Discrete representation and resampling in limb-sounding measurements

The processes of discretization, interpolation, and resampling are frequently used in data analysis. Here the formalism of functional spaces is used as a framework for the description and characterization of both the measurement operation and these subsequent processes. The tools provided by this formalism are applied to the problem of resampling of atmospheric volume mixing ratio vertical profiles obtained with limb-sounding measurements. In particular, a resampling method that uses the conservation of the vertical column as a constraint is presented and compared with other methods. The effects of the resampling process in terms of error propagation and loss of vertical resolution are also evaluated.