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Cristina Primo, Christopher A. T. Ferro, Ian T. Jolliffe, and David B. Stephenson

1. Introduction Probabilistic forecasts represent the uncertainty in a prediction by a probability distribution for the predictand. This distribution may be derived from historical errors of deterministic forecasts or from ensemble forecasts (see Leith 1974 ; Ehrendorfer 1997 ; Stephenson and Doblas-Reyes 2000 , and references therein). In the latter case, probabilistic forecasts for binary events are often obtained as the relative frequency with which the event occurs in the ensemble. For

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Fumin Ren, Chenchen Ding, Da-Lin Zhang, Deliang Chen, Hong-li Ren, and Wenyu Qiu

1. Introduction Considerable progress has been made in numerical weather prediction (NWP) during the past decades due partly to a steady accumulation of scientific knowledge and partly to technological advances in utilizing a variety of observations and gaining computing power ( Bauer et al. 2015 ). Despite the steady progress, significant forecast errors in today’s NWP models are still present, especially in processing atmospheric statistical properties that are not directly available from the

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Brian J. Etherton

1. Introduction Incorrect weather forecasts cause problems ranging from mere inconvenience to significant loss of life and property. Computer model forecasts, also referred to as guidance, are a valuable tool used by weather forecasters. Predictions by forecast agencies should improve if the accuracy of computer model guidance is increased. In addition to improving accuracy, producing guidance of similar accuracy but in less time is also beneficial to forecasters, as it would allow users of

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Aaron J. Hill, Gregory R. Herman, and Russ S. Schumacher

and are considered supplementarily in a “significant severe” weather class ( Hales 1988 ; Edwards et al. 2015 ). Collectively, these hazards have inflicted more than 1100 fatalities and $36.4B in damages across the contiguous United States (CONUS) in 2010–18 ( NWS 2018 ). While inherently dangerous and damaging phenomena, accurate severe weather forecasts can increase preparedness and help mitigate inclement weather losses. The hazards associated with severe weather are further encumbered by the

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Yue Zheng, Kiran Alapaty, Jerold A. Herwehe, Anthony D. Del Genio, and Dev Niyogi

1. Introduction Numerical weather prediction (NWP) forecast models have been greatly improved, motivated by the role of providing accurate forecasts about severe weather events to mitigate the loss of life and property. Furthermore, credibility of climate change simulations at urban scales can be increased by first improving the accuracy of high-resolution model simulations at weather prediction time scales ( Chen et al. 2011 ). In particular, moist processes play an important role in properly

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Felix Fundel, Andre Walser, Mark A. Liniger, Christoph Frei, and Christof Appenzeller

, those techniques usually compare a set of past model forecasts with observations in order to identify systematic relationships that can be used to correct the current forecast operationally. The successful application of various ensemble calibration techniques has been shown in a comparison study by Wilks (2006a) as well as Wilks and Hamill (2007) . However, those techniques are not designed to calibrate rare events, especially rare precipitation events, as the sample size of the training

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Phillip E. Shafer and Henry E. Fuelberg

1. Introduction Cloud-to-ground (CG) lightning is one of the leading causes of weather-related fatalities in the United States ( Holle et al. 1999 ). In fact, Curran et al. (2000) showed that only river and flash floods ranked higher than lightning in terms of deaths. Aside from the loss of life, CG lightning damages trees, buildings, and utility lines, often leading to power outages and disruptions to communications. Improved forecasts of CG lightning would have many potential societal

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Leonard A. Smith, Hailiang Du, and Sarah Higgins

1. Introduction Forecasters are often faced with an ensemble of model simulations that are to be incorporated into quantitative forecast system and presented as a probabilistic forecast. Indeed, ensembles of initial conditions have been operational in weather centers in both the United States ( Kirtman et al. 2014 ) and Europe ( Palmer et al. 2004 ; Weisheimer et al. 2009 ) since the early 1990s, and there is a significant literature on their interpretation ( Raftery et al. 2005 ; Hoeting et

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Aaron J. Hill, Christopher C. Weiss, and Brian C. Ancell

initiation ( Doswell and Bosart 2001 ). Although the importance of drylines in severe storm development is fairly well understood, forecasting their position, intensity, and the severe thunderstorms forced by the boundary remains difficult. Errors, for example, in the precise location of the parent synoptic cyclone, the distribution of boundary layer moisture (e.g., Holt et al. 2006 ), the intensity of capping inversions, and the strength of vertical mixing processes are critical components that

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Veronica J. Berrocal, Adrian E. Raftery, and Tilmann Gneiting

1. Introduction Ensemble prediction systems have been developed to generate probabilistic forecasts of weather quantities that address the two major sources of forecast uncertainty in numerical weather prediction: uncertainty in initial conditions, and uncertainty in model formulation. Originally suggested by Epstein (1969) and Leith (1974) , ensemble forecasts have been operationally implemented on the synoptic scale ( Toth and Kalnay 1993 ; Houtekamer et al. 1996 ; Molteni et al. 1996

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