Retrieval error comparison for several inversion techniques used in limb‐scanning millimeter‐wave spectroscopy

Abstract

The Rodgers formal retrieval error analysis allows the quantitative determination of such important retrieval properties as the total retrieval error, the contributions from the relevant error sources, the vertical resolution, and the inversion bias. Therefore it is a powerful tool for the objective evaluation and comparison of retrieval techniques. We have applied this error analysis to five numerical inversion techniques (the direct inversion, the linear constrained inversion, the optimal estimation inversion, the general relaxation inversion, and the Twomey‐modified Chahine relaxation inversion) used for the retrieval of middle atmospheric constituent concentrations from limb‐scanning millimeter‐wave spectroscopic measurements. As an example of such measurements, we use the geometry and instrument characteristic of the millimeter‐wave atmospheric sounder (MAS) experiment, which has flown on the first three ATLAS series of spacelab shuttle missions (March 1992, April 1993, and November 1994). We find that the relaxation methods have somewhat better vertical resolution but are slightly more sensitive to measurement errors than the constrained matrix methods. However, for the assumed MAS instrument characteristics, the total retrieval error is similar for all of the inversion schemes. We also tested the error predicted by the theoretical analysis against numerical simulations and find good agreement. Trade‐offs of these retrieval characteristics for several cases of measurement error and a priori profile uncertainty are presented.