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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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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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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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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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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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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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M. P. Mittermaier and G. Csima

, and cascaded from short- to longer wavelengths. Lorenz showed this too, though this aspect has generally been less publicized. Irrespective of the error sources, the loss of predictability and the impact on forecast skill remain among the main reasons why an ensemble approach is necessary at the kilometer scale, with a new verification approach to match this modeling requirement. For many national weather services, the value added by running a kilometer-scale ensemble over a deterministic

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Andrew W. Wood and John C. Schaake

other periods are also used. The primary operational methods for seasonal streamflow forecasting are linear regression (e.g., Garen 1992 ) and Ensemble Streamflow Prediction (ESP), a technique based on hydrologic modeling ( Twedt et al. 1977 ). The former has been (for most of the last century) and is the standard approach ( Wood and Lettenmaier 2006 ), but the latter method is rapidly being brought to the forefront, a shift enabled by advances in computing, digital data access, and model

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Eric P. Grimit and Clifford F. Mass

1. Introduction Ensemble numerical weather prediction (NWP) provides an approach for incorporating both initial conditions and model uncertainty into the forecast process while automatically accounting for flow dependence ( Ehrendorfer 1997 ; Palmer 2000 ). Given an ideal ensemble prediction system, one that accurately accounts for all sources of forecast uncertainty, the verifying truth should be indistinguishable from the members of the forecast ensemble ( Anderson 1996 ; Hamill 2001 ). The

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