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Patrick Nima Raanes, Alberto Carrassi, and Laurent Bertino

1. Introduction The ensemble Kalman filter (EnKF) is a popular method for doing data assimilation (DA) in the geosciences. This study is concerned with the treatment of model noise in the EnKF forecast step. a. Relevance and scope While uncertainty quantification is an important end product of any estimation procedure, it is paramount in DA because of the sequentiality and the need to correctly weight the observations at the next time step. The two main sources of uncertainty in a forecast are

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Robin J. T. Weber, Alberto Carrassi, and Francisco J. Doblas-Reyes

caused by the displacement of the model state onto the observed values lying outside the model attractor. At the expense of larger initial errors, the objective of AI is to keep the initial state close to the model attractor and reduce the drift. The mean forecast error is less dependent on lead time and, as argued by Magnusson et al. (2013) , the use of standard a posteriori bias correction techniques is more robust. Anomaly initialization can reduce initialization shocks, but is unable to avoid

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María E. Dillon, Yanina García Skabar, Juan Ruiz, Eugenia Kalnay, Estela A. Collini, Pablo Echevarría, Marcos Saucedo, Takemasa Miyoshi, and Masaru Kunii

; Miyoshi and Kunii 2011 ). Another important parameter is the multiplicative inflation, whose role is to prevent underestimation of the forecast error covariance leading to filter divergence ( Anderson and Anderson 1999 ). In this work, the adaptive inflation technique developed by Miyoshi (2011) and implemented within WRF-LETKF by Miyoshi and Kunii (2012) is used. This method allows an online estimation of a location and time-dependent optimal inflation factor based on the innovation statistics

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Nicholas A. Gasperoni and Xuguang Wang

sampling error; however, a time-forecast component is added to the localization problem, such that a straightforward application of fixed localization techniques would not guarantee accurate impact estimates. To partially address the issue, Kalnay et al. (2012) proposed two methods of moving localization: 1) using a model-forecast nonlinear incremental evolution of the localization function, and 2) advecting the localization center using the climatological group velocity of dominant wavenumbers. Ota

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Daisuke Hotta, Tse-Chun Chen, Eugenia Kalnay, Yoichiro Ota, and Takemasa Miyoshi

observation improved or degraded the 24-h forecast. Their formulation exploits an adjoint sensitivity technique and is applicable to variational DA systems. Major operational NWP centers soon adopted this technique (e.g., Cardinali 2009 ; Gelaro and Zhu 2009 ; Ishibashi 2010 ; Lorenc and Marriott 2014 ) and showed that it is a powerful diagnostic. Its ensemble-based formulation, ensemble FSO (EFSO), was devised by Liu and Kalnay (2008) and Li et al. (2010) for the local ensemble transform Kalman

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Daryl T. Kleist and Kayo Ide

Appropriate Time (3DVar-FGAT) method ( Rabier et al. 1998 ; Lawless 2010 ), which employs 4D model states at the appropriate time to compute innovations but only solves for a solution at a single time, typically at the center of a window. The major drawbacks to the 4DVar technique are the computational cost, complications related to developing and maintaining linearized forecast models and their corresponding adjoints, and the basic assumption of linearity for the incremental formulation, which may be

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James A. Cummings and Ole Martin Smedstad

assimilated from the data denial change the value of the remaining observations. Because of the computational expense and difficulty in interpretation of the results, an OSE is performed intermittently and is not a viable method for routine determination of observation data impacts. An alternative approach has been developed to estimate the impact of the observations on the forecast by using an adjoint sensitivity method ( Langland and Baker 2004 ). The technique computes the variation in forecast error

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Kazumasa Aonashi, Kozo Okamoto, Tomoko Tashima, Takuji Kubota, and Kosuke Ito

. , 129 , 2776 – 2790 , doi: 10.1175/1520-0493(2001)129<2776:DDFOBE>2.0.CO;2 . Houtekamer , P. L. , and H. L. Mitchell , 1998 : Data assimilation using an ensemble Kalman filter technique . Mon. Wea. Rev. , 126 , 796 – 811 , doi: 10.1175/1520-0493(1998)126<0796:DAUAEK>2.0.CO;2 . Ikawa , M. , and K. Saito , 1991 : Description of a nonhydrostatic model developed at the Forecast Research Department of the MRI. MRI Tech. Rep. 28, 238 pp. [Available online at http

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Jean-François Caron, Thomas Milewski, Mark Buehner, Luc Fillion, Mateusz Reszka, Stephen Macpherson, and Judy St-James

. 7c,d ). Similar improvements can also be seen at shorter lead times (not shown). Fig . 7. As in Fig. 5 , but for experiments ENF (red) and 4DF (blue). 2) Ground-based GPS Forecasts of precipitable water were compared to the values derived from GB-GPS ZTD observations. 4 The confidence intervals for the scores reported here and in the following subsection were estimated from the bootstrap resampling technique described in Candille et al. (2007 , see their section 2c). Figure 8 shows the

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Juanzhen Sun, Hongli Wang, Wenxue Tong, Ying Zhang, Chung-Yi Lin, and Dongmei Xu

1. Introduction The variational data assimilation (DA) technique has been widely used in operational centers as well as in research communities to provide analysis and initialization for numerical models. The technique can be implemented with a three-dimensional (3DVar) or a four-dimensional (4DVar) variational data assimilation approach; the latter requires the use of a prediction model as the constraint. The variational method seeks to find the optimal analysis by minimizing a cost function

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