## 1 Introduction
### Optical Proxies of Properties of Sediment Particles
#### 1.1.2 Size  
Suspended sediment ranges in size from sub-\(\upmu\)m-sized clay platelets to mm-sized sand and even larger flocs. It also encompasses plankton, non-algal organic particles, and aggregates that can be mixture of both organic and inorganic particles. We ignore in this paper particles capable of sinking at speeds \(>\)10 mm s\({}^{-1}\). These are rarely in suspension and, when they are in suspension, concentrations may saturate optical instruments. Optical proxies for size information include size distributions inverted from measurements of near forward scattering at several angles [12], the exponents of power-law fits of the particulate attenuation or backscattering spectrum [13; 14; 15] (but see [16]), and the fluctuation in optical signals, which can be used to obtain the average size of suspended particles [17]. Images of particles have also been used to derive size distributions, particularly of larger flocs and aggregates (e.g., [1; 3]).  
Theoretically, the maximal response of attenuation or scattering per volume (equivalent to mass if density is constant) occurs for single-grain sediment near \((D/\lambda)(n-1)\sim 1\) where \(\lambda\) is the wavelength in water (\(=0.75\lambda_{\text{air}}\)), \(D\) is the particle diameter, and \(n\) is the index of refraction of the particle relative to water ([18], Figure 1). For solid inorganic particles with \(n=1.15\) at \(\lambda_{\text{air}}=660\) nm, the maximal attenuation per mass occurs for small particles with diameters between 0.8-3.2 \(\upmu\)m. This dependency decreases as \(1/D\) as \(D\) increases, and it increases for larger indices of refraction (Figure 1). Increases in the index of refraction are typically associated with increases in the inorganic fraction in the particle suspension [19].  
The dependence of attenuation or scattering per unit of suspended mass on size should limit their use for estimation of SPM in suspensions with varying particle size, yet they are reasonably precise proxies for SPM across a range of environments, as discussed previously. This paradox is resolved if particles in suspension are not primarily single solid particles, but rather are agglomerations of particles separated by relatively large volumes of interstitial fluid and transparent organic material [1; 20]. Terminology used to describe particle agglomerations in suspension can be ambiguous. Here we refer to a \"floc\" as an agglomeration of material that forms in suspension at relatively short times scales (e.g., tides) that is susceptible to breakup under increasing shear stress. We use the term \"aggregate\" to refer to an agglomeration that has undergone multiple cycles of resuspension and deposition, during which it has become more compacted and more strongly bound. While the component particles in flocs and aggregates may be similar, the density and settling velocity of aggregates is greater [21]. Flocs and aggregates typically sink faster than their component particles [22; 23]. Flocs are broken by shear, including that generated by turbulence and by sinking, limiting their maximal size to about1 cm [20; 22; 24; 25; 26]. Aggregates, because they are more compact and stronger, are not broken easily by shear. In terms of their optical properties, flocs, if sufficiently porous, can maintain the efficiency of scattering of the particles of which they are made [27], resulting in mass-specific optical properties that are independent of floc size. These theoretical results were validated in laboratory and field experiments that found that attenuation and backscattering to SPM ratios remained relatively constant despite large changes in particle size [1; 28]. More densely packed aggregates theoretically should have mass-specific optical attenuation, scattering and backscattering coefficients that decrease with increasing aggregate size, but at a rate that is less than the \(1/D\) dependence of solid particles. This theoretical relationship has not been demonstrated with measurements.