TYPE Original Research
PUBLISHED 21 May 2024
DOI 10.3389/fmars.2024.1378488

OPEN ACCESSEDITED BY

Huiyu Zhou,
University of Leicester, United Kingdom
REVIEWED BY

Zhigang Cao,
Chinese Academy of Sciences (CAS), China
Hongwei Guo,
Nankai University, China*CORRESPONDENCE

Xiang Gong
gongxiang@qust.edu.cn
RECEIVED 02 February 2024
ACCEPTED 01 May 2024
PUBLISHED 21 May 2024
CITATION

Zhao X, Gong X, Gong X, Liu J, Wang G,
Wang L, Guo X and Gao H (2024) Evolution of
3-D chlorophyll in the northwestern Paciﬁc
Ocean using a Gaussian-activation deepneural network model.
Front. Mar. Sci. 11:1378488.
doi: 10.3389/fmars.2024.1378488

Evolution of 3-D chlorophyll in
the northwestern Paciﬁc Ocean
using a Gaussian-activation deepneural network model
Xianzhi Zhao 1,2, Xiang Gong 1,2*, Xun Gong 3,4,5, Jiyao Liu 1,2,
Guoju Wang 1,2, Lixin Wang 1,2,6, Xinyu Guo 7 and Huiwang Gao 8,9School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao, China,
Qingdao Innovation Center of Artiﬁcial Intelligence Ocean Technology, Qingdao University of
Science and Technology, Qingdao, China, 3 Institute for Advanced Marine Research, China Universityof Geosciences, Guangzhou, China, 4 State Key Laboratory of Biogeology and Environmental Geology,
Hubei Key Laboratory of Marine Geological Resources, China University of Geosciences,
Wuhan, China, 5 Key Laboratory of Computing Power Network and Information Security, Ministry of
Education, Shandong Computer Science Center (National Supercomputer Center in Jinan), Qilu
University of Technology (Shandong Academy of Sciences), Jinan, China, 6 CAS Key Laboratory of
Ocean Circulation and Waves, Institute of Oceanology, Chinese Academy of Sciences,
Qingdao, China, 7 Center for Marine Environmental Study, Ehime University, Matsuyama, Japan,
8
Frontiers Science Center for Deep Ocean Multispheres and Earth System and Key Laboratory ofMarine Environment and Ecology, Ministry of Education, Ocean University of China, Qingdao, China,
9
Laboratory for Marine Ecology and Environmental Science, Qingdao Marine Science and Technology
Center, Qingdao, China
12

COPYRIGHT© 2024 Zhao, Gong, Gong, Liu, Wang, Wang,
Guo and Gao. This is an open-access article
distributed under the terms of the Creative
Commons Attribution License (CC BY). The
use, distribution or reproduction in otherforums is permitted, provided the original
author(s) and the copyright owner(s) are
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which does not comply with these terms.

Insufﬁcient studies in characterizing vertical structure of Chlorophyll-a (Chl-a) in
the ocean critically limit better understanding about marine ecosystem based on
global climate change. In this study, we developed a Gaussian-activation deepneural network (Gaussian-DNN) model to assess vertical Chl-a structure in theupper ocean at high spatial resolution. Our Gaussian-DNN model used the input
variables including satellite data of sea surface Chl-a and in-situ vertical physics
proﬁles (temperature and salinity) in the northwestern Paciﬁc Ocean (NWPO).
After validation test based on two independent datasets of BGC-Argo and shipmeasurement, we applied the Gaussian-DNN model to reconstruct temporal
evolution of 3-D Chl-a structure in the NWPO. Our modelling results successfully
explain over 80% of the Chl-a vertical proﬁles in the NWPO at a horizontal
resolution of 1° × 1° and 1 m vertical resolution within upper 300 meters during
2004 to 2022. Moreover, according to our modelling results, the Subsurface
Chlorophyll Maxima (SCMs) and total Chl-a within 0-300 m depths wereextracted and presented seasonal variability overlapping longer-time trends ofspatial discrepancies all over the NWPO. In addition, our sensitivity testingsuggested that sea-water temperatures predominantly control 3-D structuresof the Chl-a in the tropical NWPO, while salinity played a key role in thetemperate gyre of the NWPO. Here, our development of the Gaussian-DNN
model may also be applied to craft long term, 3-D Chl-a products in the
global ocean.

KEYWORDS

deep neural network, Gaussian activation, 3-D chlorophyll structure, subsurface
chlorophyll maximum, long-term trend

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potential impacts of network design along ocean depths in accuracy
to the results. There are some studies that utilize vertical variables aspredictors. For example, Sauzède et al. (2016) utilized an ANN
model to infer vertical proﬁles of the particulate backscattering
coefﬁcient based on surface ocean-color estimates, vertical potential
densities, and mixed-layer depths. Similarly, Hu et al. (2023)
employed a Random Forest (RF) method to retrieve vertical Chl-a
proﬁles in the northern Indian Ocean, utilizing surface ocean-color
estimates, vertical temperature and salinity, and mixed-layer depths
as inputs. Although their studies improved the estimation accuracyof 3-D structure by incorporating vertical physical properties, theysolely demonstrate the feasibility of climatology monthly verticalstructure or are restricted to the time span of the input data, leaving
the long-term 3-D Chl-a reconstruction problem unresolved.
The NWPO boasts one of the richest marine ecosystems(Naiman et al., 1992) with abundant and diverse ﬁshery resourcesin the global ocean (Chikuni, 1986), and the atmosphere-ocean
coupled system in the NWPO is closely linked to the global
warming and also provides critical feedbacks (Xie et al., 2009;
Kulk et al., 2020; Shi et al., 2023). A few of studies investigatedthe variabilities of surface Chl-a on the long-term trends in the
NWPO (Hammond et al., 2020; Chen et al., 2022b; Yu et al., 2023).
Signiﬁcant negative trends of surface Chl-a are generally observedin the oligotrophic gyres of the NWPO during 1998–2020 (Yu et al.,2023). In the subarctic gyres of the NWPO, surface Chl-a presented
an increased tendency during 1997–2020 (Chen et al., 2022b).
However, given the prevailing SCMs in the NWPO (Cornec et al.,2021; Chen et al., 2022a; Wang et al., 2023a), caution is warranted
when extending conclusions from surface Chl-a to water-column
integrated Chl-a. Meanwhile, the lack of long-term 3-D Chl-astructure means that trends in water-column integrated Chl-a in
the NWPO remain an open question.
In this study, we engaged in extrapolative prediction for longterm, gridded vertical Chl-a proﬁles in the NWPO using anenhanced deep neural network (DNN) model. DNN models, as asubset of deep learning, are distinguished by their multiple hidden
layers compared to ANN models, which typically have a single
hidden layer. They possess the capability to autonomously extract
intricate features from raw data and demonstrate higher scalability
in managing extensive and complex datasets (Li et al., 2020).
Moreover, DNN models have been certiﬁed to exhibit superior
performance in retrieving vertical bio-optical properties (e.g., Chl-a,nitrate) compared to ANN models (Chen et al., 2022a; Wang et al.,2023a, b) and RF models (Wang et al., 2023a) in the NWPO.
Therefore, through the precise reconstruction of 3-D Chl-a using
an enhanced DNN model, our study aims to an improved
understanding of the variability of SCMs characteristics and longterm trends in depth-integrated Chl-a in the NWPO. This, inturn, aids in elucidating the regional carbon cycle and marine
ecosystem dynamics, while also offering valuable insights for
future projections.
This paper is organized as: Section 2 provides the detailed
information on the DNN model based on a Gaussian activation
function (named as Gaussian-DNN), along with the data used formodel training, validation, and reconstruction, as well as theevaluation methods employed in this study. In Section 3, the1 Introduction
Marine phytoplankton provides nearly half of the global
primary production (Behrenfeld, 2001) and plays critical roles inregulating ecosystem and carbon cycle in the global ocean (Gregget al., 2003; Anderson et al., 2021). Popularly, Chlorophyll-aconcentration (Chl-a) has served as an index in estimating
phytoplankton biomass, primary production, and the trophic
condition in the ocean (Volpe et al., 2012; Colella et al., 2016;
Hammond et al., 2020). So far, satellite remote sensing is a major
source of marine Chl-a data, meanwhile these data are limited
within the surface ocean that contains generally less than 20% of theeuphotic depths for phytoplankton photosynthesis process (Gordon
and McCluney, 1975; Matthes et al., 2023), thus unable to reveal
subsurface chlorophyll maxima (SCMs) beneath the surface mixed
layer. The SCMs are a ubiquitous and prominent characteristic inboth coastal seas and open oceans, commonly believed to form in
speciﬁc regions of the water column where opposing gradients oflight and nutrients, coupled with turbulent mixing, create
conditions conducive to optimal phytoplankton growth (Cullen
and Eppley, 1981; Letelier et al., 2004; Beckmann and Hense, 2007;
Cullen, 2015; Cornec et al., 2021). The SCMs signiﬁcantly
contribute to primary production, highlighting their crucial rolein marine ecosystems (Fennel and Boss, 2003; Gong et al., 2015,2017). Therefore, the mis-detection of SCMs by satellite leads tolimitation and also signiﬁcant errors in estimating temporal
evolution of 3-D structure in the Chl-a production, with regional
errors even to 120% (Piatt et al., 1989; Fernand et al., 2013; Bouman
et al., 2020).
Since the 1980s, how to retrieval Chl-a vertical distributions
from surface-ocean data has been a subject of considerable attention
since the 1980s (Morel and Berthon, 1989). Statistical extrapolation
method is employed to derive vertical proﬁle of Chl-a, commonly
by incorporating satellite-derived data (Morel and Berthon, 1989;
Richardson et al., 2003; Uitz et al., 2006). This approach involves
partitioning oceanic waters into trophic categories based on theirsurface Chl-a values, ranging mainly from 0.01 mg m-3 to over 10
mg m-3. The mean vertical Chl-a proﬁle in each category is thencomputed using generalized Gaussian functions (Platt et al., 1988;
Gong et al., 2015). However, this method fails adequately describing
the shape of Chl-a proﬁles in various areas and on daily timescales.
In parallel, numerical models simulating gridded vertical Chl-a
proﬁles show large discrepancies, likely attributed to inconsistentmodeling parameters strategy and various grid-mesh resolutions(Varela et al., 1992; Moeller et al., 2019; Masuda et al., 2021; Shuet al., 2022).
Recently, more and more artiﬁcial intelligence technology is
employed to reconstruct vertical structure of ocean Chl-a on thebasis of satellite remote sensing data. For instance, Sammartino
et al. (2018) utilized an artiﬁcial neural network (ANN) model(single hidden layer) on sea surface temperature (SST) and surface
Chl-a data, to infer the vertical proﬁles of Chl-a in the
Mediterranean Sea. Similarly, also based on SST and surfaceocean Chl-a datasets, Chen et al. (2022a) and Wang et al. (2023a)
analyzed SCMs in the northwestern Paciﬁc Ocean (NWPO) using
deep learning models. However, their studies commonly overlooked

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3,759 vertical Chl-a proﬁles, along with paired temperature and salinity
data, was retained for training the Gaussian-DNN model. Following
the assumptions of Cornec et al. (2021) about phytoplankton living
habitat, we applied our model for the ocean of 0–300 m.
In our analysis, based on our statistical analysis on SCMs
characteristics (See Chen et al., 2022a), the 35 proﬁling ﬂoats of
the BGC-Argo are catalogued to three boxes to represent the tropics(12–24°N), the subtropical (24–38°N) and temperate (38–54°N)
gyres, respectively (Figure 1A), aiming to illustrate the variations invertical Chl-a distribution across latitudes in the NWPO.

trained Gaussian-DNN was validated using two independent
datasets and proceeded to reconstruct long-term 3-D Chl-astructures in the NWPO. Furthermore, based on thereconstruction, Section 3 analyzed the spatiotemporal variationsof SCM characteristics and long-term trends in depth-integrated
Chl-a in water columns. Section 4 includes a sensitivity test for
input variables and a discussion on the importance of each input inthe developed DNN model for controlling the spatiotemporal
distribution of Chl-a in the NWPO, along with a discussion on
the uncertainties of our DNN model. In the end, a summary of our
key ﬁndings are illustrated in Section 5.

2.1.2 Validation data from ship measurements
To assess the robustness and generalization of the trained DNN
model on datasets from different sources, the datasets of Japan
Meteorological Agency (JMA) from April 2015 to March 2021
(https://www.jma.go.jp/jma/indexe.html) are obtained, as shown in
Figure 1B. We retained a total of 937 proﬁles of Chl-a and theircorresponding temperature-salinity proﬁles. The Chl-a data from
JMA spans a range of 0 to 19.83 mg m-3. Similar to the dataprocessing for BGC-Argo ﬂoat data, after ﬁltering out Chl-a proﬁleswith sea surface values greater than 6.5 mg m-3, 924 proﬁlesremained for deployment in the trained Gaussian-DNN model.
The vertical resolution of the Chl-a data in the JMA dataset is atstandard layers of 0, 5, 10, 25, 50, 75, 100, 150, 200, 250, and 300 m,
and the predicted Chl-a values at these depths were output from thetrained Gaussian-DNN model.
All retained measurement points were utilized for validating theGaussian-DNN model. The choice of N-S transects at 137°E and165°E was driven by their comprehensive tempo-spatial coverage
across all seasons and multiple sub-regions, rendering them ideal
for elucidating the validation process.

2 Data and methods
2.1 Data processing
2.1.1 Training data from BiogeochemicalArgo dataset
The BGC-Argo program, a pioneering initiative utilizing proﬁling
ﬂoats for ocean-wide and distributed ocean monitoring (Bittig et al.,2019), collects 3-D ocean variables including temperature, salinity and
Chl-a (https://biogeochemical-argo.org/). Field data utilized to train the
DNN model were obtained from 35 BGC-Argo proﬁling ﬂoats in the
NWPO region of 123 - 180°E, 12 - 54°N, as shown in Figure 1A. In
total, BGC-Argo ﬂoats provide 3941 vertical Chl-a proﬁles, spanning all
seasons from July 2017 to October 2022. In the data preparation stage,
we ﬁrst corrected the overestimation of BGC-Argo Chl-a byimplementing a factor-two adjustment, as recommended by Cornec
et al. (2021). Subsequently, we identiﬁed and removed 9 vertical Chl-a
proﬁles with sea surface values exceeding 6.5 mg m-3, following thecriteria established by Venrick et al. (1987). Additionally, upon visualinspection, 173 proﬁles were ﬂagged as abnormal and excluded fromthe dataset. Among these, 123 proﬁles exhibited consistentconcentrations with minor ﬂuctuations within the surface 20 m,
while the remaining 50 proﬁles displayed anomalously high values
below a depth of 250 meters, identiﬁed using the 3s rule. Furthermore,
we applied the Savitzky-Golay ﬁltering method to reﬁne the remaining
proﬁles (Press and Teukolsky, 1990). Ultimately, a dataset comprisingA

2.1.3 Reconstruction data from satellite and Argo
Satellite Chl-a data were obtained to reconstruct gridded
vertical distribution of Chl-a in the NWPO by using the trained
DNN model. Monthly Level-3 Chl-a data products from the
MODIS Aqua satellite, with a standard resolution of 9 km, werecollected from January 2004 to June 2022, sourced from the NASA
Goddard Space Flight Center (http://oceancolor.gsfc.nasa.gov/,B

FIGURE 1(A) Locations and measurement months of 35 BGC-Argo buoys in the Northwest Paciﬁc Ocean. (B) Ship measured sites during cruises RF and KS
from Japan Maritime Agency (JMA). Data at N-S transects of 137°E and 165°E highlighted to present the validation process.

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3-D Chl-a structures. This synchronization began in January 2004,aligning with the earliest available thermohaline data provided by
the BOA-Argo dataset. Additionally, to ensure compatibility with
the BOA-Argo data, the MODIS gap-free Chl-a data underwent
processing to achieve a spatial resolution of 1°×1° using a bilinear
interpolation method. This yielded a surface Chl-a dataset
containing a total of 400,044 data points, with 109 points
surpassing 6.5 mg m-3. Given the negligible inﬂuence of relatively
small percentage of high values (0.03%) on network performanceand the constitution of data, we retained these 109 points. Overall,the input data used for reconstruction consisted of monthly datasets
spanning from January 2004 to June 2022, characterized by a spatial
resolution of 1°×1° and a vertical resolution of 1 meter.

accessed on 13 April 2023). Subsequently, we conducted acomparative analysis between MODIS Chl-a values and thosederived from BGC-Argo datasets. The results are comparable
between them, although some discrepancies are noted within thedomain of 0–0.2 mg m-3 (Supplementary Figure 1). This indicatesthe potential effectiveness of MODIS data in complementing ourGaussian-DNN model trained with BGC-Argo data.
Within the MODIS Chl-a dataset we acquired, there is an overall
missing rate of approximately 5% in the NWPO, primarily attributable
to cloud cover. Spatially, the regions with high missing data rates aretemperate waters (BOX3), with an average missing data rate of about
30% (Supplementary Figure 2). Following this, the subtropical area
(BOX2) exhibits an average missing data rate of about 10%.
Conversely, the tropical region (BOX1) shows minimal missing data.
Given our focus on reconstructing the 3-D gridded Chl-a structureusing surface Chl-a, we applied the Data Interpolating Empirical
Orthogonal Functions (DINEOF) method to ﬁll in the gaps of
MODIS Chl-a (see Supplementary Figure 3). DINEOF is aninterpolation method suitable for handling remote sensing andoceanographic data with missing values (Beckers and Rixen, 2003;
Alvera-Azcárate et al., 2005; Liu and Wang, 2018, 2023). It decomposes
data into spatial and temporal components using empirical orthogonal
functions (EOFs) and utilizes linear combinations of orthogonal
functions to estimate missing values. By selecting the most important
spatial and temporal modes and employing an iterative optimization
strategy to progressively reﬁne the estimates, DINEOF is capable ofproducing relatively accurate interpolation results, contributing to therestoration of data integrity and accuracy.
Additionally, temperature-salinity proﬁles obtained from Argo
proﬁling buoys were utilized as gridded high-resolution data,
allowing the incorporation of known deep hydrographic
information into the inference of gridded Chl-a vertical proﬁles.
These temperature and salinity proﬁles were obtained from theglobal ocean Argo grid dataset (BOA-Argo), accessible through the
C h in a A r g o Re al - Ti m e D a t a C e n t e r w e b si t e (http://
www.argo.org.cn/) or the Argo Program Ofﬁce website (http://
www.argo.ucsd.edu/). This dataset is available from January 2004
onwards, with a spatial resolution of 1°×1°. The BOA-Argo dataset
was generated through Barnes successive corrections following
stringent quality recontrol of real-time global ocean Argo data (Liet al., 2017). It is also available for download from the Argo
Program Ofﬁce website (http://www.argo.ucsd.edu/). Extensive
evaluations have conﬁrmed its robust comparability with various
other Argo gridded datasets, including WOA13, Roemmich-Argo,
Jamestec-Argo, EN4-Argo, and IPRC-Argo, across multiple metrics
such as climatology, independent observations, mixed-layer depth,
and more (Li et al., 2017). This dataset comprises 48 vertical levels
between 0 and 1975 meters in depth, with intervals as follows: 5 m,
10–200 m at 10 m intervals, 220–500 m at 20 m intervals, 600–1500m at 100 m intervals, 1750 m, and 1950 m. To retrieve the depthresolved Chl-a proﬁles, we employed linear interpolation to adjust
the BOA-Argo temperature-salinity proﬁles to a 1-meter interval
within the 0–300 m depth range.
The monthly MODIS Chl-a and BOA-Argo thermohaline data
were synchronized to create the input dataset for reconstructing

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2.2 DNN model conﬁguration
DNN, a deep learning method characterized by multiple hidden
layers in its neural network architecture, was employed in our study
with 4 hidden layers (Figure 2). Compared with a conventional
ANN, the use of multiple hidden layers allows DNN models to learn
more efﬁcient and compact representations of the data, leading tobetter scalability and performance on large-scale datasets (Li et al.,2020). Generally, operation of our DNN model involves two main
steps of forward propagation and backward propagation. In the
back-propagation step, our DNN model is trained with the Adam
optimizer utilized gradient descent. To prevent overﬁtting, we
additionally employed a dropout technique, strategicallydiscarding some neurons. Through continuous iterations between
these two steps, our DNN model minimizes the loss value within
training procedure.
Our DNN model employed a Gaussian radial basis function(Equation 1) as the nonlinear activation function (Figure 2).
f = e−p(Xj −b)2(1)

where Xj is the value of the jth output in the hidden layer, b is thebias term. The Gaussian radial basis function exhibits a bell-shaped
curve, resembling a quadratic function for the center values of input
variables (Sharma et al., 2020). Compared to conventional
activation functions such as sigmoid or tanh, the Gaussian
activation function has been shown to offer superior performancein solving nonlinear problems (Gundogdu et al., 2015). It is notablethat Chen et al. (2022a) demonstrated that the Gaussian activation
function is more effective in capturing SCMs features compared tothe sigmoid activation function.
In the set-up of our DNN model, we deliberately initialize thebias term b in the Gaussian radial basis function to 0. It diverges
from the methodology employed by Chen et al. (2022a), who
computed the bias term based on the annual mean of SCMs
depth. This deliberate choice empowers our DNN model to not
only replicate the SCMs phenomena, as demonstrated by Chen et al.
(2022a), but also to invert vertical Chl-a proﬁles for other types in
the NWPO (see Section 3).
As is widely acknowledged in the ﬁeld, neural networks lack asingular conﬁguration or deﬁnitive solution (Scardi, 1996;

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FIGURE 2

The structure of the enhanced Gaussian-activation deep neural network (Gaussian-DNN). The input elements for the Gaussian-DNN include sea
surface Chl-a, vertical properties such as temperature and salinity, along with corresponding geographical coordinates (longitude, latitude, and water
depth) and temporal information (month). The output predictor represents the vertical distribution of Chl-a concentrations with a 1 m interval within
the 0–300 m water depth range.

Gaussian-DNN output, vertical structure of Chl-a within 0–300 m
water depths at 1 m resolution is predicted.
Before the training process, all the data employed for modeltraining processes a normalization to ensure dimensionless andwithin the same magnitude, as illustrated in Supplementary Equation
S1. Then, all variables at each data point were centered around 0 with avariance of 1 (Supplementary Equation S1). Our utilization of theGaussian-DNN model used randomly selected 75% of all the available
input data for training, with the rest 25% data for test. In addition, 15%of the training set was randomly chosen as a validation set to assess
whether the Gaussian-DNN model is overﬁtting or not. It is noted that,to ensure the stability and reliability of the subsequent data analysis, we
ran the trained model 10 times and analyzed the average of the resultsfrom these 10 runs.

Sammartino et al., 2018). Therefore, in determining the setup of theparameters in our DNN model, we engaged in an exhaustive
exploration through numerous empirical simulations, selecting
conﬁgurations that showcased superior performance on thevalidation set. Among the numerous of tests conducted, eachvarying in momentum, learning rates, the number of hidden layers,
and the number of units in the hidden layers, the conﬁguration wesettled upon demonstrated the most optimal performance relative toour desired output, as detailed in Table 1. For example, with setting
the batch size set to 100,000, we achieved convergence of bothtraining and validation losses, indicating that the model adeptly
learns the intricate patterns embedded within the data. This batch
size translates to selecting 333 proﬁles from the pool of 3,759 proﬁlesfor training during each iteration. Given that our dataset comprises
3,759 Chl-a proﬁles, each containing 300 values in depths, thisconﬁguration ensures efﬁcient utilization of the available data.
In our Gaussian-DNN model, input variables included sea
surface Chl-a and 3D-structure of sea-water temperatures andsalinities, as well as their geographic (latitude, longitude anddepth) and time (year and month) information (see Figure 2).
Physically, the inclusion of temperature and salinity in theGaussian-DNN model aids to capture the vertical stratiﬁcation
structure, and thus improves model ability in discerning vertical
patterns of Chl-a (Sauzède et al., 2016; Hu et al., 2023). Thus, in the

2.3 Statistical evaluation indexes
Multiple metrics capture various aspects of model performance.
Nash-Sutcliffe model efﬁciency (NSE) evaluates accuracy andprecision, while Root Mean Squared Error (RMSE), Mean
Absolute Error (MAE), and Mean Absolute Percentage Error(MAPE) speciﬁcally measure accuracy by assessing the difference
between model results and observations. These accuracy metrics areless sensitive to covariance and are often used alongside a
correlation metric. To ensure comprehensive model performanceassessment, at least four indices are recommended (Olsen et al.,2016). Therefore, our modeling results underwent validation using
ﬁve statistical metrics on the validation datasets: NSE (Equation 2),
Pearson’s Correlation [r, (Equation 3)], RMSE (Equation 4), MAE(Equation 5), and MAPE (Equation 6).

TABLE 1 Parameters of the Gaussian-DNN model.

Network Parameter

Parameter

Hidden layer depth

4

Number of hidden neurons

64,128, 128, 64

Momentum

0.9

Epoch

150

Batch size

100000

Learning rate

0.01

Dropout rate

0.1

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NSE = 1 − oi=1n(pi − xi )22
oi=1 (xi − x)nnp)(xi − x)oi=1 (pi −ﬃq
ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
r = qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
n2
n2
oi=1 (pi − p) oi=1 (xi − x)

05

(2)

(3)

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RMSE =

rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
1 nðp − xi Þ2n oi=1 i
1 n
jp − x i j
n oi=1 i(5)
1 n  pi − xi 
MAPE = oi=1 
n
xi 

(6)

MAE =

all over the NWPO. Subsequently, we applied the trained GaussianDNN model to the three sub-regions.
As shown in Figure 3, scatter plots spanning 0–300 m water
depth range were generated for the entire NWPO and also eachindividual sub-region. The estimated Chl-a values within 0–200 m
are closely aligned with the observed data. Speciﬁcally, points within
the SCMs layer, notably those surpassing 0.1 mg m-3 at 100–150 m
in BOX1, 0.5 mg m-3 at 50–100 m in BOX2, and 1 mg m-3 at 0–50 m
in BOX3) were brought into line with the diagonal bisector. The
slightly overestimated low Chl-a concentrations (< 0.01 mg m-3)
occurred below 200 m of water depth, which may be attributed toerrors in the predicted Chl-a values obtained from low quality of
BGC-Argo measurements due to a high noise-to-signal ratio (thebackground noise in the measurements is signiﬁcant compared tothe actual signal representing Chl-a concentrations). Similar
instances of overestimation for small Chl-a values have been
observed in other artiﬁcial intelligent models (Sammartino et al.,2018; Chen et al., 2022a; Hu et al., 2023).

(4)

where n is the number of samples, pi is the model estimatedvalues and xi is the observed Chl-a concentration.

3 Results
3.1 Validation of Gaussian-DNN model
The effective performance of our Gaussian-DNN model wasassessed against BGC-Argo in the test set of the BGC-Argo dataset

A

E

F

G

H

I

J

K

L

B

C

D

FIGURE 3

Evaluation of the model’s performance on the test set in the entire NWPO (A, E, I) and three BOXes (B-D, F-H, J-L). (A-D) Scatter plot depicting theobserved Chl-a concentration (x-axis) versus the Gaussian-DNN-estimated Chl-a values (y-axis). (E-H) The mean of observed value (blue line) and the meanof DNN predicted values (orange line) in each BOX. The blue and yellow shades are the standard variance of the model results and observations,
respectively, which overlap and form the gray shade. (I-L) The RMSE and MAE between observation and model estimates at different depths.

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blooms occur in winter. In summary, this quantitative analysis
enhances the credibility of our Gaussian-DNN model outputs in thetest set at a daily time scale, demonstrating accuracy and precision.
In our modeling results across various water depths, theaveraged vertical Chl-a proﬁles for the NWPO and each subregion closely mirror their BGC-Argo structures, respectively(Figures 3E-H). More speciﬁcally, the Gaussian-DNN results
exhibited smaller ﬂuctuations in the surface and SCM layers. The
generally low RMSEs (MAEs) within the 0–300 m depth range
exhibit maximal values of less than 0.2 mg m-3 (0.1 mg m-3) acrossthe entire NWPO (Figure 3I). Within each sub-region, the highest
RMSE and MAE are consistently observed within the SCM layers(Figures 3J-L). Additionally, high errors in BOX2 and BOX3 arealso observed at the surface layer, with RMSE values close to 0.2 mg
m-3 and MAE up to 0.1 mg m-3 in BOX3. Such discrepancy may
become larger due to higher Chl-a variance within the SCM layer(e.g., the yellow shaded area in Figures 3F-H). Potentially, this willaffect network’s prediction accuracy for vertical Chl-a proﬁles.
Furthermore, we compared monthly averaged Chl-a proﬁles in
the Gaussian-DNN model output with the BGC-Argo (Figure 4).

Figure 3 also provides the statistical evaluation of our GaussianDNN model. The NWPO and its three sub-regions consistently
exhibit high NSE values, ranging from 80% to 90%. This suggeststhat the input variables, including sea surface Chl-a, depth-resolved
water temperature and salinity, can effectively account for the
majority of vertical Chl-a variability. The strong correlations(r>0.89) coupled with low errors (RMSE<0.21 mg m - 3 ,MAE<0.10 mg m-3, and MAPE<37%) indicate that the GaussianDNN model accurately captures the vertical structure andmagnitudes of Chl-a concentrations in all regions of the NWPO.
Additionally, in the three sub-regions, the errors (RMSE, MAE, and
MAPE) increase along with latitudes, although MAPE in BOX2 isclose to that in BOX3. This trend indicates that the model performs
better in low-latitude waters (BOX1) than in higher-latitude waters(BOX2 and BOX3). The observed difference in performance can be
attributed, in part, to the varying change rate of Chl-a vertical shape(SCMs characteristics) with latitudes. As illustrated in Figure 4,
vertical Chl-a proﬁles in the tropical region maintain nearly
constant SCMs characteristics, while in subtropical and temperateregions, SCMs are more prominent during summer, and surface

A-1

A-2

A-3

A-4

A-5

A-6

A-7

A-8

A-9

A-10

A-11

A-12

B-1

B-2

B-3

B-4

B-5

B-6

B-7

B-8

B-9

B-10

B-11

B-12

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C-5

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C-8

C-9

C-10

C-11

C-12

D-1

D-2

D-3

D-4

D-5

D-6

D-7

D-8

D-9

D-10

D-11

D-12

FIGURE 4

Aggregated Chl-a vertical proﬁles from the test set in the overall region are in terms of months. The blue and orange solid lines represent the meanof observed value and the mean of Gaussian-DNN predicted Chl-a, respectively. The blue and yellow shades are the standard variance of the model
results and observations, respectively, which overlapped and formed the gray shade. (A) Overall area, (B) BOX1 (12–24°N waters), (C) BOX2 (24–38°N
waters), and (D) BOX3 (38–54°N waters).

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alongside MLP and RF methods. In contrast to the GaussianDNN model, the MLP model utilizes the Rectiﬁed Linear Unit
(ReLU) as the activation function and consists of four hidden layers(also named ReLU-DNN). To assess and quantify the enhancementin the performance of Gaussian-DNN model, we employedidentical datasets for training and testing across all three models.
Figure 5 presents a radar diagram depicting the relative
deviation between MLP, RF, and the Gaussian-DNN model. In
comparison with the RF method, MLP exhibits a reduced bias,
particularly in mid-to-high latitude regions where relative
deviations fall within the range of -13% to 12%. These ﬁndings
underscore the superior accuracy and performance of the DNN
models (Gaussian-DNN, ReLU-DNN) over RF, especially in thehigh-latitude areas of the NWPO.
When contrasting the results of our Gaussian-DNN model withthat of MLP in the NWPO (Figure 5A), we observed a slightdecrease (less than 5.5%) in the values of NSE and r. Meanwhile,
RMSE, MAE, and MAPE displayed a more signiﬁcant increase,reaching up to 26.8%. Speciﬁcally, in tropical waters the disparities
in outcomes among these three models are negligible, except for theMAE derived from the MLP model (Figure 5B). This variation is
attributed to the small MAE values observed in the tropical gyre,approximately (~0.01 mg m-3). However, as we move to higher
latitudes (Figures 5B, C), particularly in subtropical waters, thedisparities in outcomes among these three models become more
pronounced (from -24.4% to 28.2%). These ﬁndings suggest that theutilization of the Gaussian activation function has a positive impact
on the accuracy of Chl-a estimation than that of ReLU. It isnoteworthy that the improvement aligns with the results obtainedby Chen et al. (2022a), who reported similar enhancements whencomparing the Gaussian function with the Sigmoid activation. Thisconsistency across studies underscores the effectiveness of theAcross the entire NWPO, monthly mean of predicted Chl-a proﬁlesalign well with the observed values, especially during the summer
and fall seasons (Figures 4A1-12). This suggests that the GaussianDNN method effectively captures various types of the vertical Chl-a
proﬁles in the NWPO.
In the tropical sub-region (BOX1), our Gaussian-DNN model
effectively reproduced seasonal cycle of the SCM phenomena.
Though seasons, SCMs consistently occur near 100–150 m andexhibit an overall low intensity less than 0.3 mg m-3 (Figures 4B112). The predicted mean vertical Chl-a proﬁles overlapped withobserved proﬁles, along with their corresponding standard variance
ranges, demonstrating the effective performance of our model inpredicting the SCMs characteristics in the tropical area. In thesubtropical sub-region (BOX2), the signiﬁcant SCMs occur from
June to November, with smaller ﬂuctuations in Gaussian-DNN
modeling results than observed Chl-a, especially within SCM layers(Figures 4C6-11, green shades). From early winter to late spring,vertical Chl-a proﬁles in this region exhibit surface blooms, which
are well reproduced by the Gaussian-DNN model with smaller
shaded areas than observed variance (Figures 4C1-5, C12). Towardhigher surface Chl-a concentrations in the temperate gyre (BOX3),
the network exhibits a slight overestimation of Chl-a during
summer and autumn (Figures 4D6-10), possibly inﬂuenced by thehigh variability of Chl-a values in the upper layer, which poseschallenges for accurate predictions, particularly in the upper layers.
Overall, the comparison of Gaussian-DNN model outputs with
BGC-Argo proﬁles shows mostly overlapping shaded areas in
Figures 4D1-12. This strengthens the ability of the GaussianDNN model to integrate, in its response, the variability of the
Chl-a ﬁeld in the NWPO.
Additionally, we conducted a comparative analysis on diverse
vertical distributions of Chl-a, involving our Gaussian-DNN

A

B

C

D

FIGURE 5

Comparing the MLP, RF and Gaussian-DNN performance in the test set by the Radar diagram of relative deviations in the NWPO (A) and three subregions (B-D).

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Gaussian activation function in reﬁning the accuracy of Chla estimation.

Figure 5). Overall, the performance of the trained Gaussian-DNN
model is satisfactory when tested with ship measurement data.

3.2 Robustness validation of Gaussian-DNN
on independent data sets

3.3 Reconstruction of long-term 3-D Chla structure

To evaluate the generalization and robustness of our trained
Gaussian-DNN model, we applied it to estimate Chl-a
concentrations using ship measurements from JMA. The JMA
data, including Chl-a, temperature, salinity, were input into thetrained Gaussian-DNN model using JMA data, while maintaining
the same training and test sets initially utilized with the BGC-Argo
data. The identical statistical parameters utilized to evaluate themodel’s performance with the BGC-Argo data were also applied toassess its performance with the JMA dataset. The statisticalindicators in Table 2 are comparable to those obtained by thetrained Gaussian-DNN for the entire NWPO (refer to Figure 3A),
indicating that our Gaussian-DNN model maintains robust
performance across different datasets. The slight discrepancy may
be attributed to the ship survey data having fewer proﬁle sample
points and a potential limitation in capturing deep Chl-a
proﬁle features.
Furthermore, two transects were selected to demonstrate themodel effectiveness, as indicated in Figure 1B by the two red verticaldashed lines representing the 137°E and 165°E transects. When
compared to ship measurements, the Gaussian-DNN model
successfully reproduced the vertical distribution of Chl-a alongthe 137°E section, with most differences falling within the rangeof -0.1 to 0.1 mg m-3 (Figures 6A-C). The predicted values for the
165°E section correspond well to the observed values (Figures 6DF). However, relatively large deviations (0.2 to 0.3 mg m-3) aremainly observed at high latitudes above 40°N, such as 40°N, 44°N,
and 48°N. These discrepancies could stem from variations in the
input data sourced from JMA and BGC-Argo (Supplementary
Figure 4). For example, water temperatures between 2–5°C
recorded by JMA appear lower compared to those derived from
BGC-Argo ﬂoats, particularly evident in areas above 40°N along
165°E (Supplementary Figure 5). Additionally, there are similar
observations regarding salinity levels, where values between 32–36
from JMA are notably lower than those recorded by BGC-Argoﬂoats, especially in regions above 40°N along 165°E (Supplementary

To project the long-term 3-D Chl-a structure in the NWPO, the
MODIS Chl-a and BOA-Argo global gridded thermohaline data
were merged as the input dataset in the deployment phase of the
trained Gaussian-DNN model. The reconstructed monthly 3-Dstructure of Chl-a in the NWPO has a spatial resolution of 1°×1°
with fully depth-resolved vertical proﬁles in 0–300 m layer, covering
the period from January 2004 to June 2022.
We conducted a comparative analysis to evaluate theperformance of Gaussian-DNN on 3-D structures and backward
time-series prediction. Figure 7A showed the DNN-estimated surface
Chl-a values against MODIS observed ones. A high density of data
points is concentrated around the bisector, especially in the range
from 0.01 to 0.1 mg m-3. On contrary, the scatter increases in thehigher domain of Chl-a concentrations, in which the data density is
reduced (Figure 7A), revealing an underestimation of the GaussianDNN predicted values in BOX3 (see Figures 7H-J). The main factor
contributing to this discrepancy is likely the potential uncertainties ingap ﬁlling for missing MODIS Chl-a data, particularly inﬂuenced by
the high solar zenith angle, which tends to affect prediction accuracy
in high-latitude waters (Supplementary Figure 6). In depicting thetime-series patterns of surface Chl-a spanning the entire decade from2004 to 2022, our Gaussian-DNN models effectively capture theobserved seasonal and interannual variations from MODIS, despite
an overall slight overestimation of 0.1 mg m-3 (Figure 7K). It isnoteworthy that we trained the Gaussian-DNN models using datafrom the period of 2017–2022, extending backward to 2004 during
the deployment phase. This outcome underscores the impressive
generalization ability of our Gaussian-DNN model.
The vertical patterns of reconstructed Chl-a by the Gaussian-DNN
model align closely with those observed by the BGC-Argo ﬂoats within
the 0–300 m layer (Figures 7B-J). In the tropical region (BOX1), thepredicted Chl-a values with a prominent SCM in all seasons closely
match the measurements obtained from BGC-Argo ﬂoat data
(Figures 7B-D). Within the subtropical gyre of the NWPO (BOX2),
a dynamic interplay between surface blooms and the SCMs
characterizes the seasonal cycle. Our Gaussian-DNN model has
demonstrated its capability to accurately reproduce both blooms inthe surface and subsurface layer (Figures 7E-G). In the temperateregion (BOX3), our Gaussian-DNN model demonstrates a high level ofaccuracy in capturing Chl-a patterns as observed in BGC-Argo data.
However, it consistently tends to slightly underestimate the Chl-avalues in the 0–50 meter depth range, particularly during the months ofJuly to September (Figures 7H-J). This deviation is likely attributed todisparities in input data sources used for reconstruction (MODIS) andtraining (BGC-Argo) (see Figure 7K; Supplementary Figure 1).
Furthermore, the same statistical indicators that was used forthe overall evaluation of the Gaussian-DNN performance wereconsidered (see satellite matchup set in Table 2). The NSE (0.85)

TABLE 2 The statistical results obtained from the validation model using
JMA hydrological data.

Metrics

Ship Measurements
Test SetSatellite Matchup
Test Set

NSE

0.85

0.84

r

0.92

0.91

RMSE

0.12

0.08

MAE

0.06

0.04

MAPE

44.90%

36.01%

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A

D

B

E

C

F

FIGURE 6

Vertical distribution of Chl-a concentrations along the 137°E section derived from (A) observation data and (B) the model estimates. (C) The difference
between (A, B). (D-F) Same as (A-C) but along the 165°E section.

Northern India Ocean is inferred by the combined use of 18
input variables from BGC-Argo and satellite data in the RFmodel, obtaining an NSE and RMSE of 0.96 and 0.01 mg m-3,
respectively. The comparison of our statistical results with those of
Hu et al. (2023) highlighted that, even with some uncertainties andsome limits, our network, applied on 7 out of 18 input variables
shows a prediction accuracy very close to other models. Overall, thevalidation conﬁrms that the Gaussian-DNN model serves as an

was close to those obtained on BGC-Argo (0.93) and shipmeasurements (0.84), indicating the effectiveness of input
variables on predicting Chl-a. The others statistical parameters,
r=0.91, RMSE = 0.08 mg m-3 and MAE = 0.04 mg m-3, were of thesame order of magnitude of those obtained on test sets of BGCArgo and ship measurements (Figures 3A–D; Table 2). Analogous
results were obtained in previous and similar works as, e.g., that of
Hu et al. (2023), in which the vertical proﬁle of Chl-a in the

A

B

E

H

C

F

I

D

G

J

K

FIGURE 7(A) Density plot of DNN-reconstructed surface Chl-a values against MODIS values. Monthly vertical Chl-a from 2004 to 2022 in (B–D) BOX1, (E–G)
BOX2, and (H–J) BOX3 from BGC-Argo (top panel), Gaussian-DNN model (middle panel), and the differences between them (Gaussian-DNN model
outputs minus BGC-Argo, bottom pane), respectively. (K) Comparison of Gaussian-DNN reconstruction results with time-series patterns of sea
surface Chl-a from MODIS and BGC-Argo observations for the period 2004–2022.

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poleward in fall and winter. In parallel, the majority of oligotrophic
subtropical and tropical waters began expanding in the late summer,
reached their spatial maximum in the autumn, and then contracted in
the winter and spring.
The seasonal indices were calculated using an additive
decomposition model (Hyndman and Athanasopoulos, 2021),
with the calculation formula represented by (Supplementary
Equation S2). SCMs exhibit distinct patterns in both intensity anddepth (Figures 8C, D), showcasing intriguing seasonal variations
across different regions. Within temperate waters, SCMs intensity
displays bi-modal peaks from late spring through early fall,featuring a shallow SCM during summer (Figures 8C, D).
Conversely, subtropical waters experience a singular peak in
SCMs intensity during spring, with the deepest SCM recorded in
the fall (Figures 8C, D). In tropical oligotrophic waters, while theSCMs intensity remains stable, there are noticeable seasonalvariations in SCMs depth, with the shallowest SCMs occurring in
May and the deepest in December (Figure 8D).

effective tool for generating long-term, 3-D Chl-a data by merging
satellite Chl-a information and temperature-salinity ﬂoat proﬁles.

3.4 Spatio-temporal patterns of
SCMs characteristics
Using the reconstructed long-term 3-D Chl-a proﬁles in the
NWPO, we calculated the depth of the Chl-a maximum in eachindividual proﬁle which has the 1 m vertical resolution. Here, we
designated the peak Chl-a value in each individual proﬁle as SCMs
intensity and identiﬁed its location as SCMs depth, taking
advantage of the notably high vertical resolution. Subsequently,
we assessed the spatio-temporal variability of SCMs characteristics(depth and intensity).
Spatially, the intensity of SCMs exhibits a distinct upward trend
across latitude zones (Figure 8A), ranging from 0.21±0.03 mg m-3 inthe tropical gyre to 0.36±0.16 mg m-3 in subtropical waters, andpeaking at 0.79±0.50 mg m-3 in the temperate area. Concurrently, theSCMs depth decreases with higher latitude zones, measuring 121 ± 17m, 54 ± 31 m, and 13 ± 14 m, respectively. A distinct transition band
was evident between the high intensity of SCMs temperate waters andthe low-intensity subtropical waters (Figures 8A, B). The
geographical location of subsurface Chl-a transition bands near the
Kuroshio–Oyashio convergence region exhibited seasonal migration
dynamics, extending equatorward in spring and summer and shifting

3.5 Long-term trend of total Chl-a during
2004–2022
To broaden insights beyond surface-level observations, we
conducted an assessment of the long-term trends in total Chl-a
within the water column. This involved computing the monthly

A

B

C

D

FIGURE 8

Climatological monthly SCMs intensity (A) and SCMs depth (B) in the NWPO and the corresponding seasonal indices of SCMs intensity (C) and SCMs depth (D).

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interannual variability in the NWPO during the period of 2004–
2022, with notable linear trends observed in tropical and subtropicalgyres (Figure 9). For instance, the depth-integrated Chl-a in the tropicalgyre shows a minimum in 2007 and a peak value in 2009. On average,
the depth-integrated Chl-a in the tropical region exhibits an increasing
trend of 0.0016 mg m-2 yr-1 (p=0.05). In the subtropical region, a more
pronounced decreasing trend of 0.0033 mg m-2 yr-1 is observed(p<0.01). However, no signiﬁcant linear trend is found in thetemperate area (p=0.12). To provide a detailed depiction of thespatial distribution of long-term variations in the NWPO, wecalculated the linear trend for each pixel (Figure 9G). Noted that alltrends mentioned in the following sections are statistically signiﬁcant at
a signiﬁcance level of p< 0.05.
The locations with signiﬁcant increasing (decreasing) patterns
in depth-integrated Chl-a exhibit a patchy distribution (Figure 9G).
Predominantly, increasing trends were observed in the tropicalmean of depth-integrated Chl-a within the 0–300 m depth range,
utilizing the reconstructed monthly 3-D Chl-a data in the NWPO
from 2004 to 2022. Subsequently, we evaluated the trends of total
Chl-a using a Locally Weighted Scatterplot Smoothing (LOWSS)
method (Cleveland et al., 1990). The LOWSS smoother operates byﬁtting a weighted polynomial regression for a given time ofobservation, with weights decreasing as the distance from thenearest neighbor increases (Dagum and Luati, 2003). Thisapproach enables us to separate the seasonal component from thetrend component, providing a deseasonalized trend component(Supplementary Figure 7).
The average depth-integrated Chl-a in the NWPO for the period
2004–2022 stood at 35 ± 19 mg m-2, exhibiting noteworthy spatial
distinctions across the tropical (20 ± 4 mg m-2), subtropical (36 ± 13
mg m-2), and temperate (55 ± 20 mg m-2) gyres. For the long-term timeseries analysis, the depth-integrated Chl-a exhibits signiﬁcant

A

D

B

E

C

F

G

FIGURE 9(A-C) Time series of depth-integrated Chl-a in three BOXes of the northwest Paciﬁc Ocean during the period of 2004–2022. (D-F) Interannual
variation of depth-integrated Chl-a in three BOXes. (G) Spatial pattern of trends (unit: mg m-2 yr-1) of depth-integrated Chl-a. Warm colors indicate
positive trends, cold colors represent negative trends, and white signiﬁes no detected trends. Note that only data that passed the conﬁdence tests(p< 0.05) were displayed.

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latitude increasing (Table 3). This underscores the substantial
contribution of sea surface Chl-a as an input variable to theGaussian-DNN model, especially in the temperate waters withhigh Chl-a concentrations.
Generally, vertical distribution of water temperature plays amore important role in estimation of Chl-a in comparison withsalinity in tropical and subtropical gyres of the NWPO; for thetemperate areas, the latter is more essential than the former. This isconsistent with the understanding from the in situ observations. For
example, in the tropical area of NWPO the everlasting SCMs were
found in the vicinity of the thermocline, consisting with thenitracline, hence being of an essential feature of the typicaltropical structure (Herbland and Voituriez, 1979; Cullen, 1982;
Radenac and Rodier, 1996; Cullen, 2015). While in the highlatitude waters, observations revealed that the vertical distributionof Chl-a that was closely related to the seasonal evolution of
halocline and pycnocline (Anderson, 1969; Ishida et al., 2009).
In addition, the sensitivity results illustrate that the verticalphysical properties should be deliberated in reconstructing thevertical Chl-a proﬁles. Analogous results have been found innorthern India Ocean (Hu et al., 2023). Compared with previous
studies applied on surface measurements only (SST and surface
Chl-a), adding vertical physics properties (water temperature andsalinity) as input variables leads the NSE increasing from ~70% to~90% (Sammartino et al., 2018; Chen et al., 2022a; Wang et al.,2023a). Here, we emphasize that in the tropical area of the NWPO,
surface Chl-a and vertical temperature proﬁles are two effective
input variables in accurately estimating vertical Chl-a proﬁles. For
the high-latitude waters, both vertical proﬁles of temperature andsalinity together with surface Chl-a are non-negligible.

gyre, while negative trends were notable in the subtropical section.
In the temperate gyre, originating from the marginal seas,
continuous patches with increasing depth-integrated Chl-a
extended toward the northeast in the NWPO, forming a nearlycontiguous belt with positive interannual trends. Off the Sea of
Okhotsk, patches with positive depth-integrated Chl-a trends wereconsistently distributed along the chain of islands, exhibiting anannual increasing rate of ~0.002 mg m−2 yr−1. Further northeast,
similar patches with increasing depth-integrated Chl-a wereobserved off the southern region of the Bering Sea. However, in
the remaining part of the temperate gyre, the depth-integrated Chla exhibited a decreasing trend at a rate of ~-0.002 mg m−2 yr−1.
Overall, the linear trend across the entire temperate area was notfound to be statistically signiﬁcant.

4 Discussion
4.1 Sensitivity of input variables
As a data-driven model, the effectiveness of a DNN is notably
inﬂuenced by the selection of input variables (Reichstein et al., 2019).
We conducted a series of sensitivity experiments for three watersheds
to examine how sea surface Chl-a and vertical physical properties(water temperature and salinity) inﬂuence the accuracy of ourestimations. In each experiment, only one input variable wasremoved, keeping the other input variables unchanged.
As depicted in Table 3, in Exp-without T, where we removed thetemperature variable, a notable reduction in model performance isobserved, particularly in low-latitude seas, with the RMSE
decreasing by 17.62% and the MAE decreasing by 13.71%. In
mid- and high-latitude waters (BOX2 and BOX3), the inﬂuenceof water temperature on the estimated Chl-a proﬁles appears to beless signiﬁcant. In Exp-without S, the reduction in model
performance after removing salinity was not as substantial as
when temperature was removed. The inﬂuence of salinity was
only observed to some extent in mid- and high-latitude waters(less than 5%). Nonetheless, the signiﬁcance of salinity’scontribution to the model’s effectiveness should not be overlooked.
When sea surface Chl-a was removed in Exp-without Chl-a, themodel performance in the three sub-regions was diminished,particularly in the high-latitude gyre. The RMSE decreased by
5.24%, 11.76%, and 95.10%, respectively, and the MAE also
exhibited varying degrees of reduction from 4.84% to 48.4% along

4.2 Variability discrepancy between
subsurface Chl-a and surface Chl-a
It is well-established that the satellite record effectively captures
global phytoplankton responses but is conﬁned to present changes
in the surface ocean environment. However, the presence of SCMs
necessitates caution when extrapolating conclusions from thesurface to water-column-integrated production or when
predicting potential impacts of future ocean warming (Behrenfeld
et al., 2016).
The characteristics of SCMs in the NWPO demonstratesigniﬁcant spatial variability along with seasonal ﬂuctuations

TABLE 3 Relative deviation of sensitivity experiments from the trained Gaussian-DNN models with Root Mean Square Error (RMSE) and Mean
Absolute Error (MAE).

RMSE

MAE

Experiment12 -24°N

24 -38°N

38 -54°N

12 -24°N

24 -38°N

38 -54°N

Exp-without T-17.62%-6.72%-3.26%-13.71%-6.02%-3.19%

Exp-without S-0.48%-3.64%-4.90%

0%-4.87%-4.52%

Exp-without Chl-a-5.24%-11.76%-95.10%-4.84%-11.17%-48.4%

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to the response of phytoplankton to factors such as light availability
and water stratiﬁcation. The observed patterns underscore theintricate interplay between environmental factors andphytoplankton dynamics in shaping the seasonal variability of
Chl-a in both surface and subsurface layers of the NWPO.
Furthermore, we conducted a comparative analysis of the longterm trends of Chl-a in the surface layer and depth-integrated Chl-a
within the water column of the NWPO. Notably, distinct trends
between depth-integrated Chl-a and surface Chl-a were observed
across the NWPO. For instance, during the period from 2004 to
2022, the estimated depth-integrated Chl-a exhibited opposite
trends in the tropical and subtropical regions, with a moresigniﬁcant decreasing tendency observed in the latter region(Figure 9). Conversely, no signiﬁcant trend in surface Chl-a wasobserved in the subtropical water during 1997–2020 (Chen et al.,2022b), while a clear positive trend was evident in the tropical water(Chen et al., 2022b; Yu et al., 2023). Moving toward higher latitude
waters (BOX3, Figure 9G), our analysis revealed increasing
interannual trends for depth-integrated Chl-a in parts of thetemperate section, which aligned with trends noted in remotesensing Chl-a (Chen et al., 2022b). This disparity between the trendsof depth-integrated Chl-a and surface Chl-a can be attributed to thepresence of SCMs in the tropical and subtropical gyres, which
contrasts with the near-surface blooms observed in the temperate
gyre of the NWPO.

during 2004–2022 (Figure 8). This spatial variability of SCMs
characteristics closely resembles the observed patterns in surface
Chl-a levels based on ocean color data in the NWPO (Hou et al.,2016; Chen et al., 2022b). As latitudes increase, SCMs intensity (its
depth) also tends to increase (decrease), leading to the formation ofa distinct transition band between the high intensity of SCMs intemperate waters and the low-intensity subtropical waters(Figures 8A, B). This transition band has also been noted in thespatial patterns of surface Chl-a (Chen et al., 2022b). During coldseasons (winter and spring), the transition band of subsurface Chl-a
extends equatorward, while during warm seasons (summer andfall), it shifts poleward. This seasonal migration correlates withvariations in the strength of the Kuroshio Extension surface
transport and its associated southern recirculation (Qiu et al.,2014; Yang and Liang, 2018). Notably, the seasonal migration
pattern of the transition band of subsurface Chl-a differs fromthat of surface Chl-a, with the surface transition band moving
equatorward in fall and winter, and poleward in spring and summer(Chen et al., 2022b). Further exploration is needed to understandthe reasons for this discrepancy in seasonal cycles between
subsurface and surface Chl-a transition bands.
For the seasonality, the dual peaks of SCM intensity in thetemperate waters during spring and autumn (Figure 8C) are mainly
triggered by reduced vertical stability (Bailey and Werdell, 2006).
Due to intensiﬁed vertical mixing in early winter, phytoplankton in
the SCM layer is entrained upward to the surface mixed layer,
leading to enhanced surface Chl-a during this period (Behrenfeld
and Boss, 2014; Lacour et al., 2019; Xing et al., 2020). For thesubtropical gyre, the initiation of high values in SCMs intensity
during spring resembled that observed in temperature oceans(Figure 8C). This occurrence can be attributed to sufﬁcientnutrients brought to the ocean upper layer by previous
wintertime mixing, higher temperature, light and vertical stability
conditions (Sverdrup, 1953; Siegel, 2002). During summertime, themixed layer depths were notably shallow, and robust stratiﬁcation
conﬁned nutrient supplementation within the subsurface layer,
resulting in evaluations of ecological signiﬁcance of SCMs
(Furuya, 1990; Venrick, 1993). In the tropical NWPO, theexistence of a permanent halocline and pycnocline, hinders thevertical transport of nutrient-rich deep water to the nutrientexhausted surface mixed layer, giving rise to a persistent SCM
throughout the year (Anderson, 1969; Cullen, 2015). Consequently,
the SCMs intensity shows minimal seasonal variations in thetropical gyre of the NWPO.
In general, the seasonal dynamics of subsurface Chl-a
resembled those observed in surface Chl-a based on ocean color
data in the NWPO (Hou et al., 2016; Chen et al., 2022b). However,there is a temporal disparity in the onset of seasonal peaks between
the surface layer and subsurface layer. As shown in Figures 8C, D,
there is a two-month delay in the intensity of SCMs as latitude
increases. In contrast, the surface bloom exhibits a one-month delay(Chen et al., 2022b). For instance, in the subtropical gyre, themaximal SCMs intensity is reached in March, extending into May
in temperate waters. In comparison, the surface bloom extends
from March in subtropical waters to April in the temperate gyre
(Chen et al., 2022b). This temporal discrepancy is likely attributed

Frontiers in Marine Science

4.3 Uncertainties and implication in 3-D
Chl-a reconstruction
In this study, vertical physical properties such as watertemperature and salinity within the 0–300 m water depth were
utilized as crucial predictors. These properties are essential for
accurately predicting vertical Chl-a proﬁles in the NWPO
(Table 3) as they govern the availability of nutrients for
phytoplankton across different layers of the water column. The
ﬂuctuations in thermohaline observations directly inﬂuence theprediction of Chl-a concentrations. For example, signiﬁcantvariations were observed in the vertical distributions oftemperature and salinity in three proﬁles from Float 2903354 in
BOX3 compared to other locations (Supplementary Figure 8). This
discrepancy resulted in predicted Chl-a values within the upper 100
m depth that were notably higher than the observed values, leading
to several scattered points between 0.1 and 1 mg m-3 on the y-axis
exhibiting considerable deviation from the 1:1 line, indicative of anearly horizontal distribution (Figure 3D). In addition, theuncertainties associated with thermohaline proﬁles from BGCArgo and BOA-Argo ﬂoats signiﬁcantly inﬂuence the accuracy ofour developed Gaussian-DNN model, particularly noticeable in thetemperate gyre of the NWPO. For instance, in the tropical gyre,
there is an evident upwelling in April presented by BGC-Argo(Supplementary Figure 9), resulting in a shoaling SCM (Figure 7),
while a constantly reconstructed SCM based on stable stratiﬁcation
is presented by BOA-Argo (Supplementary Figure 9). In thetemperate waters, salinities from BOA-Argo are higher than thosefrom BGC-Argo in the 0–50 m depth, especially during summer

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10.3389/fmars.2024.1378488

and autumn seasons (Supplementary Figure 9), leading to an
overestimation of Chl-a in the upper layer (Figure 7J).
To further assess the model’s sensitivity to the uncertainty of
input physical variables, we conducted eight experiments in eachBOX region. Speciﬁcally, we introduced temperature uncertainties
of ±0.2°C within both the surface 20 meters and the depth range of
0–300 meters. For salinity, uncertainty was assumed to be ±1% of
the average surface values in each BOX region, resulting in values of±0.349, ± 0.345, and ±0.328, respectively. The results, depicted in
Supplementary Figure 10, reveal that slight variations intemperature or salinity have a negligible effect on the model’s
performance compared to its original state in BOX1. However, In
BOX2 and BOX3, we observed a notable increase in RMSEs above a
depth of 150 meters. This suggests that even minor variations inwater temperature and salinity occurring within the surface layer,
can have a signiﬁcant impact on the performance of our DNN
model in these regions. This ﬁnding underscores the signiﬁcance ofwater temperature and salinity as critical predictors for vertical Chla proﬁles, particularly in mid- and high-latitude waters.
Furthermore, the accuracy of surface Chl-a is a crucial input
variable that signiﬁcantly impacts the reconstruction outcomes,
particularly in temperate waters (Table 3). Two main uncertainties
are associated with surface Chl-a. One arises during the preprocessingof surface Chl-a derived from different datasets (BGC-Argo and
MODIS data). To address this, we conducted a retraining of theGaussian-DNN model. This involved incorporating half of the Chl-avalues from BGC-Argo in BOX3 while leaving the rest of the training
data unchanged. The results showed a signiﬁcant reduction in
disparities between our Gaussian-DNN model and the MODIS(refer to Supplementary Figure 11), which also helps clarify theoverestimation illustrated in Figure 7K.
The other signiﬁcant source of uncertainty arises from the gap
ﬁlling process of MODIS data, particularly pronounced in highlatitude waters where the missing rate of MODIS Chl-a data tends
to be higher (refer to Supplementary Figure 2). The accuracy of thisﬁlling process may be compromised by the elevated solar zenith
angle prevalent in these regions, thereby inﬂuencing prediction
accuracy. To address this, we conducted a re-run of the GaussianDNN model by masking the missing MODIS data. The resulting
density scatter plot revealed the disappearance of the severe
underestimation for high Chl-a concentration in Figure 6A (seeSupplementary Figure 6), highlighting the inﬂuence of interpolation
uncertainty on the accuracy of Chl-a reconstruction. Therefore,
integrating a diverse range of Chl-a data sources, such as individual
satellites like MODIS, SeaWiFS, MERIS, and VIIRS, as well ascomposite satellite products like OC-CCI, and enhancing theaccuracy of gap ﬁlling techniques, can help to improve theperformance of our Gaussian-DNN model in reconstructing longterm 3-D Chl-a structures.
With the continuous and anticipated future availability ofspatio-temporal depth-resolved physics datasets, the prospect ofdeveloping long-term 3-D global Chl-a datasets is becoming
feasible. This product is positioned to comprehensively capture
the multifaceted changes expected with upcoming climate change,
offering a holistic understanding of phytoplankton dynamics acrossdifferent dimensions of the water column.

Frontiers in Marine Science

5 Conclusion
In this study, we developed a Gaussian-DNN model to construct
long-term 3-D Chl-a structures by inputting satellite Chl-a with
BOA-Argo thermohaline proﬁles, featuring a spatial resolution of
1°×1° and a vertical resolution of 1 m within the 0–300 m water depth
from 2004 to 2022 in the NWPO. The trained Gaussian-DNN modelusing BGC-Argo ﬂoat data was successfully applied to JMA shipmeasurements, demonstrating its robust generalization ability. The
experiments for input sensitivity demonstrated a crucial role of ocean
water temperatures in estimating Chl-a in the subtropical gyre, whilea switch to salinity in the temperate gyre. The estimated SCMs in the
NWPO exhibited spatial divergence of signiﬁcant seasonality.
Opposing trends of total Chl-a in water columns were observed in
the tropical and subtropical gyres during 2004–2022, insigniﬁcanttrend was characterized in the temperate area, mostly attributed tospatial discrepancies in tendencies. Overall, the developed GaussianDNN model, alongside the growing availability of thermohaline
datasets, holds signiﬁcant promise for constructing long-term 3-D
Chl-a in the NWPO, offering comprehensive insights into themultifaceted changes expected in future climate change scenarios.

Data availability statement
The raw data supporting the conclusions of this article will bemade available by the authors, without undue reservation.

Author contributions
XZ: Data curation, Formal analysis, Investigation, Methodology,
Software, Validation, Visualization, Writing – original draft. XiaG:
Conceptualization, Formal analysis, Funding acquisition,
Investigation, Methodology, Project administration, Resources,
Validation, Writing – review & editing. XunG: Formal analysis,
Funding acquisition, Writing – review & editing. JL: Data curation,
Formal analysis, Methodology, Writing – review & editing. GW:
Data curation, Formal analysis, Methodology, Writing – review &editing. LW: Data curation, Formal analysis, Methodology, Writing –review & editing. XinG: Data curation, Formal analysis, Writing –review & editing. HG: Formal analysis, Funding acquisition,
Supervision, Writing – review & editing.

Funding
The author(s) declare ﬁnancial support was received for the
research, authorship, and/or publication of this article. This work
was supported by the Ministry of Science and Technology of thePeople’s Republic of China (2019YFE0125000), National Nature
Science Foundation of China-Shandong Joint Fund (U1906215),
and the National Natural Science Foundation of China (41406010).
This work was also supported by the Key Laboratory of Coastal
Environmental Processes and Ecological Remediation, Chinese
Academy of Sciences Opening Fund (2020KFJJ04).

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10.3389/fmars.2024.1378488

Acknowledgments

Publisher’s note

The authors would like to thank the International Argo
Program and the China Argo Real-Time Data Center that
contribute to the BGC-Argo data and BOA-Argo, which werecollected and made freely available. The Argo Program is part of
the Global Ocean Observing System. The authors are very gratefulto Jianqiang Chen for his helpful advices.

All claims expressed in this article are solely those of theauthors and do not necessarily represent those of their afﬁliatedorganizations, or those of the publisher, the editors and thereviewers. Any product that may be evaluated in this article, or
claim that may be made by its manufacturer, is not guaranteed or
endorsed by the publisher.

Conﬂict of interest

Supplementary material

The authors declare that the research was conducted in theabsence of any commercial or ﬁnancial relationships that could beconstrued as a potential conﬂict of interest.

The Supplementary Material for this article can be found online
at: https://www.frontiersin.org/articles/10.3389/fmars.2024.
1378488/full#supplementary-material

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