State analysis using the Local Ensemble Transform Kalman Filter (LETKF) and the three-layer circulation structure of the Luzon Strait and the South China Sea
A new circulation model of the western North Pacific Ocean based on the parallelized version of the Princeton Ocean Model and incorporating the Local Ensemble Transform Kalman Filter (LETKF) data assimilation scheme has been developed. The new model assimilates satellite data and is tested for the period January 1 to April 3, 2012 initialized from a 24-year simulation to estimate the ocean state focusing in the South China Sea (SCS). Model results are compared against estimates based on the optimum interpolation (OI) assimilation scheme and are validated against independent Argo float and transport data to assess model skills. LETKF provides improved estimates of the western North Pacific Ocean state including transports through various straits in the SCS. In the Luzon Strait, the model confirms, for the first time, the three-layer transport structure previously deduced in the literature from sparse observations: westward in the upper and lower layers and eastward in the middle layer. This structure is shown to be robust, and the related dynamics are analyzed using the results of a long-term (18 years) unassimilated North Pacific Ocean model. Potential vorticity and mass conservations suggest a basin-wide cyclonic circulation in the upper layer of the SCS (z > −570 m), an anticyclonic circulation in the middle layer (−570 m ≥ z > −2,000 m), and, in the abyssal basin (<−2,000 m), the circulation is cyclonic in the north and anticyclonic in the south. The cyclone–anticyclone abyssal circulation is confirmed and explained using a deep-layer reduced-gravity model as being caused by overflow over the deep sill of the Luzon Strait, coupled with intense, localized upwelling west of the strait.
KeywordsThree-layer circulation of South China Sea Three-layer Luzon Strait transport Local Ensemble Transform Kalman Filter (LETKF) Data assimilation Ocean modeling
The western North Pacific Ocean and South China Sea (SCS) adjacent to the Asian continent play a significant role in regional and global weather and climate variability (e.g., Hu et al. 2000; Xie et al. 2003; Qu et al. 2004, 2006a, 2009; Xue et al. 2004; Gan et al. 2006; Wang et al. 2006; Gordon et al. 2012; Sprintall et al. 2012). South China Sea is among the world’s biologically most diverse ecosystem which is threatened by economic developments and anthropogenic inputs (Liu 2013). Understanding and predicting the ocean circulation in that region are of interest for both scientific research and ecosystem management studies.
East of the Luzon Strait, the Kuroshio flows north-northeastward, and a branch of it intrudes into the SCS through the Luzon Strait. Northeast of Taiwan, a branch of the Kuroshio also enters the East China Sea (ECS; Isobe 2008). The Kuroshio waters modify the marginal seas’ heat and salt fluxes, as well as biogeochemical balances (Liu et al. 2000). Monsoon winds, tides, and rivers have significant influences on the circulation and mixing of the marginal seas (Qu 2000; Guo et al. 2006; Isobe 2008). Warm and cold eddies affect heat and salt transports, the surface winds, and possibly also the intensity and spawning of typhoons (Oey et al. 2013).
Regional, high-resolution circulation models are useful for both understanding processes and providing practical services to the community, such as tracking pollutants, identification of fishing grounds, and for search and rescue. Recently, we have developed a comprehensive ocean prediction system—the Advanced Taiwan Ocean Prediction (ATOP) system (Oey et al. 2013). The ATOP system is now operational; once a day, it provides −7-day analysis and +7-day forecast for the North Pacific Ocean (http://mpipom.ihs.ncu.edu.tw) by assimilating satellite data using a simple statistical optimum interpolation (OI) scheme. This paper develops a western North Pacific regional model of ATOP and implements the Local Ensemble Transform Kalman Filter (LETKF; Hunt et al. 2007; see the extensive list of references in Xu et al. 2013a) scheme for data assimilation. LETKF has been successfully used in atmospheric studies, such as Szunoygh et al. (2005) and Miyoshi et al. (2010). The method has now been applied to the ocean. Miyazawa et al. (2012) implemented the LETKF algorithm into the parallelized version of the Princeton Ocean Model (POM; Jordi and Wang 2012) and showed that the method can simulate well the complex interactions between the Kuroshio and coastal seas south of Japan. Xu et al. (2013a) used LETKF to analyze the Loop Current and eddy variability in the Gulf of Mexico. For the SCS, a number of numerical models (e.g., Shaw and Chao 1994; Metzger and Hurlburt 1996, 2001; Chu et al. 1999; Xue et al. 2004; Gan et al. 2006; Hsin et al. 2012; Lan et al. 2013) have been developed to study its circulation. However, a data-assimilated analysis using LETKF in the SCS has not been previously attempted. The first goal of this study is therefore to produce and validate a test case of LETKF data-assimilated analysis for the western North Pacific Ocean focusing on the SCS and compare the results with the ATOP analysis using the OI scheme, as well as with observations.
The SCS is connected to the Pacific Ocean by the Luzon Strait which with a sill depth of ∼2,000 m is the only deep pathway between the two basins. The Kuroshio intrudes into SCS through the upper Luzon Strait, and deep water overflows from the denser Pacific to the relatively lighter SCS below about 1,500 m (Qu et al. 2006b). The structure of the middle layer remains unclear but water mass analysis suggests an outflow of SCS intermediate water (SCSIW) which may be traced to locations as far north as the Okinawa Trough (Chen and Wang 1998; Chen 2005). The mechanisms for the Kuroshio intrusion and the deep overflow have attracted considerable attention (e.g., Qu et al. 2006b). Further studies are still needed to understand the mechanisms. The upper layer circulations have been extensively studied by previous observation and modeling studies (e.g., Qu 2000; Gan et al. 2006; and references cited above). On the other hand, apart from a few studies (Wang et al. 2011; Lan et al. 2013), the intermediate and deep circulations have rarely been discussed. The second goal of this study is therefore to use LETKF analysis and the long-term results (1991–2008) of an unassimilated run (Oey et al. 2013) to quantitatively estimate the Luzon Strait transport (LST) and then, as a third goal, to explain the three-layer structure of LST and mean circulation of the SCS. To the best of our knowledge, this is the first time that the three-layer circulation structures of the Luzon Strait and SCS have been simulated in a model.
The paper is organized as follows. Section 2 describes the model and Section 3 LETKF. Section 4 compares LETKF and OI analysis results against observations and shows the existence of the three-layer flow structure in the Luzon Strait. Section 5 demonstrates the robustness of the three-layer structure using the long-term unassimilated model run and explains the corresponding basin-wide circulation in the SCS. Discussions and conclusions are given in Section 6.
2 Regional North Pacific models
The WPac is forced by six-hourly NCEP 0.5° × 0.5° Global Forecast System (GFS; http://nomads.ncdc.noaa.gov/data.php) wind. Boundary conditions are zero normal flux (of any kind) across solid boundaries. Along the open boundaries, World Ocean Atlas (WOA) climatological T and S from NODC (http://www.nodc.noaa.gov/OC5/WOA05/pr_woa05.html) are specified within 1.5°-wide flow-relaxation zones (Oey and Chen 1992a, b). Transports across the open boundaries are specified from Pac10 together with the Flather radiation scheme (Oey and Chen 1992a, b). In this way, boundary transports consistent with large-scale (e.g., wind) forcing are retained, while the baroclinic velocity is consistent with the observed WOA climatology. At the sea surface, the sea surface temperature (SST) is relaxed to monthly WOA values using an e-folding time constant of 1/30 day−1. The sea surface salinity (SSS) is similarly relaxed to climatological WOA values. The WPac uses OI method to assimilate AVISO (Archiving, Validation and Interpretation of Satellite Oceanographic data) satellite sea surface height anomaly (SSHA, http://www.aviso.oceanobs.com/) data. The optimally interpolated gridded, daily data provided by SSALTO/DUACS on a 1/3° × 1/3° Mercator grid is used. The SSHA data (η) over water depth <500 m is excluded since they tend to be less accurate near the coasts. The gridded SSHA data was projected to the subsurface temperature (T) field using pre-computed correlation factors (FT) derived from a 24-year (1988–2011) free-running Pac10 experiment (Exp.Pac10) without data assimilation (Oey et al. 2013). The free-running experiment was forced by the cross-calibrated multi-platform (CCMP; Atlas et al. 2009) from July 1987 to December 2009 and 0.5° × 0.5° GFS from January 2010 to December 2011. The calculation was then repeated to yield a total of 48 years. The long-term integration ensures that a statistical equilibrium eddy field has been reached. The last 21-year (1991–2011) results are then used to compute the correlation factors which are then linearly interpolated onto the western North Pacific model grid. The analysis of potential temperature is computed as Ta = T + FT < η >, where <•> denotes time averaging. The scheme therefore weighs more on using altimetry data in regions where the correlations between T and η are high, but Ta ≈ T where the correlation is low. The details can be found in Yin and Oey (2007) and Oey et al. (2013). This experiment using the OI data assimilation scheme is ongoing from January 2012 through present; for comparison with LETKF, the results from January 1 to April 3, 2012 are used in this study (named Exp.OI).
An identical experiment as Exp.OI is conducted but with LETKF implemented into ATOP and assimilating the same SSHA data from AVISO (named Exp.LETKF). LETKF, first proposed by Ott et al. (2004) and modified by Hunt et al. (2007), solves the ensemble Kalman filter equations in local patches in a parallel computational setup. It uses the Gaussian approximation and employs an ensemble model to estimate the time evolution of the mean and background error covariance. The ensemble mean represents the maximum likelihood estimate of the analysis state.
Horizontal localization scale (σobs; number of grids)
Vertical localization scale (σobs)
Observation error of SSHA
Time interval of LETKF
In practice, the ensemble Kalman filter equations may decouple from the “true” system. Model error is one reason, but even for a perfect model, the filter tends to underestimate the uncertainty in its state estimates, leading to overconfidence in the background estimates. In other words, the dynamics of the data assimilation ignores the observations when the discrepancy is too large. An ad hoc procedure to counter this tendency is to inflate either the background covariance or the analysis covariance during each assimilation cycle. In the study, a constant factor larger than 1 multiplies Wa during each cycle. This method is called “multiplicative inflation.” It reduces the influence of past observation on current analysis.
LETKF data assimilation is initialized on January 1, 2012, with 32 ensemble members. The initial members are randomly sampled from the outputs of the ongoing OI assimilative analyses, described previously, but excluding the data-assimilative analysis period from January 1 to April 3, 2012. The time interval for LETKF is 2 days. In the algorithm, the random samples are used to initialize LETKF iteration, and with injection of observations, the system becomes insensitive to the initial samples. The parameters (Table 1) are selected based on extensive sensitivity tests following the methodologies which are described in details in Xu et al. (2013a). Our goal is not to repeat reporting these sensitivity tests; rather, as stated in Section 1, we will (i) demonstrate the first successful implementation of LETKF in SCS, (ii) show the robust three-layer circulation structures which were previously inferred based on sparse observations, and (iii) provide dynamical interpretations of the circulation structures.
4 Comparing Exp.OI, Exp.LETKF, and observations
Our goal here is to validate the model in three different ways. In Section 4.1, LETKF is compared with OI by assessing their results against AVISO A. In Section 4.2, we compare LETKF and OI analyses against temperature and salinity data from Argo floats. In Section 4.3, we describe the modeled Luzon Strait transports and compare them against transports estimated from observations and other model outputs.
4.1 Comparisons against AVISO satellite observations
The reduction of analysis errors of LETKF compared with those of OI is consistent with our previous experiences using these two methods in western boundary regions with strong mesoscale features (Xu et al. 2013a); as detailed in that paper, LETKF benefits from its use of the time-evolving error covariance (see their Fig. 3 and discussions).
4.2 Comparisons against Argo float data
Averaged model skill, root mean squared (RMS) errors, and bias, evaluated from Argo temperature (T) and salinity (S) data
4.3 Transports through the Luzon Strait and other sections and comparison with literature
Luzon Strait transports (Sv) from observations and models
1. Tian et al. (2006)
October 4 to 6, 2005
2. Liao et al. (2008)
November 28 to December 27, 1998
3. Yuan et al. (2008a)
August 28 to September 10, 1994
4. Yuan et al. (2008b)
March 17 to April 15, 2002
5. Yuan et al. (2009)
March 8 to 27, 1992
6. Zhou et al. (2009)
September 18 to 20 2006
7. Yang et al. (2010)
July 5 to 14, 2007
January 20 to April 3, 2012
January 20 to April 3, 2012
11. Zhang et al. (2010)
12. Hsin et al. (2012)
In the upper layer, all of the observed transport estimates, except for Yang et al. (2010), are westward into the SCS and range from −0.8 Sv (Yuan et al. 2008b) to as much as −10.3 Sv (Liao et al. 2008). The durations of observations were from a few days to 1 month in different seasons; the shortness of the observation periods may explain the large variability of the transport estimates. For example, Yang et al. (2010) attributed the large outflow transport (+5 Sv) in the upper layer to the presence of an anticyclonic eddy east of the Luzon Strait during their observation. In the middle layer, all observed estimates show outflow transports ≈0.22∼5 Sv from SCS into the North Pacific Ocean. In the lower layer, westward inflows ranging from −0.1 to −2 Sv prevail. Wyrtki (1961; see also Qu et al. 2006b) suggested that the near-bottom inflow of Pacific water may be driven by the baroclinic pressure gradient induced by density difference between the open Pacific and SCS waters.
In order to compare with the observed estimates, we use the same depth ranges as used by Tian et al. (2006), 0–500, 500–1,500, and 1,500 m–bottom, to calculate the corresponding three-layer transports for Exp.OI and Exp.LETKF and obtain −3.7 and −5.5 Sv in the upper layer, 5.6 and 4.8 Sv in the middle, and −1.5 and −1.7 Sv for the lower layer (Table 3, entries 8 and 9). These model transports are within the range of the observed estimates. Most importantly, the models show a robust three-layer transport structure, which is particularly distinct in the case of Exp.LETKF (Table 3, entry #9). The modeled deep inflows occur inside deep troughs in the strait where the current speeds are strong 0.3∼0.4 m s−1 (Fig. 7) suggesting a topographically controlled deep flow (Whitehead et al. 1974; Qu et al. 2006b).
Comparisons of the Kuroshio transports east of Luzon and southeast of Taiwan (see Fig. 1 for transect locations) against other published modeled and observed transports are also conducted. For Exp.LETKF, the upper 500-m transport averaged over the simulation period is 22.6 Sv east of Luzon at 18° N and 20.3 Sv southeast of Taiwan. Estimates of the transport are 15∼35 Sv east of Luzon at 18° N by Sheu et al. (2010) and approximately 21∼22 Sv northeast of Taiwan by Johns et al. (2001). The present modeled transports generally agree with these estimates. Note that the transport difference between the southern and northern transects of the Kuroshio (north minus south) is −1.3 Sv, which is smaller in magnitude than the transport into the SCS of −5.5 Sv. It indicates that there is a large amount of water (∼−4.2 Sv) coming from the open Pacific Ocean. This result is consistent with the idea in the literature that there is intrusion of Pacific waters into the SCS. The intrusion could be induced by the large-scale meridional gradient of the wind stress curl and pressure gradient setup in the Pacific (Chang and Oey 2012), the local wind stress curl over the Luzon Strait in winter (Metzger and Hurlburt 1996), and westward propagating subtropical counter current eddies (Chang and Oey 2012).
The Luzon Strait is the only deep channel that connects the SCS with the Pacific Ocean. In the model, the sill depth of the Luzon Strait is 2,000 m, below which the SCS is therefore completely closed. The second and third deepest straits are Mindoro–Panay strait which is about 570 m and the Balabac Strait which is ∼130 m both connecting SCS to the Sulu Sea. South of the Sulu Sea, the Sibutu Passage sill is ∼235 m, and southwest of SCS, the Karimata Strait is ∼50 m. To the north, the Taiwan Strait is ∼70 m. We compute LETKF transport time series through Taiwan, Luzon, Sibutu, and Karimata straits (Fig. 8; for locations, see Fig. 1) which together enclose SCS. The LST is highly variable; some of the strong inflow transport appear to be related to the strong winter monsoon wind, e.g., in middle to end of February of 2012 (Oey et al. 2014). The mean Karimata transport and transport through Sibutu passage are negative, i.e., outflow from SCS, although the Sibutu transport (−0.6 ± 1.4 Sv) is not significantly different from zero. The mean Taiwan Strait transport is about −0.3 ± 1.3 Sv, but it too does not differ significantly from zero, consistent with transport observations in the strait under strong northeasterly monsoon winds in winter (Lin et al. 2005).
5 The three-layer circulation structure of the Luzon Strait and South China Sea
The three-layer structure of the LST appears to be a robust observed feature which may be dynamically related to the circulation of the SCS. The model of Chao et al. (1996; see their Figs. 2, 3, and 4 and descriptions) appears to indicate inflow at z = −150 m, outflow at z = −900 m, and inflow at z = −2,000 m in the Luzon Strait, but no integrated transports were given. Xue et al. (2004) were interested more in horizontal rather than vertical structure of the LST; it is difficult to discern a three-layer vertical structure from their results (see their Fig. 10 and descriptions). In the near-global model (based on MOM) of Qu et al. (2006a), interleaving inflows and outflows exist below 400 m, but the authors stated that the simulated LST did not show a three-layer structure in the vertical (see their p. 3648, Section 4a). Zhang et al. (2010) analyzed 2-year (2005–2006) mean LST using the outputs from a data-assimilated global model (based on the HYCOM) and compared them with the observations of Tian et al. (2006). Depth ranges (0–300, 300–1,200, and 1,200 m–bottom) different from those used by Tian et al. (2006; see Table 3) were used to define the upper, middle, and lower layers. The results (Table 3 entry #11) show westward inflows into SCS in the upper and middle layers and outflow into the North Pacific Ocean in the lower layer. Hsin et al. (2012) computed 7-year mean (2002–2008) LST from a regional model (based on POM) and concluded that there is “…outflow from 20 to 150 m, inflow from 150 to 1,200 m, outflow from 1,200 to 2,300 m, and little net transport below that” (see paragraph 16 of their paper). Except for the outflow in the near-surface layer, their Fig. 6 basically indicates a two-layer structure: inflow from 150 to 1,200 m and outflow below 1,200 m; the latter is similar to the result of Zhang et al. (2010).
5.1 Mean circulation in the South China Sea
The surface layer is considered to be driven by eddies and other fast and energetic processes. Below, we only implicitly consider this layer through the Ekman pumping that it imparts onto the layer immediately below—i.e., the upper layer. The goal is to explain the basin-scale, long-term mean circulations in the three subsurface layers and how they may relate to the Luzon transports.
5.2 Upper layer
This layer has two openings: one at Luzon with qL1fL/H1 < 0(influx) and the other one at Mindoro Strait with qM1fM/H1 > 0 (outflux). Here, subscripts L and M denote Luzon and Mindoro, respectively, and “1” denotes layer 1 or the upper layer. From the numerical model (Fig. 11, left), we find that |qM1| < |qL1|, and since fM < fL, influx of PV into SCS exceeds outflux. The net contribution of PV fluxes, − ∑ i = 1Nqifi/Hi, to the basin’s circulation ∮ Cru. l ds is therefore cyclonic. The upper layer is also acted on by Ekman pumping ∇ × τ which is positive for SCS (Qu 2000) contributing also to a cyclonic circulation. The resulting basin’s circulation in the upper layer is therefore cyclonic, as sketched in the left lower panel of Fig. 11.
5.3 Middle layer
Here, the basin only has one opening in the Luzon Strait where numerical model shows an outflow, and therefore, the basin’s circulation is anticyclonic (Fig. 11, middle).
5.4 Abyssal (lower) layer
Here the basin is closed, and the RHS term of Eq. (9) = 0, hence ∮ Cru. l ds = 0, and the circulation for the abyssal basin is zero. Therefore, anticyclonic circulation in one region must be compensated by cyclonic circulation somewhere else (Chang and Oey 2011). As described above, the Pac10 model shows deep eddying gyres of alternating signs: cyclonic in the north and anticyclonic in the south (Fig. 11, right panels).
5.5 Connection with the Luzon Strait transport
The deep circulation (bottom panel of Fig. 13) is compared with that obtained from Exp.Pac10 (Fig. 11, top right panel). Along the northern edge of SCS, the reduced-gravity simulation shows a northeastward flow due to the nature of the forcing in the simple model (Yang and Price 2000); the eastward flow in the Exp.Pac10 is very weak. Apart from this difference, the simple model captures well the general features of the abyssal circulation seen in Exp.Pac10. A western boundary current exists in the northern SCS; it flows west-southwestward and then around the eastern side of a deep seamount (near 114° E, 16° N) in the west, as seen also in Fig. 11. In the southwestern basin, an anticyclonic circulation is seen, as is also found for Exp.Pac10. The anticyclone becomes weak if Q = 0 (not shown), suggesting the importance of forcing on the abyssal circulation by upwelling west of the Luzon Strait as the Pacific water overflows into the SCS.
Cyclonic circulation in the northern part of the SCS was inferred by Wang et al. (2011) based on T and S data. Near the southwestern corner of the SCS, however, they found another cyclonic circulation. Lan et al. (2013) proposed a basin-scale cyclonic circulation using the Hybrid Coordinate Ocean Model. The authors propose based on Eq. (9) (τ = 0) that positive PV induced by the inflow (u.n < 0) from Luzon Strait was balanced by the PV dissipation along the boundary. As in the present model, their model SCS is closed below 2,000 m, and they applied Eq. (9) assuming a sill depth of 2,400 m. In contrast to Chao et al. (1996) and Exp.Pac10, anticyclone was not observed. A long-term observation of the deep SCS circulation is required to clarify the circulation pattern in the southwestern SCS.
This study has achieved three goals. First, a LETKF data-assimilation scheme was successfully implemented into an ocean prediction system of the western North Pacific Ocean. The results are compared against satellite and Argo float data and also against estimates based on a simpler OI assimilation scheme, for the test period from January 20 to April 3, 2012. When compared against the OI scheme, the LETKF scheme shows generally improved solutions over the modeled region of the western North Pacific. A comparison of the modeled transports through the Luzon Strait (and at other sections) against observed transports taken from the literature has been carried out. The second goal that we have accomplished is that the analyzed Luzon Strait transports from both OI and LETKF show a three-layer structure: inflow (into SCS) in the upper layer, outflow in the middle layer (defined as 500–1,500 m), and inflow in the lower layer. The three-layer structure and transports agree well with observed transport estimates, except in one case when there was only a two-layer structure when a mesoscale eddy was present in the strait during the field program. A review of the literature indicates that this is the first time that the observed three-layer transport structure in the Luzon Strait has been successfully simulated in a model.
The three-layer transport structure in the Luzon Strait imposes strong dynamical constraints on the possible time-mean basin-scale circulations in the SCS. The third goal is therefore to find and explain such solutions in the model. In order to do this, instead of the regional western North Pacific model with data assimilations, we resort to the long-term integration results of a basin-scale model of the entire North Pacific Ocean forced by a blended satellite and reanalysis wind product. Eighteen-year mean transports in the Luzon Strait again show a robust three-layer structure which confirms LETKF and OI analyses. We deduce by conservations of mass and potential vorticity that the mean circulations in the SCS consist also of three layers. The upper layer (−120 m > z > −570 m) circulation is cyclonic driven by Ekman pumping by the wind stress curl and by inflow through the Luzon Strait. The middle layer (−570∼−2,000 m) is anticyclonic due to outflow transport through the Luzon Strait. The abyssal basin (<−2,000 m) is driven by deep overflow from the Luzon Strait, which produces localized upwelling; the resulting deep circulation is cyclonic in the northern portion of the SCS, but it is anticyclonic in the southern portion.
We are grateful to the three reviewers and the editor for their comments and suggestions that improved the manuscript. We thank Y.-L. Chang, Y.-C. Lin, and M.-C. Chang of the ATOP Group for their assistance in running the mpiPOM. The supports for FHX from the National Basic Research Program of China (973 Program, Grant No. 2013CB956603) and from the start-up funds of the Tsinghua University are acknowledged. LYO is grateful for the award from the Taiwan’s Foundation for the Advancement of Outstanding Scholarship and acknowledges partial supports from the National Science Council and the National Central University.
- Atlas R, Hoffman RN, Ardizzone J, Leidner M, Jusem JC (2009) Development of a new cross-calibrated, multi-platform (CCMP) ocean surface wind product. AMS 13th Conference on Integrated Observing and Assimilation Systems for Atmosphere, Oceans, and Land Surface (IOAS-AOLS)Google Scholar
- Berntsen J, Oey LY (2010) Estimation of the internal pressure gradient in sigma-coordinate ocean models: comparison of second-, fourth-, and sixth-order schemes. Ocean Dyn 60:317–330Google Scholar
- Blumberg AF, Mellor GL (1987) A description of a three-dimensional coastal ocean circulation model. In: Heap N (ed) Three-dimensional coastal ocean models, coastal estuarine stud, vol 4. AGU, Washington, DC, pp 1–16Google Scholar
- Chang Y, Oey L (2013) Loop Current growth and eddy shedding using models and observations Part 1: numerical process experiments and satellite altimetry data. J Phys Oceanogr 43:669–689Google Scholar
- Chu PC, Edmons NL, Fan CW (1999) Dynamical mechanisms for the South China Sea seasonal circulation and thermohaline variabilities. J Phys Oceanogr 29:2971–2989Google Scholar
- Liao G, Yuan Y, Xu X (2008) Three dimensional diagnostic study of the circulation in the South China Sea during winter 1998. J Oceanogr 64:803–814Google Scholar
- Lin SF, Tang TY, Jan S, Chen CJ (2005) Taiwan Strait current in winter. Cont Shelf Res 25(9):1023–1042Google Scholar
- Lin X, Oey L-Y, Wang D-P (2007) Altimetry and drifter assimilations of Loop Current and eddies. JGR 112:C05046Google Scholar
- Mellor GL, Blumberg AF (1985) Modeling vertical and horizontal diffusivities with the Sigma Coordinate system. Mon Weather Rev 113:1379–1383Google Scholar
- Metzger EJ, Hurlburt H (2001) The importance of high horizontal resolution and accurate coastline geometry in modeling South China Sea inflow. Geophys Res Lett 28(6):1059–1062Google Scholar
- Oey L-Y, Ezer T, Forristall G, Cooper C, DiMarco S, Fan S (2005) An exercise in forecasting Loop Current and eddy frontal positions in the Gulf of Mexico. Geophys Res Let 32:L12611, 2005GL023253Google Scholar
- Oey LY, Chang YL, Lin YC et al (2013) ATOP-the Advanced Taiwan Ocean Prediction System based on the mpiPOM. Part 1: model descriptions, analyses and results. Terr Atmos Ocean Sci 2013:24Google Scholar
- Qu T, Du Y, Sasaki H (2006a) South China Sea throughflow: a heat and freshwater conveyor. Geophys Res Lett 33:23Google Scholar
- Shaw PT, Chao SY (1994) Surface circulation in South China Sea. Deep Sea Res Part I 40:1663–1683Google Scholar
- Stommel H (1958) The abyssal circulation. Letter to the editors. Deep Sea Res 5:80–82Google Scholar
- Wang C, Wang W, Wang D, Wang Q (2006) Interannual variability of the South China Sea associated with El Niño. J Geophys Res 111:C3Google Scholar
- Whitehead JA, Leetmaa A, Knox RA (1974) Rotating hydraulics of strait and sill flows. Geophys Fluid Dyn 6:101–125Google Scholar
- Willmott CJ (1981) On the validation of models. Phys Geogr 2:184–194Google Scholar
- Wyrtki K (1961) Physical oceanography of the Southeast Asian waters. Scripps Inst Oceanogr Univ Calif, La Jolla 2:195Google Scholar
- Yang Q, Tian J, Zhao W (2010) Observation of Luzon Strait transport in summer 2007. Deep Sea Res Part I 57:670–676Google Scholar
- Yin XQ, Oey LY (2007) Bred-ensemble ocean forecast of loop current and rings. Ocean Model 17:300–326Google Scholar
- Yuan Y, Liao G, Yang C (2008a) The Kuroshio near the Luzon Strait and circulation in the northern South China Sea during August and September 1994. J Oceanogr 64:777–788Google Scholar
- Yuan Y, Liao G, Guan W, Wang H, Lou R, Chen H (2008b) The circulation in the upper and middle layers of the Luzon Strait during spring 2002. J Geophys Res 113:C06004Google Scholar
- Yuan Y, Liao G, Yang C (2009) A diagnostic calculation of the circulation in the upper and middle layers of the Luzon Strait and the northern South China Sea during March 1992. Dyn Atmos Oceans 47:86–113Google Scholar
- Zhang Z, Zhao W, Tian J, Liang X (2013) A mesoscale eddy pair southwest of Taiwan and its influence on deep circulation. J Geophys Res Oceans. doi:10.1002/2013JC008994
- Zhou H, Nan F, Shi M, Zhou L, Guo P (2009) Characteristics of water exchange in the Luzon Strait during September 2006. Chin J Oceanology Limnol 27(3):650–665Google Scholar
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