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Junjie Liu, Hong Li, Eugenia Kalnay, Eric J. Kostelich, and Istvan Szunyogh

1. Introduction Humidity is an important dynamical variable in numerical weather forecast models because it not only determines the occurrence of precipitation, but also changes temperature through evaporation and condensation processes and affects winds by changing the pressure gradient. However, because of the special error characteristics of humidity variables, the poor quality of observations, and the model errors related with moisture parameterizations ( Dee and da Silva 2003 ), humidity

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Hong Li, Eugenia Kalnay, Takemasa Miyoshi, and Christopher M. Danforth

atmospheric data assimilation. Mon. Wea. Rev. , 123 , 1128 – 1145 . Dee , D. P. , and A. M. da Silva , 1998 : Data assimilation in the presence of forecast bias. Quart. J. Roy. Meteor. Soc. , 124 , 269 – 295 . Dee , D. P. , and R. Todling , 2000 : Data assimilation in the presence of forecast bias: The GEOS moisture analysis. Mon. Wea. Rev. , 128 , 3268 – 3282 . Evensen , G. , 1994 : Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods

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Seung-Jong Baek, Istvan Szunyogh, Brian R. Hunt, and Edward Ott

the presence of forecast bias. Quart. J. Roy. Meteor. Soc. , 124 , 269 – 295 . Dee , D. P. , and R. Todling , 2000 : Data assimilation in the presence of forecast bias: The GEOS moisture analysis. Mon. Wea. Rev. , 128 , 3268 – 3282 . Derber , J. C. , 1989 : A variational continuous assimilation technique. Mon. Wea. Rev. , 117 , 2437 – 2446 . Drécourt , J. , H. Madsen , and D. Rosbjerg , 2006 : Bias aware Kalman filters: Comparison and improvements. Adv. Water Resour

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Derek J. Posselt and Tomislava Vukicevic

through a cloud system following the mean flow. The model consists of a single-column version of the National Aeronautics and Space Administration (NASA) Goddard Cumulus Ensemble (GCE) model ( Tao and Simpson 1993 ; Tao et al. 2003 ). As in the fully three-dimensional version of the GCE, base-state vertical profiles of potential temperature and moisture are fixed and the model predicts perturbations on these base-state profiles. In our idealized framework, clouds are generated by forcing the model

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