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Models for Strongly-nonlinear Evolution of Long Internal Waves in ...

By: T. Sakai; L. G. Redekopp

Description: Department of Aerospace & Mechanical Engineering, University of Southern California, Los Angeles, CA 90089-1191, USA. Models describing the evolution of long internal waves are proposed that are based on different polynomial approximations of the exact expression for the phase speed of uni-directional, fully-nonlinear, infinitely-long waves in the two-layer model of a density stratified environment. It is argued that a quartic KdV model, one that employ...

Amick, C. and Turner, R.: A global theory of internal waves in two-fluid systems., Trans. Am. Math. Soc., 298, 431–481, 1986.; Apel, J., Holbrook, J., Liu, A., and Tsai, J.: The Sulu Sea internal soliton experiment., J. Phys. Oceanogr., 15, 1625–1651, 1985.; Antenucci, J., Imberger, J., and Saggio, A.: Seasonal evolution of the basin-scale internal wave field in a large stratified lake., Limnol. Oceanogr., 45, 1621–1638, 2000.; Benjamin, T.: Internal waves of finite ampl...

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Climate Spectrum Estimation in the Presence of Timescale Errors : ...

By: D. Fleitmann; E. W. Wolff; R. Röthlisberger; D. Scholz; M. Mudelsee; A. Mangini

Description: British Antarctic Survey, Cambridge, UK. We introduce an algorithm (called REDFITmc2) for spectrum estimation in the presence of timescale errors. It is based on the Lomb-Scargle periodogram for unevenly spaced time series, in combination with the Welch's Overlapped Segment Averaging procedure, bootstrap bias correction and persistence estimation. The timescale errors are modelled parametrically and included in the simulations for determining (1...

Robinson, P. M.: Estimation of a time series model from unequally spaced data, Stoch. Process. Appl., 6, 9–24, 1977.; Röthlisberger, R., Mudelsee, M., Bigler, M., de Angelis, M., Fischer, H., Hansson, M., Lambert, F., Masson-Delmotte, V., Sime, L., Udisti, R., and Wolff, E. W.: The Southern Hemisphere at glacial terminations: insights from the Dome C ice core, Clim. Past, 4, 345–356, 2008.; Scargle, J. D.: Studies in astronomical time series analysis. II. Statistical asp...

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Experimental Study of Nonlinear Interaction of Plasma Flow with Ch...

By: J. Buechner; M. F. Marcucci; M. Dunlop; J. Blecki; H. Rème; M. André; J. G. Trotignon; S. Savin; A. Skalsky; J. L. Rauch; S. Romanov; A. Fazakerley; Y. Khotyaintsev; P. M. E. Décréau; E. Amata; Y. V. Bogdanova

Description: Istituto di Fisica dello Spazio Interplanetario, INAF, Via del fosso del cavaliere 100, 00133 Roma, Italy. We study plasma transport at a thin magnetopause (MP), described hereafter as a thin current sheet (TCS), observed by Cluster at the southern cusp on 13 February 2001 around 20:01 UT. The Cluster observations generally agree with the predictions of the Gas Dynamic Convection Field (GDCF) model in the magnetosheath (MSH) up to the MSH boundary layer,...

André, M., Vaivads, A., Buchert, S. C., Fazakerley, A. N., and Lahiff, A.: Thin electron-scale layers at the magnetopause, Geophys. Res. Lett., 31, L03803, doi:10.1029/2003GL018137, 2004.; Balogh, A., Carr, C. M., AcuÑa, M. H., Dunlop, M. W., Beek, et al.: The Cluster magnetic field investigation: overview of in-flight performance and initial results, Ann. Geophys., 19, 1207–1217, 2001.; Belmont, G. and Rezeau, L.: Magnetopause reconnection induced by Hall-MHD fluctuatio...

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A Mixture Theory for Geophysical Fluids : Volume 11, Issue 1 (25/0...

By: A. C. Eringen

Description: 15 Red Tail Drive, Littleton, Co., 80126-5001, USA. A continuum theory is developed for a geophysical fluid consisting of two species. Balance laws are given for the individual components of the mixture, modeled as micropolar viscous fluids. The continua allow independent rotational degrees of freedom, so that the fluids can exhibit couple stresses and a non-symmetric stress tensor. The second law of thermodynamics is used to develop constitutive equati...

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Another Look at Climate Sensitivity : Volume 17, Issue 2 (17/03/2010)

By: M. Ghil; I. Zaliapin

Description: Department of Mathematics and Statistics, University of Nevada, Reno, USA. We revisit a recent claim that the Earth's climate system is characterized by sensitive dependence to parameters; in particular, that the system exhibits an asymmetric, large-amplitude response to normally distributed feedback forcing. Such a response would imply irreducible uncertainty in climate change predictions and thus have notable implications for climate science and clim...

Allen, M. R. and Frame, D. J.: Call off the quest, Science, 318(5850), 582–583, 2007.; Andronov, A. A. and Pontryagin, L. S.: Systèmes grossiers, Dokl. Akad. Nauk. SSSR, 14(5), 247–250, 1937.; Arfken, G.: Taylor's Expansion, Mathematical Methods for Physicists, 3rd ed., Orlando, FL, Academic Press, pp. 303–313, 1985.; Bryan, F.: High-latitude salinity effects and interhemispheric thermohaline circulations, Nature, 323, 301–304, 1986.; Budyko, M. I.: The effect of solar r...

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Classification of Probability Densities on the Basis of Pearson’s ...

By: B. Lefebvre; V. Krasnoselskikh; V. Podladchikov; O. Podladchikova

Description: Max-Planck-Institut für Aeronomie, Max-Planck-Str. 2, D-37191 Katlenburg-Lindau, Germany. An important task for the problem of coronal heating is to produce reliable evaluation of the statistical properties of energy release and eruptive events such as micro-and nanoflares in the solar corona. Different types of distributions for the peak flux, peak count rate measurements, pixel intensities, total energy flux or emission measures increas...

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Estimation of the Local Response to a Forcing in a High Dimensiona...

By: P. H. Haynes; J. G. Esler; F. C. Cooper

Description: Atmospheric, Oceanic and Planetary Physics, University of Oxford, Oxford, UK. The fluctuation-dissipation theorem (FDT) has been proposed as a method of calculating the response of the earth's atmosphere to a forcing. For this problem the high dimensionality of the relevant data sets makes truncation necessary. Here we propose a method of truncation based upon the assumption that the response to a localised forcing is spatially localised, as an alternat...

Abramov, R. V. and Majda, A. J.: Blended response algorithms for linear fluctuation-dissipation for complex nonlinear dynamical systems, Nonlinearity, 20, 2793–2821, doi:10.1088/0951-7715/20/12/004, 2007.; Boffetta, G., Lacorata, G., Musacchio, S., and Vulpiani, A.: Relaxation of finite perturbations: Beyond the fluctuation-response relation, Chaos, 13, 806–811, doi:10.1...

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Multifractality and Intermittency in the Solar Wind : Volume 14, I...

By: W. M. MacEk

Description: Faculty of Mathematics and Natural Sciences. College of Sciences, Cardinal Stefan Wyszyński University in Warsaw, Dewajtis 5, 01-815 Warszawa, Poland. Within the complex dynamics of the solar wind's fluctuating plasma parameters, there is a detectable, hidden order described by a chaotic strange attractor which has a multifractal structure. The multifractal spectrum has been investigated using Voyager (magnetic field) data in the outer heliosphere and...

Albano, A M., Muench, J., Schwartz, C., Mees, A I., and Rapp, P E.: Singular-value decomposition and the Grassberger-Procaccia algorithm, Phys. Rev. A, 38, 3017–3026, 1988.; Burlaga, L F.: Lognormal and multifractal distributions of the heliospheric magnetic field, J. Geophys. Res., 106, 15 917–15 927, 2001.; Bruno, R., Carbone, V., Veltri, P., Pietropaolo, E., and Bavassano, B.: Identifying intermittent events in the solar wind, Planet. Space Sci., 49, 1201–1210, 2001.;...

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Chaos in Magnetospheric Radio Emissions : Volume 9, Issue 5/6 (30/...

By: F. A. Borotto; E. L. Rempel; A. C.-l. Chian

Description: World Institute for Space Environment Research – WISER, NITP/WISER, Adelaide University, Adelaide, SA 5005, Australia. A three-wave model of auroral radio emissions near the electron plasma frequency was proposed by Chian et al. (1994) involving resonant interactions of Langmuir, whistler and Alfvén waves. Chaos can occur in the nonlinear evolution of this three-wave process in the magnetosphere. In particular, two types of intermittency,...

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Ion Motion in the Current Sheet with Sheared Magnetic Field – Part...

By: A. I. Neishtadt; L. M. Zelenyi; A. V. Artemyev

Description: Space Research Institute, RAS, Profsouznaya st., 84/32, GSP-7, 117997 Moscow, Russia. We present a theory of trapped ion motion in the magnetotail current sheet with a constant dawn–dusk component of the magnetic field. Particle trajectories are described analytically using the quasi-adiabatic invariant corresponding to averaging of fast oscillations around the tangential component of the magnetic field. We consider particle dynamics in the quasi-adiaba...

Anastasiadis, A., Gontikakis, C., and Efthymiopoulos, C.: Particle Interactions with Single or Multiple 3D Solar Reconnecting Current Sheets, Sol. Phys., 253, 199–214, doi:10.1007/s11207-008-9234-4, 2008.; Arnold, V. I.: Catastrophe Theory, Springer-Verlag, Berlin, 3rd Edn., 1992.; Arnold, V. I., Kozlov, V. V., and Neishtadt, A. I.: Mathematical Aspects of Classical and Celestial Mechanics, Dynamical Systems III. En...

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The Scaling Behaviour of the Edges of Gravity Data : Volume 20, Is...

By: G. R. J. Cooper

Description: School of Geosciences, University of the Witwatersrand, Johannesburg, South Africa. Measurements of the earth's gravity field are widely used in geophysical exploration programs. The geological interpretation process often involves the identification of the boundaries, or edges, of different regions. This can be achieved through a variety of techniques. This paper examines the statistical distribution of the size of the edges produced by a synthetic grav...

Buchmann, J. P.: Exploration of a geophysical anomaly at Trompsburg, Orange Free State, South Africa, Trans. Geol. Soc. South Africa, 63, 1–10, 1960.; Cooper, G. R. J.: Fractal convergence properties of geophysical inversion, Comput. Graphics, 24, 603–609, 2000.; Bohnenstiehl, D. R. and Kleinrock, M. C.: Faulting and fault scaling on the median valley floor of the trans-Atlantic geotraverse (TAG) segment,  26° N on the Mid-Atlantic Ridge, J. Geophys. Res., 104, 29351, 29...

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Model Error in Weather Forecasting : Volume 8, Issue 6 (30/11/-0001)

By: J. Barkmeijer; T. N. Palmer; L. Smith; D. Orrell

Description: Mathematical Institute, University of Oxford, 24-29 St Giles’, Oxford OX1 3LB, UK. Operational forecasting is hampered both by the rapid divergence of nearby initial conditions and by error in the underlying model. Interest in chaos has fuelled much work on the first of these two issues; this paper focuses on the second. A new approach to quantifying state-dependent model error, the local model drift, is derived and deployed both in examp...

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Testing and Modelling Autoregressive Conditional Heteroskedasticit...

By: P. H. A. J. M Van Gelder; J. K. Vrijling; J. Ma; W. Wang

Description: Faculty of Water Resources and Environment, Hohai University, Nanjing, 210098, China. Conventional streamflow models operate under the assumption of constant variance or season-dependent variances (e.g. ARMA (AutoRegressive Moving Average) models for deseasonalized streamflow series and PARMA (Periodic AutoRegressive Moving Average) models for seasonal streamflow series). However, with McLeod-Li test and Engle's Lagrange Multiplier test, clear evidences ...

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Verification of Intense Precipitation Forecasts from Single Models...

By: F. Atger

Description: Météo-France, Toulouse, France. The performance of single models and ensemble prediction systems has been investigated with respect to quantitative precipitation forecasts. Evaluation is based on the potential economic value of + 72 h/ + 96 h forecasts. The verification procedure consists of taking into account all precipitation amounts that are predicted in the vicinity of an observation in order to compute spatial, multi-event conti...

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Long's Equation in Terrain Following Coordinates : Volume 16, Issu...

By: M. Humi

Description: Department of Mathematical Sciences, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609, USA. Long's equation describes two dimensional stratified atmospheric flow over terrain which is represented by the geometry of the domain. The solutions of this equation over simple topography were investigated analytically and numerically by many authors. In this paper we derive a new terrain following formulation of this equation which incorp...

Baines, P. G.: Topographic effects in Stratified flows, Cambridge Univ.\ Press, New-York, 1995.; Nappo, C. J.: Atmospheric Gravity Waves, Academic Press, Boston, 2002.; Davis, K. S.: Flow of Nonuniformly Stratified Fluid of Large Depth over Topography, M.Sc. thesis in Mechanical Engineering, MIT, Cambridge, MA, 1999.; Dewan, E. M., Picard, R. H., O'Neil, R. R., Gardiner, H. A., Gibson, J., Mill, J. D., Richards, E., Kendra, M., and Gallery, W. O.: MSX satellite observati...

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Precision Variational Approximations in Statistical Data Assimilat...

By: P. J. Rozdeba; H. D. I. Abarbanel; N. Kadakia; J. Ye; J. C. Quinn

Description: Department of Physics, University of California, San Diego, La Jolla, CA 92093-0374, USA. Data assimilation transfers information from observations of a complex system to physically-based system models with state variables x(t). Typically, the observations are noisy, the model has errors, and the initial state of the model is uncertain, so the data assimilation is statistical. One can thus ask questions about expected values of...

Abarbanel, H. D.: Predicting the Future: Completing Models of Observed Complex Systems, Springer, New York, 2013.; Aguiar e Oliviera, H., Ingber, L., Petraglia, A., Petraglia, M. R., and Machado, M. A. S.: Stochastic Global Optimization and Its Applications with Fuzzy Adaptive Simulated Annealing, Vol. 35, Springer, New York, 2012.; Eibern, H. and Schmidt, H.: A four-dimensional variational chemistry data assimilation scheme for Eulerian chemistry transport modeling, J. ...

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Corrigendum to Thermal Energy Generation in the Earth Published in...

By: J. R. Reitz; F. J. Mayer

Description: Mayer Applied Research Inc., 1417 Dicken Drive, Ann Arbor, MI 48103, USA. No abstract available.

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Preface Nonlinear and Scaling Processes in Hydrology and Soil Scie...

By: Q. Cheng; J. L. M. P. De Lima; W. F. Krajewski; A. M. Tarquis; H. Gaonac'H

Description: CEIGRAM, E.T.S. Ing. Agrónomos, Universidad Politécnica de Madrid, Madrid, Spain. No abstract available.

Biswas, A., Si, B. C., and Walley, F. L.: Spatial relationship between $\delta^15$N and elevation in agricultural landscapes, Nonlin. Processes Geophys., 15, 397–407, http://dx.doi.org/10.5194/npg-15-397-2008doi:10.5194/npg-15-397-2008, 2008.; Cheng, Q., Li, L., and Wang, L.: Characterization of peak flow events with local singularity method, Nonlin. Processes Geophys., 16, 503–513, http://dx.doi.org/10.5194/npg-16-503-2009doi:10.5194/npg-16-503-2009, 2009.; de Lima, M. ...

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Energy-based Predictions in Lorenz System by a Unified Formalism a...

By: F. Maimone; R. Langone; V. Pelino; A. Pasini

Description: CNR, Institute of Atmospheric Pollution Research, Rome, Italy. In the framework of a unified formalism for Kolmogorov-Lorenz systems, predictions of times of regime transitions in the classical Lorenz model can be successfully achieved by considering orbits characterised by energy or Casimir maxima. However, little uncertainties in the starting energy usually lead to high uncertainties in the return energy, so precluding the chance of accurate multi-ste...

Bishop, C. M.: Neural networks for pattern recognition, Oxford University Press, New York, USA, 1995.; Boudjema, G. and Cazelles, B.: Extraction of nonlinear dynamics from short and noisy time series, Chaos Soliton. Fract., 12, 2051–2069, doi:10.1016/S0960-0779(00)00163-6, 2001.; Corti, S., Molteni, F., and Palmer, T. N.: Signature of recent climate change in frequencies of natural atmospheric circulation, Nature, 398, 799–802, doi:10.1038/19745, 1999.; Deloncle, A., Ber...

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Granulometric Characterization of Sediments Transported by Surface...

By: C. S. Souza; V. P. Singh; J. L. M. P. De Lima

Description: Department of Civil Engineering, Faculty of Science and Technology – Campus 2, University of Coimbra, 3030-788 Coimbra, Portugal. Due to the combined effect of wind and rain, the importance of storm movement to surface flow has long been recognized, at scales ranging from headwater scales to large basins. This study presents the results of laboratory experiments designed to investigate the influence of moving rainfall storms on the dynamics of sediment t...

Bagnold R. A.: An approach to the sediment transport problem from general physics, US Geological Survey Professional Paper, 422–1, 11–137, 1966.; Bras, R. and Rodrigues-Iturbe, I.: Rainfall generation: a nonstationary time-varying multidimensional model, Water Resour. Res., 12(3), 450–454, 1976.; Bryan, R. B. and Poesen, J.: Laboratory experiments on the influence of slope length on runoff, percolation and rill development, Earth Surf. Processes, 14, 211–231, 1989.; Eagl...

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