In this paper transport processes in coastal waters are described by stochastic differential equations (SDEs). These SDEs are also called particle models (PMs). By interpreting a Fokker-Planck equation associated with the SDE as an advection diffusion equation (ADE), it is possible to derive the underlying PM which is exactly consistent with the ADE. Both the ADE and the related classical PM do not take into account accurately the short term spreading behaviour of particles. In the PM this shortcoming is due to the driving noise in the SDE which is modelled as a Brownian motion and therefore has independent increments. To improve the behaviour of the model shortly after the release of pollution we develop an improved PM forced by a coloured noise process representing the short-term correlated turbulent velocity of the particles. This way a more accurate and detailed short-term initial spreading behaviour of particles is achieved. For long-term simulations both the improved and classical PMs are consistent with the ADE. However, the improved PM is relatively easier to handle numerically than a corresponding ADE. In this paper both models are applied to a real life pollution problem in the Dutch coastal waters.