A weighted least squares approach for estimation of land surface temperature using constraint equations

Abstract

Estimation of land surface temperature and emissivity has taken on a great deal of importance in recent remote sensing studies. The estimation of temperature and emissivity from thermal radiation observations is involved with an under-determined equation set. In this study, an approach is proposed to overcome the problem based on statistical theory of observations and error propagation. First, the under-determined radiance equations have been completed using two NDVI-based equations for the mean and difference emissivities as constraint equations. The two added constraint equations provide the possibility of weighted least squares solution to estimate temperature and emissivity from the over-determined equation set simultaneously. The weights have been calculated based on the uncertainty of each of the equations. The weighting basis of the proposed approach allows statistical control on the uncertainties. The advantages of the weighted least squares solution which is contributed by this study are weighted observations used in the solution, the uncertainty considerations of the used observations, uncertainty propagation control, statistical standard deviation estimation for the unknowns, statistical quality control criteria, and the opportunity of systematic error detection. The numerical efficiency of the proposed approach is examined using a great number of simulated sample data. Then, the proposed approach is validated using the in situ measurements of land surface temperature. The validations accompanied by some statistical tests represent the acceptable performance and accuracy of the proposed approach (approximately 0.5°K for LST standard deviation and approximately 0.0075 for standard deviation of the bands 31 and 32 emissivities). In addition, the simplicity and robustness of the proposed approach may be regarded as a considerable achievement. © 2008 American Society for Photogrammetry and Remote Sensing.