# Lagrangian Modeling of Marine Microplastics Fate and Transport: The State of the Science
## 1 Introduction
Accordingly, their physical (mainly size, density, and shape), chemical, and biological properties may change as a result of their ambient environment properties, including sea surface temperature, sunlight, salinity, etc. The growth of ultrafine bacteria or microorganisms and the attachment of organic material, invertebrates, and algae on the exterior surfaces of these particles cause biofouling that results in not only density and size increases in the particles but consequently decreases buoyancy [48]. Thus, it can be concluded that the sinking process can be accelerated by biofouling [49] and may result in the sedimentation of fouled particles. In addition, microplastics have been widely pervasive in marine habitats [26; 50] due to physical transport processes including horizontal and vertical advection and diffusion. Previous studies have shown that microplastics have reached very remote regions in the Arctic [51] and Antarctic [52; 53]. They can be found on the sea surface [54], the seabed [55], and also in deep-sea sediments [56; 57]. Predicting such transport processes, given their dependencies on different hydrological and atmospheric variables spanning over a wide temporal and spatial scale, is important for the accurate simulation of microplastics' fate and transport in water bodies. The transport of microplastics in water bodies is controlled by advection and dispersion driven by ambient currents, Stokes drift, sinking, resuspension, beaching and washing-off, deposition, aggregation, degradation, and fouling, which need to be simulated by numerical models. Four sources for transport processes can be considered: (1) ambient currents (e.g., tidal and wind-driven flows), leading to transport by advection; (2) wind-induced drift, i.e., windage, which is an additional advection term because of wind drag and has an undeniable effect on plastic particles' displacement [58]--in other words, the wind-driven drag force exerted on the water's surface causes the drifting of floating particles exposed to wind; (3) wave action; and (4) buoyancy, which influences the vertical transport. Indeed,the influence of buoyancy on vertical transport and associated vertical mixing can be significant [59]. Physical processes involved in the transport and fate of microplastics can occur at different spatio-temporal scales, which makes the simulation challenging. In this respect, short-term processes (e.g., particle-particle interactions at local and regional scales) may last for several hours or a few days [60]; however, medium-term processes including biofouling, sedimentation, and advection from freshwater bodies to marine environments may occur within several days or weeks [44]. Long-term processes need months or even years to be completed [61]. For instance, some processes, such as degradation (or fragmentation), sinking, and transport (due to advection and diffusion) from coastal water bodies to oceans are long-term processes that increase computational costs. From the spatial scale perspective, the simulation of physical processes in large study areas with global scales is of orders of thousands of square kilometers, while the computational domains for regional and local areas are of orders of hundreds and tens of square kilometers, respectively. Numerical simulation has been widely employed in the past decades to predict marine microplastics' behavior [62; 63; 64; 65; 66; 67; 68]. There are also some studies that have predicted the main sources, transport, and fate of microplastics under different environmental conditions based on numerical simulations [69; 70; 71; 72; 73]. Some of these studies have employed particle-tracking [61] and hydrodynamic models [74], individually or coupled with each other [75; 76; 77]. Numerical modeling is inexpensive by far in comparison with experimental measurements and in situ observations and can predict potential accumulation zones in remote areas where water quality monitoring is not feasible.