Characterization and error analysis of profiles retrieved from remote sounding measurements

Abstract

The characterization and error analysis of profiles retrieved from remote measurements present conceptual problems, particularly concerning interlevel correlations between errors, the smoothing effect of remote sounding and the contribution of a priori information to profile. A formal analysis for profile retrieval is developed which is independent of the nature of the retrieval method, provided that the measurement process can be characterized adequately. The relationship between the retrieved and true profiles is expressed in terms of a smoothing function which can be straightforwardly calculated. The retrieval error separates naturally into three components, (1) random error due to measurement noise, (2) systematic error due to uncertain model parameters and inverse model bias, and (3) null‐space error due to the inherent finite vertical resolution of the observing system. A recipe is given for evaluating each of the components in any particular case. Most of the error terms appear as covariance matrices, rather than simple error variances. These matrices can be interpreted in terms of “error patterns”, which are statistically independent contributions to the total error. They are the multidimensional equivalent of “error bars”. An approach is described which clarifies the relation of a priori data to the retrieved profile, and identifies a priori in cases where it is not an explicit part of the retrieval.

Remote sensing of mesospheric temperature and O2(1Σ) band volume emission rates with the high‐resolution Doppler imager

“…These sensitivities had to be refined after the instrument was in orbit, and this proved to be the most difficult task in tuning the inversion algorithm. These sen-60 sitivities change slightly, depending on the azimuth of the telescope relative to the spacecraft and depending on whether UARS The profiles in Figure 11 can be thought of as the columns of a sensitivity kernel matrix Kb as given by Rodgers [1990]. The column corresponding to a 3% perturbation for the medium line is not shown, because it is the negative of the sum of the two profiles shown.…”

“…We will follow the guidelines given by Rodgers [1990] for presenting an error analysis of the temperature and VER retrieval. …”

Ozone profile retrieval from backscattered ultraviolet radiances: The inverse problem solved by regularization

“…The effect of statistical measurement noise on the retrieved profile, the retrieval noise, can be calculated in a straightforward way [Rodgers, 1990]. However, systematic errors are also present in the measured reflectance, which are harder to characterize.…”

Correlation of aerosol and carbon monoxide at 45°S: Evidence of biomass burning emissions

“…For all spectra, these three CO lines were fitted simultaneously. Figure I illustrates the mixing ratio averaging kernels [Rodgers, 1990] which provide a direct assessment of the theoretical altitude sensitivity of the measurements in the absence of measurement and forward model parameter errors. The signal to noise ratio of the spectra, defined here as the depth of the CO absorption divided by the random noise (as determined at the center of black lines), was about 400.…”