The characterization and error anaysis 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 straighforwardly 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. ¿ American Geophysical Union 1990