Error Analysis for Estimation of Trace Vapor Concentration Pathlength in Stack Plumes

Abstract

Near-infrared hyperspectral imaging is finding utility in remote sensing applications such as detection and quantification of chemical vapor effluents in stack plumes. Optimizing the sensing system or quantification algorithms is difficult because reference images are rarely well characterized. The present work uses a radiance model for a down-looking scene and a detailed noise model for dispersive and Fourier transform spectrometers to generate well-characterized synthetic data. These data were used with a classical least-squares-based estimator in an error analysis to obtain estimates of different sources of concentration-pathlength quantification error in the remote sensing problem. Contributions to the overall quantification error were the sum of individual error terms related to estimating the background, atmospheric corrections, plume temperature, and instrument signal-to-noise ratio. It was found that the quantification error depended strongly on errors in the background estimate and second-most on instrument signal-to-noise ratio. Decreases in net analyte signal (e.g., due to low analyte absorbance or increasing the number of analytes in the plume) led to increases in the quantification error as expected. These observations have implications on instrument design and strategies for quantification. The outlined approach could be used to estimate detection limits or perform variable selection for given sensing problems.

Estimation of trace vapor concentration pathlength in plumes for remote sensing applications from hyperspectral images

“…Synthetic images were generated using the IR-SAGE code described briefly here (see references [12] and [13] for more information). The images are similar to those generated for the study in reference [1] except that a different set of plume analytes was used, and also analyte spectral temperature dependence was included.…”

“…Synthetic hyperspectral images were generated using the InfraRed Systems Analysis in General Environments (IR-SAGE) code. 12,13 The IR-SAGE code is discussed only briefly below.…”

“…Previous work showed that the temperature mismatch could result in significant error. 12 A simple model was used here that estimated the observed spectrum as the interpolation of three spectra measured at three different temperatures.…”

Impact of background and atmospheric variability on infrared hyperspectral chemical detection sensitivity

“…In this model, the radiance received by the instrument is calculated directly using the physics model given by Sheen et al 3 and Gallagher et al 4,5 . The received radiance includes the ground radiance, plume radiance, atmospheric upwelling radiance, and internal instrument noise (NESR, or noise equivalent spectral radiance).…”

“…This type of model does not require extensive mathematical development to add new instruments or scenarios. The IR-SAGE model, including the physics models describing the radiance incident on the instrument and a description of the generalized least squares estimation techniques is described by Sheen et al 3 and Gallagher et al 4,5 .…”