On the Information Content of Umkehr Observations

Principal component analysis has been used to determine the number of linearly independent pieces of information that may be inferred from Umkehr observations. The analysis indicates that there are at most four such pieces of information in each Umkehr curve. A simple physical explanation is given for this result. The linearized evaluation method of Dütsch (1959) has been examined by eigenvalue analysis to determine the number of pieces of information that may be computed from the system. The result of the statistical analysis is confirmed, viz., that there are at most four pieces of information about the vertical distribution of ozone to be determined. In particular, there is no possibility of determining, from Umkehr observations, whether or not there exists a secondary maximum of ozone concentration in the lower stratosphere. Methods of obtaining smoothed vertical distributions are discussed and it is pointed out that the distributions obtained are not invariant under different scalings of the linear evaluation system. In view of the non-uniqueness of the Umkehr solutions, a brief discussion of the present-day usefulness of the measurements is presented.