Deep–Sea Research I 195 (2023) 104005

Contents lists available at ScienceDirect

Deep-Sea Research Part I
journal homepage: www.elsevier.com/locate/dsri

Estimation of nitrate concentration and its distribution in the northwestern
Pacific Ocean by a deep neural network model
Lixin Wang a, b, Zhenhua Xu b, c, d, e, f, *, Xiang Gong a, **, Peiwen Zhang b, c, d, Zhanjiu Hao b, c, d, e,
Jia You b, c, d, e, Xianzhi Zhao a, Xinyu Guo gaSchool of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao, China
CAS Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Chinese Academy of Sciences, Qingdao, China
Pilot National Laboratory for Marine Science and Technology, Qingdao, ChinadCenter for Ocean Mega-Science, Chinese Academy of Sciences, Qingdao, ChinaeCollege of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing, Chinaf
CAS Engineering Laboratory for Marine Ranching, Institute of Oceanology, Chinese Academy of Sciences, Qingdao, ChinagCenter for Marine Environmental Study, Ehime University, 2-5 Bunkyo-cho, Matsuyama, 790-8577, Japanbc

A R T I C L E I N F O

A B S T R A C T

Keywords:
NitrateSpatial distribution
Deep neural network
Northwestern pacific ocean

As a fundamental nutrient for marine biogeochemical processes, the magnitude and spatial distribution of nitrateconcentrations are insufficiently measured in the interior ocean. In the present study, a deep neural network(DNN) model was developed to estimate nitrate concentrations in the upper northwestern Pacific Ocean (NPO).
This model takes the temperature and salinity profiles as the primary input variables. Since the subtropical andtropical regions are featured by different spatial patterns of nitrate concentrations, we separately trained themodel to improve the prediction skill. The predictive results indicate that the DNN model performs well in
depicting both spatial and seasonal variability of nitrate concentrations. The sensitivity experiments show thattemperature is the dominant factor for the nitrate estimation, while salinity has a relatively small effect, but it
cannot be ignored in improving the prediction accuracy. Furthermore, using the temperature and salinity datafrom World Ocean atlas (2018), we found our DNN model has a good generalization ability on nitrate estimationin NPO. This model can be applied to further studies on nitrate’s spatiotemporal variability and mechanism
around the global ocean.

1. Introduction
As a principal nitrogenous substance, the nitrate plays a key role innutrient support for the photosynthesis in the ocean through the direct
consumption by the primary producers. The spatial distribution andtemporal variability of the nitrate are heterogeneous due to the con­sumption of biogeochemical processes (Webb, 2021). The northwestern
Pacific Ocean (NPO), an essential transportation channel for nitrate andother nutrients, is very critical for the global biogeochemical fluxes(Sarmiento et al., 2004; Tsunogai, 2002). In the past century, the nitratein the NPO has increased rapidly (Kim et al., 2011). Given the possible
impact of rapid nitrate changes in the NPO on ecological environment
conditions (Li and Wang, 2013), it is of significance to strengthen theobservation ability of marine nitrate concentration and develop methods

to estimate nitrate concentration (Wang et al., 2018).
The spatial distribution of nitrate, especially the vertical profile, isthe key to reveal the uptake and replenishment of nitrate (Kanda, 2008).
The in-situ observations and Biogeochemistry Argo (BGC-Argo) are thecommonly used methods to measure nitrate concentrations (Talley
et al., 2016; Yang et al., 2020). However, the high cost leads to thecoarse and insufficient spatiotemporal sample resolution. The in-situ
observation cannot accurately record the continuous change of nitrate,
which further limits the understanding of biogeochemical processes(Sauzède et al., 2017). In addition to the direct observation, previous
studies use various properties, including temperature, salinity, chloro­
phyll, etc., to empirically estimate nitrate concentration (Goes et al.,
2000; Guo et al., 2014; Huang et al., 2016; Xiu and Chai, 2011; Yasunaka
et al., 2014; Zhou et al., 2021). However, the empirical formula has a* Corresponding author. CAS Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Chinese Academy of Sciences, Qingdao, China.
** Corresponding author.
E-mail addresses: xuzhenhua@qdio.ac.cn (Z. Xu), gongxiang@qust.edu.cn (X. Gong).
https://doi.org/10.1016/j.dsr.2023.104005
Received 30 November 2022; Received in revised form 20 February 2023; Accepted 21 February 2023
Available online 23 February 2023
0967-0637/© 2023 Elsevier Ltd. All rights reserved.

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poor performance on the estimation of nitrate concentration due to thecomplex relationships between nitrate and other properties.
Machine learning is a promising tool for solving this problem since it
can fit the nonlinear relationship between multiple parameters (Donget al., 2022; X. Li et al., 2022; Z. Li et al., 2022; Zhang and Li, 2022).
Many kinds of neural networks have been utilized in the geophysical andbiogeochemical community over the past few decades (Friedrich andOschlies, 2009; Jamet et al., 2012; Mustapha et al., 2014). In early days,
the artificial neural network (ANN) has been applied to construct amodel to estimate nutrient concentrations (Sarangi, 2011; Zare et al.,2011). Steinhoff et al. (2010) used a self-organizing map for estimating
two-dimensional sea surface nitrate in the North Atlantic and North
Pacific. However, the ANN model has only one hidden layer, whicheasily falls into the problem of local minima and overfitting and results
in an inaccurate estimation. DNN with more hidden layers can overcome
the drawbacks of ANN (Khumprom and Yodo, 2019; Kim et al., 2019). In
addition, the drop-out method in the DNN model can handle unexpected
outliers efficiently. Therefore, the DNN model has recently been widelyused to estimate nitrate concentration in the world’s oceans (Fourrier
et al., 2020; Sauzède et al., 2017).
As a data-driven method, a large amount of observation is needed tobuild a DNN model. Benefiting from the seasonally repeated cruises by
the Japan Maritime Agency (JMA) in the NPO, many observed profilesof nitrate were obtained. Therefore, it can be used to build and train the
DNN model. Because of the importance of nitrate transport in NPO, thestudies on the spatial distribution of nitrate have never stopped (Goeset al., 1999; Rafter et al., 2012; Yasunaka et al., 2014). To map the
spatial distributions of nitrate concentration in upper 1000 m of NPO,
we developed a regional model based on the DNN structure. The
different ocean environments, including the circulation system, strati­
fication, internal wave field, etc., feature the subtropical and tropicalregions with distinct characteristics (Chen et al., 2021; Feng et al., 2010;
Sun et al., 2007). The relationship between nitrate and other variables
may be affected by the above factors. Because the DNN model is data
dependent, inconsistent relationships between input and output vari­ables in different regions will affect results. Hence, we separately built
the DNN model in subregions, including the subtropical region and thetropical region, which can have better performance on estimating (Chenet al., 2022; Goes et al., 1999). Based on the data from World Ocean
Atlas (2018) (WOA18), we further assessed the generalization ability of
our DNN model on nitrate estimation in NPO.
The remainder of the paper is organized as follows: Section 2 de­scribes the details of the data, model and evaluation methods used in thisstudy. Section 3 demonstrate the performance of the DNN model. The
sensitivity of input variables of the model and the spatial distribution of
nitrate are discussed in Section 4. Section 5 is the summary.

Fig. 1. Geographic distribution of 832 vertical profiles from the dataset ofJapan Meteorological Agency (JMA) in the northwestern Pacific Ocean (NPO)used in this study. Different shapes of symbols represent R\V Keifu (KS) and R\V
Ryofu (RF), respectively. The season are marked with different four colors.

downloaded from the Asia Pacific Data Research Center (ARDRC, htt
p://apdrc.soest.hawaii.edu/as/v6/search), with a spatial resolution of
0.25◦ × 0.25◦ . Temperature and salinity from WOA18 were standard­
ized before input to make them dimensionless and of the same order ofmagnitude. For each grid, all data are clustered around 0 with a varianceof 1.
2.2. DNN model
The DNN model is a more sophisticated artificial neural networkwith multiple hidden layers. The connection of multiple hidden layers
enables the model to fit complex relationship between the input vari­ables (i.e., temperature, salinity, location, time, etc.) and the output
variables (i.e., Nitrate concentration). As shown in Fig. 2, DNN generally
includes the input layer, several hidden layers and output layer. The
DNN model transmits signals from the input layer to the hidden layers
through forward propagation. The processed signals from the neurons in
hidden layers are further transmitted into the output layer and thenoutput an initial value. After the comparison between the initial value
and the target value, backward propagation is used to adjust the weightof signals in the hidden layers and further reduce the error using the
optimization algorithm. The activation function is added in the hidden
layers to improve the fitting ability of the model. Compared to Sigmoid
and Tanh activation function, ReLU does not use all neurons to avoid
overfitting during the training process (Lu et al., 2020). At the sametime, because the derivative of ReLU function is constant, the training
process will not suffer from the problem of gradient disappearance, sothat a deeper network structure can be available. The SoftMax functionis adopted to prevent from the value of gradient becoming zero, since theweights and biases are not updated in every backpropagation step dur­ing the training process (Sharma et al., 2017). Therefore, in the front andrear hidden layers, the activation function is ReLu, and the activation
function in the middle hidden layer is SoftMax.

2. Data and methods
2.1. Data
The in-situ data used in the model are measured by the Japan
Meteorological Agency (JMA) from January 2015 to March 2021
(https:/www.data.jma.go.jp/). The observations were carried out by R/
V Keifu and R/V Ryofu at 120◦ E− 180◦ E and 9◦ S− 34◦ N. Quality control
is necessary before collating these observations into a dataset used forthe DNN model. There are two criteria for quality control: (1). theprofiles whose depths are less than 1000 m are not considered; (2). theprofile whose missing values account for more than half of the total data
are excluded. Then we applied linear interpolation on these preprocessed data to fill in the missing values (Chen et al., 2022; Sam­martino et al., 2018). After pre-processing, a dataset including 832
vertical nitrate profiles covering January 2015 to March 2021 was used
to train and test the designed DNN model (Fig. 1).
WOA18 (Garcia et al., 2019) was also used to evaluate the general­
ization ability of the DNN model. This monthly dataset can be

2.3. Training process
The input variables used in the training process are latitude, longi­
tude, temperature, salinity, time (month), and depth (Fig. 2). The reason
for choosing geolocation and observation time is that the nitrate dis­tribution varied seasonally and spatially. The model can find the2

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Deep-Sea Research Part I 195 (2023) 104005

Fig. 2. The schematic representation of the deep neural network (DNN) model. f is the activation function, including ReLu (cyan) and SoftMax (orange).

nonlinear relationship between the input variables and the nitrateconcentration at different depths (Bittig et al., 2018; Sauzède et al.,2017; Steinhoff et al., 2010). The output is the vertical distribution of
nitrate concentration from sea surface to 1000 m.
The DNN model was trained by 80% of the profiles, and tested by theremaining 20% in each region. To efficiently update the network
weights and accelerate convergence, the Adam optimizer is used with
optimizer learning rate of 0.01 to reduce the loss in the training process.
In addition, to avoid over-fitting, we applied the dropout technique todiscard some neurons. During the training process, 15% of the training
set was randomly selected as a validation set to verify whether the DNN
model was over-fitted. The mean square error (MSE) of the training set
and the verification set is taken as a loss function:
MSE =

n
( obs
)2
1∑
x − xprein i=1 iThree statistical indexes were chosen: the mean absolute error(MAE), the root mean squared error (RMSE), and the Nash-Sutcliffe ef­
ficiency criteria (NSE). The MAE and RMSE are commonly used toevaluate the error of the machine learning model, the NSE is commonlyused to quantify the simulation accuracy (Lou et al., 2021; Sun et al.,2021; Uddin et al., 2022).
(2)

Table 1Model parameters.

Hidden layer depth
Numbers of neurons per hidden layer
Learning rate
Dropout rate
Batch sizeEpochoptimizer
Training set
Validation set
Test setParameter setting
Tropical region

Subtropical region

364,64,64
0.01
0.05
60000
150
Adma
80%
15% of training set
20%

364,64,64
0.01
0.05
60000
150
Adma
80%
15% of training set
20%

(4)

Before assessing the regional performance of the DNN model, we
check the impact of the data amounts on the model performance. It isfound that both the RMSE and MAE converge after the percentage ofdata used reaching 60% of total 832 profiles (figure not shown). The
regional performance of the trained DNN model in the tropical andsubtropical regions has been evaluated using the test dataset. Similar
with the training process, the data on the test set is normalized in thesame way. The model output is back-normalized to compare with theoriginal data and measure model’s performance.
Scatter plots of nitrate concentrations from the JMA observations
and the model estimates show that most of the points are close to the
diagonal bisector, while only very few data points diverge from it, with a
low RMSE value of 0.7 μmol/L and a high NSE values of 0.99 (Fig. 3).
These results suggest that the nitrate concentration estimated by themodel is close to the observed value. It means our model performs wellin the magnitude of nitrate concentration for the upper 1000 m in both
tropical and subtropical regions.
Compared with the observed profiles of nitrate concentration in eachregion, the model estimates are very close to the observed results in both
values and vertical structures (Fig. 4). The mean value of nitrate esti­mates from the DNN model almost coincides with that of the observa­
tions, and their biases are also small (Fig. 4c and f). The model
performance in the tropical region is slightly worse than that in thesubtropical region, especially in depth with high nitrate gradient(Fig. 4c). In the tropical region of NPO, the cyclonic circulation patterncauses the seawater’s divergence and upwelling, resulting in shallower
thermocline and promoting the upward supply of nutrients (Lukas andLindstrom, 1991; Ma and Sun, 2015). By contrast, in the subtropicalregion, the anticyclonic circulation pattern makes the seawater
converge and sink, leading to deeper thermocline which impedes the
upward supply of nutrients from the deeper layers (Long et al., 2022;
Ren and Riser, 2010). Because of the reverse T-N relation, the verticalprofiles of nitrate are similar to the temperature profiles (Figs. 4 and 5,
Goes et al., 2000; Morin et al., 1993; Kudela and Dugdale, 1996).

2.4. Statistical evaluation index

Model parameter)2∑n ( obs
x − xprei
NSE = 1 − ∑ni=1( i)2obs− xobsmean
i=1 xi3.1. The regional performance of DNN model

(1)

n ⃒
⃒
1∑
⃒xobs − xpre ⃒in i=1 i(3)

3. Results

According to the performance of the training set and validation set,
the parameters of the DNN model were determined for each region(Table 1).

MAE =√̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
n1∑
2(xobs − xpre
i )n i=1 i

RMSE =

3

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Fig. 3. Scatter plots of the observed nitrate concentration (x-axis) and the estimated nitrate concentration (y-axis) based on the test datasets of the (a) tropical regionand (b) subtropical region. The black dotted line is the diagonal bisector, and the color indicates the point density.

Fig. 4. Vertical profiles of (a) the observed nitrate concentration, (b) the model estimates and (c) the bias between observation and model estimates in the tropicalregion. The color shadings are the standard variances. (d–f) Same as (a–c) but in the subtropical regions.

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Fig. 5. Vertical profiles of the observed temperature in the (a) tropical region and (b) subtropical region. The pink shading is the standard variances.

Resulting in different model effects in the two areas. Both the nitracline
and thermocline occur in 50–300 m of tropical region, and the model’s
performance in this area is relatively poor. Overall, the performance of
the DNN model in tropical region and subtropical region is satisfactory.
We evaluate the performance of the DNN model according to three
key statistical parameters (Table 2). High NSE values are shown in bothregions, which suggests that input variables can explain over 99% of
nitrate variability at different depths (Sauzède et al., 2017). The RMSE
value is 0.92 μmol/L (0.48 μmol/L) and the MAE value is 0.72 μmol/L(0.38 μmol/L) in the tropical (subtropical) regions. It means the mag­nitudes of nitrate concentration in both two regions are well estimated.
As shown in Fig. 4 c and f, the mean bias error show that maximal bias
(0.5–1.1 μmol/L) occurs at about 40–300 m in the tropical region, whilein the subtropical region, the large mean bias error merge about 40–180
m. This difference illustrates that our subregion-based model depicts
different features of the nitrate profiles over the two regions and that themodel performs well in predicting the vertical structure.

by the DNN model has a slightly higher bias in winter, compared tosummer (Fig. 6a–f), which is similar the research results of Silió-Calzada
et al. (2008). The upper thermocline undergoes a seasonal verticalmigration in the tropical region: shallower in summer and deeper inwinter (Yu and McPhaden, 1999). Because the undulations in thenitracline followed that of the thermocline, the seasonal variations of
nitrate profiles are similar to that of temperature profile (George et al.,2013). In the subtropical region, the average values almost coincide, andthe standard variances are comparable (Fig. 7a–f). Although the sea­sonal variation in the thermocline is more significant in the subtropicalregion, almost all the nitrate in the upper layer is depleted, resulting inless seasonal variation in nitrate (Yasunaka et al., 2014). Unlike theresults in the tropical region, the vertical profile of bias is so close to thezero line. In general, the model performs better in the subtropical region
than in the tropical region. The difference in the performance may be
due to the different nitrate change rate in the two regions (Lewis et al.,
1986; Rafter et al., 2012).

3.2. The seasonal performance of DNN model

3.3. The zonal and meridional performance of DNN model

To assess the model’s capability to estimate nitrate in different sea­
sons, the vertical profiles of estimated nitrate in summer (June toAugust) and winter (December to February) are shown in Fig. 6 andFig. 7. The regionally averaged nitrate profile predicted by the DNN
model is comparable to the observations in both two seasons. The pre­dicted nitrate concentrations fluctuate within the observation varianceswith small biases. In the tropical region, nitrate concentration estimatedTo further verify the prediction ability of the DNN model, two key
observed sections were selected: one is the zonal section along 9◦ N from136◦ E to 164◦ E, and the other is the meridional section along 137◦ E
from 13◦ N to 35◦ N. Fig. 8 shows the vertical distribution of nitrateconcentrations along the 9◦ N section and 137◦ E section from JMA data
and the DNN model estimations. It can be clearly seen that the spatial
distribution of the model estimated nitrate agrees well with the JMA
observations. Most of the observed features are well reproduced by the
DNN model.
For the 9◦ N section, the nitrate concentration changes significantlywith depth in the upper 200 m. Below 200 m, the nitrate concentration
rises from 30 μmol/L at 200 m to 40 μmol/L at 1000 m, and the verticalgradient getting decreases as depth increases (Fig. 8a and b). The nitrateconcentration below 200 m estimated by the model is slightly smaller
than the JMA observation, with the differences (JMA minus DNN) up to

Table 2
Statistical parameters of the DNN model in the tropical and subtropical regions.
Evaluation indicators

Tropical region

Subtropical region

NSE
RMSE (μmol/L)
MAE (μmol/L)

0.99
0.92
0.72

0.99
0.48
0.38

5

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Fig. 6. Vertical profiles of (a) the observed nitrate concentration, (b) the model estimates, and (c) the bias between observation and model estimates in the tropicalregion during summer. The color shadings are the standard variances. (d–f) Same as (a–c) but during winter.

1.5 μmol/L (Fig. 8c). The most obvious difference occurs within the
100–200 m depth, where the estimated nitrate is relatively larger thanthe JMA observations with a maximum difference of more than 2 μmol/
L. It should be noted that the 100–200 m depth corresponds to thethermocline. The changing temperature in the thermocline may affectthe performance of the DNN model.
For the 137◦ E section, as shown in Fig. 8f, relatively large nitratedifferences are present in the depth range of 100–150 m between 17.5◦ N
and 22.5◦ N, and the JMA values are 2 μmol/L higher than the estimatedvalues. The subtropical front in the Subtropical Countercurrent region
cause rapid change of temperature and salinity in this area, thus
reducing the accuracy of the model (Zhang et al., 2007). The errors in
the DNN model along the 9◦ N section and 137◦ E section are about 0.43μmol/L and 0.32 μmol/L, respectively. The results show that the DNN
model can well depict nitrate concertation’s zonal and meridionalvariations.

3.4. Performance comparison between DNN and ANN model
Prior to this study, the ANN model has been commonly applied toestimate nitrate concentration (Wang et al., 2018; Zhang et al., 2002).
Compared with the DNN model, the ANN model has only one hidden
layer. To evaluate the improvement of model performance by including
more hidden layers, we used the same datasets to train and test both the
ANN and DNN model.
As shown in Table 3, both the RMSE and MAE of DNN model are
lower than that of ANN. The RMSE of DNN model in the tropical regionis 0.25 μmol/L less than 0.17 μmol/L of the ANN model, and model error
is reduced by about 21%. In the subtropical region, the RMSE of the DNN
model is 14% smaller than that of the ANN model. Compared with the
ANN model, the DNN model with more hidden layers can significantly
reduce the estimation error of nitrate concentration.

6

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Fig. 7. Vertical profiles of (a) the observed nitrate concentration, (b) the model estimates, and (c) the bias between observation and model estimates in the sub­tropical region during summer. The color shadings are the standard variances. (d–f) Same as (a–c) but during winter.

4. Discussion

and Garside, 1995). To investigate how salinity affect the accuracy of
estimation, a series of sensitivity experiments were set up (Table 4). In
the Experiment 1, salinity is not considered as the input variable, while
in Experiment 2, the salinity is included. In the tropical region, the RMSEof the estimated nitrate in the Experiment 1 is 1.01 μmol/L, and the MAE
is 0.73 μmol/L. While the RMSE and MAE of estimated nitrate in theExperiment 2 are 0.92 μ mol/L and 0.72 μmol/L, respectively. In thesubtropical region, the RMSE and MAE of Experiment 1 are 0.58 μmol/L
and 0.46 μmol/L, while the RMSE and MAE of Experiment 2 aredecreased obviously and are 0.48 μmol/L and 0.38 μmol/L, respectively.
In subtropical region, inputting salinity can significantly increase theperformance of the DNN model with a decrease of ~17% in RMSE and
MAE. It means that the estimation from the DNN model fits the obser­
vations better when considering salinity. The improvement is notevident in the tropical region, where the RMSE and MAE decreased byonly 9% and 1.4%, respectively. The results suggest that salinity canmake the nitrate estimation more accurate, especially in high latitudes.

4.1. Sensitivity of input variables
Through forward and backward propagation, the DNN model adjusts
the weight of input variables and extracts the implicit relationship formodel estimation (Reichstein et al., 2019). However, different input
variables will greatly affect the prediction skill of the model (Gevrey
et al., 2003; May et al., 2011). Traditional methods for estimating nitrateconcentration mostly only consider temperature, because there is anapparent relationship between temperature and nitrate (Kudela andDugdale, 1996; Morin et al., 1993). However, the complex spatial andtemporal variability of the temperature-nitrate relationship hinders its
further application in large regions (Sun et al., 2007; Silió-Calzada et al.,2008).
Our designed model not only considers temperature, but also thesalinity, whose impact on the estimation should not be ignored (Garside7

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Fig. 8. Vertical distribution of nitrate concentrations along the 9◦ N section derived from (a) observation data and (b) the model estimates. (c) The difference between(a) and (b). (d–f) Same as (a–c) but along the 137◦ E section.

concentration. The 137◦ E section is selected because of the significant
meridional variations of nitrate which have been reproduced by ourtrained model (Fig. 8d–f).
The NSE, RMSE, and MAE of nitrate concentration estimated using
WOA18 temperature and salinity are 0.96, 1.99 μmol/L, and 1.57 μmol/
L, respectively. The value of NSE was lower than that obtained using
JMA data. Overall, the trained model can reproduce the distribution of
nitrate along the 137◦ E section (Fig. 9a and b). The differences are more
obvious in the nitrate-cline, especially in 4◦ N and 31◦ N (Fig. 9c). The
nitrate concentration is underestimated. We checked the temperature
difference between WOA18 and JMA data. The temperature data of
WOA and JMA show obvious differences in some areas, such as the areaaround 4◦ N and 31◦ N (Fig. 10). This is similar to the nitrate difference(Fig. 9c). As shown in Fig. 10, the JMA temperature is lower than
WOA18 temperature in the area around 4◦ N and 31◦ N. According to theinverse temperature-nitrate relation (Kudela and Chavez, 2000; Strick­land et al., 1970; Traganza et al., 1983), it is clear that why the nitrateconcentration obtained is underestimated.

Table 3
Performance indicators of the ANN and DNN model based on the 20% validation
dataset.
Study area

Evaluation indicators

Tropical region

RMSE (μmol/L)
MAE (μmol/L)
RMSE (μmol/L)
MAE (μmol/L)

Subtropical region

Model
ANN

DNN

1.17
0.94
0.57
0.46

0.92
0.72
0.49
0.38

Table 4
Performance indicators of the DNN model in the sensitivity experiments.
Experiments

Study area

Evaluation
indicators

DNN

Improvement

Experiment 1(without salinity)

TropicalregionSubtropicalregionTropicalregionSubtropicalregionRMSE (μmol/L)
MAE (μmol/L)
RMSE (μmol/L)
MAE (μmol/L)
RMSE (μmol/L)
MAE (μmol/L)
RMSE (μmol/L)
MAE (μmol/L)

1.01
0.73
0.58
0.46
0.92
0.72
0.48
0.38

–
–
–
–
9%
1.4%
17.2%
17.4%

Experiment 2 (withsalinity)

5. Conclusions
In this study, a DNN model is developed and applied to estimate
nitrate concentrations in the upper NPO. The results indicated that thedesigned DNN model can estimate nitrate concentration accurately inboth tropical region (NSE = 0.99, RMSE = 0.92 μmol/L, MAE = 0.48
μmol/L) and subtropical region (NSE = 0.99, RMSE = 0.72 μmol/L,
MAE = 0.38 μmol/L). The DNN model performs well in both winter andsummer (RMSE less than 1.04 μmol/L), indicating that the DNN model
has a good seasonal applicability for the nitrate estimation in NPO. In
addition, compared with observations along a zonal section (9◦ N sec­tion) and a meridional section (137◦ E section), the DNN model also does
well in reproducing the zonal and meridional distribution of nitrate. The

This circumstance reminds us that salinity should be carefully consid­
ered when predicting nitrate concentrations in middle and highlatitudes.
4.2. Vertical distribution of nitrate estimated by WOA18 data
To verify the generalization ability of our trained DNN model, bothtemperature and salinity data of WOA18 were used to estimate nitrate8

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Fig. 9. Vertical distribution of nitrate concentrations along the 137◦ E section derived from (a) observation data and (b) the model estimates based on WOA18 data.
(c) The difference between (a) and (b).

Fig. 10. Difference between JMA and WOA18 temperature (JMA minus WOA18) along the 137◦ E section.

sensitivity experiments demonstrated that inputting salinity could
significantly increase the accuracy of estimation, especially in the sub­tropical region. By inputting the temperature and salinity profiles fromWOA18 data into our trained DNN model, we demonstrate that ourmodel has a good generalization ability. The vertical distribution of
nitrate along the 137◦ E section estimated from WOA18 data agrees wellwith the observed distribution.
As a data-dependence method, the model performance was highly
dependent on data quality. It means that in some circumstances, themodel performance may be significantly weakened by the scarcity ofdata. For example, due to the lack of data in spring and autumn, we areunable to train a model which can depict the distribution in these two
seasons. A future improvement of our model involves employing

additional input variables such as chlorophyll (Goes et al., 1999, 2000)
and dissolved oxygen (Sauzède et al., 2017) that potentially affect ni­
trate concentrations. Once the nitrate has been accurately estimated, it
can be used for practical applications, such as new production estimatesand understanding the global carbon cycle.
Author contributions
Conceptualization, Z.H.X., X.G.; Methodology, W.L.X., X.G.; Formal
analysis: W.L.X., P.W.Z., Z.J.H, J.Y., X.Z.Z; Writing - Original draft, W.L.
X., P.W.Z., Z.J.H, J.Y.; Writing - Reviewing & Editing, Z.H.X., X.G., W.L.
X., P.W.Z., Z.J.H, J.Y., and X.Y.G..

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Declaration of competing interest

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The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.
Data availability
The datasets for this study are publicly available. The in-situ data areprovided by the Japan Meteorological Agency (JMA, https:/www.data.
jma.go.jp). This monthly dataset of World Ocean Atlas (2018) can be
downloaded from the Asia Pacific Data Research Center (ARDRC,
http://apdrc.soest.hawaii.edu/as/v6/search).
Acknowledgments
This study was jointly supported by the Strategic Priority Research
Program of the Chinese Academy of Sciences and the National Nature
Science Foundation of China-Shandong Joint Fund (XDA22050202,
U1906215, XDB42000000), National Natural Science Foundation ofChina (92058202), the Scientific and Technological Innovation Project
financially supported by Laoshan Laboratory (LSKJ202202502), Key
Deployment Project of Center for Ocean Mega Research of Science,
Chinese Academy of Sciences (COMS2020Q07), the project jointly
funded by the CAS and CSIRO (133244KYSB20190031).
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