This work was partly completed while the first author (Luo) worked on his Ph.D. thesis at Columbia University and NASA Goddard Institute for Space Studies with funding support from the NASA Radiation Sciences Program. The first author would also like to thank the Cooperative Institute for Research in the Atmosphere (CIRA) Postdoctoral Fellowship Program and Dr. Thomas Vonder Haar for supporting the completion of this study. We benefited from conversation with Dr. David Rind. Thanks are also due to two anonymous reviewers for their helpful comments.
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