ALBERT

Description: The concept of exchangeability in ensemble forecasting Nonlinear Processes in Geophysics, 18, 1-5, 2011 Author(s): J. Bröcker and H. Kantz A set of random variables is exchangeable if its joint distribution function is invariant under permutation of the arguments. The concept of exchangeability is discussed, with a view towards potential application in evaluating ensemble forecasts. It is argued that the paradigm of ensembles being an independent draw from an underlying distribution function is probably too narrow; allowing ensemble members to be merely exchangeable might be a more versatile model. The question is discussed whether established methods of ensemble evaluation need alteration under this model, with reliability being given particular attention. It turns out that the standard methodology of rank histograms can still be applied. As a first application of the exchangeability concept, it is shown that the method of minimum spanning trees to evaluate the reliability of high dimensional ensembles is mathematically sound.

Description: A statistical mechanical approach for the computation of the climatic response to general forcings Nonlinear Processes in Geophysics, 18, 7-28, 2011 Author(s): V. Lucarini and S. Sarno The climate belongs to the class of non-equilibrium forced and dissipative systems, for which most results of quasi-equilibrium statistical mechanics, including the fluctuation-dissipation theorem, do not apply. In this paper we show for the first time how the Ruelle linear response theory, developed for studying rigorously the impact of perturbations on general observables of non-equilibrium statistical mechanical systems, can be applied with great success to analyze the climatic response to general forcings. The crucial value of the Ruelle theory lies in the fact that it allows to compute the response of the system in terms of expectation values of explicit and computable functions of the phase space averaged over the invariant measure of the unperturbed state. We choose as test bed a classical version of the Lorenz 96 model, which, in spite of its simplicity, has a well-recognized prototypical value as it is a spatially extended one-dimensional model and presents the basic ingredients, such as dissipation, advection and the presence of an external forcing, of the actual atmosphere. We recapitulate the main aspects of the general response theory and propose some new general results. We then analyze the frequency dependence of the response of both local and global observables to perturbations having localized as well as global spatial patterns. We derive analytically several properties of the corresponding susceptibilities, such as asymptotic behavior, validity of Kramers-Kronig relations, and sum rules, whose main ingredient is the causality principle. We show that all the coefficients of the leading asymptotic expansions as well as the integral constraints can be written as linear function of parameters that describe the unperturbed properties of the system, such as its average energy. Some newly obtained empirical closure equations for such parameters allow to define such properties as an explicit function of the unperturbed forcing parameter alone for a general class of chaotic Lorenz 96 models. We then verify the theoretical predictions from the outputs of the simulations up to a high degree of precision. The theory is used to explain differences in the response of local and global observables, to define the intensive properties of the system, which do not depend on the spatial resolution of the Lorenz 96 model, and to generalize the concept of climate sensitivity to all time scales. We also show how to reconstruct the linear Green function, which maps perturbations of general time patterns into changes in the expectation value of the considered observable for finite as well as infinite time. Finally, we propose a simple yet general methodology to study general Climate Change problems on virtually any time scale by resorting to only well selected simulations, and by taking full advantage of ensemble methods. The specific case of globally averaged surface temperature response to a general pattern of change of the CO 2 concentration is discussed. We believe that the proposed approach may constitute a mathematically rigorous and practically very effective way to approach the problem of climate sensitivity, climate prediction, and climate change from a radically new perspective.

Description: Rank-Ordered Multifractal Analysis (ROMA) of probability distributions in fluid turbulence Nonlinear Processes in Geophysics, 18, 261-268, 2011 Author(s): C. C. Wu and T. Chang Rank-Ordered Multifractal Analysis (ROMA) was introduced by Chang and Wu (2008) to describe the multifractal characteristic of intermittent events. The procedure provides a natural connection between the rank-ordered spectrum and the idea of one-parameter scaling for monofractals. This technique has successfully been applied to MHD turbulence simulations and turbulence data observed in various space plasmas. In this paper, the technique is applied to the probability distributions in the inertial range of the turbulent fluid flow, as given in the vast Johns Hopkins University (JHU) turbulence database. In addition, a new way of finding the continuous ROMA spectrum and the scaled probability distribution function (PDF) simultaneously is introduced.

Description: Using a variance-based sensitivity analysis for analyzing the relation between measurements and unknown parameters of a physical model Nonlinear Processes in Geophysics, 18, 269-276, 2011 Author(s): J. Zhao and C. Tiede An implementation of uncertainty analysis (UA) and quantitative global sensitivity analysis (SA) is applied to the non-linear inversion of gravity changes and three-dimensional displacement data which were measured in and active volcanic area. A didactic example is included to illustrate the computational procedure. The main emphasis is placed on the problem of extended Fourier amplitude sensitivity test (E-FAST). This method produces the total sensitivity indices (TSIs), so that all interactions between the unknown input parameters are taken into account. The possible correlations between the output an the input parameters can be evaluated by uncertainty analysis. Uncertainty analysis results indicate the general fit between the physical model and the measurements. Results of the sensitivity analysis show quite different sensitivities for the measured changes as they relate to the unknown parameters of a physical model for an elastic-gravitational source. Assuming a fixed number of executions, thirty different seeds are observed to determine the stability of this method.

Description: Inversion of Schlumberger resistivity sounding data from the critically dynamic Koyna region using the Hybrid Monte Carlo-based neural network approach Nonlinear Processes in Geophysics, 18, 179-192, 2011 Author(s): S. Maiti, G. Gupta, V. C. Erram, and R. K. Tiwari Koyna region is well-known for its triggered seismic activities since the hazardous earthquake of M =6.3 occurred around the Koyna reservoir on 10 December 1967. Understanding the shallow distribution of resistivity pattern in such a seismically critical area is vital for mapping faults, fractures and lineaments. However, deducing true resistivity distribution from the apparent resistivity data lacks precise information due to intrinsic non-linearity in the data structures. Here we present a new technique based on the Bayesian neural network (BNN) theory using the concept of Hybrid Monte Carlo (HMC)/Markov Chain Monte Carlo (MCMC) simulation scheme. The new method is applied to invert one and two-dimensional Direct Current (DC) vertical electrical sounding (VES) data acquired around the Koyna region in India. Prior to apply the method on actual resistivity data, the new method was tested for simulating synthetic signal. In this approach the objective/cost function is optimized following the Hybrid Monte Carlo (HMC)/Markov Chain Monte Carlo (MCMC) sampling based algorithm and each trajectory was updated by approximating the Hamiltonian differential equations through a leapfrog discretization scheme. The stability of the new inversion technique was tested in presence of correlated red noise and uncertainty of the result was estimated using the BNN code. The estimated true resistivity distribution was compared with the results of singular value decomposition (SVD)-based conventional resistivity inversion results. Comparative results based on the HMC-based Bayesian Neural Network are in good agreement with the existing model results, however in some cases, it also provides more detail and precise results, which appears to be justified with local geological and structural details. The new BNN approach based on HMC is faster and proved to be a promising inversion scheme to interpret complex and non-linear resistivity problems. The HMC-based BNN results are quite useful for the interpretation of fractures and lineaments in seismically active region.

Description: Resurrecting dead-water phenomenon Nonlinear Processes in Geophysics, 18, 193-208, 2011 Author(s): M. J. Mercier, R. Vasseur, and T. Dauxois We revisit experimental studies performed by Ekman on dead-water (Ekman, 1904) using modern techniques in order to present new insights on this peculiar phenomenon. We extend its description to more general situations such as a three-layer fluid or a linearly stratified fluid in presence of a pycnocline, showing the robustness of dead-water phenomenon. We observe large amplitude nonlinear internal waves which are coupled to the boat dynamics, and we emphasize that the modeling of the wave-induced drag requires more analysis, taking into account nonlinear effects. Dedicated to Fridtjöf Nansen born 150 yr ago (10 October 1861).

Description: Excitation of low frequency oscillations in a planetary magnetosheath by supersonic shear flow Nonlinear Processes in Geophysics, 18, 209-221, 2011 Author(s): N. Borisov and M. Fränz We show that the slow magnetosonic (SM) perturbations generated in the vicinity of the magnetopause, due to the excitation of the Kelvin-Helmholtz (K.-H.) instability in the case of a supersonic flow velocity, are transformed into fast magnetosonic (FM) waves which can propagate into the magnetosheath. Under the conditions discussed in this paper, the FM wave has negative energy in the stationary (magnetospheric) coordinate frame. Due to this the outgoing FM wave increases the growth rate of the K.-H. instability excited at the magnetopause. Within the linear theory, we investigate the influence of the excited FM wave on the growth rate of the K.-H. instability. Simultaneously we predict the transformation of the SM mode into kinetic Alfvén (KA) mode. Thus, in general, two types of waves with different polarizations (the KA wave and the FM wave) should appear in the magnetosheath due to the excitation of the K.-H. instability. At the same time, the SM perturbations are only present in the localized region where the K.-H. instability is excited. To correctly describe the excitation of waves, we use two-fluid (for electrons and ions) magnetohydrodynamics. This approach is more general than the ideal magnetohydrodynamics and allows us to take into account the effects associated with the finite Larmor radius of ions. Also it can be used to investigate the K.-H. instability in a multi-component plasma, or in the case where the frequency of perturbations is of the order of the gyrofrequency of oxygen ions which may occur, for example, at the magnetosheath of Mars.

Description: Probabilistic downscaling of precipitation data in a subtropical mountain area: a two-step approach Nonlinear Processes in Geophysics, 18, 223-234, 2011 Author(s): R. Haas and K. Born In this study, a two-step probabilistic downscaling approach is introduced and evaluated. The method is exemplarily applied on precipitation observations in the subtropical mountain environment of the High Atlas in Morocco. The challenge is to deal with a complex terrain, heavily skewed precipitation distributions and a sparse amount of data, both spatial and temporal. In the first step of the approach, a transfer function between distributions of large-scale predictors and of local observations is derived. The aim is to forecast cumulative distribution functions with parameters from known data. In order to interpolate between sites, the second step applies multiple linear regression on distribution parameters of observed data using local topographic information. By combining both steps, a prediction at every point of the investigation area is achieved. Both steps and their combination are assessed by cross-validation and by splitting the available dataset into a trainings- and a validation-subset. Due to the estimated quantiles and probabilities of zero daily precipitation, this approach is found to be adequate for application even in areas with difficult topographic circumstances and low data availability.

Description: Tidally induced internal motion in an Arctic fjord Nonlinear Processes in Geophysics, 21, 87-100, 2014 Author(s): E. Støylen and I. Fer The internal response in a stratified, partially enclosed basin subject to semi-diurnal tidal forcing through a narrow entrance is investigated. The site is located above the critical latitude where linear internal waves of lunar semi-diurnal frequency are not permitted to propagate freely. Generation and propagation of tidally induced internal Kelvin waves are studied, for baroclinically sub- and supercritical conditions at the mouth of the fjord, using a non-linear 3-D numerical model in an idealized basin and in Van Mijenfjorden, Svalbard, using a realistic topography. The model results are compared to observations of hydrography and currents made in August 2010. Results from both the model and measurements indicate the presence of internal Kelvin waves, even when conditions at the fjord entrance are supercritical. The entrance of Van Mijenfjorden is split into two sounds. Sensitivity experiments by closing each sound separately reveal that internal Kelvin waves are generated at both sounds. When the conditions are near supercritical, a wave pulse propagates inward from the fjord entrance at the beginning of each inflow phase of the tidal cycle. The leading crest is followed by a series of smaller amplitude waves characterized as non-linear internal solitons. However, higher model resolution is needed to accurately describe the influence of small-scale mixing and processes near the sill crest in establishing the evolution of the flow and internal response in the fjord.

Description: Stochastic formalism-based seafloor feature discrimination using multifractality of time-dependent acoustic backscatter Nonlinear Processes in Geophysics, 21, 101-113, 2014 Author(s): K. Haris and B. Chakraborty Dual-frequency echo-envelope data acquired using the normal-incidence single-beam echosounder system (SBES) have been examined to study its scale invariant properties. The scaling and multifractality of the SBES echo envelopes (at 33 and 210 kHz) were validated by applying a stochastic-based multifractal analysis technique. The analyses carried out substantiate the hierarchy of multiplicative cascade dynamics in the echo envelopes, demonstrating a first-order multifractal phase transition. The resulting scale invariant parameters (α, C 1 , and H ) establish gainful information that can facilitate distinctive delineation of the sediment provinces in the central part of the western continental shelf of India. The universal multifractal parameters among the coarse and fine sediments exhibit subtle difference in α and H , whereas the codimension parameter C 1 representing the sparseness of the data varies. The C 1 values are well clustered at both the acoustic frequencies, demarcating the coarse and fine sediment provinces. Statistically significant correlations are noticeable between the computed C 1 values and the ground truth sediment information. The variations in the multifractal parameters and their behavior with respect to the ground truth sediment information are in good corroboration with the previously estimated sediment geoacoustic inversion results obtained at the same locations.

Description: The Rossby wave extra invariant in the dynamics of 3-D fluid layers and the generation of zonal jets Nonlinear Processes in Geophysics, 21, 49-59, 2014 Author(s): A. M. Balk We consider an adiabatic-type (approximate) invariant that was earlier obtained for the quasi-geostrophic equation and the shallow water system; it is an extra invariant, in addition to the standard ones (energy, enstrophy, momentum), and it is based on the Rossby waves. The presence of this invariant implies the energy transfer from small-scale eddies to large-scale zonal jets. We show that this extra invariant can be extended to the dynamics of a three-dimensional (3-D) fluid layer on the beta plane. Combined with the investigation of other researchers, this 3-D extension implies enhanced generation of zonal jets. For a general physical system, the presence of an extra invariant (in addition to the energy–momentum and wave action) is extremely rare. We summarize the unique conservation properties of geophysical fluid dynamics (with the beta effect) that allow for the existence of the extra invariant, and argue that its presence in various geophysical systems is a strong indication that the formation of zonal jets is indeed related to the extra invariant. Also, we develop a new, more direct, way to establish extra invariants (without using cubic corrections). For this, we introduce the small denominator lemma.

Description: Stochastic electron motion driven by space plasma waves Nonlinear Processes in Geophysics, 21, 61-85, 2014 Author(s): G. V. Khazanov, A. A. Tel’nikhin, and T. K. Kronberg Stochastic motion of relativistic electrons under conditions of the nonlinear resonance interaction of particles with space plasma waves is studied. Particular attention is given to the problem of the stability and variability of the Earth's radiation belts. It is found that the interaction between whistler-mode waves and radiation-belt electrons is likely to involve the same mechanism that is responsible for the dynamical balance between the accelerating process and relativistic electron precipitation events. We have also considered the efficiency of the mechanism of stochastic surfing acceleration of cosmic electrons at the supernova remnant shock front, and the accelerating process driven by a Langmuir wave packet in producing cosmic ray electrons. The dynamics of cosmic electrons is formulated in terms of a dissipative map involving the effect of synchrotron emission. We present analytical and numerical methods for studying Hamiltonian chaos and dissipative strange attractors, and for determining the heating extent and energy spectra.

Description: The comparative study of chaoticity and dynamical complexity of the low-latitude ionosphere, over Nigeria, during quiet and disturbed days Nonlinear Processes in Geophysics, 21, 127-142, 2014 Author(s): B. O. Ogunsua, J. A. Laoye, I. A. Fuwape, and A. B. Rabiu The deterministic chaotic behavior and dynamical complexity of the space plasma dynamical system over Nigeria are analyzed in this study and characterized. The study was carried out using GPS (Global Positioning System) TEC (Total Electron Content) time series, measured in the year 2011 at three GPS receiver stations within Nigeria, which lies within the equatorial ionization anomaly region. The TEC time series for the five quietest and five most disturbed days of each month of the year were selected for the study. The nonlinear aspect of the TEC time series was obtained by detrending the data. The detrended TEC time series were subjected to various analyses for phase space reconstruction and to obtain the values of chaotic quantifiers like Lyapunov exponents, correlation dimension and also Tsallis entropy for the measurement of dynamical complexity. The observations made show positive Lyapunov exponents (LE) for both quiet and disturbed days, which indicates chaoticity, and for different days the chaoticity of the ionosphere exhibits no definite pattern for either quiet or disturbed days. However, values of LE were lower for the storm period compared with its nearest relative quiet periods for all the stations. The monthly averages of LE and entropy also show no definite pattern for the month of the year. The values of the correlation dimension computed range from 2.8 to 3.5, with the lowest values recorded at the storm period of October 2011. The surrogate data test shows a significance of difference greater than 2 for all the quantifiers. The entropy values remain relatively close, with slight changes in these values during storm periods. The values of Tsallis entropy show similar variation patterns to those of Lyapunov exponents, with a lot of agreement in their comparison, with all computed values of Lyapunov exponents correlating with values of Tsallis entropy within the range of 0.79 to 0.81. These results show that both quantifiers can be used together as indices in the study of the variation of the dynamical complexity of the ionosphere. The results also show a strong play between determinism and stochasticity. The behavior of the ionosphere during these storm and quiet periods for the seasons of the year are discussed based on the results obtained from the chaotic quantifiers.

Description: Scaling properties of rainfall and desert dust in the Canary Islands Nonlinear Processes in Geophysics, 20, 1079-1094, 2013 Author(s): I. Peñate, J. M. Martín-González, G. Rodríguez, and A. Cianca Precipitation and desert dust event occurrence time series measured in the Canary Islands region are examined with the primary intention of exploring their scaling characteristics as well as their spatial variability in terms of the island's topography and geographical orientation. In particular, the desert dust intrusion regime in the islands is studied in terms of its relationship with visibility. Analysis of dust and rainfall events over the archipelago exhibits distributions in time that obey power laws. Results show that the rain process presents a high clustering and irregular pattern on short timescales and a more scattered structure for long ones. In contrast, dustiness presents a more uniform and dense structure and, consequently, a more persistent behaviour on short timescales. It was observed that the fractal dimension of rainfall events shows an important spatial variability, which increases with altitude, as well as towards northern latitudes and western longitudes.

Description: Relativistic surfatron process for Landau resonant electrons in radiation belts Nonlinear Processes in Geophysics, 21, 115-125, 2014 Author(s): A. Osmane and A. M. Hamza Recent theoretical studies of the nonlinear wave-particle interactions for relativistic particles have shown that Landau resonant orbits could be efficiently accelerated along the mean background magnetic field for propagation angles θ in close proximity to a critical propagation θ c associated with a Hopf–Hopf bifurcation condition. In this report, we extend previous studies to reach greater modeling capacities for the study of electrons in radiation belts by including longitudinal wave effects and inhomogeneous magnetic fields. We find that even though both effects can limit the surfatron acceleration of electrons in radiation belts, gains in energy of the order of 100 keV, taking place on one tenth of a millisecond, are sufficiently strong for the mechanism to be relevant to radiation belt dynamics.

Description: Brief Communication: Weibel, Firehose and Mirror mode relations Nonlinear Processes in Geophysics, 21, 143-148, 2014 Author(s): R. A. Treumann and W. Baumjohann Excitation of Weibel magnetic fields in an initially non-magnetized though anisotropic plasma may trigger other low-frequency instabilities fed by pressure anisotropy. It is shown that under Weibel-like stable conditions the Weibel-like thermal fluctuation magnetic field allows for restricted Firehose-mode growth. In addition, low-frequency Whistlers can also propagate in the plasma under certain anisotropic conditions. When the Weibel-like mode becomes unstable, Firehose instability ceases but Mirror modes take over. This will cause bubble structures in the Weibel-like field in addition to filamentation.

Description: Recurrence time distribution and temporal clustering properties of a cellular automaton modelling landslide events Nonlinear Processes in Geophysics, 20, 1071-1078, 2013 Author(s): E. Piegari, R. Di Maio, and A. Avella Reasonable prediction of landslide occurrences in a given area requires the choice of an appropriate probability distribution of recurrence time intervals. Although landslides are widespread and frequent in many parts of the world, complete databases of landslide occurrences over large periods are missing and often such natural disasters are treated as processes uncorrelated in time and, therefore, Poisson distributed. In this paper, we examine the recurrence time statistics of landslide events simulated by a cellular automaton model that reproduces well the actual frequency-size statistics of landslide catalogues. The complex time series are analysed by varying both the threshold above which the time between events is recorded and the values of the key model parameters. The synthetic recurrence time probability distribution is shown to be strongly dependent on the rate at which instability is approached, providing a smooth crossover from a power-law regime to a Weibull regime. Moreover, a Fano factor analysis shows a clear indication of different degrees of correlation in landslide time series. Such a finding supports, at least in part, a recent analysis performed for the first time of an historical landslide time series over a time window of fifty years.

Description: Large eddy simulation model for wind-driven sea circulation in coastal areas Nonlinear Processes in Geophysics, 20, 1095-1112, 2013 Author(s): A. Petronio, F. Roman, C. Nasello, and V. Armenio In the present paper a state-of-the-art large eddy simulation model (LES-COAST), suited for the analysis of water circulation and mixing in closed or semi-closed areas, is presented and applied to the study of the hydrodynamic characteristics of the Muggia bay, the industrial harbor of the city of Trieste, Italy. The model solves the non-hydrostatic, unsteady Navier–Stokes equations, under the Boussinesq approximation for temperature and salinity buoyancy effects, using a novel, two-eddy viscosity Smagorinsky model for the closure of the subgrid-scale momentum fluxes. The model employs: a simple and effective technique to take into account wind-stress inhomogeneity related to the blocking effect of emerged structures, which, in turn, can drive local-scale, short-term pollutant dispersion; a new nesting procedure to reconstruct instantaneous, turbulent velocity components, temperature and salinity at the open boundaries of the domain using data coming from large-scale circulation models (LCM). Validation tests have shown that the model reproduces field measurement satisfactorily. The analysis of water circulation and mixing in the Muggia bay has been carried out under three typical breeze conditions. Water circulation has been shown to behave as in typical semi-closed basins, with an upper layer moving along the wind direction (apart from the anti-cyclonic veering associated with the Coriolis force) and a bottom layer, thicker and slower than the upper one, moving along the opposite direction. The study has shown that water vertical mixing in the bay is inhibited by a large level of stable stratification, mainly associated with vertical variation in salinity and, to a minor extent, with temperature variation along the water column. More intense mixing, quantified by sub-critical values of the gradient Richardson number, is present in near-coastal regions where upwelling/downwelling phenomena occur. The analysis of instantaneous fields has detected the presence of large cross-sectional eddies spanning the whole water column and contributing to vertical mixing, associated with the presence of sub-surface horizontal turbulent structures. Analysis of water renewal within the bay shows that, under the typical breeze regimes considered in the study, the residence time of water in the bay is of the order of a few days. Finally, vertical eddy viscosity has been calculated and shown to vary by a couple of orders of magnitude along the water column, with larger values near the bottom surface where density stratification is smaller.

Description: 20th century intraseasonal Asian monsoon dynamics viewed from Isomap Nonlinear Processes in Geophysics, 20, 725-741, 2013 Author(s): A. Hannachi and A. G. Turner The Asian summer monsoon is a high-dimensional and highly nonlinear phenomenon involving considerable moisture transport towards land from the ocean, and is critical for the whole region. We have used daily ECMWF reanalysis (ERA-40) sea-level pressure (SLP) anomalies on the seasonal cycle, over the region 50–145° E, 20° S–35° N, to study the nonlinearity of the Asian monsoon using Isomap. We have focused on the two-dimensional embedding of the SLP anomalies for ease of interpretation. Unlike the unimodality obtained from tests performed in empirical orthogonal function space, the probability density function, within the two-dimensional Isomap space, turns out to be bimodal. But a clustering procedure applied to the SLP data reveals support for three clusters, which are identified using a three-component bivariate Gaussian mixture model. The modes are found to appear similar to active and break phases of the monsoon over South Asia in addition to a third phase, which shows active conditions over the western North Pacific. Using the low-level wind field anomalies, the active phase over South Asia is found to be characterised by a strengthening and an eastward extension of the Somali jet. However during the break phase, the Somali jet is weakened near southern India, while the monsoon trough in northern India also weakens. Interpretation is aided using the APHRODITE gridded land precipitation product for monsoon Asia. The effect of large-scale seasonal mean monsoon and lower boundary forcing, in the form of ENSO, is also investigated and discussed. The outcome here is that ENSO is shown to perturb the intraseasonal regimes, in agreement with conceptual ideas.

Description: Transformation of internal solitary waves at the "deep" and "shallow" shelf: satellite observations and laboratory experiment Nonlinear Processes in Geophysics, 20, 743-757, 2013 Author(s): O. D. Shishkina, J. K. Sveen, and J. Grue An interaction of internal solitary waves with the shelf edge in the time periods related to the presence of a pronounced seasonal pycnocline in the Red Sea and in the Alboran Sea is analysed via satellite photos and SAR images. Laboratory data on transformation of a solitary wave of depression while passing along the transverse bottom step were obtained in a tank with a two-layer stratified fluid. The certain difference between two characteristic types of hydrophysical phenomena was revealed both in the field observations and in experiments. The hydrological conditions for these two processes were named the "deep" and the "shallow" shelf respectively. The first one provides the generation of the secondary periodic short internal waves – "runaway" edge waves – due to change in the polarity of a part of a soliton approaching the shelf normally. Another one causes a periodic shear flow in the upper quasi-homogeneous water layer with the period of incident solitary wave. The strength of the revealed mechanisms depends on the thickness of the water layer between the pycnocline and the shelf bottom as well as on the amplitude of the incident solitary wave.

Description: Dispersion of aerosol particles in the free atmosphere using ensemble forecasts Nonlinear Processes in Geophysics, 20, 759-770, 2013 Author(s): T. Haszpra, I. Lagzi, and T. Tél The dispersion of aerosol particle pollutants is studied using 50 members of an ensemble forecast in the example of a hypothetical free atmospheric emission above Fukushima over a period of 2.5 days. Considerable differences are found among the dispersion predictions of the different ensemble members, as well as between the ensemble mean and the deterministic result at the end of the observation period. The variance is found to decrease with the particle size. The geographical area where a threshold concentration is exceeded in at least one ensemble member expands to a 5–10 times larger region than the area from the deterministic forecast, both for air column "concentration" and in the "deposition" field. We demonstrate that the root-mean-square distance of any particle from its own clones in the ensemble members can reach values on the order of one thousand kilometers. Even the centers of mass of the particle cloud of the ensemble members deviate considerably from that obtained by the deterministic forecast. All these indicate that an investigation of the dispersion of aerosol particles in the spirit of ensemble forecast contains useful hints for the improvement of risk assessment.

Description: Joint state and parameter estimation with an iterative ensemble Kalman smoother Nonlinear Processes in Geophysics, 20, 803-818, 2013 Author(s): M. Bocquet and P. Sakov Both ensemble filtering and variational data assimilation methods have proven useful in the joint estimation of state variables and parameters of geophysical models. Yet, their respective benefits and drawbacks in this task are distinct. An ensemble variational method, known as the iterative ensemble Kalman smoother (IEnKS) has recently been introduced. It is based on an adjoint model-free variational, but flow-dependent, scheme. As such, the IEnKS is a candidate tool for joint state and parameter estimation that may inherit the benefits from both the ensemble filtering and variational approaches. In this study, an augmented state IEnKS is tested on its estimation of the forcing parameter of the Lorenz-95 model. Since joint state and parameter estimation is especially useful in applications where the forcings are uncertain but nevertheless determining, typically in atmospheric chemistry, the augmented state IEnKS is tested on a new low-order model that takes its meteorological part from the Lorenz-95 model, and its chemical part from the advection diffusion of a tracer. In these experiments, the IEnKS is compared to the ensemble Kalman filter, the ensemble Kalman smoother, and a 4D-Var, which are considered the methods of choice to solve these joint estimation problems. In this low-order model context, the IEnKS is shown to significantly outperform the other methods regardless of the length of the data assimilation window, and for present time analysis as well as retrospective analysis. Besides which, the performance of the IEnKS is even more striking on parameter estimation; getting close to the same performance with 4D-Var is likely to require both a long data assimilation window and a complex modeling of the background statistics.

Description: Current challenges for pre-earthquake electromagnetic emissions: shedding light from micro-scale plastic flow, granular packings, phase transitions and self-affinity notion of fracture process Nonlinear Processes in Geophysics, 20, 771-792, 2013 Author(s): K. Eftaxias and S. M. Potirakis Are there credible electromagnetic (EM) potential earthquake (EQ) precursors? This a question debated in the scientific community and there may be legitimate reasons for the critical views. The negative view concerning the existence of EM potential precursors is enhanced by features that accompany their observation which are considered as paradox ones, namely, these signals: (i) are not observed at the time of EQs occurrence and during the aftershock period, (ii) are not accompanied by large precursory strain changes, (iii) are not accompanied by simultaneous geodetic or seismological precursors and (iv) their traceability is considered problematic. In this work, the detected candidate EM potential precursors are studied through a shift in thinking towards the basic science findings relative to granular packings, micron-scale plastic flow, interface depinning, fracture size effects, concepts drawn from phase transitions, self-affine notion of fracture and faulting process, universal features of fracture surfaces, recent high quality laboratory studies, theoretical models and numerical simulations. We try to contribute to the establishment of strict criteria for the definition of an emerged EM anomaly as a possibly EQ-related one, and to the explanation of potential precursory EM features which have been considered as paradoxes. A three-stage model for EQ generation by means of pre-EQ fracture-induced EM emissions is proposed. The claim that the observed EM potential precursors may permit a real-time and step-by-step monitoring of the EQ generation is tested.

Description: A variational formulation for translation and assimilation of coherent structures Nonlinear Processes in Geophysics, 20, 793-801, 2013 Author(s): M. Plu The assimilation of observations from teledetected images in geophysical models requires one to develop algorithms that would account for the existence of coherent structures. In the context of variational data assimilation, a method is proposed to allow the background to be translated so as to fit structure positions deduced from images. Translation occurs as a first step before assimilating all the observations using a classical assimilation procedure with specific covariances for the translated background. A simple validation is proposed using a dynamical system based on the one-dimensional complex Ginzburg–Landau equation in a regime prone to phase and amplitude errors. Assimilation of observations after background translation leads to better scores and a better representation of extremas than the method without translation.

Description: Thermal energy generation in the earth Nonlinear Processes in Geophysics, 21, 367-378, 2014 Author(s): F. J. Mayer and J. R. Reitz We show that a recently introduced class of electromagnetic composite particles can explain some discrepancies in observations involving heat and helium released from the earth. Energy release during the formation of the composites and subsequent nuclear reactions involving the composites are described that can quantitatively account for the discrepancies and are expected to have implications in other areas of geophysics – for example, a new picture of heat production and volcanism in the earth is presented.

Description: Provision of boundary conditions for a convection-permitting ensemble: comparison of two different approaches Nonlinear Processes in Geophysics, 21, 393-403, 2014 Author(s): C. Marsigli, A. Montani, and T. Paccagnella The current resolution of the operational global models favours the possibility of driving convection-permitting limited-area model (LAM) simulations directly, sparing the necessity for an intermediate step with a coarser-resolution LAM. Though the resolution of global ensemble systems is generally lower than that of deterministic ones, it is also possible to consider this opportunity in the field of ensemble forecasting. The aim of this paper is to investigate the effect of this choice for driving a convection-permitting ensemble based on the COSMO model, for a specific application, namely the forecast of intense autumn precipitation events over Italy. The impact of the direct nesting in the ECMWF global ensemble is compared to a two-step nesting, which makes use of a LAM ensemble system with parametrised convection. Results show that the variability introduced in the geopotential field by the direct nesting is usually contained within the uncertainty described by the standard ensemble, and differences between pairs of members following different nesting approaches are generally smaller than the ensemble error, computed with respect to analysis. The relation between spread and error is even improved by the direct nesting approach. In terms of precipitation, it is found that the forecasts issued by members with different nesting approaches generally have differences at spatial scales between 16 and 180 km, depending on the case, hence not negligible. Nevertheless, the skill of the LAM ensemble precipitation forecasts, evaluated by means of an objective verification, is comparable. Therefore, the overall quality of the 2.8 km ensemble for the specific application is not deteriorated by the provision of lower resolution lateral boundary conditions directly from the global ensemble.

Description: Multiscaling and joint multiscaling description of the atmospheric wind speed and the aggregate power output from a wind farm Nonlinear Processes in Geophysics, 21, 379-392, 2014 Author(s): R. Calif and F. G. Schmitt We consider here wind speed time series and the aggregate output wind power from a wind farm. We study their scaling statistics in the framework of fully developed turbulence and Kolmogorov's theory. We estimate their Fourier power spectra and consider their scaling properties in the physical space. We show that the atmospheric wind speed and the aggregate power output from a wind farm are intermittent and multifractal over a wide range of scales. The coupling between simultaneous data of the wind speed and aggregate power output is investigated through a joint multifractal description using the generalized correlation functions (GCFs). This multiscaling test is compatible with a linear relation between the wind speed and the aggregate power output fluctuations for timescales T ⩾ 10 3 s ≃ 15 min.

Description: Alfvén waves in space and astrophysical dusty plasmas Nonlinear Processes in Geophysics, 21, 405-416, 2014 Author(s): V. Jatenco-Pereira, A. C.-L. Chian, and N. Rubab In this paper, we present some results of previous works on Alfvén waves in a dusty plasma in different astrophysical and space regions by taking into account the effect of superthermal particles on the dispersive characteristics. We show that the presence of dust and superthermal particles sensibly modify the dispersion of Alfvén waves. The competition between different damping processes of kinetic Alfvén waves and Alfvén cyclotron waves is analyzed. The nonlinear evolution of Alfvén waves to chaos is reviewed. Finally, we discuss some applications of Alfvén waves in the auroral region of space plasmas, as well as stellar winds and star-forming regions of astrophysical plasmas.

Description: Latitudinal variation of stochastic properties of the geomagnetic field Nonlinear Processes in Geophysics, 21, 347-356, 2014 Author(s): J. A. Wanliss, K. Shiokawa, and K. Yumoto We explore the stochastic fractal qualities of the geomagnetic field from 210 mm ground-based magnetometers during quiet and active magnetospheric conditions. We search through 10 yr of these data to find events that qualify as quiet intervals, defined by Kp ≤ 1 for 1440 consecutive minutes. Similarly, active intervals require Kp ≥ 4 for 1440 consecutive minutes. The total for quiet intervals is ~ 4.3 x 10 6 and 2 x 10 8 min for active data points. With this large number of data we characterize changes in the nonlinear statistics of the geomagnetic field via measurements of a fractal scaling. A clear difference in statistical behavior during quiet and active intervals is implied through analysis of the scaling exponents; active intervals generally have larger values of scaling exponents. This suggests that although 210 mm data appear monofractal on shorter timescales, the scaling changes, with overall variability are more likely described as a multifractional Brownian motion. We also find that low latitudes have scaling exponents that are consistently larger than for high latitudes.

Description: FLIP-MHD-based model sensitivity analysis Nonlinear Processes in Geophysics, 21, 539-553, 2014 Author(s): C. Skandrani, M. E. Innocenti, L. Bettarini, F. Crespon, J. Lamouroux, and G. Lapenta The state of the art in the forecast of the background solar wind speed and of the interplanetary magnetic field at Earth is based on the use as boundary conditions for heliospheric models of the input data provided by solar observations. Magnetogram synoptic maps are used to obtain information on the magnetic field configuration at the solar source surface. Magnetic field inputs at the solar source surface thus constitute one of the main external sources of errors in solar wind models. The assimilation of data into forecasting models used in the terrestrial domain showed the ability to control model state errors. A sensitivity study performed through the analysis of the ensemble variances and the representers technique is used here to assess how process and model state errors propagate in a nonlinear two-dimensional MagnetoHydro Dynamic (MHD) system. The aim is to understand the impact of the source surface input parameters on the evolution of MHD heliospheric models and the potentialities of data assimilation techniques in solar wind forecasting. The representer technique in fact allows one to understand how far from the observation point the improvement granted from the assimilation of a measure propagates.

Description: An ETKF approach for initial state and parameter estimation in ice sheet modelling Nonlinear Processes in Geophysics, 21, 569-582, 2014 Author(s): B. Bonan, M. Nodet, C. Ritz, and V. Peyaud Estimating the contribution of Antarctica and Greenland to sea-level rise is a hot topic in glaciology. Good estimates rely on our ability to run a precisely calibrated ice sheet evolution model starting from a reliable initial state. Data assimilation aims to provide an answer to this problem by combining the model equations with observations. In this paper we aim to study a state-of-the-art ensemble Kalman filter (ETKF) to address this problem. This method is implemented and validated in the twin experiments framework for a shallow ice flowline model of ice dynamics. The results are very encouraging, as they show a good convergence of the ETKF (with localisation and inflation), even for small-sized ensembles.

Description: Scale invariant events and dry spells for medium-resolution local rain data Nonlinear Processes in Geophysics, 21, 555-567, 2014 Author(s): A. Deluca and Á. Corral We analyze distributions of rain-event sizes, rain-event durations, and dry-spell durations for data obtained from a network of 20 rain gauges scattered in a region of the northwestern Mediterranean coast. While power-law distributions model the dry-spell durations with a common exponent 1.50 ± 0.05, density analysis is inconclusive for event sizes and event durations, due to finite size effects. However, we present alternative evidence of the existence of scale invariance in these distributions by means of different data collapses of the distributions. These results demonstrate that scaling properties of rain events and dry spells can also be observed for medium-resolution rain data.

Description: Nonlinear dynamics approach to the predictability of the Cane–Zebiak coupled ocean–atmosphere model Nonlinear Processes in Geophysics, 21, 155-163, 2014 Author(s): L. Siqueira and B. Kirtman The predictability of the Cane–Zebiak coupled ocean–atmosphere model is investigated using nonlinear dynamics analysis. Newer theoretical concepts are applied to the coupled model in order to help quantify maximal prediction horizons for finite amplitude perturbations on different scales. Predictability analysis based on the maximum Lyapunov exponent considers infinitesimal perturbations, which are associated with errors in the smallest fastest-evolving scales of motion. However, these errors become irrelevant for the predictability of larger scale motions. In this study we employed finite-size Lyapunov exponent analysis to assess the predictability of the Cane–Zebiak coupled ocean–atmosphere model as a function of scale. We demonstrate the existence of fast and slow timescales, as noted in earlier studies, and the expected enhanced predictability of the anomalies on large scales. The final results and conclusions clarify the applicability of these new methods to seasonal forecasting problems.

Description: An experimental study of regime transitions in a differentially heated baroclinic annulus with flat and sloping bottom topographies Nonlinear Processes in Geophysics, 21, 237-250, 2014 Author(s): M. Vincze, U. Harlander, Th. von Larcher, and C. Egbers A series of laboratory experiments has been carried out in a thermally driven rotating annulus to study the onset of baroclinic instability, using horizontal and uniformly sloping bottom topographies. Different wave flow regimes have been identified and their phase boundaries – expressed in terms of appropriate non-dimensional parameters – have been compared to the recent numerical linear stability analysis of von Larcher et al. (2013). In the flat bottom case, the numerically predicted alignment of the boundary between the axisymmetric and the regular wave flow regime was found to be consistent with the experimental results. However, once the sloping bottom end wall was introduced, the detected behaviour was qualitatively different from that of the simulations. This disagreement is thought to be the consequence of nonlinear wave–wave interactions that could not be resolved in the framework of the numerical study. This argument is supported by the observed development of interference vacillation in the runs with sloping bottom, a mixed flow state in which baroclinic wave modes exhibiting different drift rates and amplitudes can co-exist.

Description: A hybrid variational ensemble data assimilation for the HIgh Resolution Limited Area Model (HIRLAM) Nonlinear Processes in Geophysics, 21, 303-323, 2014 Author(s): N. Gustafsson, J. Bojarova, and O. Vignes A hybrid variational ensemble data assimilation has been developed on top of the HIRLAM variational data assimilation. It provides the possibility of applying a flow-dependent background error covariance model during the data assimilation at the same time as full rank characteristics of the variational data assimilation are preserved. The hybrid formulation is based on an augmentation of the assimilation control variable with localised weights to be assigned to a set of ensemble member perturbations (deviations from the ensemble mean). The flow-dependency of the hybrid assimilation is demonstrated in single simulated observation impact studies and the improved performance of the hybrid assimilation in comparison with pure 3-dimensional variational as well as pure ensemble assimilation is also proven in real observation assimilation experiments. The performance of the hybrid assimilation is comparable to the performance of the 4-dimensional variational data assimilation. The sensitivity to various parameters of the hybrid assimilation scheme and the sensitivity to the applied ensemble generation techniques are also examined. In particular, the inclusion of ensemble perturbations with a lagged validity time has been examined with encouraging results.

Description: One-dimensional modelling of upper ocean mixing by turbulence due to wave orbital motion Nonlinear Processes in Geophysics, 21, 325-338, 2014 Author(s): M. Ghantous and A. V. Babanin Mixing of the upper ocean affects the sea surface temperature by bringing deeper, colder water to the surface. Because even small changes in the surface temperature can have a large impact on weather and climate, accurately determining the rate of mixing is of central importance for forecasting. Although there are several mixing mechanisms, one that has until recently been overlooked is the effect of turbulence generated by non-breaking, wind-generated surface waves. Lately there has been a lot of interest in introducing this mechanism into ocean mixing models, and real gains have been made in terms of increased fidelity to observational data. However, our knowledge of the mechanism is still incomplete. We indicate areas where we believe the existing parameterisations need refinement and propose an alternative one. We use two of the parameterisations to demonstrate the effect on the mixed layer of wave-induced turbulence by applying them to a one-dimensional mixing model and a stable temperature profile. Our modelling experiment suggests a strong effect on sea surface temperature due to non-breaking wave-induced turbulent mixing.

Description: Sensibility to noise of new multifractal fusion methods for ocean variables Nonlinear Processes in Geophysics, 21, 291-301, 2014 Author(s): A. Turiel, J. Isern-Fontanet, and M. Umbert The repeated observation of the same signatures of mesoscale and submesoscale features in different ocean variables indicates that some common, non-linear processes affect them to a significant extent. A new method to exploit these common signatures to improve the quality of a noisy variable (i.e. increasing the signal-to-noise ratio) using another variable as template has recently been introduced. The method is based on superimposing the multifractal structure of singularity exponents from the template variable to the variable to be enhanced. In this paper, we will discuss the sensitivity of this method to the presence of noise of different types and amplitude. Our results indicate that multifractal methods can be a key to enhancing the existing databases of remote sensing images and give hints about non-linear dynamics of the ocean.

Description: Ion acceleration by parallel propagating nonlinear Alfvén wave packets in a radially expanding plasma Nonlinear Processes in Geophysics, 21, 339-346, 2014 Author(s): Y. Nariyuki, T. Umeda, T. K. Suzuki, and T. Hada The numerical simulation of the nonlinear evolution of the parallel propagating Alfvén waves in a radially expanding plasma is performed by using a kinetic-fluid model (the Vlasov–MHD model). In our study, both the nonlinear evolution of the Alfvén waves and the radial evolution of the velocity distribution function (VDF) are treated simultaneously. On the other hand, important ion kinetic effects such as ion cyclotron damping and instabilities driven by the non-equilibrium ion velocity distributions are not included in the present model. The results indicate that the steepened Alfvén wave packets outwardly accelerate ions, which can be observed as the beam components in the interplanetary space. The energy of imposed Alfvén waves is converted into the longitudinal fluctuations by the nonlinear steepening and the nonlinear Landau damping. The wave shoaling due to the inhomogeneity of the phase velocity is also observed.

Description: Application of multifractal analysis to the study of SAR features and oil spills on the ocean surface Nonlinear Processes in Geophysics, 21, 439-450, 2014 Author(s): A. M. Tarquis, A. Platonov, A. Matulka, J. Grau, E. Sekula, M. Diez, and J. M. Redondo The use of synthetic aperture radar (SAR) to investigate the ocean surface provides a wealth of useful information that is very seldom used to its full potential. Here we will discuss the application of multifractal techniques to detect oil spills and the dynamic state of the sea regarding turbulent diffusion. We present different techniques in order to relate the shape of the multifractal spectral functions and the maximum fractal dimension to the behaviour of the ocean surface. We compare eddy and sheared dominated flows with convective driven flows and discuss the different features and observation methods. We also compare the scaling of different oil spills detected by means of SAR images. Recent spills and weathered ones are selected and compared to investigate their behaviour in different spatial and temporal ranges. We calculate the partition function based on the grey intensity value of each SAR pixel deriving several types of multifractal spectra as a function of spill residence time estimated for each image. Image manipulations are seen to reduce the speckle noise and thus distinguish much better the texture of the oil spill images. The results are used to discuss how eddy diffusivity may be estimated and used in a description of the ocean surface using a simple turbulence kinematic simulation model to predict the shape of oil spills. Differences in the multifractal spectrum among SAR images may detect the slicks due to plankton and also provide information on the age of the oil spills, on the Lagrangian turbulent structure and on ocean surface diffusivity.

Description: Regional and inter-regional effects in evolving climate networks Nonlinear Processes in Geophysics, 21, 451-462, 2014 Author(s): J. Hlinka, D. Hartman, N. Jajcay, M. Vejmelka, R. Donner, N. Marwan, J. Kurths, and M. Paluš Complicated systems composed of many interacting subsystems are frequently studied as complex networks. In the simplest approach, a given real-world system is represented by an undirected graph composed of nodes standing for the subsystems and non-oriented unweighted edges for interactions present among the nodes; the characteristic properties of the graph are subsequently studied and related to the system's behaviour. More detailed graph models may include edge weights, orientations or multiple types of links; potential time-dependency of edges is conveniently captured in so-called evolving networks. Recently, it has been shown that an evolving climate network can be used to disentangle different types of El Niño episodes described in the literature. The time evolution of several graph characteristics has been compared with the intervals of El Niño and La Niña episodes. In this study we identify the sources of the evolving network characteristics by considering a reduced-dimensionality description of the climate system using network nodes given by rotated principal component analysis. The time evolution of structures in local intra-component networks is studied and compared to evolving inter-component connectivity.

Description: Particle trajectories beneath wave-current interaction in a two-dimensional field Nonlinear Processes in Geophysics, 19, 185-197, 2012 Author(s): Y.-Y. Chen, H.-C. Hsu, and H.-H. Hwung Within the Lagrangian reference framework we present a third-order trajectory solution for water particles in a two-dimensional wave-current interaction flow. The explicit parametric solution highlights the trajectory of a water particle and the wave kinematics above the mean water level and within a vertical water column, which were calculated previously by an approximation method using an Eulerian approach. Mass transport associated with a particle displacement can now be obtained directly in Lagrangian form without using the transformation from Eulerian to Lagrangian coordinates. In particular, the Lagrangian wave frequency and the Lagrangian mean level of particle motion can also be obtained, which are different from those in an Eulerian description. A series of laboratory experiments are performed to measure the trajectories of particles. By comparing the present asymptotic solution with laboratory experiments data, it is found that theoretical results show excellent agreement with experimental data. Moreover, the influence of a following current is found to increase the relative horizontal distance traveled by a water particle, while the converse is true in the case of an opposing current.

Description: Multifractal detrended fluctuation analysis in examining scaling properties of the spatial patterns of soil water storage Nonlinear Processes in Geophysics, 19, 227-238, 2012 Author(s): A. Biswas, T. B. Zeleke, and B. C. Si Knowledge about the scaling properties of soil water storage is crucial in transferring locally measured fluctuations to larger scales and vice-versa. Studies based on remotely sensed data have shown that the variability in surface soil water has clear scaling properties (i.e., statistically self similar) over a wider range of spatial scales. However, the scaling property of soil water storage to a certain depth at a field scale is not well understood. The major challenges in scaling analysis for soil water are the presence of localized trends and nonstationarities in the spatial series. The objective of this study was to characterize scaling properties of soil water storage variability through multifractal detrended fluctuation analysis (MFDFA). A field experiment was conducted in a sub-humid climate at Alvena, Saskatchewan, Canada. A north-south transect of 624-m long was established on a rolling landscape. Soil water storage was monitored weekly between 2002 and 2005 at 104 locations along the transect. The spatial scaling property of the surface 0 to 40 cm depth was characterized using the MFDFA technique for six of the soil water content series (all gravimetrically determined) representing soil water storage after snowmelt, rainfall, and evapotranspiration. For the studied transect, scaling properties of soil water storage are different between drier periods and wet periods. It also appears that local controls such as site topography and texture (that dominantly control the pattern during wet states) results in multiscaling property. The nonlocal controls such as evapotranspiration results in the reduction of the degree of multiscaling and improvement in the simple scaling. Therefore, the scaling property of soil water storage is a function of both soil moisture status and the spatial extent considered.

Description: Optimal solution error covariance in highly nonlinear problems of variational data assimilation Nonlinear Processes in Geophysics, 19, 177-184, 2012 Author(s): V. Shutyaev, I. Gejadze, G. J. M. Copeland, and F.-X. Le Dimet The problem of variational data assimilation (DA) for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition, boundary conditions and/or model parameters. The input data contain observation and background errors, hence there is an error in the optimal solution. For mildly nonlinear dynamics, the covariance matrix of the optimal solution error can be approximated by the inverse Hessian of the cost function. For problems with strongly nonlinear dynamics, a new statistical method based on the computation of a sample of inverse Hessians is suggested. This method relies on the efficient computation of the inverse Hessian by means of iterative methods (Lanczos and quasi-Newton BFGS) with preconditioning. Numerical examples are presented for the model governed by the Burgers equation with a nonlinear viscous term.

Description: Topological complexity of frictional interfaces: friction networks Nonlinear Processes in Geophysics, 19, 215-225, 2012 Author(s): H. O. Ghaffari and R. P. Young Through research conducted in this study, a network approach to the correlation patterns of void spaces in rough fractures (crack type II) was developed. We characterized friction networks with several networks characteristics. The correlation among network properties with the fracture permeability is the result of friction networks. The revealed hubs in the complex aperture networks confirmed the importance of highly correlated groups to conduct the highlighted features of the dynamical aperture field. We found that there is a universal power law between the nodes' degree and motifs frequency (for triangles it reads T(k) ∝ k β (β ≈ 2 ± 0.3)). The investigation of localization effects on eigenvectors shows a remarkable difference in parallel and perpendicular aperture patches. Furthermore, we estimate the rate of stored energy in asperities so that we found that the rate of radiated energy is higher in parallel friction networks than it is in transverse directions. The final part of our research highlights 4 point sub-graph distribution and its correlation with fluid flow. For shear rupture, we observed a similar trend in sub-graph distribution, resulting from parallel and transversal aperture profiles (a superfamily phenomenon).

Description: Coherence and predictability of extreme events in irregular waves Nonlinear Processes in Geophysics, 19, 199-213, 2012 Author(s): A. L. Latifah and E. van Groesen This paper concerns the description and the predictability of a freak event when at a certain position information in the form of a time signal is given. The prediction will use the phase information for an estimate of the position and time of the occurrence of a large wave, and to predict the measure of phase coherence at the estimated focussing position. The coherence and the spectrum will determine an estimate for the amplitude. After adjusting for second order nonlinear effects, together this then provides an estimate of the form of a possible freak wave in the time signal, which will be described by a pseudo-maximal signal. In the exceptional case of a fully coherent signal, it can be described well by a so-called maximal signal. We give four cases of freak waves for which we compare results of predictions with available measured (and simulated) results by nonlinear AB-equation (van Groesen and Andonowati, 2007; van Groesen et al., 2010). The first case deals with dispersive focussing, for which all phases are (designed to be) very coherent at position and time of focussing; this wave is nearly a maximal wave. The second case is the Draupner wave, for which the signal turns out to be recorded very close to its maximal wave height. It is less coherent but can be described in a good approximation as a pseudo-maximal wave. The last two cases are irregular waves which were measured at MARIN (Maritime Research Institute Netherlands); in a time trace of more than 1000 waves freak-like waves appeared "accidentally". Although the highest wave is less coherent than the other two cases, this maximal crest can still be approximated by a pseudo-maximal wave.

Description: Distribution of petrophysical properties for sandy-clayey reservoirs by fractal interpolation Nonlinear Processes in Geophysics, 19, 239-250, 2012 Author(s): M. Lozada-Zumaeta, R. D. Arizabalo, G. Ronquillo-Jarillo, E. Coconi-Morales, D. Rivera-Recillas, and F. Castrejón-Vácio The sandy-clayey hydrocarbon reservoirs of the Upper Paleocene and Lower Eocene located to the north of Veracruz State, Mexico, present highly complex geological and petrophysical characteristics. These reservoirs, which consist of sandstone and shale bodies within a depth interval ranging from 500 to 2000 m, were characterized statistically by means of fractal modeling and geostatistical tools. For 14 wells within an area of study of approximately 6 km 2 , various geophysical well logs were initially edited and further analyzed to establish a correlation between logs and core data. The fractal modeling based on the R/S (rescaled range) methodology and the interpolation method by successive random additions were used to generate pseudo-well logs between observed wells. The application of geostatistical tools, sequential Gaussian simulation and exponential model variograms contributed to estimate the spatial distribution of petrophysical properties such as effective porosity (PHIE), permeability (K) and shale volume (VSH). From the analysis and correlation of the information generated in the present study, it can be said, from a general point of view, that the results not only are correlated with already reported information but also provide significant characterization elements that would be hardly obtained by means of conventional techniques.

Description: Dynamics of a seismogenic fault subject to variable strain rate Nonlinear Processes in Geophysics, 18, 431-439, 2011 Author(s): M. Dragoni and A. Piombo The behaviour of seismogenic faults is generally investigated under the assumption that they are subject to a constant strain rate. We consider the effect of a slowly variable strain rate on the recurrence times of earthquakes generated by a single fault. To this aim a spring-block system is employed as a low-order analog of the fault. Two cases are considered: a sinusoidal oscillation in the driver velocity and a monotonic change from one velocity value to another. In the first case, a study of the orbit of the system in the state space suggests that the seismic activity of the equivalent fault is organized into cycles that include several earthquakes and repeat periodically. Within each cycle the recurrence times oscillate about an average value equal to the recurrence period for constant strain rate. In the second case, the recurrence time changes gradually from the value before the transition to the value following it. Asymptotic solutions are also given, approximating the case when the amplitude of the oscillation or of the monotonic change is much smaller than the average driver velocity and the period of oscillation or the duration of the transition is much longer than the recurrence times of block motions. If the system is not isolated but is subject to perturbations in stress, the perturbation anticipates or delays the subsequent earthquake. The effects of stress perturbations in the two cases of strain rate oscillations and monotonic change are considered.

Description: Number-average size model for geological systems and its application in economic geology Nonlinear Processes in Geophysics, 18, 447-454, 2011 Author(s): Q. F. Wang, L. Wan, Y. Zhang, J. Zhao, and H. Liu Various natural objects follow a number-size relationship in the fractal domain. In such relationship, the accumulative number of the objects beyond a given size shows a power-law relationship with the size. Yet in most cases, we also need to know the relationship between the accumulative number of the objects and their average size. A generalized number-size model and a number-average size model are constructed in this paper. In the number-average size model, the accumulative number shows a power-law relationship with the average size when the given size is much less than the maximum size of the objects. When the fractal dimension D s of the number-size model is smaller than 1, the fractal dimension D s of the number-average size model is almost equal to 1; and when D s 〉 1, the D m is approximately equal to D s . In mineral deposits, according to the number-average size model, the ore tonnage may show a fractal relationship with the grade, as the cutoff changes for a single ore deposit. This is demonstrated by a study of the relationship between tonnage and grade in the Reshuitang epithermal hot-spring gold deposit, China.

Description: Identification of dynamical transitions in marine palaeoclimate records by recurrence network analysis Nonlinear Processes in Geophysics, 18, 545-562, 2011 Author(s): J. F. Donges, R. V. Donner, K. Rehfeld, N. Marwan, M. H. Trauth, and J. Kurths The analysis of palaeoclimate time series is usually affected by severe methodological problems, resulting primarily from non-equidistant sampling and uncertain age models. As an alternative to existing methods of time series analysis, in this paper we argue that the statistical properties of recurrence networks – a recently developed approach – are promising candidates for characterising the system's nonlinear dynamics and quantifying structural changes in its reconstructed phase space as time evolves. In a first order approximation, the results of recurrence network analysis are invariant to changes in the age model and are not directly affected by non-equidistant sampling of the data. Specifically, we investigate the behaviour of recurrence network measures for both paradigmatic model systems with non-stationary parameters and four marine records of long-term palaeoclimate variations. We show that the obtained results are qualitatively robust under changes of the relevant parameters of our method, including detrending, size of the running window used for analysis, and embedding delay. We demonstrate that recurrence network analysis is able to detect relevant regime shifts in synthetic data as well as in problematic geoscientific time series. This suggests its application as a general exploratory tool of time series analysis complementing existing methods.

Description: Turbulent spectra and spectral kinks in the transition range from MHD to kinetic Alfvén turbulence Nonlinear Processes in Geophysics, 18, 587-597, 2011 Author(s): Y. Voitenko and J. De Keyser A weakly dispersive range (WDR) of kinetic Alfvén turbulence is identified and investigated for the first time in the context of the MHD/kinetic turbulence transition. We find perpendicular wavenumber spectra ∝ k ⊥ −3 and ∝ k ⊥ −4 formed in WDR by strong and weak turbulence of kinetic Alfvén waves (KAWs), respectively. These steep WDR spectra connect shallower spectra in the MHD and strongly dispersive KAW ranges, which results in a specific double-kink (2-k) pattern often seen in observed turbulent spectra. The first kink occurs where MHD turbulence transforms into weakly dispersive KAW turbulence; the second one is between weakly and strongly dispersive KAW ranges. Our analysis suggests that partial turbulence dissipation due to amplitude-dependent non-adiabatic ion heating may occur in the vicinity of the first spectral kink. The threshold-like nature of this process results in a conditional selective dissipation that affects only the largest over-threshold amplitudes and that decreases the intermittency in the range below the first spectral kink. Several recent counter-intuitive observational findings can be explained by the coupling between such a selective dissipation and the nonlinear interaction among weakly dispersive KAWs.

Description: A chaotically driven model climate: extreme events and snapshot attractors Nonlinear Processes in Geophysics, 18, 573-580, 2011 Author(s): T. Bódai, Gy. Károlyi, and T. Tél In a low-order chaotic global atmospheric circulation model the effects of deterministic chaotic driving are investigated. As a result of driving, peak-over-threshold type extreme events, e.g. cyclonic activity in the model, become more extreme, with increased frequency of recurrence. When the characteristic time of the driving is comparable to that of the undriven system, a resonance effect with amplified variance shows up. For very fast driving we find a reduced enhancement of variance, which is also the case with white noise driving. Snapshot attractors and their natural measures are determined as a function of time, and a resonance effects is also identified. The extreme value statistics of group maxima is found to follow a Weibull distribution.

Description: Nonlinear optimization set pair analysis model (NOSPAM) for assessing water resource renewability Nonlinear Processes in Geophysics, 18, 599-607, 2011 Author(s): X. H. Yang, X. J. Zhang, X. X. Hu, Z. F. Yang, and J. Q. Li There is much uncertain information which is very difficult to quantify in the water resource renewability assessment (WRRA). The index weights are the key parameters in the assessment model. To assess the water resource renewability rationally, a novel nonlinear optimization set pair analysis model (NOSPAM) is proposed, in which a nonlinear optimization model based on gray-encoded hybrid accelerating genetic algorithm is given to determine the weights by optimizing subjective and objective information, as well as an improved set pair analysis model based on the connection degree is established to deal with certain-uncertain information. In addition, a new calculating formula is established for determining certain-uncertain information quantity in NOSPAM. NOSPAM is used to assess the water resource renewability of the nine administrative divisions in the Yellow River Basin. Results show that NOSPAM can deal with the uncertain information, subjective and objective information. Compared with other nonlinear assessment methods (such as the gray associate analysis method and fuzzy assessment method), the advantage of NOSPAM is that it can not only rationally determine the index weights, but also measure the uncertain information quantity in the WRRA. This NOSPAM model is an extension to nonlinear assessment models.

Description: Predicting heat flow in the 2001 Bhuj earthquake ( M w =7.7) region of Kachchh (Western India), using an inverse recurrence method Nonlinear Processes in Geophysics, 18, 611-625, 2011 Author(s): N. Vedanti, O. P. Pandey, R. P. Srivastava, P. Mandal, S. Kumar, and V. P. Dimri Terrestrial heat flow is considered an important parameter in studying the regional geotectonic and geodynamic evolutionary history of any region. However, its distribution is still very uneven. There is hardly any information available for many geodynamically important areas. In the present study, we provide a methodology to predict the surface heat flow in areas, where detailed seismic information such as depth to the lithosphere-asthenosphere boundary (LAB) and crustal structure is known. The tool was first tested in several geotectonic blocks around the world and then used to predict the surface heat flow for the 2001 Bhuj earthquake region of Kachchh, India, which has been seismically active since historical times and where aftershock activity is still continuing nine years after the 2001 main event. Surface heat flow for this region is estimated to be about 61.3 mW m −2 . Beneath this region, heat flow input from the mantle as well as the temperatures at the Moho are quite high at around 44 mW m −2 and 630 °C, respectively, possibly due to thermal restructuring of the underlying crust and mantle lithosphere. In absence of conventional data, the proposed tool may be used to estimate a first order heat flow in continental regions for geotectonic studies, as it is also unaffected by the subsurface climatic perturbations that percolate even up to 2000 m depth.

Description: Electron acoustic solitons in the presence of an electron beam and superthermal electrons Nonlinear Processes in Geophysics, 18, 627-634, 2011 Author(s): S. Devanandhan, S. V. Singh, G. S. Lakhina, and R. Bharuthram Arbitrary amplitude electron acoustic solitons are studied in an unmagnetized plasma having cold electrons and ions, superthermal hot electrons and an electron beam. Using the Sagdeev pseudo potential method, theoretical analysis is carried out by assuming superthermal hot electrons having kappa distribution. The results show that inclusion of an electron beam alters the minimum value of spectral index, κ, of the superthermal electron distribution and Mach number for which electron-acoustic solitons can exist and also changes their width and electric field amplitude. For the auroral region parameters, the maximum electric field amplitudes and soliton widths are found in the range ~(30–524) mV m −1 and ~(329–729) m, respectively, for fixed Mach number M = 1.1 and for electron beam speed of (660–1990) km s −1 .

Description: Similarities between extreme events in the solar-terrestrial system by means of nonextensivity Nonlinear Processes in Geophysics, 18, 563-572, 2011 Author(s): G. Balasis, C. Papadimitriou, I. A. Daglis, A. Anastasiadis, I. Sandberg, and K. Eftaxias The dynamics of complex systems are founded on universal principles that can be used to describe disparate problems ranging from particle physics to economies of societies. A corollary is that transferring ideas and results from investigators in hitherto disparate areas will cross-fertilize and lead to important new results. In this contribution, we investigate the existence of a universal behavior, if any, in solar flares, magnetic storms, earthquakes and pre-seismic electromagnetic (EM) emissions, extending the work recently published by Balasis et al. (2011a). A common characteristic in the dynamics of the above-mentioned phenomena is that their energy release is basically fragmentary, i.e. the associated events are being composed of elementary building blocks. By analogy with earthquakes, the magnitude of the magnetic storms, solar flares and pre-seismic EM emissions can be appropriately defined. Then the key question we can ask in the frame of complexity is whether the magnitude distribution of earthquakes, magnetic storms, solar flares and pre-fracture EM emissions obeys the same law. We show that these apparently different extreme events, which occur in the solar-terrestrial system, follow the same energy distribution function. The latter was originally derived for earthquake dynamics in the framework of nonextensive Tsallis statistics.

Description: Assimilation of Earth rotation parameters into a global ocean model: excitation of polar motion Nonlinear Processes in Geophysics, 18, 581-585, 2011 Author(s): J. Saynisch, M. Wenzel, and J. Schröter The oceanic contribution to Earth rotation anomalies can be manifold. Possible causes are a change of total ocean mass, changes in current speed or location and changes in mass distribution. To derive the governing physical mechanisms of oceanic Earth rotation excitation we assimilate Earth rotation observations with a global circulation ocean model. Before assimilation, observations of length of day and polar motion were transformed into estimates of ocean angular momentum. By using the adjoint 4D-VAR assimilation method we were able to reproduce these estimated time series. Although length of day was assimilated simultaneously the analysis in this paper focuses on the oceanic polar motion generation. Our results show that changes in mass distribution and currents contribute to oceanic polar motion generation. Both contributions are highly correlated and show similar amplitudes. The changes in the model done by the assimilation procedure could be related to changes in the atmospheric forcing. Since for geometrical reasons the change of total ocean mass does not project on polar motion, we conclude that the polar motion is mainly generated by a geostrophic response to atmospheric momentum forcing. In geostrophic currents mass displacement and current speed entail each other. This way the large similarity of mass and current generated ocean angular momentum can be explained.

Description: New significance test methods for Fourier analysis of geophysical time series Nonlinear Processes in Geophysics, 18, 643-652, 2011 Author(s): Z. Zhang and J. Moore When one applies the discrete Fourier transform to analyze finite-length time series, discontinuities at the data boundaries will distort its Fourier power spectrum. In this paper, based on a rigid statistics framework, we present a new significance test method which can extract the intrinsic feature of a geophysical time series very well. We show the difference in significance level compared with traditional Fourier tests by analyzing the Arctic Oscillation (AO) and the Nino3.4 time series. In the AO, we find significant peaks at about 2.8, 4.3, and 5.7 yr periods and in Nino3.4 at about 12 yr period in tests against red noise. These peaks are not significant in traditional tests.

Description: Synchronization and desynchronization in the Olami-Feder-Christensen earthquake model and potential implications for real seismicity Nonlinear Processes in Geophysics, 18, 635-642, 2011 Author(s): S. Hergarten and R. Krenn The Olami-Feder-Christensen model is probably the most studied model in the context of self-organized criticality and reproduces several statistical properties of real earthquakes. We investigate and explain synchronization and desynchronization of earthquakes in this model in the nonconservative regime and its relevance for the power-law distribution of the event sizes (Gutenberg-Richter law) and for temporal clustering of earthquakes. The power-law distribution emerges from synchronization, and its scaling exponent can be derived as τ = 1.775 from the scaling properties of the rupture areas' perimeter. In contrast, the occurrence of foreshocks and aftershocks according to Omori's law is closely related to desynchronization. This mechanism of foreshock and aftershock generation differs strongly from the widespread idea of spontaneous triggering and gives an idea why some even large earthquakes are not preceded by any foreshocks in nature.

Description: A fault and seismicity based composite simulation in northern California Nonlinear Processes in Geophysics, 18, 955-966, 2011 Author(s): M. B. Yıkılmaz, E. M. Heien, D. L. Turcotte, J. B. Rundle, and L. H. Kellogg We generate synthetic catalogs of seismicity in northern California using a composite simulation. The basis of the simulation is the fault based "Virtual California" (VC) earthquake simulator. Back-slip velocities and mean recurrence intervals are specified on model strike-slip faults. A catalog of characteristic earthquakes is generated for a period of 100 000 yr. These earthquakes are predominantly in the range M = 6 to M = 8, but do not follow Gutenberg-Richter (GR) scaling at lower magnitudes. In order to model seismicity on unmapped faults we introduce background seismicity which occurs randomly in time with GR scaling and is spatially associated with the VC model faults. These earthquakes fill in the GR scaling down to M = 4 (the smallest earthquakes modeled). The rate of background seismicity is constrained by the observed rate of occurrence of M 〉 4 earthquakes in northern California. These earthquakes are then used to drive the BASS (branching aftershock sequence) model of aftershock occurrence. The BASS model is the self-similar limit of the ETAS (epidemic type aftershock sequence) model. Families of aftershocks are generated following each Virtual California and background main shock. In the simulations the rate of occurrence of aftershocks is essentially equal to the rate of occurrence of main shocks in the magnitude range 4 〈 M 〈 7. We generate frequency-magnitude and recurrence interval statistics both regionally and fault specific. We compare our modeled rates of seismicity and spatial variability with observations.

Description: Multiscale characterization of pore spaces using multifractals analysis of scanning electronic microscopy images of carbonates Nonlinear Processes in Geophysics, 18, 941-953, 2011 Author(s): M. S. Jouini, S. Vega, and E. A. Mokhtar Pore spaces heterogeneity in carbonates rocks has long been identified as an important factor impacting reservoir productivity. In this paper, we study the heterogeneity of carbonate rocks pore spaces based on the image analysis of scanning electron microscopy (SEM) data acquired at various magnifications. Sixty images of twelve carbonate samples from a reservoir in the Middle East were analyzed. First, pore spaces were extracted from SEM images using a segmentation technique based on watershed algorithm. Pores geometries revealed a multifractal behavior at various magnifications from 800x to 12 000x. In addition, the singularity spectrum provided quantitative values that describe the degree of heterogeneity in the carbonates samples. Moreover, for the majority of the analyzed samples, we found low variations (around 5%) in the multifractal dimensions for magnifications between 1700x and 12 000x. Finally, these results demonstrate that multifractal analysis could be an appropriate tool for characterizing quantitatively the heterogeneity of carbonate pore spaces geometries. However, our findings show that magnification has an impact on multifractal dimensions, revealing the limit of applicability of multifractal descriptions for these natural structures.

Description: The effect of stochastic perturbations on plankton transport by internal solitary waves Nonlinear Processes in Geophysics, 18, 1001-1012, 2011 Author(s): M. Stastna, F. J. Poulin, C. Subich, and J. V. Mecking Internal solitary and solitary-like waves are a commonly observed feature of density stratified natural waters, including lakes and the coastal ocean. Since such waves induce significant currents throughout the water column they can be responsible for significant transport of both passive and swimming biota. We consider simple models of moving zooplankton based on the Langevin equation. The small amplitude randomness significantly alters the nature of particle motion. In particular, passage through the wave leads to strongly non Gaussian particle distributions. When the plankton swims to return to its equilibrium photic level, a steady state that balances randomness, swimming and wave-induced motions is possible. We discuss possible implications of this steady state for organisms that feed on plankton.

Description: An artificial neural network technique for downscaling GCM outputs to RCM spatial scale Nonlinear Processes in Geophysics, 18, 1013-1028, 2011 Author(s): R. Chadwick, E. Coppola, and F. Giorgi An Artificial Neural Network (ANN) approach is used to downscale ECHAM5 GCM temperature ( T ) and rainfall ( R ) fields to RegCM3 regional model scale over Europe. The main inputs to the neural network were the ECHAM5 fields and topography, and RegCM3 topography. An ANN trained for the period 1960–1980 was able to recreate the RegCM3 1981–2000 mean T and R fields with reasonable accuracy. The ANN showed an improvement over a simple lapse-rate correction method for T , although the ANN R field did not capture all the fine-scale detail of the RCM field. An ANN trained over a smaller area of Southern Europe was able to capture this detail with more precision. The ANN was unable to accurately recreate the RCM climate change (CC) signal between 1981–2000 and 2081–2100, and it is suggested that this is because the relationship between the GCM fields, RCM fields and topography is not constant with time and changing climate. An ANN trained with three ten-year "time-slices" was able to better reproduce the RCM CC signal, particularly for the full European domain. This approach shows encouraging results but will need further refinement before becoming a viable supplement to dynamical regional climate modelling of temperature and rainfall.

Description: Emergent behavior in a coupled economic and coastline model for beach nourishment Nonlinear Processes in Geophysics, 18, 989-999, 2011 Author(s): E. D. Lazarus, D. E. McNamara, M. D. Smith, S. Gopalakrishnan, and A. B. Murray Developed coastal areas often exhibit a strong systemic coupling between shoreline dynamics and economic dynamics. "Beach nourishment", a common erosion-control practice, involves mechanically depositing sediment from outside the local littoral system onto an actively eroding shoreline to alter shoreline morphology. Natural sediment-transport processes quickly rework the newly engineered beach, causing further changes to the shoreline that in turn affect subsequent beach-nourishment decisions. To the limited extent that this landscape/economic coupling has been considered, evidence suggests that towns tend to employ spatially myopic economic strategies under which individual towns make isolated decisions that do not account for their neighbors. What happens when an optimization strategy that explicitly ignores spatial interactions is incorporated into a physical model that is spatially dynamic? The long-term attractor that develops for the coupled system (the state and behavior to which the system evolves over time) is unclear. We link an economic model, in which town-manager agents choose economically optimal beach-nourishment intervals according to past observations of their immediate shoreline, to a simplified coastal-dynamics model that includes alongshore sediment transport and background erosion (e.g. from sea-level rise). Simulations suggest that feedbacks between these human and natural coastal processes can generate emergent behaviors. When alongshore sediment transport and spatially myopic nourishment decisions are coupled, increases in the rate of sea-level rise can destabilize economically optimal nourishment practices into a regime characterized by the emergence of chaotic shoreline evolution.

Description: Investigating the connection between complexity of isolated trajectories and Lagrangian coherent structures Nonlinear Processes in Geophysics, 18, 977-987, 2011 Author(s): I. I. Rypina, S. E. Scott, L. J. Pratt, and M. G. Brown It is argued that the complexity of fluid particle trajectories provides the basis for a new method, referred to as the Complexity Method (CM), for estimation of Lagrangian coherent structures in aperiodic flows that are measured over finite time intervals. The basic principles of the CM are explained and the CM is tested in a variety of examples, both idealized and realistic, and in different reference frames. Two measures of complexity are explored in detail: the correlation dimension of trajectory, and a new measure – the ergodicity defect. Both measures yield structures that strongly resemble Lagrangian coherent structures in all of the examples considered. Since the CM uses properties of individual trajectories, and not separation rates between closely spaced trajectories, it may have advantages for the analysis of ocean float and drifter data sets in which trajectories are typically widely and non-uniformly spaced.

Description: Influence of the nonlinearity on statistical characteristics of long wave runup Nonlinear Processes in Geophysics, 18, 967-975, 2011 Author(s): P. Denissenko, I. Didenkulova, E. Pelinovsky, and J. Pearson Runup of long irregular waves on a plane beach is studied experimentally in the water flume at the University of Warwick. Statistics of wave runup (displacement and velocity of the moving shoreline and their extreme values) is analyzed for the incident wave field with the narrow band spectrum for different amplitudes of incident waves (different values of the breaking parameter Br σ ). It is shown experimentally that the distribution of the shoreline velocity does not depend on Br σ and coincides with the distribution of the vertical velocity in the incident wave field as it is predicted in the statistical theory of nonlinear long wave runup. Statistics of runup amplitudes shows the same behavior as that of the incident wave amplitudes. However, the distribution of the wave runup on a beach differs from the statistics of the incident wave elevation. The mean sea level at the coast rises with an increase in Br σ causing wave set-up on a beach, which agrees with the theoretical predictions. At the same time values of skewness and kurtosis for wave runup are similar to those for the incident wave field and they might be used for the forecast of sea floods at the coast.

Description: Inferring internal properties of Earth's core dynamics and their evolution from surface observations and a numerical geodynamo model Nonlinear Processes in Geophysics, 18, 657-674, 2011 Author(s): J. Aubert and A. Fournier Over the past decades, direct three-dimensional numerical modelling has been successfully used to reproduce the main features of the geodynamo. Here we report on efforts to solve the associated inverse problem, aiming at inferring the underlying properties of the system from the sole knowledge of surface observations and the first principle dynamical equations describing the convective dynamo. To this end we rely on twin experiments. A reference model time sequence is first produced and used to generate synthetic data, restricted here to the large-scale component of the magnetic field and its rate of change at the outer boundary. Starting from a different initial condition, a second sequence is next run and attempts are made to recover the internal magnetic, velocity and buoyancy anomaly fields from the sparse surficial data. In order to reduce the vast underdetermination of this problem, we use stochastic inversion, a linear estimation method determining the most likely internal state compatible with the observations and some prior knowledge, and we also implement a sequential evolution algorithm in order to invert time-dependent surface observations. The prior is the multivariate statistics of the numerical model, which are directly computed from a large number of snapshots stored during a preliminary direct run. The statistics display strong correlation between different harmonic degrees of the surface observations and internal fields, provided they share the same harmonic order, a natural consequence of the linear coupling of the governing dynamical equations and of the leading influence of the Coriolis force. Synthetic experiments performed with a weakly nonlinear model yield an excellent quantitative retrieval of the internal structure. In contrast, the use of a strongly nonlinear (and more realistic) model results in less accurate static estimations, which in turn fail to constrain the unobserved small scales in the time integration of the evolution scheme. Evaluating the quality of forecasts of the system evolution against the reference solution, we show that our scheme can improve predictions based on linear extrapolations on forecast horizons shorter than the system e -folding time. Still, in the perspective of forthcoming data assimilation activities, our study underlines the need of advanced estimation techniques able to cope with the moderate to strong nonlinearities present in the geodynamo.

Description: Self-sustained vibrations in volcanic areas extracted by Independent Component Analysis: a review and new results Nonlinear Processes in Geophysics, 18, 925-940, 2011 Author(s): E. De Lauro, S. De Martino, M. Falanga, and M. Palo We investigate the physical processes associated with volcanic tremor and explosions. A volcano is a complex system where a fluid source interacts with the solid edifice so generating seismic waves in a regime of low turbulence. Although the complex behavior escapes a simple universal description, the phases of activity generate stable (self-sustained) oscillations that can be described as a non-linear dynamical system of low dimensionality. So, the system requires to be investigated with non-linear methods able to individuate, decompose, and extract the main characteristics of the phenomenon. Independent Component Analysis (ICA), an entropy-based technique is a good candidate for this purpose. Here, we review the results of ICA applied to seismic signals acquired in some volcanic areas. We emphasize analogies and differences among the self-oscillations individuated in three cases: Stromboli (Italy), Erebus (Antarctica) and Volcán de Colima (Mexico). The waveforms of the extracted independent components are specific for each volcano, whereas the similarity can be ascribed to a very general common source mechanism involving the interaction between gas/magma flow and solid structures (the volcanic edifice). Indeed, chocking phenomena or inhomogeneities in the volcanic cavity can play the same role in generating self-oscillations as the languid and the reed do in musical instruments. The understanding of these background oscillations is relevant not only for explaining the volcanic source process and to make a forecast into the future, but sheds light on the physics of complex systems developing low turbulence.

Description: Magnetic reconnection as an element of turbulence Nonlinear Processes in Geophysics, 18, 675-695, 2011 Author(s): S. Servidio, P. Dmitruk, A. Greco, M. Wan, S. Donato, P. A. Cassak, M. A. Shay, V. Carbone, and W. H. Matthaeus In this work, recent advances on the study of reconnection in turbulence are reviewed. Using direct numerical simulations of decaying incompressible two-dimensional magnetohydrodynamics (MHD), it was found that in fully developed turbulence complex processes of reconnection locally occur (Servidio et al., 2009, 2010a). In this complex scenario, reconnection is spontaneous but locally driven by the fields, with the boundary conditions provided by the turbulence. Matching classical turbulence analysis with a generalized Sweet-Parker theory, the statistical features of these multiple-reconnection events have been identified. A discussion on the accuracy of our algorithms is provided, highlighting the necessity of adequate spatial resolution. Applications to the study of solar wind discontinuities are reviewed, comparing simulations to spacecraft observations. New results are shown, studying the time evolution of these local reconnection events. A preliminary study on the comparison between MHD and Hall MHD is reported. Our new approach to the study of reconnection as an element of turbulence has broad applications to space plasmas, shedding a new light on the study of magnetic reconnection in nature.

Description: Bias correction and post-processing under climate change Nonlinear Processes in Geophysics, 18, 911-924, 2011 Author(s): S. Vannitsem The statistical and dynamical properties of bias correction and linear post-processing are investigated when the system under interest is affected by model errors and is experiencing parameter modifications, mimicking the potential impact of climate change. The analysis is first performed for simple typical scalar systems, an Ornstein-Uhlenbeck process (O-U) and a limit point bifurcation. It reveals system's specific (linear or non-linear) dependences of biases and post-processing corrections as a function of parameter modifications. A more realistic system is then investigated, a low-order model of moist general circulation, incorporating several processes of high relevance in the climate dynamics (radiative effects, cloud feedbacks...), but still sufficiently simple to allow for an extensive exploration of its dynamics. In this context, bias or post-processing corrections also display complicate variations when the system experiences temperature climate changes up to a few degrees. This precludes a straightforward application of these corrections from one system's state to another (as usually adopted for climate projections), and increases further the uncertainty in evaluating the amplitudes of climate changes.

Description: Gottwald Melborune (0–1) test for chaos in a plasma Nonlinear Processes in Geophysics, 19, 53-56, 2012 Author(s): D. R. Chowdhury, A. N. S. Iyengar, and S. Lahiri Plasma is a highly complex system exhibiting a rich variety of nonlinear dynamical phenomena. In the last two decades or so there has been a spurt of growth in exploring unconventional nonlinear dynamical methods of analysis, like chaos theory, multi fractal analysis, self organized criticality etc. of experimental data from different plasma systems. Investigation of fluctuating plasma parameters is very important since they are correlated with transport of particles, and energy. In time series analysis, it is considered of key importance to determine whether the data measured from the system is regular, deterministically chaotic, or random. The two important parameters that are in general estimated are the correlation dimension and the Lyapunov exponent. Though correlation dimension helps in determining the complexity of a system, Lyapunov exponent reveals if the system is chaotic or not and also helps in prediction to some extent. In spite of its extensive usage, estimation of Lyapunov exponent can be quite tedious and sometimes suffers from some disadvantages like reliability in the presence of noise, requirement of phase space reconstruction etc., and hence it is necessary to explore other possibilities of estimating the chaoticity of a data. In this paper we have analysed for chaoticity, the nonlinear floating potential fluctuations from a glow discharge plasma system by the 0–1 test and compared it with the results obtained from Lyapunov exponent.

Description: Multiplicative cascade processes and information integration for predictive mapping Nonlinear Processes in Geophysics, 19, 57-68, 2012 Author(s): Q. Cheng This paper presents a new model proposed on the basis of multiplicative cascade process (MCP) theory for integrating spatial information to be used for mineral resources prediction and environmental impact assessment. Probability of a spatial point event is defined as the probability that a small map calculating unit (map unit) randomly selected from a study area contains one or more points. The probability that such unit randomly selected from a subarea with known spatial binary map patterns (evidential layers) contains one or more points is defined as the posterior point event probability. In this paper, processes of integrating multiple binary map patterns that divide the study area into smaller areas with updated posterior probabilities are viewed as multiplicative cascade processes resulting in a new log-linear model for calculating conditional probabilities from the multiple evidential input layers. The coefficients (weights) involved in this model measuring degree of spatial correlation between point event and the evidential layers are found to be associated with singularity indices involved in multifractal modeling. It is demonstrated that the model is simple and easy to be implemented in comparison with the existing weights of evidence model which is commonly applied in spatial decision modeling. In addition, the posterior probability as the end product of a multiplicative cascade process can be used to describe multifractality and singularity which are useful properties for characterizing spatial distribution of predicted point events. A case study of tin mineral potential mapping in the Gejiu mineral district in China is used to illustrate principles and use of the modeling process. Four binary layers: formation of limestone, buffer distance for intersections of three groups of faults, local and regional geochemical anomalies of elements As, Sn, Cu, Pb, Zn and Cd, were combined for mapping potential areas for occurrence of tin mineral deposits.

Description: Scaling laws of diffusion and time intermittency generated by coherent structures in atmospheric turbulence Nonlinear Processes in Geophysics, 19, 113-126, 2012 Author(s): P. Paradisi, R. Cesari, A. Donateo, D. Contini, and P. Allegrini We investigate the time intermittency of turbulent transport associated with the birth-death of self-organized coherent structures in the atmospheric boundary layer. We apply a threshold analysis on the increments of turbulent fluctuations to extract sequences of rapid acceleration events, which is a marker of the transition between self-organized structures. The inter-event time distributions show a power-law decay ψ(τ) ~ 1/τ μ , with a strong dependence of the power-law index μ on the threshold. A recently developed method based on the application of event-driven walking rules to generate different diffusion processes is applied to the experimental event sequences. At variance with the power-law index μ estimated from the inter-event time distributions, the diffusion scaling H , defined by ⟨ X 2 ⟩ ~ t 2 H , is independent from the threshold. From the analysis of the diffusion scaling it can also be inferred the presence of different kind of events, i.e. genuinely transition events and spurious events, which all contribute to the diffusion process but over different time scales. The great advantage of event-driven diffusion lies in the ability of separating different regimes of the scaling H . In fact, the greatest H , corresponding to the most anomalous diffusion process, emerges in the long time range, whereas the smallest H can be seen in the short time range if the time resolution of the data is sufficiently accurate. The estimated diffusion scaling is also robust under the change of the definition of turbulent fluctuations and, under the assumption of statistically independent events, it corresponds to a self-similar point process with a well-defined power-law index μ D ~ 2.1, where D denotes that μ D is derived from the diffusion scaling. We argue that this renewal point process can be associated to birth and death of coherent structures and to turbulent transport near the ground, where the contribution of turbulent coherent structures becomes dominant.

Description: Statistical analysis of polychaete population density: dynamics of dominant species and scaling properties in relative abundance fluctuations Nonlinear Processes in Geophysics, 19, 45-52, 2012 Author(s): B. Quiroz-Martinez, F. G. Schmitt, and J.-C. Dauvin We consider here the dynamics of two polychaete populations based on a 20 yr temporal benthic survey of two muddy fine sand communities in the Bay of Morlaix, Western English Channel. These populations display high temporal variability, which is analyzed here using scaling approaches. We find that population densities have heavy tailed probability density functions. We analyze the dynamics of relative species abundance in two different communities of polychaetes by estimating in a novel way a "mean square drift" coefficient which characterizes their fluctuations in relative abundance over time. We show the usefulness of using new tools to approach and model such highly variable population dynamics in marine ecosystems.

Description: Albedo parametrization and reversibility of sea ice decay Nonlinear Processes in Geophysics, 19, 81-94, 2012 Author(s): M. Müller-Stoffels and R. Wackerbauer The Arctic's sea ice cover has been receding rapidly in recent years, and global climate models typically predict a further decline over the next century. It is an open question whether a possible loss of Arctic sea ice is reversible. We study the stability of Arctic model sea ice in a conceptual, two-dimensional energy-based regular network model of the ice-ocean layer that considers ARM's longwave radiative budget data and SHEBA albedo measurements. Seasonal ice cover, perennial ice and perennial open water are asymptotic states accessible by the model. We show that the shape of albedo parameterization near the melting temperature differentiates between reversible continuous sea ice decrease under atmospheric forcing and hysteresis behavior. Fixed points induced solely by the surface energy budget are essential for understanding the interaction of surface energy with the radiative forcing and the underlying body of ice/water, particularly close to a bifurcation point. Future studies will explore ice edge stability and reversibility in this lattice model, generalized to a latitudinal transect with spatiotemporal lateral atmospheric heat transfer and high spatial resolution.

Description: Structural and statistical properties of the collocation technique for error characterization Nonlinear Processes in Geophysics, 19, 69-80, 2012 Author(s): S. Zwieback, K. Scipal, W. Dorigo, and W. Wagner The validation of geophysical data sets (e.g. derived from models, exploration techniques or remote sensing) presents a formidable challenge as all products are inherently different and subject to errors. The collocation technique permits the retrieval of the error variances of different data sources without the need to specify one data set as a reference. In addition calibration constants can be determined to account for biases and different dynamic ranges. The method is frequently applied to the study and comparison of remote sensing, in-situ and modelled data, particularly in hydrology and oceanography. Previous studies have almost exclusively focussed on the validation of three data sources; in this paper it is shown how the technique generalizes to an arbitrary number of data sets. It turns out that only parts of the covariance structure can be resolved by the collocation technique, thus emphasizing the necessity of expert knowledge for the correct validation of geophysical products. Furthermore the bias and error variance of the estimators are derived with particular emphasis on the assumptions necessary for establishing those characteristics. Important properties of the method, such as the structural deficiencies, dependence of the accuracy on the number of measurements and the impact of violated assumptions, are illustrated by application to simulated data.

Description: Complexity signatures in the geomagnetic H component recorded by the Tromsø magnetometer (70° N, 19° E) over the last quarter of a century Nonlinear Processes in Geophysics, 21, 1051-1058, 2014 Author(s): C. M. Hall Solar disturbances, depending on the orientation of the interplanetary magnetic field, typically result in perturbations of the geomagnetic field as observed by magnetometers on the ground. Here, the geomagnetic field's horizontal component, as measured by the ground-based observatory-standard magnetometer at Tromsø (70° N, 19° E), is examined for signatures of complexity. Twenty-five year-long 10 s resolution data sets are analysed for fluctuations with timescales of less than 1 day. Quantile–quantile plots are employed first, revealing that the fluctuations are better represented by Cauchy rather than Gaussian distributions. Thereafter, both spectral density and detrended fluctuation analysis methods are used to estimate values of the generalized Hurst exponent, α. The results are then compared with independent findings. Inspection and comparison of the spectral and detrended fluctuation analyses reveal that timescales between 1 h and 1 day are characterized by fractional Brownian motion with a generalized Hurst exponent of ~1.4, whereas including timescales as short as 1 min suggests fractional Brownian motion with a generalized Hurst exponent of ~1.6.

Description: Nonlinear fluctuation analysis for a set of 41 magnetic clouds measured by the Advanced Composition Explorer (ACE) spacecraft Nonlinear Processes in Geophysics, 21, 1059-1073, 2014 Author(s): A. Ojeda González, W. D. Gonzalez, O. Mendes, M. O. Domingues, and R. R. Rosa The statistical distribution of values in the signal and the autocorrelations (interpreted as the memory or persistence) between values are attributes of a time series. The autocorrelation function values are positive in a time series with persistence, while they are negative in a time series with anti-persistence. The persistence of values with respect to each other can be strong, weak, or nonexistent. A strong correlation implies a "memory" of previous values in the time series. The long-range persistence in time series could be studied using semivariograms, rescaled range, detrended fluctuation analysis and Fourier spectral analysis, respectively. In this work, persistence analysis is to study interplanetary magnetic field (IMF) time series. We use data from the IMF components with a time resolution of 16 s. Time intervals corresponding to distinct processes around 41 magnetic clouds (MCs) in the period between March 1998 and December 2003 were selected. In this exploratory study, the purpose of this selection is to deal with the cases presenting the three periods: plasma sheath, MC, and post-MC. We calculated one exponent of persistence (e.g., α, β, Hu , Ha ) over the previous three time intervals. The persistence exponent values increased inside cloud regions, and it was possible to select the following threshold values: α ( j ) = 1.392, Ha ( j ) = 0.327, and Hu ( j ) = 0.875. These values are useful as another test to evaluate the quality of the identification. If the cloud is well structured, then the persistence exponent values exceed thresholds. In 80.5% of the cases studied, these tools were able to separate the region of the cloud from neighboring regions. The Hausdorff exponent ( Ha ) provides the best results.

Description: On quartet interactions in the California Current system Nonlinear Processes in Geophysics, 21, 887-900, 2014 Author(s): L. M. Ivanov, C. A. Collins, and T. M. Margolina Sea surface height (SSH) altimetry observations for 1992 to 2009 off California are used to show that observed quasi-zonal jets were likely driven by near-resonance interactions between different scales of the flow. Quartet (modulational) instability dominated and caused non-local transfer of energy from waves and eddies to biannual oscillations and quasi-zonal jets. Two types of quartets were identified: those composed of scales corresponding to (a) quasi-zonal jets, annual and semiannual Rossby waves and mesoscale eddies, and (b) biannual oscillations, semiannual Rossby waves and mesoscale eddies. The spectral centroid regularly shifted into the domain of low-order modes. However, the spectrum of SSHs does not demonstrate a power behavior. This says that the classical inverse cascade is absent. For a case with bottom friction, quartet instability required the existence of a certain level of dissipativity in the flow.

Description: Topology and seasonal evolution of the network of extreme precipitation over the Indian subcontinent and Sri Lanka Nonlinear Processes in Geophysics, 21, 901-917, 2014 Author(s): V. Stolbova, P. Martin, B. Bookhagen, N. Marwan, and J. Kurths This paper employs a complex network approach to determine the topology and evolution of the network of extreme precipitation that governs the organization of extreme rainfall before, during, and after the Indian Summer Monsoon (ISM) season. We construct networks of extreme rainfall events during the ISM (June–September), post-monsoon (October–December), and pre-monsoon (March–May) periods from satellite-derived (Tropical Rainfall Measurement Mission, TRMM) and rain-gauge interpolated (Asian Precipitation Highly Resolved Observational Data Integration Towards the Evaluation of Water Resources, APHRODITE) data sets. The structure of the networks is determined by the level of synchronization of extreme rainfall events between different grid cells throughout the Indian subcontinent. Through the analysis of various complex-network metrics, we describe typical repetitive patterns in North Pakistan (NP), the Eastern Ghats (EG), and the Tibetan Plateau (TP). These patterns appear during the pre-monsoon season, evolve during the ISM, and disappear during the post-monsoon season. These are important meteorological features that need further attention and that may be useful in ISM timing and strength prediction.

Description: Effective coastal boundary conditions for tsunami wave run-up over sloping bathymetry Nonlinear Processes in Geophysics, 21, 987-1005, 2014 Author(s): W. Kristina, O. Bokhove, and E. van Groesen An effective boundary condition (EBC) is introduced as a novel technique for predicting tsunami wave run-up along the coast, and offshore wave reflections. Numerical modeling of tsunami propagation in the coastal zone has been a daunting task, since high accuracy is needed to capture aspects of wave propagation in the shallower areas. For example, there are complicated interactions between incoming and reflected waves due to the bathymetry and intrinsically nonlinear phenomena of wave propagation. If a fixed wall boundary condition is used at a certain shallow depth contour, the reflection properties can be unrealistic. To alleviate this, we explore a so-called effective boundary condition, developed here in one spatial dimension. From the deep ocean to a seaward boundary, i.e., in the simulation area, we model wave propagation numerically over real bathymetry using either the linear dispersive variational Boussinesq or the shallow water equations. We measure the incoming wave at this seaward boundary, and model the wave dynamics towards the shoreline analytically, based on nonlinear shallow water theory over bathymetry with a constant slope. We calculate the run-up heights at the shore and the reflection caused by the slope. The reflected wave is then influxed back into the simulation area using the EBC. The coupling between the numerical and analytic dynamics in the two areas is handled using variational principles, which leads to (approximate) conservation of the overall energy in both areas. We verify our approach in a series of numerical test cases of increasing complexity, including a case akin to tsunami propagation to the coastline at Aceh, Sumatra, Indonesia.

Description: Improving the ensemble transform Kalman filter using a second-order Taylor approximation of the nonlinear observation operator Nonlinear Processes in Geophysics, 21, 955-970, 2014 Author(s): G. Wu, X. Yi, L. Wang, X. Liang, S. Zhang, X. Zhang, and X. Zheng The ensemble transform Kalman filter (ETKF) assimilation scheme has recently seen rapid development and wide application. As a specific implementation of the ensemble Kalman filter (EnKF), the ETKF is computationally more efficient than the conventional EnKF. However, the current implementation of the ETKF still has some limitations when the observation operator is strongly nonlinear. One problem in the minimization of a nonlinear objective function similar to 4D-Var is that the nonlinear operator and its tangent-linear operator have to be calculated iteratively if the Hessian is not preconditioned or if the Hessian has to be calculated several times. This may be computationally expensive. Another problem is that it uses the tangent-linear approximation of the observation operator to estimate the multiplicative inflation factor of the forecast errors, which may not be sufficiently accurate. This study attempts to solve these problems. First, we apply the second-order Taylor approximation to the nonlinear observation operator in which the operator, its tangent-linear operator and Hessian are calculated only once. The related computational cost is also discussed. Second, we propose a scheme to estimate the inflation factor when the observation operator is strongly nonlinear. Experimentation with the Lorenz 96 model shows that using the second-order Taylor approximation of the nonlinear observation operator leads to a reduction in the analysis error compared with the traditional linear approximation method. Furthermore, the proposed inflation scheme leads to a reduction in the analysis error compared with the procedure using the traditional inflation scheme.

Description: Representing model error in ensemble data assimilation Nonlinear Processes in Geophysics, 21, 971-985, 2014 Author(s): C. Cardinali, N. Žagar, G. Radnoti, and R. Buizza The paper investigates a method to represent model error in the ensemble data assimilation (EDA) system. The ECMWF operational EDA simulates the effect of both observations and model uncertainties. Observation errors are represented by perturbations with statistics characterized by the observation error covariance matrix whilst the model uncertainties are represented by stochastic perturbations added to the physical tendencies to simulate the effect of random errors in the physical parameterizations (ST-method). In this work an alternative method (XB-method) is proposed to simulate model uncertainties by adding perturbations to the model background field. In this way the error represented is not just restricted to model error in the usual sense but potentially extends to any form of background error. The perturbations have the same correlation as the background error covariance matrix and their magnitude is computed from comparing the high-resolution operational innovation variances with the ensemble variances when the ensemble is obtained by perturbing only the observations (OBS-method). The XB-method has been designed to represent the short range model error relevant for the data assimilation window. Spread diagnostic shows that the XB-method generates a larger spread than the ST-method that is operationally used at ECMWF, in particular in the extratropics. Three-dimensional normal-mode diagnostics indicate that XB-EDA spread projects more than the spread from the other EDAs onto the easterly inertia-gravity modes associated with equatorial Kelvin waves, tropical dynamics and, in general, model error sources. The background error statistics from the above described EDAs have been employed in the assimilation system. The assimilation system performance showed that the XB-method background error statistics increase the observation influence in the analysis process. The other EDA background error statistics, when inflated by a global factor, generate analyses with 30–50% smaller degree of freedom of signal. XB-EDA background error variances have not been inflated. The presented EDAs have been used to generate the initial perturbations of the ECMWF ensemble prediction system (EPS) of which the XB-EDA induces the largest EPS spread, also in the medium range, leading to a more reliable ensemble. Compared to ST-EDA , XB-EDA leads to a small improvement of the EPS ignorance skill score at day 3 and 7.

Description: A non-Gaussian analysis scheme using rank histograms for ensemble data assimilation Nonlinear Processes in Geophysics, 21, 869-885, 2014 Author(s): S. Metref, E. Cosme, C. Snyder, and P. Brasseur One challenge of geophysical data assimilation is to address the issue of non-Gaussianities in the distributions of the physical variables ensuing, in many cases, from nonlinear dynamical models. Non-Gaussian ensemble analysis methods fall into two categories, those remapping the ensemble particles by approximating the best linear unbiased estimate, for example, the ensemble Kalman filter (EnKF), and those resampling the particles by directly applying Bayes' rule, like particle filters. In this article, it is suggested that the most common remapping methods can only handle weakly non-Gaussian distributions, while the others suffer from sampling issues. In between those two categories, a new remapping method directly applying Bayes' rule, the multivariate rank histogram filter (MRHF), is introduced as an extension of the rank histogram filter (RHF) first introduced by Anderson (2010). Its performance is evaluated and compared with several data assimilation methods, on different levels of non-Gaussianity with the Lorenz 63 model. The method's behavior is then illustrated on a simple density estimation problem using ensemble simulations from a coupled physical–biogeochemical model of the North Atlantic ocean. The MRHF performs well with low-dimensional systems in strongly non-Gaussian regimes.

Description: Simulations of nonlinear harmonic generation by an internal wave beam incident on a pycnocline Nonlinear Processes in Geophysics, 21, 855-868, 2014 Author(s): S. Wunsch, H. Ku, I. Delwiche, and R. Awadallah Internal wave beams generated by oceanic tidal flows propagate upward and interact with the increasing stratification found at the pycnocline. The nonlinear generation of harmonic modes by internal wave beams incident on a pycnocline has recently been demonstrated by laboratory experiments and numerical simulations. In these previous studies, the harmonic modes were trapped within the pycnocline because their frequencies exceeded that of the stratified fluid below. Here, two-dimensional numerical simulations are used to explore the effect of incidence angle on harmonic generation at a thin pycnocline. At incidence angles less than 30 degrees (typical of oceanic beams), the lowest harmonic mode freely radiates in the form of an internal wave beam rather than being trapped within the pycnocline. The results indicate that nonlinear refraction is the primary mechanism for harmonic generation at incidence angles exceeding 30 degrees, but that interaction of the incident and reflected beams is more important at smaller incidence angles. The simulations are compared to weakly nonlinear theory based on refraction at the pycnocline. The results yield good agreement for trapped harmonics, but weakly nonlinear theory substantially underpredicts the amplitude of the radiated harmonics.

Description: Horton laws for hydraulic–geometric variables and their scaling exponents in self-similar Tokunaga river networks Nonlinear Processes in Geophysics, 21, 1007-1025, 2014 Author(s): V. K. Gupta and O. J. Mesa An analytical theory is developed that obtains Horton laws for six hydraulic–geometric (H–G) variables (stream discharge Q , width W , depth D , velocity U , slope S , and friction n' ) in self-similar Tokunaga networks in the limit of a large network order. The theory uses several disjoint theoretical concepts like Horton laws of stream numbers and areas as asymptotic relations in Tokunaga networks, dimensional analysis, the Buckingham Pi theorem, asymptotic self-similarity of the first kind, or SS-1, and asymptotic self-similarity of the second kind, or SS-2. A self-contained review of these concepts, with examples, is given as "methods". The H–G data sets in channel networks from three published studies and one unpublished study are summarized to test theoretical predictions. The theory builds on six independent dimensionless river-basin numbers . A mass conservation equation in terms of Horton bifurcation and discharge ratios in Tokunaga networks is derived. Assuming that the H–G variables are homogeneous and self-similar functions of stream discharge, it is shown that the functions are of a power law form. SS-1 is applied to predict the Horton laws for width, depth and velocity as asymptotic relationships. Exponents of width and the Reynolds number are predicted and tested against three field data sets. One basin shows deviations from theoretical predictions. Tentatively assuming that SS-1 is valid for slope, depth and velocity, corresponding Horton laws and the H–G exponents are derived. Our predictions of the exponents are the same as those previously predicted for the optimal channel network (OCN) model. In direct contrast to our work, the OCN model does not consider Horton laws for the H–G variables, and uses optimality assumptions. The predicted exponents deviate substantially from the values obtained from three field studies, which suggests that H–G in networks does not obey SS-1. It fails because slope, a dimensionless river-basin number, goes to 0 as network order increases, but, it cannot be eliminated from the asymptotic limit. Therefore, a generalization of SS-1, based on SS-2, is considered. It introduces two anomalous scaling exponents as free parameters, which enables us to show the existence of Horton laws for channel depth, velocity, slope and Manning friction. These two exponents are not predicted here. Instead, we used the observed exponents of depth and slope to predict the Manning friction exponent and to test it against field exponents from three studies. The same basin mentioned above shows some deviation from the theoretical prediction. A physical reason for this deviation is given, which identifies an important topic for research. Finally, we briefly sketch how the two anomalous scaling exponents could be estimated from the transport of suspended sediment load and the bed load. Statistical variability in the Horton laws for the H–G variables is also discussed. Both are important open problems for future research.

Description: Spatial analysis of oil reservoirs using detrended fluctuation analysis of geophysical data Nonlinear Processes in Geophysics, 21, 1043-1049, 2014 Author(s): R. A. Ribeiro, M. V. M. Mata, L. S. Lucena, U. L. Fulco, and G. Corso We employ the detrended fluctuation analysis (DFA) technique to investigate spatial properties of an oil reservoir. This reservoir is situated at Bacia de Namorados, RJ, Brazil. The data correspond to well logs of the following geophysical quantities: sonic, gamma ray, density, porosity and electrical resistivity, measured in 56 wells. We tested the hypothesis of constructing spatial models using data from fluctuation analysis over well logs. To verify this hypothesis, we compare the matrix of distances of well logs with the differences in DFA exponents of geophysical quantities using a spatial correlation function and the Mantel test. Our data analysis suggests that the sonic profile is a good candidate for representing spatial structures. Then, we apply the clustering analysis technique to the sonic profile to identify these spatial patterns. In addition, we use the Mantel test to search for correlations between DFA exponents of geophysical quantities.

Description: Long-term changes in the north–south asymmetry of solar activity: a nonlinear dynamics characterization using visibility graphs Nonlinear Processes in Geophysics, 21, 1113-1126, 2014 Author(s): Y. Zou, R. V. Donner, N. Marwan, M. Small, and J. Kurths Solar activity is characterized by complex dynamics superimposed onto an almost periodic, approximately 11-year cycle. One of its main features is the presence of a marked, time-varying hemispheric asymmetry, the deeper reasons for which have not yet been completely uncovered. Traditionally, this asymmetry has been studied by considering amplitude and phase differences. Here, we use visibility graphs, a novel tool of nonlinear time series analysis, to obtain complementary information on hemispheric asymmetries in dynamical properties. Our analysis provides deep insights into the potential and limitations of this method, revealing a complex interplay between factors relating to statistical and dynamical properties, i.e., effects due to the probability distribution and the regularity of observed fluctuations. We demonstrate that temporal changes in the hemispheric predominance of the graph properties lag those directly associated with the total hemispheric sunspot areas. Our findings open a new dynamical perspective on studying the north–south sunspot asymmetry, which is to be further explored in future work.

Description: Correlations between climate network and relief data Nonlinear Processes in Geophysics, 21, 1127-1132, 2014 Author(s): T. K. D. Peron, C. H. Comin, D. R. Amancio, L. da F. Costa, F. A. Rodrigues, and J. Kurths In the last few years, the scientific community has witnessed an ongoing trend of using ideas developed in the study of complex networks to analyze climate dynamics. This powerful combination, usually called climate networks, can be used to uncover non-trivial patterns of weather changes throughout the years. Here we investigate the temperature network of the North American region and show that two network characteristics, namely degree and clustering, have marked differences between the eastern and western regions. We show that such differences are a reflection of the presence of a large network community on the western side of the continent. Moreover, we provide evidence that this large community is a consequence of the peculiar characteristics of the western relief of North America.

Description: An improved ARIMA model for precipitation simulations Nonlinear Processes in Geophysics, 21, 1159-1168, 2014 Author(s): H. R. Wang, C. Wang, X. Lin, and J. Kang Auto regressive integrated moving average (ARIMA) models have been widely used to calculate monthly time series data formed by interannual variations of monthly data or inter-monthly variation. However, the influence brought about by inter-monthly variations within each year is often ignored. An improved ARIMA model is developed in this study accounting for both the interannual and inter-monthly variation. In the present approach, clustering analysis is performed first to hydrologic variable time series. The characteristics of each class are then extracted and the correlation between the hydrologic variable quantity to be predicted and characteristic quantities constructed by linear regression analysis. ARIMA models are built for predicting these characteristics of each class and the hydrologic variable monthly values of year of interest are finally predicted using the modeled values of corresponding characteristics from ARIMA model and the linear regression model. A case study is conducted to predict the monthly precipitation at the Lanzhou precipitation station in Lanzhou, China, using the model, and the results show that the accuracy of the improved model is significantly higher than the seasonal model, with the mean residual achieving 9.41 mm and the forecast accuracy increasing by 21%.

Description: Estimating time delays for constructing dynamical networks Nonlinear Processes in Geophysics, 21, 929-937, 2014 Author(s): E. A. Martin and J. Davidsen Dynamical networks – networks inferred from multivariate time series – have been widely applied to climate data and beyond, resulting in new insights into the underlying dynamics. However, these inferred networks can suffer from biases that need to be accounted for to properly interpret the results. Here, we report on a previously unrecognized bias in the estimate of time delays between nodes in dynamical networks inferred from cross-correlations, a method often used. This bias results in the maximum correlation occurring disproportionately often at large time lags. This is of particular concern in dynamical networks where the large number of possible links necessitates finding the correct time lag in an automated way. We show that this bias can arise due to the similarity of the estimator to a random walk, and are able to map them to each other explicitly for some cases. For the random walk there is an analytical solution for the bias that is closely related to the famous Lévy arcsine distribution, which provides an upper bound in many other cases. Finally, we show that estimating the cross-correlation in frequency space effectively eliminates this bias. Reanalysing large lag links (from a climate network) with this method results in a distribution peaked near zero instead, as well as additional peaks at the originally assigned lag. Links that are reassigned smaller time lags tend to have a smaller distance between them, which indicates that the new time delays are physically reasonable.

Description: Logit-normal mixed model for Indian monsoon precipitation Nonlinear Processes in Geophysics, 21, 939-953, 2014 Author(s): L. R. Dietz and S. Chatterjee Describing the nature and variability of Indian monsoon precipitation is a topic of much debate in the current literature. We suggest the use of a generalized linear mixed model (GLMM), specifically, the logit-normal mixed model, to describe the underlying structure of this complex climatic event. Four GLMM algorithms are described and simulations are performed to vet these algorithms before applying them to the Indian precipitation data. The logit-normal model was applied to light, moderate, and extreme rainfall. Findings indicated that physical constructs were preserved by the models, and random effects were significant in many cases. We also found GLMM estimation methods were sensitive to tuning parameters and assumptions and therefore, recommend use of multiple methods in applications. This work provides a novel use of GLMM and promotes its addition to the gamut of tools for analysis in studying climate phenomena.

Description: Non-parametric Bayesian mixture of sparse regressions with application towards feature selection for statistical downscaling Nonlinear Processes in Geophysics, 21, 1145-1157, 2014 Author(s): D. Das, J. Dy, J. Ross, Z. Obradovic, and A. R. Ganguly Climate projections simulated by Global Climate Models (GCMs) are often used for assessing the impacts of climate change. However, the relatively coarse resolutions of GCM outputs often preclude their application to accurately assessing the effects of climate change on finer regional-scale phenomena. Downscaling of climate variables from coarser to finer regional scales using statistical methods is often performed for regional climate projections. Statistical downscaling (SD) is based on the understanding that the regional climate is influenced by two factors – the large-scale climatic state and the regional or local features. A transfer function approach of SD involves learning a regression model that relates these features (predictors) to a climatic variable of interest (predictand) based on the past observations. However, often a single regression model is not sufficient to describe complex dynamic relationships between the predictors and predictand. We focus on the covariate selection part of the transfer function approach and propose a nonparametric Bayesian mixture of sparse regression models based on Dirichlet process (DP) for simultaneous clustering and discovery of covariates within the clusters while automatically finding the number of clusters. Sparse linear models are parsimonious and hence more generalizable than non-sparse alternatives, and lend themselves to domain relevant interpretation. Applications to synthetic data demonstrate the value of the new approach and preliminary results related to feature selection for statistical downscaling show that our method can lead to new insights.

Description: Development of a hybrid variational-ensemble data assimilation technique for observed lightning tested in a mesoscale model Nonlinear Processes in Geophysics, 21, 1027-1041, 2014 Author(s): K. Apodaca, M. Zupanski, M. DeMaria, J. A. Knaff, and L. D. Grasso Lightning measurements from the Geostationary Lightning Mapper (GLM) that will be aboard the Geostationary Operational Environmental Satellite – R Series will bring new information that can have the potential for improving the initialization of numerical weather prediction models by assisting in the detection of clouds and convection through data assimilation. In this study we focus on investigating the utility of lightning observations in mesoscale and regional applications suitable for current operational environments, in which convection cannot be explicitly resolved. Therefore, we examine the impact of lightning observations on storm environment. Preliminary steps in developing a lightning data assimilation capability suitable for mesoscale modeling are presented in this paper. World Wide Lightning Location Network (WWLLN) data was utilized as a proxy for GLM measurements and was assimilated with the Maximum Likelihood Ensemble Filter, interfaced with the Nonhydrostatic Mesoscale Model core of the Weather Research and Forecasting system (WRF-NMM). In order to test this methodology, regional data assimilation experiments were conducted. Results indicate that lightning data assimilation had a positive impact on the following: information content, influencing several dynamical variables in the model (e.g., moisture, temperature, and winds), and improving initial conditions during several data assimilation cycles. However, the 6 h forecast after the assimilation did not show a clear improvement in terms of root mean square (RMS) errors.

Description: Corrigendum to "Number-average size model for geological systems and its application in economic geology" published in Nonlin. Processes Geophys., 18, 447–454, 2011 Nonlinear Processes in Geophysics, 18, 513-513, 2011 Author(s): Q. F. Wang, L. Wan, Y. Zhang, J. Zhao, and H. Liu No abstract available.

Description: Bayesian neural network modeling of tree-ring temperature variability record from the Western Himalayas Nonlinear Processes in Geophysics, 18, 515-528, 2011 Author(s): R. K. Tiwari and S. Maiti A novel technique based on the Bayesian neural network (BNN) theory is developed and employed to model the temperature variation record from the Western Himalayas. In order to estimate an a posteriori probability function, the BNN is trained with the Hybrid Monte Carlo (HMC)/Markov Chain Monte Carlo (MCMC) simulations algorithm. The efficacy of the new algorithm is tested on the well known chaotic, first order autoregressive (AR) and random models and then applied to model the temperature variation record decoded from the tree-ring widths of the Western Himalayas for the period spanning over 1226–2000 AD. For modeling the actual tree-ring temperature data, optimum network parameters are chosen appropriately and then cross-validation test is performed to ensure the generalization skill of the network on the new data set. Finally, prediction result based on the BNN model is compared with the conventional artificial neural network (ANN) and the AR linear models results. The comparative results show that the BNN based analysis makes better prediction than the ANN and the AR models. The new BNN modeling approach provides a viable tool for climate studies and could also be exploited for modeling other kinds of environmental data.

Description: Statistical inference from atmospheric time series: detecting trends and coherent structures Nonlinear Processes in Geophysics, 18, 537-544, 2011 Author(s): A. Gluhovsky Standard statistical methods involve strong assumptions that are rarely met in real data, whereas resampling methods permit obtaining valid inference without making questionable assumptions about the data generating mechanism. Among these methods, subsampling works under the weakest assumptions, which makes it particularly applicable for atmospheric and climate data analyses. In the paper, two problems are addressed using subsampling: (1) the construction of simultaneous confidence bands for the unknown trend in a time series that can be modeled as a sum of two components: deterministic (trend) and stochastic (stationary process, not necessarily an i.i.d. noise or a linear process), and (2) the construction of confidence intervals for the skewness of a nonlinear time series. Non-zero skewness is attributed to the occurrence of coherent structures in turbulent flows, whereas commonly employed linear time series models imply zero skewness.

Description: Sampling and analysis of chemical element concentration distribution in rock units and orebodies Nonlinear Processes in Geophysics, 19, 23-44, 2012 Author(s): F. P. Agterberg Existing sampling techniques applied within known orebodies, such as sampling along mining drifts, yield element concentration values for larger blocks of ore if they are extended into their surroundings. The resulting average concentration values have relatively small "extension variance". These techniques can be used for multifractal modeling as well as ore reserve estimation approaches. Geometric probability theory can aid in local spatial covariance modeling. It provides information about increase of variability of element concentration over short distances exceeding microscopic scale. In general, the local clustering of ore crystals results in small-scale variability known as the "nugget effect". Parameters to characterize spatial covariance estimated from ore samples subjected to chemical analysis for ore reserve estimation may not be valid at local scale because of the nugget effect. The novel method of local singularity mapping applied within orebodies provides new insights into the nature of the nugget effect. Within the Pulacayo orebody, Bolivia, local singularity for zinc is linearly related with logarithmically transformed concentration value. If there is a nugget effect, moving averages resulting from covariance models or estimated by other methods that have a smoothing effect, such as kriging, can be improved by incorporating local singularities indicating local element enrichment or depletion. Although there have been many successful applications of the multifractal binomial/ p model, its application within the Pulacayo orebody results in inconsistencies, indicating some shortcomings of this relatively simple approach. Local singularity analysis and universal multifractal modeling are two promising new approaches to improve upon results obtained by commonly used geostatistical techniques and use of the binomial/ p model. All methods in this paper are illustrated using a single example (118 Pulacayo zinc values), and several techniques are applied to other orebody datasets (Whalesback copper deposit, Witwatersrand goldfields and Black Cargo titanium deposit). Additionally, it is discussed that nugget effects exist in a binary series of alternating mostly gneiss and metabasite previously derived from KTB borehole velocity and lithology logs, and within a series of 2796 copper concentration values from this same drill-hole.

Description: Nucleation and growth of geological faults Nonlinear Processes in Geophysics, 18, 529-536, 2011 Author(s): D. Stoyan and R. Gloaguen We present a new model of fault nucleation and growth based on the Weibull theory, already widely used in fracture research engineering. We propose that, according to a birth-and-growth process, germs (nuclei) are born at random instants at random spatial locations and then grow with time. This leads to a satisfactory formulation of fault length distribution, different from classical statistical laws. Especially, this formulation reconciles previous analyses of fault datasets displaying power-law and/or exponential behaviors. The Weibull parameters can be statistically estimated in a simple way. We show that the model can be successfully fitted to natural data in Kenya and Ethiopia. In contrast to existing descriptive models developed for geological fault systems, such as fractal approaches, the Weibull theory allows to characterize the strength of the material, i.e. its resistance to deformation. Since this model is very general, we expect that it can be applied in many situations, and for simulations of geological fracture processes. The model is independent of deformation intensity and type and therefore allows a better constraint of the seismic risk in threatened regions.

Description: Nonlinear wave effects at the non-reflecting beach Nonlinear Processes in Geophysics, 19, 1-8, 2012 Author(s): I. Didenkulova and E. Pelinovsky Nonlinear effects at the bottom profile of convex shape (non-reflecting beach) are studied using asymptotic approach (nonlinear WKB approximation) and direct perturbation theory. In the asymptotic approach the nonlinearity leads to the generation of high-order harmonics in the propagating wave, which result in the wave breaking when the wave propagates shoreward, while within the perturbation theory besides wave deformation it leads to the variations in the mean sea level and wave reflection (waves do not reflect from "non-reflecting" beach in the linear theory). The nonlinear corrections (second harmonics) are calculated within both approaches and compared between each other. It is shown that for the wave propagating shoreward the nonlinear correction is smaller than the one predicted by the asymptotic approach, while for the offshore propagating wave they have a similar asymptotic. Nonlinear corrections for both waves propagating shoreward and seaward demonstrate the oscillatory character, caused by interference of the incident and reflected waves in the second-order perturbation theory, while there is no reflection in the linear approximation (first-order perturbation theory). Expressions for wave set-up and set-down along the non-reflecting beach are found and discussed.

Description: Bistable systems with stochastic noise: virtues and limits of effective one-dimensional Langevin equations Nonlinear Processes in Geophysics, 19, 9-22, 2012 Author(s): V. Lucarini, D. Faranda, and M. Willeit The understanding of the statistical properties and of the dynamics of multistable systems is gaining more and more importance in a vast variety of scientific fields. This is especially relevant for the investigation of the tipping points of complex systems. Sometimes, in order to understand the time series of given observables exhibiting bimodal distributions, simple one-dimensional Langevin models are fitted to reproduce the observed statistical properties, and used to investing-ate the projected dynamics of the observable. This is of great relevance for studying potential catastrophic changes in the properties of the underlying system or resonant behaviours like those related to stochastic resonance-like mechanisms. In this paper, we propose a framework for encasing this kind of studies, using simple box models of the oceanic circulation and choosing as observable the strength of the thermohaline circulation. We study the statistical properties of the transitions between the two modes of operation of the thermohaline circulation under symmetric boundary forcings and test their agreement with simplified one-dimensional phenomenological theories. We extend our analysis to include stochastic resonance-like amplification processes. We conclude that fitted one-dimensional Langevin models, when closely scrutinised, may result to be more ad-hoc than they seem, lacking robustness and/or well-posedness. They should be treated with care, more as an empiric descriptive tool than as methodology with predictive power.