Rapid Evaluation of Mean Concentration Fields in Lagrangian Stochastic Modelling Using a Density Kernel Estimator

摘要

Lagrangian Stochastic (LS) particle models have proven to be a useful computational tool for the description and prediction of dispersion of pollutant releases in complex meteorological situations (e.g., space-and time-varying situations pertaining to complex flow and turbulence). However, simulating the emitted pollutant by following the trajectories of many 'marked' fluid elements released from the source distribution brings up the difficulty of the correct estimation of the mean concentration of the dispersing pollutant from the particle trajectory information. Recently, the density kernel estimation method has been proposed and applied successfully to estimate mean concentrations from Lagrangian Stochastic particle models. However, the computational effort needed by this method increases as N(exp 2) (assuming the number of receptor locations N(sub r) at which the concentration is required is comparable to the number of fluid particles N(sub p) used in the trajectory simulation, so N(sub r) = N(sub p) -N) and, in consequence, the method has not been widely used because of the significant computer resources required. Here, we describe a novel algorithm for calculating the kernel estimate of the mean concentration field whose computational complexity scales only as N. The technique uses a tesselation (subdivision) of space in cubic cells of side length h (where h is the bandwidth of the kernel function), and then associates a linked-list data structure with each cell that is used as a bookkeeping device to keep track of the 'marked' fluid particles in that cell. The fast approach developed here has been verified by comparing results with the direct implementation of the kernel estimator and with the conventional box-counting estimator for the mean concentration field.