A Stepwise Refining Algorithm of Temperature and Emissivity Separation for Hyperspectral Thermal Infrared Data

This is the authors' abstract. We don't add key points for this paper.

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Land surface temperature (LST) and land surface emissivity (LSE) are two key parameters in numerous environmental studies. In this paper, a stepwise refining temperature and emissivity separation (SRTES) algorithm is proposed based on the analysis of the relationship between surface self-emission and atmospheric downward spectral radiance in a narrow spectral region. The SRTES algorithm utilizes the residue of atmospheric downward spectral radiance in the calculated surface self-emission as a criterion and adopts a stepwise refining method to determine both the emissivity at the location of an atmospheric emission line in a narrow spectral region and the surface temperature. Three methods have been used to evaluate the SRTES algorithm. First, numerical experiments are conducted to evaluate if the SRTES algorithm can accurately retrieve the “true” LST and LSE from the simulated data. When a noise equivalent spectral error of <formula formulatype="inline"><tex Notation="TeX">2.5\ e⁻⁹\ W/cm²/sr/cm⁻¹</tex></formula> is added into the simulated data, the retrieved temperature bias <formula formulatype="inline"><tex Notation="TeX">(Tbias)</tex></formula> is 0.04 <formula formulatype="inline"><tex Notation="TeX">±</tex></formula> 0.04 K, and the root-mean-square error (rmse) of the retrieved emissivity is below 0.002 except in the extremities of the 714–1250 <formula formulatype="inline"> <tex Notation="TeX">cm⁻¹</tex></formula> spectral region. Second, <emphasis emphasistype="italic">in situ</emphasis> measurements are used to validate the SRTES algorithm. The average rmse of the retrieved emissivity of ten samples is about 0.01 in the 750–1050 <formula formulatype="inline"><tex Notation="TeX">cm⁻¹</tex></formula> spectral region and is 0.02 in the 1051–1250 <formula formulatype="inline"><tex Notation="TeX">cm⁻¹</tex></formula> spectral region, but the rmse is larger when the sample emissivity is relatively low. Third, our new algorithm is compared with the iterative spectrally smooth temperature and emissivity separation (ISSTES) algorithm using both a simulated data set and <emphasis emphasistype="italic">in situ</emphasis> measurements. The comparison demonstrates that the SRTES algorithm performs better than the ISSTES algorithms, and it can overcome some of the common drawbacks in the existing hyperspectral TES algorithms for the accurate retrieval of both temperature and emissivity. </para>