ALBERT

Description: Beyond multifractional Brownian motion: new stochastic models for geophysical modelling Nonlinear Processes in Geophysics, 20, 643-655, 2013 Author(s): J. Lévy Véhel Multifractional Brownian motion (mBm) has proved to be a useful tool in various areas of geophysical modelling. Although a versatile model, mBm is of course not always an adequate one. We present in this work several other stochastic processes which could potentially be useful in geophysics. The first alternative type is that of self-regulating processes : these are models where the local regularity is a function of the amplitude, in contrast to mBm where it is tuned exogenously. We demonstrate the relevance of such models for digital elevation maps and for temperature records. We also briefly describe two other types of alternative processes, which are the counterparts of mBm and of self-regulating processes when the intensity of local jumps is considered in lieu of local regularity: multistable processes allow one to prescribe the local intensity of jumps in space/time, while this intensity is governed by the amplitude for self-stabilizing processes .

Description: Non-extensivity and long-range correlations in the earthquake activity at the West Corinth rift (Greece) Nonlinear Processes in Geophysics, 20, 713-724, 2013 Author(s): G. Michas, F. Vallianatos, and P. Sammonds In the present work the statistical properties of the earthquake activity in a highly seismic region, the West Corinth rift (Central Greece), are being studied by means of generalized statistical physics. By using a dataset that covers the period 2001–2008, we investigate the earthquake energy distribution and the distribution of the time intervals (interevent times) between the successive events. As has been reported previously, these distributions exhibit complex statistical properties and fractality. By using detrended fluctuation analysis (DFA), a well-established method for detection of long-range correlations in non-stationary signals, it is shown that long-range correlations are also present in the earthquake activity. The existence of these properties motivates us to use non-extensive statistical physics (NESP) to investigate the statistical properties of the frequency-magnitude and the interevent time distributions, along with other well-known relations in seismology, such as the gamma distribution for interevent times. The results of the analysis indicate that the statistical properties of the earthquake activity can be successfully reproduced by means of NESP and that the earthquake activity at the West Corinth rift is correlated at all-time scales.

Description: The impact of initial spread calibration on the RELO ensemble and its application to Lagrangian dynamics Nonlinear Processes in Geophysics, 20, 621-641, 2013 Author(s): M. Wei, G. Jacobs, C. Rowley, C. N. Barron, P. Hogan, P. Spence, O. M. Smedstad, P. Martin, P. Muscarella, and E. Coelho A number of real-time ocean model forecasts were carried out successfully at Naval Research Laboratory (NRL) to provide modeling support and numerical guidance to the CARTHE GLAD at-sea experiment during summer 2012. Two RELO ensembles and three single models using NCOM and HYCOM with different resolutions were carried out. A calibrated ensemble system with enhanced spread and reliability was developed to better support this experiment. The calibrated ensemble is found to outperform the un-calibrated ensemble in forecasting accuracy, skill, and reliability for all the variables and observation spaces evaluated. The metrics used in this paper include RMS error, anomaly correlation, PECA, Brier score, spread reliability, and Talagrand rank histogram. It is also found that even the un-calibrated ensemble outperforms the single forecast from the model with the same resolution. The advantages of the ensembles are further extended to the Lagrangian framework. In contrast to a single model forecast, the RELO ensemble provides not only the most likely Lagrangian trajectory for a particle in the ocean, but also an uncertainty estimate that directly reflects the complicated ocean dynamics, which is valuable for decision makers. The examples show that the calibrated ensemble with more reliability can capture trajectories in different, even opposite, directions, which would be missed by the un-calibrated ensemble. The ensembles are applied to compute the repelling and attracting Lagrangian coherent structures (LCSs), and the uncertainties of the LCSs, which are hard to obtain from a single model forecast, are estimated. It is found that the spatial scales of the LCSs depend on the model resolution. The model with the highest resolution produces the finest, small-scale, LCS structures, while the model with lowest resolution generates only large-scale LCSs. The repelling and attracting LCSs are found to intersect at many locations and create complex mesoscale eddies. The fluid particles and drifters in the middle of these tangles are subject to attraction and repulsion simultaneously from these two kinds of LCSs. As a result, the movements of particles near the Deepwater Horizon (DWH) location are severely limited. This is also confirmed by the Lagrangian trajectories predicted by the ensembles.

Description: Multifractal properties of embedded convective structures in orographic precipitation: toward subgrid-scale predictability Nonlinear Processes in Geophysics, 20, 605-620, 2013 Author(s): M. Nogueira, A. P. Barros, and P. M. A. Miranda Rain and cloud fields produced by fully nonlinear idealized cloud resolving numerical simulations of orographic convective precipitation display statistical multiscaling behavior, implying that multifractal diagnostics should provide a physically robust basis for the downscaling and sub-grid scale parameterizations of moist processes. Our results show that the horizontal scaling exponent function (and respective multiscaling parameters) of the simulated rainfall and cloud fields varies with atmospheric and terrain properties, particularly small-scale terrain spectra, atmospheric stability, and advective timescale. This implies that multifractal diagnostics of moist processes for these simulations are fundamentally transient, exhibiting complex nonlinear behavior depending on atmospheric conditions and terrain forcing at each location. A particularly robust behavior found here is the transition of the multifractal parameters between stable and unstable cases, which has a clear physical correspondence to the transition from stratiform to organized (banded and cellular) convective regime. This result is reinforced by a similar behavior in the horizontal spectral exponent. Finally, our results indicate that although nonlinearly coupled fields (such as rain and clouds) have different scaling exponent functions, there are robust relationships with physical underpinnings between the scaling parameters that can be explored for hybrid dynamical-statistical downscaling.

Description: A top-down model to generate ensembles of runoff from a large number of hillslopes Nonlinear Processes in Geophysics, 20, 683-704, 2013 Author(s): P. R. Furey, V. K. Gupta, and B. M. Troutman We hypothesize that total hillslope water loss for a rainfall–runoff event is inversely related to a function of a lognormal random variable, based on basin- and point-scale observations taken from the 21 km 2 Goodwin Creek Experimental Watershed (GCEW) in Mississippi, USA. A top-down approach is used to develop a new runoff generation model both to test our physical-statistical hypothesis and to provide a method of generating ensembles of runoff from a large number of hillslopes in a basin. The model is based on the assumption that the probability distributions of a runoff/loss ratio have a space–time rescaling property. We test this assumption using streamflow and rainfall data from GCEW. For over 100 rainfall–runoff events, we find that the spatial probability distributions of a runoff/loss ratio can be rescaled to a new distribution that is common to all events. We interpret random within-event differences in runoff/loss ratios in the model to arise from soil moisture spatial variability. Observations of water loss during events in GCEW support this interpretation. Our model preserves water balance in a mean statistical sense and supports our hypothesis. As an example, we use the model to generate ensembles of runoff at a large number of hillslopes for a rainfall–runoff event in GCEW.

Description: A mechanism for catastrophic filter divergence in data assimilation for sparse observation networks Nonlinear Processes in Geophysics, 20, 705-712, 2013 Author(s): G. A. Gottwald and A. J. Majda We study catastrophic filter divergence in data assimilation procedures whereby the forecast model develops severe numerical instabilities leading to a blow-up of the solution. Catastrophic filter divergence can occur in sparse observational grids with small observational noise for intermediate observation intervals and finite ensemble sizes. Using a minimal five-dimensional model, we establish that catastrophic filter divergence is a numerical instability of the underlying forecast model caused by the filtering procedure producing analyses which are not consistent with the true dynamics, and stiffness caused by the fast attraction of the inconsistent analyses towards the attractor during the forecast step.

Description: Sub-inertial modulation of nonlinear Kelvin waves in the coastal zone Nonlinear Processes in Geophysics, 20, 357-364, 2013 Author(s): D. V. Stepanov and V. V. Novotryasov Observational evidence is presented for interaction between nonlinear internal Kelvin waves at the ω t,i (where the ω t is the semidiurnal frequency and the ω i is the inertial frequency) and random oscillations of the background coastal current at the sub-inertial Ω frequency in the Japan/East Sea. Enhanced coastal currents at the sum ω + and difference ω-frequencies ω ± =ω t,i ± Ω have properties of propagating Kelvin waves, which suggests permanent energy exchange from the sub-inertial band to the mesoscale ω ± band. This interaction may be responsible for a greater-than-predicted intensification, steepening and breaking of boundary-trapped Kelvin waves. The problem of interaction between the nonlinear Kelvin wave at the frequency ω and the low-frequency narrowband noise with representative frequency Ω≪ω is investigated using the theory of nonlinear weak dispersion waves.

Description: Application of wavelet transform for evaluation of hydrocarbon reservoirs: example from Iranian oil fields in the north of the Persian Gulf Nonlinear Processes in Geophysics, 20, 231-238, 2013 Author(s): M. R. Saadatinejad and H. Hassani The Persian Gulf and its surrounding area are some of the biggest basins and have a very important role in producing huge amounts of hydrocarbon, and this potential was evaluated in order to explore the target for geoscientists and petroleum engineers. Wavelet transform is a useful and applicable technique to reveal frequency contents of various signals in different branches of science and especially in petroleum studies. We applied two major capacities of continuous mode of wavelet transform in seismic investigations. These investigations were operated to detect reservoir geological structures and some anomalies related to hydrocarbon to develop and explore new petroleum reservoirs in at least 4 oilfields in the southwest of Iran. It had been observed that continuous wavelet transform results show some discontinuities in the location of faults and are able to display them more clearly than other seismic methods. Moreover, continuous wavelet transform, utilizing Morlet wavelet, displays low-frequency shadows on 4 different iso-frequency vertical sections to identify reservoirs containing gas. By comparing these different figures, the presence of low-frequency shadows under the reservoir could be seen and we can relate these variations from anomalies at different frequencies as an indicator of the presence of hydrocarbons in the target reservoir.

Description: Distributed allocation of mobile sensing swarms in gyre flows Nonlinear Processes in Geophysics, 20, 657-668, 2013 Author(s): K. Mallory, M. A. Hsieh, E. Forgoston, and I. B. Schwartz We address the synthesis of distributed control policies to enable a swarm of homogeneous mobile sensors to maintain a desired spatial distribution in a geophysical flow environment, or workspace. In this article, we assume the mobile sensors (or robots) have a "map" of the environment denoting the locations of the Lagrangian coherent structures or LCS boundaries. Using this information, we design agent-level hybrid control policies that leverage the surrounding fluid dynamics and inherent environmental noise to enable the team to maintain a desired distribution in the workspace. We discuss the stability properties of the ensemble dynamics of the distributed control policies. Since realistic quasi-geostrophic ocean models predict double-gyre flow solutions, we use a wind-driven multi-gyre flow model to verify the feasibility of the proposed distributed control strategy and compare the proposed control strategy with a baseline deterministic allocation strategy. Lastly, we validate the control strategy using actual flow data obtained by our coherent structure experimental testbed.

Description: Four-dimensional ensemble-variational data assimilation for global deterministic weather prediction Nonlinear Processes in Geophysics, 20, 669-682, 2013 Author(s): M. Buehner, J. Morneau, and C. Charette The goal of this study is to evaluate a version of the ensemble-variational data assimilation approach (EnVar) for possible replacement of 4D-Var at Environment Canada for global deterministic weather prediction. This implementation of EnVar relies on 4-D ensemble covariances, obtained from an ensemble Kalman filter, that are combined in a vertically dependent weighted average with simple static covariances. Verification results are presented from a set of data assimilation experiments over two separate 6-week periods that used assimilated observations and model configuration very similar to the currently operational system. To help interpret the comparison of EnVar versus 4D-Var, additional experiments using 3D-Var and a version of EnVar with only 3-D ensemble covariances are also evaluated. To improve the rate of convergence for all approaches evaluated (including EnVar), an estimate of the cost function Hessian generated by the quasi-Newton minimization algorithm is cycled from one analysis to the next. Analyses from EnVar (with 4-D ensemble covariances) nearly always produce improved, and never degraded, forecasts when compared with 3D-Var. Comparisons with 4D-Var show that forecasts from EnVar analyses have either similar or better scores in the troposphere of the tropics and the winter extra-tropical region. However, in the summer extra-tropical region the medium-range forecasts from EnVar have either similar or worse scores than 4D-Var in the troposphere. In contrast, the 6 h forecasts from EnVar are significantly better than 4D-Var relative to radiosonde observations for both periods and in all regions. The use of 4-D versus 3-D ensemble covariances only results in small improvements in forecast quality. By contrast, the improvements from using 4D-Var versus 3D-Var are much larger. Measurement of the fit of the background and analyzed states to the observations suggests that EnVar and 4D-Var can both make better use of observations distributed over time than 3D-Var. In summary, the results from this study suggest that the EnVar approach is a viable alternative to 4D-Var, especially when the simplicity and computational efficiency of EnVar are considered. Additional research is required to understand the seasonal dependence of the difference in forecast quality between EnVar and 4D-Var in the extra-tropics.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: Large eddy simulation of sediment transport over rippled beds Nonlinear Processes in Geophysics, 21, 1169-1184, 2014 Author(s): J. C. Harris and S. T. Grilli Wave-induced boundary layer (BL) flows over sandy rippled bottoms are studied using a numerical model that applies a one-way coupling of a "far-field" inviscid flow model to a "near-field" large eddy simulation (LES) Navier–Stokes (NS) model. The incident inviscid velocity and pressure fields force the LES, in which near-field, wave-induced, turbulent bottom BL flows are simulated. A sediment suspension and transport model is embedded within the coupled flow model. The numerical implementation of the various models has been reported elsewhere, where we showed that the LES was able to accurately simulate both mean flow and turbulent statistics for oscillatory BL flows over a flat, rough bed. Here we show that the model accurately predicts the mean velocity fields and suspended sediment concentration for oscillatory flows over full-scale vortex ripples. Tests show that surface roughness has a significant effect on the results. Beyond increasing our insight into wave-induced oscillatory bottom BL physics, sophisticated coupled models of sediment transport such as that presented have the potential to make quantitative predictions of sediment transport and erosion/accretion around partly buried objects in the bottom, which is important for a vast array of bottom deployed instrumentation and other practical ocean engineering problems.

Description: Dependence of sandpile avalanche frequency–size distribution on coverage extent and compactness of embedded toppling threshold heterogeneity: implications for the variation of Gutenberg–Richter b value Nonlinear Processes in Geophysics, 21, 1185-1193, 2014 Author(s): L.-Y. Chiao and Q. Liu The effects of the spatiotemporal evolution of failure threshold heterogeneity on the dynamics of fault criticality, and thus on regional seismogenesis, have attracted strong interest in the field of regional seismotectonics. The heterogeneity might be a manifestation of the macroscopic distribution and multiscale strength variation of asperities, the distinct regional stress level, and (microscopically) heterogeneous fault surface roughness or friction regimes. In this study, rather than attempting to mimic the complex microscale slipping physics on a fault surface, sandpile cellular automata were implemented with a straightforward toppling rule. The objective is to examine the influence of distinct configurations of the embedded heterogeneous toppling threshold field on the global system avalanche event statistics. The examination results revealed that increasing the coverage extent and decreasing the compactness of the heterogeneous failure threshold, rather than the magnitude, range of contrast, diversity, or the geometric configuration of the threshold heterogeneity, leads to a systematic increase in the scaling exponent of the avalanche event power law statistics, implying the importance of mutual interaction among toppling sites with distinct thresholds. For tectonic provinces with differing stress regimes evolving spatio temporally, it is postulated that the distinct extent and compactness of the heterogeneous failure threshold are critical factors that manifest in the reported dynamic variations of seismicity scaling.

Description: Instability and change detection in exponential families and generalized linear models, with a study of Atlantic tropical storms Nonlinear Processes in Geophysics, 21, 1133-1143, 2014 Author(s): Y. Lu and S. Chatterjee Exponential family statistical distributions, including the well-known normal, binomial, Poisson, and exponential distributions, are overwhelmingly used in data analysis. In the presence of covariates, an exponential family distributional assumption for the response random variables results in a generalized linear model. However, it is rarely ensured that the parameters of the assumed distributions are stable through the entire duration of the data collection process. A failure of stability leads to nonsmoothness and nonlinearity in the physical processes that result in the data. In this paper, we propose testing for stability of parameters of exponential family distributions and generalized linear models. A rejection of the hypothesis of stable parameters leads to change detection. We derive the related likelihood ratio test statistic. We compare the performance of this test statistic to the popular normal distributional assumption dependent cumulative sum (Gaussian CUSUM) statistic in change detection problems. We study Atlantic tropical storms using the techniques developed here, so to understand whether the nature of these tropical storms has remained stable over the last few decades.

Description: 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).

Description: 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.

Description: 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.

Description: 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.

Description: Spatial patterns of linear and nonparametric long-term trends in Baltic sea-level variability Nonlinear Processes in Geophysics, 19, 95-111, 2012 Author(s): R. V. Donner, R. Ehrcke, S. M. Barbosa, J. Wagner, J. F. Donges, and J. Kurths The study of long-term trends in tide gauge data is important for understanding the present and future risk of changes in sea-level variability for coastal zones, particularly with respect to the ongoing debate on climate change impacts. Traditionally, most corresponding analyses have exclusively focused on trends in mean sea-level. However, such studies are not able to provide sufficient information about changes in the full probability distribution (especially in the more extreme quantiles). As an alternative, in this paper we apply quantile regression (QR) for studying changes in arbitrary quantiles of sea-level variability. For this purpose, we chose two different QR approaches and discuss the advantages and disadvantages of different settings. In particular, traditional linear QR poses very restrictive assumptions that are often not met in reality. For monthly data from 47 tide gauges from along the Baltic Sea coast, the spatial patterns of quantile trends obtained in linear and nonparametric (spline-based) frameworks display marked differences, which need to be understood in order to fully assess the impact of future changes in sea-level variability on coastal areas. In general, QR demonstrates that the general variability of Baltic sea-level has increased over the last decades. Linear quantile trends estimated for sliding windows in time reveal a wide-spread acceleration of trends in the median, but only localised changes in the rates of changes in the lower and upper quantiles.

Description: On closure parameter estimation in chaotic systems Nonlinear Processes in Geophysics, 19, 127-143, 2012 Author(s): J. Hakkarainen, A. Ilin, A. Solonen, M. Laine, H. Haario, J. Tamminen, E. Oja, and H. Järvinen Many dynamical models, such as numerical weather prediction and climate models, contain so called closure parameters. These parameters usually appear in physical parameterizations of sub-grid scale processes, and they act as "tuning handles" of the models. Currently, the values of these parameters are specified mostly manually, but the increasing complexity of the models calls for more algorithmic ways to perform the tuning. Traditionally, parameters of dynamical systems are estimated by directly comparing the model simulations to observed data using, for instance, a least squares approach. However, if the models are chaotic, the classical approach can be ineffective, since small errors in the initial conditions can lead to large, unpredictable deviations from the observations. In this paper, we study numerical methods available for estimating closure parameters in chaotic models. We discuss three techniques: off-line likelihood calculations using filtering methods, the state augmentation method, and the approach that utilizes summary statistics from long model simulations. The properties of the methods are studied using a modified version of the Lorenz 95 system, where the effect of fast variables are described using a simple parameterization.

Description: Comprehensive analysis of tornado statistics in comparison to earthquakes: intensity and temporal behaviour Nonlinear Processes in Geophysics, 20, 47-57, 2013 Author(s): L. Schielicke and P. Névir Tornadoes and earthquakes are characterised by a high variability in their properties concerning intensity, geometric properties and temporal behaviour. Earthquakes are known for power-law behaviour in their intensity (Gutenberg–Richter law) and temporal statistics (e.g. Omori law and interevent waiting times). The observed similarity of high variability of these two phenomena motivated us to compare the statistical behaviour of tornadoes using seismological methods and quest for power-law behaviour. In general, the statistics of tornadoes show power-law behaviour partly coextensive with characteristic scales when the temporal resolution is high (10 to 60 min). These characteristic scales match with the typical diurnal behaviour of tornadoes, which is characterised by a maximum of tornado occurrences in the late afternoon hours. Furthermore, the distributions support the observation that tornadoes cluster in time. Finally, we shortly discuss a possible similar underlying structure composed of heterogeneous, coupled, interactive threshold oscillators that possibly explains the observed behaviour.

Description: Quantifying soil complexity using network models of soil porous structure Nonlinear Processes in Geophysics, 20, 41-45, 2013 Author(s): M. Samec, A. Santiago, J. P. Cárdenas, R. M. Benito, A. M. Tarquis, S. J. Mooney, and D. Korošak This paper describes an investigation into the properties of spatially embedded complex networks representing the porous architecture of soil systems. We suggest an approach to quantify the complexity of soil pore structure based on the node-node link correlation properties of the networks. We show that the complexity depends on the strength of spatial embedding of the network and that this is related to the transition from a non-compact to compact phase of the network.

Description: Analysis of asymmetries in propagating mode-2 waves Nonlinear Processes in Geophysics, 20, 59-69, 2013 Author(s): J. Olsthoorn, A. Baglaenko, and M. Stastna Using numerical simulations performed with a pseudo-spectral incompressible Navier–Stokes solver, we describe the asymmetries that arise in the recirculating core of mode-2 internal, solitary-like waves. The waves are generated in a manner consistent with many laboratory studies, namely via the collapse of a region of mixed fluid. Analysis of the simulations reveals that asymmetries across both the wave crest and the pycnocline centre develop in the spatial distribution of density, kinetic energy and a passive tracer transported by the mode-2 waves. The simulations are extended to three-dimensions to allow for the formation of spanwise instabilities. We find that three-dimensionalization modifies the structure and energetics of the core, but that the majority of the results obtained from two dimensional simulations remain valid. Taken together, our simulations demonstrate that the cores of solitary-like mode-2 waves are different then their counterparts for mode-1 waves and that their accurate characterization on both lab and field scales should account for the core asymmetry across the pycnocline centre.

Description: Ion motion in the current sheet with sheared magnetic field – Part 1: Quasi-adiabatic theory Nonlinear Processes in Geophysics, 20, 163-178, 2013 Author(s): A. V. Artemyev, A. I. Neishtadt, and L. M. Zelenyi We present a theory of trapped ion motion in the magnetotail current sheet with a constant dawn–dusk component of the magnetic field. Particle trajectories are described analytically using the quasi-adiabatic invariant corresponding to averaging of fast oscillations around the tangential component of the magnetic field. We consider particle dynamics in the quasi-adiabatic approximation and demonstrate that the principal role is played by large (so called geometrical) jumps of the quasi-adiabatic invariant. These jumps appear due to the current sheet asymmetry related to the presence of the dawn–dusk magnetic field. The analytical description is compared with results of numerical integration. We show that there are four possible regimes of particle motion. Each regime is characterized by certain ranges of values of the dawn–dusk magnetic field and particle energy. We find the critical value of the dawn–dusk magnetic field, where jumps of the quasi-adiabatic invariant vanish.

Description: Conditioning model output statistics of regional climate model precipitation on circulation patterns Nonlinear Processes in Geophysics, 19, 623-633, 2012 Author(s): F. Wetterhall, F. Pappenberger, Y. He, J. Freer, and H. L. Cloke Dynamical downscaling of Global Climate Models (GCMs) through regional climate models (RCMs) potentially improves the usability of the output for hydrological impact studies. However, a further downscaling or interpolation of precipitation from RCMs is often needed to match the precipitation characteristics at the local scale. This study analysed three Model Output Statistics (MOS) techniques to adjust RCM precipitation; (1) a simple direct method (DM), (2) quantile-quantile mapping (QM) and (3) a distribution-based scaling (DBS) approach. The modelled precipitation was daily means from 16 RCMs driven by ERA40 reanalysis data over the 1961–2000 provided by the ENSEMBLES (ENSEMBLE-based Predictions of Climate Changes and their Impacts) project over a small catchment located in the Midlands, UK. All methods were conditioned on the entire time series, separate months and using an objective classification of Lamb's weather types. The performance of the MOS techniques were assessed regarding temporal and spatial characteristics of the precipitation fields, as well as modelled runoff using the HBV rainfall-runoff model. The results indicate that the DBS conditioned on classification patterns performed better than the other methods, however an ensemble approach in terms of both climate models and downscaling methods is recommended to account for uncertainties in the MOS methods.

Description: A typical wave wake from high-speed vessels: its group structure and run-up Nonlinear Processes in Geophysics, 20, 179-188, 2013 Author(s): I. Didenkulova and A. Rodin High-amplitude water waves induced by high-speed vessels are regularly observed in Tallinn Bay, the Baltic Sea, causing intense beach erosion and disturbing marine habitants in the coastal zone. Such a strong impact on the coast may be a result of a certain group structure of the wave wake. In order to understand it, here we present an experimental study of the group structure of these wakes at Pikakari beach, Tallinn Bay. The most energetic vessel waves at this location (100 m from the coast at the water depth 2.7 m) have amplitudes of about 1 m and periods of 8–10 s and cause maximum run-up heights on a beach up to 1.4 m. These waves represent frequency modulated packets where the largest and longest waves propagate ahead of other smaller amplitude and period waves. Sometimes the groups of different heights and periods can be separated even within one wave wake event. The wave heights within a wake are well described by the Weibull distribution, which has different parameters for wakes from different vessels. Wave run-up heights can also be described by Weibull distribution and its parameters can be connected to the parameters of the distribution of wave heights 100 m from the coast. Finally, the run-up of individual waves within a packet is studied. It is shown that the specific structure of frequency modulated wave packets, induced by high-speed vessels, leads to a sequence of high wave run-ups at the coast, even when the original wave heights are rather moderate. This feature can be a key to understanding the significant impact on coasts caused by fast vessels.

Description: Fractal analysis of ULF electromagnetic emissions in possible association with earthquakes in China Nonlinear Processes in Geophysics, 19, 577-583, 2012 Author(s): Y. Ida, D. Yang, Q. Li, H. Sun, and M. Hayakawa The long-term data (during the period of 1 March 2003 through 31 December 2006) of ULF geomagnetic variations observed at Kashi station (geographic coordinates: 39.5° N, 76.0° E) in China have been used to investigate the long-term variation of fractal dimension of ULF emissions. We have studied the changes in fractal dimension in association with several earthquakes around the observation station. It is then found that a significant change (or decrease) in the fractal dimension of the Z component took place before the 1 September 2003 earthquake, which lends a further support to our previous finding based on our improved polarization analysis for the same earthquake. The results obtained are discussed in the contexts of a few aspects (detectability of seismogenic emissions, comparison with previous results by other analysis methods, the importance of fractal analysis in the nonlinear process of the lithosphere and earthquake prediction).

Description: Predictability of a low-order interactive ensemble Nonlinear Processes in Geophysics, 19, 273-282, 2012 Author(s): L. Siqueira and B. Kirtman In this paper, numerical and analytical studies were performed to uncover the mechanisms controlling the changes in ensemble spread of a low-order coupled model with multiple atmospheric realizations. An interactive ensemble approach was applied to a coupled dynamical system based on two versions of the Lorenz 63 model designed in order to imitate the behavior of a coupled system with different time scales. In the dynamic system used in this work the spread of ensemble members is highly dependent on the mean state corresponding to asymmetries in predictability. The slowness of the slow model and the intensity of the boundary forcing anomalies both contribute to the asymmetry and phase locking of both subsystems. The mechanisms controlling the fast model spread were uncovered revealing uncertainty dynamics depending on the location of ensemble members in the fast model phase space and implicitly on the slowness and magnitude of the slow model anomalies.

Description: Interaction of a monopole vortex with an isolated topographic feature in a three-layer geophysical flow Nonlinear Processes in Geophysics, 20, 107-119, 2013 Author(s): E. A. Ryzhov and K. V. Koshel In the frame of a three-layer, quasi-geostrophic analytical model of an f -plane geophysical flow, the Lagrangian advection induced by the interaction of a monopole vortex with an isolated topographic feature is addressed. Two different cases when the monopole is located either within the upper or the middle layer are of our interest. In the bottom layer, there is a delta-function topographic feature, which generates a closed recirculation region in its vicinity due to the background flow. This recirculation region extends to the middle and upper layers, and it plays the role of a topographic vortex. The interaction between the monopole and the topographic vortex causes a complex, including chaotic, advection of fluid particles. We show that the model's parameters, namely the monopole and topographic vortices' strengths and initial positions, and the layers' depths and densities, are responsible for the diverse advection patterns. While the patterns are rather complicated, one can single out two major processes, which mostly govern the fluid particle advection. The first one is the variation in time of the system's phase space structure, so that within the closed region of the topographic vortex, there appear periodically unclosed particle pathways by which the particles leave the topographic vortex. The second one is chaotic advection that arises from the nonstationarity of the monopole–topography interaction.

Description: Characterization of turbulence stability through the identification of multifractional Brownian motions Nonlinear Processes in Geophysics, 20, 97-106, 2013 Author(s): K. C. Lee Multifractional Brownian motions have become popular as flexible models in describing real-life signals of high-frequency features in geoscience, microeconomics, and turbulence, to name a few. The time-changing Hurst exponent, which describes regularity levels depending on time measurements, and variance, which relates to an energy level, are two parameters that characterize multifractional Brownian motions. This research suggests a combined method of estimating the time-changing Hurst exponent and variance using the local variation of sampled paths of signals. The method consists of two phases: initially estimating global variance and then accurately estimating the time-changing Hurst exponent. A simulation study shows its performance in estimation of the parameters. The proposed method is applied to characterization of atmospheric stability in which descriptive statistics from the estimated time-changing Hurst exponent and variance classify stable atmosphere flows from unstable ones.

Description: A tri-stage cluster identification model for accurate analysis of seismic catalogs Nonlinear Processes in Geophysics, 20, 143-162, 2013 Author(s): S. J. Nanda, K. F. Tiampo, G. Panda, L. Mansinha, N. Cho, and A. Mignan In this paper we propose a tri-stage cluster identification model that is a combination of a simple single iteration distance algorithm and an iterative K-means algorithm. In this study of earthquake seismicity, the model considers event location, time and magnitude information from earthquake catalog data to efficiently classify events as either background or mainshock and aftershock sequences. Tests on a synthetic seismicity catalog demonstrate the efficiency of the proposed model in terms of accuracy percentage (94.81% for background and 89.46% for aftershocks). The close agreement between lambda and cumulative plots for the ideal synthetic catalog and that generated by the proposed model also supports the accuracy of the proposed technique. There is flexibility in the model design to allow for proper selection of location and magnitude ranges, depending upon the nature of the mainshocks present in the catalog. The effectiveness of the proposed model also is evaluated by the classification of events in three historic catalogs: California, Japan and Indonesia. As expected, for both synthetic and historic catalog analysis it is observed that the density of events classified as background is almost uniform throughout the region, whereas the density of aftershock events are higher near the mainshocks.

Description: Scaling for lobe and cleft patterns in particle-laden gravity currents Nonlinear Processes in Geophysics, 20, 121-130, 2013 Author(s): A. Jackson, B. Turnbull, and R. Munro Lobe and cleft patterns are frequently observed at the leading edge of gravity currents, including non-Boussinesq particle-laden currents such as powder snow avalanches. Despite the importance of the instability in driving air entrainment, little is known about its origin or the mechanisms behind its development. In this paper we seek to gain a better understanding of these mechanisms from a laboratory scale model of powder snow avalanches using lightweight granular material. The instability mechanisms in these flows appear to be a combination of those found in both homogeneous Boussinesq gravity currents and unsuspended granular flows, with the size of the granular particles playing a central role in determining the wavelength of the lobe and cleft pattern. When scaled by particle diameter a relationship between the Froude number and the wavelength of the lobe and cleft pattern is found, where the wavelength increases monotonically with the Froude number.

Description: Inversion of the western Pacific subtropical high dynamic model and analysis of dynamic characteristics for its abnormality Nonlinear Processes in Geophysics, 20, 131-142, 2013 Author(s): M. Hong, R. Zhang, J. X. Li, J. J. Ge, and K. F. Liu Based on time series data of 500 hPa potential field from NCEP/NCAR (National Center for Environmental Forecast of American/National Center for Atmospheric Research), a novel consideration of empirical orthogonal function (EOF) time–space separation and dynamic system reconstruction for time series is introduced. This method consists of two parts: first, the dynamical model inversion and model parameter optimization are carried out on the EOF time coefficient series using the genetic algorithm (GA), and, second, a nonlinear dynamic model representing the subtropical high (SH) activity and its abnormality is established. The SH activity and its abnormal mechanism is studied using the developed dynamical model. Results show that the configuration and diversification of the SH equilibriums have good correspondence with the actual short–medium term abnormal activity of the SH. Change of SH potential field brought by the combination of equilibriums is more complex than that by mutation, and their exhibition patterns are different. The mutation behavior from high-value to low-value equilibriums of the SH in summer corresponds with the southward drop of the SH in the observed weather process. The combination behavior of the two steady equilibriums corresponds with disappearance of the "double-ridge" phenomenon of the SH. Dynamical mechanisms of these phenomena are explained.

Description: Wavefield decomposition and phase space dynamics of the seismic noise at Volcàn de Colima, Mexico: evidence of a two-state source process Nonlinear Processes in Geophysics, 20, 71-84, 2013 Author(s): M. Palo and P. Cusano We analyse the seismic noise recorded at the Colima Volcano (Mexico) in the period December 2005–May 2006 by four broadband three-component seismic stations. Specifically, we characterize the spectral content of the signal and follow its time evolution along all the data set. Moreover, we infer the properties of the attractor in the phase space by false nearest neighbours analysis and Grassberger–Procaccia algorithm, and adopt a time-domain decomposition method (independent component analysis) to find the basic constituents (independent components) of the system. Constraints on the seismic wavefield are inferred by the polarization analysis. We find two states of the background seismicity visible in different time-intervals that are Phase A and Phase B. Phase A has a spectrum with two peaks at 0.15 Hz and 0.3 Hz, with the latter dominating, an attractor of correlation dimension close to 3, three quasi-monochromatic independent components, and a relevant fraction of crater-pointing polarization solutions in the near-field. In Phase B, the spectrum is preserved but with the highest peak at 0.15 Hz, the attractor has a correlation dimension close to 2, two independent components are extracted, and the polarization solutions are dominated by Rayleigh waves incoming from the southwest direction. We depict two sources acting on the background seismicity that are the microseismic noise loading on the Pacific coastline and a low-energy volcanic tremor. A change in the amplitude of the microseismic noise can induce the switching from a state of the system to the other.

Description: Review Article: "The Lagrangian description of aperiodic flows: a case study of the Kuroshio Current" Nonlinear Processes in Geophysics, 19, 449-472, 2012 Author(s): C. Mendoza and A. M. Mancho This article reviews several recently developed Lagrangian tools and shows how their combined use succeeds in obtaining a detailed description of purely advective transport events in general aperiodic flows. In particular, because of the climate impact of ocean transport processes, we illustrate a 2-D application on altimeter data sets over the area of the Kuroshio Current, although the proposed techniques are general and applicable to arbitrary time dependent aperiodic flows. The first challenge for describing transport in aperiodical time dependent flows is obtaining a representation of the phase portrait where the most relevant dynamical features may be identified. areas that are related to confinement regions. This representation is accomplished by using global Lagrangian descriptors that when applied for instance to the altimeter data sets retrieve over the ocean surface a phase portrait where the geometry of interconnected dynamical systems is visible. The phase portrait picture is essential because it evinces which transport routes are acting on the whole flow. Once these routes are roughly recognised, it is possible to complete a detailed description by the direct computation of the finite time stable and unstable manifolds of special hyperbolic trajectories that act as organising centres of the flow.

Description: Cosmic rays and stochastic magnetic reconnection in the heliotail Nonlinear Processes in Geophysics, 19, 351-364, 2012 Author(s): P. Desiati and A. Lazarian Galactic cosmic rays are believed to be generated by diffusive shock acceleration processes in Supernova Remnants, and the arrival direction is likely determined by the distribution of their sources throughout the Galaxy, in particular by the nearest and youngest ones. Transport to Earth through the interstellar medium is expected to affect the cosmic ray properties as well. However, the observed anisotropy of TeV cosmic rays and its energy dependence cannot be explained with diffusion models of particle propagation in the Galaxy. Within a distance of a few parsec, diffusion regime is not valid and particles with energy below about 100 TeV must be influenced by the heliosphere and its elongated tail. The observation of a highly significant localized excess region of cosmic rays from the apparent direction of the downstream interstellar flow at 1–10 TeV energies might provide the first experimental evidence that the heliotail can affect the transport of energetic particles. In particular, TeV cosmic rays propagating through the heliotail interact with the 100–300 AU wide magnetic field polarity domains generated by the 11 yr cycles. Since the strength of non-linear convective processes is expected to be larger than viscous damping, the plasma in the heliotail is turbulent. Where magnetic field domains converge on each other due to solar wind gradient, stochastic magnetic reconnection likely occurs. Such processes may be efficient enough to re-accelerate a fraction of TeV particles as long as scattering processes are not strong. Therefore, the fractional excess of TeV cosmic rays from the narrow region toward the heliotail direction traces sightlines with the lowest smearing scattering effects, that can also explain the observation of a harder than average energy spectrum.

Description: Calibration of a radiocarbon age Nonlinear Processes in Geophysics, 19, 345-350, 2012 Author(s): D. J. Keenan The calibration of a radiocarbon age to a calendar date is reviewed. It is shown that the commonly-used programs for calibration sometimes give results that are significantly in error.

Description: Magnetic transfer function entropy and the 2009 M w = 6.3 L'Aquila earthquake (Central Italy) Nonlinear Processes in Geophysics, 19, 401-409, 2012 Author(s): G. Cianchini, A. De Santis, D. R. Barraclough, L. X. Wu, and K. Qin With the aim of obtaining a deeper knowledge of the physical phenomena associated with the 2009 L'Aquila (Central Italy) seismic sequence, culminating with a M w = 6.3 earthquake on 6 April 2009, and possibly of identifying some kind of earthquake-related magnetic or geoelectric anomaly, we analyse the geomagnetic field components measured at the magnetic observatory of L'Aquila and their variations in time. In particular, trends of magnetic transfer functions in the years 2006–2010 are inspected. They are calculated from the horizontal to vertical magnetic component ratio in the frequency domain, and are very sensitive to deep and lateral geoelectric characteristics of the measurement site. Entropy analysis, carried out from the transfer functions with the so called transfer function entropy, points out clear temporal burst regimes of a few distinct harmonics preceding the main shock of the seismic sequence. A possible explanation is that they could be related to deep fluid migrations and/or to variations in the micro-/meso-fracturing that affected significantly the conductivity (ordered/disordered) distribution in a large lithospheric volume under the seismogenic layer below L'Aquila area. This interpretation is also supported by the analysis of hypocentres depths before the main shock occurrence.

Description: Haar wavelets, fluctuations and structure functions: convenient choices for geophysics Nonlinear Processes in Geophysics, 19, 513-527, 2012 Author(s): S. Lovejoy and D. Schertzer Geophysical processes are typically variable over huge ranges of space-time scales. This has lead to the development of many techniques for decomposing series and fields into fluctuations Δ v at well-defined scales. Classically, one defines fluctuations as differences: (Δ v diff = v(x +Δ x )- v(x) and this is adequate for many applications (Δ x is the "lag"). However, if over a range one has scaling Δ v ∝ Δ x H , these difference fluctuations are only adequate when 0 〈 H 〈 1. Hence, there is the need for other types of fluctuations. In particular, atmospheric processes in the "macroweather" range ≈10 days to 10–30 yr generally have −1 〈 H 〈 0, so that a definition valid over the range −1 〈 H 〈 1 would be very useful for atmospheric applications. A general framework for defining fluctuations is wavelets. However, the generality of wavelets often leads to fairly arbitrary choices of "mother wavelet" and the resulting wavelet coefficients may be difficult to interpret. In this paper we argue that a good choice is provided by the (historically) first wavelet, the Haar wavelet (Haar, 1910), which is easy to interpret and – if needed – to generalize, yet has rarely been used in geophysics. It is also easy to implement numerically: the Haar fluctuation (Δ v Haar at lag Δ x is simply equal to the difference of the mean from x to x + Δ x /2 and from x +Δ x /2 to x +Δ x . Indeed, we shall see that the interest of the Haar wavelet is this relation to the integrated process rather than its wavelet nature per se. Using numerical multifractal simulations, we show that it is quite accurate, and we compare and contrast it with another similar technique, detrended fluctuation analysis. We find that, for estimating scaling exponents, the two methods are very similar, yet Haar-based methods have the advantage of being numerically faster, theoretically simpler and physically easier to interpret.

Description: An experimental study of the Atlantic variability on interdecadal timescales Nonlinear Processes in Geophysics, 19, 335-343, 2012 Author(s): M. Vincze, I. M. Jánosi, E. Barsy, T. Tél, and A. Várai A series of laboratory experiments has been carried out to model the basic dynamics of the multidecadal variability observed in North Atlantic sea surface temperature (SST) records. According to the minimal numerical sector model introduced by te Raa and Dijkstra (2002), the three key components to excite such a low-frequency variability are rotation, meridional temperature gradient and additive thermal noise in the surface heat forcing. If these components are present, periodic perturbations of the overturning background flow are excited, leading to thermal Rossby mode like propagation of anomalous patches in the SST field. Our tabletop scale setup was built to capture this phenomenon, and to test whether the aforementioned three components are indeed sufficient to generate a low-frequency variability in the system. The results are compared to those of the numerical models, as well as to oceanic SST reanalysis records. To the best of our knowledge, the experiment described here is the very first to investigate the dynamics of the North Atlantic multidecadal variability in a laboratory-scale setup.

Description: Implicit particle filtering for models with partial noise, and an application to geomagnetic data assimilation Nonlinear Processes in Geophysics, 19, 365-382, 2012 Author(s): M. Morzfeld and A. J. Chorin Implicit particle filtering is a sequential Monte Carlo method for data assimilation, designed to keep the number of particles manageable by focussing attention on regions of large probability. These regions are found by minimizing, for each particle, a scalar function F of the state variables. Some previous implementations of the implicit filter rely on finding the Hessians of these functions. The calculation of the Hessians can be cumbersome if the state dimension is large or if the underlying physics are such that derivatives of F are difficult to calculate, as happens in many geophysical applications, in particular in models with partial noise, i.e. with a singular state covariance matrix. Examples of models with partial noise include models where uncertain dynamic equations are supplemented by conservation laws with zero uncertainty, or with higher order (in time) stochastic partial differential equations (PDE) or with PDEs driven by spatially smooth noise processes. We make the implicit particle filter applicable to such situations by combining gradient descent minimization with random maps and show that the filter is efficient, accurate and reliable because it operates in a subspace of the state space. As an example, we consider a system of nonlinear stochastic PDEs that is of importance in geomagnetic data assimilation.

Description: Grid preparation for magnetic and gravity data using fractal fields Nonlinear Processes in Geophysics, 19, 291-296, 2012 Author(s): M. Pilkington and P. Keating Most interpretive methods for potential field (magnetic and gravity) measurements require data in a gridded format. Many are also based on using fast Fourier transforms to improve their computational efficiency. As such, grids need to be full (no undefined values), rectangular and periodic. Since potential field surveys do not usually provide data sets in this form, grids must first be prepared to satisfy these three requirements before any interpretive method can be used. Here, we use a method for grid preparation based on a fractal model for predicting field values where necessary. Using fractal field values ensures that the statistical and spectral character of the measured data is preserved, and that unwanted discontinuities at survey boundaries are minimized. The fractal method compares well with standard extrapolation methods using gridding and maximum entropy filtering. The procedure is demonstrated on a portion of a recently flown aeromagnetic survey over a volcanic terrane in southern British Columbia, Canada.

Description: Identification of uranium targets based on airborne radiometric data analysis by using multifractal modeling, Tark and Avanligh 1:50 000 sheets, NW Iran Nonlinear Processes in Geophysics, 19, 283-289, 2012 Author(s): P. Afzal, A. Zia Zarifi, and A. Bijan Yasrebi Airborne geophysical anomaly separation using conventional statistics and the fractal/multifractal concentration-area (C-A) method has been applied to the Tark and Avanligh 1:50 000 sheets in NW Iran. The geophysical survey that resulted in the airborne geophysical data was conducted for uranium exploration in both areas. Selected anomalies were further investigated by using surface radiometric data. Firstly, threshold values to define anomalies were determined and compared by means of conventional statistical methods. Several relatively large anomalies were identified with uranium (U) equal to 1.7 eppm and 1.9 eppm in the Tark and Avanligh areas, respectively; locally these U anomalies have magnitudes exceeding 3.5 eppm in both areas. Log-log plots obtained for the C-A method indicate existence of two separate stages of U enrichment, with a major event being the cause of U concentration values above 6.1 and 3.4 eppm in the Tark and Avanligh areas, respectively. These higher intensity anomalies are located in the northwestern part of the Tark and in the southern part of the Avanligh sheets. In both areas, the C-A anomalies were further investigated using ground radiometric data and XRF analysis revealing higher than 150 and 280 ppm U concentration values in the two areas, respectively. Correlation between the anomalies and geological units show that the anomalies are associated with limestone and sandstone units.

Description: Reconnection studies under different types of turbulence driving Nonlinear Processes in Geophysics, 19, 297-314, 2012 Author(s): G. Kowal, A. Lazarian, E. T. Vishniac, and K. Otmianowska-Mazur We study a model of fast magnetic reconnection in the presence of weak turbulence proposed by Lazarian and Vishniac (1999) using three-dimensional direct numerical simulations. The model has been already successfully tested in Kowal et al. (2009) confirming the dependencies of the reconnection speed V rec on the turbulence injection power P inj and the injection scale l inj expressed by a constraint V rec ~ P inj 1/2 l inj 3/4 and no observed dependency on Ohmic resistivity. In Kowal et al. (2009), in order to drive turbulence, we injected velocity fluctuations in Fourier space with frequencies concentrated around k inj = 1/ l inj , as described in Alvelius (1999). In this paper, we extend our previous studies by comparing fast magnetic reconnection under different mechanisms of turbulence injection by introducing a new way of turbulence driving. The new method injects velocity or magnetic eddies with a specified amplitude and scale in random locations directly in real space. We provide exact relations between the eddy parameters and turbulent power and injection scale. We performed simulations with new forcing in order to study turbulent power and injection scale dependencies. The results show no discrepancy between models with two different methods of turbulence driving exposing the same scalings in both cases. This is in agreement with the Lazarian and Vishniac (1999) predictions. In addition, we performed a series of models with varying viscosity ν . Although Lazarian and Vishniac (1999) do not provide any prediction for this dependence, we report a weak relation between the reconnection speed with viscosity, V rec ~ ν −1/4 .

Description: Oscillating forcings and new regimes in the Lorenz system: a four-lobe attractor Nonlinear Processes in Geophysics, 19, 315-322, 2012 Author(s): V. Pelino, F. Maimone, and A. Pasini It has been shown that forced Lorenz models generally maintain their two-lobe structure, just giving rise to changes in the occurrence of their regimes. Here, using the richness of a unified formalism for Kolmogorov-Lorenz systems, we show that introducing oscillating forcings can lead to the birth of new regimes and to a four-lobe attractor. Analogies within a climate dynamics framework are mentioned.

Description: A 2-D FEM thermal model to simulate water flow in a porous media: Campi Flegrei caldera case study Nonlinear Processes in Geophysics, 19, 323-333, 2012 Author(s): V. Romano, U. Tammaro, and P. Capuano Volcanic and geothermal aspects both exist in many geologically young areas. In these areas the heat transfer process is of fundamental importance, so that the thermal and fluid-dynamic processes characterizing a viscous fluid in a porous medium are very important to understand the complex dynamics of the these areas. The Campi Flegrei caldera, located west of the city of Naples, within the central-southern sector of the large graben of Campanian plain, is a region where both volcanic and geothermal phenomena are present. The upper part of the geothermal system can be considered roughly as a succession of volcanic porous material (tuff) saturated by a mixture formed mainly by water and carbon dioxide. We have implemented a finite elements approach in transient conditions to simulate water flow in a 2-D porous medium to model the changes of temperature in the geothermal system due to magmatic fluid inflow, accounting for a transient phase, not considered in the analytical solutions and fluid compressibility. The thermal model is described by means of conductive/convective equations, in which we propose a thermal source represented by a parabolic shape function to better simulate an increase of temperature in the central part (magma chamber) of a box, simulating the Campi Flegrei caldera and using more recent evaluations, from literature, for the medium's parameters (specific heat capacity, density, thermal conductivity, permeability). A best-fit velocity for the permeant is evaluated by comparing the simulated temperatures with those measured in wells drilled by Agip (Italian Oil Agency) in the 1980s in the framework of geothermal exploration. A few tens of days are enough to reach the thermal steady state, showing the quick response of the system to heat injection. The increase in the pressure due to the heat transport is then used to compute ground deformation, in particular the vertical displacements characteristics of the Campi Flegrei caldera behaviour. The vertical displacements range from 1 cm to 10 cm in accordance with the mini uplift, characterizing the recent behaviour of the caldera. The time needed to move fluid particles from the bottom to the upper layer (years) is compatible with the timing of the mini uplift.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: Intrinsic low-frequency variability of the Gulf Stream Nonlinear Processes in Geophysics, 19, 155-164, 2012 Author(s): G. Quattrocchi, S. Pierini, and H. A. Dijkstra In this paper a process study aimed at analyzing the low-frequency variability of intrinsically oceanic origin of the Gulf Stream (GS) and GS extension (GSE) is presented. An eddy-permitting reduced-gravity nonlinear shallow water model is implemented in an idealized North Atlantic Ocean, with schematic boundaries including the essential geometric features of the coastline and a realistic zonal basin width at all latitudes. The forcing is provided by a time-independent climatological surface wind stress obtained from 41 years of monthly ECMWF fields. The model response yields strong intrinsic low-frequency fluctuations on the interannual to decadal time scales. The modelled time-averaged GS/GSE flows are found to exhibit several features that can also be deduced from satellite altimeter data, such as the Florida Current seaward deflection, the GS separation at Cape Hatteras, and the overall structure of the GSE. The intrinsic low-frequency variability yields two preferred states of the GSE differing in latitudinal location that also have their counterpart in the altimeter data. A preliminary analysis of the variability in terms of dynamical systems theory is carried out by using the lateral eddy viscosity as the control parameter. A complex transition sequence from a steady state to irregular low-frequency variability emerges, in which Hopf and global bifurcations can be identified.

Description: Collisionless magnetic reconnection in a plasmoid chain Nonlinear Processes in Geophysics, 19, 145-153, 2012 Author(s): S. Markidis, P. Henri, G. Lapenta, A. Divin, M. V. Goldman, D. Newman, and S. Eriksson The kinetic features of plasmoid chain formation and evolution are investigated by two dimensional Particle-in-Cell simulations. Magnetic reconnection is initiated in multiple X points by the tearing instability. Plasmoids form and grow in size by continuously coalescing. Each chain plasmoid exhibits a strong out-of plane core magnetic field and an out-of-plane electron current that drives the coalescing process. The disappearance of the X points in the coalescence process are due to anti-reconnection, a magnetic reconnection where the plasma inflow and outflow are reversed with respect to the original reconnection flow pattern. Anti-reconnection is characterized by the Hall magnetic field quadrupole signature. Two new kinetic features, not reported by previous studies of plasmoid chain evolution, are here revealed. First, intense electric fields develop in-plane normally to the separatrices and drive the ion dynamics in the plasmoids. Second, several bipolar electric field structures are localized in proximity of the plasmoid chain. The analysis of the electron distribution function and phase space reveals the presence of counter-streaming electron beams, unstable to the two stream instability, and phase space electron holes along the reconnection separatrices.

Description: Turbulence in a global magnetohydrodynamic simulation of the Earth's magnetosphere during northward and southward interplanetary magnetic field Nonlinear Processes in Geophysics, 19, 165-175, 2012 Author(s): M. El-Alaoui, R. L. Richard, M. Ashour-Abdalla, R. J. Walker, and M. L. Goldstein We report the results of MHD simulations of Earth's magnetosphere for idealized steady solar wind plasma and interplanetary magnetic field (IMF) conditions. The simulations feature purely northward and southward magnetic fields and were designed to study turbulence in the magnetotail plasma sheet. We found that the power spectral densities (PSDs) for both northward and southward IMF had the characteristics of turbulent flow. In both cases, the PSDs showed the three scale ranges expected from theory: the energy-containing scale, the inertial range, and the dissipative range. The results were generally consistent with in-situ observations and theoretical predictions. While the two cases studied, northward and southward IMF, had some similar characteristics, there were significant differences as well. For southward IMF, localized reconnection was the main energy source for the turbulence. For northward IMF, remnant reconnection contributed to driving the turbulence. Boundary waves may also have contributed. In both cases, the PSD slopes had spatial distributions in the dissipative range that reflected the pattern of resistive dissipation. For southward IMF there was a trend toward steeper slopes in the dissipative range with distance down the tail. For northward IMF there was a marked dusk-dawn asymmetry with steeper slopes on the dusk side of the tail. The inertial scale PSDs had a dusk-dawn symmetry during the northward IMF interval with steeper slopes on the dawn side. This asymmetry was not found in the distribution of inertial range slopes for southward IMF. The inertial range PSD slopes were clustered around values close to the theoretical expectation for both northward and southward IMF. In the dissipative range, however, the slopes were broadly distributed and the median values were significantly different, consistent with a different distribution of resistivity.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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).

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.