Sensitivity and Uncertainty in Matched-Filter-Based Gas Detection With Imaging Spectroscopy

Recent advances in remote imaging spectroscopy have increased its utility for detecting and quantifying greenhouse gas emissions. In fact, multiple airborne and space-based instruments are actively used to estimate methane emissions. Many of these measurements are made using matched-filter-based detection and estimation algorithms. In this work, we present new methods for quantifying and improving the accuracy and uncertainty of these algorithms. Two new metrics are proposed that capture the biases and uncertainties in gas quantity measurements stemming from local surface and atmospheric variation, observation and solar geometries, and sensor noise. We show that one of these, termed the “sensitivity,” can be used to correct the bias in the gas concentration length estimates due to variable atmospheres and backgrounds, reducing the estimator’s root mean squared (rms) error in spectra that deviate from the mean spectrum. The second, termed the “uncertainty,” represents the bias-removed statistical uncertainty in the corrected estimator. Expressions for the rms error both with and without the correction are provided along with interpretation to help quantify the various noise sources. The utility of the metrics is demonstrated using data from the Earth Surface Mineral Dust Source Investigation (EMIT) imaging spectrometer currently collecting Earth observations onboard the International Space Station (ISS). The EMIT data also demonstrates the potential accuracy increase afforded by the sensitivity correction over variable surface types. These metrics and their concomitant estimator accuracy increases could prove valuable for future work in quantifying gas source emission rates and their uncertainties, instrument design, and machine learning-based detection methods.