The area-to-mass ratio and fractal dimension of marine flocs

Optical instruments have proved invaluable in the study of suspended matter in the sea but the measurements they provide are more closely related to the cross-sectional area of the particles in suspension than the mass measured by filtration or predicted by theory. In this paper, we examine the factors controlling the relationship between particle area and mass, using the fractal model of particle structure as a theoretical framework. Both theory and observation agree that the area-to-mass ratio of particles (symbol A*) decreases with increasing fractal dimension (symbol Nf) as particles hide behind each other in compact flocs. The equation A* = 0.253–0.081Nf, in which A* is in m² g⁻¹ explains 81% of the variance in the area:mass ratio at 151 stations in coastal waters. In contrast, the effect of floc size on A* is small. Three optical parameters – beam attenuation, diffuse attenuation and remote sensing reflectance, expressed per unit mass of suspended material, all decrease with increasing Nf. As our understanding of the flocculation process grows and it becomes possible to predict the fractal dimension of particles as a function of the environmental conditions in which the flocs form, these results will lead to improved calibration of optical instruments in terms of the mass concentration of suspended materials and to better models of sediment suspension and transport.