Error analysis for a temperature and emissivity retrieval algorithm for hyperspectral imaging data

Abstract

In hyperspectral thermal data analysis, temperature–emissivity separation (TES) has the same function as reflectance retrieval in the visible and shortwave infrared. The problem, however, is more complicated because, in the thermal infrared (TIR), the surface emits and reflects radiation. The measured radiance is a function of the material's surface emissivity and temperature, reflected down‐welling radiance (clear sky, cloud environment) and the path radiance (temperature and water vapour or ozone profiles). The current implementation of the Automatic Retrieval of Temperature and EMIssivity using Spectral Smoothness (ARTEMISS) uses a look‐up table (LUT) to determine the best‐fitting atmosphere that results in the smallest residual to our own version ARTemiss ISAC (ARTISAC) of the In‐Scene Atmospheric Compensation (ISAC) estimated transmission. Over the past few years, we have developed an end‐to‐end simulation of the hyperspectral exploitation process by generating synthetic data to simulate datasets with ‘known’ ground truth, modelling propagation through the atmosphere, adding sensor effects (telescope, detector, readout electronics) and radiometric and spectral calibration, and testing the TES algorithm. We present an error analysis in which we shifted the band centres, varied the full‐width at half‐maximum (FWHM) of the spectral response function, changed the spectral resolution, added noise, and varied the atmospheric model. We also discuss a general method to retrieve the spectral smile as a function of wavelength and the FWHM from hyperspectral data with only approximate spectral calibration. We found that our algorithm has problems finding a unique solution when the water vapour exceeds about 3 g cm⁻² and we discuss remedies for this situation. To speed up the LUT generation we have developed fast and robust initial atmospheric parameter estimators (water vapour, ozone, near‐surface atmospheric layer temperature) based on channel ratios and brightness temperatures in atmospheric absorption regions for the longwave infrared.

Acknowledgements

We thank Drs Ronald Lockwood and Michael Hoke from the Air Force Research Laboratory, Hanscom AFB, MA, which supported this research during the author's year as a distinguished AFRL National Laboratory Fellow and later under BAA contracts F19628‐03‐0066 and FA8718‐05‐C‐0065. Many helpful comments to improve the paper were made by the two anonymous reviewers.