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Eric Gilleland, David Ahijevych, Barbara G. Brown, Barbara Casati, and Elizabeth E. Ebert

1. Introduction Small-scale variability in high-resolution weather forecasts presents a challenging problem for verifying forecast performance. Traditional verification scores provide incomplete information about the quality of a forecast because they only make comparisons on a point-to-point basis with no regard to spatial information [ Baldwin and Kain (2006) ; Casati et al. (2008) ; see Wilks (2005) and Jolliffe and Stephenson (2003) for more on traditional verification scores]. For

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Christopher A. Davis, Barbara G. Brown, Randy Bullock, and John Halley-Gotway

1. Introduction Recent work by numerous authors has highlighted a series of novel methods for verifying the numerical prediction of highly localized, irregular fields such as precipitation. These novel methods are summarized in a companion article by Gilleland et al. (2009 , manuscript submitted to Wea. Forecasting ). Several methods fall under the heading of displacement verification methods, wherein spatial structures are examined objectively. Perhaps the most well-known methods of this

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Eric Gilleland, Johan Lindström, and Finn Lindgren

1. Introduction As forecast models have progressed to higher-resolution grids, their usefulness to most users has increased. Unfortunately, traditional forecast verification scores [e.g., root-mean-square error (RMSE), probability of detection (POD), etc.; Jolliffe and Stephenson (2003) ; Wilks (2006) ] that are calculated on a gridpoint-to-gridpoint basis often conclude that the models do not perform as well as lower-resolution models. For example, increased small-scale variability results

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Elizabeth E. Ebert

1. Introduction High space and time resolution quantitative precipitation forecasts (QPFs) are becoming increasingly available for use in such weather-related applications as heavy rain, flooding, landslides, and other high-impact weather prediction and hydrological applications such as streamflow prediction and water management. High-resolution modeling allows for more realistic structure and variability in the rainfall patterns, including better representation of topographically influenced

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Valliappa Lakshmanan and John S. Kain

approximates two images (the forecast and observed), we show in section 3 that it is possible to analyze the parameters of the component Gaussians to infer translation, rotation, and scaling transformations. a. Relationship to verification approaches The new methods of verifying model forecasts that have been proposed can be categorized into (a) filtering-based methods that operate on the neighborhood of pixels or on the basis of decomposition and (b) displacement methods that rely either on features or

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Elizabeth E. Ebert and William A. Gallus Jr.

1. Introduction As the spatial and temporal resolution of forecasts from numerical weather prediction (NWP) models grows increasingly finer, there is a need for spatial verification approaches that adequately reflect the quality of these forecasts without overpenalizing errors at the grid scale. Many new spatial verification strategies have been proposed, including neighborhood or fuzzy verification, scale decomposition, features-based verification, and field deformation approaches [for reviews

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David Ahijevych, Eric Gilleland, Barbara G. Brown, and Elizabeth E. Ebert

1. Introduction With advances in computing power, numerical guidance has become available on increasingly finer scales. Mesoscale phenomena such as squall lines and hurricane rainbands are routinely forecasted. While the simulated reflectivity field and precipitation distribution have more realistic spatial structure and can provide valuable guidance to forecasters on the mode of convective evolution ( Weisman et al. 2008 ), the traditional verification scores often do not reflect improvement

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Jason E. Nachamkin

1. Introduction With the advent of high-resolution numerical forecasts, repeated experiments have highlighted the limitations of the traditional verification measures (e.g., RMS, threat score) in describing the intrinsic value added by these forecasts ( Koch 1985 ; White et al. 1999 ; Ebert and McBride 2000 ; Zepeda-Arce et al. 2000 ; Colle et al. 2001 ; Mass et al. 2002 ; Baldwin et al. 2002 Ahijevych et al. 2009 , hereafter AGBE ). At issue is the added variance incurred from

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Eric Gilleland, David A. Ahijevych, Barbara G. Brown, and Elizabeth E. Ebert

Numerous new methods have been proposed for using spatial information to better quantify and diagnose forecast performance when forecasts and observations are both available on the same grid. The majority of the new spatial verification methods can be classified into four broad categories (neighborhood, scale separation, features based, and field deformation), which themselves can be further generalized into two categories of filter and displacement. Because the methods make use of spatial information in widely different ways, users may be uncertain about what types of information each provides, and which methods may be most beneficial for particular applications. As an international project, the Spatial Forecast Verification Methods Inter-Comparison Project (ICP; was formed to address these questions. This project was coordinated by NCAR and facilitated by the WMO/World Weather Research Programme (WWRP) Joint Working Group on Forecast Verification Research. An overview of the methods involved in the project is provided here with some initial guidelines about when each of the verification approaches may be most appropriate. Future spatial verification methods may include hybrid methods that combine aspects of filter and displacement approaches.

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Heini Wernli, Christiane Hofmann, and Matthias Zimmer

1. Introduction During the past few years, many novel techniques have been developed to assess the quality of quantitative precipitation forecasts (QPFs). A major aim of these methods is to overcome the double-penalty problem, which is inherent in classical gridpoint-based verification strategies ( Jolliffe and Stephenson 2003 ) when applied to richly structured QPFs. This problem arises for instance if an observed precipitation feature is displaced in the forecast. An error measure like, for

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