Investigating suspended particulate matter in coastal waters using the fractal theory

Suspended particulate matters (SPM) in coastal waters were investigated with an approach combining suspended particulate matter concentrations (SPMCs) measured by an optical backscatter sensor (OBS), particle size distributions measured by a laser in situ scattering transmissometer (LISST), and the fractal theory. The aim was to investigate whether changes in the fractal dimension indicate variations in the SPM composition. The method relies on the fractal theory that relates the floc excess density ∆ρ to the ratio between floc size D f and primary particle size D p as follows: Δρ = ( ρ p – ρ w )[ D f / D p ] nf − 3 . The best-fit fractal dimension nf was determined by matching the OBS-derived SPMC and the SPMC calculated from the LISST assuming fixed primary particle size and density. This method was applied to measurements from four tidal cycles characterized by different organic matter (OM) contents. Spurious data caused by schlieren were identified and discarded. The fractal dimension was relatively homogeneous over each tidal cycle except one where a strong apparent decrease in the fractal dimension was related to an important episode of sediment resuspension. This apparent decrease could result from the limit of the LISST to measure valid data when SPMC is high enough to induce multiple scattering and/or a change in the SPM population in suspension. Results showed also strong differences between the tidal cycles such as an increase of the fractal dimension with increasing OM content. Sensitivity analyses of fractal dimension and settling velocity were performed on major parameters: primary particle size and density, slope of the OBS calibration relationship, and optical model of inversion of the LISST. Results showed that the assumed primary particle size and the OBS calibration relationship significantly affect fractal dimension and settling velocity calculations.