Variability of relationship between the volume scattering function at 180° and the backscattering coefficient for aquatic particles
Lianbo Hu, Xiaodong Zhang, Yuanheng Xiong, Deric J. Gray, Ming-Xia He
Abstract
Properly interpreting lidar (light detection and ranging) signal for characterizing particle distribution relies on a key parameter, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>χ</mml:mi> <mml:mi>p</mml:mi> </mml:msub> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>π</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> , which relates the particulate volume scattering function (VSF) at 180° ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>β</mml:mi> <mml:mi>p</mml:mi> </mml:msub> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>π</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> ) that a lidar measures to the particulate backscattering coefficient ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>b</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext class="MJX-tex-mathit" mathvariant="italic">bp</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ). However, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>χ</mml:mi> <mml:mi>p</mml:mi> </mml:msub> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>π</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> has been seldom studied due to challenges in accurately measuring <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>β</mml:mi> <mml:mi>p</mml:mi> </mml:msub> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>π</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>b</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext class="MJX-tex-mathit" mathvariant="italic">bp</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> concurrently in the field. In this study, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>χ</mml:mi> <mml:mi>p</mml:mi> </mml:msub> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>π</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> , as well as its spectral dependence, was re-examined using the VSFs measured in situ at high angular resolution in a wide range of waters. <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>β</mml:mi> <mml:mi>p</mml:mi> </mml:msub> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>π</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> , while not measured directly, was inferred using a physically sound, well-validated VSF-inversion method. The effects of particle shape and internal structure on the inversion were tested using three inversion kernels consisting of phase functions computed for particles that are assumed as homogenous sphere, homogenous asymmetric hexahedra, or coated sphere. The reconstructed VSFs using any of the three kernels agreed well with the measured VSFs with a mean percentage difference <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mo><</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>5</mml:mn> </mml:mrow> <mml:mi mathvariant="normal">%</mml:mi> </mml:math> at scattering angles <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mo><</mml:mo> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>170</mml:mn> </mml:mrow> <mml:mo>∘</mml:mo> </mml:msup> </mml:math> . At angles immediately near or equal to 180°, the reconstructed <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>β</mml:mi> <mml:mi>p</mml:mi> </mml:msub> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>π</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> depends strongly on the inversion kernel. <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>χ</mml:mi> <mml:mi>p</mml:mi> </mml:msub> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>π</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> derived with the sphere kernels was smaller than those derived with the hexahedra kernel but consistent with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>χ</mml:mi> <mml:mi>p</mml:mi> </mml:msub> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>π</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> estimated directly from high-spectral-resolution lidar and in situ backscattering sensor. The possible explanation was that the sphere kernels are able to capture the backscattering enhancement feature near 180° that has been observed for marine particles. <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>χ</mml:mi> <mml:mi>p</mml:mi> </mml:msub> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>π</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> derived using the coated sphere kernel was generally lower than those derived with the homogenous sphere kernel. Our result suggests that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>χ</mml:mi> <mml:mi>p</mml:mi> </mml:msub> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>π</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> is sensitive to the shape and internal structure of particles and significant error could be induced if a fixed value of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>χ</mml:mi> <mml:mi>p</mml:mi> </mml:msub> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>π</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> is to be used to interpret lidar signal collected in different waters. On the other hand, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>χ</mml:mi> <mml:mi>p</mml:mi> </mml:msub> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>π</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> showed little spectral dependence.