Characterizing Variations in Concentration Data Measured From Unknown Releases
Abstract
The statistics of concentration data, measured during unknown atmospheric dispersion events, are not fully understood although they are required in modeling, assessment, uncertainty analysis, and information fusion. The concentrations measured over a field of monitoring network is regarded as a vector which contains both magnitude and direction. Traditional statistics (mean, standard deviations, etc.) based on magnitude of concentration data summarize data properties but are limited in characterizing variations in data and their modeling quality. Comparatively, directions are efficient in providing valuable information to address these issues. Here we propose a statistical framework which transforms concentration measurements into directions projected on a hypersphere and analyzes their orientation and distribution. The directional data measured in identical conditions are expected to be rotationally symmetric around its principal axis and follow Watson distribution. The clustering parameter of Watson distribution measures tightness of directional data and, thus, can measure indirectly variations in observed data. It is shown that the clustering parameter is able to summarize an overall variation in data and modeling quality of data in a dispersion trial. The study analyzes real data taken from continuous release experiments, called “Fusion Field Trials,” conducted at Dugway Proving Ground, Utah, United States.