| Summary: | Kernel smoothers are often used in Lagrangian particle dispersion simulations to estimate the concentration distribution of tracer gasses, pollutants etc. Their main disadvantage is that they suffer from the curse of dimensionality, i.e., they converge at a rate of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>4</mn><mo>/</mo><mo>(</mo><mi>d</mi><mo>+</mo><mn>4</mn><mo>)</mo></mrow></semantics></math></inline-formula> with <i>d</i> the number of dimensions. Under the assumption of horizontally homogeneous meteorological conditions, we present a kernel density estimator that estimates a 3D concentration field with the faster convergence rate of a 1D kernel smoother, i.e., <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>4</mn><mo>/</mo><mn>5</mn></mrow></semantics></math></inline-formula>. This density estimator has been derived from the Langevin equation using path integral theory and simply consists of the product between a Gaussian kernel and a 1D kernel smoother. Its numerical convergence rate and efficiency are compared with that of a 3D kernel smoother. The convergence study shows that the path integral-based estimator has a superior convergence rate with efficiency, in mean integrated squared error sense, comparable with the one of the optimal 3D Epanechnikov kernel. Horizontally homogeneous meteorological conditions are often assumed in near-field range dispersion studies. Therefore, we illustrate the performance of our method by simulating experiments from the Project Prairie Grass data set.
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