Gaussian Error Propagation not applicable to the Smoothing Error
When a profile is transformed from a coarser altitude grid to a finer one, Gaussian error propagation must not be applied to the profiles's smoothing error, because this would lead to underestimation of this error in the finer grid. It is thus questionable if the smoothing error indeed has the nature of a retrieval error.
When Gaussian error propagation is applied to the smoothing error, its reduction is computationally intuitive, because interpolation between values with anticorrelated errors leads to error cancellation; physically, however, this is counterintuitive because interpolation cannot reduce the smoothing error.
For more details, see http://www.atmos-meas-tech.net/7/3023/2014/amt-7-3023-2014.pdf