Optimal Estimation Of Concentrations InParticle-type Transport Models

Abstract

When dealing with a pollutant in coastal waters, it is important to know where and how it is transported. Since the initial concentration gradient is very steep, often a particle model is used to simulate the transport of the pollutant. In a particle model the spread of a solute is simulated by means of a large set of tracks (of individual particles) and from this ensemble concentrations must be derived. This last step is far from trivial. Particles represent mass rather than concentrations, and while the particle positions are a finite and discrete set, the observed concentrations generally have a continuous and smooth spatial form. This paper discusses some ideas, also known in density estimation theory, to solve this problem. Instead of using histogram-like functions (where the number of particles in a gridcell is counted), the concept of the point spread function (psf) is introduced. A psf spreads the mass of a particle across a small interval surrounding its position, thus providing a smoother estimate for the concentration profile of the pollutant. The asymptotic behaviour of the estimation error is analyzed for a large number of particles in both ID and 2D problems. In the ID case, optimal point spread functions with smallest estimation errors are derived. The various estimation procedures are then applied to realistic real-life water pollution problems. Transactions on Ecology and the Environment vol 18, © 1998 WIT Press, www.witpress.com, ISSN 1743-3541 312 Environmental Coastal Regions