Ensemble post‐processing using member‐by‐member approaches: theoretical aspects

Schaeybroeck, Bert Van; Vannitsem, Stéphane

doi:10.1002/qj.2397

Cited by 74 publications

(82 citation statements)

References 31 publications

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“…The ensemble CRPS (eCRPS) is based on the alternative formulation for equation (Gneiting & Raftery, ):

CRPS ((),, F, o) = E_{F} (||, X - o) - \frac{1}{2} E_{F} (⌈⌉, X - X^{'}),

where E F denotes statistical expectation with respect to the predictive distribution F ( x ), and X and X ' are independent realizations from F ( x ). Substitution of sample averages from the forecast ensemble for the expectations in equation (Ferro et al, ; Van Schaeybroeck & Vannitsem, ) yields

e CRPS = \frac{1}{n} \sum_{t = 1}^{n} ([], \frac{1}{m} \sum_{k = 1}^{m} ((), x_{t, k} - y_{t}) - \frac{δ_{t}}{2}),

where

δ_{t} = \frac{1}{m ((), m - 1)} \sum_{j = 1}^{m} ([]||, \sum_{k = 1}^{m}, x_{t, j} - x_{t, k}) .

…”

Section: Methodsmentioning

confidence: 99%

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Spring Onset Predictability in the North American Multimodel Ensemble

2018

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The predictability of spring onset is assessed using an index of its interannual variability (the “extended spring index” or SI‐x) and output from the North American Multimodel Ensemble reforecast experiment. The input data to compute SI‐x were treated with a daily joint bias correction approach, and the SI‐x outputs computed from the North American Multimodel Ensemble were postprocessed using an ensemble model output statistic approach—nonhomogeneous Gaussian regression. This ensemble model output statistic approach was used to quantify the effects of training period length and ensemble size on forecast skill. The lead time for predicting the timing of spring onset is found to be from 10 to 60 days, with the higher end of this range located along a narrow band between 35°N to 45°N in the eastern United States. Using continuous rank probability scores and skill score (SS) thresholds, this study demonstrates that ranges of positive predictability of SI‐x fall into two categories: 10–40 and 40–60 days. Using higher skill thresholds (SS equal to 0.1 and 0.2), predictability is confined to a lower range with values around 10–30 days. The postprocessing work using joint bias correction improves the predictive skill for SI‐x relative to the untreated input data set. Using nonhomogeneous Gaussian regression, a positive change in the SS is noted in regions where the skill with joint bias correction shows evidence of improvement. These findings suggest that the start of spring might be predictable on intraseasonal time horizons, which in turn could be useful for farmers, growers, and stakeholders making decisions on these time scales.

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“…The ensemble CRPS (eCRPS) is based on the alternative formulation for equation (Gneiting & Raftery, ):

CRPS ((),, F, o) = E_{F} (||, X - o) - \frac{1}{2} E_{F} (⌈⌉, X - X^{'}),

e CRPS = \frac{1}{n} \sum_{t = 1}^{n} ([], \frac{1}{m} \sum_{k = 1}^{m} ((), x_{t, k} - y_{t}) - \frac{δ_{t}}{2}),

where

δ_{t} = \frac{1}{m ((), m - 1)} \sum_{j = 1}^{m} ([]||, \sum_{k = 1}^{m}, x_{t, j} - x_{t, k}) .

…”

Section: Methodsmentioning

confidence: 99%

“…where E F denotes statistical expectation with respect to the predictive distribution F (x), and X and X' are independent realizations from F (x). Substitution of sample averages from the forecast ensemble for the expectations in equation (8) (Ferro et al, 2008;Van Schaeybroeck & Vannitsem, 2015) yields…”

Section: Organization Modelmentioning

confidence: 99%

Spring Onset Predictability in the North American Multimodel Ensemble

2018

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“…Straightforward substitution of sample averages within a forecast ensemble for the expectations in Eq. yields the ensemble CRPS (eCRPS: Van Schaeybroeck and Vannitsem, )

italiceCRPS ((),, {boldx}_{t}, y_{t}) = \frac{1}{m} true {truefalse\sum}_{k = 1}^{m} (||, x_{t, k} - y_{t}) - \frac{δ_{t}}{2},

where m is the ensemble size, and the x t,k are the ensemble members for forecast occasion t .Here

δ_{t} = \frac{2}{m ((), m - 1)} true {truefalse\sum}_{k = 2}^{m} true {truefalse\sum}_{j = 1}^{k - 1} (||, x_{t, k} - x_{t, j})

is twice the dispersion metric known as the L‐scale (Hosking, ), and the first term in Eq. is the mean absolute error within the ensemble.…”

Section: Minimizing Crps While Enforcing Calibrationmentioning

confidence: 99%

“…Van Schaeybroeck and Vannitsem (), abbreviated as VSV hereafter, proposed the MBM ensemble postprocessing scheme defined by

{\overset{true˜}{x}}_{t, k} = a + b {\overset{true‾}{x}}_{t} + ({}, c + \frac{d}{δ_{t}}) ((), x_{t, k} - {\overset{true‾}{x}}_{t}),

…”

Section: Experimental Set‐upmentioning

confidence: 99%

Enforcing calibration in ensemble postprocessing

Wilks

2017

Quart J Royal Meteoro Soc

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Desirable attributes of probability forecasts are maximal sharpness, consistent with calibration (‘reliability’). The usual procedure of optimizing ensemble‐postprocessing parameters by minimizing a proper scoring rule such as the continuous ranked probability score or the ‘ignorance’ (i.e. negative log‐likelihood) does not guarantee the necessary calibration condition, potentially compromising the value of the resulting forecasts to users. The calibration condition can be enforced by including a miscalibration penalty in the loss function to be minimized in parameter estimation. The procedure is illustrated using ensemble forecasts for minimum temperatures and wind speeds, postprocessed using member‐by‐member algorithms.

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“…The latest advances in EMOS include utilizing extended logistic regression (Messner et al, 2014), left-censored Generalised Extreme Value distribution (GEV0: Scheuerer, 2014) and Censored and Shifted Gamma distribution (CSG0: Scheuerer and Hamill, 2015;Baran and Nemoda, 2016;Taillardat et al, 2019), which have been proved to well match the complicated precipitation variables. If only one set of parameters is estimated in the training process and only one single distribution is constructed according to the test data, the post-processing model is defined as a single model, such as regression-based models (Van Schaeybroeck and Vannitsem, 2015). The essential difference among the above parametric models is the variety of their parametric distributions.…”

Section: Introductionmentioning

confidence: 99%

Mixture probabilistic model for precipitation ensemble forecasting

Yang

Zhang

et al. 2019

Quart J Royal Meteoro Soc

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Statistical post‐processing approaches are widely employed to construct improved probabilistic meteorological forecasts from numerical weather prediction. However, generating calibrated and sharp probabilistic forecasts is challenging. In this article, a post‐processing approach, Mixture Probabilistic Model (MPM), is proposed to calibrate probabilistic ensemble forecasts subject to sharpness. In particular, the proposed MPM is applied to precipitation forecasting. First, the Censored and Shifted Gamma (CSG0) distribution is considered as the probability density function (PDF) for precipitation. Then, the predictive PDF of MPM is mixed by the individual PDFs which are fitted from raw ensemble members. Finally, to estimate optimal weight parameters for the mixture of individual PDFs, the Dirichlet distribution is utilized and the skills of the mixture model and individuals are both taken into consideration. The proposed MPM was tested using Innsbruck ensemble precipitation data and 6 h accumulated precipitation ensemble forecast data in east China from August to November 2017. Compared with raw forecasts and three state‐of‐the‐art post‐processing approaches, MPM showed improved performance for all verification scores. The quantitative and qualitative analyses of results in both cases indicate the potential and effectiveness of MPM for precipitation ensemble forecasting.

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Ensemble post‐processing using member‐by‐member approaches: theoretical aspects

Cited by 74 publications

References 31 publications

Spring Onset Predictability in the North American Multimodel Ensemble

Spring Onset Predictability in the North American Multimodel Ensemble

Enforcing calibration in ensemble postprocessing

Mixture probabilistic model for precipitation ensemble forecasting

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