# Lagrangian Modeling of Marine Microplastics Fate and Transport: The State of the Science
## 4 Numerical Lagrangian Models
### CaMPSim-3D  
Canadian microplastic simulation (CaMPSim), the newest three-dimensional Eulerian-Lagrangian framework [98], has been developed recently for simulating microplastics' fate and transport in different aquatic environments. CaMPSim-3D is based on the coupling of a three-dimensional Lagrangian particle-tracking model and TELEMAC modeling system as the Eulerian hydrodynamic numerical model. Similar to procedures followed by the aforesaid models, hydrodynamic inputs such as atmospheric pressure, the direction and speed of the wind, hydrodynamic and water quality parameters (including velocity, temperature, salinity, water level, and algae concentration), wave height and direction as well as its time period, and characteristics of suspended sediments that are all prepared by the Eulerian model are fed into the Lagrangian particle-tracking model. On the other hand, CaMPSim-3D considers the physical properties of microplastics (such as density, size, and shape) and physical processes (including the effect of positive/negative buoyancy,advection, biofouling, spatio-temporal varying diffusion, degradation, washing-off, and beaching, etc.). In CaMPSim-3D, the physical properties of plastic particles such as density, diameter, gravity, and shape are parameterized in the calculation of the rising or settling velocity. Unlike TrackMPD, the formulation employed in CaMPSim-3D for calculating the settling velocity can be used for particles with different shapes, such as spherules, films, fragments, and fibers [98]. CaMPSim-3D calculates the settling velocity (\(v_{s}\)) based on force balance formulation Equations (5) and (6) provided for Newtonian fluids [98]. CaMPSim-3D can predict the formation of biofilm layers on plastic particles. In this respect, CaMPSim-3D utilizes some proposed empirical equations for estimating the biofilm thickness, e.g., Equations (7)-(9). In addition, CaMPSim-3D considers the degradation of microplastics based on empirical relationships provided in the literature, e.g., Equation (10). However, it cannot simulate both types of aggregation (i.e., hetero- and homo-aggregation) that microplastics undergo. As with some of the aforementioned models, the Lagrangian particle-tracking model, CaMPSim-3D, can simulate not only the advection and diffusion of particles but also beaching and washing-off. It is also capable of considering the effect of buoyancy on particle movement [98]. In CaMPSim-3D, the displacement of particles due to horizontal and vertical advection is calculated by solving the first- to the fourth-order of Equations (19)-(21). In addition, the vertical displacement velocity of particles (\(v_{p}\)) is calculated based on the vertical component of flow velocity, and particle settling/rising velocity (\(v_{s}\), obtained from Equation (5)), as shown in Equation (28) [98]. Furthermore, CaMPSim-3D considers the impact of wind as a driving factor on the transport of microplastics (see Equations (20)-(22). The turbulent diffusion of plastic particles is simulated in CaMPSim-3D by using a modified relationship, as shown in Equation (29) as a function of \(K\) (diffusion coefficient, see Equation (14)), \(\Delta t\) (the time step), \(R\) (a random number obtained from a normal distribution, which varies between \(-1\) and \(1\)), and \(K_{p}\) (diffusion coefficient at \(X_{p}\) as a function of \(t\)) [98]. \(K_{p}\) is calculated using the eddy viscosity (\(\theta_{t}\)) calculated by the Eulerian hydrodynamic model [98]. Moreover, CaMPSim-3D predicts resuspension and deposition as well as beaching and washing-off using the proposed relationships (see Equation (16)). One of the advantages of CaMPSim-3D, in comparison with the aforesaid models, is its ability to employ an unstructured grid [98]. It should be mentioned that the CaMPSim-3D model reads hydrodynamic parameters from an Eulerian hydrodynamic model (TELEMAC). Although this approach has some benefits by reducing interpolation errors, it imposes more computational time for point locations in an unstructured mesh.