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Ill-posed inverse problems of the limb remote sounding of the atmosphere

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Abstract

We consider inverse problems of limb refractometry and microwave sounding. Such problems are usually reduced to Abel-type integral equations and solved by virtue of the known inverse transform. However, this method does not yield a solution for some formulations of the problem. In particular, this concerns cases where the measured value is known at only a fraction of the impact height range in which the solution is searched for. In refractometry, this situation is inevitable if a wavelike stratification of the atmosphere takes place. Other examples of ill-posed problems are the inverse problem of limb microwave sounding with account of the finite width of the antenna pattern and the problem of reconstruction of a gas component profile along a fixed direction from the thermal radiation spectrum. We suggest methods of solution for such problems based on the Tikhonov principle of generalized residual. Numerical simulations of height profile reconstruction are presented for the refraction index and ozone content in inverse problems of refractometry and microwave sounding, respectively.

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Authors
  1. K. P. Gaikovich
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  2. M. B. Chernyaeva
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Institue of Microstructure Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 9, pp. 858–869, August 1999.

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Gaikovich, K.P., Chernyaeva, M.B. Ill-posed inverse problems of the limb remote sounding of the atmosphere. Radiophys Quantum Electron 42, 753–763 (1999). https://doi.org/10.1007/BF02676861

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