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Bo Cui, Zoltan Toth, Yuejian Zhu, and Dingchen Hou

1. Introduction Over the last decade, a global forecast model–based global ensemble forecast system [such as the National Centers for Environmental Prediction’s (NCEP) Global Ensemble Forecast System (GEFS)] has been found to be useful for medium-range probabilistic forecasting. Ensemble forecasting has been embraced as a practical way of estimating the uncertainty of weather forecasts and of making probabilistic forecasts ( Toth and Kalnay 1993 , 1997 ; Molteni et al. 1996 ; Houtekamer et

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David A. Unger, Huug van den Dool, Edward O’Lenic, and Dan Collins

1. Introduction a. Background An ensemble forecasting system addresses the chaotic nature of the atmosphere by providing a dynamic estimate of the prediction confidence. Such systems exploit the stochastic nature of the atmosphere by generating many solutions based on slightly perturbed initial states ( Toth and Kalnay 1993 ). The chaotic nature of the predicted system leads the model solutions to diverge from one another with time, resulting in different realizations representing possible

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Juhui Ma, Yuejian Zhu, Dingchen Hou, Xiaqiong Zhou, and Malaquias Peña

1. Introduction Ensemble generation methods seek to create a set of initial perturbations representative of analysis errors in a numerical weather prediction system, with the goal to improve its probabilistic forecast performance. The analysis errors can be decomposed into nongrowing and growing modes ( Toth and Kalnay 1997 ). The nongrowing error modes, mainly stemming from observational errors, have a large dimensional subspace, and cannot be sampled well with a limited number of ensemble

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Aaron Johnson, Xuguang Wang, Ming Xue, and Fanyou Kong

1. Introduction Early studies on the impact of ensemble perturbations beyond initial and lateral boundary conditions (ICs/LBCs) have focused on cumulus-parameterizing (CP) resolution 1 or only limited sampling of sources of forecast uncertainty (e.g., Arribas et al. 2005 ; Jankov et al. 2005 ; Gallus and Bresch 2006 ; Jankov et al. 2007 ; Kong et al. 2007 , Aligo et al. 2007 ; Clark et al. 2008 ; Weisman et al. 2008 ; Palmer et al. 2009 ; Berner et al. 2011 ; Hacker et al. 2011

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Paul J. Roebber

’Steen and Werth 2009 ; Bakhshaii and Stull 2009 ; Roebber 2010 , 2013 ), work in this area has been ongoing since the 1960s (e.g., Fogel 1999 ). In Roebber (2013) , the “method of tribes” was introduced, a concept similar to the “multiple worlds” of Bakhshaii and Stull (2009) , although in the former instance this idea was used as a means to generate large ensembles of algorithms. These ensembles were shown to produce probabilistic forecasts for 500-hPa height with superior skill to those obtained

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Sabrina Rainwater and Brian Hunt

information from recent observations, resulting in an estimate of the current atmospheric state used to initialize subsequent forecasts. One tool for assessing forecast uncertainty is an “ensemble prediction system” ( Leith 1974 ) in which an ensemble of initial conditions are evolved by the model. Ideally, the ensemble of forecasts samples the future atmospheric state, thinking of it as a random variable. Weather services generally make a single forecast at a high resolution, determined by their

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Elizabeth A. Satterfield and Craig H. Bishop

1. Introduction Ensemble perturbations are designed to sample the distribution of analysis and forecast errors. Initial ensemble perturbations that are designed to represent the initial condition error distribution are added to the best available analysis to create the ensemble of initial conditions from which the ensemble forecast is made using one or more nonlinear (possibly stochastic) models ( Toth and Kalnay 1997 ; Toth et al. 2001 ; Palmer et al. 1998 ; Houtekamer et al. 1996 ). Hence

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Xubin Zhang

mentioned above inevitably result in uncertainties in NWP ( Lorenz 1963 ; Zhang et al. 2006 ). To cope with such forecast uncertainties, ensemble forecasting has developed over the past three decades and now becomes an important and useful approach ( Leith 1974 ; Wilks 2006 ). With increasing computer resources, convection-permitting (~4 km or less; Kain et al. 2008 ) ensemble forecasting has recently commenced to address convective-scale forecast uncertainties, which are characterized by high

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Craig H. Bishop, Teddy R. Holt, Jason Nachamkin, Sue Chen, Justin G. McLay, James D. Doyle, and William T. Thompson

ensemble perturbations in variable resolution models is that the scale of the perturbations needs to vary in accordance with the scales of variability resolved by the model. Methods of creating initial perturbations for limited-area models that are based on ensembles of global model states ( Grimit and Mass 2002 ; Marsigli et al. 2005 ; Walser et al. 2006 ) are a priori incapable of meeting this requirement. Limited-area adjoint approaches ( Xu et al. 2001 ; Homar et al. 2006 ) have not included

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Aaron Johnson, Xuguang Wang, Fanyou Kong, and Ming Xue

1. Introduction Since ensemble forecasting was recognized as a practical way to provide probabilistic forecasts ( Leith 1974 ), global-scale medium-range ensemble forecasting has undergone dramatic advancement (e.g., Toth and Kalnay 1993 ; Molteni et al. 1996 ; Houtekamer et al. 1996 ; Hamill et al. 2000 ; Wang and Bishop 2003 , 2005 ; Wang et al. 2004 , 2007 ; Wei et al. 2008 ). Meso/regional-scale short-range ensemble forecasting has also been studied for over a decade (e.g., Du et

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