## 1 Introduction  
Ocean color remote sensing has been focused on phytoplankton due to the important role that they play in the global biogeochemical cycles and ocean food webs [1; 2]. With the development of remote sensing technology, a variety of approaches have been developed to remotely obtain information about phytoplankton, such as their chlorophyll concentration [3; 4; 5], functional groups, and size classes [6; 7; 8; 9; 10; 11]. The most widely used satellite-based product of phytoplankton is chlorophyll \(a\) concentration ([Chl-a], mg-m\({}^{-3}\)) [3; 4; 5; 12; 13]. Satellite retrieved [Chl-a] has been utilized in estimation of phytoplankton biomass, primary production, and detection of harmful algal blooms [14; 15]. However, many studies have indicated that [Chl-a] alone is not a good indicator of phytoplankton biomass or physiological status [16; 17; 18; 19; 20]. Some accessory pigments have been recognized as biomarkers for phytoplankton groups or species [18; 21; 22; 23; 24]. These accessory pigments provide better estimation of the biomass of particular phytoplankton groups or species, such as phycocyanin (PC) for cyanobacteria [25; 26]. The variation in the accessory pigment composition has been widely used in estimating different phytoplankton functional groups [27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42], and physiological status of the phytoplankton [43; 44]. In an effort to obtain pigment concentrations beyond [Chl-a] from remote sensing reflectance (\(R_{\rm rs}(\lambda)\), sr\({}^{-1}\)), phycocyanin concentration, instead of [Chl-a], has been retrieved and used as a better index for cyanobacteria biomass and potential toxicity for cyanobacteria bloom waters [25; 26]. To obtain phycocyanin and [Chl-a], empirical and semi-analytical methods have been proposed and good results obtained in their application to bloom detection and monitoring [13; 25; 26]. Either empirical or analytical, these methods are based upon relationships between bio-optical information and one or two pigment concentrations. Empirical approaches have been the most widely used to obtain information for two or more pigments. Similar to the empirical relationships used by NASA for the estimation of [Chl-a] from \(R_{\rm rs}(\lambda)\)[4], [PERSON] et al. [45] developed empirical relationships between High-Performance Liquid Chromatography (HPLC) measured pigment concentrations and \(R_{\rm rs}(\lambda)\) for coastal waters in the northeast coast of the United States. [PERSON] et al. [46] directly used satellite-derived [Chl-a] as model input to retrieve other pigments in the Atlantic Ocean off the east coast of United States with the underlining assumption that all accessory pigments co-vary with chlorophyll \(a\). Semi-analytical models, which are based on mechanistic relationships derived from radiative transfer, allow the estimation of inherent optical properties (absorption and backscattering) from \(R_{\rm rs}(\lambda)\) measured by any radiometer [47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62]. These semi-analytical models make it possible to obtain optical properties of the water components simultaneously from measured \(R_{\rm rs}(\lambda)\). Taking advantage of this property of semi-analytical algorithms, [PERSON] et al. [63] incorporated the Gaussian decomposition method proposed by [PERSON] and [PERSON] [64] into a semi-analytical model, termed as multi-pigment inversion model (MuPI), and demonstrated the potential of obtaining Gaussian peak heights representing the absorption coefficients from various pigments. [PERSON] et al. [65] also adopted a similar scheme and applied it to hyperspectral in situ \(R_{\rm rs}(\lambda)\) measurements from the open ocean for the estimation of accessory pigments. However, as demonstrated in many studies [37; 39; 64; 65; 66], the assumption that each Gaussian amplitude represents the light absorption of one specific pigment is not always feasible. This is further shown in [PERSON] et al.