Determination of cloud liquid water distribution using 3D cloud tomography

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Abstract
The cloud microwave tomography method for remotely retrieving 3D distributions of cloud Liquid Water Content (LWC) was originally proposed by Warner et al. in the 1980s but has lain dormant since then. This paper revisits and extends the cloud tomography method by rigorously examining the nature of the resultant mathematical problem and its close relationship to the physical configuration of microwave radiometers. The singular value decomposition (SVD) analysis reveals that the retrieval of cloud LWC fields from microwave emission is highly ill‐posed, and requires special techniques to solve it. The truncated SVD approach along with the L‐curve method for choosing the optimal truncating point is used to obtain a better retrieval of cloud LWC. A group of sensitivity studies show that the retrieval accuracy is determined by several factors, including the number of radiometers, the spatial resolution of output, the number of scanning angles, the radiometer characteristics (e.g., noise level, beam width), the physical arrangement of radiometers, and the uncertainty in the ancillary temperature and water vapor mixing ratio data. When more radiometers and/or more scanning angles are used, and/or the radiometer beam width is reduced, and/or when a coarser output resolution is acceptable, the retrieval problem becomes less ill‐posed, and a better retrieval can be obtained. Moreover, the observation system simulations demonstrate that the cloud tomography method is able to retrieve the cloud structures generated by cloud resolving models with a good accuracy. For a setup consisting of four microwave radiometers of typical noise level 0.3 K, the tomography method is capable of retrieving the LWC to within 5% of the maximum LWC in the simulated stratocumulus and broken cumulus cases, with a spatial resolution of a few hundred meters.

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