Retrieving Pigment Concentrations Based on Hyperspectral Measurements of the Phytoplankton Absorption Coefficient in Global Oceans

Phytoplankton communities, which can be easily observed by optical sensors deployed on various types of platforms over diverse temporal and spatial scales, are crucial to marine ecosystems and biogeochemical cycles, and accurate pigment concentrations make it possible to effectively derive information from them. To date, there is no practical approach, however, to retrieving concentrations of detailed pigments from phytoplankton absorption coefficients (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="normal">a</mi><mrow><mi>ph</mi></mrow></msub></mrow></semantics></math></inline-formula>) with acceptable accuracy and robustness in global oceans. In this study, a novel method, which is a stepwise regression method improved by early stopping (the ES-SR method) based on the derivative of hyperspectral <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="normal">a</mi><mrow><mi>ph</mi></mrow></msub></mrow></semantics></math></inline-formula>, was proposed to retrieve pigment concentrations. This method was developed from an extensive global dataset collected from layers at different depths and contains phytoplankton pigment concentrations and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="normal">a</mi><mrow><mi>ph</mi></mrow></msub></mrow></semantics></math></inline-formula>. In the case of the logarithm, strong correlations were found between phytoplankton pigment concentrations and the absolute values of the second derivative (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi mathvariant="normal">a</mi><mrow><mi>ph</mi></mrow><mrow><mo>″</mo></mrow></msubsup></mrow></semantics></math></inline-formula>)/the fourth derivative (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi mathvariant="normal">a</mi><mrow><mi>ph</mi></mrow><mrow><mfenced><mn>4</mn></mfenced></mrow></msubsup></mrow></semantics></math></inline-formula>) of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="normal">a</mi><mrow><mi>ph</mi></mrow></msub></mrow></semantics></math></inline-formula>. According to these correlations, the ES-SR method is effective in obtaining the characteristic wavelengths of phytoplankton pigments for pigment concentration inversion. Compared with the Gaussian decomposition method and principal component regression method, which are based on the derivatives, the ES-SR method implemented on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi mathvariant="normal">a</mi><mrow><mi>ph</mi></mrow><mrow><mo>″</mo></mrow></msubsup></mrow></semantics></math></inline-formula> is the optimum approach with the greatest accuracy for each phytoplankton pigment. More than half of the determination coefficient values (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>R</mi><mn>2</mn></msup><msub><mrow></mrow><mrow><mi>log</mi></mrow></msub></mrow></semantics></math></inline-formula>) for all pigments, which were retrieved by performing the ES-SR method on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi mathvariant="normal">a</mi><mrow><mi>ph</mi></mrow><mrow><mo>″</mo></mrow></msubsup></mrow></semantics></math></inline-formula>, exceeded 0.7. The values retrieved for all pigments fit well to the one-to-one line with acceptable root mean square error (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>RMSE</mi></mrow><mrow><mi>log</mi></mrow></msub></mrow></semantics></math></inline-formula>: 0.146–0.508) and median absolute percentage error (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>MPE</mi></mrow><mrow><mi>log</mi></mrow></msub></mrow></semantics></math></inline-formula>: 8.2–28.5%) values. Furthermore, the poor correlations between the deviations from the values retrieved by the ES-SR method and impact factors related to pigment composition and cell size class show that this method has advantageous robustness. Therefore, the ES-SR method has the potential to effectively monitor phytoplankton community information from hyperspectral optical data in global oceans.