Inverse problems theory and application: analysis of the two-temperature method for land-surface temperature and emissivity estimation

The two-temperature method (TTM) allows the separation of land-surface temperature and land-surface emissivity information from radiance measurements, and therefore, the solution can be uniquely determined by the data. However, the inverse problem is still an ill-posed problem, since the solution does not depend continuously on the data. Accordingly, we have used some mathematical tools, which are suited for analyses of ill-posed problems in order to show TTM properties, evaluate it, and optimize its estimations. Related to this last point, we have shown that it is necessary to constrain the problem, either by defining a region of physically admissible solutions and/or by using regularization methods, in order to obtain stable results. Besides, the results may be improved by using TTM with systems that possess a high temporal resolution, as well as by acquiring observations near the maximum and minimum of the diurnal temperature range.