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 tested against multiband infrared radiometric imagery from the Terra MODIS (Moderate Resolution Imaging Spectroradiometer) instrument. The algorithm employed requires minimal knowledge of surface emissivity, 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 night-time 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 vertical bar ZA vertical bar < 30 degrees. Level 1b radiances were used to obtain 500 LST estimates per granule for comparison with the Level 2 MODIS LST product. The Bayesian LST estimators accurately reproduce standard MODIS product LST values. In particular, the mean discrepancy for the MAP retrievals is vertical bar <Delta T >vertical bar < 0.3K, and its standard deviation does not exceed 1K. The +/- 68% confidence intervals for individual LST estimates associated with assumed uncertainty in surface emissivity are of order 0.8K. 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. Provided the support [T-min, T-max] for the calculation of the expectation value brackets the maximum in the joint posterior probability for LST, the fixed point converges to the MAP LST estimate in the limit T-max - T-min -> 0.