## 4 Discussion  
Based on the initial model of [PERSON] et al. [63] that was developed for bloom waters, we have demonstrated that using a set of refined parameters for the Gaussian curves for global waters (Table 2), the MuPI model demonstrates consistent performance in \(a_{\text{Gau}}(\lambda)\) retrievals on a global scale, as shown in Figures 3 and 4 and Table 5. Compared with HPLC measurements, the estimates of [Chl-a], [Chl-b], [Chl-c], [PPC] and [PSC] from satellite \(R_{\text{rs}}(\lambda)\) showed reasonable accuracies, with the mean UAPD of 38%, 78%, 65%, 36%, and 47% respectively (Figure 5). Further, the distribution of these pigments and their ratios to [Chl-a], were obtained from MERIS measurements on the global scale (Figures 8 and 9). The phytoplankton pigment ratios are critical indicators of the variation in phytoplankton groups and species due to their physiological adaptation to changes in nutrients, temperature, and light availability over time and space. The HPLC measured pigment concentrations and ratios have been widely used for determining the phytoplankton taxonomic composition and estimating the biomass of different groups, such as in CHEMTAX [27] and PFT analyses [10]. However, lacking effective methods, the estimation of phytoplankton pigments from satellite remote sensing has been limited to only [Chl-a] in the past decades [3; 4; 5], and the efforts made to obtain the accessory pigments  
Figure 8: Global distributions of chlorophyll \(b\) (Chl-a), chlorophyll \(c\) (Chl-c), photoprotective carotenoids (PPC) and photosynthetic carotenoids (PSC) from 2007 L3 annual MERIS \(R_{\text{rs}}(\lambda)\) imagery. Figure 9: Global distributions of the accessory pigment to chlorophyll \(a\) ratios: ratio of concentrations of chlorophyll \(b\) (Chl-b/Chl-a), chlorophyll \(c\) (Chl-c/Chl-a), photoprotective carotenoids (PPC/Chl-a), and photosynthetic carotenoids to chlorophyll \(a\) (PSC/Chl-a). have been more or less based on empirical relationships with Chl-a [45; 46]. Thus, these products provided limited ability to capture the variation in the physiological status of phytoplankton. However, these unknown physiological variations in phytoplankton pigments have been one of the main uncertainties in traditional phytoplankton remote sensing models that use [Chl-a] as input to represent the phytoplankton biomass, such as the traditional [Chl-a] based primary productivity [14; 20]. MuPI, as shown in this study, fills in this gap by obtaining not only the accessory pigment concentrations but also their ratios to [Chl-a] on the global scale, and reasonable accuracy has been obtained in validation with in situ data. [Chl-a] is by far the easiest quantity to validate as it is routinely measured. An independent evaluation of the model has been conducted with the MERIS match-up dataset (Figure 7). This dataset contains nearly simultaneous in situ [Chl-a] measurements and MERIS \(R_{\text{rs}}(\lambda)\) at coincident locations. To evaluate other pigments, an independent evaluation was conducted with MERIS \(R_{\text{rs}}(\lambda)\) and in situ HPLC match-ups from 2002 to 2012 near Bermuda (Figure 5). The match-up dataset contains data from different seasons over a decadal scale. Use of the model with the match-up dataset from BATS confirms good overall behavior of the MuPI model for pigment concentration and pigment ratio retrievals, demonstrating the ability of the model to obtain accurate information from satellite ocean color imagery. However, because of the limitation of in situ pigment concentrations, the potential of obtaining PE and PC concentrations from satellite remote sensing data was not addressed in this study. The main difficulty in making the model more applicable with any waterbody comes from the parameterization of the Gaussian curves, particularly the empirical relationships among \(a_{\text{Gau}}(\lambda)\).