Abstract
Abstract. Remote sensing of atmospheric state variables typically relies on the inverse solution of the radiative transfer equation. An adequately characterized retrieval provides information on the uncertainties of the estimated state variables as well as on how any constraint or a priori assumption affects the estimate. Reported characterization data should be intercomparable between different instruments, empirically validatable, grid-independent, usable without detailed knowledge of the instrument or retrieval technique, traceable and still have reasonable data volume. The latter may force one to work with representative rather than individual characterization data. Many errors derive from approximations and simplifications used in real-world retrieval schemes, which are reviewed in this paper, along with related error estimation schemes. The main sources of uncertainty are measurement noise, calibration errors, simplifications and idealizations in the radiative transfer model and retrieval scheme, auxiliary data errors, and uncertainties in atmospheric or instrumental parameters. Some of these errors affect the result in a random way, while others chiefly cause a bias or are of mixed character. Beyond this, it is of utmost importance to know the influence of any constraint and prior information on the solution. While different instruments or retrieval schemes may require different error estimation schemes, we provide a list of recommendations which should help to unify retrieval error reporting.
Highlights
Observations from remote sensing instruments are central to many studies in atmospheric science
If we represent the best known a priori statistics about the targeted atmospheric state as xa, its covariance matrix as Sa, and the inverse of this matrix as R and continue to assume Gaussian error distributions, we get a Bayesian solution that is usually referred to as an “optimal estimate” (Rodgers, 1976) or a “maximum a posteriori (MAP) solution” (Rodgers, 2000) and is fully compatible with the Bayes (1763) theorem and information theory by Shannon (1948) and gives the solution a probabilistic interpretation in the sense of the maximum a posteriori probability: x MAP = xa + KTSy−,1totalK + S−a 1 −1KTS−y,1total y − F . (6)
The relevance of some components of the state vector for the measurements is temporarily ignored, and the retrieval solves the inverse problem only for a part of the state values, using only a subset of the measurements. This approach lends itself to problems where it is adequate to assume that the Jacobian matrix K has an almost block-diagonal structure, that is, that there are state variables which have no significant influence on some of the measurements under analysis and vice versa
Summary
Observations from remote sensing instruments are central to many studies in atmospheric science. The robustness of the conclusions drawn in these studies is critically dependent on the characteristics of the reported data, including their uncertainty, resolution, and dependence on any a priori information. Adequate communication of these data characteristics is essential. Two prominent examples from this plethora of problem areas are error-weighted multi-instrument time series and trend calculations, or data merging This paper discusses these issues and proposes a common framework for the appropriate communication of uncertainty and other measurement characteristics. We list conditions of adequacy of the reporting of error and uncertainty (desiderata), which summarize the information that should be provided to the data user We identify unsolved problems and applications which might not be fully covered by our framework (Sect. 8)
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