The continuous ranked probability score for circular variables and its application to mesoscale forecast ensemble verification

Abstract

SUMMARYAn analogue of the linear continuous ranked probability score is introduced that applies to probabilistic forecasts of circular quantities, such as wind direction. This scoring rule is proper and thereby discourages hedging. The circular continuous ranked probability score reduces to angular distance when the forecast is deterministic, just as the linear continuous ranked probability score generalizes the absolute error. Furthermore, the circular continuous ranked probability score provides a direct way of comparing deterministic forecasts, discrete forecast ensembles, and post-processed forecast ensembles that can take the form of circular probability density functions.The circular continuous ranked probability score is used in this study to compare predictions of 10 m wind direction for 361 cases of mesoscale, short-range ensemble forecasts over the North American Pacific Northwest. Simple, calibrated probability forecasts based on the ensemble mean and its forecast error history over the period outperform probability forecasts constructed directly from the ensemble sample statistics. These results suggest that short-term forecast uncertainty is not yet well predicted at mesoscale resolutions near the surface, despite the inclusion of multi-scheme physics diversity and surface boundary parameter perturbations in the mesoscale ensemble design.

Survey-based forecast distributions for Euro Area growth and inflation: ensembles versus histograms

“…where 1(A) is the indicator function of the event A. Closed-form expressions of the integral in (1) are available for several types of distributions F, such as the two types we use below: the two-piece normal distribution (Gneiting and Thorarinsdottir 2010) and mixtures of normal distributions (Grimit et al 2006). Our implementation is based on the R package scoringRules (Jordan et al 2016) which includes both of these variants.…”

Estimation of the Continuous Ranked Probability Score with Limited Information and Applications to Ensemble Weather Forecasts

“…with Grimit et al (2006) p i=1 ω i = 1, ω i=1,..., p > 0 Generalized extreme value: Y ∼ G E V (μ, σ, ξ ) Friederichs and Thorarinsdottir (2012) Generalized Pareto: Y ∼ G P D(μ, σ, ξ ) Friederichs and Thorarinsdottir (2012) Log-normal: ln(Y ) ∼ N (μ, σ ) Baran and Lerch (2015) Normal: Y ∼ N (μ, σ ) Gneiting et al (2005) Square-root truncated normal: √ Y ∼ N 0 (μ, σ ) Hemri et al (2014) Truncated normal: Y ∼ N 0 (μ, σ ) Thorarinsdottir and Gneiting (2010) The reference of the original article where to find the formula is also given. Taillardat et al (2016) gathers the closed form expression of the CRPS for these and other distributions in Appendix A, this score for an ensemble is minimized if all the members x i equal the median of F, which is obviously not the purpose of an ensemble.…”

Circular‐circular regression model with a spike at zero

“…When the error follows wrapped Cauchy distribution, then a model mixed with a wrapped Cauchy distribution with the known value of parameter very close to 1 may also be used for the fixed parameter part in the zero-inflated regression setup. As the wrapped Cauchy distribution has a heavy tail, thus, we have compared the two distributions based on CPRS as mentioned in Grimit et al 22 to check which one of the distribution goes better with the approximation for the true model. We have taken training data at two sample sizes n = 35 and n = 70 and test data of size 40% of the training data.…”