Contribution of Deep Vertical Velocity to Deficiency of Sverdrup Transport in the Low-Latitude North Pacific

Kun Zhang aCAS Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, and Center for Ocean Mega-Science, Chinese Academy of Sciences, Qingdao, China
bLaboratory for Ocean and Climate Dynamics, Laoshan Laboratory, Qingdao, China

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https://orcid.org/0000-0001-9918-6690
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Qiang Wang cKey Laboratory of Marine Hazards Forecasting, Ministry of Natural Resources, Hohai University, Nanjing, China
dCollege of Oceanography, Hohai University, Nanjing, China

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Baoshu Yin aCAS Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, and Center for Ocean Mega-Science, Chinese Academy of Sciences, Qingdao, China
bLaboratory for Ocean and Climate Dynamics, Laoshan Laboratory, Qingdao, China
eUniversity of Chinese Academy of Sciences, Beijing, China

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Dezhou Yang aCAS Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, and Center for Ocean Mega-Science, Chinese Academy of Sciences, Qingdao, China
bLaboratory for Ocean and Climate Dynamics, Laoshan Laboratory, Qingdao, China
eUniversity of Chinese Academy of Sciences, Beijing, China

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Lina Yang fCollege of Ocean and Meteorology, Guangdong Ocean University, Zhanjiang, China

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Abstract

Deep vertical velocity is a critical factor causing deficiencies in Sverdrup theory. However, few studies have focused on its influence in the low-latitude western Pacific. Through multiple analyses of observational, reanalysis, and simulation data, this study explored the contribution of deep nonzero vertical velocity to the Sverdrup transport inaccuracy in the low-latitude North Pacific. The vertical velocities inducing relatively small non-Sverdrup transport exist within 1500–2500 m, which exhibit similar patterns with opposite values to the south and north of 13°N. The zonally integrated meridional volume transport associated with these vertical velocities displays nonnegligible dipolar zonal bands west of approximately 150°W. The positive and negative transport bands, centered at 11° and 17°N, can reach an amplitude of approximately 8.0 Sv (1 Sv ≡ 106 m3 s−1) when integrated from the eastern boundary to 140°E. On average, such integrated meridional transport makes up roughly half of the prominent Sverdrup transport discrepancies in the central-western Pacific. Further investigation indicated that the spatial pattern of these vertical velocities is modulated by ocean topography and deep meridional currents. Moreover, a near-global test suggested that the meridional non-Sverdrup transport related to deep vertical velocity is widespread and undergoes remarkable multidecadal variation. This study reveals the disruptive role of deep vertical velocity in disturbing the Sverdrup balance and emphasizes the consideration of its long-term variation when diagnosing wind-driven circulation changes using Sverdrup theory.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Kun Zhang, kzhang@qdio.ac.cn

Abstract

Deep vertical velocity is a critical factor causing deficiencies in Sverdrup theory. However, few studies have focused on its influence in the low-latitude western Pacific. Through multiple analyses of observational, reanalysis, and simulation data, this study explored the contribution of deep nonzero vertical velocity to the Sverdrup transport inaccuracy in the low-latitude North Pacific. The vertical velocities inducing relatively small non-Sverdrup transport exist within 1500–2500 m, which exhibit similar patterns with opposite values to the south and north of 13°N. The zonally integrated meridional volume transport associated with these vertical velocities displays nonnegligible dipolar zonal bands west of approximately 150°W. The positive and negative transport bands, centered at 11° and 17°N, can reach an amplitude of approximately 8.0 Sv (1 Sv ≡ 106 m3 s−1) when integrated from the eastern boundary to 140°E. On average, such integrated meridional transport makes up roughly half of the prominent Sverdrup transport discrepancies in the central-western Pacific. Further investigation indicated that the spatial pattern of these vertical velocities is modulated by ocean topography and deep meridional currents. Moreover, a near-global test suggested that the meridional non-Sverdrup transport related to deep vertical velocity is widespread and undergoes remarkable multidecadal variation. This study reveals the disruptive role of deep vertical velocity in disturbing the Sverdrup balance and emphasizes the consideration of its long-term variation when diagnosing wind-driven circulation changes using Sverdrup theory.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Kun Zhang, kzhang@qdio.ac.cn

1. Introduction

Ocean circulation regulates global climate and marine ecosystems by storing and redistributing mass and energy (e.g., carbon, freshwater, nutrients, and heat). Therefore, theories attempting to explain large-scale, time-averaged ocean circulation have attracted substantial attention and have been discussed for several decades. Under a linear dynamic framework, Sverdrup (1947) established a simple yet powerful balance [the Sverdrup balance (SB)] between meridional transport in the interior ocean and local wind stress curl without acquiring detailed information on baroclinicity. As a cornerstone theory of physical oceanography, SB depicts a straightforward map of upper wind-driven circulation (Godfrey 1989; Pedlosky 1996; Huang 2009; Bull et al. 2020; Chen et al. 2022; Peng et al. 2022).

Estimating the transport of widespread western boundary currents (WBCs), characterized by their narrow and fast-flowing nature, presents a challenge due to limited observations. In the Pacific, SB provides a rough yet convenient approach to approximate WBC transport by balancing the interior transport. Notably, it is of great significance to utilize this theory to estimate the WBCs in the low-latitude North Pacific (i.e., the southward Mindanao Current and the northward Kuroshio), which critically modulate ocean dynamics and global climate (Wu et al. 2012; Hu et al. 2015). To date, despite the availability of abundant hydrographic and reanalysis data, Sverdrup theory remains a valuable tool for assessing the impacts of wind changes on ocean circulation and associated WBCs, particularly on decadal to multidecadal time scales and under climate warming scenarios (e.g., McPhaden and Zhang 2002; de Boer and Johnson 2007; Thomas et al. 2012, 2014; Zhang et al. 2017; Beadling et al. 2018; Wang and Wu 2018; Y. Zhang et al. 2020; H. Yang et al. 2022).

Continuous efforts have been made to examine the accuracy of SB. Limited by insufficient measurements, early validations usually analyzed one-time observations along several transects in the tropical or subtropical Atlantic and Pacific (Leetma et al. 1977; Meyers 1980; Wunsch and Roemmich 1985; Böning et al. 1991; Schmitz et al. 1992; Hautala et al. 1994). These results indicated that SB is applicable in the interior but loses adequacy in the western regions. With the advent of the Argo project (Roemmich et al. 2004; Johnson et al. 2022) and high-performance oceanic reanalysis datasets (K. Zhang et al. 2020), reliable descriptions of steady oceanic general circulation become attainable, enabling the validation of Sverdrup theory at basin to global scales. Wunsch (2011) conducted a global pointwise assessment of SB using an ocean synthesis of ECCO-GODAE and found acceptable discrepancies in the tropical Pacific. Similarly, a global pointwise evaluation by Gray and Riser (2014) using Argo data demonstrated the promising performance of SB in the low-latitude Pacific.

Nonetheless, pointwise evaluation alone of SB is insufficient. Small discrepancies at individual points could still lead to failure when testing integrally. For instance, despite the acceptable pointwise evaluation in the low-latitude North Pacific, the zonally integrated meridional Sverdrup transport remarkably overestimates the upper-ocean circulation in the western regions (Zhang et al. 2013; Yuan et al. 2014; Yang and Yuan 2016). The Sverdrup transport errors exceeding 10.0 Sv (1 Sv ≡ 106 m3 s−1) occur as zonal bands west of the date line and immediately to the north and south of the North Equatorial Current bifurcation latitude (NECBL). The reasons for these discrepancies remain controversial. Yuan et al. (2014) argued that nonlinearity is an important candidate by excluding wind stress uncertainty through an analysis of dynamically consistent simulation data. Conversely, Zhou et al. (2019) found that such discrepancies vary drastically under different wind products and that the integrated Sverdrup transport derived from QSCAT wind has the smallest error.

Another important source of non-Sverdrup transport is the vertical velocity (denoted as w) in the deep oceans, which was assumed to be zero at a certain depth in Sverdrup (1947). However, previous studies have suggested the low possibility of such deep no-motion layers (Wunsch 2011; Gray and Riser 2014). The vertical distributions and changes in heat content and salinity also imply the presence of vertical motions in the deep oceans (Liang et al. 2015, 2017a; Liu et al. 2019). Several studies have found that bottom topography and topography-induced vertical velocity can upset SB (Wunsch and Roemmich 1985; Vivier et al. 1999). The bottom pressure torque and the joint effect of baroclinicity and relief (JEBAR) can impose significant limitations on the applicability of SB (Marchuk et al. 1973; Stewart et al. 2021). An estimation by Pedlosky (1996) suggested that the bottom w generated under weak horizontal currents with a magnitude of 10−3 m s−1 and a regular topographic slope is comparable to the surface Ekman pumping velocity. Such intense bathymetry-related w, which may induce non-Sverdrup transport, can be detected from the seafloor to several kilometers above it (Liang et al. 2017b). Furthermore, an analysis based on ECCO-GODAE indicated that w-related (selected at 1400 m) non-Sverdrup transport is approximately twice as large as that induced by nonlinearity (Thomas et al. 2014).

However, limited studies have focused on the influence of deep vertical velocities in the low-latitude western Pacific, where significant Sverdrup transport discrepancies have been noted. One important reason is that oceanic vertical velocity is weak, ranging from 10−7 to 10−5 m s−1, and cannot be directly measured at large spatial scales (Liao et al. 2022a,b). Fortunately, over the past several decades, the lack of vertical velocity data has been ameliorated by the explosive increase in oceanic simulation and reanalysis data (Stammer et al. 2016). Therefore, this study evaluated the contribution of deep w to the deficiency of Sverdrup transport in the low-latitude North Pacific through combined analyses of multiple oceanic and atmospheric datasets. The following questions were explored: From an integration viewpoint, at which depth does vertical velocity cause the smallest non-Sverdrup transport? What are the spatial characteristics of such deep vertical velocity? Can it induce remarkable meridional volume transport? If so, to what extent does the w-related meridional transport contribute to the Sverdrup transport discrepancy? What are the possible factors regulating the distribution of the deep vertical velocity?

The remainder of this paper is organized as follows. The data and methods are described in section 2. The main results are presented in section 3, followed by a discussion in section 4. Finally, a summary is presented in section 5.

2. Data and methodology

a. Data

Multiple data of surface wind, hydrographic or satellite observations, and oceanic reanalysis or simulation were analyzed to evaluate the effects of vertical velocity. To mitigate uncertainties arising from model bias and observational errors, we conducted analyses using ensemble wind and oceanic vertical velocity data (Zhou et al. 2019; Liao et al. 2022a). Most datasets have time coverages longer than 20 years, whose climatological averages can be used to diagnose steady ocean circulation (Wunsch 2011). The details are as follows.

1) Surface wind products

Five 10-m wind datasets, including two coarse- and three fine-resolution datasets (see Table 1), were employed to calculate Ekman and Sverdrup transport. The two coarse-resolution datasets are JRA-55 (Kobayashi et al. 2015; https://jra.kishou.go.jp/JRA-55/) and NCEP–DOE Reanalysis 2 (NCEP2; Kanamitsu et al. 2002; https://psl.noaa.gov/data/gridded/data.ncep.reanalysis2.html). The three fine-resolution datasets are the Cross-Calibrated Multi-Platform (CCMP; Atlas et al. 2011; https://www.remss.com/measurements/ccmp), ERA-Interim (Simmons et al. 2007; http://apdrc.soest.hawaii.edu), and QSCAT (Ricciardulli and Wentz 2015; https://www.remss.com/missions/qscat).

Table 1.

Summary of 10-m wind products.

Table 1.

2) Hydrographic and satellite observations

Temperature and salinity from Argo and the World Ocean Atlas 2018 (WOA18) were used to calculate geostrophic currents. The monthly gridded Argo data from 2004 to 2018 were generated by optimal interpolation with a horizontal resolution of 1° × 1° and 58 vertical levels above 2000 m (Roemmich and Gilson 2009; http://sio-argo.ucsd.edu). WOA18 provides 0.25° × 0.25° objectively analyzed climatological temperature and salinity with 102 vertical layers in the upper 5500 m (https://www.ncei.noaa.gov/access/world-ocean-atlas-2018/). Two state-of-the-art satellite products, the 1/3° × 1/3° Ocean Surface Current Analysis Real-Time (OSCAR; Dohan 2017; http://www.oscar.noaa.gov) and 1/4° × 1/4° AVISO (https://data.marine.copernicus.eu/products), were used for data validation.

3) Oceanic reanalysis and simulation data

Vertical velocities from five datasets, including three reanalyses and two simulations (available from the Asia–Pacific Data Research Center; APDRC; http://apdrc.soest.hawaii.edu), were examined (Table 2). The three reanalyses are the Estimating the Circulation and Climate of the Ocean, Phase II (ECCO2; Menemenlis et al. 2008), the NCEP Global Ocean Data Assimilation System (GODAS; Behringer et al. 1998), and the ECMWF Ocean Analysis/Reanalysis System 3 (ORAS3; Balmaseda et al. 2008). The two simulation data are the Ocean General Circulation Model for the Earth Simulator (OFES; Sasaki et al. 2008) with the two resolutions of 0.1° × 0.1° (denoted as OFES1) and 0.5° × 0.5° (denoted as OFES5). Compared to reanalysis data, model simulations are more dynamically consistent by precluding the impacts of data assimilation and wind-forcing uncertainty. Related analyses using simulation data can clarify the influence of vertical velocity more directly. In addition, ocean bathymetry from the 5-min gridded ETOPO5 (https://www.eea.europa.eu/data-and-maps/data/world-digital-elevation-model-etopo5) was used to explore the impacts of topography on deep vertical velocity formation.

Table 2.

Summary of vertical velocity in five oceanic products.

Table 2.

b. Methodology

1) Meridional Sverdrup transport from a zonally integrated view

In a linear regime with low Rossby and Ekman numbers, the momentum and continuity equations governing the stationary interior ocean are expressed as follows (Sverdrup 1947; Pedlosky 1996):
ρfk×u=p+τ/z,
u/x+υ/y+w/z=0,
where the notations are conventional with u = (u, υ) being horizontal velocity. Variables ρ, f, and p represent seawater density, the Coriolis parameter, and pressure, respectively. After taking the vertical curl component of Eq. (1a) and subsequently integrating it from a certain depth H to the surface, we obtain
βV=f(w0wH)+curlz(τ0τH),
where β is the meridional gradient of f, curlz refers to the vertical component of the curl, and τ0 = (τx, τy) denotes wind stress. If bottom stress is negligible and the vertical velocities at the surface and H are zero, SB at an individual point is obtained as follows:
βV=curlzτ0/ρ0.
The zonally integrated meridional Sverdrup transport (VS, named S) at an arbitrary longitude x incorporates geostrophic transport (VG; named MGT) and Ekman transport (VE, named E):
1ρ0βxExCurlzτ0dx=xExH0υgdzdx+(1ρ0fxExτxdx),
where xE is the eastern boundary. The left term is VS, and the two right terms are VG and VE. In this study, VG was calculated using observational hydrographic data from Argo and WOA18. If neglecting the inaccuracy of VE, the Sverdrup transport discrepancy is estimated as the difference of VSVE and VG, of which VS and VE are obtained from multiple wind products. Notably, VS, VG, VE, and SE are integration variables. For brevity, the meridional volume transport integrated from the eastern boundary to various longitudes is hereinafter referred to as the integrated meridional transport. Therefore, on the western side of the ocean, these zonally integrated metrics reflect basinwide changes.

2) Meridional volume transport related to deep vertical velocity

According to Eqs. (2) and (3), the integrated meridional volume transport related to wH can be calculated as follows:
Vw=fβxExwHdx.
The term Vw was obtained using the vertical velocity from the five selected oceanic datasets. By comparing VS − VE − VG and Vw, the contribution of deep vertical velocities to the Sverdrup transport discrepancy can be estimated. Similarly, the Sverdrup discrepancy (VS − VE − VG) and Vw are zonal cumulative variables as well.

3) Wind stress derived from 10-m wind

For a given 10-m wind speed (V10), the wind stress magnitude τ is calculated using the bulk parameterization formula:
τ=ρaCDV102,
where ρa is the air density and CD is a dimensionless drag coefficient. To reduce uncertainty in wind stress, CD was estimated using three different schemes (i.e., Garratt 1977; Large and Pond 1981; Foreman and Emeis 2010).

4) Absolute geostrophic currents (AGCs)

Using Argo and WOA18 hydrographic data, the AGCs beneath 400 m were calculated using the P-vector approach (Chu 1995). The P vector determines AGCs based on the intersections of potential vorticity surfaces and isopycnals. The AGCs above 400 m, where the conservation between potential vorticity and density may fail, were obtained through a traditional dynamic height calculation using the referenced velocity at 400 m derived from the P vector.

5) Pattern correlation and its significance test

The Pearson correlation coefficient was used to quantify the pattern correlation between two variables. The statistical significance of the correlation was examined by the t test. The effective sample size Ne, instead of sample size N, was used in significance tests and was estimated following Bretherton et al. (1999):
Ne=N×(1r1,x×r1,y)/(1+r1,x×r1,y),
where r1,x and r1,y are the lag-one autocorrelation coefficients of the two series.

3. Results

a. Data validation

The vertical velocities in the five ocean products were validated indirectly because of the absence of large-scale observations. In the Pacific region of 5°–25°N, all data resemble similar large-scale circulation with the OSCAR currents (Figs. 1a–f). The dominant surface current is the westward North Equatorial Current (NEC) with a maximum velocity of 0.3 m s−1 (Hu et al. 2020; Huang et al. 2022; Zhang et al. 2022). Eastward flows of the weak North Pacific Subtropical Countercurrent (STCC) and vigorous North Equatorial Countercurrent (NECC) occur near 20° and 5°N, respectively. It is noted that the coarse-resolution data (OSCAR, GODAS, and ORAS3) have limitations in resolving the WBCs, especially the Kuroshio. Despite these limitations, most datasets exhibit consistent current intensity with OSCAR, except for ORAS3, which has stronger NEC and NECC.

Fig. 1.
Fig. 1.

Climatological surface or near-surface currents: (a) OSCAR, (b) ECCO2, (c) GODAS, (d) ORAS3, (e) OFES1, and (f) OFES5, (g) AVISO-derived geostrophic currents, and for the AGCs derived from (h) Argo and (i) WOA18 using the P-vector method.

Citation: Journal of Physical Oceanography 53, 11; 10.1175/JPO-D-23-0006.1

As shown in Fig. 2, the vertical profiles of temperature and potential density along 137°E closely resemble WOA18 and long-term observations from the Japan Meteorological Agency (Oka et al. 2018). In detail, temperature undergoes strong variation from the surface to 700 m. High temperatures exceeding 28°C are confined within the upper 100 m of the tropics, indicating the Pacific warm pool. The isopycnals in all datasets exhibit northward deepening in the lower layers and northward shoaling in the upper 200 m from 18° to 24°N, corresponding to the NEC and the STCC, respectively. Compared with the others, the near-surface temperatures in the OFES outputs are slightly colder, possibly because of the lack of data assimilation.

Fig. 2.
Fig. 2.

Vertical profiles of climatological temperature (shading; °C) and potential density (thin contours; kg m−3) derived from (a) WOA18 and (b)–(f) five oceanic datasets. Bold curves denote the isopycnal of 26.7 kg m−3.

Citation: Journal of Physical Oceanography 53, 11; 10.1175/JPO-D-23-0006.1

Furthermore, the AGCs calculated using the P-vector with Argo and WOA18 were compared with the AVISO-derived geostrophic currents. As illustrated in Figs. 1h and 1i, the climatological AGCs from Argo and WOA18 are nearly identical, featuring the marked westward NEC embedded within 9°–14°N. The AGCs exhibit a pattern similar to that of the AVISO geostrophic currents, although small differences exist. In detail, the AGCs in the Mindanao Dome are more vigorous, and the relevant Kuroshio is not prominent. However, significant disparities exist between the AGCs and near-surface currents from oceanic data and OSCAR. There are significant northward motions in the near-surface currents, which are primarily attributable to the Ekman currents forced by trade winds. Additional reliability tests of the AGCs derived from the P vector, such as comparisons with direct mooring measurements, are available in Yuan et al. (2014) and L. Yang et al. (2022).

b. The Sverdrup transport discrepancy

Before examining the influence of w, the integrated Sverdrup transport, SE, and MGTs were examined. The zonally integrated meridional Sverdrup transport averaged among various wind forcings (15 groups generated by five wind products and three drag coefficient schemes) reveals two opposite zonal bands in the central-western Pacific (Fig. 3a). Near the western boundary, the southern positive and northern negative bands, with magnitudes of 32.0 and −25.0 Sv, are centered at 10° and 18.5°N, respectively. This pattern reflects the stronger Mindanao Current and weaker Kuroshio, considering the WBCs as compensating flows. Regarding SE, it displays weak positive (a magnitude of ∼10.0 Sv) and strong negative (approximately −30.0 Sv) zonal bands to the south and north of 12.0°N, respectively (Fig. 3b). As shown in Figs. 3d and 3e, the MGTs derived from Argo and WOA18 are similar, except for a few small-scale signals in the latter. They are both negative to the west of the date line.

Fig. 3.
Fig. 3.

Mean zonally integrated meridional (a) Sverdrup transport and (b) SE calculated from multiple wind stress generated by five wind products (NCEP2, JRA55, ERA-Interim, QSCAT, and CCMP) and three drag coefficient schemes (Garratt 1977; Large and Pond 1981; Foreman and Emeis 2010). (e),(f) The mean Sverdrup transport discrepancy represented by SE minus (c) Argo-derived or (d) WOA18-derived MGTs, where the integration depth for calculating MGTs is selected at 1900 m. The gray contours in (a),(b) and (e),(f) denote the relevant standard deviations.

Citation: Journal of Physical Oceanography 53, 11; 10.1175/JPO-D-23-0006.1

If SB is accurate, SE should match the MGTs without any discrepancies. However, compared with the positive signals of SE in the western Pacific from 7° to 12°N, the negative MGTs are much weaker and even reach zero. Here, the integration depth for calculating MGTs is 1900 m and the reason for selecting this depth will be clarified in the next subsection. Moreover, although both MGTs and SE show prominent negative signals north of 15.0°N, the former has weaker intensity. Such differences indicate the existence of Sverdrup transport discrepancies. The Sverdrup transport discrepancies based on Argo and WOA18 MGTs are shown in Figs. 3e and 3f. A basin-scale positive band occurs over 6°–15°N. Its amplitude increases with zonal integration and ranges from 5.0 to 18.0 Sv near the Philippine coast, accounting for 30%–60% of the integrated Sverdrup transport. To the north of 15°N, a narrow weaker negative band exists, which ranges from −8.0 to −3.0 Sv in the west. In comparison, the relevant integrated Sverdrup transport is from approximately −25.0 to −10.0 Sv. The dipolar bands to the north and south of 15°N are consistent with the results of Zhang et al. (2013) and Yuan et al. (2014), although their Sverdrup transport discrepancy is defined contrarily as MGT minus SE.

The uncertainties in the integrated Sverdrup transport and SE induced by wind forcing were assessed using relevant standard deviations (STDs). For the integrated Sverdrup transport, the STDs are small in most areas. Relatively large STDs of ∼3.0 Sv occur in the western Pacific. In the case of SE, the pattern of STDs is similar but slightly larger. Particularly, STDs greater than 6.0 Sv are embedded within a small band west of the date line and over 6°–10.0°N. Figure S1 in the online supplemental material indicates that these uncertainties are primarily caused by SE derived from QSCAT wind. In this small band, the QSCAT-derived SE shows zero or even negative signals, whereas the values in the other datasets are positive. Furthermore, because the Hawaiian Islands are difficult to resolve in NCEP2, the STDs near 20°N are larger.

c. Vertical velocity at selected depths

To minimize the effects of vertical velocity, a critical depth H should be determined before evaluation. A chart indicating the depth of minimum |w| is shown in Fig. 4a. The depths of the minimum |w| vary from 1000 to 3000 m over most of the examined domain. In both east–west and north–south directions, these depths present an inverted saddle shape, with deeper depths in the middle. In detail, the deep depths occur in the area of 150°E–140°W, 8°–17°N and near the Philippine coast. Such geographical distribution seems relevant to the seafloor topography, which is deeper from 8° to 17°N in the central-western regions. The critical depths obtained from each product were also checked. Regarding the noisy characteristics of w, an arbitrary 3° × 3° spatial average was employed (referred to as the smoothed data). As shown in Fig. S2, for both the original and smoothed data, the depths of the minimum |w| are similar to the result in Fig. 4a. Hereinafter, vertical velocity refers to the unsmoothed velocity unless described otherwise.

Fig. 4.
Fig. 4.

(a) Depth at which the ensemble mean |w| reaches its minimum and (b)–(d) vertical velocity averaged within the interior Pacific over 5°–10°N, 10°–15°N, and 15°–20°N, respectively. Purple curves in (a) denote the 5000-m isobar in ETOPO5 with deeper regions stippled.

Citation: Journal of Physical Oceanography 53, 11; 10.1175/JPO-D-23-0006.1

The zonal mean depth where w shows the smallest impact was also explored. Figures 4b–d display the vertical velocities averaged over the interior Pacific of 5°–10°N, 10°–15°N, and 15°–20°N, respectively. Overall, the vertical velocities exhibit significant Ekman suctions in the upper layer, peaking at 40–80 m. Compared with the cases over 10°–15°N and 15°–20°N, the upper vertical velocities over 5°–10°N are less consistent, with the GODAS and ORAS3 results showing opposite signs. Large uncertainties below 3500 m occur in all cases, possibly due to differences in model vertical resolution and bottom topography. However, the vertical velocities of 1500–2500 m show less uncertainty and remain comparatively small. In Fig. 4b, the vertical velocities around 1500–2500 m are close to zero. In contrast, the mean vertical velocities below 300 m are positive at 10°–15°N (Fig. 4c) and negative at 15°–20°N (Fig. 4d). Consequently, it is difficult to identify the critical depth without vertical motion in these two bands.

Thus, a depth of ∼2000 m is applicable. To maintain consistency with Yuan et al. (2014), H was set to 1900 m. The patterns of smoothed (unsmoothed) vertical velocities at 1900 m are shown in Fig. 5 (Fig. S3). No vertical interpolation is implemented, and only the vertical velocity nearest the examined depth is shown. Notably, all products exhibit two zonal bands with upward (downward) velocities immediately south (north) of the NECBL. The two bands are pronounced west of 150°W. There is an asymmetry of meridional intensity, with the southern band stronger than the northern one. Despite the prominent similarities among the five products, small differences exist. For instance, the southern positive band in ORAS3 is weaker and occurs at lower latitudes. Figure 6 further displays w averaged over 130°E–100°W. The zonally averaged w shows a dipole pattern with the zero point located around 13°N. The southern pole, centered at 11°N, has a magnitude of 5 × 10−7 m s−1, which is twice that of the northern pole at 17°N.

Fig. 5.
Fig. 5.

Distributions of smoothed vertical velocity (m s−1) at 1900 m: (a)–(e) for five oceanic datasets and (f) for their ensemble mean. The dotted regions in (f) indicate that the velocities show the same sign in at least four datasets.

Citation: Journal of Physical Oceanography 53, 11; 10.1175/JPO-D-23-0006.1

Fig. 6.
Fig. 6.

Ensemble-mean vertical velocity averaged within 130°E–100°W at selected depths: (a) original data and (b) smoothed data. Shadings denote ±1 STD from the mean.

Citation: Journal of Physical Oceanography 53, 11; 10.1175/JPO-D-23-0006.1

The vertical velocities at 1500 and 2500 m also show consistent zonal dipolar bands north and south of the NECBL (Figs. S4 and S5). As illustrated in Fig. 6, the zonally averaged vertical velocities at the three depths show high similarities, with a minimum pattern correlation larger than 0.88 (significant at the 95% confidence level). These slight differences in w are expected to result in similar meridional volume transport patterns. Hence, the analysis based on the vertical velocity at 1900 m is representative. These findings are consistent with those of Thomas et al. (2014). By analyzing ECCO-GODAE, they found an optimal level of 2600 m when evaluating the w-related non-Sverdrup error from 35°S to 35°N from a zonal integration perspective. Moreover, similar performance was observed within 1000–3000 m.

d. Non-Sverdrup transport related to deep vertical velocity

Given the negligible differences among the vertical velocities from 1500 to 2500 m, Vw calculated using the vertical velocity at 1900 m was investigated as an example. Figure 7 shows that the patterns of Vw in all datasets present two contrasting zonal bands, similar to those of w according to Eq. (5). With increasing integration longitude, the two bands become more apparent west of 150°W, reaching a mean amplitude of 8.0 Sv in the western regions. The northward and southward meridional transport bands are located approximately south and north of the NECBL. The southern band is smoother, with one extreme at 11°N. The northern band, especially in the fine-resolution data, exhibits a striation-like structure with two or three extremes. Additionally, a weak negative transport band exists near the southern rim, but it is weaker in ORAS3 or even absent in ECCO2.

Fig. 7.
Fig. 7.

Integrated meridional transport related to the vertical velocity at 1900 m (Sv): (a)–(e) for five oceanic datasets and (f) for their ensemble mean. Black curves represent the lines of zero value. The dotted regions in (f) indicate that Vw shows the same sign in at least four datasets.

Citation: Journal of Physical Oceanography 53, 11; 10.1175/JPO-D-23-0006.1

Considering Vw along 140°E as an example, the dipolar bands in the western Pacific were shown more directly in Fig. 8a. Although small differences exist, the pattern correlations among the five oceanic products still range from 0.64 to 0.91 (Table S1). The mean Vw has one positive extreme at ∼12°N and two marked negative extremes around 15° and 17.5°N. In contrast to the distinct meridional asymmetry of w, the positive and negative extremes of Vw are comparable. The southern extreme reaches 9.0 Sv, slightly exceeding the northern extremes of −7.0 Sv. The alleviated asymmetry of Vw could be attributed to changes of f/β. It increases with poleward shifting in the Northern Hemisphere and thus results in considerable Vw at high latitudes. Vw at depths of 1500 and 2500 m was examined as well, demonstrating similar patterns and intensities (Fig. S5). Given such trivial differences, hereafter, Vw refers to the integrated meridional transport associated with w at 1900 m unless stated otherwise.

Fig. 8.
Fig. 8.

(a) Integrated meridional transport along 140°E related to vertical velocity at 1900 m and (b) its comparison with the corresponding Sverdrup transport discrepancies based on Argo and WOA18 MGTs.

Citation: Journal of Physical Oceanography 53, 11; 10.1175/JPO-D-23-0006.1

For further clarification, a pointwise examination of the w-related meridional transport is depicted in Fig. 9a. West of 150°W, the pointwise w-related non-Sverdrup transport presents southern positive and northern negative signals, which cumulatively contribute to the dipolar Vw near the western boundary. Compared with the values in the central-western Pacific, the pointwise transport values in the east are much weaker or even show reversed signs. The eastern pointwise transport values have trivial or opposing contributions to the integrated Vw in the west. For a quantitative assessment, the w-related meridional transport integrated within every 10° longitude interval was calculated (Figs. 9b,c). For the positive or negative band, the vertical velocities in each longitude interval west of 160°W result in an integrated meridional transport ranging from 0.5 to 1.5 Sv. By contrast, the corresponding values induced by w in the eastern regions are negligible, with the majority approaching zero.

Fig. 9.
Fig. 9.

(a) Pointwise w-related meridional transport calculated in the interpolated 0.25° × 0.25° grid. The w-related meridional transport integrated within every 10° longitude interval is plotted (b) for the average of 10°–12°N and (c) for the average of 15°–17°N. All results are calculated using w at 1900 m. Blue dots, central magenta lines, and error bars denote mean, median, and extreme values, respectively.

Citation: Journal of Physical Oceanography 53, 11; 10.1175/JPO-D-23-0006.1

e. Contribution of Vw to the Sverdrup transport discrepancy

A comparison between Figs. 3 and 7 suggests that Vw varies in phase with the Sverdrup transport discrepancies. The extremes of Vw occur at almost the same locations as those of SE minus MGTs. Compared to the latter, the former has weaker amplitudes over 6°–15°N, but it exhibits comparable intensity to the north. Figure 8b illustrates a comparison of the two integrated terms near the western boundary (specifically at 140°E). At 11°N, Vw reaches an amplitude of ∼10.0 Sv, which accounts for one-half of the Sverdrup transport discrepancies. Between 15° and 20°N, the two terms have comparable amplitudes of around 7.0 Sv. Such extremes of Vw account for approximately 30.0% of the integrated Sverdrup transport at the corresponding locations.

To explore the relationship between Vw and the Sverdrup transport discrepancy, their pattern correlations at various longitudes are shown in Fig. 10. Note that Vw and the transport discrepancy are both one-dimensional latitude-dependent variables when calculating such correlations, which are integrated values from the eastern boundary to each longitude. When integrated within the eastern Pacific, the correlations are either negative or insignificant. In this circumstance, the Sverdrup transport errors cannot be dominated by nonzero vertical velocities. This is consistent with Figs. 9b and 9c, where w-related transport is small in the eastern Pacific. However, as the zonal integration extends into the western Pacific, significant in-phase correlations emerge. In particular, rapid growth of correlation coefficients occurs when the integration longitude shifts westward from 140°W to 160°E. We speculate that the remarkable pointwise Vw in the central-western Pacific (see Fig. 9a) significantly affects the integrated Sverdrup transport errors near the western coast. Similar results can be inferred from Fig. S7, in which Vw and the Sverdrup transport discrepancy at various longitudes and latitudes are plotted.

Fig. 10.
Fig. 10.

Pattern correlations between Vw and the mean integrated Sverdrup transport discrepancies at various longitudes. Thin and bold lines denote the correlations between the Sverdrup transport discrepancies and Vw derived from the five oceanic products and their average. Missing values indicate the existence of land grids along the examined longitude.

Citation: Journal of Physical Oceanography 53, 11; 10.1175/JPO-D-23-0006.1

To quantify the contribution of Vw to the Sverdrup transport discrepancy, we defined a contribution rate γ as follows:
γ=100%×[1|(VSVEVG)Vw|/|VSVEVG|].
In most central-western Pacific regions where the Sverdrup transport discrepancies are greater than 2.0 Sv, Vw is indeed important with positive contribution rates greater than 40% and up to 90% (Fig. 11). The contribution rates in the north (40%–80%) are larger than those in the south (20%–60%). Conversely, in regions with small Sverdrup transport discrepancies, the contribution rates are primarily negative. For instance, negative values exist along 7°N, possibly due to nonlinearity caused by the energetic NECC. The negative values are also found within the NECBL variation region of 13°–16°N. Distinct transitions from negative to positive contribution rates occur at 120°–160°W, highlighting the crucial role of vertical velocities in the central-western Pacific.
Fig. 11.
Fig. 11.

Contribution rate of Vw to the Sverdrup transport discrepancy derived from (a) Argo and (b) WOA18. Regions with Sverdrup transport errors smaller than 2.0 Sv are dotted.

Citation: Journal of Physical Oceanography 53, 11; 10.1175/JPO-D-23-0006.1

f. Possible formation mechanism of deep vertical velocity

It is important to clarify the formation of the dipolar vertical velocities in the central-western basin since the associated Vw remarkably contributes to the Sverdrup transport errors. As mentioned in section 3b, the w distribution appears to be related to ocean topography. Liang et al. (2017b) also stated that topographic controls are dominant for vertical velocity in deep oceans, which can show influence from the seafloor to even 3000 m above it. The bottom vertical velocity along bathymetry can be expressed as
wb=ubηbx+υbηby,
where η represents water depth and the subscript b denotes the sea bottom.

To understand the formation of deep w, both ocean topography and deep currents should be analyzed. Since Vw is a zonally integrated variable, only the interaction between topography and deep meridional currents was analyzed. Note that deep zonal currents can also cause meridional transport via topographically induced vortex stretching. However, such pointwise meridional transport anomalies on the east and west sides of a topographic slope are often opposite and may cancel each other out during zonal integration or averaging. Meridionally, especially in the central-western basin, shallow bathymetries represented by submerged plateaus and island chains occur near the southern and northern edges (Fig. 12a). In contrast, deep bathymetries are located in the middle of 10°–16°N. The relevant zonally averaged depth exhibits a U-like shape, with the deepest value located at 13°N (Fig. 12b). This location coincides with that of zero vertical velocity, as shown in Fig. 5. Moreover, the U-shaped topography occurs primarily within 150°E–150°W, where the two zonal w bands are remarkable.

Fig. 12.
Fig. 12.

Relation between ocean topography and deep vertical velocity: (a) topography from ETOPO5; (b) zonally averaged topography; (c) zonally averaged vertical velocities at selected depths (mean of the five oceanic data); (d) standardized zonally averaged meridional gradient of bathymetry (red line) and vertical velocity at 4000 m. Zonal averages are conducted within 140°E–100°W.

Citation: Journal of Physical Oceanography 53, 11; 10.1175/JPO-D-23-0006.1

These findings suggest the topographic control of vertical velocities from the seafloor to 2000 m. To clarify this, we checked the vertical velocities at the three selected depths of 1900, 3000, and 4000 m. As the bottom bathymetries in the five oceanic products are not consistent, w at 4000 m was treated as a proxy for wb. Although w at 4000 m is noisy, significant pattern correlations between w at 1900 and 3000 m with w at 4000 m still exist, showing values of 0.65 and 0.66, respectively (Fig. 12c). This suggests that the vertical velocities between 1900 and 3000 m are affected by wb. As illustrated in Fig. 12d, the zonally averaged vertical velocity at 4000 m exhibits meridional variations opposite ∂ηb/∂y, with a correlation of −0.55. Despite the complex distributions shown in Figs. S8a and S8b, the pointwise comparison between wb and ∂ηb/∂y indicates the existence of such negative correlations. More positive w values and negative meridional topography gradients exist north of 13°N, and vice versa to the south. Note that the pointwise w is also correlated with ∂ηb/∂x, whose effects could be offset during zonal integration.

Considering the negative correlation between ∂ηb/∂y and wb, we infer that southward currents exist in the deep ocean. To verify this, the WOA18-derived meridional geostrophic velocity averaged over the Pacific basin was plotted (Fig. 13). The mean meridional velocities between 2000 and 5000 m are negative at most locations. Southward velocities occur primarily at 3000–4000 m, and stronger southward currents occur around 11° and 16°N. Such locations are consistent with the extremes of deep vertical velocity because stronger currents cause larger vertical velocities. Moreover, the meridional velocities within 2000–3000 m are southward at 8° and 18°N, which correspond to the shallow bathymetries shown in Fig. 12a. Figure S8c further suggests that deep southward meridional currents are prominent in the central Pacific. These deep currents could be related to North Pacific Deep Water, which flows southward below 2500 m (Macdonald et al. 2009; Kawabe and Fujio 2010).

Fig. 13.
Fig. 13.

Meridional geostrophic currents from 2000 to 5000 m averaged within 140°E–100°W with an interval of 100 m. Blue, red, and green dashed lines represent meridional velocities in 2000–3000, 3000–4000, and 4000–5000 m, respectively.

Citation: Journal of Physical Oceanography 53, 11; 10.1175/JPO-D-23-0006.1

4. Discussion

Sverdrup transport discrepancy could be induced by nonzero vertical velocity, wind stress uncertainty, or nonlinearity. Although ensemble wind products and drag coefficient schemes are used to reduce wind stress uncertainty, the STDs of SE remain detectable in Figs. 9a and 9b. Instead of using the ensemble technique, the OFES simulation, which is a pure model run without assimilation, is more dynamically consistent with wind forcing. The access to wind stress used in OFES1 at APDRC facilitates more effective exclusion of the effects of wind stress uncertainty. As shown in Figs. S9 and S10, a high similarity between Vw and the Sverdrup transport discrepancy still exists. Compared with Fig. 11, the most positive contribution regions remain unchanged. This indicates that our estimated contribution of deep vertical velocity to the Sverdrup discrepancy is not an artifact of wind stress uncertainty.

Nonlinearity could be influential in regions with strong currents (Yuan et al. 2014; Thomas et al. 2014), such as the Mindanao Dome and the NECC. An in-depth discussion on nonlinearity is thereby needed but beyond the scope of this study. Another question is whether the concerned deep vertical velocity is model dependent. Although model bathymetry and resolution undoubtedly affect w, its dipolar structure was captured in all selected datasets. To validate this pattern further, additional data should be investigated. The latest ECCOv4r4 is a good choice because its physical variables are dynamically consistent and fit observations reasonably (Forget et al. 2015; Liang and Yu 2016). In addition, simulation data from the Coupled Model Intercomparison Project phase 6 (CMIP6; Eyring et al. 2016) Earth system models also provide such an opportunity for investigation.

According to the global w distribution in the previous studies (e.g., Wunsch 2011), vertical velocities in other regions could also critically affect SB. Using the GODAS vertical velocity at 1900 m, we examined Vw in the low to midlatitudes (Fig. 14). As f/β increases from the tropics to high latitudes, Vw is more noticeable in higher latitudes. In particular, large values occur in the Southern Ocean, which might be caused by interaction between the equivalent-barotropic currents and topography, vigorous deep vertical convection, and large values of f/β. Notably, the alternating bands in the Pacific at 5°–30°N and the large positive values in the North Atlantic are consistent with the patterns of Sverdrup transport errors shown in Yang et al. (2016). Compared to the pointwise results of Thomas et al. (2014), Vw exhibits similar patterns in most regions, except for remarkable positive signals in the Atlantic at 30°–40°N. This difference may be related to the specific patterns of w in ECCO-GODAE and GODAS, which requires further validation.

Fig. 14.
Fig. 14.

Near-global integrated meridional transport calculated from the GODAS climatological vertical velocity at 1900 m. Zero values are shown as dotted lines.

Citation: Journal of Physical Oceanography 53, 11; 10.1175/JPO-D-23-0006.1

The preceding text has revealed the significant contribution of vertical velocity to Sverdrup transport errors. As decadal variations and trends exist in vertical velocity (Liao et al. 2022a), Vw also changes. To clarify this, we examined Vw associated with the GODAS w averaged over 1981–2000 and 2001–20. Although the Vw patterns in the two periods are similar, distinct intensity differences exist in some regions (Fig. 15). For instance, the zonal dipolar bands in the western low-latitude Pacific are more remarkable during 2001–20, with the largest transport difference reaching 8.0 Sv. Furthermore, significant changes of Vw were also detected in the Southern Ocean, the Kuroshio Extension region, and the midlatitude Atlantic. As ocean topography remains unchanged at this time scale, the variation of deep meridional currents is believed to account for these changes. When conducting a diagnosis using Sverdrup theory, such long-term variation or trend of w could conceal realistic wind-induced circulation changes and thereby needs to be considered on decadal to multidecadal time scales.

Fig. 15.
Fig. 15.

Near-global integrated meridional transport calculated from the GODAS vertical velocity (at 1900 m) averaged over (a) 1981–2000, (b) 2001–20, and (c) their difference (latter minus former).

Citation: Journal of Physical Oceanography 53, 11; 10.1175/JPO-D-23-0006.1

5. Summary

Sverdrup theory is an important tool for diagnosing changes in wind-driven circulation within the interior ocean and the WBCs as compensating flows. Significant Sverdrup transport discrepancies have been noticed in the low-latitude northwestern Pacific. Nonzero vertical velocities in deep layers, together with nonlinearity and wind stress uncertainty, are responsible for such discrepancy. To date, the impact of vertical velocity remains poorly understood. Through combined analyses of hydrographic observations, surface wind products, and ocean reanalysis/simulation data, this study explored the spatial patterns of deep vertical velocity and revealed its contribution to the inaccuracy of meridional Sverdrup transport from a zonal integration view.

Our finding revealed that the vertical velocities between 1500 and 2500 m exhibit similar patterns and induce the smallest meridional non-Sverdrup transport. These vertical velocities exhibit two zonal bands characterized by upward (downward) velocities immediately south (north) of the NECBL, which are more prominent in the central-western Pacific. Markedly, the amplitude of the southern band is approximately twice that of the northern band. The integrated volume transport Vw associated with the vertical velocity at 1900 m exhibits a similar pattern. The meridional asymmetry in vertical velocity was alleviated in Vw, which has southern and northern extrema of approximately 9.0 and −7.0 Sv along 140°E. It is speculated that the poleward increase of f/β, which is proportional to Vw, might be responsible for the weakened asymmetry. Hence, vertical velocities at high latitudes may deserve more attention.

The Vw has noteworthy intensity and exhibits high similarity with the Sverdrup transport discrepancy, as assessed by the difference of SE and Argo- or WOA18-derived MGTs. This supports the vital role played by deep vertical velocity in inducing inaccuracy of meridional Sverdrup transport. Quantitatively, the contribution rate of Vw to the Sverdrup transport discrepancy is positive at most locations. Such positive contribution rates primarily exist west of 150°W, which is attributed to the remarkable vertical velocity in this region. Meridionally, larger contribution rates occur in the north (40%–80%) than in the south (20%–60%). We argue that bottom topography, whose zonal average exhibits a U-shape with a maximal depth at 13°N, and deep southward currents potentially result in this patterned vertical velocity within 1500–2500 m.

In this study, we explored the spatial pattern of deep nonzero vertical velocity and its significant impact on the validity of Sverdrup theory in the low-latitude Pacific. We also clarified how bottom topography and deep currents jointly influence the formation of such deep vertical velocity. These findings offer valuable insights for the accurate diagnosis of wind-driven circulation changes using Sverdrup theory. The discussions highlight the insufficiency of regional investigations and emphasize the need for further exploration of additional datasets. Moreover, to interpret results more accurately, variations or trends in vertical velocity should be considered when using Sverdrup theory to diagnose long-term wind-driven circulation changes.

Acknowledgments.

The authors appreciate two anonymous reviewers for their constructive suggestions and thoughtful comments. This work was supported by the National Natural Science Foundation of China (92158202, 42090044, and 42076017). The authors appreciate the data service provided by APDRC and the analysis support from Oceanographic Data Center, IOCAS.

Data availability statement.

All data are available on public websites. Related information has been described in section 2a.

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