, the Chl aconcentrations retrieved by the IDNN model were compared with BGC-Argo observations
at the matchup stations.

Remote Sens. 2022, 14, 632

by side in Figure 8. Compared to our IDNN model results, the mean value of R2
obtained by the MLP-1 and MLP-3 decrease in all three BOXes, while RMSE and M
increase significantly in BOX2 and BOX3 (>55%), especially obtained by the MLP-1 m(86–196%). This suggests that the IDNN model exhibited a better performance, anof 19
MLP-3 model has a similar capability with the IDNN model in the14tropicalsea(BOX1).

Remote Sens. 2021, 13, x FOR PEER REVIEW
15 of 20
Figuredeviation
for MLP-3(brown)(brown)
and MLP-1(green)modelsfrom theIDNNfrom
modelthein IDNN
Figure8.8.Relative
Relativedeviation
for MLP-3
and
MLP-1(green)models
BOX1,
BOX2,
and BOX3.
in BOX1,
BOX2,
and BOX3.

In terms of SCM intensity and thickness, the MLP-3 model performed better th
MLP-1, although the mean values were underestimated by the MLP models in BOX
BOX2 (Figure 9a,b). While in the BOX3, both the MLP-1 and MLP-3 models failed tothe presence of SCM in the vertical Chl a profiles (Figure 9c). Therefore, the MLP-3 m
is more capable of predicting SCM characteristics than the MLP-1 model; however
MLP models are not adapted to the subpolar sea areas.

Figure9.9.Modeling
ModelingChl
Chlaaprofiles
profiles byby thethe IDNN
IDNN andof ofthethe northFigureand MLP
MLPmodelsmodelsininthree
threeBOXes
BOXes(a–c)(a–c)
northwestern
Pacific
Ocean.
The
configuration
of
MLP-1
is
6-10-1,
that
is,
6
input
variables,10
hiddenwestern Pacific Ocean. The configuration of MLP-1 is 6-10-1, that is, 6 input variables, 10 hidden
nodes,andand 11 output.
output. The
is 6-3*64-1,
that thatis, 3 hidden
layers layers
and 64 andnodes64innodes
each in each
nodes,TheMLP-3
MLP-3modelmodel
is 6-3*64-1,
is, 3 hidden
hiddenlayer.
hidden layer.

Statistically, the determination coefficients ranged within 0.47–0.79, with the average

3.5.
of theIDNN5).Modelto Satellite
Data
R2 Application= 0.64 on the testset (Table
Analogous
result was
obtained by Sammartino et al. [24]

2 was lower
by using
remote-sensing
dataprediction
with an R2capability= 0.63. Here,the averagevalue of Rdata,
To evaluate
the IDNN
using
remote-sensing
the Chl a con
than that obtained by the IDNN using BGC-Argo data (the average of 0.73) (Table 3), imcentrations retrieved by the IDNN model were compared with BGC-Argo observations aplying a possible influence of the satellite retrieval uncertainties on the prediction accuracy,
thematchupespecially
forstations.
the BOX3. The other statistical indexes, ρ > 0.86, RMSE < 0.14 mg m−3 andStatistically,thedetermination
rangedwithin 0.47–0.79,
with
MAPE% < 15%, arealmostthe same as coefficients
those obtained
from BGC-Argo
input (Table3). the
The average
2
Rstatistical= 0.64 on
the testset (Table
5).IDNN
Analogous
obtainedby Sammartino
results
indicatethat themodel isresultrobustwas
for theremote-sensing
data, withet al. [242slightly
lessaccuracyinthesubpolarregion.
by using remote-sensing data with an R = 0.63. Here, the average value of R2 was lower

than that obtained by the IDNN using BGC-Argo data (the average of 0.73) (Table 3), im
plying a possible influence of the satellite retrieval uncertainties on the prediction accu
racy, especially for the BOX3. The other statistical indexes, 𝜌 > 0.86, RMSE < 0.14 mg m−
and MAPE% < 15%, are almost the same as those obtained from BGC-Argo input (Table

Remote Sens. 2022, 14, 632

15 of 19

Table 5. Statistical results of the comparison between the observed Chl a values and the predicted
Chl a concentrations by the IDNN models using remote-sensing data. R2 refers to the determination
coefficient, ρ to the Pearson’s correlation coefficient, RMSE denotes the root mean square error, andRemote Sens. 2021, 13, x FOR PEER REVIEW
16 of 20MAPE represents the mean absolute percentage error.
Region
Index

BOX1

BOX2

BOX3

detail, the two mean profiles (orange and blue lines) are almost overlapped in the BOX1,
2
0.79 below the SCM0.66
0.47 10a). The
except forR a slightly overestimation
depth (110–140 m) (Figure
ρ
0.91
0.86
0.89
Chl a concentrations above the SCM depth in the BOX2 (<80 m) are relatively
overestiRMSE
0.00460.026
0.14
mated (Figureof overestimation enlarges
from the upper
SCM layer to
MAPE 10b). The scope
0.037
0.076
0.15
the lower part (20–80 m) in the BOX3 (Figure 10c).
Moreover, the performance of IDNN is compared with the MLP-1 method by using
Figure 10 shows that the mean vertical Chl a profile inferred by the IDNN from remoteremote-sensing data as input variables (Figure 10a–c). In the BOX1 and BOX2, the MLP-1
sensing data agrees well with the mean BGC-Argo profile in each BOX, validating themodel captures weaker SCMs than the observed one, especially in the BOX1. While in thegood prediction accuracy of the IDNN model in the northwestern Pacific Ocean. In detail,
BOX3,
SCM
phenomenon
is presented
thealmost
predicted
profile inbythetheBOX1,
MLP-1
model.
thetwo nomean
profiles(orange andblue lines)inare
overlapped
exceptSimilarresultsareobtainedtothoseinferredfromthe
BGC-Argo
reportedinSectionfor a slightly overestimation below the SCM depth (110–140 m) (Figure 10a). The Chl a3.4.
In general, the above
comparisons
betweenthetheobserved
and m)
thearepredicted
profilesconfirm theconcentrations
the SCM
depth in
BOX2 (<80relatively
overestimatedapplicability
of
our
IDNN
model
to
extendtheremote-sensing-based
surface
information(Figure 10b). The scope of overestimation enlarges from the upper SCM layer to the lower
to thesubsurface
layer.
part(20–80m) in the
BOX3 (Figure 10c).

Figureofofthethemean
profilesof observed
values(blue (blueline), IDNN
predictions(orange(orFigure10.
10.ComparisonsComparisonsmean
profilesof observed
valuesline), IDNN
predictions
angeandline),and predictions
MLP-1 predictions(greendash line)
inferredfrom remote-sensing
data (a–c).
in threeline),
MLP-1(green dashline) inferredfrom
remote-sensing
data in three BOXes
BOXes (a–c).

Moreover, the performance of IDNN is compared with the MLP-1 method by using
remote-sensing
4. Conclusionsdata as input variables (Figure 10a–c). In the BOX1 and BOX2, the MLP-1
model captures weaker SCMs than the observed one, especially in the BOX1. While in the
In this study, for the first time, we developed and applied an improved DNN model
BOX3, no SCM phenomenon is presented in the predicted profile by the MLP-1 model.
withGaussian radial basis activation function, to retrieve the vertical structure of Chl a
Similar results are obtained to those inferred from the BGC-Argo reported in Section 3.4.
concentrationand the associatedSCM
in thenorthwestern
Pacific Ocean.
In
general, the comparisons
betweenthe characteristics
observed and thepredicted
profiles confirm
theThe
annually
averaged
SCM
depth
was
incorporated
into
the
bias
term
and
the Gaussian
applicability of our IDNN model to extend the remote-sensing-based surface information
radialbasis activationtothe subsurface
layer. function via the training process of the DNN model, which improved the prediction capability of model from surface-ocean Chl a data and SST. The
4.
Conclusions
verticalstructure of Chl a concentration and SCM characteristics, which were estimatedby ourDNNmodel,
a goodin different
seasons
In this study,
for showed
the first time,
weagreement
developedwith
andobservations
applied an improved
DNN
modelandalong
thetrajectoryof
BGC-Argo
floats.
Comparedtoaseriesofneuralnetwork
methods,
with Gaussian radial basis activation function, to retrieve the vertical structure of Chl a
our IDNN model with Gaussian radial basis activation function captured the SCM characteristics in the northwestern Pacific Ocean, especially in subpolar areas with high surface Chl a concentrations. Moreover, the SCM characteristics were reproduced well by
our IDNN model inputting remote-sensing surface data.

Remote Sens. 2022, 14, 632

16 of 19concentration and the associated SCM characteristics in the northwestern Pacific Ocean.
The annually averaged SCM depth was incorporated into the bias term and the Gaussianradial basis activation function via the training process of the DNN model, which improved
the prediction capability of model from surface-ocean Chl a data and SST. The verticalstructure of Chl a concentration and SCM characteristics, which were estimated by our DNN
model, showed a good agreement with observations in different seasons and along the
trajectory of BGC-Argo floats. Compared to a series of neural network methods, our IDNN
model with Gaussian radial basis activation function captured the SCM characteristics
in the northwestern Pacific Ocean, especially in subpolar areas with high surface Chl aconcentrations. Moreover, the SCM characteristics were reproduced well by our IDNN
model inputting remote-sensing surface data.
This study used surface-ocean Chl a and SST as input variables for the IDNN model
to reconstruct the non-uniform vertical Chl a profiles. A future improvement of our model
involves employing additional input variables—such as photosynthetically active radiation,light attenuation coefficient, and oceanographic parameters (e.g., sea surface height andwind components)—that potentially affect SCM characteristics. Meanwhile, the training
process of present IDNN is pixel-to-pixel without considering temporal variations ofneighboring pixels, which is similar to other shallow ANN models. Thus, a deep learningtechnique with a combination of convolution neural network (CNN) and a long short-term
memory (LSTM) neural network will be adopted to predict the target by considering thetime series of the most correlated surrounding pixels.
Author Contributions: Conceptualization, X.G. (Xiang Gong); Data curation, J.C. and X.X.; Formal
analysis, X.G. (Xinyu Guo), X.X. and K.L.; Funding acquisition, X.G. (Xun Gong), X.X. and X.G.
(Xiang Gong); Investigation, J.C., X.G. (Xun Gong) and X.G. (Xiang Gong); Methodology, J.C. and X.G.
(Xiang Gong); Project administration, X.G. (Xiang Gong); Resources, X.G. (Xiang Gong); Software, J.C.;
Supervision, H.G.; Validation, J.C.; Visualization, J.C.; Writing—original draft, J.C.; Writing—review
and editing, X.G. (Xun Gong), X.G. (Xinyu Guo) and X.G. (Xiang Gong). All authors have read andagreed to the published version of the manuscript.
Funding: This work was supported by the Ministry of Science and Technology of the People’s Republic of China (2019YFE0125000), the National Nature Science Foundation of China-Shandong Joint
Fund (U1906215), and the National Natural Science Foundation of China (41876032 and 41890805).
Acknowledgments: We would like to acknowledge the International Argo Program and the national
programs that contribute to the BGC-Argo data, which were collected and made freely available (https://argo.ucsd.edu, https://www.ocean-ops.org, accessed on 19 April 2021). The Argo Program is partof the Global Ocean Observing System. This work was partly supported by the Ministry of Education,
Culture, Sports, Science and Technology, Japan (MEXT) to a project on Joint Usage/Research Center–
Leading Academia in Marine and Environment Pollution Research (LaMer). This work was also
supported by the Key Laboratory of Coastal Environmental Processes and Ecological Remediation,
Chinese Academy of Sciences Opening Fund (2020KFJJ04).
Conflicts of Interest: The authors declare no conflict of interest.

Appendix A
Table A1. Basic statistical evaluations used for the assessment of the IDNN performance.
Determination Coefficient
Pearson’s Correlation Coefficient
Root Mean Square Error
Mean Absolute Percentage Error
Mean Bias Error
Mean Relative Bias Error

R2 = 1 −∑in=1 ( xi − pi )22

∑in=1 ( xi − x )∑in=1 ( pi − p)( xi − x )
q
q
ρ=
2
2
∑in=1 ( pi − p)∑in=1 ( xi − x )

q

2
1 n
n ∑ i =1 ( p i − x i )np−xMAPE = n1 ∑ i x i
ii =1
MBE = n1 ∑in=1 ( pi − xi )p −xMRBE = n1 ∑in=1 i x ii

RMSE =

Note: n is the amount of data number, pi is the model estimated values and xi is the observed Chl a.

Remote Sens. 2021, 13, x FOR PEER REVIEW
RemoteFOR PEER REVIEW
RemoteSens.
Sens.2021,
2022,13,
14,x632

18 of 20
1817ofof20
19

Figure A1. Locations and measuring months of 16 BGC—Argo profiles without SCM in the northFigurePacific
A1.Locations
Locationsandmeasuring
measuringmonths
monthsofof16
16BGC—Argo
BGC—Argoprofiles
profileswithout
withoutSCM
SCMininthe
thenorthnorthwestern
Ocean. andFigureA1.
westernPacificPacificOcean.
Ocean.
western

FigureAggregatedchlorophyllverticalverticalprofiles
profilesfrom
fromthethetesttest set
set inin BOX2
BOX2 during
FigureA2.A2.
Aggregatedchlorophyll
during four
fourseasonsseasons(a),duringsummer(b),duringautumn(c),(c),after
removing
profileswithextremevalues(over(a),
duringsummer(b),andandduringautumnafter
removing
two
withextremevaluesFigureA2.
Aggregatedchlorophyll
verticalprofilesfromthetwotest
setprofiles
in BOX2
duringfour
seasons3 )−3between 0–50 m. The blue and red solid lines represent the mean of observed value and
4 mg
m−m
(over
4 mg
) between
The blueand redrepresent
meanwithof observed(a),duringsummer(b),0–50
andm.
duringautumn(c), solid
after lines
removing
two theprofilesextremevalue
values−3) IDNN
the
mean
IDNN
predicted
a, respectively.
The
pink
andrepresent
green
shadesare thearevarianceandthepredicteda,respectively.
Thelinespink
and green
shadesthe standard
(over
4mean
mgofmofbetween
0–50Chlm. ChlThe
blue
and red
solid
the
mean
ofstandard
observedvalue
varianceof
the results
model
results
and observations,
respectively,
which
overlap
and
form
the
brown
and
themodelmeanof IDNNpredicted
Chl a,respectively,
respectively.
The pink
andandgreen
shadesare thestandardof theandobservations,which
overlapform
the brown
shade.
shade.
variance of the model results and observations, respectively, which overlap and form the brownshade.

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