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Stephen Cusack and Alberto Arribas

1. Introduction Uncertainties in forecasts arise from errors in both the initialization and subsequent modeled evolution and are amplified by the chaotic nonlinear dynamics of the climate system (e.g., Lorenz 1963 , 1993 ). These sources of uncertainty are sampled by current ensemble prediction systems to produce a probability distribution function (pdf) of a predictand (e.g., Toth and Kalnay 1993 ; Palmer et al. 1993 ). Therefore, the forecast is probabilistic in nature, and a full

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Xiaosong Yang, Timothy DelSole, and Hua-Lu Pan

1. Introduction Leith (1978) proposed a novel method for empirically correcting a dynamical forecast model in which a term is added to the governing equations that subtracts the predicted tendency error at each time step. This type of empirical correction method differs from after-the-fact correction methods, such as subtracting the bias of a forecast, in that the former involves modifying the dynamical equations while the latter involves modifying the forecast after the unmodified model

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Suzana J. Camargo and Anthony G. Barnston

1. Introduction Tropical cyclones (TCs; see the appendix for a list of the acronyms used in this paper) are one of the most devastating types of natural disasters. Seasonal forecasts of TC activity could help the preparedness of coastal populations for an upcoming TC season and reduce economical and human losses. Currently, many institutions issue operational seasonal TC forecasts for various regions. In most cases, these are statistical forecasts, such as the Atlantic hurricane outlooks

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Roman Krzysztofowicz and W. Britt Evans

1. Introduction a. Forecasting stochastic process An element of sensible weather is typically forecasted and observed at predetermined times in the daily cycle. The associated sequence of predictands (variates whose realizations are forecasted) forms a discrete-time stochastic process , or a time series, which can be characterized by its marginal distribution functions and its temporal dependence structure (in particular, the autocorrelation structure). For a continuous element, such as

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Stephen Cusack and Alberto Arribas

1. Introduction The future state of the atmosphere is influenced by chaotic internal dynamics (e.g., Lorenz 1969 ; Lau 1981 ; Hendon and Hartmann 1985 ; Branstator 1995 ) that can amplify the uncertainties in forecast system initialization and formulation to produce different possible seasonal climate states. Seasonal forecasting systems employ ensembles of simulations to sample these uncertainties, and the prediction of a meteorological quantity is most appropriately viewed as a

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Allen B. White, Daniel J. Gottas, Arthur F. Henkel, Paul J. Neiman, F. Martin Ralph, and Seth I. Gutman

1. Introduction The “snow level” is a term used by National Oceanic and Atmospheric Administration’s (NOAA) forecasters at the National Weather Service (NWS) to ascribe the altitude in the atmosphere where falling snow melts to rain. The snow level should be distinguished from another term used by forecasters, the “free atmosphere freezing level,” which is the altitude corresponding to the 0°C isotherm. However, in cloud physics and in other fields, the term “melting level” is often used in

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Barry H. Lynn, Guy Kelman, and Gary Ellrod

and Gilson 2009 ). Various diagnostic approaches have been developed to predict lightning in forecast models (e.g., McCaul et al. 2009 ; Dahl et al. 2011 ). Recently, Fierro et al. (2013) implemented a physics-based, explicit lightning scheme within the Weather Research and Forecasting (WRF) Model ( Skamarock et al. 2008 ) that treats space charges as state variables and explicitly solves for the three components of the ambient electric field. Additionally, Lynn et al. (2012) developed a

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Rebecca E. Morss, Julie L. Demuth, and Jeffrey K. Lazo

1. Introduction Because the atmosphere is a dynamical system that exhibits limited predictability, weather forecasts are unavoidably uncertain. Meteorologists have recognized forecasts’ inherent uncertainty since the early days of modern weather forecasting ( Murphy 1998 ; NRC 2006 ). Moreover, users of weather forecasts have substantial experience with forecasts and subsequent weather and, thus, likely understand that forecasts are imperfect. Despite this recognition of forecast uncertainty

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Kieran T. Bhatia, David S. Nolan, Andrea B. Schumacher, and Mark DeMaria

1. Introduction An accurate forecast of a major tropical cyclone (TC) landfall represents one of the most remarkable feats of the earth sciences. Forecasting agencies can now produce skillful 120-h forecasts of the intensity, timing, and location of a TC making landfall. These long-range TC forecasts appear particularly impressive within the context of other natural disasters, such as earthquakes, tornadoes, tsunamis, and volcanic eruptions, which can only be diagnosed hours or sometimes

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Elisa Brussolo, Jost von Hardenberg, and Nicola Rebora

1. Introduction Precipitation intensity represents the crucial atmospheric variable for the operational assessment of hydrometeorological risks; unfortunately, it is also one of the most difficult to forecast reliably by current weather models. Uncertainty in quantitative precipitation forecasts (QPFs) arises as a result of measurement errors, incomplete observations, insufficiently resolved initial conditions, an incomplete representation of the physics of the problem, finite numerical

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