To cleanup marine plastics, accurate modeling is needed. We outline and illustrate a new partial-differential-equation methodology for characterizing and modeling plastic transports in time and space (4D), showcasing results for Massachusetts Bay. We couple our primitive equation model for ocean dynamics with our composition based advection for Lagrangian transport. We show that the ocean physics predictions have skill by comparison with synoptic data. We predict the fate of plastics originating from four sources: rivers, beach and nearshore, local Bay, and remote offshore. We analyze the transport patterns and the regions where plastics accumulate, comparing results with and without plastic settling. Simulations agree with existing debris and plastics data. They also show new results: (i) Currents set-up by wind events strongly affect floating plastics. Winds can for example prevent Merrimack outflows reaching the Bay; (ii) There is significant chaotic stirring between nearshore and offshore floating plastics as explained by ridges of Lagrangian Coherent Structures (LCSs); (iii) With 4D plastic motions and settling, plastics from the Merrimack and nearshore regions can settle to the seabed before offshore advection; (iv) Internal waves and tides can bring plastics downward and out of main currents, leading to settling to the deep bottom. (v) Attractive LCSs ridges are frequent in the northern Cape Cod Bay, west of the South Shore, and southern Stellwagen Bank. They lead to plastic accumulation and sinking along thin subduction zones.