Comparison of Bayesian Land Surface Temperature algorithm performance with Terra MODIS observations

An approach to land surface temperature (LST) estimation that relies upon Bayesian inference has been validated against multiband infrared radiometric imagery from the Terra MODIS instrument. Bayesian LST estimators are shown to reproduce standard MODIS product LST values starting from a parsimoniously chosen (hence, uninformative) range of prior band emissivity knowledge. Two estimation methods have been tested. The first is the iterative contraction mapping of joint expectation values for LST and surface emissivity described in a previous paper. In the second method, the Bayesian algorithm is reformulated as a Maximum A-Posteriori (MAP) search for the maximum joint a-posteriori probability for LST, given observed sensor aperture radiances and a-priori probabilities for LST and emissivity. Two MODIS data granules each for daytime and nighttime were used for the comparison. The granules were chosen to be largely cloud-free, with limited vertical relief in those portions of the granules for which the sensor zenith angle |ZA| < 30. Level 1B radiances were used to obtain LST estimates for comparison with the Level 2 MODIS LST product. The agreement of LST estimates obtained by both algorithms with the MODIS LST values is good: For all four granules, the mean discrepancy 〈∆T 〉 < 1K, and its standard deviation does not exceed 1K. Of note, 68% confidence intervals for the LST uncertainty associated with assumed uncertainty in surface emissivity are of order 1.5K. The Appendix presents a proof of convergence of the iterative contraction mapping algorithm. The expectation values of surface temperature in multiple bands, and jointly in all bands, converge to a fixed point, within a stipulated convergence criterion. The fixed point exists independently of the Preprint submitted to Elsevier September 24, 2009 accuracy of the resulting LST estimate, but in certain cases is unique. In the event that the support for the calculation of the expectation value is constrained to bracket the maximum in the posterior probability for LST, the fixed point converges to the MAP LST estimate as the number of iterations grows without bound.