The effects of nonlinearity on analysis and retrieval errors
EYRE, J.R.
The error characteristics of an optimal retrieval/analysis are well understood for the linear problem, and linear theory has also been widely used to assess the approximate error characteristics of weakly nonlinear problems. However, in the context of preparations for advanced infra-red sounders, it has become apparent that linear theory will lead to an over-optimistic assessment of performance, and particularly of the potential contribution of water vapour channels to the accuracy of temperature retrieval/analysis. In this paper, the effects of nonlinearities in the radiative transfer on retrieval/analysis errors are investigated theoretically for the general variational retrieval/assimilation problem. It is shown that these effects can be treated as an addditional source of "forward model" error, which we call nonlinearity error. The distribution of nonlinearity error is inherently non-Gaussian and a potential source of significant bias in the retrieval/analysis. Also, the magnitudes of analysis error and nonlinearity error are mutually dependent. Strategies for quantifying this error source are proposed. They are relevant not only to the assessment of the information content of advanced sounder data but also to the mitigation of nonlinear effects during retrieval or assimilation.
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