ALBERT

Description: In the forecasting of binary events, verification measures that are “equitable” were defined by Gandin and Murphy to satisfy two requirements: 1) they award all random forecasting systems, including those that always issue the same forecast, the same expected score (typically zero), and 2) they are expressible as the linear weighted sum of the elements of the contingency table, where the weights are independent of the entries in the table, apart from the base rate. The authors demonstrate that the widely used “equitable threat score” (ETS), as well as numerous others, satisfies neither of these requirements and only satisfies the first requirement in the limit of an infinite sample size. Such measures are referred to as “asymptotically equitable.” In the case of ETS, the expected score of a random forecasting system is always positive and only falls below 0.01 when the number of samples is greater than around 30. Two other asymptotically equitable measures are the odds ratio skill score and the symmetric extreme dependency score, which are more strongly inequitable than ETS, particularly for rare events; for example, when the base rate is 2% and the sample size is 1000, random but unbiased forecasting systems yield an expected score of around −0.5, reducing in magnitude to −0.01 or smaller only for sample sizes exceeding 25 000. This presents a problem since these nonlinear measures have other desirable properties, in particular being reliable indicators of skill for rare events (provided that the sample size is large enough). A potential way to reconcile these properties with equitability is to recognize that Gandin and Murphy’s two requirements are independent, and the second can be safely discarded without losing the key advantages of equitability that are embodied in the first. This enables inequitable and asymptotically equitable measures to be scaled to make them equitable, while retaining their nonlinearity and other properties such as being reliable indicators of skill for rare events. It also opens up the possibility of designing new equitable verification measures.

Description: Field line resonances have been observed for decades by ground-based and in situ instruments. The driving mechanism(s) are still unclear, although previous work has provided strong grounds that coherent waves in the solar wind may be a source. Here we present further evidence, with the use of multitaper analysis, a sophisticated spectrum estimation technique. A set of windows (dpss tapers) is chosen with characteristics that best suit the width of the narrowband peaks to be identified. The orthogonality of the windows allows for a confidence level (of say 95%) against a null hypothesis of a noisy spectrum, so that significant peaks can be identified. Employing multitaper analysis we can determine the phase and amplitude coherence at the sampling rate of the data sets and, over their entire duration. These characteristics make this technique superior to single windowing or wavelet analysis. A high degree of phase and amplitude (greater then 95%) coherence is demonstrated between a 2.1 mHz field line resonance observed by the SHARE radar at Sanae, Antarctica and the solar wind oscillation detected by WIND and ACE satellites.