A Lagrangian Model for Dispersion in the Atmospheric Boundary Layer

A Random Walk Model for simulating dispersion in the daytime boundary layer has been developed. The model is a one-dimensional model, in which the horizontal dispersion is considered negligible. The model can simulate dispersion for a continuous range of atmospheric stabilities from neutral to convective ones. The probability density function of the vertical velocities, which is an input parameter of the model, is constructed by adding two Gaussians, and it is given by the second, the third and the fourth order moment of vertical velocities. The transition between stabilities is controlled by a continuous function of height and stability. The parameters of the probability density function, that are necessary also for calculating the value of the transition function, are found by solving the system of the moment equations together with two additional equations derived from closure assumptions. The parameterizations of atmospheric turbulence are chosen in a way as to ensure a continuous transition with stability. The model was first applied to reproduce results from water tank experiments, where dispersion in free convective situations is simulated. It was subsequently applied to data from the so-called Copenhagen experiment, in which a tracer was released in near neutral and unstable conditions. In both cases the model was able to reproduce experimental results, showing that it is well suited for simulating dispersion for a broad range of stabilities.