Numerical regularization for atmospheric inverse problems

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The retrieval problems in atmospheric remote sensing are classified as discrete ill-posed problems, which exhibit instability under data perturbations. These issues can be addressed through numerical regularization methods that stabilize solutions by incorporating additional information. This research monograph presents and analyzes numerical algorithms for atmospheric retrieval, targeting physicists and engineers with a background in numerical linear algebra and matrix computations. While the book includes practical details, readers are encouraged to consult the cited literature for robust and efficient algorithm implementation. The analysis adopts a semi-stochastic data model, which, while theoretically distinct from a deterministic framework, shows no significant practical differences. The introductory chapter outlines the state of the art in passive atmospheric remote sensing, followed by Chapter 2, which discusses the concept of ill-posedness in linear discrete equations. To demonstrate the challenges of solving discrete ill-posed problems, the text examines temperature retrieval via nadir sounding and analyzes the solvability of the discrete equation using the singular value decomposition of the forward model matrix.