2 University of Chinese Academy of Sciences, Beijing 100049, China
The ocean has an important role in the carbon cycle of the earth. Numerous studies have been motivated by a need to better underst and biogeochemical and carbon cycles within the upper ocean (Longhurst,1991; Feely et al., 2004) . Particulate organic carbon (POC) is one area of substantial interest, and is significant to biological pump and carbon-based estimates of primary production (Longhurst,1991; Bishop et al., 1999; Ducklow et al., 2001; Behrenfeld et al., 2005) . It consists of autotrophic and heterotrophic microorganisms and detrital particles suspended in the seawater. Unfortunately,temporal and spatial variations of POC stock have not been fully characterized over ocean-basin and global scales,because conventional oceanographic sampling is sparse (Allison et al., 2010) .
To overcome this limitation,advances in instruments for recording in situ and remote measurements of optical parameters have allowed for POC proxies (Cetinić et al., 2012) . These optical proxies include the total particulate scattering (bp (λ) ) ,particulate backscattering coefficient (bbp (λ) ) ,particulate beam attenuation coefficient (cp (λ) ) ,normalized water leaving radiance (Lwn (λ) ) , and spectral remote-sensing reflectance (Rrs (λ) ) (Stramski et al., 1999; Loisel et al., 2001; Mishonov et al., 2003; Behrenfeld et al., 2005; Stramska and Stramski, 2005; Pabi and Arrigo, 2006; Grob et al., 2007; Stramski et al., 2008; Son et al., 2009; Stramska,2009; Allison et al., 2010; Wang et al., 2011; Cetinić et al., 2012) . Among these approaches,empirical b and ratio algorithms have proven to be reliable, and have been used to routinely process ocean color satellite data to estimate the POC surface concentration (Stramski et al., 2008) . These equations compareRrs (λB) /Rrs (555) to the POC,where λBis the blue b and .
However,there is a limited amount of data available for developing POC b and ratio equations,when compared with field data for building empirical chlorophyll a (Chl- a) equations. Only a small number of studies were based on simultaneously collected POC and optical parameter field data (Stramski et al., 1999; Stramska and Stramski, 2005; Pabi and Arrigo, 2006; Stramski et al., 2008; Allison et al., 2010) . In addition to the limitations of simultaneous field data,regional differences in bio-optical properties can also confound the inversion results. For example,several studies have highlighted differences between similar analyses of POC and Rrs (λB) /Rrs (555) in different oceanic regions (Stramska and Stramski, 2005; Pabi and Arrigo, 2006; Stramski et al., 2008; Son et al., 2009; Allison et al., 2010) . One source of this variability may be “natural” and inherent to the types of particles that exist in seawater (Cetinić et al., 2012) . At the individual POC particle level,the carbon content of planktonic cells is coupled with the particle size and refractive index. These are primary determinants of particle backscattering coefficients (Verity et al., 1992; Montagnes et al., 1994) . As a result,the relationship between POC and the optical quantities of the ocean varies according to different POC distributions for different particle types and sizes. Other sources may be related to particular methods (Cetinić et al., 2012) . Therefore,we expect that regional ocean color algorithms will perform better if they are established on a regional basis (Hooker et al., 2000; Allison et al., 2010) .
In this study,we used field data collected from several cruises over the South China Sea (SCS) to develop a regional empirical equation that relates blue-to-green b and ratios forRrs (λ) to POC surface concentration. Our main objective was to improve POC inversion accuracy in the SCS. We compared in situ measured POC with satellite-derived POC to evaluate the regional and global formulas. Using 12 years (2002–2013) of remotely sensed data,we also analyzed the seasonal and annual variations of POC in the southwest of Luzon Strait (where winter phytoplankton blooms are common) . 2 METHODS AND DATA 2.1 Study area and field measurements
The SCS is the largest marginal sea of the west Pacific Ocean, and has an area of approximately 3.5 million km2. The East Asian monsoon is important to the hydrological features and upper layer circulations of the SCS. Runoff from the Pearl,Red, and Mekong Rivers carries large quantities of fresh water and dissolved nutrients into the SCS. These special oceanographic conditions have a huge impact on the dynamics of the ecosystem in coastal and open seas, and mean that the bio-optical properties of the SCS have some regional characteristics (Wang et al., 2007; Zhao et al., 2014) . For our POC studies,we took samples from coastal and offshore waters between 2007 and 2013. The locations of the sampling stations are shown in Fig. 1. These cruises (Table 1) included: (1) five cruises in the northern South China Sea (NSCS) (August–September in 2007,2008,2011,2010, and 2012) ; (2) one cruise in the SCS (April–May in 2010) ; and (3) one moored optical buoy site (114.291°E,22.061°N) located near the Dangan Isl and s (water depth of approximately 30 m and an observation period of 16 days between August 13 to 28 of 2007) . During each SCS and NSCS cruise,we used Niskin bottles to collect water samples at the surface, and at depths of 25 m,50 m, and 75 m for some stations. At the optical buoy station,we collected water samples at the sea surface each day at 9:00,12:00, and 15:00.2.1.1 POC determinations
We filtered 0.4–4 L of surface seawater through pre-combusted (450°C for 5 h) 25 mm Whatman GF/F glass fiber filters under a low vacuum. Following filtration,we froze these samples in liquid nitrogen and stored them at -80°C until a post cruise analysis could be performed in the laboratory. We selected a number of unused filters from each lot of precombusted fi lters as blanks,to quantify the background amount of organic carbon in the filters. To remove the inorganic carbon,we applied 0.25 mL of 10% HCL to each sample filter and dried the acid-treated filters at 55°C. The POC concentrations were then measured using an elemental analyzer (Flash EA-Delta V) . The analytical uncertainty of POC was less than 5% for duplicate measurements (Wang et al., 2011) . Adsorption of dissolved organic carbon (DOC) onto the filters during fi ltration was corrected by subtracting 2.0 μmol C from the total POC contained in the filter (Gardner et al., 2003) .
For the development of the POC algorithm,samples collected at the near-surface (<5 m) were considered. For the validation of the regional algorithms,the field POC data also include measurements from August–September NSCS cruise in 2010 and 2013 in addition to the data from the seven cruises listed above. 2.1.2 Particle and colored dissolved organic matter
(CDOM) absorption coefficient measurements We filtered water samples (0.5–3 L) from certain depths using a 25-mm glass fiber filter (Whatman GF/F) at a low vacuum. Filters were kept in liquid nitrogen before analysis. In the laboratory,we measured the absorption spectra of the particles (ap (λ) ) using an ultraviolet-visible spectrophotometer (Shimadzu,UV-2550) equipped with an integrating sphere. Spectraw ere acquired between 240 and 800 nm with a 1-nm step. Then,phytoplankton pigments were removed from the filter using a methanol treatment for 90–180 min (Kishino et al., 1985) . The sample filter was rescanned to measure the non-algal absorption spectra (ad (λ) ) using the same method. The absorption spectra of aph (λ) were determined using the difference between ap (λ) and ad (λ) . All spectraw ere shifted to zero in the near infrared by subtracting the average optical density between 750 and 800 nm,to minimize any possible differences between the sample and reference filters (Bricaud et al., 2010) . The path-length amplification effect was corrected according to the method proposed by Roesler (1998) . We determined the absorption of colored dissolved organic matter (CDOM) ,a CDOM (λ) ,according to the procedure described by Babin et al. (2003) . A baseline correction was applied by subtracting the absorbance value averaged over a 5-nm interval around 685 nm from all the spectral values. 2.1.3 Radiometric measurements
The spectral remote-sensing reflectance (Rrs (λ) ,in /sr) is defined as the ratio of the nadir water-leaving radiance (Lw (0 +,λ) ) to the downwelling plane irradiance (Ed (0 +,λ) ) ,where both quantities are measured just above the sea surface. We used two sources of remotely sensed reflectance. At the moored optical buoy site,we used hyper-spectral radiometers to measure the downwelling plane irradiance (Ed (z,λ) ) and the upwelling radiance (Lu (z,λ) ) from 400 to 800 nm (with a spectral resolution of 1 nm) at three depths (1 m above the sea surface, and approximately 0.3 m and 2.3 m below the sea surface) . The entire dataset was automatically recorded at hourly intervals between 8:00 and 18:00, and sent to the laboratory using GPRS (general packet radio service) and CDMA (code division multiple access) networks. For more data processing details,please refer to Zhao et al. (2008) . We corrected for self-shading effects according to Gordon and Ding (1992) .
For the SCS and NSCS cruises,theRrs (λ) values were determined from measurements of the underwater vertical profiles of Lu (z,λ) and Ed (z,λ) using a free-fall profiler (containing OCI/R-200 radiometers from Satlantic,Inc.) . The center wavelengths were 412,443,490,520,555,620, and 665 nm and the b and width was approximately 10 nm. These dataw ere not recorded until the instrument was tens of meters from the ship,to minimize the shipshading effect. The incident irradiances in the same seven channels above the sea surface (Es (λ,0 +) ) were simultaneously recorded by a complementary surface unit,placed on the deck away from the shadows. We processed the initial data using Prosoft ver. 7.7 (Satlantic,Inc.) to determineRrs (λ) . 2.2 Satellite data and matching procedures
To assess the performance of the POC algorithm,we compared the in situ data to the matched satellite data. We used the Aqua Moderate Resolution Imaging Spectroradiometer (MODIS-Aqua) level 2 local area coverage (LAC,1.1 km resolution at nadir) satellite data,downloaded from the NASA Ocean Color Web site (http://oceancolor.gsfc.nasa.gov/cgi/browse.pl?sen=am) . These data are from MODIS-Aqua Reprocessing 2012.0. After obtaining the satellite estimates ofRrs (λ) ,we applied the b and ratio POC algorithms to estimate the satellite-derived POC for comparison.
We matched the data based on the closest spatial and temporal LAC satellite pixels to the in situ measurements,within a certain threshold. The matching procedures were similar to Bailey and Werdell (2006) . First,we found the 3×3-pixel window that was closest to the location of the in situ measurement within a time interval of ±4 h. Second,we discarded poor quality pixels from the window (as defined by the quality control flags in the data products (i.e.,problems due to clouds,stray light,glint,atmospheric correction failure,high top-ofatmosphere radiance,low water-leaving radiance,large solar/viewing angles, and navigation failure) . Third,if more than 50% of the pixels in each window remained,then the pixel window was accepted for the subsequent matching analysis. We computed the coefficient of median spatial variation (CV) for each of the selected b and s,for the remotely sensed reflectance and POC. Finally,we excluded satellite retrievals with extreme variations (CV>0.15) from the defined window, and determined the matched satellite value using the average of the remaining pixels.
This strict criterion produced 20 in situ and satellite data matched pairs for MODIS-Aqua. To maximize the number of high quality matched pairs,we relaxed the acceptable time interval to ±48 h to get a moreobjective and persuasive assessment. We determined the temporal variability using a temporal variance check. The variance was defined as the matched data (within±48 h) divided by all satellite data between 48 h before and 96 h after the current time. The st and ard deviation of the variance had a mean of 13.61% (±6.8%) . This is comparable to the uncertainties in the in situ POC measurements. Thus,we used an extended ±48 h time window to compared the satellite and in situ data. This resulted in 40 more matched data pairs. Among these 60 matched pairs,43 were not used to develop the algorithm. 3 RESULT AND DISCUSSION 3.1 Reflectance b and ratio algorithm for POC
Figure 2 shows the relationships between POC and the blue-to-green b and ratios of remotely sensed refl ectance. We examined b and ratios Rrs (443) / Rrs (555) ,Rrs (490) / Rrs (555) , and Rrs (510) / Rrs (555) , and the maximum b and ratio (MBR) ,which is the largest of the three ratios. All these regression analyses were based on the ordinary least squares Model I regression technique (Sokal and Rohlf, 1995) . The formulas used to calculate the error statistics are provided in Table 2. A summary of the regression parameters and error statistics for various relationships are given in Table 3.
Our comparison of the error statistics (Table 3) suggests that the power functions are a good fit to our POC and b and ratio data. These results are consistent with previous research from other oceanic regions (Stramska and Stramski, 2005; Stramski et al., 2008; Son et al., 2009; Allison et al., 2010) . The determination coefficient (R2) exceeded 0.9 for Rrs (443) / Rrs (555) ,Rrs (490) / Rrs (555) , and Rrs (510) / Rrs (555) . The empirical formula for POC compared to Rrs (443) /Rrs (555) had a mean normalized bias (MNB) of -2.52% and anormalized root mean square error (NRMS) of 31.1%. The error statistics are similar for POC compared to Rrs (490) / Rrs (555) . The results comparing POC and Rrs (510) /Rrs (555) or the MBR are inferior. Overall,for the dataset consisting of 120 pairs of field measurements,we found that the simple power functions comparing POC to Rrs (443) /Rrs (555) or Rrs (490) /Rrs (555) resulted in slightly better error statistics than the other relationships. These results suggest that the power function POC=262.173 [ Rrs (443) / Rrs (555) ] -0.940is presently the best choice for applications in the SCS.
Our estimates of the best fit power function are different to similar analyses of POC and reflectance measurements in other oceanic regions (Fig. 3) . For example,the slope of POC versus Rrs (443) /Rrs (555) in the SCS is less steep than that in the Southern Ocean (Allison et al., 2010) . The differences between the fitted parameters at different regions suggest that there are some variabilities in the b and ratio algorithms that depend on location. This also implies that we must establish a regional algorithm for the SCS.
Rrs (λB) /Rrs (555) has been recognized as a basis for empirical equations for estimating chlorophyll a (Chla) for many years (O’Reilly et al., 1998) . These equations rely on the fact that changes in b and ratios are largely because of variations in the absorption coefficients of particles caused by different pigmentcontaining phytoplankton and co-varying detrital matter. A similar rationale can be applied to the empirical POC algorithm,using the hypothesis that the b and ratios are largely driven by the absorption coefficient associated with all the POC-containing particles. Based on simultaneous measurements of absorption coefficients (Fig. 4) ,we briefly explored how variations in the absorption coefficient affect the blue-to-green reflectance ratios in the SCS. This type of analysis is helpful for underst and ing why POC can be obtained using the b and ratios of remotely sensedreflectances.
We know from radiative transfer modeling that the b and ratio involving the blue wave b and centered at λB and the green wave b and centered at 555 nm has an approximate relationship with bb) and a (λ) (Gordon et al., 1975; Morel,1988) . That is,
Observations have shown that variations in blueto-green reflectance ratio are largely driven by changes to the absorption b and ratio,a (555) / a (λB) (Allison et al., 2010) . In the following analysis,we set λB=443 to be consistent with our empirical formula. For brevity,the symbol aw+a indicates the sum of the absorption coefficients of pure water and particles,aw + ap . Similarly abbreviated symbols are used for other absorption components. Figure 5 displays Rrs (443) /Rrs (555) versus aph+w (555) / aph+w (443) ,Rrs (443) /Rrs (555) versus ad+w (555) / ad+w (443) ,Rrs (443) /Rrs (555) versus ap+w (555) / ap+w (443) , and Rrs (443) /Rrs (555) versus aCDOM+w (555) / aCDOM+w (443) . These data indicate that phytoplankton and non-algal particulate matter are both important to the blue-togreen reflectance ratio. Rrs (443) /Rrs (555) versus aCDOM+w (555) / aCDOM+w (443) has the largest scatter of data points,especially for large aCDOM+w (555) / aCDOM+w (443) . This result is similar to the observations of Allison et al. (2010) . They noted that this scatter can be an important source of “noise” in the relationship between the reflectance b and ratios and inherent optical properties, and hence a source of noise in the POC b and ratio algorithm.
To analyze the relationship between POC and ap +w (555) / ap+w (443) ,we used measurements of POC and particulate absorption coefficients from all depths of seawater (239 pairs for surface waters, and 201 pairs for under surface waters (25–100 m) ) . Figure 6 shows that ap +w (555) / ap+w (443) decreased as POC increased. This may be because various types of organic particles (such as detritus,heterotrophic organisms, and phytoplankton) all exhibit an increase in absorption from the green to the blue spectral region (Fig. 7) (Stramski et al., 2008) . Our results also indicate that we can estimate POC from the blue-togreen b and ratio of reflectance primarily because of the relationship between POC and the green-to-blue spectral slope of the particle absorption coefficients. All the factors (such as phytoplankton species and particle size distribution (PSD) ) that affect this relationship (POC versus spectral slopes) may have an impact on the empirical reflectance b and ratio algorithm. This makes the algorithm region dependent.3.2 Validation of the POC Algorithms and possibleerror sources
Figure 8 compares the matched observations of satellite-derived POC for the global algorithm and in situ POC measurements,using the matching criteria described in Section 2.2. The error parameters and associated formulas are listed in Table 4. These error parameters are similar to Bailey and Werdell (2006) . MR is the median of the ratio of satellite-derived values to in situ values for a given variable, and provides a measure of the overall bias of the satellite data relative to the in situ data. SIQR is the semiinterquartile range of the satellite to in situ ratio, and indicates the spread of the data. MPD is the median of the difference in relative percentages, and gives the overall degree of agreement between the satellite and in situ measurements. RMSD is the root mean square deviation, and is used to assess uncertainties in the data.
There was a reasonable trend and correlation between the satellite-derived (global algorithm,Fig. 8a) and in situ POC values over their dynamic range. The satellite-derived POC based on the global algorithm tended to underestimate the in situ values,with a median bias of -22.8% (MR=0.772) . The MPD was 15.04%, and the RMSD was 59.23 mg/m3. The matched data based on the regional algorithm were a considerably better fit than those from the global algorithm (Fig. 8b) . The median bias was approximately +2.7%,the MPD was 2.75%, and the RMSD was 47.30 mg/m3.
It is important to note that the validation points cover coastal and open ocean waters,which means our b and ratio empirical algorithm should perform reasonably well over vast areas of the SCS. Although the number of matched data points for validation is not enough to provide a definite verification of POC algorithms in the SCS,our results suggest that the regional b and ratio algorithm produces more accurate results than the global algorithm.
There are two main reasons for a mismatch between in situ measured POC and satellite-derived POC. The first is that there may be uncertainties in the satellitederived spectralRrs (λ) data,especially for satellitederived remotely sensed reflectance ratios (Rrs (443) / Rrs (555) ) . Previous assessments showed that MODIS overestimated Rrs (443) /Rrs (555) (by 20.2% for RPD) in the SCS (Zhao et al., 2014) . This overestimation of Rrs (443) /Rrs (555) could lead to an underestimation of POC. Uncertainties inRrs (λ) also indicate that atmospheric correction procedures must be improved. The POC algorithm is the second reason for mismatches. The comparison results listed in Fig. 3 clearly show that the global algorithm underestimates the POC,especially at low concentrations. This may mean that the underestimates of the st and ard MODIS POC products in the SCS were because of: (1) overestimates of Rrs (443) / Rrs (555) ; or (2) underestimates of the global algorithm. The regional algorithm produced significantly improved results (Table 4) . The above analysis implies that the selection of proper POC algorithm is very critical in the SCS.
There may be other possible error sources that affect the validation results. First,some errors are inherent to the algorithm. CDOM and the variable compositions of particles can introduce noise to POC b and ratio algorithm. For example,the higher absorption of CDOM in the blue b and may result in an overestimate of POC. Second,in situ measurements may contain some uncertainties because of various experimental and environmental factors. The calibration,dark signal,data processing, and deployment strategy can introduce errors into radiometric measurements. POC values are also subject to several potential sources of errors (Moran et al., 1999; Gardner et al., 2003; Stramski et al., 2008) . Third,within-day variabilities of POC at a fixed location also confound the validation results (Cui et al., 2013; Gernez et al., 2014) . 3.3 Satellite estimates of POC in the southwest
Luzon Strait Luzon Strait connects the Western Pacific Ocean to the SCS. The biological processes in this region are influenced by complex hydrological conditions,including Kuroshio intrusion (Farris and Wimbush, 1996) ,mesoscale eddies (Wu and Chiang, 2007) , and internal waves (Liu and Hsu, 2004) . Several oceanographic studies have investigated winter phytoplankton blooms near Luzon Strait. We combined MODIS-Aqua and our empirical formula to investigate the variability of seasonal and inter-annual distributions of POC in the southwest of Luzon Strait. 3.3.1 Study area and satellite-derived data
Phytoplankton blooms often occur in winter (Dec.–Feb.) in the southwest of Luzon Strait, and are typically centered at 119.0°E,19.0°N covering an area of 2.58×104 km2off the coast of the northwest Philippines (Wang et al., 2010) . Our study area is located between 18.0°–121.0°E and 17.0°–21.0°N,along part of the Malina trench (Fig. 9) . This area is affected by the northeast (in winter) and southwest (in summer) monsoons (Shang et al., 2012) .
For the satellite data,we downloaded the 2002–2013 MODIS-Aqua Level-3 st and ard mapped image product (daily) from the NASA Ocean Color Web site (http://www.oceancolor.gsfc.nasa.gov) . Then,we applied our regional empirical algorithm based on the b and ratio Rrs (443) /Rrs (555) to calculate the MODISderived POC. To evaluate the spatial and temporal variations of surface POC in the southwest of Luzon Strait,we combined daily images into monthly,seasonal, and inter-annual mean images using a cylindrical projection with the SeaWiFS Data Analysis System (SeaDAS 7.1) .
For the MODIS-derived Chl-a,previous assessments showed that the st and ard OC3 algorithm produced overestimates (Zhao et al., 2014) . To improve the accuracy of the Chl- ainversion,we developed a regional OC3 algorithm based on 123 matched pairs of in situ data (in situ Rrsmatched with in situ Chl- a) . Using the same matching procedures,we found 82 validation points. The validation results are shown in Table 5. The assessment results based on the regional OC3 algorithm were a considerably better fit than those from the st and ard algorithm. Although some uncertainties remain after using the regional algorithm,we believe that we can reasonably analyze the variation trends of Chl- aover a long time series. The OC3 Chl- aequation is3.3.2 Surface concentration of POC in the southwest of Luzon Strait
The time-series of monthly mean POC concentrations obtained over a 12-year period are displayed in Fig. 10. We found that the monthly patterns were quite similar from year to year. The POC to Chl- aratios were between 200 and 700, and tended to decrease with increasing Chl- a concentration. Significant seasonal changes in the spatial mean POC revealed that it is typically high in winter (exceeds 100 mg/m3) , and weak during other seasons (less than 60 mg/m3) ,as shown in Fig. 11.
We derived a monthly climatology using data from 2002 to 2013. Each image is a composite of 12 years of data for that month. The statistical characteristics of each month are shown in Fig. 12. From December to February (which encompass the peak growing season for phytoplankton) ,the probability density functions of POC are generally broader and have higher frequencies of high POC (>90 mg/m3) when compared with the rest of the year.
In the southwest of Luzon Strait,northeast monsoonal winds in winter enhance Ekman pumping convective mixing in the upper ocean. This increases the mixed layer thickness via entrainment. Nutrients will arrive,support the growth of phytoplankton from the subsurface to the upper layer, and enhance the concentration of POC and biomass (Wang et al., 2010; Shang et al., 2012) . In other seasons,Ekman pumping and entrainment is so weak that nutrients cannot be transported toward the surface. This is why POC and Chl- ahave regular seasonal changes.
By considering a seasonal climatology of remotely sensed data for winter (Fig. 13) ,we found that there were lower POC concentrations in 2004,2008, and 2011, and that the highest POC concentrations occurred in 2013. The POC to Chl- aratios were below 300 in 2003 and 2013. These results imply that the intensity of physical and biological processes in this area have inter-annual variations. The oscillations of the northeast monsoonal wind strength may be a key factor. When the monsoon is weak or has a short duration,the reduced biomass affects the average POC concentrations. Additionally,inter-annual variations of Kuroshio intrusions in this area can also be important to the biological processes.4 CONCLUSION
In this paper,we developed regional empirical equations for estimating surface concentration of POC using remotely sensed reflectance. Based on 120 paired field measurements,we selected the simple power function POC=262.173[ Rrs (443) / Rrs (555) ] -0.940as the regional equation for the SCS. To assess the performance of our regional and global formulas,we used a relaxed matching method to compare an algorithm-derived satellite data product with in situ measurements. Although there were a limited number of matched data points in this study (60 pairs) ,the validation results suggest that the regional b and ratio equation produces better POC estimates from ocean color remotely sensed data in the SCS than the global algorithm. Our results also show that the b and ratio empirical formula is largely driven by the relationship between POC and the green-to-blue ratio of the particle absorption coefficient. CDOM can be an important source of noise in the POC b and ratio equation. Regional differences in the empirical method may be related to the optical properties between particle types and changes in the detailed composition of particle compositions. Further studies using more data and techniques (such as radiative transfer-based modeling) are needed to determine these causes. When applying the regional empirical equations to the southwest of Luzon Strait,we found that the POC concentration is higher in winter under the influence of a northeast monsoonal wind. POC exhibits regular seasonal and inter-annual variations in this area.
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