Equivalence of data fusion and simultaneous retrieval

Remote sensing observations of chemical and physical processes occurring in the atmosphere are presently made from space by several instruments and more instruments will be available in the future. We present a new data fusion method that can be used for the combination of two or more atmospheric vertical profiles measured by different instruments in the same location. The algorithm used for the fusion takes into account both the covariance matrix and the averaging kernel matrix of the fusing profiles and can be considered to be a generalization of weighted and arithmetic means. In turn, these means can be considered approximations of the new data fusion method, which for its comprehensive approach is referred to as complete fusion. The complete fusion method uses standard retrieval products and has very simple implementation requirements. We compare the performance of complete fusion with those of weighted and arithmetic means using the measurements of the MIPAS (Michelson Interferometer for Passive Atmospheric Sounding) instrument onboard the ENVISAT satellite. A MIPAS limb sounding sequence is divided in two complementary data sets and two profiles are independently retrieved from the two sets of observations. The two profiles are fused using complete fusion as well as weighted and arithmetic means. The results of these fusions are compared with the profile retrieved using simultaneously all the observations of the sequence. The complete fusion perfectly reproduces the results of the simultaneous retrieval from the point of view of values, of error estimates and of number of degrees of freedom. Weighted and arithmetic means differ from simultaneous retrieval and are characterized by errors that are smaller than observed differences. This apparent contradiction is explained, as shown by the analysis of the number of degrees of freedom, by the poor vertical resolution of weighted and arithmetic means that prevents an adequate representation of the shape of the profiles.