Pisarenko V.F.,Prediction Institute |
Sornette D.,ETH Zurich
European Physical Journal: Special Topics | Year: 2012
We ask the question whether it is possible to diagnose the existence of "Dragon-Kings" (DK), namely anomalous observations compared to a power law background distribution of event sizes. We present two new statistical tests, the U-test and the DK-test, aimed at identifying the existence of even a single anomalous event in the tail of the distribution of just a few tens of observations. The DK-test in particular is derived such that the p-value of its statistic is independent of the exponent characterizing the null hypothesis, which can use an exponential or power law distribution. We demonstrate how to apply these two tests on the distributions of cities and of agglomerations in a number of countries. We find the following evidence for Dragon-Kings: London in the distribution of city sizes of Great Britain; Moscow and St-Petersburg in the distribution of city sizes in the Russian Federation; and Paris in the distribution of agglomeration sizes in France. True negatives are also reported, for instance the absence of Dragon-Kings in the distribution of cities in Germany. © 2012 EDP Sciences and Springer.
Flatau M.,U.S. Navy |
Kim Y.-J.,U.S. Navy |
Kim Y.-J.,Prediction Institute
Journal of Climate | Year: 2013
A tropical-polar connection and its seasonal dependence are examined using the real-time multivariate Madden-Julian oscillation (MJO) (RMM) index and daily indices for the annular modes, the Arctic Oscillation (AO) and the Antarctic Oscillation (AAO). On the intraseasonal time scale, the MJO appears to force the annular modes in both hemispheres. On this scale, during the cold season, the convection in the Indian Ocean precedes the increase of the AO/AAO. Interestingly, during the boreal winter (Southern Hemisphere warm season), strong MJOs in the Indian Ocean are related to a decrease ofthe AAO index, and AO/AAO tendencies are out of phase. On the longer time scales, a persistent AO/AAO anomaly appears to influence the convection in the tropical belt and impact the distribution of MJO-preferred phases. It is shown that this may be a result of the sea surface temperature (SST) changes related to a persistent AO, with cooling over the Indian Ocean and warming over Indonesia. In the Southern Hemisphere, the SST anomalies are to some extent also related to a persistent AAOpattern, but this relationship is much weaker and appears only during the Southern Hemisphere cold season. Onthe basis of these results, a mechanism involving the air-sea interaction in the tropics is suggested as a possible link between persistent AO and convective activity in the Indian Ocean and western Pacific.
Shin H.H.,U.S. National Center for Atmospheric Research |
Hong S.-Y.,Prediction Institute
Monthly Weather Review | Year: 2015
Parameterization of the unresolved vertical transport in the planetary boundary layer (PBL) is one of the key physics algorithms in atmospheric models. This study attempts to represent the subgrid-scale (SGS) turbulent transport in convective boundary layers (CBLs) at gray-zone resolutions by investigating the effects of grid-size dependency in the vertical heat transport parameterization for CBL simulations. The SGS transport profile is parameterized based on the 2013 conceptual derivation by Shin and Hong. First, nonlocal transport via strong updrafts and local transport via the remaining small-scale eddies are separately calculated. Second, the SGS nonlocal transport is formulated by multiplying a grid-size dependency function with the total nonlocal transport profile fit to the large-eddy simulation (LES) output. Finally, the SGS local transport is formulated by multiplying a grid-size dependency function with the total local transport profile, which is calculated using an eddy-diffusivity formula. The new algorithm is evaluated against the LES output and compared with a conventional nonlocal PBL parameterization. For ideal CBL cases, by considering the scale dependency in the parameterized vertical heat transport, improvements over the conventional nonlocal K-profile model appear in mean profiles, resolved and SGS vertical transport profiles with their grid-size dependency, and the energy spectrum. Real-case simulations for convective rolls show that the simulated roll structures are more robust with stronger intensity when the new algorithm is used. © 2015 American Meteorological Society.
Frisch U.,French National Center for Scientific Research |
Zheligovsky V.,French National Center for Scientific Research |
Zheligovsky V.,Prediction Institute
Communications in Mathematical Physics | Year: 2014
It has been known for some time that a 3D incompressible Euler flow that has initially a barely smooth velocity field nonetheless has Lagrangian fluid particle trajectories that are analytic in time for at least a finite time Serfati (C. R. Acad. Sci. Paris Série I 320:175-180, 1995), Shnirelman (Glob. Stoch. Anal., http://arxiv.org/abs/1205.5837v1, 2012). Here an elementary derivation is given, based on Cauchy's form of the Euler equations in Lagrangian coordinates. This form implies simple recurrence relations among the time-Taylor coefficients of the Lagrangian map, used here to derive bounds for the C1,γ Hölder norms of the coefficients and infer temporal analyticity of Lagrangian trajectories when the initial velocity is C1,γ. © 2013 Springer-Verlag Berlin Heidelberg.
Podvigina O.,French National Center for Scientific Research |
Podvigina O.,Prediction Institute
Nonlinearity | Year: 2013
Heteroclinic cycles, unions of equilibria and connection trajectories, can be structurally stable in a Γ-equivariant system due to the existence of invariant subspaces. A structurally stable heteroclinic cycle is called simple if all connecting trajectories are one-dimensional. Heteroclinic cycles where equilibria are related by a symmetry γ ∈ Γ are called homoclinic. This paper presents a complete study of simple homoclinic cycles in . We find all symmetry groups Γ such that a Γ-equivariant dynamical system in can possess a simple homoclinic cycle. We introduce a classification of simple homoclinic cycles in based on the action of the system symmetry group. For systems in , we list all classes of simple homoclinic cycles. For each class, we derive necessary and sufficient conditions for asymptotic stability and fragmentary asymptotic stability in terms of eigenvalues of linearization near the steady state involved in the cycle. For any action of the groups Γ which can give rise to a simple homoclinic cycle, we list classes to which the respective homoclinic cycles belong, thus determining the conditions for the asymptotic stability of these cycles. © 2013 IOP Publishing Ltd & London Mathematical Society.