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Michael Scheuerer and Thomas M. Hamill

(positive probability of being exactly zero, continuous value range for positive precipitation amounts) makes it difficult to find an adequate parametric distribution model. Forecast uncertainty typically increases with the magnitude of expected precipitation amounts; this must be taken into account when setting up a model for the conditional distribution of observed precipitation amounts given the ensemble forecasts. High precipitation amounts occur very infrequently; a customized treatment of these

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Yu Zhang, Limin Wu, Michael Scheuerer, John Schaake, and Cezar Kongoli

amounts. The CSGD is practically identical to the P3 distribution used in modeling the marginals in MMGD [Eq. (3) ]. Although the formulation of P3 permits a negative value of y [Eq. (3) ], the precipitation forecast or observation is guaranteed to be nonnegative. Therefore, a negative value in the shift parameter δ would help assign a positive probability associated with zero precipitation. A distinct feature of CSGD is that both the climatological (unconditional) distribution of the

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Manuel Gebetsberger, Jakob W. Messner, Georg J. Mayr, and Achim Zeileis

randomly selecting subsamples. Each block is predicted with models trained on the remaining nine-tenths of data. Thus independent forecasts (test data) for the whole period are available to compute verification measures [e.g., continuous ranked probability score (CRPS)] for each event. Averages over these scores are either derived directly on the test data once, or in case for the evaluation of lead time performance, a bootstrap approach is used to estimate the sampling distribution of these averages

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Michael Scheuerer, Scott Gregory, Thomas M. Hamill, and Phillip E. Shafer

the wet-bulb temperature profiles affects the predictive performance in the opposite way. While the more flexible distribution model does not seem to benefit the freezing precipitation types, the better approximation of the distributions of SN and RA profiles that result from modeling skewness in the PCs translates into improved skill of the resulting probability forecasts. Finally, Fig. 6 highlights the necessity of regularizing the empirical covariance matrices. Without regularization, skill

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Thomas M. Hamill, Eric Engle, David Myrick, Matthew Peroutka, Christina Finan, and Michael Scheuerer

, the National Weather Service instituted the National Blend of Models project, called simply the National Blend hereafter. Under the National Blend, the NWS desires to generate calibrated, high-resolution forecast guidance from statistically postprocessed multimodel ensembles for use in digital forecasting at weather forecast offices and national centers ( Glahn and Ruth 2003 ). While a straightforward estimation of probabilities from the four-center MME relative frequencies was shown in H12 to

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Renaud Marty, Isabella Zin, Charles Obled, Guillaume Bontron, and Abdelatif Djerboua

recently seen a growing interest in this latter technique, which adapts well-forecast synoptic variables issued by meteorological models to provide a conditional distribution for more local variables like the expected rainfall ( Bliefernicht and Bárdossy 2007 ; Gibergans-Báguena and Llasat 2007 ; Diomede et al. 2008 ). Also, Hamill et al. (2006 , 2008) highlight that statistical calibration of NWP output can also be done to improving NWP predictive skill by using a long set of reforecasts. In this

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Emiel van der Plas, Maurice Schmeits, Nicolien Hooijman, and Kees Kok

the skill saturates after selecting three to four predictors (including the threshold). Fig . 4. Ranked probability skill score [full lines indicate the mean, dashed lines indicate the maximum and minimum of the distribution over the 30 different training periods using thresholds 0.3, 1, and 2 mm (3 h) −1 ] for forecasts of the three models from 0600 UTC + 15 h to 0600 UTC + 18 h (limited area models) and 0000 UTC + 21 h to 0000 UTC + 24 h (ECMWF) as a function of the number of predictors used

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Elizabeth A. Satterfield and Craig H. Bishop

1. Introduction Ensemble perturbations are designed to sample the distribution of analysis and forecast errors. Initial ensemble perturbations that are designed to represent the initial condition error distribution are added to the best available analysis to create the ensemble of initial conditions from which the ensemble forecast is made using one or more nonlinear (possibly stochastic) models ( Toth and Kalnay 1997 ; Toth et al. 2001 ; Palmer et al. 1998 ; Houtekamer et al. 1996 ). Hence

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Sun-Seon Lee, Ja-Yeon Moon, Bin Wang, and Hae-Jeong Kim

forecasts (i.e., Pr_F) exhibit similar distribution to observations although the forecast lead time of the pentad 2 forecast is relatively long (9–13 days). Major regions with high probability such as the WNP and South China Sea during BSISO1 phase 7 in July are captured in all models. Fig . 9. The P-dependent probability of extreme precipitation estimated by (a),(e) the observed BSISO1 and (b)–(d) and (f)–(h) the BSISO1 forecast of pentad 2, for (left) BSISO1 phase 7 in July and (right) phase 6 in

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Jakob W. Messner, Georg J. Mayr, Daniel S. Wilks, and Achim Zeileis

compare (heteroscedastic) extended logistic regression with two closely related regression models from statistics that are particularly popular in econometrics (and more broadly in social sciences): (Heteroscedastic) ordered logistic regression also provides coherent forecasts of category probabilities. However, it differs from extended logistic regression in that no continuous distribution is assumed or specified by the model. (Heteroscedastic) censored regression also fits conditional logistic

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