ALBERT

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Description: A stochastic nonlinear oscillator model for glacial millennial-scale climate transitions derived from ice-core data Nonlinear Processes in Geophysics, 19, 595-603, 2012 Author(s): F. Kwasniok and G. Lohmann A stochastic Duffing-type oscillator model, i.e noise-driven motion with inertia in a potential landscape, is considered for glacial millennial-scale climate transitions. The potential and noise parameters are estimated from a Greenland ice-core record using a nonlinear Kalman filter. For the period from 60 to 20 ky before present, a bistable potential with a deep well corresponding to a cold stadial state and a shallow well corresponding to a warm interstadial state is found. The system is in the strongly dissipative regime and can be very well approximated by an effective one-dimensional Langevin equation.

Description: Reconnection current sheet structure in a turbulent medium Nonlinear Processes in Geophysics, 19, 605-610, 2012 Author(s): E. T. Vishniac, S. Pillsworth, G. Eyink, G. Kowal, A. Lazarian, and S. Murray In the presence of turbulence, magnetic field lines lose their dynamical identity and particles entrained on field lines diffuse through space at a rate determined by the amplitude of the turbulence. In previous work (Lazarian and Vishniac, 1999; Kowal et al., 2009; Eyink et al., 2011) we showed that this leads to reconnection speeds which are independent of resistivity. In particular, in Kowal et al. (2009) we showed that numerical simulations were consistent with the predictions of this model. Here we examine the structure of the current sheet in simulations of turbulent reconnection. Laminar flows consistent with the Sweet-Parker reconnection model produce very thin and well ordered currents sheets. On the other hand, the simulations of Kowal et al. (2009) show a strongly disordered state even for relatively low levels of turbulence. Comparing data cubes with and without reconnection, we find that large scale field reversals are the cumulative effect of many individual eddies, each of which has magnetic properties which are not very different from turbulent eddies in a homogeneous background. This implies that the properties of stationary and homogeneous MHD turbulence are a reasonable guide to understanding turbulence during large scale magnetic reconnection events. In addition, dissipation and high energy particle acceleration during reconnection events take place over a macroscopic volume, rather than being confined to a narrow zone whose properties depend on microscopic transport coefficients.

Description: Complete synchronization of chaotic atmospheric models by connecting only a subset of state space Nonlinear Processes in Geophysics, 19, 611-621, 2012 Author(s): P. H. Hiemstra, N. Fujiwara, F. M. Selten, and J. Kurths Connected chaotic systems can, under some circumstances, synchronize their states with an exchange of matter and energy between the systems. This is the case for toy models like the Lorenz 63, and more complex models. In this study we perform synchronization experiments with two connected quasi-geostrophic (QG) models of the atmosphere with 1449 degrees of freedom. The purpose is to determine whether connecting only a subset of the model state space can still lead to complete synchronization (CS). In addition, we evaluated whether empirical orthogonal functions (EOF) form efficient basis functions for synchronization in order to limit the number of connections. In this paper, we show that only the intermediate spectral wavenumbers (5–12) need to be connected in order to achieve CS. In addition, the minimum connection timescale needed for CS is 7.3 days. Both the connection subset and the connection timescale, or strength, are consistent with the time and spatial scales of the baroclinic instabilities in the model. This is in line with the fact that the baroclinic instabilities are the largest source of divergence between the two connected models. Using the Lorenz 63 model, we show that EOFs are nearly optimal basis functions for synchronization. The QG model results show that the minimum number of EOFs that need to be connected for CS is a factor of three smaller than when connecting the original state variables.

Description: Brief communication "Stratospheric winds, transport barriers and the 2011 Arctic ozone hole" Nonlinear Processes in Geophysics, 19, 687-692, 2012 Author(s): M. J. Olascoaga, M. G. Brown, F. J. Beron-Vera, and H. Koçak The Arctic stratosphere throughout the late winter and early spring of 2011 was characterized by an unusually severe ozone loss, resulting in what has been described as an ozone hole. The 2011 ozone loss was made possible by unusually cold temperatures throughout the Arctic stratosphere. Here we consider the issue of what constitutes suitable environmental conditions for the formation and maintenance of a polar ozone hole. Our discussion focuses on the importance of the stratospheric wind field and, in particular, the importance of a high latitude zonal jet, which serves as a meridional transport barrier both prior to ozone hole formation and during the ozone hole maintenance phase. It is argued that stratospheric conditions in the boreal winter/spring of 2011 were highly unusual inasmuch as in that year Antarctic-like Lagrangian dynamics led to the formation of a boreal ozone hole.

Description: Corrigendum to "Scaling laws of diffusion and time intermittency generated by coherent structures in atmospheric turbulence" published in Nonlin. Processes Geophys., 19, 113–126, 2012 Nonlinear Processes in Geophysics, 19, 685-685, 2012 Author(s): P. Paradisi, R. Cesari, A. Donateo, D. Contini, and P. Allegrini No abstract available.

Description: Combining inflation-free and iterative ensemble Kalman filters for strongly nonlinear systems Nonlinear Processes in Geophysics, 19, 383-399, 2012 Author(s): M. Bocquet and P. Sakov The finite-size ensemble Kalman filter (EnKF-N) is an ensemble Kalman filter (EnKF) which, in perfect model condition, does not require inflation because it partially accounts for the ensemble sampling errors. For the Lorenz '63 and '95 toy-models, it was so far shown to perform as well or better than the EnKF with an optimally tuned inflation. The iterative ensemble Kalman filter (IEnKF) is an EnKF which was shown to perform much better than the EnKF in strongly nonlinear conditions, such as with the Lorenz '63 and '95 models, at the cost of iteratively updating the trajectories of the ensemble members. This article aims at further exploring the two filters and at combining both into an EnKF that does not require inflation in perfect model condition, and which is as efficient as the IEnKF in very nonlinear conditions. In this study, EnKF-N is first introduced and a new implementation is developed. It decomposes EnKF-N into a cheap two-step algorithm that amounts to computing an optimal inflation factor. This offers a justification of the use of the inflation technique in the traditional EnKF and why it can often be efficient. Secondly, the IEnKF is introduced following a new implementation based on the Levenberg-Marquardt optimisation algorithm. Then, the two approaches are combined to obtain the finite-size iterative ensemble Kalman filter (IEnKF-N). Several numerical experiments are performed on IEnKF-N with the Lorenz '95 model. These experiments demonstrate its numerical efficiency as well as its performance that offer, at least, the best of both filters. We have also selected a demanding case based on the Lorenz '63 model that points to ways to improve the finite-size ensemble Kalman filters. Eventually, IEnKF-N could be seen as the first brick of an efficient ensemble Kalman smoother for strongly nonlinear systems.

Description: Mass and momentum transfer by solitary internal waves in a shelf zone Nonlinear Processes in Geophysics, 19, 265-272, 2012 Author(s): N. Gavrilov, V. Liapidevskii, and K. Gavrilova The evolution of large amplitude internal waves propagating towards the shore and more specifically the run up phase over the "swash" zone is considered. The mathematical model describing the generation, interaction, and decaying of solitary internal waves of the second mode in the interlayer is proposed. The exact solution specifying the shape of solitary waves symmetric with respect to the unperturbed interface is constructed. It is shown that, taking into account the friction on interfaces in the mathematical model, it is possible to describe adequately the change in the phase and amplitude characteristics of two solitary waves moving towards each other before and after their interaction. It is demonstrated that propagation of large amplitude solitary internal waves of depression over a shelf could be simulated in laboratory experiments by internal symmetric solitary waves of the second mode.

Description: Achieving fast reconnection in resistive MHD models via turbulent means Nonlinear Processes in Geophysics, 19, 251-263, 2012 Author(s): G. Lapenta and A. Lazarian Astrophysical fluids are generally turbulent and this preexisting turbulence must be taken into account for models of magnetic reconnection in astrophysical, solar or heliospheric environments. In addition, reconnection itself induces turbulence which provides an important feedback on the reconnection process. In this paper we discuss both the theoretical model and numerical evidence that magnetic reconnection becomes fast in the approximation of resistive MHD. We consider the relation between the Lazarian and Vishniac turbulent reconnection theory and Lapenta's numerical experiments testifying of the spontaneous onset of turbulent reconnection in systems which are initially laminar.

Description: Multiple equilibria and oscillatory modes in a mid-latitude ocean-forced atmospheric model Nonlinear Processes in Geophysics, 19, 479-499, 2012 Author(s): B. Deremble, E. Simonnet, and M. Ghil Atmospheric response to a mid-latitude sea surface temperature (SST) front is studied, while emphasizing low-frequency modes induced by the presence of such a front. An idealized atmospheric quasi-geostrophic (QG) model is forced by the SST field of an idealized oceanic QG model. First, the equilibria of the oceanic model and the associated SST fronts are computed. Next, these equilibria are used to force the atmospheric model and compute its equilibria when varying the strength of the oceanic forcing. Low-frequency modes of atmospheric variability are identified and associated with successive Hopf bifurcations. The origin of these Hopf bifurcations is studied in detail, and connected to barotropic instability. Finally, a link is established between the model's time integrations and the previously obtained equilibria.

Description: The mechanism of non-linear photochemical oscillations in the mesopause region Nonlinear Processes in Geophysics, 19, 501-512, 2012 Author(s): M. Yu. Kulikov, O. L. Vadimova, S. K. Ignatov, and A. M. Feigin The mechanism of generation of 2-day photochemical oscillations in the mesopause region (80–90 km) has been studied analytically. The initial system of equations of chemical kinetics describing the temporal evolution of O, O 3 , H, OH and HO 2 concentrations with allowance for diurnal variations of solar radiation has been simplified successively to a system of two nonlinear first-order time equations with sinusoidal external forcing. The obtained system has a minimum number of terms needed for generation of 2-day oscillations. Linearization of this system near the period-doubling threshold permits separating explicitly a particular case of the Mathieu equation ẍ + α · sin ω t · x = 0, in which the first sub-harmonic (ω/2) of the exciting force starts to grow exponentially when the amplitude of external forcing (α) exceeds its threshold value. Finally, a system of two simplest differential equations with power-law nonlinearity has been derived that allows analytical investigation of the effect of arising of reaction-diffusion waves in the mesospheric photochemical system.

Description: Predictability of extreme values in geophysical models Nonlinear Processes in Geophysics, 19, 529-539, 2012 Author(s): A. E. Sterk, M. P. Holland, P. Rabassa, H. W. Broer, and R. Vitolo Extreme value theory in deterministic systems is concerned with unlikely large (or small) values of an observable evaluated along evolutions of the system. In this paper we study the finite-time predictability of extreme values, such as convection, energy, and wind speeds, in three geophysical models. We study whether finite-time Lyapunov exponents are larger or smaller for initial conditions leading to extremes. General statements on whether extreme values are better or less predictable are not possible: the predictability of extreme values depends on the observable, the attractor of the system, and the prediction lead time.

Description: Brief communication "Improving the actual coverage of subsampling confidence intervals in atmospheric time series analysis" Nonlinear Processes in Geophysics, 19, 473-477, 2012 Author(s): A. Gluhovsky and T. Nielsen In atmospheric time series analysis, where only one record is typically available, subsampling (which works under the weakest assumptions among resampling methods), is especially useful. In particular, it yields large-sample confidence intervals of asymptotically correct coverage probability. Atmospheric records, however, are often not long enough, causing a substandard coverage of subsampling confidence intervals. In the paper, the subsampling methodology is extended to become more applicable in such practically important cases.

Description: Application of concentration-volume fractal method in induced polarization and resistivity data interpretation for Cu-Mo porphyry deposits exploration, case study: Nowchun Cu-Mo deposit, SE Iran Nonlinear Processes in Geophysics, 19, 431-438, 2012 Author(s): L. Daneshvar Saein, I. Rasa, N. Rashidnejad Omran, P. Moarefvand, and P. Afzal The aim of this study is the utilization of the concentration-volume ( C-V ) fractal method based on geoelectrical data including induced polarization (IP) and resistivity (RS) in targeting areas hosting different sulfidic mineralization zones in Nowchun Cu-Mo porphyry deposit, SE Iran. The C-V fractal model employed in this research in order to separate high and moderate sulfidic zones from low sulfidic zone and barren wall rocks in the deposit is corresponding to chargeability and resistivity. Results obtained from the C-V method indicate that there is a positive correlation between subsurface mineralization and sulfide mineralized zones; additionally, use of the C-V method based on geophysical data is recognized as an accurate approach for delineation of various mineralization zones in the depth for optimization of mineral exploration operation, particularly in porphyry deposits.

Description: Application of k -means and Gaussian mixture model for classification of seismic activities in Istanbul Nonlinear Processes in Geophysics, 19, 411-419, 2012 Author(s): H. S. Kuyuk, E. Yildirim, E. Dogan, and G. Horasan Two unsupervised pattern recognition algorithms, k -means, and Gaussian mixture model (GMM) analyses have been applied to classify seismic events in the vicinity of Istanbul. Earthquakes, which are occurring at different seismicity rates and extensions of the Thrace-Eskisehir Fault Zone and the North Anatolian Fault (NAF), Turkey, are being contaminated by quarries operated around Istanbul. We have used two time variant parameters, complexity, the ratio of integrated powers of the velocity seismogram, and S/P amplitude ratio as classifiers by using waveforms of 179 events (1.8 〈 M 〈 3.0). We have compared two algorithms with classical multivariate linear/quadratic discriminant analyses. The total accuracies of the models for GMM, k -means, linear discriminant function (LDF), and quadratic discriminant function (QDF) are 96.1%, 95.0%, 96.1%, 96.6%, respectively. The performances of models are discussed for earthquakes and quarry blasts separately. All methods clustered the seismic events acceptably where QDF slightly gave better improvements compared to others. We have found that unsupervised clustering algorithms, for which no a-prior target information is available, display a similar discriminatory power as supervised methods of discriminant analysis.

Description: Possible link between Holocene East Asian monsoon and solar activity obtained from the EMD method Nonlinear Processes in Geophysics, 19, 421-430, 2012 Author(s): H. Y. Liu, Z. S. Lin, X. Z. Qi, Y. X. Li, M. T. Yu, H. Yang, and J. Shen It is thought that East Asian monsoon (EAM) is linked and sensitive to solar activity. In this paper, we have decomposed the Dongge cave speleothem δ 18 O record (proxy for EAM), and Δ 14 C and 10 Be (proxies for solar activity) time series into variations at different time scales with the empirical mode decomposition (EMD) method to reveal the possible link between the EAM variability and solar activity. There are some common cycles in the EAM and solar variability from centennial to millennial scales, indicating a possible link between EAM and solar activity at these time scales. The correlation between EAM and solar activity is much higher at millennial scales than at centennial scales, which means direct responses to the solar variation are more likely at time scales longer than a few hundred years. At ~30, 60 and 600 yr time scales, the variation in EAM is amplified by the solar amplitude modulation at ~100, 200 and 2200 yr time scales.

Description: Evolutionary modeling-based approach for model errors correction Nonlinear Processes in Geophysics, 19, 439-447, 2012 Author(s): S. Q. Wan, W. P. He, L. Wang, W. Jiang, and W. Zhang The inverse problem of using the information of historical data to estimate model errors is one of the science frontier research topics. In this study, we investigate such a problem using the classic Lorenz (1963) equation as a prediction model and the Lorenz equation with a periodic evolutionary function as an accurate representation of reality to generate "observational data." On the basis of the intelligent features of evolutionary modeling (EM), including self-organization, self-adaptive and self-learning, the dynamic information contained in the historical data can be identified and extracted by computer automatically. Thereby, a new approach is proposed to estimate model errors based on EM in the present paper. Numerical tests demonstrate the ability of the new approach to correct model structural errors. In fact, it can actualize the combination of the statistics and dynamics to certain extent.

Description: Review article "On the origins of decadal climate variability: a network perspective" Nonlinear Processes in Geophysics, 19, 559-568, 2012 Author(s): A. A. Tsonis and K. L. Swanson This review is a synthesis of work spanning the last 25 yr. It is largely based on the use of climate networks to identify climate subsystems/major modes and to subsequently study how their collective behavior explains decadal variability. The central point is that a network of coupled nonlinear subsystems may at times begin to synchronize. If during synchronization the coupling between the subsystems increases, the synchronous state may, at some coupling strength threshold, be destroyed shifting climate to a new regime. This climate shift manifests itself as a change in global temperature trend. This mechanism, which is consistent with the theory of synchronized chaos, appears to be a very robust mechanism of the climate system. It is found in the instrumental records, in forced and unforced climate simulations, as well as in proxy records spanning several centuries.

Description: Forecast improvement in Lorenz 96 system Nonlinear Processes in Geophysics, 19, 569-575, 2012 Author(s): L. Basnarkov and L. Kocarev Contemporary numerical weather prediction schemes are based on ensemble forecasting. Ensemble members are obtained by taking different (perturbed) models started with different initial conditions. We introduce one type of improved model that represents interactive ensemble of individual models. The improved model's performance is tested with the Lorenz 96 toy model. One complex model is considered as reality, while its imperfect models are taken to be structurally simpler and with lower resolution. The improved model is defined as one with tendency that is weighted average of the tendencies of individual models. The weights are calculated from past observations by minimizing the average difference between the improved model's tendency and that of the reality. It is numerically verified that the improved model has better ability for short-term prediction than any of the individual models.

Description: Estimation and calibration of observation impact signals using the Lanczos method in NOAA/NCEP data assimilation system Nonlinear Processes in Geophysics, 19, 541-557, 2012 Author(s): M. Wei, M. S. F. V. De Pondeca, Z. Toth, and D. Parrish Despite the tremendous progress that has been made in data assimilation (DA) methodology, observing systems that reduce observation errors, and model improvements that reduce background errors, the analyses produced by the best available DA systems are still different from the truth. Analysis error and error covariance are important since they describe the accuracy of the analyses, and are directly related to the future forecast errors, i.e., the forecast quality. In addition, analysis error covariance is critically important in building an efficient ensemble forecast system (EFS). Estimating analysis error covariance in an ensemble-based Kalman filter DA is straightforward, but it is challenging in variational DA systems, which have been in operation at most NWP (Numerical Weather Prediction) centers. In this study, we use the Lanczos method in the NCEP (the National Centers for Environmental Prediction) Gridpoint Statistical Interpolation (GSI) DA system to look into other important aspects and properties of this method that were not exploited before. We apply this method to estimate the observation impact signals (OIS), which are directly related to the analysis error variances. It is found that the smallest eigenvalue of the transformed Hessian matrix converges to one as the number of minimization iterations increases. When more observations are assimilated, the convergence becomes slower and more eigenvectors are needed to retrieve the observation impacts. It is also found that the OIS over data-rich regions can be represented by the eigenvectors with dominant eigenvalues. Since only a limited number of eigenvectors can be computed due to computational expense, the OIS is severely underestimated, and the analysis error variance is consequently overestimated. It is found that the mean OIS values for temperature and wind components at typical model levels are increased by about 1.5 times when the number of eigenvectors is doubled. We have proposed four different calibration schemes to compensate for the missing trailing eigenvectors. Results show that the method with calibration for a small number of eigenvectors cannot pick up the observation impacts over the regions with fewer observations as well as a benchmark with a large number of eigenvectors, but proper calibrations do enhance and improve the impact signals over regions with more data. When compared with the observation locations, the method generally captures the OIS over regions with more observation data, including satellite data over the southern oceans. Over the tropics, some observation impacts may be missed due to the smaller background errors specified in the GSI, which is not related to the method. It is found that a large number of eigenvectors are needed to retrieve impact signals that resemble the banded structures from satellite observations, particularly over the tropics. Another benefit from the Lanczos method is that the dominant eigenvectors can be used in preconditioning the conjugate gradient algorithm in the GSI to speed up the convergence.

Description: Scaling properties of planetary calderas and terrestrial volcanic eruptions Nonlinear Processes in Geophysics, 19, 585-593, 2012 Author(s): L. Sanchez and R. Shcherbakov Volcanism plays an important role in transporting internal heat of planetary bodies to their surface. Therefore, volcanoes are a manifestation of the planet's past and present internal dynamics. Volcanic eruptions as well as caldera forming processes are the direct manifestation of complex interactions between the rising magma and the surrounding host rock in the crust of terrestrial planetary bodies. Attempts have been made to compare volcanic landforms throughout the solar system. Different stochastic models have been proposed to describe the temporal sequences of eruptions on individual or groups of volcanoes. However, comprehensive understanding of the physical mechanisms responsible for volcano formation and eruption and more specifically caldera formation remains elusive. In this work, we propose a scaling law to quantify the distribution of caldera sizes on Earth, Mars, Venus, and Io, as well as the distribution of calderas on Earth depending on their surrounding crustal properties. We also apply the same scaling analysis to the distribution of interevent times between eruptions for volcanoes that have the largest eruptive history as well as groups of volcanoes on Earth. We find that when rescaled with their respective sample averages, the distributions considered show a similar functional form. This result implies that similar processes are responsible for caldera formation throughout the solar system and for different crustal settings on Earth. This result emphasizes the importance of comparative planetology to understand planetary volcanism. Similarly, the processes responsible for volcanic eruptions are independent of the type of volcanism or geographical location.

Description: Semi-automated extraction of Deviation Indexes (DI) from satellite Persistent Scatterers time series: tests on sedimentary volcanism and tectonically-induced motions Nonlinear Processes in Geophysics, 19, 643-655, 2012 Author(s): F. Cigna, D. Tapete, and N. Casagli We develop a methodology based on satellite Persistent Scatterers (PS) time series and aimed to calculate two indexes which are capable to depict the deviation from a deformation model defined a priori. Through a simple mathematical approach, these indexes reproduce the visual process of identification of trend deviations that is usually performed manually by the radar-interpreter, and guide the prioritization of further interpretation for those areas recording significant variations within their motion history. First tests on semi-automated extraction of the Deviation Indexes (DI) from RADARSAT-1 PS data available over Southern Italy allowed the quantification of tectonically-induced land motions which occurred in February 2005 within the town of Naro, and also the clear recognition of the precursors to mud volcano eruptions which occurred in August 2008 in the village of St. Barbara. For these areas, the information level brought by the DI increases and adds onto that of other PS parameters, such as yearly velocity, standard deviation and coherence. Factors exerting influence on the DI are critically tackled within the discussions, together with the analysis of the potentials of these indexes for monitoring and warning activities of geohazards.

Description: Multifractal analysis of solar flare indices and their horizontal visibility graphs Nonlinear Processes in Geophysics, 19, 657-665, 2012 Author(s): Z. G. Yu, V. Anh, R. Eastes, and D.-L. Wang The multifractal properties of the daily solar X-ray brightness, X l and X s , during the period from 1 January 1986 to 31 December 2007 which includes two solar cycles are examined using the universal multifractal approach and multifractal detrended fluctuation analysis. Then we convert these time series into networks using the horizontal visibility graph technique. Multifractal analysis of the resulting networks is performed using an algorithm proposed by us. The results from the multifractal analysis show that multifractality exists in both raw daily time series of X-ray brightness and their horizontal visibility graphs. It is also found that the empirical K ( q ) curves of raw time series can be fitted by the universal multifractal model. The numerical results on the raw data show that the Solar Cycle 23 is weaker than the Solar Cycle 22 in multifractality. The values of h (2) from multifractal detrended fluctuation analysis for these time series indicate that they are stationary and persistent, and the correlations in the time series of Solar Cycle 23 are stronger than those for Solar Cycle 22. Furthermore, the multifractal scaling for the networks of the time series can reflect some properties which cannot be picked up by using the same analysis on the original time series. This suggests a potentially useful method to explore geophysical data.

Description: Investigation of correlation of the variations in land subsidence (detected by continuous GPS measurements) and methodological data in the surrounding areas of Lake Urmia Nonlinear Processes in Geophysics, 19, 675-683, 2012 Author(s): K. Moghtased-Azar, A. Mirzaei, H. R. Nankali, and F. Tavakoli Lake Urmia, a salt lake in the north-west of Iran, plays a valuable role in the environment, wildlife and economy of Iran and the region, but now faces great challenges for survival. The Lake is in immediate and great danger and is rapidly going to become barren desert. As a result, the increasing demands upon groundwater resources due to expanding metropolitan and agricultural areas are a serious challenge in the surrounding regions of Lake Urmia. The continuous GPS measurements around the lake illustrate significant subsidence rate between 2005 and 2009. The objective of this study was to detect and specify the non-linear correlation of land subsidence and temperature activities in the region from 2005 to 2009. For this purpose, the cross wavelet transform (XWT) was carried out between the two types of time series, namely vertical components of GPS measurements and daily temperature time series. The significant common patterns are illustrated in the high period bands from 180–218 days band (~6–7 months) from September 2007 to February 2009. Consequently, the satellite altimetry data confirmed that the maximum rate of linear trend of water variation in the lake from 2005 to 2009, is associated with time interval from September 2007 to February 2009. This event was detected by XWT as a critical interval to be holding the strong correlation between the land subsidence phenomena and surface temperature. Eventually the analysis can be used for modeling and prediction purposes and probably stave off the damage from subsidence phenomena.

Description: Fractal dimension analysis of the magnetic time series associated with the volcanic activity of Popocatépetl Nonlinear Processes in Geophysics, 19, 693-701, 2012 Author(s): E. L. Flores-Marquez, G. Galvez-Coyt, and G. Cifuentes-Nava Fractal analysis of the total magnetic field (TMF) time series from 1997 to 2003 at Popocatépetl Volcano is performed and compared with the TMF-series of the Teoloyucan Magnetic Observatory, 100 km away. Using Higuchi's fractal dimension method ( D ). The D changes over time for both series were computed. It was observed, when the time windows used to compute D increase in length, both series show nearly the same behavior. Some criteria of comparison were employed to discriminate the local effects inherent to volcano-magnetism. The simultaneous maximum in D (1.8) of the TMF series at Popocatépetl Volcano and the recovered volcanic activity indicates a scaling relation of the TMF at Popocatépetl Volcano and demonstrates a link between the magnetic field and volcanic activity.

Description: On the multi-scale nature of large geomagnetic storms: an empirical mode decomposition analysis Nonlinear Processes in Geophysics, 19, 667-673, 2012 Author(s): P. De Michelis, G. Consolini, and R. Tozzi Complexity and multi-scale are very common properties of several geomagnetic time series. On the other hand, it is amply demonstrated that scaling properties of geomagnetic time series show significant changes depending on the geomagnetic activity level. Here, we study the multi-scale features of some large geomagnetic storms by applying the empirical mode decomposition technique. This method, which is alternative to traditional data analysis and is designed specifically for analyzing nonlinear and nonstationary data, is applied to long time series of Sym-H index relative to periods including large geomagnetic disturbances. The spectral and scaling features of the intrinsic mode functions (IMFs) into which Sym-H time series can be decomposed, as well as those of the Sym-H time series itself, are studied considering different geomagnetic activity levels. The results suggest an increase of dynamical complexity and multi-scale properties for intermediate geomagnetic activity levels.

Description: Multifractal model of magnetic susceptibility distributions in some igneous rocks Nonlinear Processes in Geophysics, 19, 635-642, 2012 Author(s): M. E. Gettings Measurements of in-situ magnetic susceptibility were compiled from mainly Precambrian crystalline basement rocks beneath the Colorado Plateau and ranges in Arizona, Colorado, and New Mexico. The susceptibility meter used measures about 30 cm 3 of rock and measures variations in the modal distribution of magnetic minerals that form a minor component volumetrically in these coarsely crystalline granitic to granodioritic rocks. Recent measurements include 50–150 measurements on each outcrop, and show that the distribution of magnetic susceptibilities is highly variable, multimodal and strongly non-Gaussian. Although the distribution of magnetic susceptibility is well known to be multifractal, the small number of data points at an outcrop precludes calculation of the multifractal spectrum by conventional methods. Instead, a brute force approach was adopted using multiplicative cascade models to fit the outcrop scale variability of magnetic minerals. Model segment proportion and length parameters resulted in 26 676 models to span parameter space. Distributions at each outcrop were normalized to unity magnetic susceptibility and added to compare all data for a rock body accounting for variations in petrology and alteration. Once the best-fitting model was found, the equation relating the segment proportion and length parameters was solved numerically to yield the multifractal spectrum estimate. For the best fits, the relative density (the proportion divided by the segment length) of one segment tends to be dominant and the other two densities are smaller and nearly equal. No other consistent relationships between the best fit parameters were identified. The multifractal spectrum estimates appear to distinguish between metamorphic gneiss sites and sites on plutons, even if the plutons have been metamorphosed. In particular, rocks that have undergone multiple tectonic events tend to have a larger range of scaling exponents.

Description: The Arctic stratosphere throughout the late winter and early spring of 2011 was characterized by an unusually severe ozone loss, resulting in what has been described as an ozone hole. The 2011 ozone loss was made possible by unusually cold temperatures throughout the Arctic stratosphere. Here we consider the issue of what constitutes suitable environmental conditions for the formation and maintenance of a polar ozone hole. Our discussion focuses on the importance of the stratospheric wind field and, in particular, the importance of a high latitude zonal jet, which serves as a meridional transport barrier both prior to ozone hole formation and during the ozone hole maintenance phase. It is argued that stratospheric conditions in the boreal winter/spring of 2011 were highly unusual inasmuch as in that year Antarctic-like Lagrangian dynamics led to the formation of a boreal ozone hole.

Description: The multifractal properties of the daily solar X-ray brightness, Xl and Xs, during the period from 1 January 1986 to 31 December 2007 which includes two solar cycles are examined using the universal multifractal approach and multifractal detrended fluctuation analysis. Then we convert these time series into networks using the horizontal visibility graph technique. Multifractal analysis of the resulting networks is performed using an algorithm proposed by us. The results from the multifractal analysis show that multifractality exists in both raw daily time series of X-ray brightness and their horizontal visibility graphs. It is also found that the empirical K(q) curves of raw time series can be fitted by the universal multifractal model. The numerical results on the raw data show that the Solar Cycle 23 is weaker than the Solar Cycle 22 in multifractality. The values of h(2) from multifractal detrended fluctuation analysis for these time series indicate that they are stationary and persistent, and the correlations in the time series of Solar Cycle 23 are stronger than those for Solar Cycle 22. Furthermore, the multifractal scaling for the networks of the time series can reflect some properties which cannot be picked up by using the same analysis on the original time series. This suggests a potentially useful method to explore geophysical data.

Description: Despite the tremendous progress that has been made in data assimilation (DA) methodology, observing systems that reduce observation errors, and model improvements that reduce background errors, the analyses produced by the best available DA systems are still different from the truth. Analysis error and error covariance are important since they describe the accuracy of the analyses, and are directly related to the future forecast errors, i.e., the forecast quality. In addition, analysis error covariance is critically important in building an efficient ensemble forecast system (EFS). Estimating analysis error covariance in an ensemble-based Kalman filter DA is straightforward, but it is challenging in variational DA systems, which have been in operation at most NWP (Numerical Weather Prediction) centers. In this study, we use the Lanczos method in the NCEP (the National Centers for Environmental Prediction) Gridpoint Statistical Interpolation (GSI) DA system to look into other important aspects and properties of this method that were not exploited before. We apply this method to estimate the observation impact signals (OIS), which are directly related to the analysis error variances. It is found that the smallest eigenvalue of the transformed Hessian matrix converges to one as the number of minimization iterations increases. When more observations are assimilated, the convergence becomes slower and more eigenvectors are needed to retrieve the observation impacts. It is also found that the OIS over data-rich regions can be represented by the eigenvectors with dominant eigenvalues. Since only a limited number of eigenvectors can be computed due to computational expense, the OIS is severely underestimated, and the analysis error variance is consequently overestimated. It is found that the mean OIS values for temperature and wind components at typical model levels are increased by about 1.5 times when the number of eigenvectors is doubled. We have proposed four different calibration schemes to compensate for the missing trailing eigenvectors. Results show that the method with calibration for a small number of eigenvectors cannot pick up the observation impacts over the regions with fewer observations as well as a benchmark with a large number of eigenvectors, but proper calibrations do enhance and improve the impact signals over regions with more data. When compared with the observation locations, the method generally captures the OIS over regions with more observation data, including satellite data over the southern oceans. Over the tropics, some observation impacts may be missed due to the smaller background errors specified in the GSI, which is not related to the method. It is found that a large number of eigenvectors are needed to retrieve impact signals that resemble the banded structures from satellite observations, particularly over the tropics. Another benefit from the Lanczos method is that the dominant eigenvectors can be used in preconditioning the conjugate gradient algorithm in the GSI to speed up the convergence.

Description: In atmospheric time series analysis, where only one record is typically available, subsampling (which works under the weakest assumptions among resampling methods), is especially useful. In particular, it yields large-sample confidence intervals of asymptotically correct coverage probability. Atmospheric records, however, are often not long enough, causing a substandard coverage of subsampling confidence intervals. In the paper, the subsampling methodology is extended to become more applicable in such practically important cases.

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

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

Description: We investigate the time intermittency of turbulent transport associated with the birth-death of self-organized coherent structures in the atmospheric boundary layer. We apply a threshold analysis on the increments of turbulent fluctuations to extract sequences of rapid acceleration events, which is a marker of the transition between self-organized structures. The inter-event time distributions show a power-law decay ψ(τ) ~ 1/τμ, with a strong dependence of the power-law index μ on the threshold. A recently developed method based on the application of event-driven walking rules to generate different diffusion processes is applied to the experimental event sequences. At variance with the power-law index μ estimated from the inter-event time distributions, the diffusion scaling H, defined by ⟨ X2⟩ ~ t2H, is independent from the threshold. From the analysis of the diffusion scaling it can also be inferred the presence of different kind of events, i.e. genuinely transition events and spurious events, which all contribute to the diffusion process but over different time scales. The great advantage of event-driven diffusion lies in the ability of separating different regimes of the scaling H. In fact, the greatest H, corresponding to the most anomalous diffusion process, emerges in the long time range, whereas the smallest H can be seen in the short time range if the time resolution of the data is sufficiently accurate. The estimated diffusion scaling is also robust under the change of the definition of turbulent fluctuations and, under the assumption of statistically independent events, it corresponds to a self-similar point process with a well-defined power-law index μD ~ 2.1, where D denotes that μD is derived from the diffusion scaling. We argue that this renewal point process can be associated to birth and death of coherent structures and to turbulent transport near the ground, where the contribution of turbulent coherent structures becomes dominant.

Description: The problem of variational data assimilation (DA) for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition, boundary conditions and/or model parameters. The input data contain observation and background errors, hence there is an error in the optimal solution. For mildly nonlinear dynamics, the covariance matrix of the optimal solution error can be approximated by the inverse Hessian of the cost function. For problems with strongly nonlinear dynamics, a new statistical method based on the computation of a sample of inverse Hessians is suggested. This method relies on the efficient computation of the inverse Hessian by means of iterative methods (Lanczos and quasi-Newton BFGS) with preconditioning. Numerical examples are presented for the model governed by the Burgers equation with a nonlinear viscous term.

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

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

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

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

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

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

Description: The mechanism of generation of 2-day photochemical oscillations in the mesopause region (80–90 km) has been studied analytically. The initial system of equations of chemical kinetics describing the temporal evolution of O, O3, H, OH and HO2 concentrations with allowance for diurnal variations of solar radiation has been simplified successively to a system of two nonlinear first-order time equations with sinusoidal external forcing. The obtained system has a minimum number of terms needed for generation of 2-day oscillations. Linearization of this system near the period-doubling threshold permits separating explicitly a particular case of the Mathieu equation ẍ + α · sin ω t · x = 0, in which the first sub-harmonic (ω/2) of the exciting force starts to grow exponentially when the amplitude of external forcing (α) exceeds its threshold value. Finally, a system of two simplest differential equations with power-law nonlinearity has been derived that allows analytical investigation of the effect of arising of reaction-diffusion waves in the mesospheric photochemical system.

Description: It is thought that East Asian monsoon (EAM) is linked and sensitive to solar activity. In this paper, we have decomposed the Dongge cave speleothem δ18O record (proxy for EAM), and Δ14C and 10Be (proxies for solar activity) time series into variations at different time scales with the empirical mode decomposition (EMD) method to reveal the possible link between the EAM variability and solar activity. There are some common cycles in the EAM and solar variability from centennial to millennial scales, indicating a possible link between EAM and solar activity at these time scales. The correlation between EAM and solar activity is much higher at millennial scales than at centennial scales, which means direct responses to the solar variation are more likely at time scales longer than a few hundred years. At ~30, 60 and 600 yr time scales, the variation in EAM is amplified by the solar amplitude modulation at ~100, 200 and 2200 yr time scales.

Description: The inverse problem of using the information of historical data to estimate model errors is one of the science frontier research topics. In this study, we investigate such a problem using the classic Lorenz (1963) equation as a prediction model and the Lorenz equation with a periodic evolutionary function as an accurate representation of reality to generate "observational data." On the basis of the intelligent features of evolutionary modeling (EM), including self-organization, self-adaptive and self-learning, the dynamic information contained in the historical data can be identified and extracted by computer automatically. Thereby, a new approach is proposed to estimate model errors based on EM in the present paper. Numerical tests demonstrate the ability of the new approach to correct model structural errors. In fact, it can actualize the combination of the statistics and dynamics to certain extent.

Description: The aim of this study is the utilization of the concentration-volume (C-V) fractal method based on geoelectrical data including induced polarization (IP) and resistivity (RS) in targeting areas hosting different sulfidic mineralization zones in Nowchun Cu-Mo porphyry deposit, SE Iran. The C-V fractal model employed in this research in order to separate high and moderate sulfidic zones from low sulfidic zone and barren wall rocks in the deposit is corresponding to chargeability and resistivity. Results obtained from the C-V method indicate that there is a positive correlation between subsurface mineralization and sulfide mineralized zones; additionally, use of the C-V method based on geophysical data is recognized as an accurate approach for delineation of various mineralization zones in the depth for optimization of mineral exploration operation, particularly in porphyry deposits.

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

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

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

Description: The finite-size ensemble Kalman filter (EnKF-N) is an ensemble Kalman filter (EnKF) which, in perfect model condition, does not require inflation because it partially accounts for the ensemble sampling errors. For the Lorenz '63 and '95 toy-models, it was so far shown to perform as well or better than the EnKF with an optimally tuned inflation. The iterative ensemble Kalman filter (IEnKF) is an EnKF which was shown to perform much better than the EnKF in strongly nonlinear conditions, such as with the Lorenz '63 and '95 models, at the cost of iteratively updating the trajectories of the ensemble members. This article aims at further exploring the two filters and at combining both into an EnKF that does not require inflation in perfect model condition, and which is as efficient as the IEnKF in very nonlinear conditions. In this study, EnKF-N is first introduced and a new implementation is developed. It decomposes EnKF-N into a cheap two-step algorithm that amounts to computing an optimal inflation factor. This offers a justification of the use of the inflation technique in the traditional EnKF and why it can often be efficient. Secondly, the IEnKF is introduced following a new implementation based on the Levenberg-Marquardt optimisation algorithm. Then, the two approaches are combined to obtain the finite-size iterative ensemble Kalman filter (IEnKF-N). Several numerical experiments are performed on IEnKF-N with the Lorenz '95 model. These experiments demonstrate its numerical efficiency as well as its performance that offer, at least, the best of both filters. We have also selected a demanding case based on the Lorenz '63 model that points to ways to improve the finite-size ensemble Kalman filters. Eventually, IEnKF-N could be seen as the first brick of an efficient ensemble Kalman smoother for strongly nonlinear systems.

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

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

Description: The calibration of a radiocarbon age to a calendar date is reviewed. It is shown that the commonly-used programs for calibration sometimes give results that are significantly in error.

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

Description: Complexity and multi-scale are very common properties of several geomagnetic time series. On the other hand, it is amply demonstrated that scaling properties of geomagnetic time series show significant changes depending on the geomagnetic activity level. Here, we study the multi-scale features of some large geomagnetic storms by applying the empirical mode decomposition technique. This method, which is alternative to traditional data analysis and is designed specifically for analyzing nonlinear and nonstationary data, is applied to long time series of Sym-H index relative to periods including large geomagnetic disturbances. The spectral and scaling features of the intrinsic mode functions (IMFs) into which Sym-H time series can be decomposed, as well as those of the Sym-H time series itself, are studied considering different geomagnetic activity levels. The results suggest an increase of dynamical complexity and multi-scale properties for intermediate geomagnetic activity levels.

Description: Connected chaotic systems can, under some circumstances, synchronize their states with an exchange of matter and energy between the systems. This is the case for toy models like the Lorenz 63, and more complex models. In this study we perform synchronization experiments with two connected quasi-geostrophic (QG) models of the atmosphere with 1449 degrees of freedom. The purpose is to determine whether connecting only a subset of the model state space can still lead to complete synchronization (CS). In addition, we evaluated whether empirical orthogonal functions (EOF) form efficient basis functions for synchronization in order to limit the number of connections. In this paper, we show that only the intermediate spectral wavenumbers (5–12) need to be connected in order to achieve CS. In addition, the minimum connection timescale needed for CS is 7.3 days. Both the connection subset and the connection timescale, or strength, are consistent with the time and spatial scales of the baroclinic instabilities in the model. This is in line with the fact that the baroclinic instabilities are the largest source of divergence between the two connected models. Using the Lorenz 63 model, we show that EOFs are nearly optimal basis functions for synchronization. The QG model results show that the minimum number of EOFs that need to be connected for CS is a factor of three smaller than when connecting the original state variables.

Description: A stochastic Duffing-type oscillator model, i.e noise-driven motion with inertia in a potential landscape, is considered for glacial millennial-scale climate transitions. The potential and noise parameters are estimated from a Greenland ice-core record using a nonlinear Kalman filter. For the period from 60 to 20 ky before present, a bistable potential with a deep well corresponding to a cold stadial state and a shallow well corresponding to a warm interstadial state is found. The system is in the strongly dissipative regime and can be very well approximated by an effective one-dimensional Langevin equation.

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

Description: We study a model of fast magnetic reconnection in the presence of weak turbulence proposed by Lazarian and Vishniac (1999) using three-dimensional direct numerical simulations. The model has been already successfully tested in Kowal et al. (2009) confirming the dependencies of the reconnection speed Vrec on the turbulence injection power Pinj and the injection scale linj expressed by a constraint Vrec ~ Pinj1/2linj3/4and no observed dependency on Ohmic resistivity. In Kowal et al. (2009), in order to drive turbulence, we injected velocity fluctuations in Fourier space with frequencies concentrated around kinj = 1/linj, as described in Alvelius (1999). In this paper, we extend our previous studies by comparing fast magnetic reconnection under different mechanisms of turbulence injection by introducing a new way of turbulence driving. The new method injects velocity or magnetic eddies with a specified amplitude and scale in random locations directly in real space. We provide exact relations between the eddy parameters and turbulent power and injection scale. We performed simulations with new forcing in order to study turbulent power and injection scale dependencies. The results show no discrepancy between models with two different methods of turbulence driving exposing the same scalings in both cases. This is in agreement with the Lazarian and Vishniac (1999) predictions. In addition, we performed a series of models with varying viscosity ν. Although Lazarian and Vishniac (1999) do not provide any prediction for this dependence, we report a weak relation between the reconnection speed with viscosity, Vrec ~ ν−1/4.

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

Description: Astrophysical fluids are generally turbulent and this preexisting turbulence must be taken into account for models of magnetic reconnection in astrophysical, solar or heliospheric environments. In addition, reconnection itself induces turbulence which provides an important feedback on the reconnection process. In this paper we discuss both the theoretical model and numerical evidence that magnetic reconnection becomes fast in the approximation of resistive MHD. We consider the relation between the Lazarian and Vishniac turbulent reconnection theory and Lapenta's numerical experiments testifying of the spontaneous onset of turbulent reconnection in systems which are initially laminar.

Description: The sandy-clayey hydrocarbon reservoirs of the Upper Paleocene and Lower Eocene located to the north of Veracruz State, Mexico, present highly complex geological and petrophysical characteristics. These reservoirs, which consist of sandstone and shale bodies within a depth interval ranging from 500 to 2000 m, were characterized statistically by means of fractal modeling and geostatistical tools. For 14 wells within an area of study of approximately 6 km2, various geophysical well logs were initially edited and further analyzed to establish a correlation between logs and core data. The fractal modeling based on the R/S (rescaled range) methodology and the interpolation method by successive random additions were used to generate pseudo-well logs between observed wells. The application of geostatistical tools, sequential Gaussian simulation and exponential model variograms contributed to estimate the spatial distribution of petrophysical properties such as effective porosity (PHIE), permeability (K) and shale volume (VSH). From the analysis and correlation of the information generated in the present study, it can be said, from a general point of view, that the results not only are correlated with already reported information but also provide significant characterization elements that would be hardly obtained by means of conventional techniques.

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

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

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

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

Description: The evolution of large amplitude internal waves propagating towards the shore and more specifically the run up phase over the "swash" zone is considered. The mathematical model describing the generation, interaction, and decaying of solitary internal waves of the second mode in the interlayer is proposed. The exact solution specifying the shape of solitary waves symmetric with respect to the unperturbed interface is constructed. It is shown that, taking into account the friction on interfaces in the mathematical model, it is possible to describe adequately the change in the phase and amplitude characteristics of two solitary waves moving towards each other before and after their interaction. It is demonstrated that propagation of large amplitude solitary internal waves of depression over a shelf could be simulated in laboratory experiments by internal symmetric solitary waves of the second mode.