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

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

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

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

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

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

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

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

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

Description: Voyager 2 observation of the multifractal spectrum in the heliosphere and the heliosheath Nonlinear Processes in Geophysics, 20, 1061-1070, 2013 Author(s): W. M. Macek and A. Wawrzaszek We look in detail at the multifractal scaling of the fluctuations in the interplanetary magnetic field strength as measured onboard Voyager 2 in the entire heliosphere and even in the heliosheath. More specifically, we analyse the spectra observed by Voyager 2 in a wide range of solar activity cycles during the years 1980–2009 at various heliospheric latitudes and distances from 6 to 90 astronomical units (AU). We focus on the singularity multifractal spectrum before and after crossing the termination heliospheric shock by Voyager 2 at 84 AU from the Sun. In addition, we investigate here the parameters of the model that describe the asymmetry of the spectrum, depending on the solar cycle. It is worth noting that the spectrum is prevalently right-skewed inside the whole heliosphere. Moreover, we have possibly observed a change in the asymmetry of the spectrum at the termination shock. We show that the degree of multifractality is modulated by the solar activity. Hence these basic results also bring significant support to some earlier claims suggesting that the solar wind termination shock is asymmetric.

Description: A potential implicit particle method for high-dimensional systems Nonlinear Processes in Geophysics, 20, 1047-1060, 2013 Author(s): B. Weir, R. N. Miller, and Y. H. Spitz This paper presents a particle method designed for high-dimensional state estimation. Instead of weighing random forecasts by their distance to given observations, the method samples an ensemble of particles around an optimal solution based on the observations (i.e., it is implicit). It differs from other implicit methods because it includes the state at the previous assimilation time as part of the optimal solution (i.e., it is a lag-1 smoother). This is accomplished through the use of a mixture model for the background distribution of the previous state. In a high-dimensional, linear, Gaussian example, the mixture-based implicit particle smoother does not collapse. Furthermore, using only a small number of particles, the implicit approach is able to detect transitions in two nonlinear, multi-dimensional generalizations of a double-well. Adding a step that trains the sampled distribution to the target distribution prevents collapse during the transitions, which are strongly nonlinear events. To produce similar estimates, other approaches require many more particles.

Description: On the identification of Dragon Kings among extreme-valued outliers Nonlinear Processes in Geophysics, 20, 549-561, 2013 Author(s): M. Riva, S. P. Neuman, and A. Guadagnini Extreme values of earth, environmental, ecological, physical, biological, financial and other variables often form outliers to heavy tails of empirical frequency distributions. Quite commonly such tails are approximated by stretched exponential, log-normal or power functions. Recently there has been an interest in distinguishing between extreme-valued outliers that belong to the parent population of most data in a sample and those that do not. The first type, called Gray Swans by Nassim Nicholas Taleb (often confused in the literature with Taleb's totally unknowable Black Swans), is drawn from a known distribution of the tails which can thus be extrapolated beyond the range of sampled values. However, the magnitudes and/or space–time locations of unsampled Gray Swans cannot be foretold. The second type of extreme-valued outliers, termed Dragon Kings by Didier Sornette, may in his view be sometimes predicted based on how other data in the sample behave. This intriguing prospect has recently motivated some authors to propose statistical tests capable of identifying Dragon Kings in a given random sample. Here we apply three such tests to log air permeability data measured on the faces of a Berea sandstone block and to synthetic data generated in a manner statistically consistent with these measurements. We interpret the measurements to be, and generate synthetic data that are, samples from α-stable sub-Gaussian random fields subordinated to truncated fractional Gaussian noise (tfGn). All these data have frequency distributions characterized by power-law tails with extreme-valued outliers about the tail edges.

Description: Stability and nonlinear regimes of flow over a saturated porous medium Nonlinear Processes in Geophysics, 20, 543-547, 2013 Author(s): T. P. Lyubimova, D. T. Baydina, and D. V. Lyubimov The paper deals with the investigation of stability and nonlinear regimes of flow over the saturated porous medium applied to the problem of stability of water flow over the bottom covered with vegetation. It is shown that the velocity profile of steady plane-parallel flow has two inflection points, which results in instability of this flow. The neutral stability curves, the dependencies of critical Reynolds number and the wave number of most dangerous perturbations on the ratio of porous layer thickness to the total thickness are obtained. The nonlinear flow regimes are investigated numerically by finite difference method. It is found that at supercritical parameter values waves travelling in the direction of the base flow take place.

Description: Multifractal analysis of vertical profiles of soil penetration resistance at the field scale Nonlinear Processes in Geophysics, 20, 529-541, 2013 Author(s): G. M. Siqueira, E. F. F. Silva, A. A. A. Montenegro, E. Vidal Vázquez, and J. Paz-Ferreiro Soil penetration resistance (PR) is widely used as an indirect indicator of soil strength. Soil PR is linked to basic soil properties and correlated to root growth and plant production, and as such it is extensively used as a practical tool for assessing soil compaction and to evaluate the effects of soil management. This study investigates how results from multifractal analysis can quantify key elements of depth-dependent soil PR profiles and how this information can be used at the field scale. We analysed multifractality of 50 PR vertical profiles, measured from 0 to 60 cm depth and randomly located on a 6.5 ha sugar cane field in northeastern Brazil. The scaling property of each profile was typified by singularity, and Rényi spectra estimated by the method of moments. The Hurst exponent was used to parameterize the autocorrelation of the vertical PR data sets. The singularity and Rènyi spectra showed that the vertical PR data sets exhibited a well-defined multifractal structure. Hurst exponent values were close to 1, ranging from 0.944 to 0.988, indicating strong persistence in PR variation with soil depth. Also, the Hurst exponent was negatively and significantly correlated to coefficient of variation (CV), skewness and maximum values of the depth-dependent PR. Multifractal analysis added valuable information to describe the spatial arrangement of depth-dependent penetrometer data sets, which was not taken into account by classical statistical indices. Multifractal parameters were mapped over the experimental field and compared with mean and maximum values of PR. Combination of spatial variability survey and multifractal analysis appear to be useful to manage soil compaction.

Description: Application of singularity theory and logistic regression model for tungsten polymetallic potential mapping Nonlinear Processes in Geophysics, 20, 445-453, 2013 Author(s): Y. Liu, Q. Xia, Q. Cheng, and X. Wang Geo-anomalies with complex structures in the earth's crust may be defined as preferable hydrothermal ore-forming targets. The separation and explanation of anomaly from geological background have a profound influence on the analysis of geological evolution and the ore-forming process. Usually one of the key steps to identify favorable exploration targets is to determine the threshold to separate anomaly from geological background. In this paper, the singularity theory and concentration–area ( C – A ) fractal method was applied in determination of the threshold of geo-anomalies. According to the thresholds, four singular maps can be each divided into two segments. Each of them is correlated to the anomaly and background of the geological objects (e.g., faults, fault intersections and contacts), which reveals that the various geo-anomalies can be characterized by the singularities. The results indicate that the local singularity method can be used to identify the weak anomalies in a low background. Logistic regression model was used to combine geo-singularity maps for mineral potential mapping, which provides a useful input for further mineral exploration in the Nanling tungsten polymetallic belt, South China.

Description: Diffusion-affected passive scalar transport in an ellipsoidal vortex in a shear flow Nonlinear Processes in Geophysics, 20, 437-444, 2013 Author(s): K. V. Koshel, E. A. Ryzhov, and V. V. Zhmur By employing an analytical model for a constant-vorticity distributed vortex, namely, the ellipsoidal vortex embedded in a constant buoyancy frequency shear flow, the problem of the passive scalar transport through the vortex's boundary is addressed. Since the model's governing equations do not allow such transition to occur, we implement a low-scale diffusion process into the vortex model. Taking into consideration the diffusion term, we study the passive scalar transport in a steady state (the boundary of the ellipsoidal vortex does not change in time) and in a perturbed state (the boundary of the ellipsoidal vortex changes in time periodically) within the time scope corresponding to the characteristic life cycle of a mesoscale oceanic eddy. An increase of the passive scalar transport through the boundary in the perturbed state in comparison with the steady state due to the irregular dynamics of the surrounding flow is shown. The applicability scopes of the investigation for studying oceanic eddies in nature are discussed.

Description: Intermittency and multifractional Brownian character of geomagnetic time series Nonlinear Processes in Geophysics, 20, 455-466, 2013 Author(s): G. Consolini, R. De Marco, and P. De Michelis The Earth's magnetosphere exhibits a complex behavior in response to the solar wind conditions. This behavior, which is described in terms of mutifractional Brownian motions, could be the consequence of the occurrence of dynamical phase transitions. On the other hand, it has been shown that the dynamics of the geomagnetic signals is also characterized by intermittency at the smallest temporal scales. Here, we focus on the existence of a possible relationship in the geomagnetic time series between the multifractional Brownian motion character and the occurrence of intermittency. In detail, we investigate the multifractional nature of two long time series of the horizontal intensity of the Earth's magnetic field as measured at L'Aquila Geomagnetic Observatory during two years (2001 and 2008), which correspond to different conditions of solar activity. We propose a possible double origin of the intermittent character of the small-scale magnetic field fluctuations, which is related to both the multifractional nature of the geomagnetic field and the intermittent character of the disturbance level. Our results suggest a more complex nature of the geomagnetic response to solar wind changes than previously thought.

Description: Horizontal circulation and jumps in Hamiltonian wave models Nonlinear Processes in Geophysics, 20, 483-500, 2013 Author(s): E. Gagarina, J. van der Vegt, and O. Bokhove We are interested in the modelling of wave-current interactions around surf zones at beaches. Any model that aims to predict the onset of wave breaking at the breaker line needs to capture both the nonlinearity of the wave and its dispersion. We have therefore formulated the Hamiltonian dynamics of a new water wave model, incorporating both the shallow water and pure potential flow water wave models as limiting systems. It is based on a Hamiltonian reformulation of the variational principle derived by Cotter and Bokhove (2010) by using more convenient variables. Our new model has a three-dimensional velocity field consisting of the full three-dimensional potential velocity field plus extra horizontal velocity components. This implies that only the vertical vorticity component is nonzero. Variational Boussinesq models and Green–Naghdi equations, and extensions thereof, follow directly from the new Hamiltonian formulation after using simplifications of the vertical flow profile. Since the full water wave dispersion is retained in the new model, waves can break. We therefore explore a variational approach to derive jump conditions for the new model and its Boussinesq simplifications.

Description: Mapping local singularities using magnetic data to investigate the volcanic rocks of the Qikou depression, Dagang oilfield, eastern China Nonlinear Processes in Geophysics, 20, 501-511, 2013 Author(s): G. Chen, Q. Cheng, T. Liu, and Y. Yang The spatial structural characteristics of geological anomaly, including singularity and self-similarity, can be analysed using fractal or multifractal modelling. Here we apply the multifractal methods to potential fields to demonstrate that singularities can characterise geological bodies, including rock density and magnetic susceptibility. In addition to enhancing weak gravity and magnetic anomalies with respect to either strong or weak background levels, the local singularity index (α ≈ 2) can be used to delineate the edges of geological bodies. Two models were established to evaluate the effectiveness of mapping singularities for extracting weak anomalies and delineating edges of buried geological bodies. The Qikou depression of the Dagang oilfield in eastern China has been chosen as a study area for demonstrating the extraction of weak anomalies of volcanic rocks, using the singularity mapping technique to analyse complex magnetic anomalies caused by complex geological background. The results have shown that the singularities of magnetic data mapped in the paper are associated with buried volcanic rocks, which have been verified by both drilling and seismic survey, and the S–N and E–W faults in the region. The targets delineated for deeply seated faults and volcanic rocks in the Qikou depression should be further investigated for the potential application in undiscovered oil and gas reservoirs exploration.

Description: Derivation of Boussinesq's shoaling law using a coupled BBM system Nonlinear Processes in Geophysics, 20, 213-219, 2013 Author(s): H. Kalisch and A. Senthilkumar This paper is focused on finding rules for waveheight change in a solitary wave as it runs up a slowly increasing bottom. A coupled BBM system is used to describe the solitary waves. Expressions for energy density and energy flux associated with the BBM system are derived, and the principle of energy conservation is used to develop an equation relating the waveheight and undisturbed depth to the initial undisturbed depth and the incident waveheight. In the limit of zero waveheight, Boussinesq's shoaling law is recovered.

Description: Modeling of the near-field distribution of pollutants coming from a coastal outfall Nonlinear Processes in Geophysics, 20, 257-266, 2013 Author(s): T. P. Lyubimova, B. Roux, S. Luo, Y. N. Parshakova, and N. S. Shumilova The present study concerns the 3-D distribution of pollutants emitted from a coastal outfall in the presence of strong sea currents. The problem is solved using the nonlinear Reynolds-averaged Navier–Stokes equations in the framework of the k - ε model. The constants of the logarithmic law for the vertical velocity profile in the bottom boundary layer are obtained by processing experimental data from acoustic Doppler current profilers (ADCPs). The near-field distribution of pollutants at different distances from the diffuser is obtained in terms of the ambient flow velocity (steady or with tidal effect) and outfall discharge characteristics. It is shown that even in the case where the effluent density is substantially lower than the ambient sea water density the plume can impact the seabed, creating a risk of pollution of removable bottom sediments.

Description: Obliquely propagating electron acoustic solitons in magnetized plasmas with nonextensive electrons Nonlinear Processes in Geophysics, 20, 249-255, 2013 Author(s): H. R. Pakzad and K. Javidan The problem of small amplitude electron-acoustic solitary waves (EASWs) is discussed using the reductive perturbation theory in magnetized plasmas consisting of cold electrons, hot electrons obeying nonextensive distribution and stationary ions. The presented investigation shows that the presence of nonextensive distributed hot electrons (due to the effects of long-range interactions) causes a reduction in the soliton amplitude while its width increases. The effects of the population ratio of hot to cold electrons and also the effects of the presence of magnetic field in this situation are also discussed.

Description: Estimation of the local response to a forcing in a high dimensional system using the fluctuation-dissipation theorem Nonlinear Processes in Geophysics, 20, 239-248, 2013 Author(s): F. C. Cooper, J. G. Esler, and P. H. Haynes The fluctuation-dissipation theorem (FDT) has been proposed as a method of calculating the response of the earth's atmosphere to a forcing. For this problem the high dimensionality of the relevant data sets makes truncation necessary. Here we propose a method of truncation based upon the assumption that the response to a localised forcing is spatially localised, as an alternative to the standard method of choosing a number of the leading empirical orthogonal functions. For systems where this assumption holds, the response to any sufficiently small non-localised forcing may be estimated using a set of truncations that are chosen algorithmically. We test our algorithm using 36 and 72 variable versions of a stochastic Lorenz 95 system of ordinary differential equations. We find that, for long integrations, the bias in the response estimated by the FDT is reduced from ~75% of the true response to ~30%.

Description: Optimal localized observations for advancing beyond the ENSO predictability barrier Nonlinear Processes in Geophysics, 20, 221-230, 2013 Author(s): W. Kramer and H. A. Dijkstra The existing 20-member ensemble of 50 yr ECHAM5/MPI-OM simulations provides a reasonably realistic Monte Carlo sample of the El Niño–Southern Oscillation (ENSO). Localized observations of sea surface temperature (SST), zonal wind speed and thermocline depth are assimilated in the ensemble using sequential importance sampling to adjust the weight of ensemble members. We determine optimal observation locations, for which assimilation yields the minimal ensemble spread. Efficient observation locations for SST lie in the ENSO pattern, with the optimum located in the eastern and western Pacific for minimizing uncertainty in the NINO3 and NINO4 index, respectively. After the assimilation of the observations, we investigate how the weighted ensemble performs as a nine-month probabilistic forecast of the ENSO. Here, we focus on the spring predictability barrier with observation in the January–March (March–May) period and assess the remaining predictive power in June (August) for NINO3 (NINO4). For the ECHAM5/MPI-OM ensemble, this yields that SST observations around 110° W and 140° W provide the best predictive skill for the NINO3 and NINO4 index, respectively. Forecasts can be improved by additionally measuring the thermocline depth at 150° W.

Description: Efficient selective filtering of seismic data using multiscale decomposition Nonlinear Processes in Geophysics, 20, 207-211, 2013 Author(s): F. E. A. Leite, M. V. C. Henriques, V. C. Gurgel, and J. M. S. Filho Seismic signal processing is an important task in geophysics sounding and represents a permanent challenge in petroleum exploration. Although seismograms could in principle give us a picture of a geological structure, they are very contaminated by spurious signals and the ground roll noise is a strongly undesired signal present in the seismograms – it does not carry physical information about the deep geological structures. This fact demands a big effort in developing new filtering methodologies. Using discrete wavelet transform, an efficient filtering for suppression of the ground roll is presented. In this method, seismic data is decomposed in multiple scales. We can remove the noise as a surgical operation in each scale, just from the regions where they are present or strong, allowing us to preserve the maximum of relevant information.

Description: Nonlinear flow model for well production in an underground formation Nonlinear Processes in Geophysics, 20, 311-327, 2013 Author(s): J. C. Guo and R. S. Nie Fluid flow in underground formations is a nonlinear process. In this article we modelled the nonlinear transient flow behaviour of well production in an underground formation. Based on Darcy's law and material balance equations, we used quadratic pressure gradients to deduce diffusion equations and discuss the origins of nonlinear flow issues. By introducing an effective-well-radius approach that considers skin factor, we established a nonlinear flow model for both gas and liquid (oil or water). The liquid flow model was solved using a semi-analytical method, while the gas flow model was solved using numerical simulations because the diffusion equation of gas flow is a stealth function of pressure. For liquid flow, a series of standard log-log type curves of pressure transients were plotted and nonlinear transient flow characteristics were analyzed. Qualitative and quantitative analyses were used to compare the solutions of the linear and nonlinear models. The effect of nonlinearity upon pressure transients should not be ignored. For gas flow, pressure transients were simulated and compared with oil flow under the same formation and well conditions, resulting in the conclusion that, under the same volume rate production, oil wells demand larger pressure drops than gas wells. Comparisons between theoretical data and field data show that nonlinear models will describe fluid flow in underground formations realistically and accurately.

Description: Development and analysis of a simple model to represent the zero rainfall in a universal multifractal framework Nonlinear Processes in Geophysics, 20, 343-356, 2013 Author(s): A. Gires, I. Tchiguirinskaia, D. Schertzer, and S. Lovejoy High-resolution rainfall fields contain numerous zeros (i.e. pixels or time steps with no rain) which are either real or artificial – that is to say associated with the limit of detection of the rainfall measurement device. In this paper we revisit the enduring discussion on the source of this intermittency, e.g. whether it requires specific modelling. We first review the framework of universal multifractals (UM), which are commonly used to analyse and simulate geophysical fields exhibiting extreme variability over a wide range of scales with the help of a reduced number of parameters. However, this framework does not enable properly taking into account these numerous zeros. For example, it has been shown that performing a standard UM analysis directly on the field can lead to low observed quality of scaling and severe bias in the estimates of UM parameters. In this paper we propose a new simple model to deal with this issue. It is a UM discrete cascade process, where at each step if the simulated intensity is below a given level (defined in a scale invariant manner), it only has a predetermined probability to survive and is otherwise set to zero. A threshold can then be implemented at the maximum resolution to mimic the limit of detection of the rainfall measurement device. While also imperfect, this simple model enables explanation of most of the observed behaviour, e.g. the presence of scaling breaks, or the difference between statistics computed for single events or longer periods.

Description: The impact of nonlinearity in Lagrangian data assimilation Nonlinear Processes in Geophysics, 20, 329-341, 2013 Author(s): A. Apte and C. K. R. T. Jones The focus of this paper is on how two main manifestations of nonlinearity in low-dimensional systems – shear around a center fixed point (nonlinear center) and the differential divergence of trajectories passing by a saddle (nonlinear saddle) – strongly affect data assimilation. The impact is felt through their leading to non-Gaussian distribution functions. The major factors that control the strength of these effects is time between observations, and covariance of the prior relative to covariance of the observational noise. Both these factors – less frequent observations and larger prior covariance – allow the nonlinearity to take hold. To expose these nonlinear effects, we use the comparison between exact posterior distributions conditioned on observations and the ensemble Kalman filter (EnKF) approximation of these posteriors. We discuss the serious limitations of the EnKF in handling these effects.

Description: Effect of interchange instability on magnetic reconnection Nonlinear Processes in Geophysics, 20, 365-377, 2013 Author(s): W. Lyatsky and M. L. Goldstein We present here the results of a study of interacting magnetic fields that involves a force normal to the reconnection layer. In the presence of such force, the reconnection layer becomes unstable to interchange disturbances. The interchange instability results in formation of tongues of heated plasma that leaves the reconnection layer through its wide surface rather than through its narrow ends, as is the case in traditional magnetic reconnection models. This plasma flow out of the reconnection layer facilitates the removal of plasma from the layer and leads to fast reconnection. The proposed mechanism provides fast reconnection of interacting magnetic fields and does not depend on the thickness of the reconnection layer. This instability explains the strong turbulence and bidirectional streaming of plasma that is directed toward and away from the reconnection layer that is observed frequently above reconnection layers. The force normal to the reconnection layer also accelerates the removal of plasma islands appearing in the reconnection layer during turbulent reconnection. In the presence of this force normal to the reconnection layer, these islands are removed from the reconnection layer by the "buoyancy force", as happens in the case of interchange instability that arises due to the polarization electric field generated at the boundaries of the islands.

Description: Simulating run-up on steep slopes with operational Boussinesq models; capabilities, spurious effects and instabilities Nonlinear Processes in Geophysics, 20, 379-395, 2013 Author(s): F. Løvholt, P. Lynett, and G. Pedersen Tsunamis induced by rock slides plunging into fjords constitute a severe threat to local coastal communities. The rock slide impact may give rise to highly non-linear waves in the near field, and because the wave lengths are relatively short, frequency dispersion comes into play. Fjord systems are rugged with steep slopes, and modeling non-linear dispersive waves in this environment with simultaneous run-up is demanding. We have run an operational Boussinesq-type TVD (total variation diminishing) model using different run-up formulations. Two different tests are considered, inundation on steep slopes and propagation in a trapezoidal channel. In addition, a set of Lagrangian models serves as reference models. Demanding test cases with solitary waves with amplitudes ranging from 0.1 to 0.5 were applied, and slopes were ranging from 10 to 50°. Different run-up formulations yielded clearly different accuracy and stability, and only some provided similar accuracy as the reference models. The test cases revealed that the model was prone to instabilities for large non-linearity and fine resolution. Some of the instabilities were linked with false breaking during the first positive inundation, which was not observed for the reference models. None of the models were able to handle the bore forming during drawdown, however. The instabilities are linked to short-crested undulations on the grid scale, and appear on fine resolution during inundation. As a consequence, convergence was not always obtained. It is reason to believe that the instability may be a general problem for Boussinesq models in fjords.

Description: An extended singular spectrum transformation (SST) for the investigation of Kenyan precipitation data Nonlinear Processes in Geophysics, 20, 467-481, 2013 Author(s): N. Itoh and N. Marwan In this paper a change-point detection method is proposed by extending the singular spectrum transformation (SST) developed as one of the capabilities of singular spectrum analysis (SSA). The method uncovers change points related with trends and periodicities. The potential of the proposed method is demonstrated by analysing simple model time series including linear functions and sine functions as well as real world data (precipitation data in Kenya). A statistical test of the results is proposed based on a Monte Carlo simulation with surrogate methods. As a result, the successful estimation of change points as inherent properties in the representative time series of both trend and harmonics is shown. With regards to the application, we find change points in the precipitation data of Kenyan towns (Nakuru, Naivasha, Narok, and Kisumu) which coincide with the variability of the Indian Ocean Dipole (IOD) suggesting its impact of extreme climate in East Africa.

Description: Mapping air temperature using time series analysis of LST: the SINTESI approach Nonlinear Processes in Geophysics, 20, 513-527, 2013 Author(s): S. M. Alfieri, F. De Lorenzi, and M. Menenti This paper presents a new procedure to map time series of air temperature ( T a ) at fine spatial resolution using time series analysis of satellite-derived land surface temperature (LST) observations. The method assumes that air temperature is known at a single (reference) location such as in gridded climate data with grid size of the order of 35 km × 35 km. The LST spatial and temporal pattern within a grid cell has been modelled by the pixel-wise ratios r (x,y,t) of the LST at any location to the LST at a reference location. A preliminary analysis of these patterns over a decade has demonstrated that their intra-annual variability is not negligible, with significant seasonality, even if it is stable throughout the years. The intra-annual variability has been modeled using Fourier series. We have evaluated the intra-annual variability by theoretically calculating the yearly evolution of LST ( t ) for a range of cases as a function of terrain, land cover and hydrological conditions. These calculations are used to interpret the observed LST (x,y,t) and r (x,y,t) . The inter-annual variability has been evaluated by modeling each year of observations using Fourier series and evaluating the interannual variability of Fourier coefficients. Because of the negligible interannual variability of r (x,y,t) , LST (x,y,t) can be reconstructed in periods of time different from the ones when LST observations are available. Time series of T a are generated using the ratio r (x,y,t) and a linear regression between LST and T a . Such linear regression is applied in two ways: (a) to estimate LST at any time from observations or forecasts of T a at the reference location; (b) to estimate T a from LST at any location. The results presented in this paper are based on the analysis of daily MODIS LST observations over the period 2001–2010. The T a at the reference location was gridded data at a node of a 35 km × 35 km grid. Only one node was close to our study area and was used for the work presented here. The regression of T a on LST was determined using concurrent observations of T a at the four available weather stations in the Valle Telesina (Italy), our study area. The accuracy of our estimates is consistent with literature and with the combined accuracy of LST and T a . We obtained comparable error statistics when applying our method to LST data during periods different but adjacent to the periods used to model of r (x,y,t) . The method has also been evaluated against T a observations for earlier periods of time (1984–1988), although available data are rather sparse in space and time. Slightly larger deviation were obtained. In all cases five days of averages from estimated and observed T a were compared, giving a better accuracy.

Description: Resonant excitation of coastal Kelvin waves in the two-layer rotating shallow water model Nonlinear Processes in Geophysics, 20, 993-999, 2013 Author(s): V. Zeitlin Resonant excitation of coastal Kelvin waves by free inertia–gravity waves impinging on the coast is studied in the framework of the simplest baroclinic model: two-layer rotating shallow water with an idealized straight coast. It is shown that, with respect to the previous results obtained with the one-layer model, new resonances leading to a possible excitation of Kelvin waves appear. The most interesting ones, described in the paper, are resonances of a baroclinic inertia–gravity wave with either another wave of this kind, or with a coastal current, leading to generation of a barotropic Kelvin wave. A forced Hopf equation results in any case for the evolution of the Kelvin wave amplitude.

Description: A model of coupled oscillators applied to the aerosol–cloud–precipitation system Nonlinear Processes in Geophysics, 20, 1011-1021, 2013 Author(s): G. Feingold and I. Koren We simulate the aerosol–cloud–precipitation system as a collection of cloud elements, each coupled through physically based interactions with adjacent clouds. The equations describing the individual clouds follow from the predator–prey model of Koren and Feingold (2011) with the addition of coupling terms that derive from the flow of air between the components resulting from surface divergence or convergence of flows associated with the life cycle of an individual cell. It is shown that some degree of coupling might stabilize clouds that would ordinarily become unstable. Varying the degree of coupling strength has significant influence on the system. For weak coupling, the clouds behave as independent oscillators with little influence on one another. As the local coupling strength increases, a point is reached at which the system becomes highly synchronized, similar to the Sakaguchi et al. (1987) model. Individual cloud oscillators in close proximity to one another can be both in-phase or out-of-phase depending on the choice of the time constant for the delay in communication between components. For the case considered, further increases in coupling strength result in reduced order and eventually unstable growth. Finally it is demonstrated that the set of coupled oscillators mimics qualitatively the spatial structure and synchronized behaviour of both closed and open-cellular cloud fields observed in satellite imagery, and produced by numerically intensive large eddy simulation.

Description: Path-integrated Lagrangian measures from the velocity gradient tensor Nonlinear Processes in Geophysics, 20, 987-991, 2013 Author(s): V. Pérez-Muñuzuri and F. Huhn Spatial maps of the finite-time Lyapunov exponent (FTLE) have been used extensively to study LCS in two-dimensional dynamical systems, in particular with application to transport in unsteady fluid flows. We use the time-periodic double-gyre model to compare spatial fields of FTLE and the path-integrated Eulerian Okubo–Weiss parameter (OW). Both fields correlate strongly, and by solving the dynamics of the deformation gradient tensor, a theoretical relationship between both magnitudes has been obtained. While for long integration times more and more FTLE ridges appear that do not seem to coincide with the stable manifold, ridges in the field of path-integrated OW represent fewer additional structures.

Description: Parameter variations in prediction skill optimization at ECMWF Nonlinear Processes in Geophysics, 20, 1001-1010, 2013 Author(s): P. Ollinaho, P. Bechtold, M. Leutbecher, M. Laine, A. Solonen, H. Haario, and H. Järvinen Algorithmic numerical weather prediction (NWP) skill optimization has been tested using the Integrated Forecasting System (IFS) of the European Centre for Medium-Range Weather Forecasts (ECMWF). We report the results of initial experimentation using importance sampling based on model parameter estimation methodology targeted for ensemble prediction systems, called the ensemble prediction and parameter estimation system (EPPES). The same methodology was earlier proven to be a viable concept in low-order ordinary differential equation systems, and in large-scale atmospheric general circulation models (ECHAM5). Here we show that prediction skill optimization is possible even in the context of a system that is (i) of very high dimensionality, and (ii) carefully tuned to very high skill. We concentrate on four closure parameters related to the parameterizations of sub-grid scale physical processes of convection and formation of convective precipitation. We launch standard ensembles of medium-range predictions such that each member uses different values of the four parameters, and make sequential statistical inferences about the parameter values. Our target criterion is the squared forecast error of the 500 hPa geopotential height at day three and day ten. The EPPES methodology is able to converge towards closure parameter values that optimize the target criterion. Therefore, we conclude that estimation and cost function-based tuning of low-dimensional static model parameters is possible despite the very high dimensional state space, as well as the presence of stochastic noise due to initial state and physical tendency perturbations. The remaining question before EPPES can be considered as a generally applicable tool in model development is the correct formulation of the target criterion. The one used here is, in our view, very selective. Considering the multi-faceted question of improving forecast model performance, a more general target criterion should be developed. This is a topic of ongoing research.

Description: Modelling and simulation of waves in three-layer porous media Nonlinear Processes in Geophysics, 20, 1023-1030, 2013 Author(s): S. R. Pudjaprasetya The propagation of gravity waves in an emerged three-layer porous medium is considered in this paper. Based on the assumption that the flow can be described by Darcy's Law, an asymptotic theory is developed for small-amplitude long waves. This leads to a weakly nonlinear Boussinesq-type diffusion equation for the wave height, with coefficients dependent on the conductivities and depths of each layer. In the limit of equal conductivities of all layers, the equation reduces to the single-layer result recorded in the literature. The model equations are numerically integrated in the case of an incident monochromatic wave hitting the layers. The results exhibit dissipation and also a downstream net height rise at infinity. Wave transmission coefficient in three-layer porous media with conductivity of mangrove is discussed. Numerically, propagation of an initial solitary wave through a porous medium shows the emergence of wave reflection and transmission that both evolve as permanent waves. Additionally we examine the impact of a solitary gravity wave on a porous medium breakwater.

Description: The local ensemble transform Kalman filter and the running-in-place algorithm applied to a global ocean general circulation model Nonlinear Processes in Geophysics, 20, 1031-1046, 2013 Author(s): S. G. Penny, E. Kalnay, J. A. Carton, B. R. Hunt, K. Ide, T. Miyoshi, and G. A. Chepurin The most widely used methods of data assimilation in large-scale oceanography, such as the Simple Ocean Data Assimilation (SODA) algorithm, specify the background error covariances and thus are unable to refine the weights in the assimilation as the circulation changes. In contrast, the more computationally expensive Ensemble Kalman Filters (EnKF) such as the Local Ensemble Transform Kalman Filter (LETKF) use an ensemble of model forecasts to predict changes in the background error covariances and thus should produce more accurate analyses. The EnKFs are based on the approximation that ensemble members reflect a Gaussian probability distribution that is transformed linearly during the forecast and analysis cycle. In the presence of nonlinearity, EnKFs can gain from replacing each analysis increment by a sequence of smaller increments obtained by recursively applying the forecast model and data assimilation procedure over a single analysis cycle. This has led to the development of the "running in place" (RIP) algorithm by Kalnay and Yang (2010) and Yang et al. (2012a,b) in which the weights computed at the end of each analysis cycle are used recursively to refine the ensemble at the beginning of the analysis cycle. To date, no studies have been carried out with RIP in a global domain with real observations. This paper provides a comparison of the aforementioned assimilation methods in a set of experiments spanning seven years (1997–2003) using identical forecast models, initial conditions, and observation data. While the emphasis is on understanding the similarities and differences between the assimilation methods, comparisons are also made to independent ocean station temperature, salinity, and velocity time series, as well as ocean transports, providing information about the absolute error of each. Comparisons to independent observations are similar for the assimilation methods but the observation-minus-background temperature differences are distinctly lower for LETKF and RIP. The results support the potential for LETKF to improve the quality of ocean analyses on the space and timescales of interest for seasonal prediction and for RIP to accelerate the spin up of the system.

Description: A Lagrangian approach to the Loop Current eddy separation Nonlinear Processes in Geophysics, 20, 85-96, 2013 Author(s): F. Andrade-Canto, J. Sheinbaum, and L. Zavala Sansón Determining when and how a Loop Current eddy (LCE) in the Gulf of Mexico will finally separate is a difficult task, since several detachment re-attachment processes can occur during one of these events. Separation is usually defined based on snapshots of Eulerian fields such as sea surface height (SSH) but here we suggest that a Lagrangian view of the LCE separation process is more appropriate and objective. The basic idea is very simple: separation should be defined whenever water particles from the cyclonic side of the Loop Current move swiftly from the Yucatan Peninsula to the Florida Straits instead of penetrating into the NE Gulf of Mexico. The properties of backward-time finite time Lyapunov exponents (FTLE) computed from a numerical model of the Gulf of Mexico and Caribbean Sea are used to estimate the "skeleton" of flow and the structures involved in LCE detachment events. An Eulerian metric is defined, based on the slope of the strain direction of the instantaneous hyperbolic point of the Loop Current anticyclone that provides useful information to forecast final LCE detachments. We highlight cases in which an LCE separation metric based on SSH contours (Leben, 2005) suggests there is a separated LCE that later reattaches, whereas the slope method and FTLE structure indicate the eddy remains dynamically connected to the Loop Current during the process.

Description: Inertia–gravity waves generated by near balanced flow in 2-layer shallow water turbulence on the β-plane Nonlinear Processes in Geophysics, 20, 25-34, 2013 Author(s): A. Wirth Using a fine resolution numerical model (4000 2 × 2 grid-points) of the two-layer shallow-water equations of the mid-latitude β-plane dynamics, it is shown that there is no sudden breakdown of balance in the turbulent enstrophy cascade but a faint and continuous emission of inertia–gravity waves. The wave energy accumulates in the equator-ward region of the domain due to the Coriolis parameter depending on the latitude and dispersion relation of inertia–gravity waves.

Description: Time scale of the largest imaginable magnetic storm Nonlinear Processes in Geophysics, 20, 19-23, 2013 Author(s): V. M. Vasyliūnas The depression of the horizontal magnetic field at Earth's equator for the largest imaginable magnetic storm has been estimated (Vasyliūnas, 2011a) as −Dst ~ 2500 nT, from the assumption that the total pressure in the magnetosphere (plasma plus magnetic field perturbation) is limited, in order of magnitude, by the minimum pressure of Earth's dipole field at the location of each flux tube. The obvious related question is how long it would take the solar wind to supply the energy content of this largest storm. The maximum rate of energy input from the solar wind to the magnetosphere can be evaluated on the basis either of magnetotail stress balance or of polar cap potential saturation, giving an estimate of the time required to build up the largest storm, which (for solar-wind and magnetospheric parameter values typical of observed superstorms) is roughly between ~2 and ~6 h.

Description: Physical simulation of resonant wave run-up on a beach Nonlinear Processes in Geophysics, 20, 35-40, 2013 Author(s): A. Ezersky, N. Abcha, and E. Pelinovsky Nonlinear wave run-up on the beach caused by a harmonic wave maker located at some distance from the shore line is studied experimentally. It is revealed that under certain wave excitation frequencies, a significant increase in run-up amplification is observed. It is found that this amplification is due to the excitation of resonant mode in the region between the shoreline and wave maker. Frequency and magnitude of the maximum amplification are in good correlation with the numerical calculation results represented in the paper (Stefanakis et al., 2011). These effects are very important for understanding the nature of rogue waves in the coastal zone.

Description: Deterministic dynamics of the magnetosphere: results of the 0–1 test Nonlinear Processes in Geophysics, 20, 11-18, 2013 Author(s): S. Prabin Devi, S. B. Singh, and A. Surjalal Sharma A test for deterministic dynamics in a time series data, namely the 0–1 test (Gottawald and Melbourne, 2004, 2005), is used to study the magnetospheric dynamics. The data, corresponding to the same time period, of the auroral electrojet index AL and the magnetic field component B z of the solar wind magnetic field measured at 1 AU are used to compute the parameter K , which is zero for non-chaotic and unity for chaotic systems. For the magnetosphere and also for the turbulent solar wind, K has values corresponding to a nonlinear dynamical system with chaotic behaviour. This result is consistent with the Lyapunov exponents computed from the same time series data.

Description: Dynamics of a two-fault system with viscoelastic coupling Nonlinear Processes in Geophysics, 20, 1-10, 2013 Author(s): A. Amendola and M. Dragoni A fault system made of two segments or asperities subject to a constant strain rate is considered. The fault is modelled as a discrete dynamical system made of two blocks coupled by a Maxwell spring dashpot element and pulled at constant velocity on a rough plane. The long-term behaviour of the fault is studied by calculating the orbits of the system in the phase space. The model shows the role of viscoelastic relaxation in the Earth's crust in controlling the occurrence times of earthquakes. If a viscoelastic coupling is present, earthquakes are anticipated or delayed with respect to the elastic case. The limit cycles made of two alternate asperity failures, which are observed in the case of purely elastic coupling, are no longer produced. The model is applied to the 1964 Alaska earthquake, which was the effect of the failure of two asperities and for which a remarkable post-seismic relaxation has been observed in the subsequent decades. In such a fault system, viscoelastic coupling of the asperities appears to have a great influence on the occurrence times of earthquakes.

Description: Structuring of turbulence and its impact on basic features of Ekman boundary layers Nonlinear Processes in Geophysics, 20, 589-604, 2013 Author(s): I. Esau, R. Davy, S. Outten, S. Tyuryakov, and S. Zilitinkevich The turbulent Ekman boundary layer (EBL) has been studied in a large number of theoretical, laboratory and modeling works since F. Nansen's observations during the Norwegian Polar Expedition 1893–1896. Nevertheless, the proposed analytical models, analysis of the EBL instabilities, and turbulence-resolving numerical simulations are not fully consistent. In particular, the role of turbulence self-organization into longitudinal roll vortices in the EBL and its dependence on the meridional component of the Coriolis force remain unclear. A new set of large-eddy simulations (LES) are presented in this study. LES were performed for eight different latitudes (from 1° N to 90° N) in the domain spanning 144 km in the meridional direction. Geostrophic winds from the west and from the east were used to drive the development of EBL turbulence. The emergence and growth of longitudinal rolls in the EBL was simulated. The simulated rolls are in good agreement with EBL stability analysis given in Dubos et al. (2008). The destruction of rolls in the westerly flow at low latitude was observed in simulations, which agrees well with the action of secondary instability on the rolls in the EBL. This study quantifies the effect of the meridional component of the Coriolis force and the effect of rolls in the EBL on the internal EBL parameters such as friction velocity, cross-isobaric angle, parameters of the EBL depth and resistance laws. A large impact of the roll development or destruction is found. The depth of the EBL in the westerly flow is about five times less than it is in the easterly flow at low latitudes. The EBL parameters, which depend on the depth, also exhibit large difference in these two types of the EBL. Thus, this study supports the need to include the horizontal component of the Coriolis force into theoretical constructions and parameterizations of the boundary layer in models.

Description: Empirical correction techniques: analysis and applications to chaotically driven low-order atmospheric models Nonlinear Processes in Geophysics, 20, 199-206, 2013 Author(s): I. Trpevski, L. Basnarkov, D. Smilkov, and L. Kocarev Contemporary tools for reducing model error in weather and climate forecasting models include empirical correction techniques. In this paper we explore the use of such techniques on low-order atmospheric models. We first present an iterative linear regression method for model correction that works efficiently when the reference truth is sampled at large time intervals, which is typical for real world applications. Furthermore we investigate two recently proposed empirical correction techniques on Lorenz models with constant forcing while the reference truth is given by a Lorenz system driven with chaotic forcing. Both methods indicate that the largest increase in predictability comes from correction terms that are close to the average value of the chaotic forcing.

Description: Boussinesq modeling of surface waves due to underwater landslides Nonlinear Processes in Geophysics, 20, 267-285, 2013 Author(s): D. Dutykh and H. Kalisch Consideration is given to the influence of an underwater landslide on waves at the surface of a shallow body of fluid. The equations of motion that govern the evolution of the barycenter of the landslide mass include various dissipative effects due to bottom friction, internal energy dissipation, and viscous drag. The surface waves are studied in the Boussinesq scaling, with time-dependent bathymetry. A numerical model for the Boussinesq equations is introduced that is able to handle time-dependent bottom topography, and the equations of motion for the landslide and surface waves are solved simultaneously. The numerical solver for the Boussinesq equations can also be restricted to implement a shallow-water solver, and the shallow-water and Boussinesq configurations are compared. A particular bathymetry is chosen to illustrate the general method, and it is found that the Boussinesq system predicts larger wave run-up than the shallow-water theory in the example treated in this paper. It is also found that the finite fluid domain has a significant impact on the behavior of the wave run-up.

Description: The scaling behaviour of the edges of gravity data Nonlinear Processes in Geophysics, 20, 287-291, 2013 Author(s): G. R. J. Cooper Measurements of the earth's gravity field are widely used in geophysical exploration programs. The geological interpretation process often involves the identification of the boundaries, or edges, of different regions. This can be achieved through a variety of techniques. This paper examines the statistical distribution of the size of the edges produced by a synthetic gravity model, and compares the results with those obtained from a gravity dataset from South Africa.

Description: On the role of electromagnetic phenomena in some atmospheric processes Nonlinear Processes in Geophysics, 20, 293-304, 2013 Author(s): S. N. Artekha and A. V. Belyan A crucial part of electromagnetic phenomena in many atmospheric processes is verified by systematized data. The multilayered charged system of clouds represents some dynamically equilibrium structure kept by the ionic and polarization forces. The estimates of acting forces are presented and the necessity of taking into account the plasma-like subsystems' effect on some atmospheric phenomena is demonstrated, including the formation and the maintenance of the structure and characteristics of their movement.

Description: Brief communication "Spatial and temporal variation of wind power at hub height over Europe" Nonlinear Processes in Geophysics, 20, 305-310, 2013 Author(s): S. Gisinger, G. J. Mayr, J. W. Messner, and R. Stauffer Wind power over Europe computed from two years of the new 100 m wind product from ECMWF at 16 km horizontal resolution is 20% of maximum capacity of an exemplary wind turbine power curve. This is five percent of maximum capacity less than extrapolated from 10 m winds using model roughness in the logarithmic law, but eight percent more than multiplying 10 m winds by a constant factor of 1.28 as in a previous study. The result from the new data set happens to be very close to the actual capacity factor of 21% for European wind turbines (Boccard, 2009). The capacity factor in high power regions between 50 and 58° N and most of northernmost Africa is almost 30%. The aggregation of wind power over Europe smooths onshore day-to-day fluctuations to at most 7 percentage points during 80% of the year.

Description: An intercomparison of burnt area estimates derived from key operational products: the Greek wildland fires of 2005–2007 Nonlinear Processes in Geophysics, 20, 397-409, 2013 Author(s): D. P. Kalivas, G. P. Petropoulos, I. M. Athanasiou, and V. J. Kollias With the support of new technologies such as of remote sensing, today's societies have been able to map and analyse wildland fires at large observational scales. With regards to burnt area mapping in particular, two of the most widely used operational products are offered today by the United States National Aeronautics and Space Administration (NASA) and the European Forest Fires Information System (EFFIS) of the European Commission. In this study, a rigorous intercomparison of the burnt area estimates derived by these two products is performed in a geographical information system (GIS) environment for the Greek fires that occurred from 2005 to 2007. For the same temporal interval, the relationships of the burnt area estimates by each product are examined with respect to land use/cover and elevation derived from CORINE 2000 and the ASTER global digital elevation model (GDEM), respectively. Generally, noticeable differences were found in the burnt area estimates by the two products both spatially and in absolute numbers. The main findings are described and the differences in the burnt area estimates between the two operational datasets are discussed. The lack of precise agreement between the two products which was found does not necessarily mean that one or the other product is inaccurate. Rather, it underlines the requirement for their calibration and validation using high-resolution remote sensing data in future studies. Our work not only builds upon a series of analogous studies evaluating the accuracy of the same or similar operational products worldwide, but also contributes towards the development of standardised validation methodologies required in objectively evaluating such datasets.

Description: Features of criticality in precursory seismic electric signals and earthquakes in Greece Nonlinear Processes in Geophysics, 20, 411-416, 2013 Author(s): E. Dologlou Very recently the recordings of precursory seismic electric signals (SESsf) in the island of K o zu-shima, Japan, have been reported, and their interrelation with subsequent earthquakes was shown to be beyond chance. Almost simultaneously, the recording of SES activity in northern Greece was also reported, which was followed by a magnitude 5.7 earthquake in northern Greece. These facts strengthen the aspects on the precursory nature of SESs and also enable the updating of a previously found power law relation between the earthquake stress drop and the lead time of SESs. They led to an exponent of 0.330, which falls in the range of critical exponents for fracture. The stability of this exponent, which results from a large amount of data during the last 30 yr, is remarkable and may thus confirm features of criticality in the pre-seismic region after the SES emission. The underlying physics are also discussed.

Description: Comment on "Fractal analysis of ULF electromagnetic emissions in possible association with earthquakes in China" by Ida et al. (2012) Nonlinear Processes in Geophysics, 20, 417-421, 2013 Author(s): F. Masci and J. N. Thomas Ida et al. (2012) identified anomalous decreases in the fractal dimension of the vertical ( Z ) component of the geomagnetic field, which they interpreted as precursors to the China earthquake of 1 September 2003. According to Ida et al. (2012), short-term earthquake prediction seems to be possible only by using electromagnetic phenomena. Here, it is shown that the decreases of the fractal dimension documented by Ida et al. (2012) are not really anomalous, but they are part of the normal geomagnetic activity driven by solar–terrestrial interactions. As a consequence, these fractal dimension decreases are not related to the 1 September 2003 earthquake.

Description: Entropy-information perspective to radiogenic heat distribution in continental crust Nonlinear Processes in Geophysics, 20, 423-428, 2013 Author(s): R. N. Singh and A. Manglik Depth distribution of radiogenic heat sources in continental crust is an important parameter that controls its thermal structure as well as the mantle heat flow at the base of continental lithosphere. Various models for the depth distribution of radiogenic heat sources have been proposed. Starting from constant and exponential models based on linear heat flow–heat generation relationship the present-day layered models integrate crustal structure and laboratory measurements of radiogenic heat sources in various exposed rocks representing crustal composition. In the present work, an extended entropy theory formalism is used for estimation of radiogenic heat sources distribution in continental crust based on principle of maximum entropy (POME). The extended entropy principle yields a constant heat generation model if only a constraint given by total radiogenic heat in the crust is used and an exponential form of radiogenic heat sources distribution if an additional constraint in the form of a second moment is used in the minimization of entropy.

Description: The effect of nonlinear ionospheric conductivity enhancement on magnetospheric substorms Nonlinear Processes in Geophysics, 20, 429-435, 2013 Author(s): E. Spencer and S. Patra We introduce the effect of enhanced ionospheric conductivity into a low-order, physics-based nonlinear model of the nightside magnetosphere called WINDMI. The model uses solar wind and interplanetary magnetic field (IMF) parameters from the ACE satellite located at the L1 point to predict substorm growth, onset, expansion and recovery measured by the AL index roughly 50–60 min in advance. The dynamics introduced by the conductivity enhancement into the model behavior is described, and illustrated through using synthetically constructed solar wind parameters as input. We use the new model to analyze two well-documented isolated substorms: one that occurred on 31 July 1997 from Aksnes et al. (2002), and another on 13 April 2000 from Huang et al. (2004). These two substorms have a common feature in that the solar wind driver sharply decreases in the early part of the recovery phase, and that neither of them are triggered by northward turning of the IMF Bz. By controlling the model parameters such that the onset time of the substorm is closely adhered to, the westward auroral electrojet peaks during substorm expansion are qualitatively reproduced. Furthermore, the electrojet recovers more slowly with enhanced conductivity playing a role, which explains the data more accurately.

Description: Remarks on rotating shallow-water magnetohydrodynamics Nonlinear Processes in Geophysics, 20, 893-898, 2013 Author(s): V. Zeitlin We show how the rotating shallow-water MHD model, which was proposed in the solar tachocline context, may be systematically derived by vertical averaging of the full MHD equations for the rotating magneto fluid under the influence of gravity. The procedure highlights the main approximations and the domain of validity of the model, and allows for multi-layer generalizations and, hence, inclusion of the baroclinic effects. A quasi-geostrophic version of the model, both in barotropic and in baroclinic cases, is derived in the limit of strong rotation. The basic properties of the model(s) are sketched, including the stabilizing role of magnetic fields in the baroclinic version.

Description: Hyperbolicity in temperature and flow fields during the formation of a Loop Current ring Nonlinear Processes in Geophysics, 20, 883-892, 2013 Author(s): M. H. M. Sulman, H. S. Huntley, B. L. Lipphardt Jr., G. Jacobs, P. Hogan, and A. D. Kirwan Jr. Loop Current rings (LCRs) are among the largest mesoscale eddies in the world ocean. They arise when bulges formed by the Loop Current in the Gulf of Mexico close off. The LCR formation process may take several weeks, and there may be several separations and reattachments before final separation occurs. It is well established that this period is characterized by a persistent saddle point in the sea surface height field, as seen in both model and satellite data. We present here a detailed study of this saddle region during the formation of Eddy Franklin in 2010, over multiple days and at several depths. Using a data-assimilating Gulf of Mexico implementation of the HYbrid Coordinate Ocean Model (HYCOM), we compare the vertical structure of the currents and temperature fields on 5 and 10 June 2010. Finite-time Lyapunov exponents (FTLE) are computed from the surface down to 200 m to estimate the location of relevant transport barriers. Several new features of the saddle region associated with LCR formation are revealed: the ridges in the FTLE fields are shown to be excellent surrogates for the manifolds delineating the material flow structures with only slight degradation at depth. The intersection of the ridges representing stable and unstable manifolds drops nearly vertically through the water column at both times; remarkably, the material boundary shapes are maintained even as they are advected. Moreover, velocity stagnation points and saddle points in the temperature field are consistently found near the intersections at all depths, and their geographic positions are also nearly constant with depth.

Description: Momentum and buoyancy transfer in atmospheric turbulent boundary layer over wavy water surface – Part 2: Wind–wave spectra Nonlinear Processes in Geophysics, 20, 841-856, 2013 Author(s): Yu. I. Troitskaya, E. V. Ezhova, D. A. Sergeev, A. A. Kandaurov, G. A. Baidakov, M. I. Vdovin, and S. S. Zilitinkevich Drag and mass exchange coefficients are calculated within a self-consistent problem for the wave-induced air perturbations and mean velocity and density fields using a quasi-linear model based on the Reynolds equations with down-gradient turbulence closure. This second part of the report is devoted to specification of the model elements: turbulent transfer coefficients and wave number-frequency spectra. It is shown that the theory agrees with laboratory and field experimental data well when turbulent mass and momentum transfer coefficients do not depend on the wave parameters. Among several model spectra better agreement of the theoretically calculated drag coefficients with TOGA (Tropical Ocean Global Atmosphere) COARE (Coupled Ocean–Atmosphere Response Experiment) data is achieved for the Hwang spectrum (Hwang, 2005) with the high frequency part completed by the Romeiser spectrum (Romeiser et al., 1997).

Description: Escape rate: a Lagrangian measure of particle deposition from the atmosphere Nonlinear Processes in Geophysics, 20, 867-881, 2013 Author(s): T. Haszpra and T. Tél Due to rising or descending air and due to gravity, aerosol particles carry out a complicated, chaotic motion and move downwards on average. We simulate the motion of aerosol particles with an atmospheric dispersion model called the Real Particle Lagrangian Trajectory (RePLaT) model, i.e., by solving Newton's equation and by taking into account the impacts of precipitation and turbulent diffusion where necessary, particularly in the planetary boundary layer. Particles reaching the surface are considered to have escaped from the atmosphere. The number of non-escaped particles decreases with time. The short-term and long-term decay are found to be exponential and are characterized by escape rates. The reciprocal values of the short-term and long-term escape rates provide estimates of the average residence time of typical particles, and of exceptional ones that become convected or remain in the free atmosphere for an extremely long time, respectively. The escape rates of particles of different sizes are determined and found to vary in a broad range. The increase is roughly exponential with the particle size. These investigations provide a Lagrangian foundation for the concept of deposition rates.

Description: Momentum and buoyancy transfer in atmospheric turbulent boundary layer over wavy water surface – Part 1: Harmonic wave Nonlinear Processes in Geophysics, 20, 825-839, 2013 Author(s): Yu. I. Troitskaya, E. V. Ezhova, and S. S. Zilitinkevich The surface-drag and mass-transfer coefficients are determined within a self-consistent problem of wave-induced perturbations and mean fields of velocity and density in the air, using a quasi-linear model based on the Reynolds equations with down-gradient turbulence closure. Investigation of a harmonic wave propagating along the wind has disclosed that the surface drag is generally larger for shorter waves. This effect is more pronounced in the unstable and neutral stratification. The stable stratification suppresses turbulence, which leads to weakening of the momentum and mass transfer.

Description: Dynamics of simple earthquake model with time delay and variation of friction strength Nonlinear Processes in Geophysics, 20, 857-865, 2013 Author(s): S. Kostić, N. Vasović, I. Franović, and K. Todorović We examine the dynamical behaviour of the phenomenological Burridge–Knopoff-like model with one and two blocks, where the friction term is supplemented by the time delay τ and the variable friction strength c . Time delay is assumed to reflect the initial quiescent period of the fault healing, considered to be a function of history of sliding. Friction strength parameter is proposed to mimic the impact of fault gouge thickness on the rock friction. For the single-block model, interplay of the introduced parameters c and τ is found to give rise to oscillation death, which corresponds to aseismic creeping along the fault. In the case of two blocks, the action of c 1 , c 2 , τ 1 and τ 1 may result in several effects. If both blocks exhibit oscillatory motion without the included time delay and frictional strength parameter, the model undergoes transition to quasiperiodic motion if only c 1 and c 2 are introduced. The same type of behaviour is observed when τ 1 and τ 2 are varied under the condition c 1 = c 2 . However, if c 1 , and τ 1 are fixed such that the given block would lie at the equilibrium while c 2 and τ 2 are varied, the ( c 2 , τ 2 ) domains supporting quasiperiodic motion are interspersed with multiple domains admitting the stationary solution. On the other hand, if ( c 1 , τ 1 ) warrant oscillatory behaviour of one block, under variation of c 2 and τ 2 the system's dynamics is predominantly quasiperiodic, with only small pockets of ( c 2 , τ 2 ) parameter space admitting the periodic motion or equilibrium state. For this setup, one may also find a transient chaos-like behaviour, a point corroborated by the positive value of the maximal Lyapunov exponent for the corresponding time series.

Description: Lagrangian transport in a microtidal coastal area: the Bay of Palma, island of Mallorca, Spain Nonlinear Processes in Geophysics, 20, 921-933, 2013 Author(s): I. Hernández-Carrasco, C. López, A. Orfila, and E. Hernández-García Coastal transport in the Bay of Palma, a small region in the island of Mallorca, Spain, is characterized in terms of Lagrangian descriptors. The data sets used for this study are the output for two months (one in autumn and one in summer) of a high resolution numerical model, ROMS (Regional Ocean Model System), forced atmospherically and with a spatial resolution of 300 m. The two months were selected because of their different wind regime, which is the main driver of the sea dynamics in this area. Finite-size Lyapunov exponents (FSLEs) were used to locate semi-persistent Lagrangian coherent structures (LCS) and to understand the different flow regimes in the bay. The different wind directions and regularity in the two months have a clear impact on the surface bay dynamics, whereas only topographic features appear clearly in the bottom structures. The fluid interchange between the bay and the open ocean was studied by computing particle trajectories and residence time (RT) maps. The escape rate of particles out of the bay is qualitatively different, with a 32% greater escape rate of particles to the ocean in October than in July, owing to the different geometric characteristics of the flow. We show that LCSs separate regions with different transport properties by displaying spatial distributions of residence times on synoptic Lagrangian maps together with the location of the LCSs. Correlations between the time-dependent behavior of FSLE and RT are also investigated, showing a negative dependence when the stirring characterized by FSLE values moves particles in the direction of escape.

Description: Ion motion in the current sheet with sheared magnetic field – Part 2: Non-adiabatic effects Nonlinear Processes in Geophysics, 20, 899-919, 2013 Author(s): A. V. Artemyev, A. I. Neishtadt, and L. M. Zelenyi We investigate dynamics of charged particles in current sheets with the sheared magnetic field. In our previouspaper (Artemyev et al., 2013) we studied the particle motion in such magnetic field configurations on the basis of the quasi-adiabatic theory and conservation of the quasi-adiabatic invariant. In this paper we concentrate on violation of the adiabaticity due to jumps of this invariant and the corresponding effects of stochastization of a particle motion. We compare effects of geometrical and dynamical jumps, which occur due to the presence of the separatrix in the phase plane of charged particle motion. We show that due to the presence of the magnetic field shear, the average value of dynamical jumps is not equal to zero. This effect results in the decrease of the time interval necessary for stochastization of trapped particle motion. We investigate also the effect of the magnetic field shear on transient trajectories, which cross the current sheet boundaries. Presence of the magnetic field shear leads to the asymmetry of reflection and transition of particles in the current sheet. We discuss the possible influence of single-particle effects revealed in this paper on the current sheet structure and dynamics.

Description: Numerical investigation of algebraic oceanic turbulent mixing-layer models Nonlinear Processes in Geophysics, 20, 945-954, 2013 Author(s): T. Chacón-Rebollo, M. Gómez-Mármol, and S. Rubino In this paper we investigate the finite-time and asymptotic behaviour of algebraic turbulent mixing-layer models by numerical simulation. We compare the performances given by three different settings of the eddy viscosity. We consider Richardson number-based vertical eddy viscosity models. Two of these are classical algebraic turbulence models usually used in numerical simulations of global oceanic circulation, i.e. the Pacanowski–Philander and the Gent models, while the other one is a more recent model (Bennis et al., 2010) proposed to prevent numerical instabilities generated by physically unstable configurations. The numerical schemes are based on the standard finite element method. We perform some numerical tests for relatively large deviations of realistic initial conditions provided by the Tropical Atmosphere Ocean (TAO) array. These initial conditions correspond to states close to mixing-layer profiles, measured on the Equatorial Pacific region called the West-Pacific Warm Pool. We conclude that mixing-layer profiles could be considered as kinds of "absorbing configurations" in finite time that asymptotically evolve to steady states under the application of negative surface energy fluxes.

Description: Using ensemble data assimilation to forecast hydrological flumes Nonlinear Processes in Geophysics, 20, 955-964, 2013 Author(s): I. Amour, Z. Mussa, A. Bibov, and T. Kauranne Data assimilation, commonly used in weather forecasting, means combining a mathematical forecast of a target dynamical system with simultaneous measurements from that system in an optimal fashion. We demonstrate the benefits obtainable from data assimilation with a dam break flume simulation in which a shallow-water equation model is complemented with wave meter measurements. Data assimilation is conducted with a Variational Ensemble Kalman Filter (VEnKF) algorithm. The resulting dynamical analysis of the flume displays turbulent behavior, features prominent hydraulic jumps and avoids many numerical artifacts present in a pure simulation.

Description: Correlation-based characterisation of time-varying dynamical complexity in the Earth's magnetosphere Nonlinear Processes in Geophysics, 20, 965-975, 2013 Author(s): R. V. Donner and G. Balasis The dynamical behaviour of the magnetosphere is known to be a sensitive indicator for the response of the system to solar wind coupling. Since the solar activity commonly displays very interesting non-stationary and multi-scale dynamics, the magnetospheric response also exhibits a high degree of dynamical complexity associated with fundamentally different characteristics during periods of quiescence and magnetic storms. The resulting temporal complexity profile has been explored using several approaches from applied statistics, dynamical systems theory and statistical mechanics. Here, we propose an alternative way of looking at time-varying dynamical complexity of nonlinear geophysical time series utilising subtle but significant changes in the linear autocorrelation structure of the recorded data. Our approach is demonstrated to sensitively trace the dynamic signatures associated with intense magnetic storms, and to display reasonable skills in distinguishing between quiescence and storm periods. The potentials and methodological limitations of this new viewpoint are discussed in some detail.

Description: The study of the effect of small-scale turbulence on internal gravity waves propagation in a pycnocline Nonlinear Processes in Geophysics, 20, 977-986, 2013 Author(s): O. A. Druzhinin, L. A. Ostrovsky, and S. S. Zilitinkevich This paper presents the results of modeling the interaction between internal waves (IWs) and turbulence using direct numerical simulation (DNS). Turbulence is excited and supported by a random forcing localized in a vertical layer separated from the pycnocline. The main attention is paid to the internal wave damping due to turbulence and comparison of the results with those obtained theoretically by using the semi-empirical approach. It is shown that the IW damping rate predicted by the theory agrees well with the DNS results when turbulence is sufficiently strong to be only weakly perturbed by the internal wave; however, the theory overestimates the damping rate of IWs for a weaker turbulence. The DNS parameters are matched to the parameters of the laboratory experiment, and an extrapolation to the oceanic scales is also provided.

Description: Aeroelectric structures and turbulence in the atmospheric boundary layer Nonlinear Processes in Geophysics, 20, 819-824, 2013 Author(s): S. V. Anisimov, E. A. Mareev, N. M. Shikhova, M. V. Shatalina, S. V. Galichenko, and S. S. Zilitinkevich Complex electrical measurements with the use of sodar data show that electric field pulsation analysis is useful for electrodynamics/turbulence monitoring under different conditions. In particular, the number of aeroelectric structures (AES) generated per hour is a convenient measure of the turbulence intensity. During convectively unstable periods, as many as 5–10 AES form per hour. Under stable conditions, AES occasionally form as well, indicating the appearance of occasional mixing events reflected in the electric field perturbations. AES magnitudes under stable conditions are relatively small, except in special cases such as high humidity and fog. The analysis of electric field (EF) spectra gives additional useful information on the parameters of the atmospheric boundary layer and its turbulence. A rather sharp change in the spectrum slope takes place in the vicinity of 0.02 Hz under stable conditions. The characteristic slope of the spectrum and its change are reproduced in a simple model of EF formation.

Description: Asymmetric tide in Lake Vallunden (Spitsbergen) Nonlinear Processes in Geophysics, 20, 935-944, 2013 Author(s): A. V. Marchenko and E. G. Morozov We observed strongly asymmetric tide in a channel connecting the Van Mijen Fjord and Lake Vallunden in Spitsbergen. The channel is approximately 100 m long, 10 m wide, and 1–2 m deep. Asymmetric tide was also observed in the lake. The form of the semidiurnal tide is described by a combination of only three harmonics ( M 2 , S 2 and M 4 ) with different amplitudes and phases. The flood dominant form of the surface elevation in the channel (unlike the ebb dominant tide in the fjord) is formed over a horizontal distance of 50 m over a shallow bottom at the entrance to the channel. The tide in shallow places becomes asymmetric due to nonlinear effects caused by the influence of the bottom and especially by choking of the tidal flow over a sill that is located between the fjord and channel. We think that such a small distance, over which the form of the tide changes, is caused by the small scale of the channel related to the fjord. We suggest a numerical model related to these measurements.

Description: Fourier spectrum and shape evolution of an internal Riemann wave of moderate amplitude Nonlinear Processes in Geophysics, 20, 571-580, 2013 Author(s): E. Kartashova, E. Pelinovsky, and T. Talipova The nonlinear deformation of long internal waves in the ocean is studied using the dispersionless Gardner equation. The process of nonlinear wave deformation is determined by the signs of the coefficients of the quadratic and cubic nonlinear terms; the breaking time depends only on their absolute values. The explicit formula for the Fourier spectrum of the deformed Riemann wave is derived and used to investigate the evolution of the spectrum of the initially pure sine wave. It is shown that the spectrum has exponential form for small times and a power asymptotic before breaking. The power asymptotic is universal for arbitrarily chosen coefficients of the nonlinear terms and has a slope close to –8/3.

Description: Stable Langmuir solitons in plasma with diatomic ions Nonlinear Processes in Geophysics, 20, 581-588, 2013 Author(s): M. Dvornikov We study stable axially and spherically symmetric spatial solitons in plasma with diatomic ions. The stability of a soliton against collapse is provided by the interaction of induced electric dipole moments of ions with the rapidly oscillating electric field of a plasmoid. We derive the new cubic-quintic nonlinear Schrödinger equation, which governs the soliton dynamics and numerically solve it. Then we discuss the possibility of implementation of such plasmoids in realistic atmospheric plasma. In particular, we suggest that spherically symmetric Langmuir solitons, described in the present work, can be excited at the formation stage of long-lived atmospheric plasma structures. The implication of our model for the interpretation of the results of experiments for the plasmoids generation is discussed.

Description: Clifford algebra-based structure filtering analysis for geophysical vector fields Nonlinear Processes in Geophysics, 20, 563-570, 2013 Author(s): Z. Yu, W. Luo, L. Yi, Y. Hu, and L. Yuan A new Clifford algebra-based vector field filtering method, which combines amplitude similarity and direction difference synchronously, is proposed. Firstly, a modified correlation product is defined by combining the amplitude similarity and direction difference. Then, a structure filtering algorithm is constructed based on the modified correlation product. With custom template and thresholds applied to the modulus and directional fields independently, our approach can reveal not only the modulus similarities but also the classification of the angular distribution. Experiments on exploring the tempo-spatial evolution of the 2002–2003 El Niño from the global wind data field are used to test the algorithm. The results suggest that both the modulus similarity and directional information given by our approach can reveal the different stages and dominate factors of the process of the El Niño evolution. Additional information such as the directional stability of the El Niño can also be extracted. All the above suggest our method can provide a new powerful and applicable tool for geophysical vector field analysis.

Description: Nonlinear hydrodynamics in a Mediterranean lagoon Nonlinear Processes in Geophysics, 20, 189-198, 2013 Author(s): E. Alekseenko, B. Roux, A. Sukhinov, R. Kotarba, and D. Fougere The paper addresses the application of the nonlinear hydrodynamics model (RANS (Reynolds-averaged Navier–Stokes) equations) in a wide semi-enclosed Mediterranean lagoon (Berre lagoon), considering three natural forcing functions, i.e., sea tide propagating through a long narrow channel, wind and runoff. Main attention is focused to characteristic velocities (at free surface and bottom) and to free surface elevation associated to each of these three mechanisms, with special attention to the nearshore areas (i.e., in shallow water). The most interesting result concerns wind effects which, due to Berre lagoon bathymetry, give rise to downwind coastal jets, alongshore, in shallow water areas. Such coastal jets were never mentioned before in Berre lagoon literature.

Description: Assessment of numerical schemes for solving the advection–diffusion equation on unstructured grids: case study of the Guaíba River, Brazil Nonlinear Processes in Geophysics, 20, 1113-1125, 2013 Author(s): F. F. Pereira, C. R. Fragoso Jr., C. B. Uvo, W. Collischonn, and D. M. L. Motta Marques In this work, a first-order upwind and a high-order flux-limiter schemes for solving the advection–diffusion equation on unstructured grids were evaluated. The numerical schemes were implemented as a module of an unstructured two-dimensional depth-averaged circulation model for shallow lakes (IPH-UnTRIM2D), and they were applied to the Guaíba River in Brazil. Their performances were evaluated by comparing mass conservation balance errors for two scenarios of a passive tracer released into the Guaíba River. The circulation model showed good agreement with observed data collected at four water level stations along the Guaíba River, where correlation coefficients achieved values up to 0.93. In addition, volume conservation errors were lower than 1% of the total volume of the Guaíba River. For all scenarios, the higher order flux-limiter scheme has been shown to be less diffusive than a first-order upwind scheme. Accumulated conservation mass balance errors calculated for the flux limiter reached 8%, whereas for a first-order upwind scheme, they were close to 18% over a 15-day period. Although both schemes have presented mass conservation errors, these errors are assumed negligible compared with kinetic processes such as erosion, sedimentation or decay rates.

Description: On the nonstationarity of the decadal periodicities of the length of day Nonlinear Processes in Geophysics, 20, 1127-1135, 2013 Author(s): P. De Michelis, R. Tozzi, and G. Consolini The Earth's rotation rate is not constant, but changes on all observable timescales, from subdaily to decadal and longer. These variations are usually discussed in terms of variations in the length of the day (LoD) and are caused by processes acting within the interior, at the surface and outside of the Earth. Here, we investigate the presence of long-standing decadal variations in yearly LoD data covering the period from 1832 to 2009 by applying the Hilbert–Huang transform (HHT). The HHT has been slightly modified here to take into account the uncertainty of LoD values that has changed greatly in time due to the use of different LoD measurement techniques. The LoD time series has been completely decomposed into five intrinsic mode functions (IMF) and a residual trend. The estimation of instantaneous frequencies and related amplitudes of the obtained IMFs has allowed us to compute the Hilbert spectrum that has been used as the starting point for studying and discussing the stationarity of typical LoD timescale stationarity. The obtained results while showing the presence of multiple periodicities also indicate the absence of really stationary periodicities. Therefore, rather than considering the processes taking place in the Earth's core as the result of a superposition of oscillations (i.e. stationary mechanisms) occurring on a discrete number of different timescales, it would be better to think of a superposition of fluctuations that are intermittent in both frequency and amplitude.

Description: Maximal Lyapunov exponent variations of volcanic tremor recorded during explosive and effusive activity at Mt Semeru volcano, Indonesia Nonlinear Processes in Geophysics, 20, 1137-1145, 2013 Author(s): K. I. Konstantinou, C. A. Perwita, S. Maryanto, A. Budianto, and M. Hendrasto We analyze 25 episodes of volcanic tremor recorded from 22 November until 31 December 2009 at Mt Semeru volcano in order to investigate their spectral and dynamical properties. The overtone frequencies for most of the tremor events indicate a pattern of period-doubling, which is one possible route that can lead a system to chaotic behavior. Exponential divergence of the phase space orbits is a strong indicator of chaos and was quantified by estimating the maximal Lyapunov exponent (MLE) for all tremor events. MLEs were found to vary linearly with the number of frequency overtones present in the tremor signals. This implies that the tremor source at Semeru fluctuates between a quasi-periodic state with few overtone frequencies (2–3) and small MLEs (~0.013), and a chaotic one with more overtones (up to 8) and larger MLEs (up to 0.039). These results agree well with the tremor generation model suggested previously by Julian (1994), which describes wall oscillations of a crack excited by unsteady fluid flow. In this model, as fluid pressure increases, a period-doubling cascade leads to numerous new frequencies and a chaotic tremor signal. The temporal variation of MLEs exhibited significant fluctuations from 23 until 31 December when the eruptive activity shifted from explosive to effusive. Such a situation may reflect variable fluid pressure conditions inside the conduit, where at first magma is accumulated and subsequently is erupted, releasing the buildup of pressure. Our results give further evidence for the role of nonlinear deterministic processes in generating volcanic tremor and call for similar investigations to be conducted in other volcanoes.

Description: Complex electrical measurements with the use of sodar data show that electric field pulsation analysis is useful for electrodynamics/turbulence monitoring under different conditions. In particular, the number of aeroelectric structures (AES) generated per hour is a convenient measure of the turbulence intensity. During convectively unstable periods, as many as 5–10 AES form per hour. Under stable conditions, AES occasionally form as well, indicating the appearance of occasional mixing events reflected in the electric field perturbations. AES magnitudes under stable conditions are relatively small, except in special cases such as high humidity and fog. The analysis of electric field (EF) spectra gives additional useful information on the parameters of the atmospheric boundary layer and its turbulence. A rather sharp change in the spectrum slope takes place in the vicinity of 0.02 Hz under stable conditions. The characteristic slope of the spectrum and its change are reproduced in a simple model of EF formation.

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

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