ALBERT

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Description: Distinguishing the effects of internal and forced atmospheric variability in climate networks Nonlinear Processes in Geophysics, 21, 617-631, 2014 Author(s): J. I. Deza, C. Masoller, and M. Barreiro The fact that the climate on the earth is a highly complex dynamical system is well-known. In the last few decades great deal of effort has been focused on understanding how climate phenomena in one geographical region affects the climate of other regions. Complex networks are a powerful framework for identifying climate interdependencies. To further exploit the knowledge of the links uncovered via the network analysis (for, e.g., improvements in prediction), a good understanding of the physical mechanisms underlying these links is required. Here we focus on understanding the role of atmospheric variability, and construct climate networks representing internal and forced variability using the output of an ensemble of AGCM runs. A main strength of our work is that we construct the networks using MIOP (mutual information computed from ordinal patterns), which allows the separation of intraseasonal, intra-annual and interannual timescales. This gives further insight to the analysis of climatological data. The connectivity of these networks allows us to assess the influence of two main indices, NINO3.4 – one of the indices used to describe ENSO (El Niño–Southern oscillation) – and of the North Atlantic Oscillation (NAO), by calculating the networks from time series where these indices were linearly removed. A main result of our analysis is that the connectivity of the forced variability network is heavily affected by "El Niño": removing the NINO3.4 index yields a general loss of connectivity; even teleconnections between regions far away from the equatorial Pacific Ocean are lost, suggesting that these regions are not directly linked, but rather, are indirectly interconnected via El Niño, particularly at interannual timescales. On the contrary, on the internal variability network – independent of sea surface temperature (SST) forcing – the links connecting the Labrador Sea with the rest of the world are found to be significantly affected by NAO, with a maximum at intra-annual timescales. While the strongest non-local links found are those forced by the ocean, the presence of teleconnections due to internal atmospheric variability is also shown.

Description: Monte Carlo fixed-lag smoothing in state-space models Nonlinear Processes in Geophysics, 21, 633-643, 2014 Author(s): A. Cuzol and E. Mémin This paper presents an algorithm for Monte Carlo fixed-lag smoothing in state-space models defined by a diffusion process observed through noisy discrete-time measurements. Based on a particle approximation of the filtering and smoothing distributions, the method relies on a simulation technique of conditioned diffusions. The proposed sequential smoother can be applied to general nonlinear and multidimensional models, like the ones used in environmental applications. The smoothing of a turbulent flow in a high-dimensional context is given as a practical example.

Description: On the influence of spatial sampling on climate networks Nonlinear Processes in Geophysics, 21, 651-657, 2014 Author(s): N. Molkenthin, K. Rehfeld, V. Stolbova, L. Tupikina, and J. Kurths Climate networks are constructed from climate time series data using correlation measures. It is widely accepted that the geographical proximity, as well as other geographical features such as ocean and atmospheric currents, have a large impact on the observable time-series similarity. Therefore it is to be expected that the spatial sampling will influence the reconstructed network. Here we investigate this by comparing analytical flow networks, networks generated with the START model and networks from temperature data from the Asian monsoon domain. We evaluate them on a regular grid, a grid with added random jittering and two variations of clustered sampling. We find that the impact of the spatial sampling on most network measures only distorts the plots if the node distribution is significantly inhomogeneous. As a simple diagnostic measure for the detection of inhomogeneous sampling we suggest the Voronoi cell size distribution.

Description: Four-dimensional ensemble variational (4D-En-Var) data assimilation for the HIgh Resolution Limited Area Model (HIRLAM) Nonlinear Processes in Geophysics, 21, 745-762, 2014 Author(s): N. Gustafsson and J. Bojarova A four-dimensional ensemble variational (4D-En-Var) data assimilation has been developed for a limited area model. The integration of tangent linear and adjoint models, as applied in standard 4D-Var, is replaced with the use of an ensemble of non-linear model states to estimate four-dimensional background error covariances over the assimilation time window. The computational costs for 4D-En-Var are therefore significantly reduced in comparison with standard 4D-Var and the scalability of the algorithm is improved. The flow dependency of 4D-En-Var assimilation increments is demonstrated in single simulated observation experiments and compared with corresponding increments from standard 4D-Var and Hybrid 4D-Var ensemble assimilation experiments. Real observation data assimilation experiments carried out over a 6-week period show that 4D-En-Var outperforms standard 4D-Var as well as Hybrid 4D-Var ensemble data assimilation with regard to forecast quality measured by forecast verification scores.

Description: Scale free properties in a network-based integrated approach to earthquake pattern analysis Nonlinear Processes in Geophysics, 21, 427-438, 2014 Author(s): M. Suteanu This paper proposes a network-based method for the assessment of earthquake relationships in space–time–magnitude patterns. It is shown that networks with high values for the minimum edge weight W min enjoy strong scaling properties, as opposed to networks with low values for W min , which exhibit no such properties. The scaling behavior along the spectrum of W min values, in conjunction with the robustness regarding parameter variations, endorse the idea of a relationship between fundamental properties of seismicity and the scaling properties of the earthquake networks. Results of this method are further applied for the study of temporal changes in volcanic seismicity patterns.

Description: Lagrangian descriptors and the assessment of the predictive capacity of oceanic data sets Nonlinear Processes in Geophysics, 21, 677-689, 2014 Author(s): C. Mendoza, A. M. Mancho, and S. Wiggins We use a recently developed Lagrangian transport tool, Lagrangian descriptors , to compare the transport properties of data distributed by AVISO and numerical simulations obtained from the HYCOM model in the Yucatán–Florida current system. Our data correspond to the months from June through August 2010. Structures obtained from HYCOM are noisier than those from AVISO; however, both AVISO and HYCOM succeed in identifying Lagrangian structures that influence the paths of drifters, such as eddies, currents, lobes, etc. We find evidence in which AVISO gives the positions of important hyperbolic trajectories in a manner that is inconsistent with the trajectories of the drifters, while for the same examples HYCOM succeeds to this end.

Description: Controlling balance in an ensemble Kalman filter Nonlinear Processes in Geophysics, 21, 417-426, 2014 Author(s): G. A. Gottwald We present a method to control unbalanced fast dynamics in an ensemble Kalman filter by introducing a weak constraint on the imbalance in a spatially sparse observational network. We show that the balance constraint produces significantly more balanced analyses than ensemble Kalman filters without balance constraints and than filters implementing incremental analysis updates (IAU). Furthermore, our filter with the weak constraint on imbalance produces good rms error statistics which outperform those of ensemble Kalman filters without balance constraints for the fast fields.

Description: The role of subsidence in a weakly unstable marine boundary layer: a case study Nonlinear Processes in Geophysics, 21, 489-501, 2014 Author(s): I. M. Mazzitelli, M. Cassol, M. M. Miglietta, U. Rizza, A. M. Sempreviva, and A. S. Lanotte The diurnal evolution of a cloud free, marine boundary layer is studied by means of experimental measurements and numerical simulations. Experimental data belong to an investigation of the mixing height over inner Danish waters. The mixed-layer height measured over the sea is generally nearly constant, and does not exhibit the diurnal cycle characteristic of boundary layers over land. A case study, during summer, showing an anomalous development of the mixed layer under unstable and nearly neutral atmospheric conditions, is selected in the campaign. Subsidence is identified as the main physical mechanism causing the sudden decrease in the mixing layer height. This is quantified by comparing radiosounding profiles with data from numerical simulations of a mesoscale model, and a large-eddy simulation model. Subsidence not only affects the mixing layer height, but also the turbulent fluctuations within it. By analyzing wind and scalar spectra, the role of subsidence is further investigated and a more complete interpretation of the experimental results emerges.

Description: Force chain and contact cycle evolution in a dense granular material under shallow penetration Nonlinear Processes in Geophysics, 21, 505-519, 2014 Author(s): A. Tordesillas, C. A. H. Steer, and D. M. Walker The mechanical response of a dense granular material submitted to indentation by a rigid flat punch is examined. The resultant deformation is viewed as a process of self-organisation. Four aspects of the mechanical response (i.e. indentation resistance, failure, Reynolds' dilatancy, the undeforming "dead zone") are explored with respect to the linear and cyclic structural building blocks of granular media self-organisation: force chains and contact network cycles. Formation and breaking of 3-cycle contacts preferentially occur around and close to the punch uncovering a "dilation zone". This zone encapsulates (i) most of the indentation resistance and is populated by force chains consisting of six or more particles, (ii) all buckling force chains, and (iii) a central, near-triangular, undeforming cluster of grains beneath the punch face. Force chain buckling is confined to the zone's outer regions, beneath the corners and to the sides of the punch where surface material heave forms. Grain rearrangements here involve the creation of 6-, 7-, and 8-cycles – in contrast with Reynolds' postulated cubic packing rearrangements (i.e. 3-cycles opening up to form 4-cycles). In between these intensely dilatant regions lies a compacted triangular grain cluster which moves in near-rigid body with the punch when jammed, but this dead zone unjams and deforms in the failure regimes when adjacent force chains buckle. The long force chains preferentially percolate from the punch face, through the dead zone, fanning downwards and outwards into the material.

Description: Full-field and anomaly initialization using a low-order climate model: a comparison and proposals for advanced formulations Nonlinear Processes in Geophysics, 21, 521-537, 2014 Author(s): A. Carrassi, R. J. T. Weber, V. Guemas, F. J. Doblas-Reyes, M. Asif, and D. Volpi Initialization techniques for seasonal-to-decadal climate predictions fall into two main categories; namely full-field initialization (FFI) and anomaly initialization (AI). In the FFI case the initial model state is replaced by the best possible available estimate of the real state. By doing so the initial error is efficiently reduced but, due to the unavoidable presence of model deficiencies, once the model is let free to run a prediction, its trajectory drifts away from the observations no matter how small the initial error is. This problem is partly overcome with AI where the aim is to forecast future anomalies by assimilating observed anomalies on an estimate of the model climate. The large variety of experimental setups, models and observational networks adopted worldwide make it difficult to draw firm conclusions on the respective advantages and drawbacks of FFI and AI, or to identify distinctive lines for improvement. The lack of a unified mathematical framework adds an additional difficulty toward the design of adequate initialization strategies that fit the desired forecast horizon, observational network and model at hand. Here we compare FFI and AI using a low-order climate model of nine ordinary differential equations and use the notation and concepts of data assimilation theory to highlight their error scaling properties. This analysis suggests better performances using FFI when a good observational network is available and reveals the direct relation of its skill with the observational accuracy. The skill of AI appears, however, mostly related to the model quality and clear increases of skill can only be expected in coincidence with model upgrades. We have compared FFI and AI in experiments in which either the full system or the atmosphere and ocean were independently initialized. In the former case FFI shows better and longer-lasting improvements, with skillful predictions until month 30. In the initialization of single compartments, the best performance is obtained when the stabler component of the model (the ocean) is initialized, but with FFI it is possible to have some predictive skill even when the most unstable compartment (the extratropical atmosphere) is observed. Two advanced formulations, least-square initialization (LSI) and exploring parameter uncertainty (EPU), are introduced. Using LSI the initialization makes use of model statistics to propagate information from observation locations to the entire model domain. Numerical results show that LSI improves the performance of FFI in all the situations when only a portion of the system's state is observed. EPU is an online drift correction method in which the drift caused by the parametric error is estimated using a short-time evolution law and is then removed during the forecast run. Its implementation in conjunction with FFI allows us to improve the prediction skill within the first forecast year. Finally, the application of these results in the context of realistic climate models is discussed.

Description: Generalized binomial multiplicative cascade processes and asymmetrical multifractal distributions Nonlinear Processes in Geophysics, 21, 477-487, 2014 Author(s): Q. Cheng The concepts and models of multifractals have been employed in various fields in the geosciences to characterize singular fields caused by nonlinear geoprocesses. Several indices involved in multifractal models, i.e., asymmetry, multifractality, and range of singularity, are commonly used to characterize nonlinear properties of multifractal fields. An understanding of how these indices are related to the processes involved in the generation of multifractal fields is essential for multifractal modeling. In this paper, a five-parameter binomial multiplicative cascade model is proposed based on the anisotropic partition processes. Each partition divides the unit set (1-D length or 2-D area) into h equal subsets (segments or subareas) and m 1 of them receive d 1 (〉 0) and m 2 receive d 2 (〉 0) proportion of the mass in the previous subset, respectively, where m 1 + m 2 ≤ h. The model is demonstrated via several examples published in the literature with asymmetrical fractal dimension spectra. This model demonstrates the various properties of asymmetrical multifractal distributions and multifractal indices with explicit functions, thus providing insight into and an understanding of the properties of asymmetrical binomial multifractal distributions.

Description: Extreme fluctuations of vertical velocity in the unstable atmospheric surface layer Nonlinear Processes in Geophysics, 21, 463-475, 2014 Author(s): L. Liu, F. Hu, and X.-L. Cheng In this paper, we propose a new method to extract the extreme fluctuations of vertical velocity in the unstable atmospheric surface layer. Unlike the commonly used conditional sampling analysis, this method defines a threshold by using a systematical method and tries to reduce the artificiality in this process. It defines threshold as the position where the types of probability density functions (PDFs) of vertical velocity fluctuations begin to change character from stable distributions to truncated stable distributions. Absolute values of fluctuations greater than the threshold are considered to be extreme fluctuations. We then analyze the statistical characteristics of extracted extreme fluctuations of vertical velocity. Our results show that the amplitudes of extreme fluctuations are exponentially distributed, and the waiting times between extreme fluctuations have stretched exponential distributions. It suggests that there are statistical correlations in the time series of vertical velocity because independent time series can only have exponentially distributed waiting times. The durations of extreme fluctuations are also found to be stretched exponential distributed, while for the independent time series the distributions of durations are delta-like. Finally, the PDFs of amplitudes, waiting times and durations are all well parameterized in the context of Monin–Obukhov theory.

Description: Corrigendum to "Thermal energy generation in the earth" published in Nonlin. Processes Geophys., 21, 367–378, 2014 Nonlinear Processes in Geophysics, 21, 503-503, 2014 Author(s): F. J. Mayer and J. R. Reitz No abstract available.

Description: Finding recurrence networks' threshold adaptively for a specific time series Nonlinear Processes in Geophysics, 21, 1085-1092, 2014 Author(s): D. Eroglu, N. Marwan, S. Prasad, and J. Kurths Recurrence-plot-based recurrence networks are an approach used to analyze time series using a complex networks theory. In both approaches – recurrence plots and recurrence networks –, a threshold to identify recurrent states is required. The selection of the threshold is important in order to avoid bias of the recurrence network results. In this paper, we propose a novel method to choose a recurrence threshold adaptively. We show a comparison between the constant threshold and adaptive threshold cases to study period–chaos and even period–period transitions in the dynamics of a prototypical model system. This novel method is then used to identify climate transitions from a lake sediment record.

Description: Wavevector anisotropy of plasma turbulence at ion kinetic scales: solar wind observations and hybrid simulations Nonlinear Processes in Geophysics, 21, 1075-1083, 2014 Author(s): H. Comişel, Y. Narita, and U. Motschmann Wavevector anisotropy of ion-scale plasma turbulence is studied at various values of ion beta. Two complementary methods are used. One is multi-point measurements of magnetic field in the near-Earth solar wind as provided by the Cluster spacecraft mission, and the other is hybrid numerical simulation of two-dimensional plasma turbulence. Both methods demonstrate that the wavevector anisotropy is reduced with increasing values of ion beta. Furthermore, the numerical simulation study shows the existence of a scaling law between ion beta and the wavevector anisotropy of the fluctuating magnetic field that is controlled by the thermal or hybrid particle-in-cell simulation noise. Likewise, there is weak evidence that the power-law scaling can be extended to the turbulent fluctuating cascade. This fact can be used to construct a diagnostic tool to determine or to constrain ion beta using multi-point magnetic field measurements in space.

Description: Estimation of sedimentary proxy records together with associated uncertainty Nonlinear Processes in Geophysics, 21, 1093-1111, 2014 Author(s): B. Goswami, J. Heitzig, K. Rehfeld, N. Marwan, A. Anoop, S. Prasad, and J. Kurths Sedimentary proxy records constitute a significant portion of the recorded evidence that allows us to investigate paleoclimatic conditions and variability. However, uncertainties in the dating of proxy archives limit our ability to fix the timing of past events and interpret proxy record intercomparisons. While there are various age-modeling approaches to improve the estimation of the age–depth relations of archives, relatively little focus has been placed on the propagation of the age (and radiocarbon calibration) uncertainties into the final proxy record. We present a generic Bayesian framework to estimate proxy records along with their associated uncertainty, starting with the radiometric age–depth and proxy–depth measurements, and a radiometric calibration curve if required. We provide analytical expressions for the posterior proxy probability distributions at any given calendar age, from which the expected proxy values and their uncertainty can be estimated. We illustrate our method using two synthetic data sets and then use it to construct the proxy records for groundwater inflow and surface erosion from Lonar lake in central India. Our analysis reveals interrelations between the uncertainty of the proxy record over time and the variance of proxies along the depth of the archive. For the Lonar lake proxies, we show that, rather than the age uncertainties, it is the proxy variance combined with calibration uncertainty that accounts for most of the final uncertainty. We represent the proxy records as probability distributions on a precise, error-free timescale that makes further time series analyses and intercomparisons of proxies relatively simple and clear. Our approach provides a coherent understanding of age uncertainties within sedimentary proxy records that involve radiometric dating. It can be potentially used within existing age modeling structures to bring forth a reliable and consistent framework for proxy record estimation.

Description: Estimating model error covariance matrix parameters in extended Kalman filtering Nonlinear Processes in Geophysics, 21, 919-927, 2014 Author(s): A. Solonen, J. Hakkarainen, A. Ilin, M. Abbas, and A. Bibov The extended Kalman filter (EKF) is a popular state estimation method for nonlinear dynamical models. The model error covariance matrix is often seen as a tuning parameter in EKF, which is often simply postulated by the user. In this paper, we study the filter likelihood technique for estimating the parameters of the model error covariance matrix. The approach is based on computing the likelihood of the covariance matrix parameters using the filtering output. We show that (a) the importance of the model error covariance matrix calibration depends on the quality of the observations, and that (b) the estimation approach yields a well-tuned EKF in terms of the accuracy of the state estimates and model predictions. For our numerical experiments, we use the two-layer quasi-geostrophic model that is often used as a benchmark model for numerical weather prediction.

Description: Intermittency of earthquake cycles in a model of a three-degree-of-freedom spring-block system Nonlinear Processes in Geophysics, 21, 841-853, 2014 Author(s): Y. Abe and N. Kato We herein report the results of some numerical simulations of complex earthquake cycles using a three-degree-of-freedom spring-block model with a rate- and state-dependent friction law. The model consists of three blocks on a conveyor belt that is moving at a steady rate. Observed complex slip behaviour in the simulations is classified into five slip patterns, and for each of these the parameter dependence of the slip patterns is demonstrated by means of phase diagrams. Aperiodic slip patterns occur for wider ranges of the parameter space in the three-block system than in the two-block system. Chaotic slip behaviour known here as "intermittency" is found in the three-block system, in which two different slip patterns occur alternately with variable durations. By calculating Lyapunov exponents, we quantify the dependence of slip evolution on the initial conditions for each slip pattern. For cases where intermittent slip patterns occur, the time evolution of the Lyapunov exponent is correlated with changes in slip behaviour.

Description: Fractal dimensions of wildfire spreading Nonlinear Processes in Geophysics, 21, 815-823, 2014 Author(s): S.-L. Wang, H.-I. Lee, and S.-P. Li The time series data of 31 wildfires in 2012 in the US were analyzed. The fractal dimensions (FD) of the wildfires during spreading were studied and their geological features were identified. A growth model based on the cellular automata method is proposed here. Numerical study was performed and is shown to give good agreement with the fractal dimensions and scaling behaviors of the corresponding empirical data.

Description: Evolution of atmospheric connectivity in the 20th century Nonlinear Processes in Geophysics, 21, 825-839, 2014 Author(s): F. Arizmendi, A. C. Martí, and M. Barreiro We aim to study the evolution of the upper atmosphere connectivity over the 20th century as well as to distinguish the oceanically forced component from the atmospheric internal variability. For this purpose we build networks from two different reanalysis data sets using both linear and nonlinear statistical similarity measures to determine the existence of links between different regions of the world in the two halves of the last century. We furthermore use symbolic analysis to emphasize intra-seasonal, intra-annual and inter-annual timescales. Both linear and nonlinear networks have similar structures and evolution, showing that the most connected regions are in the tropics over the Pacific Ocean. Also, the Southern Hemisphere extratropics have more connectivity in the first half of the 20th century, particularly on intra-annual and intra-seasonal timescales. Changes over the Pacific main connectivity regions are analyzed in more detail. Both linear and nonlinear networks show that the central and western Pacific regions have decreasing connectivity from early 1900 up to about 1940, when it starts increasing again until the present. The inter-annual network shows a similar behavior. However, this is not true of other timescales. On intra-annual timescales the minimum connectivity is around 1956, with a negative (positive) trend before (after) that date for both the central and western Pacific. While this is also true of the central Pacific on intra-seasonal timescales, the western Pacific shows a positive trend during the entire 20th century. In order to separate the internal and forced connectivity networks and to study their evolution through time, an ensemble of atmospheric general circulation model outputs is used. The results suggest that the main connectivity patterns captured in the reanalysis networks are due to the oceanically forced component, particularly on inter-annual timescales. Moreover, the atmospheric internal variability seems to play an important role in determining the intra-seasonal timescale networks.

Description: Can irregularities of solar proxies help understand quasi-biennial solar variations? Nonlinear Processes in Geophysics, 21, 797-813, 2014 Author(s): A. Shapoval, J. L. Le Mouël, M. Shnirman, and V. Courtillot We define, calculate and analyze irregularity indices λ ISSN of daily series of the International Sunspot Number ISSN as a function of increasing smoothing from N = 162 to 648 days. The irregularity indices λ are computed within 4-year sliding windows, with embedding dimensions m = 1 and 2. λ ISSN displays Schwabe cycles with ~5.5-year variations ("half Schwabe variations" HSV). The mean of λ ISSN undergoes a downward step and the amplitude of its variations strongly decreases around 1930. We observe changes in the ratio R of the mean amplitude of λ peaks at solar cycle minima with respect to peaks at solar maxima as a function of date, embedding dimension and, importantly, smoothing parameter N . We identify two distinct regimes, called Q1 and Q2, defined mainly by the evolution of R as a function of N : Q1, with increasing HSV behavior and R value as N is increased, occurs before 1915–1930; and Q2, with decreasing HSV behavior and R value as N is increased, occurs after ~1975. We attempt to account for these observations with an autoregressive (order 1) model with Poissonian noise and a mean modulated by two sine waves of periods T 1 and T 2 ( T 1 = 11 years, and intermediate T 2 is tuned to mimic quasi-biennial oscillations QBO). The model can generate both Q1 and Q2 regimes. When m = 1, HSV appears in the absence of T 2 variations. When m = 2, Q1 occurs when T 2 variations are present, whereas Q2 occurs when T 2 variations are suppressed. We propose that the HSV behavior of the irregularity index of ISSN may be linked to the presence of strong QBO before 1915–1930, a transition and their disappearance around 1975, corresponding to a change in regime of solar activity.

Description: Assimilation of HF radar surface currents to optimize forcing in the northwestern Mediterranean Sea Nonlinear Processes in Geophysics, 21, 659-675, 2014 Author(s): J. Marmain, A. Molcard, P. Forget, A. Barth, and Y. Ourmières HF radar measurements are used to optimize surface wind forcing and baroclinic open boundary condition forcing in order to constrain model coastal surface currents. This method is applied to a northwestern Mediterranean (NWM) regional primitive equation model configuration. A new radar data set, provided by two radars deployed in the Toulon area (France), is used. To our knowledge, this is the first time that radar measurements of the NWM Sea are assimilated into a circulation model. Special attention has been paid to the improvement of the model coastal current in terms of speed and position. The data assimilation method uses an ensemble Kalman smoother to optimize forcing in order to improve the model trajectory. Twin experiments are initially performed to evaluate the method skills. Real measurements are then fed into the circulation model and significant improvements to the modeled surface currents, when compared to observations, are obtained.

Description: Trend analysis using non-stationary time series clustering based on the finite element method Nonlinear Processes in Geophysics, 21, 605-615, 2014 Author(s): M. Gorji Sefidmazgi, M. Sayemuzzaman, A. Homaifar, M. K. Jha, and S. Liess In order to analyze low-frequency variability of climate, it is useful to model the climatic time series with multiple linear trends and locate the times of significant changes. In this paper, we have used non-stationary time series clustering to find change points in the trends. Clustering in a multi-dimensional non-stationary time series is challenging, since the problem is mathematically ill-posed. Clustering based on the finite element method (FEM) is one of the methods that can analyze multidimensional time series. One important attribute of this method is that it is not dependent on any statistical assumption and does not need local stationarity in the time series. In this paper, it is shown how the FEM-clustering method can be used to locate change points in the trend of temperature time series from in situ observations. This method is applied to the temperature time series of North Carolina (NC) and the results represent region-specific climate variability despite higher frequency harmonics in climatic time series. Next, we investigated the relationship between the climatic indices with the clusters/trends detected based on this clustering method. It appears that the natural variability of climate change in NC during 1950–2009 can be explained mostly by AMO and solar activity.

Description: Introduction to this Special Issue "Nonlinear waves and chaos in space plasmas" Nonlinear Processes in Geophysics, 21, 583-585, 2014 Author(s): G. S. Lakhina, B. T. Tsurutani, A. C.-L. Chian, T. Hada, G. J. Morales, and R. H. J. Grimshaw

Description: Turbulence in the interstellar medium Nonlinear Processes in Geophysics, 21, 587-604, 2014 Author(s): D. Falceta-Gonçalves, G. Kowal, E. Falgarone, and A. C.-L. Chian Turbulence is ubiquitous in the insterstellar medium and plays a major role in several processes such as the formation of dense structures and stars, the stability of molecular clouds, the amplification of magnetic fields, and the re-acceleration and diffusion of cosmic rays. Despite its importance, interstellar turbulence, like turbulence in general, is far from being fully understood. In this review we present the basics of turbulence physics, focusing on the statistics of its structure and energy cascade. We explore the physics of compressible and incompressible turbulent flows, as well as magnetised cases. The most relevant observational techniques that provide quantitative insights into interstellar turbulence are also presented. We also discuss the main difficulties in developing a three-dimensional view of interstellar turbulence from these observations. Finally, we briefly present what the main sources of turbulence in the interstellar medium could be.

Description: A note on Taylor's hypothesis under large-scale flow variation Nonlinear Processes in Geophysics, 21, 645-649, 2014 Author(s): M. Wilczek, H. Xu, and Y. Narita Experimental investigations of turbulent velocity fields often invoke Taylor's hypothesis (also known as frozen turbulence approximation) to evaluate the spatial structure based on time-resolved single-point measurements. A crucial condition for the validity of this approximation is that the turbulent fluctuations are small compared to the mean velocity, in other words, that the turbulence intensity must be low. While turbulence intensity is a well-controlled parameter in laboratory flows, this is not the case in many geo- and astrophysical settings. Here we explore the validity of Taylor's hypothesis based on a simple model for the wavenumber-frequency spectrum that has recently been introduced as a generalization of Kraichnan's random sweeping hypothesis. In this model, the fluctuating velocity is decomposed into a large-scale random sweeping velocity and small-scale fluctuations, which allows for a precise quantification of the influence of large-scale flow variations. For turbulence with a power-law energy spectrum, we find that the wavenumber spectrum estimated by Taylor's hypothesis exhibits the same power-law as the true spectrum, yet the spectral energy is overestimated due to the large-scale flow variation. The magnitude of this effect, and specifically its impact on the experimental determination of the Kolmogorov constant, are estimated for typical turbulence intensities of laboratory and geophysical flows.

Description: Toward enhanced understanding and projections of climate extremes using physics-guided data mining techniques Nonlinear Processes in Geophysics, 21, 777-795, 2014 Author(s): A. R. Ganguly, E. A. Kodra, A. Agrawal, A. Banerjee, S. Boriah, Sn. Chatterjee, So. Chatterjee, A. Choudhary, D. Das, J. Faghmous, P. Ganguli, S. Ghosh, K. Hayhoe, C. Hays, W. Hendrix, Q. Fu, J. Kawale, D. Kumar, V. Kumar, W. Liao, S. Liess, R. Mawalagedara, V. Mithal, R. Oglesby, K. Salvi, P. K. Snyder, K. Steinhaeuser, D. Wang, and D. Wuebbles Extreme events such as heat waves, cold spells, floods, droughts, tropical cyclones, and tornadoes have potentially devastating impacts on natural and engineered systems and human communities worldwide. Stakeholder decisions about critical infrastructures, natural resources, emergency preparedness and humanitarian aid typically need to be made at local to regional scales over seasonal to decadal planning horizons. However, credible climate change attribution and reliable projections at more localized and shorter time scales remain grand challenges. Long-standing gaps include inadequate understanding of processes such as cloud physics and ocean–land–atmosphere interactions, limitations of physics-based computer models, and the importance of intrinsic climate system variability at decadal horizons. Meanwhile, the growing size and complexity of climate data from model simulations and remote sensors increases opportunities to address these scientific gaps. This perspectives article explores the possibility that physically cognizant mining of massive climate data may lead to significant advances in generating credible predictive insights about climate extremes and in turn translating them to actionable metrics and information for adaptation and policy. Specifically, we propose that data mining techniques geared towards extremes can help tackle the grand challenges in the development of interpretable climate projections, predictability, and uncertainty assessments. To be successful, scalable methods will need to handle what has been called "big data" to tease out elusive but robust statistics of extremes and change from what is ultimately small data. Physically based relationships (where available) and conceptual understanding (where appropriate) are needed to guide methods development and interpretation of results. Such approaches may be especially relevant in situations where computer models may not be able to fully encapsulate current process understanding, yet the wealth of data may offer additional insights. Large-scale interdisciplinary team efforts, involving domain experts and individual researchers who span disciplines, will be necessary to address the challenge.

Description: Complex networks and waveforms from acoustic emissions in laboratory earthquakes Nonlinear Processes in Geophysics, 21, 763-775, 2014 Author(s): H. O. Ghaffari, B. D. Thompson, and R. P. Young Understanding the physics of acoustic excitations emitted during the cracking of materials is one of the long-standing challenges for material scientists and geophysicists. In this study, we report novel results of applications of functional complex networks on acoustic emission waveforms emitted during the evolution of frictional interfaces. Our results show that laboratory faults at microscopic scales undergo a sequence of generic phases, including strengthening, weakening or fast slip and slow slip, leading to healing. For the first time we develop a formulation on the dissipated energy due to acoustic emission signals in terms of short-term and long-term features (i.e., networks' characteristics) of events. We illuminate the transition from regular to slow ruptures. We show that this transition can lead to the onset of the critical rupture class similar to the direct observations of this phenomenon in the transparent samples. Furthermore, we demonstrate the detailed submicron evolution of the interface due to the short-term evolution of the rupture tip. As another novel result, we find that the nucleation phase of most amplified events follows a nearly constant timescale, corresponding to the initial strengthening or locking of the interface. This likely indicates that a thermally activated process can play a crucial role near the moving crack tip.

Description: Characterizing the evolution of climate networks Nonlinear Processes in Geophysics, 21, 705-711, 2014 Author(s): L. Tupikina, K. Rehfeld, N. Molkenthin, V. Stolbova, N. Marwan, and J. Kurths Complex network theory has been successfully applied to understand the structural and functional topology of many dynamical systems from nature, society and technology. Many properties of these systems change over time, and, consequently, networks reconstructed from them will, too. However, although static and temporally changing networks have been studied extensively, methods to quantify their robustness as they evolve in time are lacking. In this paper we develop a theory to investigate how networks are changing within time based on the quantitative analysis of dissimilarities in the network structure. Our main result is the common component evolution function (CCEF) which characterizes network development over time. To test our approach we apply it to several model systems, Erdős–Rényi networks, analytically derived flow-based networks, and transient simulations from the START model for which we control the change of single parameters over time. Then we construct annual climate networks from NCEP/NCAR reanalysis data for the Asian monsoon domain for the time period of 1970–2011 CE and use the CCEF to characterize the temporal evolution in this region. While this real-world CCEF displays a high degree of network persistence over large time lags, there are distinct time periods when common links break down. This phasing of these events coincides with years of strong El Niño/Southern Oscillation phenomena, confirming previous studies. The proposed method can be applied for any type of evolving network where the link but not the node set is changing, and may be particularly useful to characterize nonstationary evolving systems using complex networks.

Description: Observing spatio-temporal clustering and separation using interevent distributions of regional earthquakes Nonlinear Processes in Geophysics, 21, 735-744, 2014 Author(s): R. C. Batac and H. Kantz Past studies that attempted to quantify the spatio-temporal organization of seismicity have defined the conditions by which an event and those that follow it can be related in space and/or time. In this work, we use the simplest measures of spatio-temporal separation: the interevent distances R and interevent times T between pairs of successive events. We observe that after a characteristic value R * , the distributions of R begin to follow that of a randomly shuffled sequence, suggesting that events separated by R 〉 R * are more likely to be uncorrelated events generated independent of one another. Interestingly, the conditional T distributions for short-distance (long-distance) events, R ≤ R * ( R 〉 R * ), peak at correspondingly short (long) T values, signifying the spatio-temporal clustering (separation) of correlated (independent) events. By considering different threshold magnitudes within a range that ensures substantial catalogue completeness, invariant quantities related to the spatial and temporal spacing of correlated events and the rate of generation of independent events emerge naturally.

Description: Testing the detectability of spatio–temporal climate transitions from paleoclimate networks with the START model Nonlinear Processes in Geophysics, 21, 691-703, 2014 Author(s): K. Rehfeld, N. Molkenthin, and J. Kurths A critical challenge in paleoclimate data analysis is the fact that the proxy data are heterogeneously distributed in space, which affects statistical methods that rely on spatial embedding of data. In the paleoclimate network approach nodes represent paleoclimate proxy time series, and links in the network are given by statistically significant similarities between them. Their location in space, proxy and archive type is coded in the node attributes. We develop a semi-empirical model for S patio- T emporally A utoco R related T ime series, inspired by the interplay of different Asian Summer Monsoon (ASM) systems. We use an ensemble of transition runs of this START model to test whether and how spatio–temporal climate transitions could be detectable from (paleo)climate networks. We sample model time series both on a grid and at locations at which paleoclimate data are available to investigate the effect of the spatially heterogeneous availability of data. Node betweenness centrality, averaged over the transition region, does not respond to the transition displayed by the START model, neither in the grid-based nor in the scattered sampling arrangement. The regionally defined measures of regional node degree and cross link ratio, however, are indicative of the changes in both scenarios, although the magnitude of the changes differs according to the sampling. We find that the START model is particularly suitable for pseudo-proxy experiments to test the technical reconstruction limits of paleoclimate data based on their location, and we conclude that (paleo)climate networks are suitable for investigating spatio–temporal transitions in the dependence structure of underlying climatic fields.

Description: The influence of surface gravity waves on the injection of turbulence in the upper ocean Nonlinear Processes in Geophysics, 21, 713-733, 2014 Author(s): M. Bakhoday Paskyabi and I. Fer Observations were made in the near-surface layer, at about 8 m depth in 132 m deep water off the coast of Ålesund in Norway, for a duration of 2.5 months in late 2011. The measurement period covers the passage of two low pressure systems with substantial wind and wave forcing. The time series of the dissipation rate of turbulent kinetic energy, ε, and the estimates of surface gravity waves are analysed. Dissipation rates varied by 5 orders of magnitude and reached 10 -5 –10 -4 W kg −1 in conditions when wind speed exceeded 15 m s −1 and the significant wave height was of the order of 10 m. The data set suggests substantial injection of turbulence from breaking surface gravity waves and Langmuir turbulence. To support and interpret the observations, numerical calculations are conducted using a second-order turbulence closure scheme based on the Mellor–Yamada level 2.5 scheme, modified to incorporate the near-surface processes such as Langmuir circulation and wave breaking. The results from a run forced by observed wind and wave fields compare favourably with the observations. Comparisons with other near-surface data sets available from the literature lend confidence on our dissipation measurements and the wave-forced simulations.

Description: Brief Communication: The recent seismic activity in Central Greece in 2013 and its precursory electric signals in terms of criticality Nonlinear Processes in Geophysics, 21, 149-153, 2014 Author(s): E. Dologlou Here, we check the obedience of new data, derived from the M w = 5.4 earthquake on 7 August 2013 in Central Greece, to a previously found power law relation by the author between the stress drop of an earthquake and the lead time of its precursory seismic electric signal (SES). An exponent value α =0.329 has been found which is in excellent agreement with previous ones reported in a series of articles by the author. This value falls in the range of critical exponents suggested by various models for fracture and is very close to a reported one which interconnects the amplitude of the SES and the magnitude of the impending earthquake. The stability of this exponent confirms the credibility of the above-mentioned power law and probably implies that real physical dynamic processes evolving to criticality are present in the pre-focal area when the SES is emitted.

Description: Barriers to transport in aperiodically time-dependent two-dimensional velocity fields: Nekhoroshev's theorem and "Nearly Invariant" tori Nonlinear Processes in Geophysics, 21, 165-185, 2014 Author(s): S. Wiggins and A. M. Mancho In this paper we consider fluid transport in two-dimensional flows from the dynamical systems point of view, with the focus on elliptic behaviour and aperiodic and finite time dependence. We give an overview of previous work on general nonautonomous and finite time vector fields with the purpose of bringing to the attention of those working on fluid transport from the dynamical systems point of view a body of work that is extremely relevant, but appears not to be so well known. We then focus on the Kolmogorov–Arnold–Moser (KAM) theorem and the Nekhoroshev theorem. While there is no finite time or aperiodically time-dependent version of the KAM theorem, the Nekhoroshev theorem, by its very nature, is a finite time result, but for a "very long" (i.e. exponentially long with respect to the size of the perturbation) time interval and provides a rigorous quantification of "nearly invariant tori" over this very long timescale. We discuss an aperiodically time-dependent version of the Nekhoroshev theorem due to Giorgilli and Zehnder (1992) (recently refined by Bounemoura, 2013 and Fortunati and Wiggins, 2013) which is directly relevant to fluid transport problems. We give a detailed discussion of issues associated with the applicability of the KAM and Nekhoroshev theorems in specific flows. Finally, we consider a specific example of an aperiodically time-dependent flow where we show that the results of the Nekhoroshev theorem hold.

Description: Power law statistics of force and acoustic emission from a slowly penetrated granular bed Nonlinear Processes in Geophysics, 21, 1-8, 2014 Author(s): K. Matsuyama and H. Katsuragi Penetration-resistant force and acoustic emission (AE) from a plunged granular bed are experimentally investigated through their power law distribution forms. An AE sensor is buried in a glass bead bed. Then, the bed is slowly penetrated by a solid sphere. During the penetration, the resistant force exerted on the sphere and the AE signal are measured. The resistant force shows power law relation to the penetration depth. The power law exponent is independent of the penetration speed, while it seems to depend on the container's size. For the AE signal, we find that the size distribution of AE events obeys power laws. The power law exponent depends on grain size. Using the energy scaling, the experimentally observed power law exponents are discussed and compared to the Gutenberg–Richter (GR) law.

Description: Estimation of permeability of a sandstone reservoir by a fractal and Monte Carlo simulation approach: a case study Nonlinear Processes in Geophysics, 21, 9-18, 2014 Author(s): U. Vadapalli, R. P. Srivastava, N. Vedanti, and V. P. Dimri Permeability of a hydrocarbon reservoir is usually estimated from core samples in the laboratory or from well test data provided by the industry. However, such data is very sparse and as such it takes longer to generate that. Thus, estimation of permeability directly from available porosity logs could be an alternative and far easier approach. In this paper, a method of permeability estimation is proposed for a sandstone reservoir, which considers fractal behavior of pore size distribution and tortuosity of capillary pathways to perform Monte Carlo simulations. In this method, we consider a reservoir to be a mono-dispersed medium to avoid effects of micro-porosity. The method is applied to porosity logs obtained from Ankleshwar oil field, situated in the Cambay basin, India, to calculate permeability distribution in a well. Computed permeability values are in good agreement with the observed permeability obtained from well test data. We also studied variation of permeability with different parameters such as tortuosity fractal dimension ( D t ), grain size ( r ) and minimum particle size ( d 0 ), and found that permeability is highly dependent upon the grain size. This method will be extremely useful for permeability estimation, if the average grain size of the reservoir rock is known.

Description: Representation of model error in a convective-scale ensemble prediction system Nonlinear Processes in Geophysics, 21, 19-39, 2014 Author(s): L. H. Baker, A. C. Rudd, S. Migliorini, and R. N. Bannister In this paper ensembles of forecasts (of up to six hours) are studied from a convection-permitting model with a representation of model error due to unresolved processes. The ensemble prediction system (EPS) used is an experimental convection-permitting version of the UK Met Office's 24-member Global and Regional Ensemble Prediction System (MOGREPS). The method of representing model error variability, which perturbs parameters within the model's parameterisation schemes, has been modified and we investigate the impact of applying this scheme in different ways. These are: a control ensemble where all ensemble members have the same parameter values; an ensemble where the parameters are different between members, but fixed in time; and ensembles where the parameters are updated randomly every 30 or 60 min. The choice of parameters and their ranges of variability have been determined from expert opinion and parameter sensitivity tests. A case of frontal rain over the southern UK has been chosen, which has a multi-banded rainfall structure. The consequences of including model error variability in the case studied are mixed and are summarised as follows. The multiple banding, evident in the radar, is not captured for any single member. However, the single band is positioned in some members where a secondary band is present in the radar. This is found for all ensembles studied. Adding model error variability with fixed parameters in time does increase the ensemble spread for near-surface variables like wind and temperature, but can actually decrease the spread of the rainfall. Perturbing the parameters periodically throughout the forecast does not further increase the spread and exhibits "jumpiness" in the spread at times when the parameters are perturbed. Adding model error variability gives an improvement in forecast skill after the first 2–3 h of the forecast for near-surface temperature and relative humidity. For precipitation skill scores, adding model error variability has the effect of improving the skill in the first 1–2 h of the forecast, but then of reducing the skill after that. Complementary experiments were performed where the only difference between members was the set of parameter values (i.e. no initial condition variability). The resulting spread was found to be significantly less than the spread from initial condition variability alone.

Description: Four-dimensional energy spectrum for space–time structure of plasma turbulence Nonlinear Processes in Geophysics, 21, 41-47, 2014 Author(s): Y. Narita A parametric model of the inertial-range energy spectrum is constructed for plasma turbulence in the four-dimensional wave vector and frequency domain. The model is based on that of the Eulerian wavenumber-frequency spectrum developed for describing fluid turbulence, and includes wave vector anisotropies in the three-dimensional wave vector domain by approximating the spectrum to a set of ellipses. The shape of the four-dimensional spectrum is determined by the Doppler shift, the Doppler broadening, and anisotropy coefficients. The model is applied to the magnetic energy spectrum in the near-Earth solar wind measured by four Cluster spacecraft, and the set of the spectral parameters are determined observationally. In this way, space–time structure of plasma turbulence can be condensed into a small number of parameters, which is suitable for evaluating the energy spectra in observational and numerical studies on the quantitative basis.

Description: On the entrainment coefficient in a forced plume: quantitative effects of source parameters Nonlinear Processes in Geophysics, 21, 269-278, 2014 Author(s): A. Matulka, P. López, J. M. Redondo, and A. Tarquis The behavior of a forced plume is mainly controlled by the source buoyancy and momentum fluxes and the efficiency of turbulent mixing between the plume and the ambient fluid (stratified or not). The interaction between the plume and the ambient fluid controls the plume dynamics and is usually represented by the entrainment coefficient α E . Commonly used one-dimensional models incorporating a constant entrainment coefficient are fundamental and very useful for predictions in geophysical flows and industrial situations. Nevertheless, if the basic geometry of the flow changes, or the type of source or the environmental fluid conditions (e.g., level of turbulence, shear, ambient stratification, presence of internal waves), new models allowing for variable entrainment are necessary. The presented paper is an experimental study based on a set of turbulent plume experiments in a calm unstratified ambient fluid under different source conditions (represented by different buoyancy and momentum fluxes). The main result is that the entrainment coefficient is not a constant and clearly varies in time within the same plume independently of the buoyancy and the source position. This paper also analyzes the influence of the source conditions on the mentioned time evolution. The measured entrainment coefficient α E has considerable variability. It ranges between 0.26 and 0.9 for variable Atwood number experiments and between 0.16 and 0.55 for variable source position experiments. As is observed, values are greater than the traditional standard value of Morton et al. (1956) for plumes and jets, which is about 0.13.

Description: Diagnostics on the cost-function in variational assimilations for meteorological models Nonlinear Processes in Geophysics, 21, 187-199, 2014 Author(s): Y. Michel Several consistency diagnostics have been proposed to evaluate variational assimilation schemes. The "Bennett-Talagrand" criterion in particular shows that the cost-function at the minimum should be close to half the number of assimilated observations when statistics are correctly specified. It has been further shown that sub-parts of the cost function also had statistical expectations that could be expressed as traces of large matrices, and that this could be exploited for variance tuning and hypothesis testing. The aim of this work is to extend those results using standard theory of quadratic forms in random variables. The first step is to express the sub-parts of the cost function as quadratic forms in the innovation vector. Then, it is possible to derive expressions for the statistical expectations, variances and cross-covariances (whether the statistics are correctly specified or not). As a consequence it is proven in particular that, in a perfect system, the values of the background and observation parts of the cost function at the minimum are positively correlated. These results are illustrated in a simplified variational scheme in a one-dimensional context. These expressions involve the computation of the trace of large matrices that are generally unavailable in variational formulations of the assimilation problem. It is shown that the randomization algorithm proposed in the literature can be extended to cover these computations, yet at the price of additional minimizations. This is shown to provide estimations of background and observation errors that improve forecasts of the operational ARPEGE model.

Description: Corrigendum to "Nonlinear dynamics approach to the predictability of the Cane–Zebiak coupled ocean–atmosphere model" published in Nonlin. Processes Geophys., 21, 155–163, 2014 Nonlinear Processes in Geophysics, 21, 201-201, 2014 Author(s): L. Siqueira and B. Kirtman No abstract available.

Description: An extended approach for spatiotemporal gapfilling: dealing with large and systematic gaps in geoscientific datasets Nonlinear Processes in Geophysics, 21, 203-215, 2014 Author(s): J. v. Buttlar, J. Zscheischler, and M. D. Mahecha Spatiotemporal observations in Earth System sciences are often affected by numerous and/or systematically distributed gaps. This data fragmentation is inherited from instrument failures, sparse measurement protocols, or unfavourable conditions (e.g. clouds or vegetation thickness in case of remote-sensing data). Missing values are problematic as they may cause analytic biases and often inhibit advanced statistical analyses. Hence, gapfilling is an undesired but necessary task in Earth System sciences. State-of-the-art gapfilling algorithms based on Singular Spectrum Analysis (SSA) exploit the information contained in periodic temporal patterns to fill gaps in the observations. Here we propose an extension of this method in order to additionally consider the spatial processes and patterns underlying most geoscientific datasets. The latter has been made possible by including a recently developed 2-D-SSA approach. Using both artificial and real-world test data, we show that simultaneously exploiting spatial and temporal patterns improves the gapfilling substantially. We outperform conventional approaches particularly for large and systematically recurring gaps. The new method is reasonably fast and can be applied with a minimum of a priori assumptions regarding the structure of the data and the distribution of gaps. The algorithm is available as a ready-to-use open source software package.

Description: Large-amplitude electromagnetic waves in magnetized relativistic plasmas with temperature Nonlinear Processes in Geophysics, 21, 217-236, 2014 Author(s): V. Muñoz, F. A. Asenjo, M. Domínguez, R. A. López, J. A. Valdivia, A. Viñas, and T. Hada Propagation of large-amplitude waves in plasmas is subject to several sources of nonlinearity due to relativistic effects, either when particle quiver velocities in the wave field are large, or when thermal velocities are large due to relativistic temperatures. Wave propagation in these conditions has been studied for decades, due to its interest in several contexts such as pulsar emission models, laser-plasma interaction, and extragalactic jets. For large-amplitude circularly polarized waves propagating along a constant magnetic field, an exact solution of the fluid equations can be found for relativistic temperatures. Relativistic thermal effects produce: (a) a decrease in the effective plasma frequency (thus, waves in the electromagnetic branch can propagate for lower frequencies than in the cold case); and (b) a decrease in the upper frequency cutoff for the Alfvén branch (thus, Alfvén waves are confined to a frequency range that is narrower than in the cold case). It is also found that the Alfvén speed decreases with temperature, being zero for infinite temperature. We have also studied the same system, but based on the relativistic Vlasov equation, to include thermal effects along the direction of propagation. It turns out that kinetic and fluid results are qualitatively consistent, with several quantitative differences. Regarding the electromagnetic branch, the effective plasma frequency is always larger in the kinetic model. Thus, kinetic effects reduce the transparency of the plasma. As to the Alfvén branch, there is a critical, nonzero value of the temperature at which the Alfvén speed is zero. For temperatures above this critical value, the Alfvén branch is suppressed; however, if the background magnetic field increases, then Alfvén waves can propagate for larger temperatures. There are at least two ways in which the above results can be improved. First, nonlinear decays of the electromagnetic wave have been neglected; second, the kinetic treatment considers thermal effects only along the direction of propagation. We have approached the first subject by studying the parametric decays of the exact wave solution found in the context of fluid theory. The dispersion relation of the decays has been solved, showing several resonant and nonresonant instabilities whose dependence on the wave amplitude and plasma temperature has been studied systematically. Regarding the second subject, we are currently performing numerical 1-D particle in cell simulations, a work that is still in progress, although preliminary results are consistent with the analytical ones.

Description: Lagrangian study of surface transport in the Kuroshio Extension area based on simulation of propagation of Fukushima-derived radionuclides Nonlinear Processes in Geophysics, 21, 279-289, 2014 Author(s): S. V. Prants, M. V. Budyansky, and M. Yu. Uleysky Lagrangian approach is applied to study near-surface large-scale transport in the Kuroshio Extension area using a simulation with synthetic particles advected by AVISO altimetric velocity field. A material line technique is proposed and applied to find out the origin of water masses in cold-core cyclonic rings pinched off from the jet in summer 2011. Tracking and Lagrangian maps provide the evidence of cross-jet transport. Fukushima-derived caesium isotopes are used as Lagrangian tracers to study transport and mixing in the area a few months after the 11 March 2011 tsunami that caused heavy damage of the Fukushima Nuclear Power Plant (FNPP). Tracking maps are computed to trace the origin of water parcels with measured levels of 134 Cs and 137 Cs concentrations collected during two research vessel (R/V) cruises in June and July 2011 in the large area of the northwest Pacific (Kaeriyama et al., 2013; Buesseler et al., 2012). It is shown that Lagrangian simulations are useful for finding the surface areas that are potentially dangerous due to the risk of radioactive contamination. The results of simulation are supported by tracks of the surface drifters that were deployed in the area.

Description: Synchronization of coupled stick-slip oscillators Nonlinear Processes in Geophysics, 21, 251-267, 2014 Author(s): N. Sugiura, T. Hori, and Y. Kawamura A rationale is provided for the emergence of synchronization in a system of coupled oscillators in a stick-slip motion. The single oscillator has a limit cycle in a region of the state space for each parameter set beyond the supercritical Hopf bifurcation. The two-oscillator system that has similar weakly coupled oscillators exhibits synchronization in a parameter range. The synchronization has an anti-phase nature for an identical pair. However, it tends to be more in-phase for a non-identical pair with a rather weak coupling. A system of three identical oscillators (1, 2, and 3) coupled in a line (with two springs k 12 = k 23 ) exhibits synchronization with two of them (1 and 2 or 2 and 3) being nearly in-phase. These collective behaviours are systematically estimated using the phase reduction method.

Description: Mitigation of coupled model biases induced by dynamical core misfitting through parameter optimization: simulation with a simple pycnocline prediction model Nonlinear Processes in Geophysics, 21, 357-366, 2014 Author(s): G.-J. Han, X.-F. Zhang, S. Zhang, X.-R. Wu, and Z. Liu Imperfect dynamical core is an important source of model biases that adversely impact on the model simulation and predictability of a coupled system. With a simple pycnocline prediction model, in this study, we show the mitigation of model biases through parameter optimization when the assimilation model consists of a "biased" time-differencing. Here, the "biased" time-differencing is defined by a different time-differencing scheme from the "truth" model that is used to produce "observations", which generates different mean values, climatology and variability of the assimilation model from the "truth" model. A series of assimilation experiments is performed to explore the impact of parameter optimization on model bias mitigation and climate estimation, as well as the role of different media parameter estimations. While the stochastic "physics" implemented by perturbing parameters can enhance the ensemble spread significantly and improve the representation of the model ensemble, signal-enhanced parameter estimation is able to mitigate the model biases on mean values and climatology, thus further improving the accuracy of estimated climate states, especially for the low-frequency signals. In addition, in a multiple timescale coupled system, parameters pertinent to low-frequency components have more impact on climate signals. Results also suggest that deep ocean observations may be indispensable for improving the accuracy of climate estimation, especially for low-frequency signals.

Description: We herein report the results of some numerical simulations of complex earthquake cycles using a three-degree-of-freedom spring-block model with a rate- and state-dependent friction law. The model consists of three blocks on a conveyor belt that is moving at a steady rate. Observed complex slip behaviour in the simulations is classified into five slip patterns, and for each of these the parameter dependence of the slip patterns is demonstrated by means of phase diagrams. Aperiodic slip patterns occur for wider ranges of the parameter space in the three-block system than in the two-block system. Chaotic slip behaviour known here as "intermittency" is found in the three-block system, in which two different slip patterns occur alternately with variable durations. By calculating Lyapunov exponents, we quantify the dependence of slip evolution on the initial conditions for each slip pattern. For cases where intermittent slip patterns occur, the time evolution of the Lyapunov exponent is correlated with changes in slip behaviour.

Description: We aim to study the evolution of the upper atmosphere connectivity over the 20th century as well as to distinguish the oceanically forced component from the atmospheric internal variability. For this purpose we build networks from two different reanalysis data sets using both linear and nonlinear statistical similarity measures to determine the existence of links between different regions of the world in the two halves of the last century. We furthermore use symbolic analysis to emphasize intra-seasonal, intra-annual and inter-annual timescales. Both linear and nonlinear networks have similar structures and evolution, showing that the most connected regions are in the tropics over the Pacific Ocean. Also, the Southern Hemisphere extratropics have more connectivity in the first half of the 20th century, particularly on intra-annual and intra-seasonal timescales. Changes over the Pacific main connectivity regions are analyzed in more detail. Both linear and nonlinear networks show that the central and western Pacific regions have decreasing connectivity from early 1900 up to about 1940, when it starts increasing again until the present. The inter-annual network shows a similar behavior. However, this is not true of other timescales. On intra-annual timescales the minimum connectivity is around 1956, with a negative (positive) trend before (after) that date for both the central and western Pacific. While this is also true of the central Pacific on intra-seasonal timescales, the western Pacific shows a positive trend during the entire 20th century. In order to separate the internal and forced connectivity networks and to study their evolution through time, an ensemble of atmospheric general circulation model outputs is used. The results suggest that the main connectivity patterns captured in the reanalysis networks are due to the oceanically forced component, particularly on inter-annual timescales. Moreover, the atmospheric internal variability seems to play an important role in determining the intra-seasonal timescale networks.

Description: Experimental investigations of turbulent velocity fields often invoke Taylor's hypothesis (also known as frozen turbulence approximation) to evaluate the spatial structure based on time-resolved single-point measurements. A crucial condition for the validity of this approximation is that the turbulent fluctuations are small compared to the mean velocity, in other words, that the turbulence intensity must be low. While turbulence intensity is a well-controlled parameter in laboratory flows, this is not the case in many geo- and astrophysical settings. Here we explore the validity of Taylor's hypothesis based on a simple model for the wavenumber-frequency spectrum that has recently been introduced as a generalization of Kraichnan's random sweeping hypothesis. In this model, the fluctuating velocity is decomposed into a large-scale random sweeping velocity and small-scale fluctuations, which allows for a precise quantification of the influence of large-scale flow variations. For turbulence with a power-law energy spectrum, we find that the wavenumber spectrum estimated by Taylor's hypothesis exhibits the same power-law as the true spectrum, yet the spectral energy is overestimated due to the large-scale flow variation. The magnitude of this effect, and specifically its impact on the experimental determination of the Kolmogorov constant, are estimated for typical turbulence intensities of laboratory and geophysical flows.

Description: A critical challenge in paleoclimate data analysis is the fact that the proxy data are heterogeneously distributed in space, which affects statistical methods that rely on spatial embedding of data. In the paleoclimate network approach nodes represent paleoclimate proxy time series, and links in the network are given by statistically significant similarities between them. Their location in space, proxy and archive type is coded in the node attributes. We develop a semi-empirical model for Spatio-Temporally AutocoRrelated Time series, inspired by the interplay of different Asian Summer Monsoon (ASM) systems. We use an ensemble of transition runs of this START model to test whether and how spatio–temporal climate transitions could be detectable from (paleo)climate networks. We sample model time series both on a grid and at locations at which paleoclimate data are available to investigate the effect of the spatially heterogeneous availability of data. Node betweenness centrality, averaged over the transition region, does not respond to the transition displayed by the START model, neither in the grid-based nor in the scattered sampling arrangement. The regionally defined measures of regional node degree and cross link ratio, however, are indicative of the changes in both scenarios, although the magnitude of the changes differs according to the sampling. We find that the START model is particularly suitable for pseudo-proxy experiments to test the technical reconstruction limits of paleoclimate data based on their location, and we conclude that (paleo)climate networks are suitable for investigating spatio–temporal transitions in the dependence structure of underlying climatic fields.

Description: Complex network theory has been successfully applied to understand the structural and functional topology of many dynamical systems from nature, society and technology. Many properties of these systems change over time, and, consequently, networks reconstructed from them will, too. However, although static and temporally changing networks have been studied extensively, methods to quantify their robustness as they evolve in time are lacking. In this paper we develop a theory to investigate how networks are changing within time based on the quantitative analysis of dissimilarities in the network structure. Our main result is the common component evolution function (CCEF) which characterizes network development over time. To test our approach we apply it to several model systems, Erdős–Rényi networks, analytically derived flow-based networks, and transient simulations from the START model for which we control the change of single parameters over time. Then we construct annual climate networks from NCEP/NCAR reanalysis data for the Asian monsoon domain for the time period of 1970–2011 CE and use the CCEF to characterize the temporal evolution in this region. While this real-world CCEF displays a high degree of network persistence over large time lags, there are distinct time periods when common links break down. This phasing of these events coincides with years of strong El Niño/Southern Oscillation phenomena, confirming previous studies. The proposed method can be applied for any type of evolving network where the link but not the node set is changing, and may be particularly useful to characterize nonstationary evolving systems using complex networks.

Description: The fact that the climate on the earth is a highly complex dynamical system is well-known. In the last few decades great deal of effort has been focused on understanding how climate phenomena in one geographical region affects the climate of other regions. Complex networks are a powerful framework for identifying climate interdependencies. To further exploit the knowledge of the links uncovered via the network analysis (for, e.g., improvements in prediction), a good understanding of the physical mechanisms underlying these links is required. Here we focus on understanding the role of atmospheric variability, and construct climate networks representing internal and forced variability using the output of an ensemble of AGCM runs. A main strength of our work is that we construct the networks using MIOP (mutual information computed from ordinal patterns), which allows the separation of intraseasonal, intra-annual and interannual timescales. This gives further insight to the analysis of climatological data. The connectivity of these networks allows us to assess the influence of two main indices, NINO3.4 – one of the indices used to describe ENSO (El Niño–Southern oscillation) – and of the North Atlantic Oscillation (NAO), by calculating the networks from time series where these indices were linearly removed. A main result of our analysis is that the connectivity of the forced variability network is heavily affected by "El Niño": removing the NINO3.4 index yields a general loss of connectivity; even teleconnections between regions far away from the equatorial Pacific Ocean are lost, suggesting that these regions are not directly linked, but rather, are indirectly interconnected via El Niño, particularly at interannual timescales. On the contrary, on the internal variability network – independent of sea surface temperature (SST) forcing – the links connecting the Labrador Sea with the rest of the world are found to be significantly affected by NAO, with a maximum at intra-annual timescales. While the strongest non-local links found are those forced by the ocean, the presence of teleconnections due to internal atmospheric variability is also shown.

Description: This paper presents an algorithm for Monte Carlo fixed-lag smoothing in state-space models defined by a diffusion process observed through noisy discrete-time measurements. Based on a particle approximation of the filtering and smoothing distributions, the method relies on a simulation technique of conditioned diffusions. The proposed sequential smoother can be applied to general nonlinear and multidimensional models, like the ones used in environmental applications. The smoothing of a turbulent flow in a high-dimensional context is given as a practical example.

Description: We use a recently developed Lagrangian transport tool, Lagrangian descriptors, to compare the transport properties of data distributed by AVISO and numerical simulations obtained from the HYCOM model in the Yucatán–Florida current system. Our data correspond to the months from June through August 2010. Structures obtained from HYCOM are noisier than those from AVISO; however, both AVISO and HYCOM succeed in identifying Lagrangian structures that influence the paths of drifters, such as eddies, currents, lobes, etc. We find evidence in which AVISO gives the positions of important hyperbolic trajectories in a manner that is inconsistent with the trajectories of the drifters, while for the same examples HYCOM succeeds to this end.

Description: Initialization techniques for seasonal-to-decadal climate predictions fall into two main categories; namely full-field initialization (FFI) and anomaly initialization (AI). In the FFI case the initial model state is replaced by the best possible available estimate of the real state. By doing so the initial error is efficiently reduced but, due to the unavoidable presence of model deficiencies, once the model is let free to run a prediction, its trajectory drifts away from the observations no matter how small the initial error is. This problem is partly overcome with AI where the aim is to forecast future anomalies by assimilating observed anomalies on an estimate of the model climate. The large variety of experimental setups, models and observational networks adopted worldwide make it difficult to draw firm conclusions on the respective advantages and drawbacks of FFI and AI, or to identify distinctive lines for improvement. The lack of a unified mathematical framework adds an additional difficulty toward the design of adequate initialization strategies that fit the desired forecast horizon, observational network and model at hand. Here we compare FFI and AI using a low-order climate model of nine ordinary differential equations and use the notation and concepts of data assimilation theory to highlight their error scaling properties. This analysis suggests better performances using FFI when a good observational network is available and reveals the direct relation of its skill with the observational accuracy. The skill of AI appears, however, mostly related to the model quality and clear increases of skill can only be expected in coincidence with model upgrades. We have compared FFI and AI in experiments in which either the full system or the atmosphere and ocean were independently initialized. In the former case FFI shows better and longer-lasting improvements, with skillful predictions until month 30. In the initialization of single compartments, the best performance is obtained when the stabler component of the model (the ocean) is initialized, but with FFI it is possible to have some predictive skill even when the most unstable compartment (the extratropical atmosphere) is observed. Two advanced formulations, least-square initialization (LSI) and exploring parameter uncertainty (EPU), are introduced. Using LSI the initialization makes use of model statistics to propagate information from observation locations to the entire model domain. Numerical results show that LSI improves the performance of FFI in all the situations when only a portion of the system's state is observed. EPU is an online drift correction method in which the drift caused by the parametric error is estimated using a short-time evolution law and is then removed during the forecast run. Its implementation in conjunction with FFI allows us to improve the prediction skill within the first forecast year. Finally, the application of these results in the context of realistic climate models is discussed.

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