Prediction of Gradation-Based Heavy Metal Mass Using Granulometric Indices of Snowmelt Particles

Urban activities, infrastructure, transportation, and vehicle/infrastructure interactions are sources of metals and particulates in the built environment. These constituents are dry deposited in surrounding aqueous, soil, or snow environments on a continual basis, wet deposited during rainfall–runoff or snowmelt events, and partition between dissolved, colloidal, and particulate phases. Once transported into the porous matrix of snow, particulates, and metals may remain in the matrix for residence times measured in days, potentially resulting in metal partitioning to the particulate-bound phase. This study examined snowmelt particulate (granulometric) and metal data from 10 similar urban land use sites separated by $26\mathrm{km}$. Results indicate a power-law relationship between granulometric indices [mass or surface area (SA)] and particulate-bound metal mass can be established for particulates of similar granulometry, land-use conditions, loadings, and exposure. Power law models (PLMs) were developed to relate granulometric mass, particle number density, total SA and particulate-bound metal mass as a function of the sediment $\left(>75\mu m\right)$ and settleable $(75-25\mu m)$ size gradation from ${4750}^{+}\mathrm{to}25\mu m$. Results indicate that a calibrated and physically based cumulative PLM, $M^{\mathrm{Me}}=\alpha (X/R{)}^{\beta }$ can predict metal mass $\left(M^{\mathrm{Me}}\right)$ from granulometric mass $\left(X\right)$ or from SA, for a specific metal. Formulation of a predictive relationship is advantageous given the relative economy of measuring granulometric indices, from which calibrated relationships between mass and particulate-bound metal mass can be established, as compared to the expense of conventional measurement of metal mass across the size gradation. The study was further motivated based on the potential application of a PLM as a predictive tool utilized with structural controls such as particle-separation unit operations, nonstructural source controls, and mass trading or mass offsetting protocols designed to target portions of the particulate gradation where the predominance of the metal mass is associated.