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Steven J. Greybush, Eugenia Kalnay, Takemasa Miyoshi, Kayo Ide, and Brian R. Hunt

). Successful NWP depends upon well-balanced initial conditions to avoid the generation of spurious inertial gravity waves such as those that ruined the 1922 Richardson forecast. By balanced, we mean an atmospheric state in the slow manifold that approximately follows physical balance equations appropriate to the scale and location, such as the geostrophic relationship. In practice, there are initialization techniques for improving the balance of an analysis, such as nonlinear normal mode initialization and

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Takemasa Miyoshi, Yoshiaki Sato, and Takashi Kadowaki

exist, bogus observation data are generated and assimilated around the typhoons. Satellite radiance data include the Advanced Microwave Sounding Unit-A (AMSU-A) channels of the National Oceanic and Atmospheric Administration (NOAA)-15/16 and Aqua satellites, AMSU-B channels of the NOAA-15/16/17 satellites, SSM/I channels of the Defense Meteorological Satellite Program (DMSP)-13/14/15 satellites, Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) channels of the TRMM satellite

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Craig H. Bishop and Daniel Hodyss

diagnostics . Mon. Wea. Rev. , 129 , 869 – 883 . El Akkraoui , A. , P. Gauthier , S. Pellerin , and S. Buis , 2008 : Intercomparison of the primal and dual formulations of variational data assimilation . Quart. J. Roy. Meteor. Soc. , 134 , 1015 – 1025 . Evensen , G. , 2003 : The ensemble Kalman filter: Theoretical formulation and practical implementation . Ocean Dyn. , 53 , 343 – 367 . Farrell , B. F. , 1989 : Optimal excitation of baroclinic waves . J. Atmos. Sci. , 46

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Thomas M. Hamill and Jeffrey S. Whitaker

approximately 2.4 days. This model is obviously much simpler than the operational numerical weather prediction models currently in use; the resolution is lower, there is no terrain, no land or water, and no atmospheric moisture. In fact, while this model is capable of supporting internal gravity waves, it does not produce an external mode. These simplifications should be kept in mind while interpreting the results and their implications for operational numerical weather prediction. b

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Jean-François Caron and Luc Fillion

spurious fast gravity waves in the early stage of the forecast. The latter being particularly important for optimal assimilation of precipitation-related data ( Errico et al. 2007 ). To improve the representation of the divergent part of the wind over precipitation areas in variational data assimilation (Var) systems, Fillion et al. (2005) extended the idea of Fisher (2003) to use the quasigeostrophic (QG) omega equation to relate mass and divergent wind increments by introducing a coupling between

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Mark Buehner, P. L. Houtekamer, Cecilien Charette, Herschel L. Mitchell, and Bin He

covariances of background error between different time levels. In the current EnKF system (and En-4D-Var approach), the same spatial localization is applied to all temporal cross covariances as for the covariances of the background error at each individual time level. This may not be appropriate in situations where the background error may have a maximum temporal cross covariance at distant locations, due to rapid advection or wave propagation over the assimilation time window. An alternative localization

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Zhiyong Meng and Fuqing Zhang

localization in ensemble data assimilation using a hierarchical ensemble filter . Physica D , 230 , 99 – 111 . Anderson , J. L. , 2009 : Spatially and temporally varying adaptive covariance inflation for ensemble filters . Tellus , 61A , 72 – 83 . Anderson , J. L. , and N. Collins , 2007 : Scalable implementations of ensemble filter algorithms for data assimilation . J. Atmos. Oceanic Technol. , 24 , 1452 – 1463 . Anderson , J. L. , B. Wyman , S. Zhang , and T. Hoar , 2005

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Loïk Berre and Gérald Desroziers

+ 1) of wave vectors ( m , n ). This was treated by fitting an analytical function to the final spatial filter, which was derived from estimated power variances. The results of these approaches to estimate the average spatial structures of sampling noise and signal are illustrated in the next section. e. Quantitative estimation results for high-dimensional NWP systems The top panel of Fig. 5 is an example of power variance spectra for the raw signal (full and dashed lines) and for the

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