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Julian Tödter and Bodo Ahrens

1. Introduction Data assimilation combines model forecasts with real-world observations to achieve an optimal estimation of the state of a dynamical system. Considering the strong sensitivity of highly nonlinear and chaotic systems such as the earth’s atmosphere with respect to initial conditions, an advanced data assimilation system is a key criterion to generate good forecasts. Furthermore, data assimilation techniques are successfully applied in a reanalysis context to reconstruct the

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Jingmin Li, Felix Pollinger, and Heiko Paeth

. Schulz , and M. Bernhardt , 2014 : Statistical downscaling of ERA-Interim forecast precipitation data in complex terrain using Lasso algorithm . Adv. Meteor. , 2014 , 1 – 16 , . Göbl , C. S. , L. Boykurt , A. Tura , G. Pacini , A. Kautzkz-Willer , and M. Mittlboeck , 2015 : Application of penalized regression techniques in modelling insulin sensitivity by correlated metabolic parameters . PLOS ONE , 10 , e0141524,

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Eric Vanden-Eijnden and Jonathan Weare

1. Introduction The assimilation of noisy observations into a model to improve its predictive capabilities is a recurring challenge in many applications. Examples include weather prediction and forecasting, robot tracking, stochastic volatility estimation, image analysis, etc. (see Doucet et al. 2001 ). In these applications and many others one is interested in predicting how the system evolves in time given a model for its dynamics and sequentially available, incomplete observations of its

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Dominik Jacques and Isztar Zawadzki

1. Introduction Because of their high spatial and temporal resolution, radar observations have great potential for improving atmospheric analyses and the ensuing forecasts. Despite 30 years ( Lilly 1990 ; Sun et al. 1991 ) of ongoing research, our skills in forecasting mesoscale convection have remained modest. Over continental scales, radar data assimilation was shown to improve forecasts for periods not exceeding 6–8 h ( Berenguer et al. 2012 ; Stratman et al. 2013 ). Over regional scales

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Ja-Rin Park, Hyeong-Bin Cheong, and Hyun-Gyu Kang

1. Introduction In numerical models and data analysis, filtering or smoothing is often used to smooth out unwanted, noiselike, small-scale variations from discrete data ( Wallington 1962 ; Shapiro 1970 ; Orszag 1971 ; Cocke 1998 ; Cocke and LaRow 2000 ; Gelb and Gleeson 2001 ; Denis et al. 2002 ; Cheong et al. 2002 , 2004 ; Feser and von Storch 2005 ; Cheong 2006 ). The numerical technique of filtering is also frequently used for decomposing the discrete grid data into two different

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Kwangjae Sung, Hyo-Jong Song, and In-Hyuk Kwon

i , χ ⁡ ( υ ) , k − 1 | k − 1 i ]   for   i = 0 , … , 2 L a , where χ ⁡ ( x ) , k | k − 1 i is the prior or forecast sigma point state vector at time k , χ ⁡ ( w ) , k − 1 | k − 1 i and χ ⁡ ( υ ) , k − 1 | k − 1 i are sigma point vectors that correspond to the model error and observation error, respectively, and z k i represents the transformed sigma point in observation space. Using the transformed sigma points obtained from Eqs. (12) and (13) , the predicted state estimate

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Paul D. Williams

numerical analysis, this technique falls into the category of implicit–explicit (IMEX) methods. The implicitly treated terms are crucial for high-frequency gravity wave oscillations, which are often of secondary importance and, which, if treated explicitly, would violate the Courant–Friedrichs–Lewy (CFL) stability condition unless impractically short time steps were taken. Semi-implicit numerical schemes are used widely in practical applications, because they suffer from neither the computational

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Timothy DelSole and Xia Feng

using techniques based on analysis of variance. Certain subtle and unverified assumptions that are required for the Shukla–Gutzler method to work, such as the fact that certain quantities follow the chi-square distribution and that the time mean is independent of its residuals, even for autocorrelated data, were clarified. Moreover, Monte Carlo experiments demonstrate that these assumptions are adequate even for autocorrelated data, provided the effective time scale T 0 is known. We derive the

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Xinrong Wu, Wei Li, Guijun Han, Lianxin Zhang, Caixia Shao, Chunjian Sun, and Lili Xuan

) have been developed to address the first issue, a localization technique is usually used to ease the second problem. The original localization scheme (e.g., Houtekamer and Mitchell 1998 ; Anderson 2001 ; Hamill et al. 2001 ; Szunyogh et al. 2008 ) was the fixed localization approach, which is usually realized by a Schur product (an element-by-element multiplication) of the ensemble-evaluated error covariance with an analytic localization operator. All fixed localization models need to determine

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Paul D. Williams

changing the time-step size changes the Kelvin wave speed and the convective and stratiform precipitation. Furthermore, in a simplified atmosphere general circulation model, Amezcua (2012) reports that the sensitivity of the skill of medium-range weather forecasts to the time-stepping method is about the same as it is to the physics parameterizations. A popular time-stepping method is the second-order centered-difference scheme, which is affectionately known as the leapfrog scheme (e.g., Haltiner

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