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J. F. Muzy; R. Baïle
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We introduce a variant of continuous random cascade models that extends former constructions introduced by BarralMandelbrot and BacryMuzy in the sense that they can be supported by sets of arbitrary fractal dimension. The so introduced sets are exactly selfsimilar stationary versions of random Cantor sets formerly introduced by Mandelbrot as "random cutouts". We discuss the main mathematical properties of our construction and compute its scaling properties. We then illustrate our...
Topics: Data Analysis, Statistics and Probability, Physics, Atmospheric and Oceanic Physics
Source: http://arxiv.org/abs/1601.03775
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The transport and shear under a Phillipstype spectrum are presented. A combined profile for monochromatic swell and a Phillipstype wind sea spectrum which can be used to investigate the shear under crossing seas is then presented.
Topics: Atmospheric and Oceanic Physics, Physics
Source: http://arxiv.org/abs/1603.06532
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Niklas Brännström; Leif Å Persson
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We consider a bilevel optimatisation method for inverse linear atmospheric dispersion problems where both linear and nonlinear model parameters are to be determined. We propose that a smooth weighted Mahalanobis distance function is used and derive sufficient conditions for when the follower problem has local strict convexity. A few toymodels are presented where local strict convexity and illposedness of the inverse problem are explored, indeed the smooth distance function is compared and...
Topics: Atmospheric and Oceanic Physics, Physics
Source: http://arxiv.org/abs/1607.04804
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Alexander M. R. Bakker; Tony E. Wong; Kelsey L. Ruckert; Klaus Keller
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Future sealevel rise poses nontrivial risks for many coastal communities. Managing these risks often relies on consensus projections like those provided by the IPCC. Yet, there is a growing awareness that the surrounding uncertainties may be much larger than typically perceived. Recently published sealevel projections appear widely divergent and highly sensitive to nontrivial model choices and the West Antarctic Ice Sheet (WAIS) may be much less stable than previously believed, enabling a...
Topics: Atmospheric and Oceanic Physics, Physics
Source: http://arxiv.org/abs/1609.07119
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James B. Elsner; Thomas H. Jagger; Tyler Fricker
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This paper estimates local tornado risk from records of past events using statistical models. First, a spatial model is fit to the tornado counts aggregated in counties with terms that control for changes in observational practices over time. Results provide a longterm view of risk that delineates the main tornado corridors in the United States where the expected annual rate exceeds two tornadoes per 10,000 square km. A few counties in the Texas Panhandle and central Kansas have annual rates...
Topics: Atmospheric and Oceanic Physics, Physics
Source: http://arxiv.org/abs/1606.07325
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Georg A. Gottwald; Daan T. Crommelin; Christian L. E. Franzke
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In this chapter we review stochastic modelling methods in climate science. First we provide a conceptual framework for stochastic modelling of deterministic dynamical systems based on the MoriZwanzig formalism. The MoriZwanzig equations contain a Markov term, a memory term and a term suggestive of stochastic noise. Within this framework we express standard model reduction methods such as averaging and homogenization which eliminate the memory term. We further discuss ways to deal with the...
Topics: Chaotic Dynamics, Nonlinear Sciences, Atmospheric and Oceanic Physics, Physics
Source: http://arxiv.org/abs/1612.07474
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Juan M. Restrepo; Shankar C. Venkataramani
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We develop a stochastic parametrization, based on a `simple' deterministic model for the dynamics of steady longshore currents, that produces ensembles that are statistically consistent with field observations of these currents. Unlike deterministic models, stochastic parameterization incorporates randomness and hence can only match the observations in a statistical sense. Unlike statistical emulators, in which the model is tuned to the statistical structure of the observation, stochastic...
Topics: Atmospheric and Oceanic Physics, Data Analysis, Statistics and Probability, Physics, Mathematics,...
Source: http://arxiv.org/abs/1612.01046
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A. L. Virovlyansky
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A method is proposed for finding the wave field components which are weakly sensitive to the sound speed perturbation in the ocean acoustic waveguides. Such a component is formed by a narrow beam of rays whose spread in vertical direction, up to the observation range, remains less than the vertical scale of perturbation. These rays pass through practically the same inhomogeneities and therefore their phases acquire close increments. If the ray amplitudes vary insignificantly, then (i) the...
Topics: Atmospheric and Oceanic Physics, Physics
Source: http://arxiv.org/abs/1610.02568
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Srikanth Toppaladoddi; John S. Wettlaufer
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We study the seasonal changes in the thickness distribution of Arctic sea ice, $g(h)$, under climate forcing. Our analytical and numerical approach is based on a FokkerPlanck equation for $g(h)$ (Toppaladoddi \& Wettlaufer \emph{Phys. Rev. Lett.} {\bf 115}, 148501, 2015), in which the thermodynamic growth rates are determined using observed climatology. In particular, the FokkerPlanck equation is coupled to the observationally consistent thermodynamic model of Eisenman \& Wettlaufer...
Topics: Atmospheric and Oceanic Physics, Physics
Source: http://arxiv.org/abs/1611.01045
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Mohamed Laib; Mikhail Kanevski
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This paper presents an initial exploration of high frequency records of extreme wind speed in two steps. The first consists in finding the suitable extreme distribution for $120$ measuring stations in Switzerland, by comparing three known distributions: Weibull, Gamma, and Generalized extreme value. This comparison serves as a basis for the second step which applies a spatial modelling by using Extreme Learning Machine. The aim is to model distribution parameters by employing a high dimensional...
Topics: Data Analysis, Statistics and Probability, Physics, Atmospheric and Oceanic Physics
Source: http://arxiv.org/abs/1609.05012
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Jonathan Demaeyer; Stéphane Vannitsem
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A stochastic subgridscale parameterization based on the Ruelle's response theory and proposed in Wouters and Lucarini [2012] is tested in the context of a loworder coupled oceanatmosphere model for which a part of the atmospheric modes are considered as unresolved. A natural separation of the phasespace into an invariant set and its complement allows for an analytical derivation of the different terms involved in the parameterization, namely the average, the fluctuation and the long memory...
Topics: Statistical Mechanics, Condensed Matter, Atmospheric and Oceanic Physics, Physics
Source: http://arxiv.org/abs/1605.00461
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Anna S. von der Heydt; Peter Ashwin
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Equilibrium climate sensitivity (ECS) is a key predictor of climate change. However, it is not very well constrained, either by climate models or by observational data. The reasons for this include strong internal variability and forcing on many time scales. In practise this means that the 'equilibrium' will only be relative to fixing the slow feedback processes before comparing palaeoclimate sensitivity estimates with estimates from model simulations. In addition, information from the late...
Topics: Atmospheric and Oceanic Physics, Physics
Source: http://arxiv.org/abs/1604.03311
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Chongsheng Cao; Jinkai Li; Edriss S. Titi
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In this paper, we consider the initialboundary value problem of the threedimensional primitive equations for oceanic and atmospheric dynamics with only horizontal viscosity and horizontal diffusivity. We establish the local, in time, wellposedness of strong solutions, for any initial data $(v_0, T_0)\in H^1$, by using the local, in space, type energy estimate. We also establish the global wellposedness of strong solutions for this system, with any initial data $(v_0, T_0)\in H^1\cap...
Topics: Fluid Dynamics, Atmospheric and Oceanic Physics, Analysis of PDEs, Physics, Mathematics, Geophysics
Source: http://arxiv.org/abs/1607.06252
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Michael Weniger; Florian Kapp; Petra Friederichs
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Due to the emergence of new high resolution numerical weather prediction (NWP) models and the availability of new or more reliable remote sensing data, the importance of efficient spatial verification techniques is growing. Wavelet transforms offer an effective framework to decompose spatial data into separate (and possibly orthogonal) scales and directions. Most wavelet based spatial verification techniques have been developed or refined in the last decade and concentrate on assessing forecast...
Topics: Atmospheric and Oceanic Physics, Physics
Source: http://arxiv.org/abs/1605.03395
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Denys Dutykh; Didier Clamond; Marx Chhay
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This manuscript is devoted to the modelling of water waves in the deep water regime with some emphasis on the underlying variational structures. The present article should be considered as a review of some existing models and modelling approaches even if new results are presented as well. Namely, we derive the deep water analogue of the celebrated SerreGreenNaghdi equations which have become the standard model in shallow water environments. The relation to existing models is discussed....
Topics: Classical Physics, Fluid Dynamics, Physics, Atmospheric and Oceanic Physics
Source: http://arxiv.org/abs/1607.00216
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Rui A. P. Perdigão; Carlos A. L. Pires; Julia Hall
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We formulate a nonlinear synergistic theory of coevolutionary systems, disentangling and explaining dynamic complexity in terms of fundamental processes for optimised data analysis and dynamic model design: Dynamic Source Analysis (DSA). DSA provides a nonlinear dynamical basis for spatiotemporal datasets or dynamical models, eliminating redundancies and expressing the system in terms of the smallest number of fundamental processes and interactions without loss of information. This optimises...
Topics: Physics, Dynamical Systems, Atmospheric and Oceanic Physics, Mathematics
Source: http://arxiv.org/abs/1611.03403