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Takuya Kawabata, Hironori Iwai, Hiromu Seko, Yoshinori Shoji, Kazuo Saito, Shoken Ishii, and Kohei Mizutani

1. Introduction Numerical weather prediction (NWP) technologies can reduce the damage to human lives and social resources caused by heavy rainfalls; their successes have however been confined to heavy rainfalls induced by strong forcings, such as large-scale low-pressure systems, fronts, and orography. Operational NWP systems have a limited capacity to forecast small-scale heavy rainfalls (10–50 km) with weak forcings owing to their coarse resolution, parameterization of cumulus convection, and

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Nicholas A. Gasperoni and Xuguang Wang

the usefulness of observations is particularly important for operational NWP centers that operate under limited budgets and need to weigh the costs and benefits of adding more observations to an already large observational dataset. There are a few basic approaches to quantifying the impact that assimilated observations have on a forecast. The first is the straightforward data-denial method, where parallel sets of analysis and forecast experiments are conducted with a “control” experiment

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Shigenori Otsuka and Takemasa Miyoshi

1. Introduction A multimodel ensemble aims to cope with model imperfections in numerical weather prediction (NWP) and has been studied extensively in recent years. In operational NWP, ensemble predictions with perturbed initial conditions have widely been used to evaluate the forecast uncertainties due to the initial condition uncertainties. This type of ensemble prediction system (EPS) was developed based on the theory of error growth due to the chaotic nature of the atmosphere (e.g., Yoden

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Chengsi Liu and Ming Xue

1. Introduction Variational data assimilation (DA) ( Le Dimet and Talagrand 1986 ; Talagrand and Courtier 1987 ) and the ensemble Kalman filter (EnKF; Evensen 1994 ) are two major advanced approaches for atmospheric DA. The variational DA approach has been successfully used at many operational numerical weather prediction (NWP) centers, first as the three-dimensional variational data assimilation (3DVar) then the four-dimensional variational data assimilation (4DVar) method (e.g., Parrish

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Daryl T. Kleist and Kayo Ide

1. Introduction Four-dimensional variational data assimilation (4DVar) techniques that use tangent-linear ( Lewis and Derber 1985 ; Courtier et al. 1994 ) or linear perturbation models ( Rawlins et al. 2007 ) and their corresponding adjoints have been shown to be powerful natural extensions to the 3DVar technique. In fact, 4DVar is the method of choice for initialization of single deterministic numerical weather prediction (NWP) applications at many operational centers ( Rabier et al. 2000

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Hyo-Jong Song and In-Hyuk Kwon

. Formulation of a 3DVAR using STCS (STCS-3DVAR) 1) A formulation of a background-error covariance model using STCS To construct a 3DVAR system based on STCS, we designed a background-error covariance model making use of STCS. Suppose that the forecast model is a hydrostatic model, and that the ns background-error samples δ on the CSGEA are given as the differences of the forecasts at the same time issued from different times, or the ensemble deviations from the mean of an ensemble forecast as follows

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Lars Nerger

. , 55 , 399 – 414 , doi: 10.1175/1520-0469(1998)055<0399:OSFSWO>2.0.CO;2 . Losa , S. N. , S. Danilov , J. Schröter , T. Janjić , L. Nerger , and F. Janssen , 2014 : Assimilating NOAA SST data into BSH operational circulation model for the North and Baltic Seas: Part 2. Sensitivity of the forecast’s skill to the prior model error statistics . J. Mar. Syst. , 129 , 259 – 270 , doi: 10.1016/j.jmarsys.2013.06.011 . Maybeck , P. S. , 1979 : Stochastic Models, Estimation, and

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Norihisa Usui, Yosuke Fujii, Kei Sakamoto, and Masafumi Kamachi

1. Introduction Ocean data assimilation, which synthesizes observations and numerical models to obtain the statistically best estimate of the ocean state, has been widely used for various purposes such as ocean monitoring, forecast, and reanalysis (e.g., Bennett 1992 , 2002 ; Ghil and Malanotte-Rizzoli 1991 ; Wunsch 1996 ; Talagrand 1997 ; Lewis et al. 2006 ; Evensen 2007 ). The variational method is one of the major approaches in data assimilation. Based on the maximum likelihood

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