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

, attention is focused on the verification of gridded forecasts with an observation field that is on the same grid (though this is not necessary for some methods), but note that methods that address the verification of forecasts on one scale against observations on a different scale do exist (e.g., Tustison et al. 2003 ). The majority of the new techniques can be broadly grouped into four categories, illustrated schematically in Fig. 1 : (i) neighborhood (or fuzzy), (ii) scale separation (or scale

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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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Eric Gilleland, Johan Lindström, and Finn Lindgren

important for gleaning useful information. We focus on the forecasting of precipitation fields because this has been the primary focus for the majority of the spatial forecast verification techniques proposed so far. However, the procedure works on a wide variety of field types (e.g., wind vectors, aerosol optical thickness, and binary fields). Hoffman et al. (1995) briefly discuss several types of displacement methods including optical flow and image warping, referred to therein as representation and

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Caren Marzban, Scott Sandgathe, Hilary Lyons, and Nicholas Lederer

the observed field. This issue has been thoroughly discussed in the literature, and a summary is provided in Ahijevych et al. (2009) . Also discussed in that work are three datasets designed to diagnose the inner workings of a number of verification techniques for a proper assessment of spatial–gridded forecasts. Among those techniques, three have been examined previously by the authors of this article; they are referred to as the cluster analysis (CA) method ( Marzban and Sandgathe 2006 , 2008

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Christian Keil and George C. Craig

1. Introduction An assessment of the forecast quality of mesoscale numerical weather prediction models is crucial (i) for model development, identifying shortcomings and systematic errors of existing models; (ii) for the documentation of the improvement of forecasting systems in time; and (iii) for the ranking and selection of “good” ensemble members for probabilistic forecasting products and as a key element in novel data assimilation techniques in high-resolution numerical weather forecasting

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Elizabeth E. Ebert and William A. Gallus Jr.

conclusions when determining which of three forecasts best agrees with the observations or for which of the nine cases the models performed best or worst. Nonetheless, it seems reasonable to expect a useful verification technique to provide results that agree with subjective determinations. AGBE describe a subjective evaluation of the WRF forecasts and indicate that a large amount of variability existed in the subjective evaluations of the three models for these nine cases. Because of the large

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Elizabeth E. Ebert

observations (field deformation). This paper focuses on the first approach. Neighborhood, also known as fuzzy, methods measure the accuracy of the forecasts within space–time neighborhoods. All grid-scale values within a spatial and/or temporal neighborhood of the observation are considered to be equally likely estimates of the true value, thus giving a probabilistic flavor to the verification process. 1 Ebert (2008) called these techniques “fuzzy” because they allow a forecast to be partially correct

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

, B. , 2010 : New developments of the intensity-scale technique within the Spatial Verification Methods Inter-Comparison Project. Wea. Forecasting , in press . Davis, C. A. , Brown B. G. , Bullock R. , and Halley-Gotway J. , 2009 : The method for object-based diagnostic evaluation (MODE) applied to numerical forecasts from the 2005 NSSL/SPC Spring Program. Wea. Forecasting , 24 , 1252 – 1267 . 10.1175/2009WAF2222241.1 Dey, C. H. , cited . 1998 : Grid identification (PDS Octet

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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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Valliappa Lakshmanan and John S. Kain

changes in the number of Gaussian components. d. Areas for further exploration This paper presents a GMM approach to model verification but is not a full-fledged verification technique. There are some unresolved questions about the GMM approach that need to be addressed in order to create a verification technique from the ideas in this paper: (i)  Association or deformation? In this paper, we approximated the observed and the forecast field by separate GMMs and picked out the

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