The Use of Gaussian Mixture Models with Atmospheric Lagrangian Particle Dispersion Models for Density Estimation and Feature Identification

Abstract

Atmospheric Lagrangian particle dispersion models, LPDM, simulate the dispersion of passive tracers in the atmosphere. At the most basic level, model output consists of the position of computational particles and the amount of mass they represent. In order to obtain concentration values, this information is then converted to a mass distribution via density estimation. To date, density estimation is performed with a nonparametric method so that output consists of gridded concentration data. Here we introduce the use of Gaussian mixture models, GMM, for density estimation. We compare to the histogram or bin counting method for a tracer experiment and simulation of a large volcanic ash cloud. We also demonstrate the use of the mixture model for automatic identification of features in a complex plume such as is produced by a large volcanic eruption. We conclude that use of a mixture model for density estimation and feature identification has potential to be very useful.

Application of Gaussian Mixture Regression for the Correction of Low Cost PM2.5 Monitoring Data in Accra, Ghana

“…GMMs may be able to detect these heterogeneous relationships and appropriately cluster model components so they can be represented by normal distributions. GMMs have been successfully implemented in a variety of fields including speech recognition and robotic learning. , Recently, GMMs have also been used in geophysical data analysis to accompany atmospheric Lagrangian particle dispersion models …”

A Fast-Converging Kernel Density Estimator for Dispersion in Horizontally Homogeneous Meteorological Conditions

“…The smaller C d (K), the closer MISE{ p(t, •; h * )} is to zero for a low amount of particles. Therefore, C d (K) is also referred to as the efficiency of the kernel K. One can show that the kernel smoother K * that minimizes (10) is the so-called Epanechnikov kernel ( [18], Section 6.1, pp. 82-83), i.e.,…”

“…Here, β 1 is related to the efficiency of the used estimator, e.g., for (6), β 1 estimates the quantity (10). The coefficients β 0 and β 1 can be estimated via a least-squares approximation of log 10 (MISE{ p(t, •; h)}).…”

“…This information can also be used to improve the performance of the kernel smoother. Despite the available computer power today, the development of fast-converging kernel density estimators is still a topical research subject in atmospheric dispersion modeling (see, e.g., [10]).…”

A Probabilistic Particle Tracking Framework for Guided and Brownian Motion Systems with High Particle Densities

“…This work presents an approach based on a Gaussian Mixture Model (GMM) [18,40]. GMMs are used for many different problems, e.g., background subtraction in images [30], superpixel segmentation [5], image denoising [59], or density estimation in atmospheric Lagrangian particle dispersion models [10]. In this work, a modified GMM is introduced as a probabilistic model to describe the movement of a particle.…”