Abstract
Using cruise observations and reanalysis data, this study analyzes the effects of wind, freshwater, and turbulent mixing on the two upwellings: one is off the eastern coast of Hainan Island (HEU) and the other is off the northeastern coast of Hainan Island (HNEU). During the cruise in 2009, the HNEU occurred with southwesterly to southeasterly wind. The relative large values of turbulent kinetic energy dissipation rate and diffusivity estimated from the Thorpe scale indicate that the upwelling water is further uplifted to the surface by strong turbulent mixing in the HNEU region. But the HEU was not observed under the southeasterly wind. During the cruise in 2012, the HNEU disappeared in the upper layer with freshwater covered and southeasterly wind, while the apparent HEU only accompanied with southwesterly wind. To obtain the general characteristics, we define three types of upwelling patterns, i.e., the intensified HEU, the intensified HNEU, and both HEU and HNEU in one day, using the reanalysis data. The composites of sea surface temperature (SST), wind, and precipitate for each upwelling pattern identify that the HNEU is associated with the prevailing southeasterly wind and can be limited in the lower layer when it is covered by freshwater. But the HEU is mainly driven by southwesterly wind but is not remarkably affected by freshwater.
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1 Introduction
Summertime coastal upwelling is one of the most important phenomena in the northern South China Sea. The upwelling over the east shelf of Hainan Island is a significant phenomenon in the northern South China Sea, known as Qiongdong upwelling (see Xie et al. 2012 for a review). In fact, the upwelling includes two upwelling components (e.g., Li et al. 2012): (1) Upwelling off the eastern coast of Hainan Island (or Hainan eastern upwelling, HEU) and (2) upwelling off the northeastern coast of Hainan Island (or Hainan northeastern upwelling, HNEU).
The HEU has been widely studied. The maximum vertical velocity of the upwelling calculated by simplified momentum equation is approximately 3 × 10−5 m s−1 (Han et al. 1990; Guo et al. 1998). The summer southwesterly monsoon is considered as the driving force for the upwelling (Jing et al. 2011). The Ekman pumping induced by the local wind stress curl is also responsible for the formation of the upwelling (Jing et al. 2009). By estimating the Ekman transport and Ekman pumping in the upwelling region, Wang et al. (2013) identified that 33 % of the total wind-driven upwelling is due to Ekman pumping, the rest is due to Ekman transport. Wind not only induces the upwelling locally, but also forces the large-scale circulation of the South China Sea to affect the upwelling (Su and Pohlmann 2009). Su et al. (2011) predicted that the wind-driven upwelling is associated with cross-shelf circulation according to the Burger number. The number is about 0.96 nearby the Hainan Island, which means that the balance of the shoreward transport and the surface offshore transport exists in the interior layer rather than in the bottom layer. They also pointed out that the freshwater from river discharges only inhibits the upwelling in the nearshore region. Besides, the vertical mixing caused by the internal waves plays a positive role in the upwelling intensification and the varying coastline determines the upwelling location (Su and Pohlmann 2009).
However, a few studies have analyzed the HNEU specifically. The local wind not only generates the upwelling (Li 1990), but also controls its variability (Li et al. 2012). Since a special bottom topography is associated with an upwelling-favorable cross-shelf circulation (e.g., Gan et al. 2009), the bottom topography off the eastern and northeastern coasts of Hainan Island interacting with current may be significant in the process of HNEU (Li et al. 2012; Song et al. 2012). Particularly, Lin et al. (2016) diagnosed that the along-isobath barotropic pressure gradient force mainly intensities the HNEU. Similarly, the HNEU is also enhanced by the large-scale circulation of the South China Sea in summer (Li et al. 2012). In addition to wind and current, eddies and tides were also reported as important factors affecting the HNEU (Yu 1987; Song et al. 2012).
However, the characteristics, especially the differences, of the HEU and HNEU have not been well understood due to the limited evidences. The analysis and comparison of the HEU and HNEU may help to better understand their detailed processes. This study aims to explore these upwelling processes using the methods and data sources described in Section 2. The results are given in Section 3 and discussed in Section 4. Section 5 is the conclusions.
2 Data and methods
2.1 Hydrographic observation and reanalysis data
The two cruises were carried out during July 16 – August 15, 2009 and during July 29 – August 21, 2012, respectively. Temperature and salinity data were conducted off the eastern and northeastern coasts of Hainan Island (Fig. 1) during the two cruises using the Seabird SBE 911 and 917 CTD (Conductivity-Temperature-Depth) profilers. The instrument accuracies of conductivity, temperature, and pressure are 3 × 10−4 S/m, 1 × 10−3 °C, and 1 dbar, respectively.
The real-time wind data were measured from the meteorological station (Wind Monitor-MA) onboard. The threshold sensitivity and the available range of the instrument are 1.1 and 0–100 m s−1, respectively. The 10-s wind data were block-averaged into 5-min intervals. In addition, a daily blended wind dataset with a resolution of 0.25°, during summers (June, July and August) from 2006 to 2012 covering the time of the two cruises, is provided by the National Climatic Data Center (http://www.ncdc.noaa.gov/). This wind data are generated by blending multiple-satellite observations and reanalysis products (Zhang et al. 2006).
The daily and high-resolution (1/20° × 1/20°) sea surface temperature (SST) data are produced by the Operational SST and Sea Ice Analysis (OSTIA) system. The SST reanalysis data are assimilated from satellite and in situ data, which are available from the website of Group for High Resolution Sea Surface Temperature (https://www.ghrsst.org/). To match the timescale of the blended wind data, we also choose the SST data for the summers in 2006–2012 (644 SST images).
The daily precipitation data are from the Version 7 Tropical Rainfall Measuring Mission (TRMM) product 3B42 (ftp://meso-a.gsfc.nasa.gov/pub). The data, in a horizontal resolution of 0.25° × 0.25°, combine multi-satellite microwave-IR estimates (Huffman et al. 2007). Similarly, the precipitation data for the summers in 2006–2012 are chosen.
2.2 Methods
Potential density σ θ is computed to estimate vertical overturning according to the Thorpe scale (L T , Thorpe 1977). In turn, the turbulent kinetic energy (TKE) dissipation rate is empirically estimated from
where N is the vertical-sorted buoyancy frequency from potential density profiles (Dillon 1982; Nash et al. 2007; Alford et al. 2011; Klymak et al. 2011). From both TKE dissipation rate ε and buoyancy frequency N, the diffusivity is computed by \( {K}_z=\varGamma \varepsilon {N}^{-2} \), where \( \varGamma \) is an efficiency parameter, commonly set as 0.2 (Osborn 1980). The noise of data is removed according to the CTD instrument resolution and the run length test (Galbraith and Kelley 1996; Stansfield et al. 2001).
The upwelling extent is identified from daily SST images using the fuzzy c-means clustering (FCM, see Sousa et al. 2008 for details), which has been successfully used in upwelling identification in many studies (e.g., Chen et al. 2012). As a fuzzy pixel classification method, the FCM aims to partition image pixels into c (the number) fuzzy clusters through iteratively approximating the minima of the objective function. Figure 2c shows an example of FCM algorithm with c = 4 clusters applied to the SST image (Fig. 2a) on July 24, 2009 corresponding to the cruise mission time. A relatively cold upwelling area is located in the shelf off the northeastern coast of Hainan Island and represented in blue (cluster c1) in the FCM image. Similarly, the non-upwelling regions with higher SST are colored by dark red (cluster c4).
Based on the all FCM images, the probability of upwelling in each SST pixel is calculated as the ratio of the number of upwelling days to the total number of SST images (644 days). To facilitate the upwelling analysis, we define the regions according to the probability distribution of upwelling and name them as HEU region and HNEU region, respectively (Fig. 2d, dashed boxes).
UINE (UIE) is short for the upwelling index of HNEU (HEU) region which is defined as the difference of averaged SST between the HNEU (HEU) region and non-upwelling region for each SST image. Larger value represents more intensified upwelling.
3 Results
3.1 Distributions of the upwelling
Apparently, a region with relatively low temperature and high salinity was located off the northeastern coast of Hainan Island at a depth of 5 m during the 2009 cruise (Fig. 3a, c). The central temperature and salinity are 26.5 °C and 33.6 psu, respectively. In contrast, during the 2012 cruise, the low temperature and high-salinity region (central temperature of 26 °C and the salinity of 33.6 psu) was over the shelf off the eastern coast of Hainan Island (Fig. 3b, d). This difference of upwelling patterns well matches with the SST images from reanalysis data as shown in Fig. 2a, b. At the depth of 20 m, the nearshore area was occupied by the low temperature and high-salinity water during both the cruises in 2009 and 2012 (Fig. 4).
3.2 Effect of wind
3.2.1 Case analysis
To verify the effect of wind, we perform a case analysis of the HNEU and HEU based on the cruise observations. A scatter diagram v (meridional component) against u (zonal component) from the real-time wind data is shown in Fig. 5. Clearly, in the HEU region, winds were southeasterly (cross-shore) during the cruise mission in summer 2009 so the HEU did not exist, while winds were southwesterly (alongshore) during the cruise mission in summer 2012, thus a strong HEU appeared. In the HNEU region, the most scattered points gather in the first quadrant of the coordinate system (southwesterly wind) during the 2012 cruise when the HNEU was not apparent. Winds swung between southwesterly and southeasterly during the 2009 cruise, but the HNEU was still observable in the upper layer.
The wind-related upwelling process can be more clearly identified through comparing wind conditions and the vertical structure of water masses. The water mass distribution is analyzed using triangle of mixing method summarized by Mamayev (1975) (see appendix for detail). Based on the θ-S diagram (Fig. 6), the percentages of the mixing ratio among the three water masses, the freshwater (FW), the upwelling water (UW), and the sea surface water (SW) are estimated. The θ-S diagram includes the data of all nearshore stations (depth <50 m) and offshore stations (depth >200 m) in the study regions in cruises of 2009 and 2012.
For the HEU, station C covered in two cruises and station D only in 2012 (located at the center of the HEU) were selected (Fig. 1). At station C of 2009, UW was lower than 75 % in the upper 40 m (Fig. 7, gray line). In contrast, the water mass with 75 % UW was uplifted to 28 m depth at the corresponding station in 2012 (Fig. 7, black line). Accordingly, the southeasterly wind (6.5 m s−1) and southwesterly wind (2.1 m s−1) were blowing at station C during the 2009 and 2012 cruises, respectively. It indicates that southwesterly wind is conductive to generation of the HEU. At the center of the HEU, the UW (>50 %) dominated the whole water column of station D in 2012 (Fig. 7, black dashed line), where the averaged wind had similar direction but larger magnitude (3.5 m s−1) comparing to the condition at station C in the cruise. It shows that the HEU is not only generated but also intensified by the southwesterly wind, which is in line with the previous studies (e.g., Jing et al. 2011).
To see effects of wind on the HNEU, we select the nearshore stations (in HNEU region) in corresponding transects in 2009 and 2012 (Fig. 1). In Fig. 8c, the vertical structure of UW in 2009 shows that the percentage of UW near the bottom layer at stations A2, A1, and AB is more than 75 %. In particular, at station A1, the 75 % contour uplifted toward 20 m depth and the 50 % contour reached to the subsurface. The averaged winds were southwesterly except at station A2 (Fig. 8a). It is different in 2012 that the water mass with over 75 % UW was limited below 30 m (Fig. 8d), while wind was southwesterly and two times larger in magnitude (Fig. 8b). Thus, the strong southwesterly wind may not be favorable to the HNEU in this case, which is further discussed in Section 4.
3.2.2 General characteristics
Here, we apply the long-term reanalysis data to provide general features of the HEU and HNEU. Three types of upwelling patterns are distinguished from the 644 SST images: (1) Intensified HEU, defined as the upwelling pattern in the days that the UIE is higher than the mean value plus the half of one standard deviation (0.5 SD) while UINE is less than the mean value minus 0.5 SD (namely, UIE > mean + 0.5 SD and UINE < mean − 0.5 SD); (2) Intensified HNEU, defined as the upwelling pattern in the days when UINE > mean + 0.5 SD and UIE < mean − 0.5 SD; and (3) Both intensified HEU and HNEU in one day, defined as the upwelling pattern in the days when UINE > mean + 0.5 SD and UIE > mean + 0.5 SD. It is noted that the range 0.5 SD is used to avoid the number of samples being not large enough to analyze. Interestingly, the third upwelling pattern occurs in 113 days, while the only intensified HEU pattern is in 29 days and the only intensified HNEU pattern is in 18 days.
The composite of SST superimposed by the composite of wind for each upwelling pattern is shown in Fig. 9. For the intensified HEU pattern (Fig. 9a), the southwesterly wind is upwelling-favorable in the HEU region, while southerly-southwesterly wind prevails in the HNEU region. The averaged UIE slowly increases from roughly 0.8 to over 1.0 °C with the steady southwesterly wind continuing for 7 days before this upwelling pattern (Fig. 10a, red vectors and bars). However, in the HNEU region, the averaged wind is southeasterly on former 4 days (from −7 to −3 days in Fig. 10a, blue vectors and bars) while the averaged UINE is stably around 0.8 °C, and then transfers to be southwesterly corresponding to the apparently decreasing of the UINE. It agrees with the results from in situ data.
The southeasterly wind dominates the HNEU region for the intensified HNEU pattern (Fig. 9b). However, the HEU disappears under the southeasterly wind. From 7 days before the upwelling pattern, corresponding to the continuously southeasterly wind, the UINE keeps the level with small increase (Fig. 10b). On the contrary, the UIE drops rapidly while the alongshore wind is replaced by the cross-shore wind. Statistically, it again highlights the important role of southwesterly wind in the HEU formation, and illustrates that southeasterly wind benefits the intensified HNEU.
During the upwelling pattern of both HEU and HNEU in one day (Fig. 9c), wind is nearly southerly in both HEU and HNEU regions. It seems that both the intensified HEU and HNEU patterns develop from this upwelling pattern according to the variations of upwelling indexes and wind shown in Fig. 10. Acting as a middle pattern of the upwelling processes, this upwelling pattern transfers to the intensified HNEU pattern when the HNEU keeps its level under the southeasterly wind but the HEU is inhibited by shoreward wind. On the other hand, the upwelling pattern becomes the intensified HEU pattern if HEU is intensified by alongshore wind but HNEU is weakened.
3.3 Effects of freshwater
3.3.1 Case analysis
The contribution of freshwater is taken account to the HNEU as well as to the HEU. In Fig. 3, one can see that the water with relatively low salinity covered a larger area of the HNEU region during the 2012 cruise than during the 2009 cruise. Sectional distributions of salinity and potential density (\( {\sigma}_{\theta } \)-1000 kg m−3) at the two selected transects are shown in Fig. 11. In these two transects, there are five stations covered in both cruises. Three other stations along the 30 m isobath are only conducted in 2009 and four other stations are only in 2012. The shoreward-lifting isopycnals elevated from offshore toward the nearshore region, and outcropped to the surface between 50 and 100 km of the transect in 2009 (Fig. 11a). In 2012, the isopycnals uplifted toward the subsurface at roughly 150 km where low potential density water was covered on the surface (Fig. 11b). In the θ-S diagram (Fig. 6), the scatters of the nearshore stations (black dots) do not overlay the ones of the offshore stations (dark and light blue dots) in the area where the percentage of FW is more than 20 %. It means that the water mass represented in this area does not originate from offshore regions. Therefore, in this study, the water mass mixing with over 20 % FW is considered as being related to FW (rFW).
We construct the sectional distributions of the rFW in the HNEU region during the 2009 and 2012 cruises (Fig. 8c, d). In 2009, the rFW only occupied the upper 10-m layer between stations A1 and A2, while the UW was apparently uplifted at station A3 (Fig. 8c) as mentioned before. In 2012, the influence extent of the rFW was upper 5 m at station B2, and extended to upper 30 m at station B1, whereas 75 % contour of UW is limited below 30 m (Fig. 8d). We compare the condition at station AB covered in both cruises. The maximum buoyancy frequency (\( {N}_{\max}^2 \)) was 1.0 ×10−2 s−2 at a depth of 27 m, matching the effective depth of the rFW in 2012 (Fig. 8d), and was over three times larger than that in 2009 (\( {N}_{\max}^2 \)=3.5×10−3 s−2) (not shown). The water mass mixing about 75 % UW was uplifted to the depth where the buoyancy frequency was close to the maximum. This co-occurrence suggests that the HNEU can be limited by the strong stratification due to freshwater in the upper layer.
But the low-salinity water was not detected in the HEU region during either cruise. The maximum percentages of FW at the three selected stations (station C in 2009, stations C and D in 2012) were roughly 16, 13, and 9 %.
3.3.2 General characteristics
To further clarify the general effect of freshwater, we also computed the composite of precipitation for each upwelling pattern (Fig. 12). Apparently, for the intensified HEU pattern (Fig. 12a), high mean precipitation is over the north of 20° N, especially on the Leizhou Peninsula (close to 20 mm h−1). But there is virtually no precipitation on average in the HEU region. We can expect that the high precipitation brings considerable freshwater to the shelf off the eastern coast of the Leizhou Peninsula and in the HNEU region. The precipitation pattern is close to the freshwater distribution in the 2012 cruise (Fig. 3d), when the HNEU disappeared in the surface. Associated with the intensified HNEU (Fig. 12b), no precipitation is over the land and shelf nearby or in the HNEU region. But the HEU region has small precipitation. In addition, for the upwelling pattern of both HEU and HNEU in one day, composited precipitation is small over lands (less than 10 mm h−1), and close to zero in the sea areas (Fig. 12c).
It again reveals the freshwater plays a negative role in the HNEU. But owing to its small magnitude (shown in both in situ and reanalysis data) in the HEU region, freshwater does not actually affect the HEU.
3.4 Effects of turbulent mixing
For dynamic processes, the northern South China Sea is featured by tides and high-frequency nonlinear internal waves, which are important in turbulence generation and diapycnal mixing (Liu and Lozovatsky 2012). The deep water has higher potential density and is diffused to the upper layer, even to the surface, by mixing processes (Jiang et al. 2011). It is worth noting that the study regions are mainly located on the nearshore shelf (water depth <50 m) (Fig. 2d). Therefore, turbulent mixing should be taken into account.
Turbulence is usually generated by variable atmospheric forcing in the surface mixed layer and tidal flows in the bottom boundary layer. The profiles of TKE dissipation rate ε and vertical diffusivity K z at selected stations in the HNEU region are shown in Fig. 8c–f. In the surface mixed layer, defined as the upper 5-m layer in the stations based on the vertical distribution of ε, the maximum ε and K z were as large as 10−5 W kg−1 and 10−3 m2 s−1. In the deeper layer, ε and K z had large variations among stations. At station A1 in 2009, the ε and K z were nearly uniform (Fig. 8c, e), which is associated with more UW reaching to the surface. In other words, since the strong turbulent mixing throughout the water column, with relatively high averaged dissipation rate ε=1.1×10−6 W kg−1 and vertical diffusivity\( {K}_z \)=2.6×10−3 m2 s−1, the uplifted deeper water was further diffused up to the surface. However, at most stations, ε and K z were small at roughly 10 m depth where the diffusing process was weak. Although large ε and K z were observed at station B1 in 2012, the dominated rFW in the whole water column retreated the upwelling process (Fig. 8d, f) owing to the strong stratification (analyzed in Section 3.3). These results show that strong turbulent mixing throughout the water column is able to further diffuse the UW to the upper layer (even surface) on the condition that the UW has been uplifted.
The turbulent mixing condition of the HEU is represented by vertical structures of ε and K z at the three selected stations in the HEU region (Fig. 13). As the condition in the HNEU region (Fig. 8), the maximum magnitudes of ε and K z existed in the surface layer in HEU stations. At station C, \( \varepsilon, \) and K z were higher in 2009 than those in 2012 throughout the water column, but the HEU was apparent during the 2012 cruise rather than during the 2009 cruise. In 2012, the ε and K z at the HEU center (station D) were higher than those at station C. Particularly in the surface and bottom layers, the ε and K z at station D were close to the orders of 10−5 W kg−1 and 10−3 m2 s−1, respectively. It suggests that the turbulent mixing does not directly generate the HEU, but further intensifies the generated HEU.
4 Discussion
Different to the HEU, the HNEU is not a classical wind-driven coastal upwelling based on the Ekman process. Remind that the upwelling pattern of both HEU and HNEU in one day is the most frequent upwelling pattern (in 113 days). We suspect that HEU and HNEU are related in most of the intensified upwelling period. As reported by Lin et al. (2016), the along-isobath wind causes the HEU, meanwhile drives current to form the HNEU through flow-topography interaction. In this study, however, the HNEU was not obvious when southwesterly wind blew (Figs. 8b and 9a) in either in situ data or reanalysis data. As noted in Section 3.1, in the 2012 cruise, the HNEU disappeared in the surface, but was apparent at a depth of 20 m (Figs. 3 and 4). By comparing the effects of wind and freshwater on the HNEU, the covered freshwater, rather than the southwesterly wind, can be the key factor that stops the deep water uplifting to the surface.
As shown in Section 3.2, the intensified HNEU pattern is associated with southeasterly wind (Fig. 9). Linking with the deduction that freshwater has a negative effect on the HNEU, we suspect that the southeasterly wind may weaken the southward extension of freshwater that originates from the north. This is consistent with Lentz and Fewings (2012) who pointed out that the shoreward wind is a substantial term that drives the shoreward flow in the upper layer over the inner shelf (water depth < 30 m).
In addition, the northeastward boundary current, a part of the South China Sea circulation in summer (Hu et al. 2000), is along the eastern coast of Hainan Island. The current-topography interaction drives the onshore transport that uplifts the UW to the upper layer (Lentz and Trowbridge 1991). Under the steady condition, the bottom Ekman transport relation (Brink and Lentz 2010) is given by \( f{U}_{BE}=-{\tau}^y/{\rho}_0 \), where the U BE is the bottom Ekman transport controlled by the bottom along-shelf friction (\( {\tau}^y \)). The cross-shelf transport can be one of interpretations for characteristics of the upwelling reflected by the spatial distribution of the relatively low temperature and high-salinity water at a depth of 20 m on the eastern shelf of Hainan Island and Leizhou Peninsula (Fig. 4).
5 Conclusions
We observed the HNEU in the summer cruise in 2009 and the HEU in the summer cruise in 2012. This study presents the comparison of the HEU and HNEU, and the analysis of the driving factors based on the hydrographic observation and reanalysis datasets: blended wind, SST, and precipitation. In order for water mass analysis, we construct the θ-S diagram based on the CTD data. The percentages of mixing ratio of three water masses (FW, UW, and SW) are calculated using the triangle of mixing method. It reveals that the HNEU was observed during the 2009 cruise when the southwesterly to southeasterly wind prevailed in the HNEU region, and the HEU occurred with the alongshore southwesterly wind during the 2012 cruise. To verify the general characteristics, we compute the composites of SST and wind for the three types of upwelling patterns (the intensified HEU, the intensified HNEU, and both HEU and HNEU in one day) based on the long-term reanalysis data. It again indicates that generally the HEU is southwesterly wind-driven, and the intensified HNEU is related to the southeasterly wind.
The rFW (the water mass mixed over 20 % FW) dominated the sea surface in the HNEU region, and formed the strong stratification with high buoyancy frequency; thus, UW cannot be uplifted continuously to the surface layer during the 2012 cruise. The precipitation composites for the three upwelling patterns display a general feature that the precipitation is close to zero around the HNEU region for the intensified HNEU pattern, but its extent southward extend to inhibit the HNEU in the surface for the intensified HEU pattern. In contrast, the turbulent mixing plays a positive role in enhancing the upwelling process. According to the vertical distribution of the TKE dissipation ε and the vertical diffusivity Kz estimated, the strong turbulent mixing could diffuse UW up to the surface. But, the freshwater and turbulent mixing did not remarkably impact on the HEU during either cruise.
In the study, however, the dynamical analysis of upwelling is limited by the lack of current data. It can be further identified by reasonable numerical modeling as well as the extensive observations. For instance, Acoustic Doppler Current Profiler (ADCP) mooring data can be used to acquire the current velocity time series and the microstructure data from Microstructure Systems (MSS) Profiler will help to improve the present understanding.
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Acknowledgments
The authors appreciate two anonymous reviewers for suggestions that improved this manuscript. This work is supported by the National Basic Research Program of China projects 2015CB954004 and 2009CB421208, and the National Natural Science Foundation of China projects 41276006 and U1405233. The authors also thank the crew of R/V Dongfanghong 2 for help with the cruise survey and Shaoling Shang for helpful comments.
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Appendix: The triangle of mixing
Appendix: The triangle of mixing
Based on the water mass analysis method summarized by Mamayev (1975), on the T-S (or θ-S) diagram, the three water masses (e.g., A, B, and C, having temperatures and salinity T A , S A ; T B , S B ; T C , S C , respectively) form a triangle of mixing (Fig. 14). The product of the complete mixing of the three water masses will have a temperature and salinity determined by the formulae of mixing:
where a, b, and c are the proportions of the three water masses. The points of mixing result of the three water masses lie within the triangle of mixing. In this study, the proportions a, b, and c are calculated by solving the formula system with the known temperature and salinity of the three water masses and the mixture.
The solution is:
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Lin, P., Hu, J., Zheng, Q. et al. Observation of summertime upwelling off the eastern and northeastern coasts of Hainan Island, China. Ocean Dynamics 66, 387–399 (2016). https://doi.org/10.1007/s10236-016-0934-2
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DOI: https://doi.org/10.1007/s10236-016-0934-2