Evaluations of the Wavelet-Transformed Temperature and Emissivity Separation Method: Lessons Learned From Simulated and Field-Measured TIR Data

Mathematically, once the measured radiance has been corrected for atmospheric effects, the only issue when determining the land surface temperature and emissivity (LST and LSE) is solving the ill-posed problem in the radiative transfer equation (RTE). Recently, based on the wavelet transform theory, a so-called wavelet-transformed temperature and emissivity separation (WTTES) method has been proposed for retrieving LST and LSE from hyperspectral data. Although, in a previous article, an initial suggestion was provided after analyzing the uncertainties under the conditions of several typical errors, it was also noted that considerable work was still necessary for achieving a reliable method for driving the WTTES algorithm, particularly under different situations. To complement the previous analysis of the WTTES algorithm, this paper presents a more detailed and comprehensive evaluation in which we changed the wavelet functions, varied the wavelet levels, and biased the atmospheric profiles. The results in this paper showed that the WTTES algorithm was insensitive to the choice of wavelet function. In addition, the WTTES algorithm could stay stable in most circumstances. A wavelet level of n = 3 was more recommend when the NEΔT was approximately 0.2 K. When a higher level of noise was found, a level of n = 4 could be then used to better overcome the noise. When a lower level of noise was found, a level of n = 2 could be used to further refine the spectral features. Additionally, we also found that the WTTES algorithm could have problems when atmospheric effects were inaccurately compensated for, especially for wet-warm profiles.