bluuebunny/crossref_metadata_2025 huggingface dataset:
North Atlantic climate variability in coupled models and data
Authors: Kravtsov S. K. , Dewar W. K. , Ghil M. , Berloff P. S. , McWilliams J. C.
Published: April 2010

Abstract. We show that the observed zonally averaged jet in the Northern Hemisphere atmosphere exhibits two spatial patterns with broadband variability in the decadal and inter-decadal range; these patterns are consistent with an important role of local, mid-latitude ocean–atmosphere coupling. A key aspect of this behaviour is the fundamentally nonlinear bi-stability of the atmospheric jet's latitudinal position, which enables relatively small sea-surface temperature anomalies associated with ocean processes to affect the large-scale atmospheric winds. The wind anomalies induce, in turn, complex three-dimensional anomalies in the ocean's main thermocline; in particular, they may be responsible for recently reported cooling of the upper ocean. Both observed modes of variability, decadal and inter-decadal, have been found in our intermediate climate models. One mode resembles North Atlantic tri-polar sea-surface temperature (SST) patterns described elsewhere. The other mode, with mono-polar SST pattern, is novel; its key aspects include interaction of oceanic turbulence with the large-scale oceanic flow. To the extent these anomalies exist, the interpretation of observed climate variability in terms of natural and human-induced changes will be affected. Coupled mid-latitude ocean-atmosphere modes do, however, suggest some degree of predictability is possible.
Tsallis and Levy statistics in the preparation of an earthquake
Authors: Contoyiannis Y. F. , Eftaxias K.
Published: April 2010

Abstract. Precursory fracture induced electromagnetic (EM) emissions, rooted in opening cracks and ranging from MHz to kHz, with the MHz appearing earlier, are produced and detected both at laboratory and geophysical scale. Recently, we have proposed the following two epochs/stages model of EQ generation: (i) The final kHz part is triggered by the fracture of high strength and large asperities that are distributed along the activated fault and sustain the system. (ii) The initial MHz part is thought to be due to the fracture of highly heterogeneous system that surrounds the family of asperities. Interestingly, the MHz EM time-series can be described in analogy with a thermal second order phase transition. Herein we focus on the MHz pre-seismic activity, and especially on the naturally arising question: what is the physical mechanism that organizes the heterogeneous system in its critical state? Combining ideas of Levy and Tsallis statistics and criticality with features hidden in the precursory MHz time-series we argue that a Levy walk type mechanism can organize the heterogeneous system to criticality. Based on a numerically produced truncated Levy walk, we propose a way to estimate in the stage of critical fluctuations: (i) the associated Levy index-a, which describes quantitatively the underlying Levy dynamics, and (ii) the range of values where the nonextesitive Tsallis index q is restricted. We also show that the kHz EM activity could not be described by a truncated Levy mechanism. This result further indicates an abrupt sweep of the population of asperities that sustain the system.
Quantification of tillage, plant cover, and cumulative rainfall effects on soil surface microrelief by statistical, geostatistical and fractal indices
Authors: Paz-Ferreiro J. , Bertol I. , Vidal Vázquez E.
Published: April 2010

Abstract. Changes in soil surface microrelief with cumulative rainfall under different tillage systems and crop cover conditions were investigated in southern Brazil. Surface cover was none (fallow) or the crop succession maize followed by oats. Tillage treatments were: 1) conventional tillage on bare soil (BS), 2) conventional tillage (CT), 3) minimum tillage (MT) and 4) no tillage (NT) under maize and oats. Measurements were taken with a manual relief meter on small rectangular grids of 0.234 and 0.156 m2, throughout growing season of maize and oats, respectively. Each data set consisted of 200 point height readings, the size of the smallest cells being 3×5 cm during maize and 2×5 cm during oats growth periods. Random Roughness (RR), Limiting Difference (LD), Limiting Slope (LS) and two fractal parameters, fractal dimension (D) and crossover length (l) were estimated from the measured microtopographic data sets. Indices describing the vertical component of soil roughness such as RR, LD and l generally decreased with cumulative rain in the BS treatment, left fallow, and in the CT and MT treatments under maize and oats canopy. However, these indices were not substantially affected by cumulative rain in the NT treatment, whose surface was protected with previous crop residues. Roughness decay from initial values was larger in the BS treatment than in CT and MT treatments. Moreover, roughness decay generally tended to be faster under maize than under oats. The RR and LD indices decreased quadratically, while the l index decreased exponentially in the tilled, BS, CT and MT treatments. Crossover length was sensitive to differences in soil roughness conditions allowing a description of microrelief decay due to rainfall in the tilled treatments, although better correlations between cumulative rainfall and the most commonly used indices RR and LD were obtained. At the studied scale, parameters l and D have been found to be useful in interpreting the configuration properties of the soil surface microrelief.
Asymmetric multifractal model for solar wind intermittent turbulence
Authors: Szczepaniak A. , Macek W. M.
Published: April 2010

Abstract. We consider nonuniform energy transfer rate for solar wind turbulence depending on the solar cycle activity. To achieve this purpose we determine the generalized dimensions and singularity spectra for the experimental data of the solar wind measured in situ by Advanced Composition Explorer spacecraft during solar maximum (2001) and minimum (2006) at 1 AU. By determining the asymmetric singularity spectra we confirm the multifractal nature of different states of the solar wind. Moreover, for explanation of this asymmetry we propose a generalization of the usual so-called p-model, which involves eddies of different sizes for the turbulent cascade. Naturally, this generalization takes into account two different scaling parameters for sizes of eddies and one probability measure parameter, describing how the energy is transferred to smaller eddies. We show that the proposed model properly describes multifractality of the solar wind plasma.
New results of investigations of whistler-mode chorus emissions
Authors: Santolík O.
Published: April 2010

Abstract. This review summarizes selected recent results obtained during investigation of whistler-mode chorus emissions in the Earth's magnetosphere. Special attention is paid to results published during the last five years, with a focus on the results of the CLUSTER project. The nonlinear nature of chorus emissions is demonstrated using both theoretical results and measurements. Selected areas of research on whistler-mode chorus are covered and the paper especially reports new results on substructure and amplitudes of chorus wave packets, on new observations of frequency differences of chorus wave packets at different points in space and on their possible interpretations, on results concerning determination of position and size of the source region of chorus, on recent observational and theoretical results which lead to improved description of propagation of chorus from its source, and, finally, on comparison of chorus measurements with corresponding values deduced from nonlinear theory and simulations.
On reliability analysis of multi-categorical forecasts
Authors: Bröcker J.
Published: April 2010

Abstract. Reliability analysis of probabilistic forecasts, in particular through the rank histogram or Talagrand diagram, is revisited. Two shortcomings are pointed out: Firstly, a uniform rank histogram is but a necessary condition for reliability. Secondly, if the forecast is assumed to be reliable, an indication is needed how far a histogram is expected to deviate from uniformity merely due to randomness. Concerning the first shortcoming, it is suggested that forecasts be grouped or stratified along suitable criteria, and that reliability is analyzed individually for each forecast stratum. A reliable forecast should have uniform histograms for all individual forecast strata, not only for all forecasts as a whole. As to the second shortcoming, instead of the observed frequencies, the probability of the observed frequency is plotted, providing and indication of the likelihood of the result under the hypothesis that the forecast is reliable. Furthermore, a Goodness-Of-Fit statistic is discussed which is essentially the reliability term of the Ignorance score. The discussed tools are applied to medium range forecasts for 2 m-temperature anomalies at several locations and lead times. The forecasts are stratified along the expected ranked probability score. Those forecasts which feature a high expected score turn out to be particularly unreliable.
Probability distributions of landslide volumes
Authors: Brunetti M. T. , Guzzetti F. , Rossi M.
Published: April 2010

Abstract. We examine 19 datasets with measurements of landslide volume, VL, for sub-aerial, submarine, and extraterrestrial mass movements. Individual datasets include from 17 to 1019 landslides of different types, including rock fall, rock slide, rock avalanche, soil slide, slide, and debris flow, with individual landslide volumes ranging over 10−4 m3≤VL≤1013 m3. We determine the probability density of landslide volumes, p(VL), using kernel density estimation. Each landslide dataset exhibits heavy tailed (self-similar) behaviour for their frequency-size distributions, p(VL) as a function of VL, for failures exceeding different threshold volumes, VL*, for each dataset. These non-cumulative heavy-tailed distributions for each dataset are negative power-laws, with exponents 1.0≤β≤1.9, and averaging β≈1.3. The scaling behaviour of VL for the ensemble of the 19 datasets is over 17 orders of magnitude, and is independent of lithological characteristics, morphological settings, triggering mechanisms, length of period and extent of the area covered by the datasets, presence or lack of water in the failed materials, and magnitude of gravitational fields. We argue that the statistics of landslide volume is conditioned primarily on the geometrical properties of the slope or rock mass where failures occur. Differences in the values of the scaling exponents reflect the primary landslide types, with rock falls exhibiting a smaller scaling exponent (1.1≤β≤1.4) than slides and soil slides (1.5≤β≤1.9). We argue that the difference is a consequence of the disparity in the mechanics of rock falls and slides.
Deep bore well water level fluctuations in the Koyna region, India: the presence of a low order dynamical system in a seismically active environment
Authors: Ramana D. V. , Chelani A. , Chadha R. K. , Singh R. N.
Published: April 2010

Abstract. Water level fluctuations in deep bore wells in the vicinity of seismically active Koyna region in western India provides an opportunity to understand the causative mechanism underlying reservoir-triggered earthquakes. As the crustal porous rocks behave nonlinearly, their characteristics can be obtained by analysing water level fluctuations, which reflect an integrated response of the medium. A Fractal dimension is one such measure of nonlinear characteristics of porous rock as observed in water level data from the Koyna region. It is inferred in our study that a low nonlinear dynamical system with three variables can predict the water level fluctuations in bore wells.
Characteristic scales in landslide modelling
Authors: Piegari E. , Di Maio R. , Milano L.
Published: April 2010

Abstract. Landslides are natural hazards occurring in response to triggers of different origins, which can act with different intensities and durations. Despite the variety of conditions that cause a landslide, the analysis of landslide inventories has shown that landslide events associated with different triggers can be characterized by the same probability distribution. We studied a cellular automaton, able to reproduce the landslide frequency-size distributions from catalogues. From the comparison between our synthetic probability distribution and the landslide area probability distribution of three landslide inventories, we estimated the typical size of a single cell of our cellular automaton model to be from 35–100 m2, which is important information if we are interested in monitoring a test area. To determine the probability of occurrence of a landslide of size s, we show that it is crucial to get information about the rate at which the system is approaching instability rather than the nature of the trigger. By varying such a driving rate, we find how the probability distribution changes and, in correspondence, how the size and the lifetime of the most probable events evolve. We also introduce a landslide-event magnitude scale based on the driving rate. Large values of the proposed intensity scale are related to landslide events with a fast approach to instability in a long distance of time, while small values are related to landslide events close together in time and approaching instability slowly.
Application of a GOY model to atmospheric boundary layer data
Authors: Vindel J. M. , Yagüe C.
Published: April 2010

Abstract. This article analyzes the possibility of applying a GOY theoretical model to atmospheric boundary layer data. Bearing this in mind, relative scaling exponents of velocity structure functions are used to compare the model with the data under study. In the model, these exponents are set based on two parameters (q and δ), which are appropriate to define the model that better features a certain atmospheric state. From these scaling exponents, the gap between 2-D and 3-D turbulence is observed in the model, depending on the fact that δ is higher or lower than unity, respectively. Atmospheric data corresponding to very different states of stratification stability have been analyzed. For convective or near-neutral situations (usually associated to 3-D turbulence), it is possible to find parameters q and δ to define a model that fits the measured data. More stable situations can be featured by GOY models with higher values of δ. However, it is clear that it is impossible to represent nocturnal situations of strong stable stratification (with a more similar behaviour to 2-D) with this type of model.
Multi-scale analysis of teleconnection indices: climate noise and nonlinear trend analysis
Authors: Franzke C.
Published: April 2010

Abstract. The multi-scale nature and climate noise properties of teleconnection indices are examined by using the Empirical Mode Decomposition (EMD) procedure. The EMD procedure allows for the analysis of non-stationary time series to extract physically meaningful intrinsic mode functions (IMF) and nonlinear trends. The climatologically relevant monthly mean teleconnection indices of the North Atlantic Oscillation (NAO), the North Pacific index (NP) and the Southern Annular Mode (SAM) are analyzed. The significance of IMFs and trends are tested against the null hypothesis of climate noise. The analysis of surrogate monthly mean time series from a red noise process shows that the EMD procedure is effectively a dyadic filter bank and the IMFs (except the first IMF) are nearly Gaussian distributed. The distribution of the variance contained in IMFs of an ensemble of AR(1) simulations is nearly χ2 distributed. To test the statistical significance of the IMFs of the teleconnection indices and their nonlinear trends we utilize an ensemble of corresponding monthly averaged AR(1) processes, which we refer to as climate noise. Our results indicate that most of the interannual and decadal variability of the analysed teleconnection indices cannot be distinguished from climate noise. The NP and SAM indices have significant nonlinear trends, while the NAO has no significant trend when tested against a climate noise hypothesis.
Finite-time Lagrangian transport analysis: stable and unstable manifolds of hyperbolic trajectories and finite-time Lyapunov exponents
Authors: Branicki M. , Wiggins S.
Published: April 2010

Abstract. We consider issues associated with the Lagrangian characterisation of flow structures arising in aperiodically time-dependent vector fields that are only known on a finite time interval. A major motivation for the consideration of this problem arises from the desire to study transport and mixing problems in geophysical flows where the flow is obtained from a numerical solution, on a finite space-time grid, of an appropriate partial differential equation model for the velocity field. Of particular interest is the characterisation, location, and evolution of transport barriers in the flow, i.e. material curves and surfaces. We argue that a general theory of Lagrangian transport has to account for the effects of transient flow phenomena which are not captured by the infinite-time notions of hyperbolicity even for flows defined for all time. Notions of finite-time hyperbolic trajectories, their finite time stable and unstable manifolds, as well as finite-time Lyapunov exponent (FTLE) fields and associated Lagrangian coherent structures have been the main tools for characterising transport barriers in the time-aperiodic situation. In this paper we consider a variety of examples, some with explicit solutions, that illustrate in a concrete manner the issues and phenomena that arise in the setting of finite-time dynamical systems. Of particular significance for geophysical applications is the notion of flow transition which occurs when finite-time hyperbolicity is lost or gained. The phenomena discovered and analysed in our examples point the way to a variety of directions for rigorous mathematical research in this rapidly developing and important area of dynamical systems theory.
The turnstile mechanism across the Kuroshio current: analysis of dynamics in altimeter velocity fields
Authors: Mendoza C. , Mancho A. M. , Rio M.-H.
Published: April 2010

Abstract. In this article we explore the utility of dynamical systems tools for visualizing transport in oceanic flows described by data sets measured from satellites. In particular we have found the geometrical skeleton of some transport processes in the Kuroshio region. To this end we have computed the special hyperbolic trajectories, and identified them as distinguished hyperbolic trajectories, that act as organizing centres of the flow. We have computed their stable and unstable manifolds, and they reveal that the turnstile mechanism is at work during several spring months in the year 2003 across the Kuroshio current. We have found that near the hyperbolic trajectories takes place a filamentous transport front-cross the current that mixes waters from both sides.
Lagrangian structure of flows in the Chesapeake Bay: challenges and perspectives on the analysis of estuarine flows
Authors: Branicki M. , Malek-Madani R.
Published: April 2010

Abstract. In this work we discuss applications of Lagrangian techniques to study transport properties of flows generated by shallow water models of estuarine flows. We focus on the flow in the Chesapeake Bay generated by Quoddy (see Lynch and Werner, 1991), a finite-element (shallow water) model adopted to the bay by Gross et al. (2001). The main goal of this analysis is to outline the potential benefits of using Lagrangian tools for both understanding transport properties of such flows, and for validating the model output and identifying model deficiencies. We argue that the currently available 2-D Lagrangian tools, including the stable and unstable manifolds of hyperbolic trajectories and techniques exploiting 2-D finite-time Lyapunov exponent fields, are of limited use in the case of partially mixed estuarine flows. A further development and efficient implementation of three-dimensional Lagrangian techniques, as well as improvements in the shallow-water modelling of 3-D velocity fields, are required for reliable transport analysis in such flows. Some aspects of the 3-D trajectory structure in the Chesapeake Bay, based on the Quoddy output, are also discussed.
Record-breaking earthquake intervals in a global catalogue and an aftershock sequence
Authors: Yoder M. R. , Turcotte D. L. , Rundle J. B.
Published: April 2010

Abstract. For the purposes of this study, an interval is the elapsed time between two earthquakes in a designated region; the minimum magnitude for the earthquakes is prescribed. A record-breaking interval is one that is longer (or shorter) than preceding intervals; a starting time must be specified. We consider global earthquakes with magnitudes greater than 5.5 and show that the record-breaking intervals are well estimated by a Poissonian (random) theory. We also consider the aftershocks of the 2004 Parkfield earthquake and show that the record-breaking intervals are approximated by very different statistics. In both cases, we calculate the number of record-breaking intervals (nrb) and the record-breaking interval durations Δtrb as a function of "natural time", the number of elapsed events. We also calculate the ratio of record-breaking long intervals to record-breaking short intervals as a function of time, r(t), which is suggested to be sensitive to trends in noisy time series data. Our data indicate a possible precursory signal to large earthquakes that is consistent with accelerated moment release (AMR) theory.
An extension of conditional nonlinear optimal perturbation approach and its applications
Authors: Mu M. , Duan W. , Wang Q. , Zhang R.
Published: April 2010

Abstract. The approach of conditional nonlinear optimal perturbation (CNOP) was previously proposed to find the optimal initial perturbation (CNOP-I) in a given constraint. In this paper, we extend the CNOP approach to search for the optimal combined mode of initial perturbations and model parameter perturbations. This optimal combined mode, also named CNOP, has two special cases: one is CNOP-I that only links with initial perturbations and has the largest nonlinear evolution at a prediction time; while the other is merely related to the parameter perturbations and is called CNOP-P, which causes the largest departure from a given reference state at a prediction time. The CNOP approach allows us to explore not only the first kind of predictability related to initial errors, but also the second kind of predictability associated with model parameter errors, moreover, the predictability problems of the coexistence of initial errors and parameter errors. With the CNOP approach, we study the ENSO predictability by a theoretical ENSO model. The results demonstrate that the prediction errors caused by the CNOP errors are only slightly larger than those yielded by the CNOP-I errors and then the model parameter errors may play a minor role in producing significant uncertainties for ENSO predictions. Thus, it is clear that the CNOP errors and their resultant prediction errors illustrate the combined effect on predictability of initial errors and model parameter errors and can be used to explore the relative importance of initial errors and parameter errors in yielding considerable prediction errors, which helps identify the dominant source of the errors that cause prediction uncertainties. It is finally expected that more realistic models will be adopted to investigate this use of CNOP.
Predictability of the monthly North Atlantic Oscillation index based on fractal analyses and dynamic system theory
Authors: Martínez M. D. , Lana X. , Burgueño A. , Serra C.
Published: April 2010

Abstract. The predictability of the monthly North Atlantic Oscillation, NAO, index is analysed from the point of view of different fractal concepts and dynamic system theory such as lacunarity, rescaled analysis (Hurst exponent) and reconstruction theorem (embedding and correlation dimensions, Kolmogorov entropy and Lyapunov exponents). The main results point out evident signs of randomness and the necessity of stochastic models to represent time evolution of the NAO index. The results also show that the monthly NAO index behaves as a white-noise Gaussian process. The high minimum number of nonlinear equations needed to describe the physical process governing the NAO index fluctuations is evidence of its complexity. A notable predictive instability is indicated by the positive Lyapunov exponents. Besides corroborating the complex time behaviour of the NAO index, present results suggest that random Cantor sets would be an interesting tool to model lacunarity and time evolution of the NAO index.
Shallow seismicity in the area of Greece: its character as seen by means of a stochastic model
Authors: Polimenakos L. C.
Published: April 2010

Abstract. Occurrence of successive earthquake events in space is analysed by means of semi-stochastic processes. The analysis employs earthquakes events with M > 5.2 from the area of Greece and its surroundings (18-31° E, 34-43° N) for the time interval 1911-1985. The sequence of earthquake occurrences can be only marginally described by a first order Markov chain model. Substitutability analysis incorporates the results of Markov Chains, revealing, though, detailed interrelations of parts (subareas) of the study area, not appreciated in Markov Chain analysis. Reactivation of particular subareas provides an insight into the level of interaction between neighbouring seismogenic sources within a subarea. The earthquake occurrence pattern provides evidence for the effect of a significant stress diffusion through time in the sense of a stress front. Taking into account the limitations of the methodologies applied, results indicate the importance of large-scale monitoring of seismicity, which assist in the identification of particular characteristics of the earthquake occurrence in space and time.
Scaling properties of gravity-driven sediments
Authors: Rothman D. H. , Grotzinger J. P.
Published: April 2010

Abstract. Recent field observations of the statistical distribution of turbidite and debris flow deposits are discussed. In some cases one finds a good fit over 1.5-2 orders of magnitude to the scaling law N(h) α h-B, where N(h) is the number of layers thicker than h. Observations show that the scaling exponent B varies widely from deposit to deposit, ranging from about 1/2 to 2. Moreover, one case is characterized by a sharp crossover in which B increases by a factor of two as h increases past a critical thickness. We propose that the variations in B, either regional or within the same deposit, are indicative of the geometry of the sedimentary basin and the rheological properties of the original gravity-driven flow. The origin of the power-law distribution remains an open question.
Asymmetry of wind waves studied in a laboratory tank
Authors: Leykin I. A. , Donelan M. A. , Mellen R. H. , McLaughlin D. J.
Published: April 2010

Abstract. Asymmetry of wind waves was studied in laboratory tank tinder varied wind and fetch conditions using both bispectral analysis of wave records and third-order statistics of the surface elevation. It is found skewness S (the normalized third-order moment of surface elevation describing the horizontal asymmetry waves) varies only slightly with the inverse wave u*/Cm (where u* is the air friction velocity and Cm is phase speed of the dominant waves). At the same time asymmetry A, which is determined from the Hilbert transform of the wave record and characterizes the skewness of the rate of change of surface elevation, increase consistently in magnitude with the ratio u*/Cm. This suggests that nonlinear distortion of the wave profile determined by the degree of wind forcing and is a sensitive indicator of wind-wave interaction processes. It is shown that the asymmetric profile of waves can described within the frameworks of the nonlinear nonspectral concept (Plate, 1972; Lake and Yuen, 197 according to which the wind-wave field can be represented as a coherent bound-wave system consisting mainly of dominant component w. and its harmonics propagating with the same speed C. , as observed by Ramamonjiaris and Coantic (1976). The phase shift between o). harmonics is found and shown to increase with the asymmetry of the waves.
Analysis of the atmosphere behaviour in the proximities of an orographic obstacle
Authors: Hernández E. , Díaz J. , Cana L. C. , García A.
Published: April 2010

Abstract. The atmospheric behaviour near an orographic obstacle has been thoroughly studied in the last decades. The first papers in this field were mainly theoretical, being more recent the laboratory experiments which represented that behaviour in ideal conditions. The numerical simulations have been addressed lately thanks to the development of computers. But the study of meteorology in complex terrain has lacked experiments in the atmosphere to understand the real influence the relief has on it. In this paper the problem has been considered from the last perspective, and so, seasons of measure of the atmospheric variables within the boundary layer have been organized with the goal of checking existing theories and bringing right conclusions from real experiment in the atmosphere. Controverted aspects of linear and nonlinear theories, as the location of critical points upwind and downwind of an orographic obstacle, will be analyzed. The results obtained show a large adequacy between the forecasted behaviour and the experimentally detected.
Nonlinear features of equatorial baroclinic Rossby waves detected in Topex altimeter observations
Authors: Glazman R. E. , Fabrikant A. , Greysukh A. M.
Published: April 2010

Abstract. Using a recently proposed technique for statistical analysis of non-gridded satellite altimeter data, regime of long equatorially-trapped baroclinic Rossby waves is studied. One-dimensional spatial and spatiotemporal autocorrelation functions of sea surface height (SSH) variations yield a broad spectrum of baroclinic Rossby waves and permit determination of their propagation speed. The 1-d wavenumber spectrum of zonal variations is given by a power-law k-2 on scales from about 103 km to 104 km. We demonstrate that the observed wave regime exhibits features of soliton turbulence developing in the long baroclinic Rossby waves. However, being limited to second statistical moments, the present analysis does not allow us to rule out a possibility of weak wave turbulence.
Scaling properties of paleomagnetic reversal sequence
Authors: Ivanov S. S.
Published: April 2010

Abstract. The history of reversals of main geomagnetic field during last 160 My is analyzed as a sequence of events, presented as a point set on the time axis. Different techniques were applied including the method of boxcounting, dispersion counter-scaling, multifractal analysis and examination of attractor behaviour in multidimensional phase space. The existence of a crossover point at time interval 0.5-1.0 My was clearly identified, dividing the whole time range into two subranges with different scaling properties. The long-term subrange is characterized by monofractal dimension 0.88 and by an attractor, whose correlation dimension converges to 1.0, that provides evidence of a deterministic dynamical system in this subrange, similar to most existing dynamo models. In the short-term subrange the fractal dimension estimated by different methods varies from 0.47 to 0.88 and the dimensionality of the attractor is obtained to be about 3.7. These results are discussed in terms of non-linear superposition of processes in the Earth's geospheres.
On the character of cosmic ray variations at f>2x10-5 Hz
Authors: Kudela K. , Flückiger E. O. , Torsti J. , Debrunner H.
Published: April 2010

Abstract. We examine the time series of cosmic ray (CR) intensity recorded by two neutron monitors (NMs) at medium latitudes for scaling properties on time scales shorter than the diurnal variation. Scaling of the data with 10 sec as well as I min resolution is shown to be complicated, indicating that there is probably not a unique process governing the CR fluctuations in the whole interval studied. For T < 20 min the general characteristics are similar to those of white noise. Above 40-60 min the scaling characteristics are dependent on the level of interplanetary disturbance. This is consistent with the concept of scattering CRs by inhomogeneities of the interplanetary magnetic field (IMF). With increasing interplanetary turbulence the dimensionality of the CR time series decreases. The region of stable scaling is, however, narrow, only up to 6 hours. Multifractality signatures in the region 1-6 hours are similar to those in the IMF, however the deviations from monofractality are relatively small.
A simple nonlinear model of low frequency (interseasonal) oscillations in the tropical atmosphere
Authors: Luo D.
Published: April 2010

Abstract. In this paper, for a prescribed normalized vertical convective heating profile, nonlinear Kelvin wave equations with wave-CISK heating over equatorial region is reduced to a sixth-order nonlinear ordinary differential equation by using the Galerkin spectral method in the case of considering nonlinear interaction between first and second baroclinic modes. Some numerical calculations are made with the fourth- order Rung-Kutta scheme. It is found that in a narrow range of the heating intensity parameter b, 30-60-day oscillation can occur through linear coupling between first and second baroclinic Kelvin wave-CISK modes for zonal wave-number one when the convective heating is confined to the lower and middle tropospheres. While for zonal wavenumber two, 30-60-day oscillation can be observed in a narrow range of b only when the convective heating is confined to the lower troposphere. However, in a wider range of this heating intensity parameter, 30-60-day oscillation can occur through nonlinear interaction between the first and second baroclinic Kelvin wave-CISK modes with zonal wavenumber one for three vertical convective heating profiles having a maximum in the upper, middle and lower tropospheres, and the total streamfield of the nonlinear first and second baroclinic Kelvin wave-CISK modes possesses a phase reversal between the upper- and lower-tropospheric wind fields. While for zonal wavenumber two, no 30-60-day oscillations can be found. Therefore, it appears that nonlinear interaction between vertical Kelvin wave-CISK modes favours the occurrence of 30-60-day oscillations, particularly, the importance of the vertical distribution of convective heating is re-emphasised.
On aspects of the measurement of non-linear turbulence processes using the cluster wave experiments
Authors: Wooliscroft L. J. C. , Dudok de Wit T. , Krasnosel'skikh V. V. , Balikhin M. A.
Published: April 2010

Abstract. The ESA/NASA Cluster mission has four identical satellites and is due for launch at the end of 1995. It will provide a unique opportunity to study medium scale processes in the region from inside the magnetopause to the solar wind. The polar orbit will allow measurements in the cusp and along auroral field lines, both regions where turbulence is to be expected. Five of the eleven instruments on each payload form the Wave Experiment Consortium (WEC); EFW, STAFF, VMISPER, WBD and DWP. The WEC is capable of a wide variety of wave and turbulence measurements. This paper outlines these capabilities and describes the form of the data which will be collected. The paper gives a discussion of how the WEC data may be analysed so as to give an insight into the non-linear processes which occur in these regions of the space plasmas. There are many ways in which a plasma may be considered to behave in a non-linear manner. We concentrate on how the spatio-temporal turbulence in the plasma may be investigated so as to yield the energy spectrum with respect to both the frequency and wave number.
Percolation on anisotropic media, the Bethe lattice revisited. Application to fracture networks
Authors: Canals M. , Ayt Ougoudal M.
Published: April 2010

Abstract. A bond-percolation model based on the Bethe Lattice is presented. This model handles anisotropic and multiscale situations where, typically, the bond probability is non unique and depends on the sites it connects. The model is governed by a set of non-linear equations which are solved numerically. As a result, the structure of the network is obtained: strengths of the backbone, dead-end roads and finite clusters. Percolation thresholds and cluster sizes are also obtained. Application to fissured media is presented and random simulations of 3D distributions of fractures show the good accuracy of the model.
Structure function measurements of the intermittent MHD turbulent cascade
Authors: Horbury T. S. , Balogh A.
Published: April 2010

Abstract. The intertmittent nature of turbulence within solar wind plasma has been demonstrated by several studies of spacecraft data. Using magnetic field data taken in high speed flows at high heliographic latitudes by the Ulysses probe, the character of fluctuations within the inertia] range is discussed. Structure functions are used extensively. A simple consideration of errors associated with calculations of high moment structure functions is shown to be useful as a practical estimate of the reliability of such calculations. For data sets of around 300 000 points, structure functions of moments above 5 are rarely reliable on the basis of this test, highlighting the importance of considering uncertainties in such calculations. When unreliable results are excluded, it is shown that inertial range polar fluctuations are well described by a multifractal model of turbulent energy transfer. Detailed consideration of the scaling of high order structure functions suggests energy transfer consistent with a "Kolmogorov" cascade.
The modified Korteweg - de Vries equation in the theory of large - amplitude internal waves
Authors: Grimshaw R. , Pelinovsky E. , Talipova T.
Published: April 2010

Abstract. The propagation of large- amplitude internal waves in the ocean is studied here for the case when the nonlinear effects are of cubic order, leading to the modified Korteweg - de Vries equation. The coefficients of this equation are calculated analytically for several models of the density stratification. It is shown that the coefficient of the cubic nonlinear term may have either sign (previously only cases of a negative cubic nonlinearity were known). Cubic nonlinear effects are more important for the high modes of the internal waves. The nonlinear evolution of long periodic (sine) waves is simulated for a three-layer model of the density stratification. The sign of the cubic nonlinear term influences the character of the solitary wave generation. It is shown that the solitary waves of both polarities can appear for either sign of the cubic nonlinear term; if it is positive the solitary waves have a zero pedestal, and if it is negative the solitary waves are generated on the crest and the trough of the long wave. The case of a localised impulsive initial disturbance is also simulated. Here, if the cubic nonlinear term is negative, there is no solitary wave generation at large times, but if it is positive solitary waves appear as the asymptotic solution of the nonlinear wave evolution.
Dynamics of large-amplitude geostrophic flows over bottom topography
Authors: Benilov E. S. , Sakov P. V.
Published: April 2010

Abstract. We examine the interaction of near-surface and near- bottom flows over bottom topography. A set of asymptotic equations for geostrophic currents in a three-layer fluid is derived. The depths of the active (top/bottom) layers are assumed small, the slope of the bottom is weak, the interfacial displacement is comparable to the depths of the thinner layers. Using the equations derived, we examine the stability of parallel flows and circular eddies. It is demonstrated that eddies with non-zero near-surface component are always unstable; eddies localized in the near-bottom layer may be stable subject to additional restrictions imposed on their horizontal profiles and bottom topography.
Reduction of Dietrich-Ruina attractors to unimodal maps
Authors: Shkoller S. , Minster J.-B.
Published: April 2010

Abstract. We present a geometric analysis of a quasi-static single degree of freedom elastic slider with a state and rate dependent friction law. In particular, we examine and characterize the regime of chaotic motions displayed by the Dieterich-Ruina model. We do so by numerically reducing the chaotic attractors to a family of unimodal maps and discuss why this suggests complex behaviour in the dynamical system.
Deterministic chaos at the ocean surface: applications and interpretations
Authors: Palmer A. J. , Fairall C. W. , Kropfli R. A.
Published: April 2010

Abstract. Ocean surface, grazing-angle radar backscatter data from two separate experiments, one of which provided coincident time series of measured surface winds, were found to exhibit signatures of deterministic chaos. Evidence is presented that the lowest dimensional underlying dynamical system responsible for the radar backscatter chaos is that which governs the surface wind turbulence. Block-averaging time was found to be an important parameter for determining the degree of determinism in the data as measured by the correlation dimension, and by the performance of an artificial neural network in retrieving wind and stress from the radar returns, and in radar detection of an ocean internal wave. The correlation dimensions are lowered and the performance of the deterministic retrieval and detection algorithms are improved by averaging out the higher dimensional surface wave variability in the radar returns.
Dynamical implications of prescribing part of a coupled system: Results from a low-order model
Authors: Wittenberg A. T. , Anderson J. L.
Published: April 2010

Abstract. It is a common procedure in climate modelling to specify dynamical system components from an external source; a prominent example is the forcing of an atmospheric model with observed sea surface temperatures. In this paper, we examine the dynamics of such forced models using a simple prototype climate system. A particular fully coupled run of the model is designated the "true" solution, and an ensemble of perturbed initial states is generated by adding small errors to the "true" initial state. The perturbed ensemble is then integrated for the same period as the true solution, using both the fully-coupled model and a model in which the ocean is prescribed exactly from the true solution at every time step. Although the prescribed forcing is error-free, the forced-atmosphere ensemble is shown to converge to spurious solutions. Statistical tests show that neither the time-mean state nor the variability of the forced ensemble is consistent with the fully-coupled system. A stability analysis reveals the source of the inconsistency, and suggests that such behaviour may be a more general feature of models with prescribed subsystems. Possible implications for model validation and predictability are discussed.
Non-linear quenching of current fluctuations in a self-exciting homopolar dynamo, proved by feedback system theory
Authors: de Paor A. M.
Published: April 2010

Abstract. Hide (Nonlinear Processes in Geophysics, 1998) has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ε has the value 1 is proved via the Popov theorem from feedback system stability theory.
Analysis and simulation of BGK electron holes
Authors: Muschietti L. , Roth I. , Ergun R. E. , Carlson C. W.
Published: April 2010

Abstract. Recent observations from satellites crossing regions of magnetic-field-aligned electron streams reveal solitary potential structures that move at speeds much greater than the ion acoustic/thermal velocity. The structures appear as positive potential pulses rapidly drifting along the magnetic field, and are electrostatic in their rest frame. We interpret them as BGK electron holes supported by a drifting population of trapped electrons. Using Laplace transforms, we analyse the behavior of one phase-space electron hole. The resulting potential shapes and electron distribution functions are self-consistent and compatible with the field and particle data associated with the observed pulses. In particular, the spatial width increases with increasing amplitude. The stability of the analytic solution is tested by means of a two-dimensional particle-in-cell simulation code with open boundaries. We consider a strongly magnetized parameter regime in which the bounce frequency of the trapped electrons is much less than their gyrofrequency. Our investigation includes the influence of the ions, which in the frame of the hole appear as an incident beam, and impinge on the BGK potential with considerable energy. The nonlinear structure is remarkably resilient
Theory of localized bipolar wave-structures and nonthermal particle distributions in the auroral ionosphere
Authors: Goldman M. V. , Oppenheim M. M. , Newman D. L.
Published: April 2010

Abstract. Bipolar wave structures and nonthermal particle distributions measured by the FAST satellite in regions of downward current are interpreted in terms of the nonlinear evolution of a two-stream instability. The instability results in holes, both in the electron distribution in phase space and in the electron density in real space. The wave potential energy, which traps the electrons, has a single minimum, and the associated electric field is bipolar. The early bipolar structures are coherent over hundreds of Debye lengths in the direction perpendicular to the magnetic field. After thousands of plasma periods the perpendicular coherence is lost, the structures break up, and electrostatic whistlers begin to dominate. Simulations and preliminary analysis of this breakup and emission process are presented.
Comments and new results about the magnetospheric chaos hypothesis
Authors: Pavlos G. P. , Athanasiu M. A. , Diamantidis D. , Rigas A. G. , Sarris E. T.
Published: April 2010

Abstract. In this study we present theoretical concepts and results concerning the hypothesis test of the magnetospheric chaos. For this reason we compare the observational behavior of the magnetospheric system with results obtained by analysing different types of stochastic and deterministic input-output systems. The results of this comparison indicate that the hypothesis of lowdimensional chaos for the magnetospheric dynamics remains a possible and fruitful concept which must be developed further.
Intergyre transport in a wind-driven, quasigeostrophic double gyre: An application of lobe dynamics
Authors: Coulliette C. , Wiggins S.
Published: April 2010

Abstract. We study the flow obtained from a three-layer, eddy-resolving quasigeostrophic ocean circulation model subject to an applied wind stress curl. For this model we will consider transport between the northern and southern gyres separated by an eastward jet. We will focus on the use of techniques from dynamical systems theory, particularly lobe dynamics, in the forming of geometric structures that govern transport. By "govern", we mean they can be used to compute Lagrangian transport quantities, such as the flux across the jet. We will consider periodic, quasiperiodic, and chaotic velocity fields, and thus assess the effectiveness of dynamical systems techniques in flows with progressively more spatio-temporal complexity. The numerical methods necessary to implement the dynamical systems techniques and the significance of lobe dynamics as a signature of specific "events", such as rings pinching off from a meandering jet, are also discussed.