Surface Temperature Downscaling From Multiresolution Instruments Based on Markov Models

Abstract

The spatial resolution of thermal infrared (TIR) instruments is often not sufficient for many applications, but this low resolution is counterbalanced by the high temporal resolution (for example the SEVIRI instrument onboard the European Meteosat 8 and 9 presents a spatial resolution of 3 km <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$ \times$</tex></formula> 3 km at nadir and a temporal resolution of 15 mn). At kilometric scales, the observed pixel is generally heterogeneous in terms of land cover, and the temperatures of the different components may present large discrepancies. This paper presents a methodology to infer the temperatures of the various land cover/use classes composing a mixed pixel, from a whole pixel measurement. To infer intra-pixel temperature, information on the mixture within each low resolution pixel, e.g., the proportions of the land cover types derived from high spatial resolution imaging, account for a first constraint. However, in the absence of supplementary constraints, the number of unknown variables is greater than the number of measurements, and there is not uniqueness of the solution. Thus, we propose to take advantage of a priori knowledge provided by a land surface model (LSM), and of the temporal and spatial correlation features of the surface temperature. We propose a new downscaling method for estimating sub pixel signal. It applies to TIR data and: the inversion procedure provides as a result, the land surface temperature (LST) temporal series of each land cover/use class (called endmember) constituting the coarse resolution pixel. Three kinds of a priori information have been introduced, namely 1) a first guess subpixel temperature derived from the SEtHyS LSM; 2) a Markov Random Chain model of the surface temperature temporal dependencies from times <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$t$</tex></formula> to <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$t + 1$</tex></formula> ; 3) a Markov Random Field model of the spatial dependencies between endmember temperatures. Then, the “Maximum A Posteriori” estimator provides the most likely endmember temperatures, given 1) the observed coarse resolution temperatures, 2) the composition of the pixels in terms of “land cover/land use,” and 3) the LSM first guess subpixel temperature values, 4) the a priori spatial and temporal Markov models. The performance of this new method has been first evaluated on simulated data (random Gaussian variables with means equal to endmember temperatures simulated using LSM). The method accuracy versus the observation errors and the number of endmembers was analyzed. The algorithm was then run on actual data, namely Meteosat SEVIRI Land Surface products acquired over an agricultural region in southeastern France. The performance evaluation was done by comparing the subpixel LST estimations to the high-resolution temperatures provided by the Terra/ASTER instrument. Due to the huge bias between sensors ( <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$ \sim$</tex></formula> 4 K), an intercalibration preprocessing between SEVIRI and ASTER was done. In this case, the achieved RMSE is lower than 2 K.