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Fuzhong Weng

. Schubert , 1974 : Interaction of cumulus cloud ensemble with the large scale environment. Part I. J. Atmos. Sci. , 31 , 674 – 701 . Bauer , P. , E. Moreau , F. Chevallier , and E. O’Keffee , 2005 : Multiple scattering microwave radiative transfer for data assimilation applications. Quart. J. Roy. Meteor. Soc. , 131 , 1259 – 1281 . Chin , M. , and Coauthors , 2002 : Tropospherical aerosol optical thickness from the GOCART model and comparisons with satellite and sun photometer

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Ruiyue Chen, Fu-Lung Chang, Zhanqing Li, Ralph Ferraro, and Fuzhong Weng

. Platnick , M. Wang , and K-N. Liou , cited . 1997 : Cloud retrieval algorithms for MODIS: Optical thickness, effective particle radius, and thermodynamic phase. MODIS Algorithm Theoretical Basis Doc. ATBD-MOD-05, 83 pp. [Available online at http://modis.gsfc.nasa.gov/data/atbd/atbd_mod05.pdf .] . King , M. D. , and Coauthors , 2003 : Cloud and aerosol properties, precipitable water, and profiles of temperature and humidity from MODIS. IEEE Trans. Geosci. Remote Sens. , 41 , 442 – 458

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Graeme L. Stephens and Christian D. Kummerow

-term statistics of cloud cover. ISCCP, for example, converts these radiances into a classification scheme based on cloud-top (pressure) height and cloud optical thickness ( Rossow and Schiffer 1999 ). GPCP was established in 1986 and merges infrared and microwave satellite estimates of precipitation with rain gauge data from more than 6000 stations ( Adler et al. 2003 ). These merged data are presented in the form of monthly mean precipitation data on a 2.5° × 2.5° latitude–longitude grid beginning in 1979

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Qing Yue, K. N. Liou, S. C. Ou, B. H. Kahn, P. Yang, and G. G. Mace

coefficient can be calculated by using the following equations ( Fu and Liou 1993 ): where IWC and D e denote the IWC and mean effective size retrieved from the MMCR data, respectively; β ext is the IR extinction coefficient; Δ z is the cloud thickness obtained from the MMCR retrieval; and c and d are constants. For columns, c ≈ −6.656 × 10 −3 and d ≈ 3.686 ( Fu and Liou 1993 ). Based on these parameterization equations, optical depth can be computed as a function of time and altitude. To

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