| Summary: | Diffuse attenuation coefficient of photosynthetically available radiation (PAR), K<sub>PAR</sub>, is a key product of ocean color remote sensing. Current ocean color algorithms generally detect only the average K<sub>PAR</sub> within one optical depth, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mrow><mi>K</mi></mrow><mrow><mi>P</mi><mi>A</mi><mi>R</mi></mrow><mrow><mi>R</mi><mi>S</mi></mrow></msubsup></mrow></semantics></math></inline-formula>. Due to the marked vertical variations of K<sub>PAR</sub>, knowledge of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mrow><mi>K</mi></mrow><mrow><mi>P</mi><mi>A</mi><mi>R</mi></mrow><mrow><mi>R</mi><mi>S</mi></mrow></msubsup></mrow></semantics></math></inline-formula> is insufficient to accurately evaluate the submarine light field. By using field in situ observations, a two-step approach, based on the development of an ocean color algorithm for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mrow><mi>K</mi></mrow><mrow><mi>P</mi><mi>A</mi><mi>R</mi></mrow><mrow><mi>R</mi><mi>S</mi></mrow></msubsup></mrow></semantics></math></inline-formula> and the relationships between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mrow><mi>K</mi></mrow><mrow><mi>P</mi><mi>A</mi><mi>R</mi></mrow><mrow><mi>R</mi><mi>S</mi></mrow></msubsup></mrow></semantics></math></inline-formula> and the average K<sub>PAR</sub> from the surface down to depth Z (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mrow><mover accent="true"><mrow><mi>K</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>P</mi><mi>A</mi><mi>R</mi></mrow><mrow><mi>Z</mi></mrow></msubsup></mrow></semantics></math></inline-formula>), was developed to remotely estimate the vertical variations in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mrow><mover accent="true"><mrow><mi>K</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>P</mi><mi>A</mi><mi>R</mi></mrow><mrow><mi>Z</mi></mrow></msubsup></mrow></semantics></math></inline-formula> in the North Pacific from the MODerate-resolution Imaging Spectrometer (MODIS) imagery. The root mean square difference of log(<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mrow><mover accent="true"><mrow><mi>K</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>P</mi><mi>A</mi><mi>R</mi></mrow><mrow><mi>Z</mi></mrow></msubsup></mrow></semantics></math></inline-formula>) in depths within the euphotic zone was around ±0.059 (in unit of m<sup>−1</sup> for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mrow><mover accent="true"><mrow><mi>K</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>P</mi><mi>A</mi><mi>R</mi></mrow><mrow><mi>Z</mi></mrow></msubsup></mrow></semantics></math></inline-formula>), which corresponded to a deviation of ±15% for the estimated <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mrow><mover accent="true"><mrow><mi>K</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>P</mi><mi>A</mi><mi>R</mi></mrow><mrow><mi>Z</mi></mrow></msubsup></mrow></semantics></math></inline-formula> and the penetration depths of PAR. Our study may provide a promising approach to detect the vertical variations of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mrow><mover accent="true"><mrow><mi>K</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>P</mi><mi>A</mi><mi>R</mi></mrow><mrow><mi>Z</mi></mrow></msubsup></mrow></semantics></math></inline-formula> and underwater PAR distributions in the North Pacific Ocean.
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