Historical weather extremes in the “Twentieth Century Reanalysis”

Meteorological or climatological extremes are rare and hence studying them requires long meteorological data sets. Moreover, for addressing the underlying atmospheric processes, detailed three-dimensional data are desired. Until recently the two requirements were incompatible as long meteorological series were only available for a few locations, whereas detailed 3-dimensional data sets such as reanalyses were limited to the past few decades. In 2011, the “Twentieth Century Reanalysis” (20CR) was released, a 6-hourly global atmospheric data set covering the past 140 years, thus combining the two properties. The collection of short papers in this volume contains case studies of individual extreme events in the 20CR data set. In this overview paper we introduce the first six cases and summarise some common findings. All of the events are represented in 20CR in a physically consistent way, allowing further meteorological interpretations and process studies. Also, for most of the events, the magnitudes are underestimated in the ensemble mean. Possible causes are addressed. For interpreting extrema it may be necessary to address individual ensemble members. Also, the density of observations underlying 20CR should be considered. Finally, we point to problems in wind speeds over the Arctic and the northern North Pacific in 20CR prior to the 1950s.

An efficient simulation algorithm for the generalized von Mises distribution of order two

In this article we propose an exact efficient simulation algorithm for the generalized von Mises circular distribution of order two. It is an acceptance-rejection algorithm with a piecewise linear envelope based on the local extrema and the inflexion points of the generalized von Mises density of order two. We show that these points can be obtained from the roots of polynomials and degrees four and eight, which can be easily obtained by the methods of Ferrari and Weierstrass. A comparative study with the von Neumann acceptance-rejection, with the ratio-of-uniforms and with a Markov chain Monte Carlo algorithms shows that this new method is generally the most efficient.

The SU(3)-invariant sector of new maximal supergravity

We investigate the SU(3)-invariant sector of the one-parameter family of SO(8) gauged maximal supergravities that has been recently discovered. To this end, we construct the N=2 truncation of this theory and analyse its full vacuum structure. The number of critical point is doubled and includes new N=0 and N=1 branches. We numerically exhibit the parameter dependence of the location and cosmological constant of all extrema. Moreover, we provide their analytic expressions for cases of special interest. Finally, while the mass spectra are found to be parameter independent in most cases, we show that the novel non-supersymmetric branch with SU(3) invariance provides the first counterexample to this.

Application of Local Rank Tests for Nonparametric Regression

Let Y_i = f(x_i) + E_i\ (1\le i\le n) with given covariates x_1\lt x_2\lt \cdots\lt x_n , an unknown regression function f and independent random errors E_i with median zero. It is shown how to apply several linear rank test statistics simultaneously in order to test monotonicity of f in various regions and to identify its local extrema.