Comparison of measurements made with two different instruments of the same atmospheric vertical profile

The validation of atmospheric remote-sensing measurements involves the comparison of vertical profiles of atmospheric constituents obtained by different instruments. This operation is a complex one because it has to take into account the measurement errors that are described by the variance-covariance matrices and the different features of the two observing systems that are described by the averaging kernels. The procedure is discussed and a method of comparison that is rigorous and does not involve degradation of the available information is developed by use of the formalism of functional spaces. The functional spaces that can be used for representation of the two profiles are reviewed, and criteria are determined for the choice of the most convenient functional space to minimize degradation of the measurements. Once the functional spaces are chosen, the components of the profiles are compared in the intersection space of these two functional spaces. If the intersection space coincides with the null vector, a pseudointersection space with useful geometrical properties can be used instead. A test of the method is made with a realistic simulation. In the test the profiles retrieved by two real instruments are simulated and quantitatively compared.