A Bayesian error model for quantifying methane and carbon dioxide column densities from hyperspectral measurements

Abstract

Many industrial combustion emissions may be detected and quantified using imaging Fourier transform spectrometers (IFTSs). Unlike a conventional infrared camera, which generates a single image integrated over a spectrum, IFTSs generate a datacube of images, each at a distinct wavenumber. The resulting intensity spectra may be used to identify the species within the plume and map their column density estimates. However, these estimates can only be interpreted properly in the context of uncertainty, some of which arises from measurement noise. This work uses Bayesian inference to propagate spectral intensity measurement noise into column density estimate uncertainty. Two distinct models for measurement noise are presented and discussed: the signal-dependant Poisson–Gaussian noise model, and the noise-equivalent spectral radiance. The measurement noise is propagated through the inference and the species density quantification model to obtain density uncertainty estimates for carbon dioxide and methane releases in a laboratory experiment.