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(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
(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
centered around m 2 . We also know V ( δ ), the variance of the change in the forecast means, from Eq. (2) above, and we have assumed that δ is normally distributed. As a result we can model the distribution of values that m 1 might take on Friday as a normal distribution with mean m 2 and variance V ( δ ), which we write as N [ m 2 , V ( δ )]. Each possible value of m 1 in this distribution corresponds to a possible probability forecast on Friday, consisting of a normal distribution
centered around m 2 . We also know V ( δ ), the variance of the change in the forecast means, from Eq. (2) above, and we have assumed that δ is normally distributed. As a result we can model the distribution of values that m 1 might take on Friday as a normal distribution with mean m 2 and variance V ( δ ), which we write as N [ m 2 , V ( δ )]. Each possible value of m 1 in this distribution corresponds to a possible probability forecast on Friday, consisting of a normal distribution
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
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
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
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
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
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
, 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
, 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
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
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
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
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
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
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
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
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
