ALBERT

Beschreibung: Corrigendum to "Breeding and predictability in the baroclinic rotating annulus using a perfect model" published in Nonlin. Processes Geophys., 15, 469–487, 2008 Nonlinear Processes in Geophysics, 18, 359-359, 2011 Author(s): R. M. B. Young and P. L. Read No abstract available.

Beschreibung: Strategies for coupling global and limited-area ensemble Kalman filter assimilation Nonlinear Processes in Geophysics, 18, 415-430, 2011 Author(s): D. Merkova, I. Szunyogh, and E. Ott This paper compares the forecast performance of four strategies for coupling global and limited area data assimilation: three strategies propagate information from the global to the limited area process, while the fourth strategy feeds back information from the limited area to the global process. All four strategies are formulated in the Local Ensemble Transform Kalman Filter (LETKF) framework. Numerical experiments are carried out with the model component of the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS) and the NCEP Regional Spectral Model (RSM). The limited area domain is an extended North-America region that includes part of the north-east Pacific. The GFS is integrated at horizontal resolution T62 (about 150 km in the mid-latitudes), while the RSM is integrated at horizontal resolution 48 km. Experiments are carried out both under the perfect model hypothesis and in a realistic setting. The coupling strategies are evaluated by comparing their deterministic forecast performance at 12-h and 48-h lead times. The results suggest that the limited area data assimilation system has the potential to enhance the forecasts at 12-h lead time in the limited area domain at the synoptic and sub-synoptic scales (in the global wave number range of about 10 to 40). There is a clear indication that between the forecast performance of the different coupling strategies those that cycle the limited area assimilation process produce the most accurate forecasts. In the realistic setting, at 12-h forecast time the limited area systems produce more modest improvements compared to the global system than under the perfect model hypothesis, and at 48-h forecast time the global forecasts are more accurate than the limited area forecasts.

Beschreibung: Spectral methods for internal waves: indistinguishable density profiles and double-humped solitary waves Nonlinear Processes in Geophysics, 18, 351-358, 2011 Author(s): M. Dunphy, C. Subich, and M. Stastna Internal solitary waves are widely observed in both the oceans and large lakes. They can be described by a variety of mathematical theories, covering the full spectrum from first order asymptotic theory (i.e. Korteweg-de Vries, or KdV, theory), through higher order extensions of weakly nonlinear-weakly nonhydrostatic theory, to fully nonlinear-weakly nonhydrostatic theories and finally exact theory based on the Dubreil-Jacotin-Long (DJL) equation that is formally equivalent to the full set of Euler equations. We discuss how spectral and pseudospectral methods allow for the computation of novel phenomena in both approximate and exact theories. In particular we construct markedly different density profiles for which the coefficients in the KdV theory are very nearly identical. These two density profiles yield qualitatively different behaviour for both exact, or fully nonlinear, waves computed using the DJL equation and in dynamic simulations of the time dependent Euler equations. For exact, DJL, theory we compute exact solitary waves with two-scales, or so-called double-humped waves.

Beschreibung: A nonlinear method of removing harmonic noise in geophysical data Nonlinear Processes in Geophysics, 18, 367-379, 2011 Author(s): Y. Jeng and C.-S. Chen A nonlinear, adaptive method to remove the harmonic noise that commonly resides in geophysical data is proposed in this study. This filtering method is based on the ensemble empirical mode decomposition algorithm in conjunction with the logarithmic transform. We present a synthetic model study to investigate the capability of signal reconstruction from the decomposed data, and compare the results with those derived from other 2-D adaptive filters. Applications to the real seismic data acquired by using an ocean bottom seismograph and to a shot gather of the ground penetrating radar demonstrate the robustness of this method. Our work proposes a concept that instead of Fourier-based approaches, the harmonic noise removal in geophysical data can be achieved effectively by using an alternative nonlinear adaptive data analysis method, which has been applied extensively in other scientific studies.

Beschreibung: Comparison of correlation analysis techniques for irregularly sampled time series Nonlinear Processes in Geophysics, 18, 389-404, 2011 Author(s): K. Rehfeld, N. Marwan, J. Heitzig, and J. Kurths Geoscientific measurements often provide time series with irregular time sampling, requiring either data reconstruction (interpolation) or sophisticated methods to handle irregular sampling. We compare the linear interpolation technique and different approaches for analyzing the correlation functions and persistence of irregularly sampled time series, as Lomb-Scargle Fourier transformation and kernel-based methods. In a thorough benchmark test we investigate the performance of these techniques. All methods have comparable root mean square errors (RMSEs) for low skewness of the inter-observation time distribution. For high skewness, very irregular data, interpolation bias and RMSE increase strongly. We find a 40 % lower RMSE for the lag-1 autocorrelation function (ACF) for the Gaussian kernel method vs. the linear interpolation scheme,in the analysis of highly irregular time series. For the cross correlation function (CCF) the RMSE is then lower by 60 %. The application of the Lomb-Scargle technique gave results comparable to the kernel methods for the univariate, but poorer results in the bivariate case. Especially the high-frequency components of the signal, where classical methods show a strong bias in ACF and CCF magnitude, are preserved when using the kernel methods. We illustrate the performances of interpolation vs. Gaussian kernel method by applying both to paleo-data from four locations, reflecting late Holocene Asian monsoon variability as derived from speleothem δ 18 O measurements. Cross correlation results are similar for both methods, which we attribute to the long time scales of the common variability. The persistence time (memory) is strongly overestimated when using the standard, interpolation-based, approach. Hence, the Gaussian kernel is a reliable and more robust estimator with significant advantages compared to other techniques and suitable for large scale application to paleo-data.

Beschreibung: Brief communication "On one mechanism of low frequency variability of the Antarctic Circumpolar Current" Nonlinear Processes in Geophysics, 18, 361-365, 2011 Author(s): O. G. Derzho and B. de Young In this paper we present a simple analytical model for low frequency and large scale variability of the Antarctic Circumpolar Current (ACC). The physical mechanism of the variability is related to temporal and spatial variations of the cyclonic mean flow (ACC) due to circularly propagating nonlinear barotropic Rossby wave trains. It is shown that the Rossby wave train is a fundamental mode, trapped between the major fronts in the ACC. The Rossby waves are predicted to rotate with a particular angular velocity that depends on the magnitude and width of the mean current. The spatial structure of the rotating pattern, including its zonal wave number, is defined by the specific form of the stream function-vorticity relation. The similarity between the simulated patterns and the Antarctic Circumpolar Wave (ACW) is highlighted. The model can predict the observed sequence of warm and cold patches in the ACW as well as its zonal number.

Beschreibung: A semi-phenomenological approach to explain the event-size distribution of the Drossel-Schwabl forest-fire model Nonlinear Processes in Geophysics, 18, 381-388, 2011 Author(s): S. Hergarten and R. Krenn We present a novel approach to explain the complex scaling behavior of the Drossel-Schwabl forest-fire model in two dimensions. Clusters of trees are characterized by their size and perimeter only, whereas spatial correlations are neglected. Coalescence of clusters is restricted to clusters of similar sizes. Our approach derives the value of the scaling exponent τ of the event size distribution directly from the scaling of the accessible perimeter of percolation clusters. We obtain τ = 1.19 in the limit of infinite growth rate, in perfect agreement with numerical results. Furthermore, our approach predicts the unusual transition from a power law to an exponential decay even quantitatively, while the exponential decay at large event sizes itself is reproduced only qualitatively.

Beschreibung: Double rank-ordering technique of ROMA (Rank-Ordered Multifractal Analysis) for multifractal fluctuations featuring multiple regimes of scales Nonlinear Processes in Geophysics, 18, 405-414, 2011 Author(s): S. W. Y. Tam and T. Chang Rank-Ordered Multifractal Analysis (ROMA), a technique capable of deciphering the multifractal characteristics of intermittent fluctuations, was originally applied to the results of a magnetohydrodynamic (MHD) simulation. Application of ROMA to measured fluctuations in the auroral zone, due to the dominant physical effects changing from kinetic to MHD as the scale increases, requires an additional level of rank-ordering in order to divide the domain of scales into regimes. An algorithm for the additional step in this double rank-ordering technique is discussed, and is demonstrated in the application to the electric field fluctuations in the auroral zone as an example. As a result of the double rank-ordering, ROMA is able to take into account the nonlinear crossover behavior characterized by the multiple regimes of time scales by providing a scaling variable and a scaling function that are global to all the time scales.

Beschreibung: Rank ordering multifractal analysis of the auroral electrojet index Nonlinear Processes in Geophysics, 18, 277-285, 2011 Author(s): G. Consolini and P. De Michelis In the second half of the 90s interest grew on the complex features of the magnetospheric dynamics in response to solar wind changes. An important series of papers were published on the occurrence of chaos, turbulence and complexity. Among them, particularly interesting was the study of the bursty and fractal/multifractal character of the high latitude energy release during geomagnetic storms, which was evidenced by analyzing the features of the Auroral Electrojet (AE) indices. Recently, the multifractal features of the small time-scale increments of AE-indices have been criticized in favor of a more simple fractal behavior. This is particularly true for the scaling features of the probability density functions (PDFs) of the AE index increments. Here, after a brief review of the nature of the fractal/multifractal features of the magnetospheric response to solar wind changes, we investigate the multifractal nature of the scaling features of the AE index increments PDFs using the Rank Ordering Multifractal Analysis (ROMA) technique. The ROMA results clearly demonstrate the existence of a hierarchy of scaling indices, depending on the increment amplitude, for the data collapsing of PDFs relative to increments at different time scales. Our results confirm the previous results by Consolini et al. (1996) and the more recent results by Rypdal and Rypdal (2010).

Beschreibung: Preface Large amplitude internal waves in the coastal ocean Nonlinear Processes in Geophysics, 18, 653-655, 2011 Author(s): R. Grimshaw, K. Helfrich, and A. Scotti No Abstract available.

Beschreibung: Size distribution and structure of Barchan dune fields Nonlinear Processes in Geophysics, 18, 455-467, 2011 Author(s): O. Durán, V. Schwämmle, P. G. Lind, and H. J. Herrmann Barchans are isolated mobile dunes often organized in large dune fields. Dune fields seem to present a characteristic dune size and spacing, which suggests a cooperative behavior based on dune interaction. In Duran et al. (2009), we propose that the redistribution of sand by collisions between dunes is a key element for the stability and size selection of barchan dune fields. This approach was based on a mean-field model ignoring the spatial distribution of dune fields. Here, we present a simplified dune field model that includes the spatial evolution of individual dunes as well as their interaction through sand exchange and binary collisions. As a result, the dune field evolves towards a steady state that depends on the boundary conditions. Comparing our results with measurements of Moroccan dune fields, we find that the simulated fields have the same dune size distribution as in real fields but fail to reproduce their homogeneity along the wind direction.

Beschreibung: Combining 2-m temperature nowcasting and short range ensemble forecasting Nonlinear Processes in Geophysics, 18, 903-910, 2011 Author(s): A. Kann, T. Haiden, and C. Wittmann During recent years, numerical ensemble prediction systems have become an important tool for estimating the uncertainties of dynamical and physical processes as represented in numerical weather models. The latest generation of limited area ensemble prediction systems (LAM-EPSs) allows for probabilistic forecasts at high resolution in both space and time. However, these systems still suffer from systematic deficiencies. Especially for nowcasting (0–6 h) applications the ensemble spread is smaller than the actual forecast error. This paper tries to generate probabilistic short range 2-m temperature forecasts by combining a state-of-the-art nowcasting method and a limited area ensemble system, and compares the results with statistical methods. The Integrated Nowcasting Through Comprehensive Analysis (INCA) system, which has been in operation at the Central Institute for Meteorology and Geodynamics (ZAMG) since 2006 (Haiden et al., 2011), provides short range deterministic forecasts at high temporal (15 min–60 min) and spatial (1 km) resolution. An INCA Ensemble (INCA-EPS) of 2-m temperature forecasts is constructed by applying a dynamical approach, a statistical approach, and a combined dynamic-statistical method. The dynamical method takes uncertainty information (i.e. ensemble variance) from the operational limited area ensemble system ALADIN-LAEF (Aire Limitée Adaptation Dynamique Développement InterNational Limited Area Ensemble Forecasting) which is running operationally at ZAMG (Wang et al., 2011). The purely statistical method assumes a well-calibrated spread-skill relation and applies ensemble spread according to the skill of the INCA forecast of the most recent past. The combined dynamic-statistical approach adapts the ensemble variance gained from ALADIN-LAEF with non-homogeneous Gaussian regression (NGR) which yields a statistical \mbox{correction} of the first and second moment (mean bias and dispersion) for Gaussian distributed continuous variables. Validation results indicate that all three methods produce sharp and reliable probabilistic 2-m temperature forecasts. However, the statistical and combined dynamic-statistical methods slightly outperform the pure dynamical approach, mainly due to the under-dispersive behavior of ALADIN-LAEF outside the nowcasting range. The training length does not have a pronounced impact on forecast skill, but a spread re-scaling improves the forecast skill substantially. Refinements of the statistical methods yield a slight further improvement.

Beschreibung: The effect of a localized geothermal heat source on deep water formation Nonlinear Processes in Geophysics, 18, 841-847, 2011 Author(s): M. Vincze, A. Várai, E. Barsy, and I. M. Jánosi In a simplified two-dimensional model of a buoyancy-driven overturning circulation, we numerically study the response of the flow to a small localized heat source at the bottom. The flow is driven by differential thermal forcing applied along the top surface boundary. We evaluate the steady state solutions versus the temperature difference between the two ends of the water surface in terms of different characteristic parameters that properly describe the transition from a weak upper-layer convection state to a robust full-depth deep convection. We conclude that a small additional bottom heat flux underneath the "cold" end of the basin is able to initiate full-depth convection even when the surface heat forcing alone is not sufficient to maintain this state.

Beschreibung: External forcing of earthquake swarms at Alpine regions: \newline example from a seismic meteorological network at Mt. Hochstaufen SE-Bavaria Nonlinear Processes in Geophysics, 18, 849-860, 2011 Author(s): V. Svejdar, H. Küchenhoff, L. Fahrmeir, and J. Wassermann In the last few years, it has been shown that above-average rainfall and the following diffusion of excess water into subsurface structures is able to trigger earthquake swarms in the uppermost brittle portion of the Earth's crust. However, there is still an ongoing debate on whether the crust already needs to be in a critical-to-failure state or whether it is sufficient that water is transported rapidly within channels and veins of karst or similar geological formations to the underlying, earthquake-generating layers. Also unknown is the role of other forcing mechanisms, possible co-variables and probably necessary tectonic loading in the triggering process of earthquakes. Because of these problems, we do not use an explicit physical model but instead analyze the meteorological and geophysical data via sophisticated statistical models. \newline We are interested in the influence of a more complete set of possible forcing parameters, including the influence of synthetic earth tides, on the occurrence of earthquake swarms. In this context, regression models are the adequate tool, since the calculation of simple correlations can be confounded by the other variables. Since our outcome variable (the number of quakes) is a count, we use Poisson regression models that include the plausible assumption of a Poisson distribution for the counts. For this study, we use nearly continuous recordings of a seismic and meteorological network in the years 2002–2008 at Mt. Hochstaufen in SE-Bavaria. Our non-linear regression model reveals correlations between external forces and the triggering of earthquakes. In addition to the still dominant influence of rainfall, theoretical estimated tidal tilt show some weak influence on the swarm generation. However, the influence of the modeled trend functions shows that rain is by far not the most important forcing mechanism present in the data.

Beschreibung: Nonlinearly combined impacts of initial perturbation from human activities and parameter perturbation from climate change on the grassland ecosystem Nonlinear Processes in Geophysics, 18, 883-893, 2011 Author(s): G. Sun and M. Mu Human activities and climate change are important factors that affect grassland ecosystems. A new optimization approach, the approach of conditional nonlinear optimal perturbation (CNOP) related to initial and parameter perturbations, is employed to explore the nonlinearly combined impacts of human activities and climate change on a grassland ecosystem using a theoretical grassland model. In our study, it is assumed that the initial perturbations and parameter perturbations are regarded as human activities and climate change, respectively. Numerical results indicate that the climate changes causing the maximum effect in the grassland ecosystem are different under disparate intensities of human activities. This implies the pattern of climate change is very critical to the maintenance or degradation of grassland ecosystem in light of high intensity of human activities and that the grassland ecosystem should be rationally managed when the moisture index decreases. The grassland ecosystem influenced by the nonlinear combination of human activities and climate change undergoes abrupt change, while the grassland ecosystem affected by other types of human activities and climate change fails to show the abrupt change under a certain range of perturbations with the theoretical model. The further numerical analyses also indicate that the growth of living biomass and the evaporation from soil surface shaded by the wilted biomass may be crucial factors contributing to the abrupt change of the grassland equilibrium state within the theoretical model.

Beschreibung: Preface "Nonlinear and scaling processes in Hydrology and Soil Science" Nonlinear Processes in Geophysics, 18, 899-902, 2011 Author(s): A. M. Tarquis, J. L. M. P. de Lima, W. F. Krajewski, Q. Cheng, and H. Gaonac'h No abstract available.

Beschreibung: Magnetic reconnection associated fluctuations in the deep magnetotail: ARTEMIS results Nonlinear Processes in Geophysics, 18, 861-869, 2011 Author(s): Z. Vörös On the basis of ARTEMIS two-probe mission magnetic reconnection (MR) outflow associated magnetic fluctuations and turbulence are analyzed on 19 February 2011. In the deep-tail, at distances between X = 45 – 51 R E , evidence for reconnection associated plasma sheet thinning was found, accompanied by heating of the plasma sheet. Correlated flow and field reversals and the large-scale Hall-effect signatures indicated the presence of the reconnection X -line. Within fast reconnection plasma outflows, magnetic fluctuations exhibit the same spectral scaling features and kinked spectra as magnetic fluctuations in the solar wind or in various parts of geospace. It was shown that the proton scale magnetic fluctuations are constrained by oblique firehose, proton cyclotron and mirror instability thresholds. For parallel plasma β || 〉 1, where the thresholds converge, perpendicular magnetic fluctuations are enhanced. Magnetic compressibility decreases with the distance to the neutral sheet, however, near the instability thresholds it is comparable to the values obtained in the solar wind.

Beschreibung: Preface "Extreme Events: Nonlinear Dynamics and Time Series Analysis" Nonlinear Processes in Geophysics, 18, 895-897, 2011 Author(s): P. Yiou, B. D. Malamud, and H. W. Rust No abstract available.

Beschreibung: Conditions for large earthquakes in a two-asperity fault model Nonlinear Processes in Geophysics, 18, 709-717, 2011 Author(s): M. Dragoni and S. Santini A fault with two asperities is modelled as a system made of two blocks coupled by a spring and sliding on a plane under the same values of static and dynamic friction. An analytical solution is given for the simultaneous motion of the blocks and the corresponding orbits are plotted in the phase space. It is proven that, whichever the initial state is, the long-term behaviour of the system is one of an infinite number of limit cycles, characterized by a particular pattern of forces. The region where the system is located when the blocks are stationary can be divided into narrow stripes corresponding to different orbits of the points belonging to them. This implies that the system is sensitive to perturbations and has relevant implications for a fault, which is subject to stress transfers from earthquakes generated by neighbouring faults. In this case, the fault may experience a larger earthquake, with the simultaneous failure of the two asperities, which restores a stress distribution compatible with periodic behaviour. The seismic moment associated with simultaneous asperity failure is always greater than the maximum value that can be released in a limit cycle. For strongly coupled asperities, the moment can be several times larger.

Beschreibung: Extreme events and long-range correlations in space weather Nonlinear Processes in Geophysics, 18, 719-725, 2011 Author(s): A. S. Sharma and T. Veeramani Space weather is driven by the solar wind and many geospace storms and substorms are natural hazards with considerable societal impact. The dynamical and statistical features of these events are complicated because of the turbulent nature of their driver, the solar wind. Large-scale data sets of geospace storms and substorms are analysed for this study of the inherent statistical characteristics of extreme events in geospace. The detrended fluctuation analysis, based on the autocorrelation functions, is used and yields scaling behavior representing long-term correlations. The scaling function is represented by two exponents, arising due mainly to the presence of the largely coherent internal dynamics of the magnetosphere and the turbulent nature of the solar wind driver.

Beschreibung: The evolution of electron current sheet and formation of secondary islands in guide field reconnection Nonlinear Processes in Geophysics, 18, 727-733, 2011 Author(s): C. Huang, Q. Lu, Z. Yang, M. Wu, Q. Dong, and S. Wang Two-dimensional (2-D) particle-in-cell (PIC) simulations are performed to investigate the evolution of the electron current sheet (ECS) in guide field reconnection. The ECS is formed by electrons accelerated by the inductive electric field in the vicinity of the X line, which is then extended along the x direction due to the imbalance between the electric field force and Ampere force. The tearing instability is unstable when the ECS becomes sufficiently long and thin, and several seed islands are formed in the ECS. These tiny islands may coalesce and form a larger secondary island in the center of the diffusion region.

Beschreibung: Ensemble Kalman filtering without the intrinsic need for inflation Nonlinear Processes in Geophysics, 18, 735-750, 2011 Author(s): M. Bocquet The main intrinsic source of error in the ensemble Kalman filter (EnKF) is sampling error. External sources of error, such as model error or deviations from Gaussianity, depend on the dynamical properties of the model. Sampling errors can lead to instability of the filter which, as a consequence, often requires inflation and localization. The goal of this article is to derive an ensemble Kalman filter which is less sensitive to sampling errors. A prior probability density function conditional on the forecast ensemble is derived using Bayesian principles. Even though this prior is built upon the assumption that the ensemble is Gaussian-distributed, it is different from the Gaussian probability density function defined by the empirical mean and the empirical error covariance matrix of the ensemble, which is implicitly used in traditional EnKFs. This new prior generates a new class of ensemble Kalman filters, called finite-size ensemble Kalman filter (EnKF-N). One deterministic variant, the finite-size ensemble transform Kalman filter (ETKF-N), is derived. It is tested on the Lorenz '63 and Lorenz '95 models. In this context, ETKF-N is shown to be stable without inflation for ensemble size greater than the model unstable subspace dimension, at the same numerical cost as the ensemble transform Kalman filter (ETKF). One variant of ETKF-N seems to systematically outperform the ETKF with optimally tuned inflation. However it is shown that ETKF-N does not account for all sampling errors, and necessitates localization like any EnKF, whenever the ensemble size is too small. In order to explore the need for inflation in this small ensemble size regime, a local version of the new class of filters is defined (LETKF-N) and tested on the Lorenz '95 toy model. Whatever the size of the ensemble, the filter is stable. Its performance without inflation is slightly inferior to that of LETKF with optimally tuned inflation for small interval between updates, and superior to LETKF with optimally tuned inflation for large time interval between updates.

Beschreibung: Three-dimensional parameterizations of the synoptic scale kinetic energy and momentum flux in the Earth's atmosphere Nonlinear Processes in Geophysics, 18, 807-827, 2011 Author(s): D. Coumou, V. Petoukhov, and A. V. Eliseev We present a new set of statistical-dynamical equations (SDEs) which can accurately reproduce the three-dimensional atmospheric fields of synoptic scale kinetic energy and momentum flux. The set of equations is closed by finding proper parameterizations for the vertical macro-turbulent diffusion coefficient and ageostrophic terms. The equations have been implemented in a new SD atmosphere model, named Aeolus . We show that the synoptic scale kinetic energy and momentum fluxes generated by the model are in good agreement with empirical data, which were derived from bandpass-filtered ERA-40 data. In addition to present-day climate, the model is tested for substantially colder (last glacial maximum) and warmer (2×CO 2 ) climates, and shown to be in agreement with general circulation model (GCM) results. With the derived equations, one can efficiently study the position and strength of storm tracks under different climate scenarios with calculation time a fraction of those of GCMs. This work prepares ground for the development of a new generation of fast Earth System Models of Intermediate Complexity which are able to perform multi-millennia simulations in a reasonable time frame while appropriately accounting for the climatic effect of storm tracks.

Beschreibung: Scaling properties of pH fluctuations in coastal waters of the English Channel: pH as a turbulent active scalar Nonlinear Processes in Geophysics, 18, 829-839, 2011 Author(s): S. B. Zongo and F. G. Schmitt We consider here pH and temperature fluctuations in marine waters, recorded at fixed points using high resolution automatic devices. We analyze time series coming from 4 monitoring stations located along French coast: one station is situated in the coastal area off Boulogne-sur-mer (Eastern English Channel) and 3 stations in the Bay of Seine. All these pH time series reveal large fluctuations at all scales similar to turbulent temperature fluctuations. We compare the pH and temperature time series through Fourier spectral analysis methods: spectra, compensated spectra, cospectra. We find good scaling properties of pH fluctuations, with power spectral slopes close to 1.5 for marine stations and 1.2 for the estuarine station. These analyses show that pH fluctuations in marine waters are strongly influenced by turbulent hydrodynamical transport, and may be considered as a turbulent active scalar.

Beschreibung: Three-dimensional magnetic reconnection through a moving magnetic null Nonlinear Processes in Geophysics, 18, 871-882, 2011 Author(s): V. S. Lukin and M. G. Linton A computational study of three-dimensional magnetic reconnection between two flux ropes through a moving reconnection site is presented. The configuration is considered in the context of two interacting spheromaks constrained by a perfectly conducting cylindrical boundary and oriented to form a single magnetic field null at its center. The initial magnetic field configuration is embedded into a uniform thermal plasma and is unstable to tilting. As the spheromaks tilt, their magnetic fields begin to reconnect at the null, subsequently displacing both the null and the reconnection site. The motion of the reconnection region and the magnetic null are shown to be correlated, with stronger correlation and faster reconnection observed in plasmas with lower thermal to magnetic pressure ratio. It is also shown that ion inertial effects allow for yet faster reconnection, but do not qualitatively change the dynamics of the process. Implications of the coupling between moving magnetic nulls and reconnection sites, as well as of possible mechanisms for fast reconnection through a moving reconnection region, are discussed. The simulations are conducted using both single-fluid and Hall MHD plasma models within the HiFi multi-fluid modeling framework.

Beschreibung: Discerning connectivity from dynamics in climate networks Nonlinear Processes in Geophysics, 18, 751-763, 2011 Author(s): M. Paluš, D. Hartman, J. Hlinka, and M. Vejmelka The bias due to dynamical memory (serial correlations) in an association/dependence measure (absolute cross-correlation) is demonstrated in model data and identified in time series of meteorological variables used for construction of climate networks. Accounting for such bias in inferring links of the climate network markedly changes the network topology and allows to observe previously hidden phenomena in climate network evolution.

Beschreibung: Lagrangian transport in a circular lake: effect of nonlinearity and the second vertical mode Nonlinear Processes in Geophysics, 18, 765-778, 2011 Author(s): T. Sakai and L. G. Redekopp Effects of the second vertical mode and nonlinearity of the background flow field on the Lagrangian transport of particle clouds are studied by employing a wind-forced linear hydrostatic model and a weakly-nonlinear, weakly-nonhydrostatic evolution model. It is confirmed that Kelvin waves primarily advect particles near the basin perimeter in a cyclonic direction, and Poincaré waves primarily advect particles in off-shore (radial) directions in a manner that is oscillatory in time with frequencies near the inertial period. The internal current associated with the second vertical mode is usually far smaller than that associated with the energetically dominant, lowest vertical mode. However, because of the disparately slow eigenspeed of the vertical mode-two Kelvin wave, the resultant particle transport associated with the vertical mode-two flow near the basin perimeter can drive transport that is comparable with that associated with the Kelvin wave of the lowest vertical mode. It is discovered that nonlinear interaction between the Kelvin-Poincaré wave pair can give birth to a solitary-like wave of large amplitude in an off-shore region. This new type of wave generates a large current and co-propagates with the Kelvin wave in a cyclonic direction and, eventually, can cause a burst of particle transport in an off-shore direction.

Beschreibung: Preface "Nonlinear plasma waves in space and laboratories" Nonlinear Processes in Geophysics, 18, 609-610, 2011 Author(s): B. Tsurutani and G. Morales No Abstract available.

Beschreibung: Dynamical changes of the polar cap potential structure: an information theory approach Nonlinear Processes in Geophysics, 18, 697-707, 2011 Author(s): I. Coco, G. Consolini, E. Amata, M. F. Marcucci, and D. Ambrosino Some features, such as vortex structures often observed through a wide spread of spatial scales, suggest that ionospheric convection is turbulent and complex in nature. Here, applying concepts from information theory and complex system physics, we firstly evaluate a pseudo Shannon entropy, H , associated with the polar cap potential obtained from the Super Dual Auroral Radar Network (SuperDARN) and, then, estimate the degree of disorder and the degree of complexity of ionospheric convection under different Interplanetary Magnetic Field (IMF) conditions. The aforementioned quantities are computed starting from time series of the coefficients of the 4th order spherical harmonics expansion of the polar cap potential for three periods, characterised by: (i) steady IMF B z 〉 0, (ii) steady IMF B z 〈 0 and (iii) a double rotation from negative to positive and then positive to negative B z . A neat dynamical topological transition is observed when the IMF B z turns from negative to positive and vice versa, pointing toward the possible occurrence of an order/disorder phase transition, which is the counterpart of the large scale convection rearrangement and of the increase of the global coherence. This result has been confirmed by applying the same analysis to a larger data base of about twenty days of SuperDARN data, allowing to investigate the role of IMF B y too.

Beschreibung: Frequency distributions: from the sun to the earth Nonlinear Processes in Geophysics, 18, 791-805, 2011 Author(s): N. B. Crosby The space environment is forever changing on all spatial and temporal scales. Energy releases are observed in numerous dynamic phenomena (e.g. solar flares, coronal mass ejections, solar energetic particle events) where measurements provide signatures of the dynamics. Parameters (e.g. peak count rate, total energy released, etc.) describing these phenomena are found to have frequency size distributions that follow power-law behavior. Natural phenomena on Earth, such as earthquakes and landslides, display similar power-law behavior. This suggests an underlying universality in nature and poses the question of whether the distribution of energy is the same for all these phenomena. Frequency distributions provide constraints for models that aim to simulate the physics and statistics observed in the individual phenomenon. The concept of self-organized criticality (SOC), also known as the "avalanche concept", was introduced by Bak et al. (1987, 1988), to characterize the behavior of dissipative systems that contain a large number of elements interacting over a short range. The systems evolve to a critical state in which a minor event starts a chain reaction that can affect any number of elements in the system. It is found that frequency distributions of the output parameters from the chain reaction taken over a period of time can be represented by power-laws. During the last decades SOC has been debated from all angles. New SOC models, as well as non-SOC models have been proposed to explain the power-law behavior that is observed. Furthermore, since Bak's pioneering work in 1987, people have searched for signatures of SOC everywhere. This paper will review how SOC behavior has become one way of interpreting the power-law behavior observed in natural occurring phenomenon in the Sun down to the Earth.

Beschreibung: A possible theory for the interaction between convective activities and vortical flows Nonlinear Processes in Geophysics, 18, 779-789, 2011 Author(s): N. Zhao, X. Y. Shen, Y. H. Ding, and M. Takahashi Theoretical studies usually attribute convections to the developments of instabilities such as the static or symmetric instabilities of the basic flows. However, the following three facts make the validities of these basic theories unconvincing. First, it seems that in most cases the basic flow with balance property cannot exist as the exact solution, so one cannot formulate appropriate problems of stability. Second, neither linear nor nonlinear theories of dynamical instability are able to describe a two-way interaction between convection and its background, because the basic state which must be an exact solution of the nonlinear equations of motion is prescribed in these issues. And third, the dynamical instability needs some extra initial disturbance to trigger it, which is usually another point of uncertainty. The present study suggests that convective activities can be recognized in the perspective of the interaction of convection with vortical flow. It is demonstrated that convective activities can be regarded as the superposition of free modes of convection and the response to the forcing induced by the imbalance of the unstably stratified vortical flow. An imbalanced vortical flow provides not only an initial condition from which unstable free modes of convection can develop but also a forcing on the convection. So, convection is more appropriately to be regarded as a spontaneous phenomenon rather than a disturbance-triggered phenomenon which is indicated by any theory of dynamical instability. Meanwhile, convection, particularly the forced part, has also a reaction on the basic flow by preventing the imbalance of the vortical flow from further increase and maintaining an approximately balanced flow.

Beschreibung: A Barnes-Hut scheme for simulating fault slip Nonlinear Processes in Geophysics, 18, 133-146, 2011 Author(s): N. M. Beeler and T. E. Tullis To account for natural spatial and temporal complexity, large-scale, long-duration calculations are required for simulations of seismicity in fault zones that host large earthquakes. Without advances in computational methods, the rate of progress in "earthquake simulator" models and associated earthquake forecasts is limited by the rates at which computer speed and storage increase. To explore improvements in computational efficiency we develop the first implementation of the Barnes-Hut algorithm (Barnes and Hut, 1986) to calculate elastic interactions in a fault model. The Barnes-Hut method is an efficient, numerical scheme that treats local forces exactly and distant forces approximately. The approach is illustrated in example simulations of non-linear fault strength in plane strain. Rudimentary error analysis indicates that efficient calculations, where execution time scales with number of grid points ( N ) as N log N , can be conducted routinely with errors on the order of 0.1%. We expect the Barnes-Hut method to be well suited for conducting initial exploration of parameter space for fault simulations with non-linear constitutive equations, and for efficient calculations of stress interaction in complex fault systems.

Beschreibung: Chaotic behavior in the flow along a wedge modeled by the Blasius equation Nonlinear Processes in Geophysics, 18, 171-178, 2011 Author(s): B. Basu, E. Foufoula-Georgiou, and A. S. Sharma The Blasius equation describes the properties of steady-state two dimensional boundary layer forming over a semi-infinite plate parallel to a unidirectional flow field. The flow is governed by a modified Blasius equation when the surface is aligned along the flow. In this paper, we demonstrate using numerical solution, that as the wedge angle increases, bifurcation occurs in the nonlinear Blasius equation and the dynamics becomes chaotic leading to non-convergence of the solution once the angle exceeds a critical value of 22°. This critical value is found to be in agreement with experimental results showing the development of shock waves in the medium and also with analytical results showing multiple solutions for wedge angles exceeding a critical value. Finally, we provide a derivation of the equation governing the boundary layer flow for wedge angles exceeding the critical angle at the onset of chaos.

Beschreibung: Post-processing through linear regression Nonlinear Processes in Geophysics, 18, 147-160, 2011 Author(s): B. Van Schaeybroeck and S. Vannitsem Various post-processing techniques are compared for both deterministic and ensemble forecasts, all based on linear regression between forecast data and observations. In order to evaluate the quality of the regression methods, three criteria are proposed, related to the effective correction of forecast error, the optimal variability of the corrected forecast and multicollinearity. The regression schemes under consideration include the ordinary least-square (OLS) method, a new time-dependent Tikhonov regularization (TDTR) method, the total least-square method, a new geometric-mean regression (GM), a recently introduced error-in-variables (EVMOS) method and, finally, a "best member" OLS method. The advantages and drawbacks of each method are clarified. These techniques are applied in the context of the 63 Lorenz system, whose model version is affected by both initial condition and model errors. For short forecast lead times, the number and choice of predictors plays an important role. Contrarily to the other techniques, GM degrades when the number of predictors increases. At intermediate lead times, linear regression is unable to provide corrections to the forecast and can sometimes degrade the performance (GM and the best member OLS with noise). At long lead times the regression schemes (EVMOS, TDTR) which yield the correct variability and the largest correlation between ensemble error and spread, should be preferred.

Beschreibung: Multi-scale interactions of geological processes during mineralization: cascade dynamics model and multifractal simulation Nonlinear Processes in Geophysics, 18, 161-170, 2011 Author(s): L. Yao and Q. Cheng Relations between mineralization and certain geological processes are established mostly by geologist's knowledge of field observations. However, these relations are descriptive and a quantitative model of how certain geological processes strengthen or hinder mineralization is not clear, that is to say, the mechanism of the interactions between mineralization and the geological framework has not been thoroughly studied. The dynamics behind these interactions are key in the understanding of fractal or multifractal formations caused by mineralization, among which singularities arise due to anomalous concentration of metals in narrow space. From a statistical point of view, we think that cascade dynamics play an important role in mineralization and studying them can reveal the nature of the various interactions throughout the process. We have constructed a multiplicative cascade model to simulate these dynamics. The probabilities of mineral deposit occurrences are used to represent direct results of mineralization. Multifractal simulation of probabilities of mineral potential based on our model is exemplified by a case study dealing with hydrothermal gold deposits in southern Nova Scotia, Canada. The extent of the impacts of certain geological processes on gold mineralization is related to the scale of the cascade process, especially to the maximum cascade division number n max . Our research helps to understand how the singularity occurs during mineralization, which remains unanswered up to now, and the simulation may provide a more accurate distribution of mineral deposit occurrences that can be used to improve the results of the weights of evidence model in mapping mineral potential.

Beschreibung: Effect of thermal pressure on upward plasma fluxes due to ponderomotive force of Alfvén waves Nonlinear Processes in Geophysics, 18, 235-241, 2011 Author(s): A. K. Nekrasov and F. Z. Feygin We consider the action of the ponderomotive force of low-frequency Alfvén waves on the distribution of the background plasma. It is assumed that the ponderomotive force for traveling waves arises as a result of the background inhomogeneity of medium under study. Expressions for the ponderomotive force obtained in this paper differ from previous analogous results. The induced magnetic moment of medium is taken into account. It is shown that the well-known Pitayevsky's formula for the magnetic moment is not complete. The role of the induced nonlinear thermal pressure in the evolution of the background plasma is considered. We give estimations for plasma displacement due to the long- and short-acting nonlinear wave perturbations. Some discussion of the ponderomotive action of standing waves is provided.

Beschreibung: On the Kalman Filter error covariance collapse into the unstable subspace Nonlinear Processes in Geophysics, 18, 243-250, 2011 Author(s): A. Trevisan and L. Palatella When the Extended Kalman Filter is applied to a chaotic system, the rank of the error covariance matrices, after a sufficiently large number of iterations, reduces to N + + N 0 where N + and N 0 are the number of positive and null Lyapunov exponents. This is due to the collapse into the unstable and neutral tangent subspace of the solution of the full Extended Kalman Filter. Therefore the solution is the same as the solution obtained by confining the assimilation to the space spanned by the Lyapunov vectors with non-negative Lyapunov exponents. Theoretical arguments and numerical verification are provided to show that the asymptotic state and covariance estimates of the full EKF and of its reduced form, with assimilation in the unstable and neutral subspace (EKF-AUS) are the same. The consequences of these findings on applications of Kalman type Filters to chaotic models are discussed.

Beschreibung: Debye-scale solitary structures measured in a beam-plasma laboratory experiment Nonlinear Processes in Geophysics, 18, 41-47, 2011 Author(s): B. Lefebvre, L.-J. Chen, W. Gekelman, P. Kintner, J. Pickett, P. Pribyl, and S. Vincena Solitary electrostatic pulses have been observed in numerous places of the magnetosphere such as the vicinity of reconnection current sheets, shocks or auroral current systems, and are often thought to be generated by energetic electron beams. We present results of a series of experiments conducted at the UCLA large plasma device (LAPD) where a suprathermal electron beam was injected parallel to a static magnetic field. Micro-probes with tips smaller than a Debye length enabled the detection of solitary pulses with positive electric potential and half-widths 4–25 Debye lengths (λ De ), over a set of experiments with various beam energies, plasma densities and magnetic field strengths. The shape, scales and amplitudes of the structures are similar to those observed in space, and consistent with electron holes. The dependance of these properties on the experimental parameters is shown. The velocities of the solitary structures (1–3 background electron thermal velocities) are found to be much lower than the beam velocities, suggesting an excitation mechanism driven by parallel currents associated to the electron beam.

Beschreibung: Earthquake forecasting based on data assimilation: sequential Monte Carlo methods for renewal point processes Nonlinear Processes in Geophysics, 18, 49-70, 2011 Author(s): M. J. Werner, K. Ide, and D. Sornette Data assimilation is routinely employed in meteorology, engineering and computer sciences to optimally combine noisy observations with prior model information for obtaining better estimates of a state, and thus better forecasts, than achieved by ignoring data uncertainties. Earthquake forecasting, too, suffers from measurement errors and partial model information and may thus gain significantly from data assimilation. We present perhaps the first fully implementable data assimilation method for earthquake forecasts generated by a point-process model of seismicity. We test the method on a synthetic and pedagogical example of a renewal process observed in noise, which is relevant for the seismic gap hypothesis, models of characteristic earthquakes and recurrence statistics of large quakes inferred from paleoseismic data records. To address the non-Gaussian statistics of earthquakes, we use sequential Monte Carlo methods, a set of flexible simulation-based methods for recursively estimating arbitrary posterior distributions. We perform extensive numerical simulations to demonstrate the feasibility and benefits of forecasting earthquakes based on data assimilation.

Beschreibung: Role of multifractal analysis in understanding the preparation zone for large size earthquake in the North-Western Himalaya region Nonlinear Processes in Geophysics, 18, 111-118, 2011 Author(s): S. S. Teotia and D. Kumar Seismicity has power law in space, time and magnitude distributions and same is expressed by the fractal dimension D , Omori's exponent p and b -value. The spatio-temporal patterns of epicenters have heterogeneous characteristics. As the crust gets self-organised into critical state, the spatio-temporal clustering of epicenters emerges to heterogeneous nature of seismicity. To understand the heterogeneous characteristics of seismicity in a region, multifractal studies hold promise to characterise the dynamics of region. Multifractal study is done on seismicity data of the North-Western Himalaya region which mainly involve seismogenic region of 1905 Kangra great earthquake in the North-Western Himalaya region. The seismicity data obtained from USGS catalogue for time period 1973–2009 has been analysed for the region which includes the October 2005 Muzafrabad-Kashmir earthquake ( M w =7.6). Significant changes have been observed in generalised dimension D q , D q spectra and b -value. The significant temporal changes in generalised dimension D q , b -value and D q −q spectra prior to occurrence of Muzaffrabad-Kashmir earthquake relates to distribution of epicenters in the region. The decrease in generalised dimension and b -value observed in our study show the relationship with the clustering of seismicity as is expected in self-organised criticality behaviour of earthquake occurrences. Such study may become important in understanding the preparation zone of large and great size earthquake in various tectonic regions.

Beschreibung: Singular value decomposition (SVD) for extraction of gravity anomaly associated with gold mineralization in Tongshi gold field, Western Shandong Uplifted Block, Eastern China Nonlinear Processes in Geophysics, 18, 103-109, 2011 Author(s): B. B. Zhao and Y. Q. Chen A singular value decomposition (SVD) program on MATLAB platform was effectively used to handle gravity signals for the Tongshi gold field. Firstly, the gravity signals were decomposed into different eigenimages with the help of singular value decomposition method (SVD). Secondly, the thresholds between the eigenvalues reflecting different layers of ore-controlling factors were established by multi-fractal method. Finally images reflecting different layers of ore-controlling factors were rebuilt. This yielded two layers of two-dimensional singular value images that depict regional and local ore-controlling factors, respectively. 1. The regional ore-controlling factor is a saddle valley with the gravity anomaly values varying from −55 to 51 μm s −2 on the NW trending swell with the gravity anomaly values varying from −55 to 567 μm s −2 on the SW side of the Mesozoic volcanic sedimentary basin with the gravity anomaly values varying from −56 to −974 μm s −2 . The saddle valley might be tectonically an extensional area where the Tongshi complex pluton and all gold deposits are located and thus this area is favorable for gold deposits. 2. The local ore-controlling factor is the Tongshi complex pluton with a negative circular gravity anomaly varying from −339 to −11 μm s −2 and the ring contact metasomatic mineralization zone around the Tongshi complex with the positive gravity anomaly varying from 37 to 345 μm s −2 . The skarn and porphyry types of gold deposits are located within the complex pluton and the Carlin and cryptobreccia types of gold deposits are located within the contact metasomatic mineralization zone. Thus both of them are potential areas for gold deposits. 3. The Tongshi gold field exhibits a typical complexity with multi-layers of ore-controlling factors.

Beschreibung: Atmospheric gravity waves in the Red Sea: a new hotspot Nonlinear Processes in Geophysics, 18, 71-79, 2011 Author(s): J. M. Magalhaes, I. B. Araújo, J. C. B. da Silva, R. H. J. Grimshaw, K. Davis, and J. Pineda The region of the Middle East around the Red Sea (between 32° E and 44° E longitude and 12° N and 28° N latitude) is a currently undocumented hotspot for atmospheric gravity waves (AGWs). Satellite imagery shows evidence that this region is prone to relatively high occurrence of AGWs compared to other areas in the world, and reveals the spatial characteristics of these waves. The favorable conditions for wave propagation in this region are illustrated with three typical cases of AGWs propagating in the lower troposphere over the sea. Using weakly nonlinear long wave theory and the observed characteristic wavelengths we obtain phase speeds which are consistent with those observed and typical for AGWs, with the Korteweg-de Vries theory performing slightly better than Benjamin-Davis-Acrivos-Ono theory as far as phase speeds are concerned. ERS-SAR and Envisat-ASAR satellite data analysis between 1993 and 2008 reveals signatures consistent with horizontally propagating large-scale internal waves. These signatures cover the entire Red Sea and are more frequently observed between April and September, although they also occur during the rest of the year. The region's (seasonal) propagation conditions for AGWs, based upon average vertical atmospheric stratification profiles suggest that many of the signatures identified in the satellite images are atmospheric internal waves.

Beschreibung: Strongly nonlinear, simple internal waves in continuously-stratified, shallow fluids Nonlinear Processes in Geophysics, 18, 91-102, 2011 Author(s): L. A. Ostrovsky and K. R. Helfrich Strongly nonlinear internal waves in a layer with arbitrary stratification are considered in the hydrostatic approximation. It is shown that "simple waves" having a variable vertical structure can emerge from a wide class of initial conditions. The equations describing such waves have been obtained using the isopycnal coordinate as a variable. Emergence of simple waves from an initial Gaussian impulse is numerically investigated for different density profiles, from two- and three-layer structure to the continuous one. Besides the first mode, examples of second- and third-mode simple waves are given.

Beschreibung: Fractal behavior in continental crustal heat production Nonlinear Processes in Geophysics, 18, 119-124, 2011 Author(s): N. Vedanti, R. P. Srivastava, O. P. Pandey, and V. P. Dimri The distribution of crustal heat production, which is the most important component in the elucidation of continental thermal structure, still remains a theoretical assumption. In general the heat production values must decrease with depth, but the form of decrease of heat production in the crust is not well understood. The commonly used heat production models are: "block model", in which heat production is constant from the surface to a given depth and the "exponential model", in which heat production diminishes as an exponential function of depth. The exponential model is more widely used wherein sources of the errors are heterogeneity of rock and long wavelength changes due to changes in lithology and tectonic elements, and as such exponential distribution does not work satisfactorily for the entire crust. In the present study, we analyze for the first time, deep crustal heat production data of six global areas namely Dharwar craton (India), Kaapvaal craton (South Africa), Baltic shield (Kola, Russia), Hidaka metamorphic belt (Japan), Nissho pluton (Japan) and Continental Deep Drilling site (KTB, Germany). The power spectrum of all the studied data sets exhibits power law behaviour. This would mean slower decay of heat production with depth, which conforms to the known geologic composition of the crust. Minimum value of the scaling exponent has been found for the KTB borehole, which is apparently related to higher heat production of gneisses, however for other study areas, scaling exponent is almost similar. We also found that the lower values of scaling exponents are related to higher heat production in the crust as is the case in KTB. Present finding has a direct relevance in computation of temperature-depth profiles in continental regions.

Beschreibung: Hidden semi-Markov Model based earthquake classification system using Weighted Finite-State Transducers Nonlinear Processes in Geophysics, 18, 81-89, 2011 Author(s): M. Beyreuther and J. Wassermann Automatic earthquake detection and classification is required for efficient analysis of large seismic datasets. Such techniques are particularly important now because access to measures of ground motion is nearly unlimited and the target waveforms (earthquakes) are often hard to detect and classify. Here, we propose to use models from speech synthesis which extend the double stochastic models from speech recognition by integrating a more realistic duration of the target waveforms. The method, which has general applicability, is applied to earthquake detection and classification. First, we generate characteristic functions from the time-series. The Hidden semi-Markov Models are estimated from the characteristic functions and Weighted Finite-State Transducers are constructed for the classification. We test our scheme on one month of continuous seismic data, which corresponds to 370 151 classifications, showing that incorporating the time dependency explicitly in the models significantly improves the results compared to Hidden Markov Models.

Beschreibung: Reply to Roe and Baker's comment on "Another look at climate sensitivity" by Zaliapin and Ghil (2010) Nonlinear Processes in Geophysics, 18, 129-131, 2011 Author(s): I. Zaliapin and M. Ghil G. H. Roe and M. B. Baker (hereafter R&B) claim that analysis of a global linear approximation to the climate system allows one to conclude that the quest for reliable climate predictions is futile. We insist that this quest is important and requires a proper understanding of the roles of both linear and nonlinear methods in climate dynamics.

Beschreibung: Comment on "Another look at climate sensitivity" by Zaliapin and Ghil (2010) Nonlinear Processes in Geophysics, 18, 125-127, 2011 Author(s): G. H. Roe and M. B. Baker Zaliapin and Ghil (hereafter, ZG) claim that the linearity of the climate feedback model in Roe and Baker (2007) (hereafter, RB) invalidates our derivation of the well-known skewed shapes of published probability distributions (pdfs) of climate sensitivity. We show here that linearity is fully justified. Nonlinearity could be of some importance only if the focus is on exotic and improbable events, which appear to be the focus of ZG, instead of the sensitivity pdfs, which were the focus of RB.

Beschreibung: Interactions between marine biota and ENSO: a conceptual model analysis Nonlinear Processes in Geophysics, 18, 29-40, 2011 Author(s): M. Heinemann, A. Timmermann, and U. Feudel We develop a conceptual coupled atmosphere-ocean-ecosystem model for the tropical Pacific to investigate the interaction between marine biota and the El Niño-Southern Oscillation (ENSO). Ocean and atmosphere are represented by a two-box model for the equatorial Pacific cold tongue and the warm pool, including a simplified mixed layer scheme. Marine biota are represented by a three-component (nutrient, phytoplankton, and zooplankton) ecosystem model. The atmosphere-ocean model exhibits an oscillatory state which qualitatively captures the main physics of ENSO. During an ENSO cycle, the variation of nutrient upwelling, and, to a small extent, the variation of photosynthetically available radiation force an ecosystem oscillation. The simplified ecosystem in turn, due to the effect of phytoplankton on the absorption of shortwave radiation in the water column, leads to (1) a warming of the tropical Pacific, (2) a reduction of the ENSO amplitude, and (3) a prolongation of the ENSO period. We qualitatively investigate these bio-physical coupling mechanisms using continuation methods. It is demonstrated that bio-physical coupling may play a considerable role in modulating ENSO variability.

Beschreibung: Is the Atlantic Multidecadal Oscillation (AMO) a statistical phantom? Nonlinear Processes in Geophysics, 18, 469-475, 2011 Author(s): M. Vincze and I. M. Jánosi In this work we critically compare the consequences of two assumptions on the physical nature of the AMO index signal. First, we show that the widely used approach based on red noise statistics cannot fully reproduce the empirical correlation properties of the record. Second, we consider a process of long range power-law correlations and demonstrate its better fit to the AMO signal. We show that in the latter case, the multidecadal oscillatory mode of the smoothed AMO index with an assigned period length of 50–70 years can be a simple statistical artifact, a consequence of limited record length. In this respect, a better term to describe the observed fluctuations of a smooth power-law spectrum is Atlantic Multidecadal Variability (AMV).

Beschreibung: Weighted complex networks applied to seismicity: the Itoiz dam (Northern Spain) Nonlinear Processes in Geophysics, 18, 477-487, 2011 Author(s): A. Jiménez and F. Luzón On 18 September 2004, an earthquake of magnitude mbLg = 4.6 was recorded near the Itoiz dam (Northern Spain). It occurred after the first impoundment of the reservoir and has been catalogued by some authors as induced seismicity. We analyzed the seismicity in the region as weighted complex networks and tried to differentiate this event from others that occurred nearby. We calculated the main topological features of the networks formed by the seismic clusters and compared them. We compared the results with a series of simulations, and showed that the clusters were better modelled with the Epidemic-Type Aftershock Sequence (ETAS) model than with random models. We found that the properties of the different clusters are grouped according to the magnitude of the main shocks and the number of events in each cluster, and that no distinct feature could be obtained for the 18 September 2004 series. We found that the nodes with the highest strength are the most important in the networks' traffic, and are associated with the events with the highest magnitude within the clusters.

Beschreibung: Scaling of peak flows with constant flow velocity in random self-similar networks Nonlinear Processes in Geophysics, 18, 489-502, 2011 Author(s): R. Mantilla, V. K. Gupta, and B. M. Troutman A methodology is presented to understand the role of the statistical self-similar topology of real river networks on scaling, or power law, in peak flows for rainfall-runoff events. We created Monte Carlo generated sets of ensembles of 1000 random self-similar networks (RSNs) with geometrically distributed interior and exterior generators having parameters p i and p e , respectively. The parameter values were chosen to replicate the observed topology of real river networks. We calculated flow hydrographs in each of these networks by numerically solving the link-based mass and momentum conservation equation under the assumption of constant flow velocity. From these simulated RSNs and hydrographs, the scaling exponents β and φ characterizing power laws with respect to drainage area, and corresponding to the width functions and flow hydrographs respectively, were estimated. We found that, in general, φ 〉 β, which supports a similar finding first reported for simulations in the river network of the Walnut Gulch basin, Arizona. Theoretical estimation of β and φ in RSNs is a complex open problem. Therefore, using results for a simpler problem associated with the expected width function and expected hydrograph for an ensemble of RSNs, we give heuristic arguments for theoretical derivations of the scaling exponents β (E) and φ (E) that depend on the Horton ratios for stream lengths and areas. These ratios in turn have a known dependence on the parameters of the geometric distributions of RSN generators. Good agreement was found between the analytically conjectured values of β (E) and φ (E) and the values estimated by the simulated ensembles of RSNs and hydrographs. The independence of the scaling exponents φ (E) and φ with respect to the value of flow velocity and runoff intensity implies an interesting connection between unit hydrograph theory and flow dynamics. Our results provide a reference framework to study scaling exponents under more complex scenarios of flow dynamics and runoff generation processes using ensembles of RSNs.

Beschreibung: Perturbing a Weather Generator using change factors derived from Regional Climate Model simulations Nonlinear Processes in Geophysics, 18, 503-511, 2011 Author(s): P. D. Jones, C. Harpham, C. M. Goodess, and C. G. Kilsby The purpose of this paper is to provide a method for perturbing Weather Generators (WGs) for future decades and to assess its effectiveness. Here the procedure is applied to the WG implemented within the UKCP09 package and assessed using data from a Regional Climate Model (RCM) simulation which provides a significant "climate change" between a control run period and a distant future. The WG is normally calibrated on observed data. For this study, data from an RCM control period (1961–1990) was used, then perturbed using the procedure. Because only monthly differences between the RCM control and scenario periods are used to perturb the WG, the direct daily RCM scenario may be considered as unseen data to assess how well the perturbation procedure reproduces the direct RCM simulations for the future.

Beschreibung: Bayesian estimation of the self-similarity exponent of the Nile River fluctuation Nonlinear Processes in Geophysics, 18, 441-446, 2011 Author(s): S. Benmehdi, N. Makarava, N. Benhamidouche, and M. Holschneider The aim of this paper is to estimate the Hurst parameter of Fractional Gaussian Noise (FGN) using Bayesian inference. We propose an estimation technique that takes into account the full correlation structure of this process. Instead of using the integrated time series and then applying an estimator for its Hurst exponent, we propose to use the noise signal directly. As an application we analyze the time series of the Nile River, where we find a posterior distribution which is compatible with previous findings. In addition, our technique provides natural error bars for the Hurst exponent.

Beschreibung: Extreme events: dynamics, statistics and prediction Nonlinear Processes in Geophysics, 18, 295-350, 2011 Author(s): M. Ghil, P. Yiou, S. Hallegatte, B. D. Malamud, P. Naveau, A. Soloviev, P. Friederichs, V. Keilis-Borok, D. Kondrashov, V. Kossobokov, O. Mestre, C. Nicolis, H. W. Rust, P. Shebalin, M. Vrac, A. Witt, and I. Zaliapin We review work on extreme events, their causes and consequences, by a group of European and American researchers involved in a three-year project on these topics. The review covers theoretical aspects of time series analysis and of extreme value theory, as well as of the deterministic modeling of extreme events, via continuous and discrete dynamic models. The applications include climatic, seismic and socio-economic events, along with their prediction. Two important results refer to (i) the complementarity of spectral analysis of a time series in terms of the continuous and the discrete part of its power spectrum; and (ii) the need for coupled modeling of natural and socio-economic systems. Both these results have implications for the study and prediction of natural hazards and their human impacts.

Beschreibung: Multifractal two-scale Cantor set model for slow solar wind turbulence in the outer heliosphere during solar maximum Nonlinear Processes in Geophysics, 18, 287-294, 2011 Author(s): W. M. Macek and A. Wawrzaszek To quantify solar wind turbulence, we consider a generalized two-scale weighted Cantor set with two different scales describing nonuniform distribution of the kinetic energy flux between cascading eddies of various sizes. We examine generalized dimensions and the corresponding multifractal singularity spectrum depending on one probability measure parameter and two rescaling parameters. In particular, we analyse time series of velocities of the slow speed streams of the solar wind measured in situ by Voyager 2 spacecraft in the outer heliosphere during solar maximum at various distances from the Sun: 10, 30, and 65 AU. This allows us to look at the evolution of multifractal intermittent scaling of the solar wind in the distant heliosphere. Namely, it appears that while the degree of multifractality for the solar wind during solar maximum is only weakly correlated with the heliospheric distance, but the multifractal spectrum could substantially be asymmetric in a very distant heliosphere beyond the planetary orbits. Therefore, one could expect that this scaling near the frontiers of the heliosphere should rather be asymmetric. It is worth noting that for the model with two different scaling parameters a better agreement with the solar wind data is obtained, especially for the negative index of the generalized dimensions. Therefore we argue that there is a need to use a two-scale cascade model. Hence we propose this model as a useful tool for analysis of intermittent turbulence in various environments and we hope that our general asymmetric multifractal model could shed more light on the nature of turbulence.

Beschreibung: Northern Hemisphere patterns of phase coherence between solar/geomagnetic activity and NCEP/NCAR and ERA40 near-surface air temperature in period 7–8 years oscillatory modes Nonlinear Processes in Geophysics, 18, 251-260, 2011 Author(s): M. Paluš and D. Novotná Beginning from the 1950's, Paluš and Novotná (2009) observed statistically significant phase coherence among oscillatory modes with the period of approximately 7–8 years detected in monthly time series of sunspot numbers, geomagnetic activity aa index, North Atlantic Oscillation (NAO) index and near-surface air temperature from several mid-latitude European stations. Focusing on geographical distribution of the phenomenon we study Northern Hemisphere patterns of phase coherence between solar/geomagnetic activity and NCEP/NCAR and ERA40 near-surface air temperature. Both the reanalysis datasets provide consistent patterns of areas with marked phase coupling between solar/geomagnetic activity and climate variability observed in continuous monthly data, independent of the season, however, confined to the temporal scale related to the oscillatory periods about 7–8 years.

Beschreibung: 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.

Beschreibung: 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.

Beschreibung: 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.

Beschreibung: 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.

Beschreibung: 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.

Beschreibung: 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).

Beschreibung: 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.

Beschreibung: 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.

Beschreibung: 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.

Beschreibung: 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.

Beschreibung: 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.

Beschreibung: 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.

Beschreibung: 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.

Beschreibung: 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.

Beschreibung: 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.

Beschreibung: 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 .

Beschreibung: 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.

Beschreibung: 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.

Beschreibung: 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.

Beschreibung: 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.

Beschreibung: 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.

Beschreibung: 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.

Beschreibung: 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.

Beschreibung: 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.

Beschreibung: 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.

Beschreibung: 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.

Beschreibung: 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.

Beschreibung: 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.

Beschreibung: 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.

Beschreibung: 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.

Beschreibung: 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.

Beschreibung: 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.

Beschreibung: 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.

Beschreibung: 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.

Beschreibung: 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.

Beschreibung: 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 Brσ). It is shown experimentally that the distribution of the shoreline velocity does not depend on Brσ 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 Brσ 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.

Beschreibung: 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.

Beschreibung: During recent years, numerical ensemble prediction systems have become an important tool for estimating the uncertainties of dynamical and physical processes as represented in numerical weather models. The latest generation of limited area ensemble prediction systems (LAM-EPSs) allows for probabilistic forecasts at high resolution in both space and time. However, these systems still suffer from systematic deficiencies. Especially for nowcasting (0–6 h) applications the ensemble spread is smaller than the actual forecast error. This paper tries to generate probabilistic short range 2-m temperature forecasts by combining a state-of-the-art nowcasting method and a limited area ensemble system, and compares the results with statistical methods. The Integrated Nowcasting Through Comprehensive Analysis (INCA) system, which has been in operation at the Central Institute for Meteorology and Geodynamics (ZAMG) since 2006 (Haiden et al., 2011), provides short range deterministic forecasts at high temporal (15 min–60 min) and spatial (1 km) resolution. An INCA Ensemble (INCA-EPS) of 2-m temperature forecasts is constructed by applying a dynamical approach, a statistical approach, and a combined dynamic-statistical method. The dynamical method takes uncertainty information (i.e. ensemble variance) from the operational limited area ensemble system ALADIN-LAEF (Aire Limitée Adaptation Dynamique Développement InterNational Limited Area Ensemble Forecasting) which is running operationally at ZAMG (Wang et al., 2011). The purely statistical method assumes a well-calibrated spread-skill relation and applies ensemble spread according to the skill of the INCA forecast of the most recent past. The combined dynamic-statistical approach adapts the ensemble variance gained from ALADIN-LAEF with non-homogeneous Gaussian regression (NGR) which yields a statistical \mbox{correction} of the first and second moment (mean bias and dispersion) for Gaussian distributed continuous variables. Validation results indicate that all three methods produce sharp and reliable probabilistic 2-m temperature forecasts. However, the statistical and combined dynamic-statistical methods slightly outperform the pure dynamical approach, mainly due to the under-dispersive behavior of ALADIN-LAEF outside the nowcasting range. The training length does not have a pronounced impact on forecast skill, but a spread re-scaling improves the forecast skill substantially. Refinements of the statistical methods yield a slight further improvement.

Beschreibung: On the basis of ARTEMIS two-probe mission magnetic reconnection (MR) outflow associated magnetic fluctuations and turbulence are analyzed on 19 February 2011. In the deep-tail, at distances between X = 45 – 51 RE, evidence for reconnection associated plasma sheet thinning was found, accompanied by heating of the plasma sheet. Correlated flow and field reversals and the large-scale Hall-effect signatures indicated the presence of the reconnection X-line. Within fast reconnection plasma outflows, magnetic fluctuations exhibit the same spectral scaling features and kinked spectra as magnetic fluctuations in the solar wind or in various parts of geospace. It was shown that the proton scale magnetic fluctuations are constrained by oblique firehose, proton cyclotron and mirror instability thresholds. For parallel plasma β|| 〉 1, where the thresholds converge, perpendicular magnetic fluctuations are enhanced. Magnetic compressibility decreases with the distance to the neutral sheet, however, near the instability thresholds it is comparable to the values obtained in the solar wind.

Beschreibung: In the last few years, it has been shown that above-average rainfall and the following diffusion of excess water into subsurface structures is able to trigger earthquake swarms in the uppermost brittle portion of the Earth's crust. However, there is still an ongoing debate on whether the crust already needs to be in a critical-to-failure state or whether it is sufficient that water is transported rapidly within channels and veins of karst or similar geological formations to the underlying, earthquake-generating layers. Also unknown is the role of other forcing mechanisms, possible co-variables and probably necessary tectonic loading in the triggering process of earthquakes. Because of these problems, we do not use an explicit physical model but instead analyze the meteorological and geophysical data via sophisticated statistical models. \newline We are interested in the influence of a more complete set of possible forcing parameters, including the influence of synthetic earth tides, on the occurrence of earthquake swarms. In this context, regression models are the adequate tool, since the calculation of simple correlations can be confounded by the other variables. Since our outcome variable (the number of quakes) is a count, we use Poisson regression models that include the plausible assumption of a Poisson distribution for the counts. For this study, we use nearly continuous recordings of a seismic and meteorological network in the years 2002–2008 at Mt. Hochstaufen in SE-Bavaria. Our non-linear regression model reveals correlations between external forces and the triggering of earthquakes. In addition to the still dominant influence of rainfall, theoretical estimated tidal tilt show some weak influence on the swarm generation. However, the influence of the modeled trend functions shows that rain is by far not the most important forcing mechanism present in the data.

Beschreibung: Space weather is driven by the solar wind and many geospace storms and substorms are natural hazards with considerable societal impact. The dynamical and statistical features of these events are complicated because of the turbulent nature of their driver, the solar wind. Large-scale data sets of geospace storms and substorms are analysed for this study of the inherent statistical characteristics of extreme events in geospace. The detrended fluctuation analysis, based on the autocorrelation functions, is used and yields scaling behavior representing long-term correlations. The scaling function is represented by two exponents, arising due mainly to the presence of the largely coherent internal dynamics of the magnetosphere and the turbulent nature of the solar wind driver.

Beschreibung: Some features, such as vortex structures often observed through a wide spread of spatial scales, suggest that ionospheric convection is turbulent and complex in nature. Here, applying concepts from information theory and complex system physics, we firstly evaluate a pseudo Shannon entropy, H, associated with the polar cap potential obtained from the Super Dual Auroral Radar Network (SuperDARN) and, then, estimate the degree of disorder and the degree of complexity of ionospheric convection under different Interplanetary Magnetic Field (IMF) conditions. The aforementioned quantities are computed starting from time series of the coefficients of the 4th order spherical harmonics expansion of the polar cap potential for three periods, characterised by: (i) steady IMF Bz 〉 0, (ii) steady IMF Bz 〈 0 and (iii) a double rotation from negative to positive and then positive to negative Bz. A neat dynamical topological transition is observed when the IMF Bz turns from negative to positive and vice versa, pointing toward the possible occurrence of an order/disorder phase transition, which is the counterpart of the large scale convection rearrangement and of the increase of the global coherence. This result has been confirmed by applying the same analysis to a larger data base of about twenty days of SuperDARN data, allowing to investigate the role of IMF By too.

Beschreibung: 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.