Validation of a Primary Production Algorithm of Vertically Generalized Production Model Derived from Multi-Satellite Data around the Waters of Taiwan

: Basin-scale sampling for high frequency oceanic primary production (PP) is available from satellites and must achieve a strong match-up with in situ observations. This study evaluated a regionally high-resolution satellite-derived PP using a vertically generalized production model (VGPM) with in situ PP. The aim was to compare the root mean square di ﬀ erence (RMSD) and relative percent bias (Bias) in di ﬀ erent water masses around Taiwan. Determined using light–dark bottle methods, the spatial distribution of VGPM derived from di ﬀ erent Chl-a data of MODIS Aqua (PP A ), MODIS Terra (PP T ), and averaged MODIS Aqua and Terra (PP A&T ) exhibited similar seasonal patterns with in situ PP. The three types of satellite-derived PPs were linearly correlated with in situ PPs, the coe ﬃ cients of which were higher throughout the year in PP A&T (r 2 = 0.61) than in PP A (r 2 = 0.42) and PP T (r 2 = 0.38), respectively. The seasonal RMSR and bias for the satellite-derived PPs were in the range of 0.03 to 0.09 and − 0.14 to − 0.39, respectively, which suggests the PP A&T produces slightly more accurate PP measurements than PP A and PP T . On the basis of environmental conditions, the subareas were further divided into China Coast water, Taiwan Strait water, Northeastern upwelling water, and Kuroshio water. The VPGM PP in the four subareas displayed similar features to Chl-a variations, with the highest PP in the China Coast water and lowest PP in the Kuroshio water. The RMSD was higher in the Kuroshio water with an almost negative bias. The PP A exhibited signiﬁcant correlations with in situ PP in the subareas; however, the sampling locations were insu ﬃ cient to yield signiﬁcant results in the China Coast water.


Introduction
Primary production (PP) refers to the production of organic carbon during photosynthesis [1]. It sets the upper limit for ocean productivity and is an essential measure of the ocean's capacity to transform carbon dioxide into particulate organic carbon at the base of the food web [2][3][4]. From a bottom-up perspective [2,5,6], PP is also a good predictor of the potential yield of the world's oceans. In situ primary production was determined by light-dark bottle methods through incubation in 300 mL dissolved oxygen (DO) bottles. This technique was modified using Winkler's method. We prepared two types of DO bottles, one of which was transparent (light bottle) and the other was wrapped in aluminum foil (dark bottle). Seawater samples were collected at depths of 5, 25, and 50 m using 10 L Niskin bottles in each station, and water samples were filtered using a 300 μm filter cloth. The filtered sample was then packed into two DO bottles: one light bottle and one dark bottle. Each bottle was filled with 300 mL of seawater, following which, measurements were taken of the temperature and dissolved oxygen using a dissolved oxygen meter (YSI Model 52).
One light bottle was placed in the incubator (constant temperature of 25 ℃, 4000 lux light). The dark bottle was set in the incubator, which was dark. After one day, the temperature and DO of the three bottles were measured. The PP was the difference in dissolved oxygen between the light and dark bottles, the formula for which was as follows: In situ PP = ([O2]L−[O2]D) × carbon atom weight/dissolved oxygen atom weight/1 day.  In situ primary production was determined by light-dark bottle methods through incubation in 300 mL dissolved oxygen (DO) bottles. This technique was modified using Winkler's method. We prepared two types of DO bottles, one of which was transparent (light bottle) and the other was wrapped in aluminum foil (dark bottle). Seawater samples were collected at depths of 5, 25, and 50 m using 10 L Niskin bottles in each station, and water samples were filtered using a 300 µm filter cloth. The filtered sample was then packed into two DO bottles: one light bottle and one dark bottle. Each bottle was filled with 300 mL of seawater, following which, measurements were taken of the temperature and dissolved oxygen using a dissolved oxygen meter (YSI Model 52).
One light bottle was placed in the incubator (constant temperature of 25°C, 4000 lux light). The dark bottle was set in the incubator, which was dark. After one day, the temperature and DO of the three bottles were measured. The PP was the difference in dissolved oxygen between the light and dark bottles, the formula for which was as follows: × carbon atom weight/dissolved oxygen atom weight/1 day.
[O 2 ]L: the dissolved oxygen in the light bottle after incubating for 1 day.
[O 2 ]D: the dissolved oxygen in the dark bottle after incubating for 1 day. The PP (mg C m −2 d −1 ) was then integrated in terms of depth (m). The depth ranged from 0-50 m.

Satellite-Derived PP Estimates
The PP model of the VGPM used in this study was based on Chl-a concentration, and the formulation and parameterization were recommended by Behrenfeld and Falkowski [19]. Maximum photosynthetic efficiency in VGPM is described as an optimal rate of photosynthesis (P B opt ) in a water column normalized to Chl-a concentration (mg·C·mg·Chl −1 ·h −1 ). The VGPM estimates the daily integrated PP in a water column of euphotic depth (PP eu , mg C m −2 day −1 ) as follows: Photosynthetically available radiation (PAR) denotes daily averaged surface photosynthetic active radiation at 400-700 nm (E·m −2 ·day −1 ), Z eu denotes euphotic depth, and DP denotes a day photoperiod. Z eu was calculated from satellite surface chlorophyll-a concentration for lower and higher total chlorophyll conditions following Morel and Berthon [36]. P B opt is expressed as a seventh-order polynomial function of SST [19], which is formulated as follows: The satellite data used in VGPM during the study period of 2009-2013 are SST, Chl-a, and PAR. MODIS Aqua/Terra daily Level 1A were downloaded from the NASA Ocean Color website. SeaDAS v6.2 was used to process high-resolution (1.1 km) local area coverage images and Chl-a data (OC3Mv6 algorithm). Daily PAR product data were downloaded from the Ocean Productivity database. Daily SST data were extracted from NOAA AVHRR SST images and had a spatial resolution of 1.1 km. The NOAA HRPT data, including AVHRR scenes, were received at a ground station at National Ocean Taiwan University. Daily DP data were produced by the Central Weather Bureau using a Precision Spectral Pyranometer. The three categories of satellite-derived PP were calculated using different MODIS Chl-a data as follows: (1) MODIS Terra evaluated primary production (PP T ), (2) MODIS Aqua evaluated primary production (PP A ), and (3) the averaged MODIS Aqua and Terra evaluated primary production (PP A&T ).
The divisions of waters around Taiwan also have different oceanographic characteristics. They were divided into 1 • gridded areas across 36 sites (Figure 2a). Cluster analysis with normalized Remote Sens. 2020, 12, 1627

of 15
Euclidean distances was used to measure levels of similarity in gridded areas in the waters around Taiwan in 2009-2013, including monthly Chl-a, SST, and PAR. Ward's method was used to illustrate the relationships between them in a dendrogram. The cluster analysis was conducted using STATISTICA 8 statistical software.
Remote Sens. 2020, 12, x FOR PEER REVIEW 5 of 15 calculated using different MODIS Chl-a data as follows: (1) MODIS Terra evaluated primary production (PPT), (2) MODIS Aqua evaluated primary production (PPA), and (3) the averaged MODIS Aqua and Terra evaluated primary production (PPA&T). The divisions of waters around Taiwan also have different oceanographic characteristics. They were divided into 1° gridded areas across 36 sites (Figure 2a). Cluster analysis with normalized Euclidean distances was used to measure levels of similarity in gridded areas in the waters around Taiwan in 2009-2013, including monthly Chl-a, SST, and PAR. Ward's method was used to illustrate the relationships between them in a dendrogram. The cluster analysis was conducted using STATISTICA 8 statistical software.

Figure 2. (a)
The waters around Taiwan were divided into 1° gridded areas for 36 sites. The subareas for the China Coast water, Taiwan Strait water, Northeastern upwelling water, and Kuroshio water were divided by the cluster tree diagram results using the monthly Chl-a, SST, and PAR during study period (2009)(2010)(2011)(2012)(2013) in (b). The monthly mean PPA&T image in 2009 was used as an example in (a).

Match-Up Data and the Assessment of Satellite PP Models
To evaluate the satellite-derived PP with in situ PP, we produced pairs of collocated satellite overpasses and in situ sampling was extracted with a time difference shorter than ± 12 h. The satellite observations have spatial averages of 3 × 3 pixels around each sample site location and were compared with field measurements.
The PP values derived from the VPGM model were regressed against in situ data and a type II linear regression model was applied, as both field and modeled data are subject to errors. The slope, intercept, and the correlation coefficient (r) were then determined. For Chl-a, the regression was performed between log-transformed values. The RMSD statistic assesses model skill such that models with lower values have higher skill, and the model bias assesses whether a model over-or underestimates PP [11]. We calculated the RMSD for n samples of PP: where ( , ) modeled PP and ( , ) represents in situ PP estimates at each site. To assess whether a model over-or underestimated PP, we calculated the bias of each model as follows:

Match-Up Data and the Assessment of Satellite PP Models
To evaluate the satellite-derived PP with in situ PP, we produced pairs of collocated satellite overpasses and in situ sampling was extracted with a time difference shorter than ± 12 h. The satellite observations have spatial averages of 3 × 3 pixels around each sample site location and were compared with field measurements.
The PP values derived from the VPGM model were regressed against in situ data and a type II linear regression model was applied, as both field and modeled data are subject to errors. The slope, intercept, and the correlation coefficient (r) were then determined. For Chl-a, the regression was performed between log-transformed values. The RMSD statistic assesses model skill such that models with lower values have higher skill, and the model bias assesses whether a model over-or underestimates PP [11]. We calculated the RMSD for n samples of PP: where (PP model,i ) modeled PP and (PP in situ,i ) represents in situ PP estimates at each site. To assess whether a model over-or underestimated PP, we calculated the bias of each model as follows:

Annual and Seasonal Trends in PP
The spatial distribution of VPGM-based production derived from AVHRR SST and MODIS Chl-a in the waters around Taiwan showed similar seasonal spatial patterns to in situ PP (Figures 3 and 4). The highest concentration of PPs was observed along the Mainland China Coast and four major upwelling regions (southwestern and northwestern coast, Taiwan Bank, and Penghu Islands) around the waters of Taiwan. Lower PP values were obtained across the whole year within the Kuroshio-influenced region in eastern parts. During the study periods, the total numbers of colocated satellite overpasses and in situ sampling sites were extracted with a time difference shorter than ± 12 h. This contained 102 sets for PP A&T , 151 for PP A, and 150 for PP T , respectively ( Table 2).

Annual and Seasonal Trends in PP
The spatial distribution of VPGM-based production derived from AVHRR SST and MODIS Chla in the waters around Taiwan showed similar seasonal spatial patterns to in situ PP (Figures 3 and  4). The highest concentration of PPs was observed along the Mainland China Coast and four major upwelling regions (southwestern and northwestern coast, Taiwan Bank, and Penghu Islands) around the waters of Taiwan. Lower PP values were obtained across the whole year within the Kuroshioinfluenced region in eastern parts. During the study periods, the total numbers of colocated satellite overpasses and in situ sampling sites were extracted with a time difference shorter than ± 12 h. This contained 102 sets for PPA&T, 151 for PPA, and 150 for PPT, respectively ( Table 2).

Comparison of Satellite-Derived and in Situ PP
To validate the model results, the three satellite-derived PP values (PPA&T, PPA, PPT) were compared with in situ PP values. They were linearly correlated with the situ PP and the coefficient was higher in PPA&T (r 2 = 0.61) than in PP (r 2 = 0.42) and PP (r 2 = 0.38) throughout the year ( Table  2). The highest correlations were observed in spring, especially for PPA&T (r 2 = 0.74) ( Figure 5).
The lowest correlations were observed in winter and were nonsignificant. Relative to the in situ PPs, the modeled PPs (PPA&T, PPA, PPT) had a RMSD of 0.37, 0.34, and 0.34, and a bias of −0.24, −0.197 and −0.174, respectively ( Table 2). The seasonal RMSR and bias were in the range of 0.03-0.09 and −0.14-0.39, respectively, for the three satellite-derived PPs. This implied that the three PPs had similar results; however, the PPA&T algorithm produced slightly more accurate PP measurements than the PPA and PPT algorithm.

Comparison of Satellite-Derived and in Situ PP
To validate the model results, the three satellite-derived PP values (PP A&T , PP A , PP T ) were compared with in situ PP values. They were linearly correlated with the situ PP and the coefficient was higher in PPA&T (r 2 = 0.61) than in PP A (r 2 = 0.42) and PP T (r 2 = 0.38) throughout the year ( Table 2). The highest correlations were observed in spring, especially for PP A&T (r 2 = 0.74) ( Figure 5).

Cluster Analysis and Characteristics in the Subareas
The cluster analysis showed that the waters around Taiwan can be divided according to environmental conditions into four subareas: China Coast water (CCW), Taiwan Strait water (TSW), Northeastern upwelling water (NUW), and Kuroshio water (KW) (Figure 2b). In terms of the relationship between SST, MODIS Aqua Chl-a, and PPA in four subareas for each 1 °C gridded, the monthly mean SSTs were in the range of 7-30 °C in CCW, 13-30 °C in TSW, 17-25 °C in NUW, and  Table 2). The seasonal RMSR and bias were in the range of 0.03-0.09 and −0.14-0.39, respectively, for the three satellite-derived PPs. This implied that the three PPs had similar results; however, the PP A&T algorithm produced slightly more accurate PP measurements than the PP A and PP T algorithm.

Cluster Analysis and Characteristics in the Subareas
The cluster analysis showed that the waters around Taiwan can be divided according to environmental conditions into four subareas: China Coast water (CCW), Taiwan Strait water (TSW), Northeastern upwelling water (NUW), and Kuroshio water (KW) (Figure 2b). In terms of the relationship between SST, MODIS Aqua Chl-a, and PP A in four subareas for each 1 • C gridded, the monthly mean SSTs were in the range of 7-30 • C in CCW, 13-30 • C in TSW, 17-25 • C in NUW, and 22-30 • C in KW, and had no clear relationships with PP A were revealed (Figure 6a). The strong correlation between PP A and MODIS Aqua Chl-a in subareas is shown in Figure 6b. The monthly mean PP A and Chl-a were in the ranges of 600-2500 mg·C·m −2 ·day −1 and 2-5 mg·m −3 in CCW, 500-1500 mg C m −2 ·day −1 and 1-3 mg·m −3 in TSW, 500-1000 mg C m −2 ·day −1 and 1-2 mg·m −3 in NUW, and 0-500 mg C m −2 ·day −1 and 0-1.5 mg·m −3 in KW.

Cluster Analysis and Characteristics in the Subareas
The cluster analysis showed that the waters around Taiwan can be divided according to environmental conditions into four subareas: China Coast water (CCW), Taiwan Strait water (TSW), Northeastern upwelling water (NUW), and Kuroshio water (KW) (Figure 2b). In terms of the relationship between SST, MODIS Aqua Chl-a, and PPA in four subareas for each 1 °C gridded, the monthly mean SSTs were in the range of 7-30 °C in CCW, 13-30 °C in TSW, 17-25 °C in NUW, and 22-30 °C in KW, and had no clear relationships with PPA were revealed (Figure 6a). The strong correlation between PPA and MODIS Aqua Chl-a in subareas is shown in Figure 6b. The monthly mean PPA and Chl-a were in the ranges of 600-2500 mg·C·m −2 ·day −1 and 2-5 mg·m −3 in CCW, 500-1500 mg C m −2 ·day −1 and 1-3 mg·m −3 in TSW, 500-1000 mg C m −2 ·day −1 and 1-2 mg·m −3 in NUW, and 0-500 mg C m −2 ·day −1 and 0-1.5 mg·m −3 in KW. The comparison of in situ data and model data for each subarea is presented in Table 3. The PPA had significant correlations with in situ PP in the TSW (r 2 = 0.26), NUW (r 2 = 0.37) and KW (r 2 = 0.14). The comparison of in situ data and model data for each subarea is presented in Table 3. The PP A had significant correlations with in situ PP in the TSW (r 2 = 0.26), NUW (r 2 = 0.37) and KW (r 2 = 0.14). PP A+T only had significant correlations with in situ PP in the TS, and PP T had no significant correlations in any of the subareas. The RMSD values were higher in the KW, ranging between 0.06-0.87, with an almost negative bias in the range of −0.74 to 0.38 (Figure 7). The RMSD in the TSW, NUW, and CCW were in the range of 0.07-0.67 with bias in the range of −0.49 to 0.27.

Discussion
Primary producers reside at the base of food webs, and thus, drive ecosystem dynamics through bottom-up forcing [11]. The global biogeochemical cycles of major elements, particularly the carbon cycle, are greatly influenced by primary producers [2]. The primary producers convert the inorganic to organic carbon by photosynthesis in the light environment, and the carbon production is referred to as gross PP [37]. Net PP is gross PP minus the phytoplankton's respiration, and it supplies to all heterotrophs in the oceans. Net community production is gross PP minus respired by autotrophs and heterotrophs [37]. Both net PP and net community production play an important factor for biological carbon circulation. Therefore, understanding the spatial and temporal dynamics of PP is invaluable in earth and life science research [38,39].
The present study provided the first assessment of a satellite-derived VPGM PP model with in situ PP estimates in the regional waters around Taiwan. In light-dark oxygen methods, not only phytoplankton but also heterotrophic bacteria and zooplankton are in the bottles. The charge in dissolved oxygen of the light bottle is affected by photosynthesis and community respiration, and the gross PP can be estimated by net community production and community respiration [37]. The light-dark oxygen method used in the present study and the 14 C method are often used to measure in situ marine PP. The light-dark oxygen method was the main approach to measure PP before the

Discussion
Primary producers reside at the base of food webs, and thus, drive ecosystem dynamics through bottom-up forcing [11]. The global biogeochemical cycles of major elements, particularly the carbon cycle, are greatly influenced by primary producers [2]. The primary producers convert the inorganic to organic carbon by photosynthesis in the light environment, and the carbon production is referred to as gross PP [37]. Net PP is gross PP minus the phytoplankton's respiration, and it supplies to all heterotrophs in the oceans. Net community production is gross PP minus respired by autotrophs and heterotrophs [37]. Both net PP and net community production play an important factor for biological carbon circulation. Therefore, understanding the spatial and temporal dynamics of PP is invaluable in earth and life science research [38,39].
The present study provided the first assessment of a satellite-derived VPGM PP model with in situ PP estimates in the regional waters around Taiwan. In light-dark oxygen methods, not only phytoplankton but also heterotrophic bacteria and zooplankton are in the bottles. The charge in dissolved oxygen of the light bottle is affected by photosynthesis and community respiration, and the gross PP can be estimated by net community production and community respiration [37]. The light-dark oxygen method used in the present study and the 14 C method are often used to measure in situ marine PP. The light-dark oxygen method was the main approach to measure PP before the 14 C method was invented [1], the latter of which is more sensitive and offers good precision, although a radioisotope needs to be added to the water samples. The acquisition, use, and disposal of the radioisotope requires specific procedures and incurs high costs. Nevertheless, it yields reliable data through a careful process using oxygen electrodes [1].
In situ measurements of PP are spatially and temporally limited and require multiple integrated sampling approaches. The use of ocean color data in PP models provides an attractive alternative to field estimations as it offers an estimation at a high spatial and temporal resolution. AVHRR SST and MODIS Chl-a have long been used to study marine characteristics; however, their availability is seriously reduced by cloud coverage. The coverage provided by AVHRR SST and MODIS Chl-a daily images in the current study were in the range 20%-80% (Figure 8 as examples), and notably lower in wintertime (<30%). Although the availability of data from microwave observations was almost 100% [40], the disadvantage of a low spatial resolution meant that it was not appropriate for use in coastal areas. The limited match-up data between the satellite-derived data and in situ measurements were relaxed to within ± 12 h in the present study, and this time difference may have affected the matching accuracy. For example, Lee et al. [41] compared the MODIS SSTs with in situ SSTs and suggested that if the time difference was ± 3 h, this would produce the smallest bias but with a lower match-up of usable data. field estimations as it offers an estimation at a high spatial and temporal resolution. AVHRR SST and MODIS Chl-a have long been used to study marine characteristics; however, their availability is seriously reduced by cloud coverage. The coverage provided by AVHRR SST and MODIS Chl-a daily images in the current study were in the range 20%-80% (Figure 8 as examples), and notably lower in wintertime (<30%). Although the availability of data from microwave observations was almost 100% [40], the disadvantage of a low spatial resolution meant that it was not appropriate for use in coastal areas. The limited match-up data between the satellite-derived data and in situ measurements were relaxed to within ± 12 h in the present study, and this time difference may have affected the matching accuracy. For example, Lee et al. [41] compared the MODIS SSTs with in situ SSTs and suggested that if the time difference was ± 3 h, this would produce the smallest bias but with a lower match-up of usable data. To make best use of this technique, it is essential to assess the accuracy of the satellite-derived products to determine the uncertainty of the data input into the models [14]. The bias and RMSD between AVHRR SST and in situ data were 0.01 and 0.64 °C and high accuracy than the MODSI SST (bias = 0.03 °C, RMSD = 0.75 °C) in the waters around Taiwan [41,42]. For the MODIS Chl-a data, the To make best use of this technique, it is essential to assess the accuracy of the satellite-derived products to determine the uncertainty of the data input into the models [14]. The bias and RMSD between AVHRR SST and in situ data were 0.01 and 0.64 • C and high accuracy than the MODSI SST (bias = 0.03 • C, RMSD = 0.75 • C) in the waters around Taiwan [41,42]. For the MODIS Chl-a data, the previous study suggested that in coastal or upwelled waters, the blue region of the water that left a radiance signal used in standard Chl-a satellite algorithms was affected by colored dissolved organic matter and detrital material in addition to phytoplankton. This resulted in the decreasing accuracy of Chl-a and therefore PP [18,20]. The matching accuracy OC3M algorithm was within 11% of in situ Chl-a in the Arabian Sea and performed better than the Garver Siegel Maritorena Model and Generalized Inherent Optical Property Chla algorithms [43]. The satellite Chl-a estimates tended to be larger than in situ reference values, and also revealed that a nonuniform Chl-a distribution in the water column can be a factor alongside the documented overestimation tendency when larger optical depth match-up stations are considered [44].
When the Chl-a derived from MODIS Aqua and Terra is compared, the MODIS Terra is more accurate in the coastal waters of the Arabian Sea [45], possibly due to differences in sensor design and time differences between the satellites' overpasses. Applying standard products of satellite-derived PP for research in the open ocean is acceptable; however, using such products in regional studies remains questionable. This is especially so when the shelf sea areas are dominated by large rivers containing a large amount of suspended particles and color-dissolved organic matter [26,35]. The estimation errors of satellite-derived PP were often the result of incorrectly applying ocean color chlorophyll algorithms and inaccurate PP data [46]. In our case, the highest correlation coefficients were obtained in the PP A+T around the waters of Taiwan in the spring. However, the highest significant correlation coefficients in the four subareas were observed for PP A . The lowest correlations for PP A+T , PP T , and PP A all occurred in wintertime. Although the RMSD and bias were lowest in PP A , the difference was not significant. We found that VPGM estimated PPs were always underestimated with satellite-derived PPs, which may be due to errors in the P B opt calculated as a function of SST [47]. However, this photosynthetic parameter also strongly depends on factors such as nutrient supply, irradiance, and dominating phytoplankton species.
Satellite SST represents temperature only in the uppermost ocean layer and P B opt , being a function of SST, differs in the lower layers, providing different photosynthetic efficiency [21]. The VGPM is one of the most widely known and applied depth-integrated/wavelength-integrated models. However, it has rarely been applied to coastal waters. Lobanova et al. [21] compared the accuracy of PP derived from the VPGM, the Platt and Sathyendranth model, and the Absorption-Based Model with in situ data in the North East Atlantic Ocean. The results revealed that the Platt and Sathyendranth model and VPGM had similar accuracy, whereas the Absorption-Based Model was not suitable for the study region. Although using in situ P B opt and Z eu may have significantly improved the estimation of VPGM PP [16], the scales of in situ measurements were too short to provide adequate coverage of high-quality regional temporal and spatial variations. Improvements in the accuracy of Chl-a from other ocean color sensors, including Medium Spectral Resolution Imaging Spectrometer and Ocean-Colour Climate Change Initiative data, will ultimately lead to an improvement in satellite PP algorithms for further research.
The VPGM PP in the four subareas of CCW, TSW, NUW, and KW also displayed similar features to Chl-a variations with the highest PP in the CCW and lowest in the KW. The RMSD was higher in the KW with an almost negative bias. The PP A had significant correlations with in situ PP in the TS, NUW, and KW; however, the sampling locations were insufficient to provide significant results in the CCW. The availability of light, the source of energy for photosynthesis; mineral nutrients, (the building blocks for new growth); and temperature, which affects metabolic rates, play crucial roles in regulating PP in the ocean [48,49]. The dominant primary producers in the Taiwan Strait are nano-and pico-phytoplankton [28]. The contribution of the microbial food web to the traditional food web is estimated to be approximately 30%, implying it has fundamental significance in the Taiwan Strait [28]. The high salinity and temperature with low nutrients originate from the TSW source in the South China Sea and KW in summertime; the strong northeastern winds then push the fresh, cold, nutrient-rich CCW southward along the western part of the Taiwan Strait [28,50]. In addition, the KW flowing through the eastern part of Taiwan is relatively deficient in nutrients, and the PP is also lower than in the other currents around Taiwan [51]. However, the nutrients increase from a depth of 200 m under short-term climatic variations such as typhoons [52], and may cause higher RMSD and bias in KW. The spatial distribution and seasonal variation of phytoplankton biomass and primary productivity are largely controlled by the input of nutrients from various water masses.

Conclusions and Future Research
The present study provided the first assessment of a satellite-derived VPGM PP model with in situ PP estimates in the regional waters around Taiwan. Understanding the PP of waters affected by global warming is critical. In particular, the East China Sea is among the large marine ecosystems that are warming most rapidly. Furthermore, from the 1950s to 2000s, the increased SST has caused 20 • C isotherms in the Taiwan Strait to gradually shift northward in the winter [53]. Climate change caused by global warming along with changes in water temperature also affect the productivity, catchability, and fishing pressure of fish species. It is important to quantify and understand the sources of variation in marine PP and increase confidence in the predictions of future fisheries yielded under uncertainty over future PP and its transfer to higher trophic levels [54]. Our results revealed that the VGPM PP derived from AVHRR SST and three types of MODIS Chl-a were linearly correlated with in situ PPs, as determined by light-dark bottles. The correlation coefficients were highest in the PP A&T around the waters of Taiwan, especially in springtime. However, the highest significant correlation coefficients in the four subareas were observed in PP A and wintertime.
Satellite models underestimate in situ PP, probably due to the depth of the phytoplankton in the water column, short-term climatic variations, and optically complex shelf waters. To better understand the PP around Taiwan with complex current systems, substantially more measurements are required across multiple years and seasons. Although initially, these can be used to quantify the productivity of different water masses, they are eventually required to further validate the available biogeochemical models in order to scale up relatively sparse measurements through time and space [18]. Additional studies include making a further comparison of in situ marine PP with the 14 C method and multi satellite-derived data, such as Ocean-Colour Climate Change Initiative (OC-CCI) data obtained from merged information derived from ocean color sensors. The VPGM is a commonly used model and exhibited significant correlations with in situ data in the present study. However, the simplest model formulation of the Eppley-Square-Root model [15] was tested as the highest skill and lowest bias model in the western boundary of East Australia [18]. The other VPGM-based models, the VGPM-Eppley model [2], and VGPM-Kameda model [17], will provide the crucial next step in conducting more comprehensive investigations by re-parameterizing the original relationships in accordance with in situ data.