One-dimensional ocean model with three types of verticalvelocities: a case study in the South China Sea

Wenfang Lu1,2,3,4& Xiao-Hai Yan2,3,4

& Lu Han2& Yuwu Jiang1

Received: 25 August 2016 /Accepted: 13 December 2016# Springer-Verlag Berlin Heidelberg 2016

Abstract In this research, three vertical velocities wereincluded in a one-dimensional (1D) ocean model for acase study of the SouthEast Asian Time-Series Study sta-tion in the South China Sea. The vertical velocitiesconsisted three processes, i.e., Ekman pumping (WEK),Eddy pumping (WEP), and the background upwelling(WBK). The quantification of WEK followed the classicalEkman pumping theory. The WEP, whose underlyingmechanism was consistent with the baroclinic modes(dominated by the first mode), was quantified by Argoobservation and altimetry data. The WBK, related withthe background circulation, was estimated from the long-term heat budget balance. The skill assessment indicatedthat the case with all three processes performed best. Thestudy confirmed the capability of the 1D model with threetypes of vertical velocities, which can reproduce the

general structure and variation of temperature in verticaldirection.

Keywords South China Sea . SEATS station .

One-dimensional model . Vertical velocity . Ekman pumping

1 Introduction

The South China Sea (SCS) is the largest marginal sea locatedin the subtropical western pacific, with the SouthEast AsianTime-Series Study (SEATS, diamond in Fig. 1) station, wherethe properties are representative for the seawater of the centralSCS within the basin interior (Wong et al. 2007a). Previously,multiple oceanic variables have been studied, including tem-perature, salinity, nutrients (Wong et al. 2007b), chlorophyll(Liu et al. 2013), and primary production (Tseng et al. 2009).

One-dimensional (1D) oceanic models are implemental tostudy the vertical thermal structure. Munk (1966) fitted thevertical profiles of temperature and salinity based on a simpleadvection-diffusion balance, suggesting the practicability of a1D model. Recently, although the advances in computer tech-nology have been making three-dimensional ocean modelingmore and more affordable, 1D models still show its merits inplanktonic ecosystemmodeling attributing to its simpler phys-ics and shorter computational time (Li et al. 2015; Sasai et al.2016; Shigemitsu et al. 2012), specifically in the parameter-tuning process. Given the relativelyweak horizontal advectioncondition at SEATS, the application of 1Dmodel was justifiedby Li et al. (2015).

Conventional 1D models simulate the vertical turbulentmixing in the oceanic mixed layer(s) (Mellor 2001).However, in the 1D context, due to the absence of horizontaldivergence, no vertical motions can be resolved essentially.Practically, the effects from vertical advection were generally

This article is part of the Topical Collection on the 8th InternationalWorkshop on Modeling the Ocean (IWMO), Bologna, Italy, 7–10June 2016

Responsible Editor: Tal Ezer

* Yuwu Jiangywjiang@xmu.edu.cn

1 State Key Laboratory of Marine Environmental Science (MEL),Xiamen University, Xiamen 361005, Fujian, China

2 Center for Remote Sensing, College of Earth, Ocean andEnvironment, University of Delaware, Newark, DE 19716, USA

3 Joint Institute for Coastal Research and Management (UD/XMUJoint-CRM), University of Delaware, Newark, DE 19716, USA

4 Joint Institute for Coastal Research and Management (UD/XMUJoint-CRM), Xiamen University, Xiamen 361005, Fujian, China

Ocean DynamicsDOI 10.1007/s10236-016-1029-9

omitted (Hood et al. 2001; Jin et al. 2006; Lévy et al. 1998;Sasai et al. 2016). The omitted advection resulted in buildingup of near-surfacemomentum and hence exaggeratively deep-ened the mixed layer and cooled the surface temperature(Mellor 2001). To balance the over-mixed ocean structure,additional numerical methods, e.g., relaxation toward obser-vational data (Chifflet et al. 2001), or adding sink terms in themomentum equations (Mellor 2001), are required. Actually,the intensive upwelling at the SEATS station suppresses themixed layer (Wong et al. 2007a), resulting in shallower mixedlayer depth. Following the work of Chifflet et al. (2001), Liet al. (2015) artificially incorporated the vertical velocity driv-en by Ekman pumping, demonstrating that vertical motion canbe prescribed and included in the 1D model. However, it isarguable whether Ekman pumping is the major contributor tothe vertical motion, especially beneath the upper mixed layer(Wong et al. 2007a). At depth, other processes may dominatethe vertical motion, e.g., eddy pumping or quasi-geostrophicpumping (Pascual et al. 2015). Thus, in this study, aside fromEkman pumping, vertical motion induced by mesoscale eddyactivity and the background upwelling are also considered.

The objective of this research is to study the behavior of theupper ocean thermal structure above intermediate layer(1000 m) in a 1D context. Especially, we focus on the pro-cesses, i.e., Ekman pumping, eddy pumping, and backgroundupwelling, which can induce vertical motion. The ultimategoal is to achieve better understanding of the processes thatcontrol the vertical thermal variability at the SEATS station,which can be further generalized to be applied in other cases inthe SCS and other parts of the ocean.

The model configuration, utilized observation data, andsensitivity experiments design are outlined in Sect. 2. And inSect. 3, analysis of the observation data as well as modelresults are shown. Furthermore, the model results areinterpreted, and the underlying physics are discussed. At last,conclusions are given in Sect. 4

2 Model configuration and data

2.1 Physical model

The 1D model was modified from the Regional OceanModeling System (ROMS). ROMS solves the Reynolds-averaged Navier-Stokes equations on topography-followingcoordinates (Shchepetkin and McWilliams 2005). TheROMSmodel has been applied in multi-purpose oceanic sim-ulations in the Taiwan Strait and northern SCS (Gan et al.2009; Li et al. 2015; Liao et al. 2013; Lin et al. 2016; Liuand Chai 2009; Lu et al. 2015;Wang et al. 2013; Xiu and Chai2011). The 1D tracer equation for any tracer q can be writtenas

∂q∂t

þ ∂ wpreq� �∂z

−q∂wpre

∂z¼ ∂

∂zAkq

∂q∂z

� �þ Fq ð1Þ

where wpre is the arbitrary vertical velocity and Akq is the eddyviscosity coefficients for q, while Fq is the surface flux for q.Details of model configuration can be seen in Appendix A. Itis noticeable that the arbitrary vertical velocity introduces non-conservation in the continuity equation; as a result, the tracerequations should be discretized in the advective form as inEq. (1), in which the third term was added in the ROMS codes(see Appendix B).

2.2 Observation data

Potential temperature and salinity profiles from Argo are ac-quired from the World Ocean Database 2013 (https://www.nodc.noaa.gov/OC5/WOD/pr_wod.html). We chose the datawithin the 2° by 2° box centered with the SEATS station torepresent the state of SEATS. And in total, 526 profiles werearchived from 2007 to 2015 (Fig. 1, blue dots). The potentialdensity (ρ) profiles (Fig. 2a) were re-constructed with Argo

Fig. 1 Location of SEATSstation (red diamond) and allArgo observational profiles (bluedots), over the bathymetry ofnorthern SCS (unit: meter). Blackcontour indicates 1000 m isobath

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observed temperature, salinity, and depth. At SEATS, thepycnocline (maximum density gradient, ∼0.042 kg m−4) is at∼−50 m and has a maximum depth of ∼−200 m (Fig. 2a).

Delay-time monthly mean sea level anomaly (SLA) wasmerged from multiple satellites and distributed by AVISO(http://www.aviso.altimetry.fr/en/data/products/sea-surface-height-products/global/msla.html). This data is on a Cartesiangrid with a resolution of 1/4 degree while the temporal range isfrom 1993 to 2014. The SLA at the SEATS station (Fig. 3b)was obtained by a linear interpolation method.

2.3 Vertical velocities

To take vertical advection into consideration, the vertical ve-locity (w) from three mechanisms was considered: Ekmanpumping (WEK), eddy pumping (WEP), and background up-welling (WBK).

First of all, the quantification of WEK follows the work ofLi et al. (2015). The distribution of WEK was described as afunction of time, depth, and the Ekman pumping vertical ve-locity (Cushman-Roisin and Beckers 2011). The Ekmanpumping vertical velocity (we) can be calculated from thewind stress curl:

we ¼ 1

ρw f∇� τ! ð2Þ

where ρw is the density of seawater, f is the local Coriolisparameter, and the curl was discretized with the NCEP re-analysis wind stress, τ, with a spatial resolution of quarterdegree. Since NCEP re-analysis was already coupled withan ocean model, it can provide optimal estimation of the sur-face stress, as well as sufficient temporal coverage. Thewe hasa magnitude of 10−6∼10−5 m s−1 (Fig. 3c).

The Ekman depth, dek, was given by

dek ¼ 0:4u*f¼ 0:4

ffiffiffiffiffiffiffiffiffiffiffiτ!

������

ρw f2

vuut ð3Þ

where u* is the friction velocity. The prescribed WEKequals to the we at the Ekman depth (seasonally approxi-mates from −30 to −160 m), and sinusoidally decays tozero at surface and at −200 m depth, which is the bottomof pycnocline.

Secondly, the WEP is defined as the w resulted from thevertical displacement of isopycnals due to the intensificationor decaying of mesoscale eddies. For the WEP, we follow theeddy pumping mechanism proposed by Siegel et al. (1999).Assuming the balance between the time derivative of ρ and itsvertical advection (without vertical mixing and horizontal pro-cesses), the displacement of isopycnals (hereafter, DoI) can beestimated:

DoIρ z; tð Þ ¼ ρ z; tð Þ− ρ zð Þh i∂ ρ zð Þh i

∂z

ð4Þ

The above-mentioned Argo-reconstructed ρ(z,t) wasapplied to estimate DoI. The temporal variability of DoIis well correlated with the SLA. The correlation coeffi-cients (CCs) between DoI and SLA are shown in Fig. 2bas a function of depth. The top 100 m, where the variationis dominated by mixing processes and Ekman pumping,was removed from the plot. Below −100 m, the CC in-creases gradually, peaks at ∼−500 m and then remainsrelatively steady to at least −1000 m. At all depths, theregression is over 99% significance.

Fig. 2 a Argo observational potential density (red, unit: kg m−3) and itsvertical gradient (blue, unit: kg m−3 m−1). b The correlation coefficient(blue) and slope (red), i.e., α in Eq. (5) of the linear regression betweenSLA and DoI at each depth, with green dots indicating that the

significance level is over 99%. c The first three EOF modes of DoI,which was calculated from Eq. (4), with the legend showing theexplained percentage of the total variance in each mode. In b, c, theparameters above −100 m are omitted

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Hence, the relation between WEP and SLA can be writtenas

WEP z; tð Þ ¼ ∂ DoI z; tð Þ½ �∂t

≈∂ α zð Þ⋅SLA tð Þ þ β zð Þ½ �

∂t

¼ α zð Þ ∂SLA tð Þ∂t

ð5Þ

where the coefficient α and β can be yielded by performing aleast-square linear regression between SLA and DoI at eachdepth. The profile of α can be seen in Fig. 2b.

At last, the WBK is specified as the vertical motiondue to the horizontal divergence of background current,which can be deduced from long-term heat balance invertical direction. The net heat input at the SEATS stationsuggests that upwelling is necessary to maintain the ther-mal structure (Wyrtki 1965). The surface net heat flux isbalanced by the cold water upwelling, and the mean ver-tical velocity can thereby be estimated by (Wyrtki 1965;Yang et al. 1999)

WBK∼1

ΔT

QρwC

ð6Þ

where ΔT is the temperature difference between sea surfacetemperature (SST) and bottom temperature [roughly 28 °C(Qu 2002)],Q is the surface net heat flux with an annual meanvalue of ∼15 W m−2 (Yang et al. 1999), and C is the specificheat capacity (4200 J kg−1 °C−1). These give an estimatedWBK of 1.4 × 10−7 m s−1.

Alternatively, WBK can be estimated from the counterbal-ance of constant eddy viscosity and vertical velocity

w∂C∂z

¼ Ak∂2C∂z2

ð7Þ

for any conservative tracer C (Munk 1966; Wang 1986).Eq. (7) has an analytical solution of

C ¼ Cb þ C0−Cbð Þexp wzAk

� �ð8Þ

where Cb and C0 are the value at bottom and at surface, re-spectively. This model is applicable when the potentialtemperature-nutrient relation is linear (Dai et al. 2009; Munk1966), which is the case below the surface at the SEATSstation (Chen et al. 2006; Lu et al. 2015). By fitting theArgo temperature profiles, w/Ak can be estimated as0 .0027 m−1 , which yie lds an upwel l ing ra te of1 .0 × 10− 6 m s− 1 g iven the eddy v i scos i ty o f3.98 × 10−4 m2 s−1 observed in the intermediate layer nearSEATS (Yang et al. 2016). The two upwelling rates are bothtested in model cases.

The WBK is consistent with the upwelling in the inter-mediate layer (above −1000 m) of the northern SCS re-ported by Qu et al. (2000) and Isobe and Namba (2001).Hence, it is presumed to act only when depth <−200 mbeneath the pycnocline, while WEK and WEP dominatethe above layer.

Fig. 3 a Three leading (1st, red;2nd, blue; and 3rd, green)principal components (PCs) fromEOF analysis of DoI. b Sea levelanomaly (SLA, unit: meter) at theSEATS station. c Ekmanpumping vertical velocity (we,unit: m s−1). Color shading isbased on positive (in red) andnegative (in blue) value of SLA. dHovmӧller diagram of the DoI(unit: meter), with green contoursindicating the zero values, and theblack dots denoting the Argo datalocation

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Altogether, the total vertical velocity, wall, is a combinationof three components:

wall ¼WEK z≥−100mð ÞWEK−WEP⋅

zþ 100

100−200≤z≤−100mð Þ

WEPþWBK z≤−200mð Þ

8><>:

ð7Þ

Sensitivity tests were designed in Table 1, to test whetherthe incorporation of the vertical velocity can improve the 1Dmodel results and to compare the relative importance of thethree vertical motion components. The results are demonstrat-ed in the next section.

3 Results and discussion

3.1 Model results

The Taylor diagram in Fig. 4 summarizes the normal-ized standard deviations (STDs), CCs, and normalizedcentered root-mean-square differences (RMSDs) of themodel cases in the simulation of the observed tempera-ture variation (also refer to Table 1 for the statistics). Ingeneral, the simulation of SST (−5 m) in all cases areclosely excellent, because the heat flux budget domi-nates the temperature variation near the air-sea interface,

Table 1 Summary of the statistics for seven model cases

Case A Case B Case C Case D Case E Case F Case G

WBK,

(unit: m s-1

)1.4×10

-71.4×10

-71.4×10

-71.4×10

-71.0×10

-6

WEP

WEK

Normalized

STD

5m 0.7094* 0.7105 0.7091 0.7402 0.7389 0.7383 0.6898

50m 0.5392 0.5352 0.5402 0.5007 0.5110 0.5029 0.5170

150m 0.1480 0.1384 0.1766 0.2497 0.3291 0.3145 0.3498

300m 0.2560 0.2167 0.5133 0.0948 0.3192 0.3084 0.3499

0-300m 0.7414 0.7619 0.7619 0.8243 0.8196 0.8072 0.8304

Normalized

RMSD

5m 0.3755 0.3749 0.3758 0.3544 0.3544 0.3552 0.3912

50m 0.7872 0.7867 0.7843 0.8367 0.8253 0.8283 0.8132

150m 1.0404 1.0362 0.9645 0.9066 0.8676 0.8719 0.8671

300m 1.0764 1.0607 0.8963 1.0053 0.8489 0.8543 0.8362

0-300m 0.3585 0.3466 0.3425 0.2825 0.2774 0.2878 0.2680

Correlation

coefficient

5m 0.9625 0.9625 0.9624 0.9671 0.9671 0.9671 0.9656

50m 0.6207 0.6222 0.6248 0.5482 0.5660 0.5619 0.5844

150m -0.2141 -0.2071 0.2793 0.4774 0.5373 0.5355 0.5267

300m -0.1883 -0.1879 0.4456 -0.0267 0.5928 0.5878 0.6010

0-300m 0.9541 0.9544 0.9564 0.9688 0.9713 0.9701 0.9724

Overall

bias

(unit: oC)

#

5m 0.7254 0.7060 0.7057 -0.2387 -0.1536 -0.1958 -0.6511

50m 1.5426 1.4864 1.4788 -1.3812 -1.1180 -1.2406 -1.4321

150m 4.2954 4.0761 4.0221 0.2030 0.4763 0.4587 0.1648

300m 3.0294 2.6719 2.7081 1.2098 1.3569 1.5487 0.4797

0-300m 3.1334 2.9232 2.9131 0.8812 0.8824 0.9752 0.6403

* Color of each row indicates the rank of model performance, from best to worst (best, 2nd,

3rd, 4th, 5th, 6th and worst), among the seven cases.

# Rank here is based on absolute value.

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and the modeled SST are less affected by subsurfacevertical motion. All model cases presented STDs of∼0.7, CCs of >0.96, and RMSDs of ∼0.40 (A5∼G5 inFig. 4) at surface. At other depths, all cases cannotperform as well as at the surface. Without any verticalvelocity, case A presents poor agreements with observa-tion. For instance, CCs at −150 m and −300 m are evennegative. For case B with WBK (1.4 × 10−7 m s−1) on-ly, slightly amended CC and smaller RMSD areachieved at −50 m, while at −150 and −300 m, thetemperature variation is even underestimated comparedwith case A. In case C including both WBK and WEP,the performance at −50 m is the best among all thecases (Table 1). However, cases A to C present largebias from the observation (3.13, 2.92, and 2.91 °C for0–300 m, respectively). Case D, incorporating WBKand WEK, generally improves the model performancecompared with the former three cases. Most of the sta-tistics in case E present best values (e.g., RMSD andCC for 0–300 m, Table 1) among cases A to F. Inparticular, when the WBK of 1.0 × 10−6 m s−1 is in-corporated, case G shows better overall performancecompared with case E (best statistics for all 0–300 m).

In case G, the temperature variation from 2007 to 2014 atSEATS are reproduced reasonable (Fig. 5a, b). On the otherhand, the Argo-observed (Fig. 5d) and modeled salinity(Fig. 5c) also shows comparable variation. The vertical heav-ing of 34.3 isohaline suggests that the vertical advection of

saltier water is well simulated, while the subsurface salinitymaximum is retained reasonably.

3.2 Discussion

The spatio-temporal distribution of DoI was re-constructedfrom Argo observation (Fig. 3d). We decomposed thespatio-temporal variability of DoI (Fig. 3d) by utilizing anempirical orthogonal function (EOF) analysis (Figs. 2c and3a). The three leading modes count for 95.5% of the totalvariance. The variation of DoI is dominated by EOF1(82.2% of the total variance) at the SEATS station below themixed layer (Wong et al. 2007a). The corresponding principalcomponents (PCs) can be seen in Fig. 3a, in comparison withthe time series of SLA in Fig. 3b. In terms of temporal vari-ability, PC1 correlates well with the altimetry-observed SLA(CC = −0.78, over 99% significance). It was previously re-vealed that the thermocline oscillation in the northern SCScorrelated well (CC = −0.462) with sea level height (Liuet al. 2001). Their conclusion presents consistency with cur-rent study.

The magnitude of DoI presents monotonic increase withrespect to depth (Fig. 2c). This is due to the monotonouslydiminished density gradient below −100 m (Fig. 2a), whichamplifies the signal of displacement at depth [Eq. (4)]. Thevertical distribution of the amplitude of DoI (Fig. 3d) is con-sistent with the larger EOF1 value at depth (Fig. 2b). Theunderlying physics of the DoI variation are baroclinic modes.

Fig. 4 Taylor diagramsummarizing the performance oftemperature simulations (labeledwith different letters) at −5 m (reddots), −50 m (magenta dots),−150 m (green dots), −300 m(blue dots), and those for alldepths above −300 m (blackdots). All RMSDs and STDswerenormalized by dividing the STDof Argo observationaltemperature at each depth. TheA150, A300, B150, B300, andD300 points are out of the figuredomain since they have negativeCCs

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The vertical structures of the EOF modes correspondwith the three leading baroclinic modes of vertical dis-placement, where the first mode dominates (Siegel et al.1999). The first baroclinic mode can be diagnosed froma free-surface, immiscible, and two-layered water col-umn (Cushman-Roisin and Beckers 2011; Gill 1982),where the fluctuation of isopycnic can be estimated with

DoI≈−gHg0H2

SLA≈−ρwHΔρH2

SLA ð8Þ

where the density difference between two layers, Δρ, is∼4 kgm−3, and ρw is a reference density of 1024 kgm

−3, whileH and H2 are the thickness of the whole water column(3800 m) and the depth of the lower layer (3500 m), respec-tively. Given these values, Eq. (8) provides a coefficient of

∼278 which is consistent with the magnitude of α (Fig. 2b). Itis noticeable that the estimated DoI

SLA ratio in Eq. (8) is propor-

tional to − 1ΔρH2

. As the depth goes deep, Eq. (8) predicts an

amplifying ratio of DoI to SLA, which is also consistent withthe profile of α in Fig. 2b.

Generally, the first baroclinic mode reveals the verticalheaving of the main thermocline (Liu et al. 2001; Siegelet al. 1999). At the intraseasonal time scale, the first baroclinicmode is majorly controlled by mesoscale eddy activities (Liuet al. 2001). Hence, the estimation of WEP from SLA, whichis shown in Eq. (5), provides a statistical method to incorpo-rate the vertical motion due to mesoscale eddies with highsignificance. Since SLA has better temporal coverage com-pared with Argo data, the time-series ofWEP can be extendedto pre-Argo era. In addition, this method can also partiallyovercome the limitation of in situ data in the SCS.

Fig. 5 Time-depth maps of case G (a, c) and Argo observed (b, d)temperature (unit: °C) and salinity (unit: PSU). Cyan contours in a, bindicate the mixed layer depth (defined by the depth of −0.5 °C from

surface temperature). Gray dots show the Argo stations, while the datawas re-sampled to regular monthly points. In c, d, bold contours are 34.3PSU isohaline, while the interval is 0.2 PSU

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By comparing case C (with WEP) with case B (withoutWEP), or case E (with WEP) with case D (without WEP),the former cases generally show better skills in reproducingthe temperature variability pattern (higher CCs and STDscloser to unity) below the surface. This indicates that the me-soscale eddy activity, which can be well represented by WEP,is the major process driving the temporal fluctuation oftemperature.

On the other hand, the incorporat ion of WEK(1.4 × 10−7 m s−1) generally improves the model (Table 1,case B vs case D), except at −50 m. However, the negativebias (case D, Table 1) near the surface suggests that the WEKmay be stronger than that required for vertical advection,resulting in the over-cooling. By comparing case E with caseD, it is suggested that the Ekman pumping alone may not beresponsible for the variability of temperature at the SEATSstation.

Considering all the three processes, case E presentsoutstanding performance among the first six model cases.Moreover, case G shows the best model skills in all cases,characterized with best STD, CC, RMSD, and overall biasfor 0–300 m (Fig. 4, also can be seen from those inmagenta in Table 1). In particular, case G largely reducesthe overall bias compared with case E (0.6403 vs0.8812 °C). All of these indicate that the method appliedhere is appropriate to quantify the vertical motion at theSEATS station.

In terms of WBK, with an assimilated model, Xu and Oey(2014) estimated a basin-wide upwelling of 1.0 Sv(1.0 × 106 m3 s−1) from the water mass imbalance (i.e., moreinput, 3.4 Sv, than output of 2.4 Sv) in the intermediate layer.The corresponding upwelling rate is ∼0.6 × 10−6 m s−1 ifd i v i d e d b y t h e a r e a o f SCS a t 5 00 m dep t h(∼1.57 × 1012 m2). Chen et al. (2001) deduced an upwellingrate of 1.7 × 10−6 m s−1 (55 m per year) from water mass ageevidence in the intermediate layer, which was also adopted byDai et al. (2009). Overall, WBK in case G (1.0 × 10−6 m s−1)falls within the values in previous studies. Case G suggeststhat this value better represents the intensity of the intermedi-ate layer upwelling. Nevertheless, the circulation in the inter-mediate layer is unclear yet and merits further study (Xu andOey 2014).

It is noticeable that the model underestimated themixed layer depth, especially in winter (Fig. 5a, b).Possible reasons are as follows: first, due to the simplephysics in the 1D model, the vertical shear from thecirculation is absent, which also contributes to turbulentmixing. Secondly, other sophisticated processes, such aswind-eddy interaction, nonlinear Ekman pumping, orsubmesoscale activities, may also play a role in verticalmixing. Last, the turbulent closure scheme was general-ly tuned in the condition where vertical advection isabsent (Large et al. 1994), which may also result in

underestimation of the mixed layer depth, as well asthe temperature variance.

The comparisons between modeled and Argo-observed sa-linity (Fig. 5c, d) also support the capability of currentmethods in simulating the 1D vertical processes. The salinityprofiles are characterized with subsurface salinity maximumwater saltier than 34.6 PSU. The source of this water can betracked back to the high-salinity North Pacific Tropical Water(Qu et al. 2000). Moreover, the vertical heaving of isohalines,as well as the relative stability of high salinity water, suggestsa quasi-equilibrium state counterbalanced by advection anddiffusion processes.

4 Conclusion

Three types of vertical velocities are included in 1Dsimulation at the SEATS station in the SCS. The verti-cal velocities considered here are WEK, WEP, andWBK. The WEK was determined from classicalEkman pumping vertical velocity and a presumed pro-file. The WEP component was yielded from the timechange rate of DoI, while the DoI was determined bythe least-squares regression between SLA and Argo-based DoI. The underlying physics are reconciled withthe first baroclinic mode of vertical displacement. TheWBK was estimated from the long-term heat balance.The sensitivity experiments suggest that the case withall three vertical velocities presents the best performancein modeling the temperature variation. The quantifica-tion of the three vertical velocities is universal andhence can be applied in the simulation of other stations.

Indeed, all the model cases underestimate the variance at alldepths, which may be due to the additional variation of thereconstructed Argo data in the 2° by 2° area compared withstationary data. This also implies that the temperature fluctu-ation in association with other processes, such as wind-eddyinteraction, quasi-geostrophic pumping, and nonlinear Ekmanpumping, can incontrovertibly induce a large variability.Neglecting these processes might also contribute to the under-estimation of temperature variability. However, incorporationof these processes is out of scope of this study, which can beconsidered in the 3D model.

Acknowledgements This study was supported by grants2013CB955704 from the National Basic Research Program and by grantsU1305231, 41476005, 41476007, and 41630963 from the NaturalScience Foundation of China. W. L. was supported by the ChinaScholarship Council during his visit to University of Delaware (No.201406310071). We thank two anonymous reviewers for their commentsthat improved the manuscript.

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Appendix A. Model configurations

The governing equation of 1D ROMSmodel in this study canbe written as

∂u∂t

þ ∂ wpreu� �∂z

−u∂wpre

∂z¼ fvþ ∂

∂zAkv

∂u∂z

� �þ τx ðA:1Þ

∂v∂t

þ ∂ wprev� �∂z

−v∂wpre

∂z¼ −fuþ ∂

∂zAkv

∂v∂z

� �þ τy ðA:2Þ

∂p∂z

¼ −ρg ðA:3Þ

∂T∂t

þ ∂ wpreT� �∂z

−T∂wpre

∂z¼ ∂

∂zAkt

∂T∂z

� �þ FT ðA:4Þ

∂S∂t

þ ∂ wpreS� �∂z

−S∂wpre

∂z¼ ∂

∂zAks

∂S∂z

� �þ FS ðA:5Þ

where u, v, andwpre are the three components of velocity; TandS are temperature and salinity; andAkv, Akt,, andAks are the eddyviscosity coefficients for momentum, temperature, and salinity,respectively; and ρ and p are the density and pressure. τx, τy, FT,and FS are the surface x-momentum, y-momentum (i.e., windstress), net heat flux, and net fresh water flux, respectively.

The model solved the top 1000 m layer of the SEATSstation, with 25 S-layers at vertical. Daily atmospheric fluxes,which were calculated from the bulk formulations (Liu et al.1979), were applied at the surface. The forcing includes windstress, downward shortwave radiation, downward longwaveradiation, air temperature, air pressure, precipitation rate, andrelative humidity, acquired from the National Centers forEnvironmental Prediction/National Center for AtmosphericResearch (NCEP/NCAR) Reanalysis data (http://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanalysis.html, Kalnayet al. 1996) distributed by the NOAA/OAR/ESRL PSD,Boulder, Colorado, USA (http://www.esrl.noaa.gov/psd/).The original data has a resolution of quarter degree. Thevertical turbulent mixing was closured by a K profileparameterization (KPP) scheme (Large et al. 1994). TheKPP scheme estimates eddy viscosity within the boundarylayer as the production of the boundary layer depth (hsbl), aturbulent velocity scale (wx), and a dimensionless third-orderpolynomial shape function G [Eq. (A.6)].

Akv ¼ hsblwxG ðA:6Þ

Beyond the surface boundary layer, the KPP scheme in-cludes vertical mixing collectively contributed by shearmixing, double diffusive process, and internal waves.

TheMellor-Yamada level 2.5 turbulent closure schemewasalso tested (Mellor and Yamada 1982). There is no significantdifference between the temperature in two models; hence, thediscussion here is based on the KPP runs. The temperature andsalinity were relaxed toward the climatological states from the

World Ocean Atlas (WOA 2013, https://www.nodc.noaa.gov/OC5/woa13/) with a nudging time (t = 4 + 16ez/100 inyears) following Li et al. (2015) and t = 7 days at −1000 m.The model was initialized with the temperature and salinityprofiles of climatological July, which was interpolated fromWOA 2013 data. The model was cycled from 2002 to 2014.From our experience, due to its simple physics, a quasi-steadystate can be achieved within 5 years; hence, it is adequate toanalyze the outputs with the data from the second cycle.

Appendix B. Implement of the vertical advectionterm

For a specific tracer q (momentum, temperature, or salinity),considering only the nonlinear terms, the tracer equation is

∂q∂t

þ u∂q∂x

þ v∂q∂y

þ w∂q∂z

¼ 0 ðB:1Þ

Combining Eq. (B.1) with the continuity equation

∂u∂x

þ ∂v∂y

þ ∂w∂z

¼ 0 ðB:2Þ

we yield

∂q∂t

þ ∂ uqð Þ∂x

þ ∂ vqð Þ∂y

þ ∂ wqð Þ∂z

¼ 0 ðB:3Þ

Equation (B.1) is in advective form while Eq. (B.3) is theso-called conservative form of tracer equation. In ROMS, aconservative form was applied in order to conserve the tracermass within any grid (Shchepetkin and McWilliams 2005).However, in this study, due to the vertical velocity and theabsence of horizontal divergence in the 1D model, the conti-nuity equation Eq. (B.2) is invalid. For the sake of consistencywith the original ROMS code, 1D tracer equation was modi-fied by

∂q∂t

þ ∂ wpreq� �∂z

−q∂wpre

∂z¼ 0 ðB:4Þ

where wpre is the vertical velocity. The third termwas added inthe ROMS subroutines step3d_t.F and step3d_uv.F. The codesare available upon request to the corresponding author(ywjiang@xmu.edu.cn).

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