An Alternative Concentration Estimator for Backward Lagrangian Stochastic Dispersion Models

Backward Lagrangian stochastic modeling is widely used to estimate emission rates from land surfaces to the atmosphere. It is also applied to calculate concentrations of pollutants due to known emission sources. A key component of this modeling technique is the concentration estimator, which relies on tracer particle trajectories to establish the relationship between concentration, emission rate, and meteorological condition. A commonly used concentration estimator is closely examined and shown to have potential inaccuracies. An alternative estimator is derived and compared with the existing one. The new estimator is tested using backward Lagrangian stochastic modeling in both Gaussian and non-Gaussian turbulence. The results demonstrate that, in many cases, the two estimators are equivalent, which explains the general success of the popular estimator. However, if the vertical velocities of some tracer particles are extremely slow when hitting the source, a significantly higher ratio of concentration to emission rate will be obtained. This spuriously high ratio will result in overestimation of the concentration if the purpose is to calculate concentrations from a known emission rate and underestimation of the emission rate if the model is used to calculate the emission rate from measured concentrations. The new estimator can avoid this unjustifiable behavior and therefore exhibits superior performance.