1 Introduction

The South China Sea (SCS) is located at the west side of the North Pacific and is the largest semi-enclosed marginal sea of the North Pacific Ocean, with a wide continental shelf and slope along the mainland coast of southern China. The upper layer large-scale circulation is predominantly seasonal, not only changing its magnitude, but also reversing direction, mainly because of the Asian monsoon seasonal cycle (Wyrtki 1961; Liu et al. 2001). The basin scale circulation pattern of the SCS has been investigated in many studies incorporating in situ measurements (e.g., Wyrtki 1961; Fang et al. 2002), satellite-based observations (Wu et al. 1998), as well as numerical simulations (Wang et al. 2006). During boreal winter, the basin scale cyclonic gyre forms a strong southwestward current known as the SCS western boundary current, flowing along the southern China continental slope and eastern Vietnam coast from Dosha Island to the region south of Vietnam. During boreal summer, the SCS western boundary current in the northern SCS (NSCS) becomes weak and variable, and needs further clarification (Fang et al. 2012).

On the other hand, deep, cold, and salty Philippine Sea water enters the SCS through the Luzon Strait and then flows out through the Taiwan, Karimata, and Mindoro Straits as shallow warm currents. This current system, a heat and freshwater conveyor, is called the South China Sea throughflow (Qu et al. 2006). During the past several decades, many investigations have produced widely varying estimates of the net volume transport through the Luzon Strait, from 0.5 to 10 Sv (1 Sv = 106 m3 s−1) (e.g., Wyrtki 1961; Hsin et al. 2012). Mean net volume transport through the Taiwan Strait is about 1 Sv in winter and 2–3 Sv in summer (Fang et al. 2009; Hu et al. 2010). The mean outflow transports through the Karimata and Mindoro Straits are, respectively, given as 3.6 Sv in boreal winter (Fang et al. 2010) and 2.4 Sv during 2004–2007 (Qu and Song 2009). However, by comparison with these transport estimates through the straits around the SCS, transport estimates in the inner SCS are very scarce. To date, there have been no volume transport time series based on in situ observations in the SCS.

In this study, we carried out a 22-month mooring deployment of five pressure-recording inverted echo sounders (PIES) in the NSCS to obtain a 22-month-long record of volume transport across the mooring array. We then estimated a 22-year-long volume transport time series by developing and using an empirical relationship between the observed volume transport and satellite altimeter-determined sea surface height anomaly difference and investigated its mean and variability, including the seasonal cycle and fluctuations induced by mesoscale eddies.

2 Data and methods

We deployed an array of five PIESs across the continental slope in the NSCS, along a satellite track (Pass114) of the TOPEX/POSEIDON and Jason-1/2 altimeters in October 2012, and maintained it until July 2014 (Fig. 1a, b). This PIES array crosses over the gap between Hainan Island and Xisha Island (Fig. 1b, c). The PIES array is roughly perpendicular to the bathymetry contours of the continental slope, i.e., the western boundary current in the NSCS, assuming the current flows along isobaths over the continental slope.

Fig. 1
figure 1

a The South China Sea (SCS) and its adjacent seas; 200 m isobaths denotes the position of shelf slope along which the SCS western boundary current flows, b detailed map of the observational site, c vertical cross-section view of bottom topography along the mooring array, d positions of hydrocasts used in computing the GEM. The TOPEX/POSEIDON and Jason-1/2 satellite altimeter track (Pass 114) is indicated with blue dots in b. Red triangles (P1, P2, P3, P4, and P5) indicate the locations of the five PIESs. The black dots and green squares indicate the positions of Argo profiles and CTD casts, respectively. “H” and “X” in a and b indicate Hainan Island and Xisha Island, respectively. “TS”, “LS”, “MS”, and “KS” in a indicate Taiwan Strait, Luzon Strait, Mindoro Strait, and Karimata Strait, respectively. Isobath depths are given in meters (color figure online)

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While the PIESs were making measurements, we performed a ship-mounted acoustic Doppler current profilers (ADCP, RDI-VM38, 38.4 kHz) survey along the PIES array and took five conductance–temperature–depth (CTD) casts at the PIES stations during 15–16 December 2012, to get data for comparison with the PIES mooring data.

The PIES measures the round-trip acoustic travel time (τ) between sea surface and bottom and the near-bottom pressure (P b). The τ measurements were used to estimate vertical profiles of temperature and specific volume anomaly by the gravest empirical mode (GEM) method (Watts et al. 2001; Zhu et al. 2003; Andres et al. 2008b) using 1355 profiles of temperature and salinity obtained by CTD and Argo measurements (Fig. 1d). The GEM errors for temperature (specific volume anomaly) are 0.77 °C (2.41 × 10−7 m3 kg−1) in the upper 300 m layer and 0.15 °C (6.51 × 10−8 m3 kg−1) for a full-depth layer, respectively (Fig. 2). The GEM-inferred temperatures on 16 December 2012 are in good agreement with those independent data measured by the CTD casts at the five PIES stations during our cruise. Root-mean-square differences (RMSDs) between the two measurements are 0.76 °C in the upper 300 m layer and 0.29 °C for a full-depth layer, respectively (Fig. 3). This indicates the measurements of τ provide good proxy for estimation of the vertical profiles of temperature by the GEM method.

Fig. 2
figure 2

Temperature (°C) and specific volume anomaly (m3 kg−1) GEM (upper panels) and their errors (bottom panels)

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Fig. 3
figure 3

Temperature profiles obtained from CTD measurements (black) and the GEM at five PIES sites. The temperature profiles for P2–P5 stations have been offset rightward by 10 °C successively

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Each P b record is processed to remove the tide and sensor drift for estimating the barotropic velocity between station pairs as follows (Donohue et al. 2010). Absolute geostrophic velocity (V) relative to a deep reference level includes both barotropic component (V bt) and baroclinic component (V bc) (Fig. 4):

Fig. 4
figure 4

Diagram (not to scale) of terms used in Eqs. (1)–(4)

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$$V = V_{\text{bc}} + V_{\text{bt}}$$
(1)

The V bc can be calculated from the PIES-measured τ data using the GEM-derived specific volume anomalies. The V bt at level Z can be calculated from the pressure gradient between two stations:

$$V_{\text{bt}} = {{(p_{1} - p_{2} )} \mathord{\left/ {\vphantom {{(p_{1} - p_{2} )} {(\Delta xf\rho }}} \right. \kern-0pt} {(\Delta xf\rho }})$$
(2)

where p 1 and p 2 are pressures at level Z1 from two stations, ρ is density, f is the Coriolis parameter (5.0 × 10−5 s−1), and Δx is the distance between two stations (Fig. 4).

Since p 1 and p 2 are not always measured at the same depth, we need to use pressure records at different depth to calculate barotropic component. For this purpose, V bt is divided into the temporal mean (\(\overline{V}_{\text{bt}}\)) and its deviation (V′bt(t)):

$$V_{\text{bt}} \left( t \right) = \overline{V}_{\text{bt}} + V^{'}_{\text{bt}} \left( t \right)$$
(3)

The V′bt(t) can be rewritten as:

$$V_{{{\text{bt}}}}^{\prime } (t) = {\raise0.7ex\hbox{${\left( {p_{1}^{\prime } (t) - p_{2}^{\prime } (t)} \right)}$} \!\mathord{\left/ {\vphantom {{\left( {p_{1}^{\prime } (t) - p_{2}^{\prime } (t)} \right)} {(\Delta xf\rho )}}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${(\Delta xf\rho )}$}} \approx {\raise0.7ex\hbox{${\left( {p_{1}^{\prime } (t) - p_{{22}}^{\prime } (t)} \right)}$} \!\mathord{\left/ {\vphantom {{\left( {p_{1}^{\prime } (t) - p_{{22}}^{\prime } (t)} \right)} {(\Delta xf\rho )}}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${(\Delta xf\rho )}$}}$$
(4)

by assuming the temporal variation of deep pressure is small (p 2′ ≈ p 22′) (see Fig. 4 for definition of p 22′). p 1′ and p 22′ can be obtained from the PIES pressure measurements at the two stations.

The velocity measured by the ship-mounted ADCP at a deep layer (800 m) and averaged between two stations, including both barotropic and baroclinic components, should be the same as that estimated by the PIES data:

$$V_{\text{ADCP}} = \overline{V}_{\text{bt}} + V^{\prime }_{\text{bt}} \left( {t_{\text{ADCP}} } \right) + V_{\text{bc}} \left( {t_{\text{ADCP}} } \right)$$
(5)

where t ADCP denotes the time of ADCP measurement. Therefore, the temporal-mean barotropic component \(\overline{V}_{\text{bt}}\) can be estimated as follows:

$$\overline{V}_{\text{bt}} = V_{\text{ADCP}} - V^{'}_{\text{bt}} \left( {t_{\text{ADCP}} } \right) - V_{\text{bc}} \left( {t_{\text{ADCP}} } \right)$$
(6)

V′bt(t ADCP) can be estimated by applying Eq. (4) to P b while \(V_{\text{bc}} \left( {t_{\text{ADCP}} } \right)\) by using the GEM-derived hydrographic data during the period of the ship-mounted ADCP measurement, respectively. The resulting \(\overline{V}_{\text{bt}}\) at the four station pairs was within a range between −1.0 and 1.5 cm s−1. Substituting \(\overline{V}_{\text{bt}}\) given by Eq. (6) into Eq. (3) and estimating V′bt(t) from records of P b and V bc from records of τ, we obtained the absolute geostrophic velocity and corresponding volume transport through the mooring section.

3 Results

3.1 Velocity structure

The vertical cross-section of the current velocity obtained by the ship-mounted ADCP measurements on 16 December 2012 shows a southwestward current with a subsurface maximum velocity core of −44.0 cm s−1 (Fig. 5a). The absolute geostrophic velocity sections, estimated from the CTD data at five PIES stations by referring to the ship-mounted ADCP velocity at 800 m (Fig. 5b) and from the GEM-derived hydrographic data and PIES pressure data as shown in Eqs. (1)–(6) (Fig. 5c), are similar to each other: both of them show a southwestward current with a strong surface velocity. Since the barotropic component of current is at an order of several cm/s, it is smaller than the baroclinic component (Fig. 5). The volume transports integrated over the section for Fig. 5a–c are −8.4, −8.0, and −8.1 Sv, respectively. Agreement of velocity structures and volume transports for Fig. 5a–c indicates that our volume transports estimated using the PIES-measured P b and τ are likely reasonable.

Fig. 5
figure 5

Vertical distribution of velocity normal to the section for the mooring array: a measured by ship-mounted ADCP; b absolute geostrophic velocity estimated using the CTD data by referring to the ship-mounted ADCP velocity at 800 m; and PIES-derived geostrophic velocities estimated by using Eqs. (1)–(6) on c 16 December 2012, d 1 July 2013 when a warm-eddy arrived, e 9 April 2014 when a cold-eddy arrived; and f mean PIES-derived geostrophic velocity for the whole mooring period. Positive (negative) values indicate northeastward (southwestward) currents. Contour interval is 10 cm s−1. Thick line shows zero velocity. Triangles on the top of each panel indicate the locations of the PIESs

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During 22 months of PIES measurement, the velocity structure and associated volume transport derived from PIES-measured P b and τ have a large variability. As two examples, the velocity was northeastward with a maximum velocity of 104.1 cm s−1 (volume transport 17.4 Sv) on 1 July 2013 (Fig. 5d) and southwestward (volume transport −7.8 Sv) on 9 April 2014 (Fig. 5e). Combined with satellite altimeter data, we know the former case (Fig. 5d) corresponds to the arrival of a warm-eddy to the section while the latter case (Fig. 5e) to that of a cold eddy, that is, the velocity at the shelf slope of NSCS is strongly influenced by arrivals of mesoscale eddies. The 22-month mean velocity shows a weak northeastward current whose volume transport is 1.0 Sv (Fig. 5f).

3.2 Estimation of a 22-year volume transport time series

Using the mooring array data, we can estimate a 22-month volume transport time series (VTPIES) from October 2012 to July 2014 across the section. However, this 22-month time series is not long enough to examine long-term variations and their statistical characters because the current during 22 months is strongly influenced by mesoscale eddies and the seasonal monsoon. To obtain a long-term volume transport time series, we established an empirical relationship between this 22-month volume transport time series and simultaneous satellite altimeter data following the methods that have been used previously for the Kuroshio and Ryukyu Current (Imawaki et al. 2001; Zhu et al. 2004; Andres et al. 2008a).

The satellite track of Pass 114 (blue dots in Fig. 1b) is a descending track passing five PIES sites. The satellite-measured sea surface height anomaly (SSHA) data along the track were first lowpass-filtered with a five-point filter corresponding to a spatial scale of about 29 km. The SSHA at each PIES site is highly correlated with τ measured by the PIES. The highest correlation coefficients were 0.91 and 0.92 at P1 and P5, respectively. The SSHA difference between P1 and P5 (ΔSSHA) is well correlated with the 40-day lowpass-filtered volume transport in the upper 200 dbar (correlation coefficient is 0.93) (Fig. 6a), and is also correlated with similarly filtered volume transport in the deep layer below 200 dbar (correlation coefficient is 0.80) (Fig. 6b). Because the volume transport in the upper 200 dbar is well correlated with the full-water-column transport (Fig. 6d), the ΔSSHA is, therefore, well correlated with the full-water-column transport (correlation coefficient is 0.90) (Fig. 6c). Using this empirical relationship, we then produce a 22-year time series of volume transport from 1992 to 2014. We refer to this volume transport time series as VTNSCS (volume transport in the NSCS).

Fig. 6
figure 6

Scatter plots of volume transport in a the upper 200 dbar, b the deep layer below 200 dbar and c the full-water-column transport against the sea surface height anomaly difference (SSHAD, unit: cm). d Scatter plots of volume transport in upper 200 dbar against the full-water-column transport. The correlation coefficient and the root-mean-square difference from the regression line are shown in the upper-left corner of each panel. The volume transport was estimated from PIES data and SSHAD was estimated from satellite altimeter data

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3.3 Variability of the VT NSCS

The VTNSCS time series is in good agreement with the VTPIES time series (Fig. 7a). Their RMSD is 3.5 Sv, much smaller than the peak-to-peak range of about 25 Sv. The VTNSCS time series is also in good agreement with the volume transport (VTHYCOM) estimated from the 1/12º global Hybrid Coordinate Ocean Model (HYCOM) results (Bleck, 2002) (blue line in Fig. 7b) with a RMSD of 3.0 Sv. Consequently, our estimated VTNSCS is likely reasonable.

Fig. 7
figure 7

a Time series of  VTPIES (red line), VTNSCS (dotted black line), and VTHYCOM (blue line) for the mooring period (October 2012–July 2014). b Time series of VTNSCS (dotted black line) and VTHYCOM (blue line) from January 1993 to December 2014 (color figure online)

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During the 22 years, VTNSCS fluctuates largely from −11.8 to 19.7 Sv, with a standard deviation of 5.3 Sv (Fig. 7b). The 22-year mean VTNSCS is −1.6 Sv, indicating a southwestward current. Maximum VTNSCS occurred in August 2010, which was due to an exceptional anticyclonic eddy around Xisha Island (Chu et al. 2014). VTNSCS typically has a positive value in the warm season and a negative value in the cold season, which indicates a monsoon cycle response of the SCS circulation.

The power spectrum of VTNSCS shows the most prominent energy at the annual period (Fig. 8). Two peaks at about 605 and 875-day are between 90 % (thin broken line in Fig. 8) and 95 % (thick broken line in Fig. 8) confidence levels, suggesting the quasi-biennial oscillation occurred in the SCS, but were weaker than that in the North Pacific (Zhu et al. 2004). The power spectra of VTNSCS show that the peak around 100-day period is not remarkable. This indicates that the mesoscale eddies with 100-day period, originating from the North Pacific Subtropical Countercurrent region (Qiu 1999) propagated westward (Yang et al. 1999; Zhu et al. 2004) may not arrive at the PIES sites or have been greatly weakened, possibly due to blocking by the northward-flowing Kuroshio as the eddies pass through the Luzon Strait.

Fig. 8
figure 8

Variance-preserving power spectrum of volume transports through the mooring array. Thick and thin broken lines indicate 95 and 90 % confidence levels based on the best-fit, first-order autoregressive model spectrum, respectively

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Since the power spectrum of VTNSCS shows the most prominent energy peak at the annual period, we average and plot the 22-year VTNSCS time series by month and by season to examine the annual cycle and seasonal variation. The monthly averaged VTNSCS changes not only in magnitude but also in direction (Fig. 9a). The monthly averaged VTNSCS has a maximum (3.6 Sv, northeastward) in July and a minimum (−7.3 Sv, southwestward) in December with a standard deviation of 3.6 Sv. The annual range (peak-to-peak difference) reaches 10.9 Sv (Fig. 9a). This annual range is larger than those of the Kuroshio in the East China Sea (Andres et al. 2008a) and south of Japan (Imawaki et al. 2001) and the Ryukyu Current southeast of Okinawa (Zhu et al. 2004), although its mean (−1.6 Sv) is much smaller than the means of Kuroshio and Ryukyu Current. The mean VTNSCS values for spring (April–May), summer (June–September), fall (October to early November), and winter (November–March) are 0.8, 2.3, −5.0, and −5.1 Sv, respectively (Fig. 9b) (the season is defined following Fang et al. 2002).

Fig. 9
figure 9

a Monthly averaged VTNSCS (black lines) and VTHYCOM (blue lines) for the 22 individual years (thin lines) and averaged over all 22 years (thick line); the two dashed lines represent ±one standard deviation of VTNSCS and VTHYCOM for each month. b Seasonal means for VTNSCS (black) and VTHYCOM (blue) (color figure online)

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The reversal date of mean VTNSCS in spring when VTNSCS changes from southwestward to northeastward is 8 April (thick black line in Fig. 9a), about 28 days after the reversal of wind direction over the SCS (figure not shown), while the reversal date of mean VTNSCS in fall (from northeastward to southwestward) is 13 September, about 15 days after the reversal of wind direction in fall.

4 Summary and discussion

We successfully carried out a 22-month mooring deployment of five PIESs along a satellite altimeter track across the continental slope in the NSCS. Using the round-trip acoustic travel time data with the GEM method, we estimated the temperature profile time series at the five PIES stations. The GEM-inferred temperatures were in good agreement with those measured independently by the CTD casts at the five PIES stations during mooring period. Then, we calculated the absolute geostrophic velocity normal to the section and obtained a 22-month-long record of volume transports by combining the GEM-derived hydrographic data, PIES pressure data, and the ship-mounted ADCP velocity data.

By using this 22-month-long record of volume transport data with satellite altimeter data, we estimated a 22-year VTNSCS in the NSCS and determined its mean and variability including the seasonal cycle and influence of mesoscale eddies. VTNSCS showed a significant seasonal reversal with an annual range of 10.9 Sv, which is much larger than its mean (−1.6 Sv). Mesoscale eddies greatly impacted VTNSCS with an upper range of about 20 Sv (Fig. 7b; in August 2010).

Currents near our mooring site are known to flow typically approximately along the isobaths of the SCS continental slope (Wang et al. 2013), but no previous studies have obtained time series of volume transport over the SCS. Our winter mean VTNSCS (−5.1 Sv) is slightly larger than that (about −4 Sv) predicted by Liu et al. (2001) from Sverdrup theory using the monthly mean Comprehensive Ocean–Atmosphere Data Set (COADS) wind-stress curl over the SCS, while our summer mean VTNSCS (2.3 Sv) is quite different from their prediction (about −3.5 Sv). This suggests that the seasonal variation of VTNSCS in the NSCS may not exactly follow Sverdrup balance, because the SCS summer circulation is weak and more complicated than that in winter (Fang et al., 2012). Nevertheless, our summer VTNSCS is the first long-term measurement evidence supporting the schematic circulation pattern in the NSCS, hypothesized by Fang et al. (2012) (see Fig. 3 in their paper). The mean VTNSCS through fall and winter is about −5 Sv, larger in magnitude than the outflow transport through the Karimata Strait (3.6 Sv) in winter (Fang et al. 2010), which indicates that part of the VTNSCS may flow out the SCS as a portion of the SCS throughflow, while some of the VTNSCS joins the inner SCS circulation in the SCS.

The mesoscale eddies near the Xisha Island are mainly from the south, propagated from the east of Vietnam, and also from the east, propagated from the region near the Luzon Strait (Wang et al. 2003, 2015). To examine how mesoscale eddies influence the VTNSCS, we plot the SSHA distributions when the VTNSCS reaches the minimum on 7 April 2013 (Fig. 10a) and the maximum on 24 June 2014 (Fig. 10b). When the VTNSCS took the minimum (maximum) value, a cyclonic (anticyclonic) eddy extended to the southeast side of observation line, making the VTNSCS southwestward (northeastward).

Fig. 10
figure 10

SSHA (cm) distribution when the volume transports takes the minimum value and the maximum value in a 7 April 2013 and b 24 June 2014, respectively. The triangles in each panel indicate the PIES positions. The regions with depth shallower than 200 m are masked

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From the 22-year time series of VTNSCS, it is known that Sverdrup balance does not fully explain the seasonality of the transport in summer. To examine the possible mechanism of the seasonal variability of VTNSCS, we plot the mean SSHA and eddy kinetic energy distributions calculated using surface geostrophic velocity from SSHA data for summer and winter (Fig. 11). The SSHA distributions show a seasonal reversal structure corresponding to the southwestward and northeastward VTNSCS in summer and winter, respectively. However, the eddy kinetic energy near our mooring area is relatively small and almost the same in the two seasons, indicating that the mesoscale eddies do not exhibit clearly seasonal variability. This means that effects of mesoscale eddies can be removed by averaging the 22-year-long data, and also implies that the mesoscale eddies may not be an important factor of seasonality of the VTNSCS. The seasonal variability of the Kuroshio transport in the East China Sea also does not follow the Sverdrup theory, whose mechanism was explained as joint effect of baroclinicity and bottom relief (JEBAR; Kagimoto and Yamagata 1997). It is suggested that similar work, such as high-resolution numerical simulation, should be carried out to examine the possible mechanism of the seasonal variability in the SCS.

Fig. 11
figure 11

SSHA distribution (cm) for a summer and b winter, and eddy kinetic energy (cm2 s−2) distribution for c summer and d winter. The triangles in each panel indicate the PIES positions. The regions with depth shallower than 200 m are masked

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The methodology, using PIES near-bottom pressure data combined with ship-mounted ADCP data to estimate barotropic velocity, is applied here for the first time in a case lacking current meter measurements such as those provided by the current pressure-recording inverted echo sounder (Andres et al. 2008b; Donohue et al. 2010). The present method has its limitations due to formula approximations. The temporal-mean barotropic component velocity \(\bar{V}_{\text{bt}}\), estimated in our geostrophic calculation using Eq. (6), were obtained from only single time ship-mounted ADCP measurement. The error of \(\bar{V}_{\text{bt}}\) is expected to be smaller than the error of the ship-mounted ADCP (about 3 cm s−1). We also note that the volume transport presented in this study is not the total volume transport of the SCS western boundary current, because our mooring array does not cover the area shallower than the water depth of P1 site (about 500 m, Fig. 1c). Nevertheless, the present study provides a useful long-term volume transport time series based on in situ observation data, which will be opened to the community in a near future (http://www.scsdata.icoc.cc/).