ALBERT

Description: Temperature distribution and Hadley circulation in an axisymmetric model Nonlinear Processes in Geophysics Discussions, 1, 1621-1655, 2014 Author(s): N. Tartaglione The impact of the temperature distribution on the Hadley circulation simulated by an axisymmetric model is studied. The temperature distributions that drive the model are modulated here by two parameters, n and k , the former controlling the horizontal broadness and the latter defining change in the vertical lapse rate. In the present study, the changes of the temperature distribution mimic changes of the energy input of the atmospheric system leaving as an invariant the equator-poles difference. Both equinoctial and time-dependent Hadley circulations are simulated and results compared. The results give evidence that concentrated temperature distributions enhance the meridional circulation and jet wind speed intensities even with a lower energy input. The meridional circulation and the subtropical jet stream widths are controlled by the broadness of horizontal temperature rather than the vertical lapse rate k , which is important only when the temperature distribution is concentrated at the equator. The jet stream position does not show any dependence with n and k , except when the temperature distribution is very wide and in such a case the jet is located at the mid-latitude. Using n = 2 and k = 1 we have the formulation of the potential temperature adopted in classical literature. A comparison with other works is performed and our results show that the model running in different configurations (equinoctial, solstitial and time-dependent) yields results similar to one another.

Description: The double layers in the plasma sheet boundary layer during magnetic reconnection Nonlinear Processes in Geophysics Discussions, 1, 1657-1671, 2014 Author(s): J. Guo and B. Yu We studied the evolutions of double layers which appear after the magnetic reconnection through two-dimensional electromagnetic particle-in-cell simulation. The simulation results show that the double layers are formed in the plasma sheet boundary layer after magnetic reconnection. At first, the double layers which have unipolar structures are formed. And then the double layers turn into bipolar structures, which will couple with another new weak bipolar structure. Thus a new double layer or tripolar structure comes into being. The double layers found in our work are about several ten Debye lengths, which accords with the observation results. It is suggested that the electron beam formed during the magnetic reconnection is responsible for the production of the double layers.

Description: Elastic envelope inversion using multicomponent seismic data without low frequency Nonlinear Processes in Geophysics Discussions, 1, 1757-1802, 2014 Author(s): C. Huang, L. Dong, Y. Liu, and B. Chi Low frequency is a key issue to reduce the nonlinearity of elastic full waveform inversion. Hence, the lack of low frequency in recorded seismic data is one of the most challenging problems in elastic full waveform inversion. Theoretical derivations and numerical analysis are presented in this paper to show that envelope operator can retrieve strong low frequency modulation signal demodulated in multicomponent data, no matter what the frequency bands of the data is. With the benefit of such low frequency information, we use elastic envelope of multicomponent data to construct the objective function and present an elastic envelope inversion method to recover the long-wavelength components of the subsurface model, especially for the S-wave velocity model. Numerical tests using synthetic data for the Marmousi-II model prove the effectiveness of the proposed elastic envelope inversion method, especially when low frequency is missing in multicomponent data and when initial model is far from the true model. The elastic envelope can reduce the nonlinearity of inversion and can provide an excellent starting model.

Description: The transient variation of the complexes of the low latitude ionosphere within the equatorial ionization anomaly region of Nigeria Nonlinear Processes in Geophysics Discussions, 1, 1855-1903, 2014 Author(s): A. B. Rabiu, B. O. Ogunsua, I. A. Fuwape, and J. A. Laoye The quest to find an index for proper characterization and description of the dynamical response of the ionosphere to external influences and its various internal irregularities has led to the study of the day to day variations of the chaoticity and dynamical complexity of the ionosphere. This study was conducted using Global Positioning System (GPS) Total Electron Content (TEC) time series, measured in the year 2011, from 5 GPS receiver stations in Nigeria which lies within the Equatorial Ionization Anomaly region. The nonlinear aspect of the TEC time series were 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 which are Lyapunov exponents LE, correlation dimension, and Tsallis entropy for the study of dynamical complexity. The results show positive Lyapunov exponents for all days which indicate chaoticity of the ionosphere with no definite pattern for both quiet and disturbed days. However values of LE were lower for the storm period compared to its nearest relative quiet periods for all the stations. Considering all the days of the year the daily/transient variations show no definite pattern for each month but day to day values of Lyapunov exponent for the entire year show a wavelike semiannual variation pattern with lower values around March, April, September and October, a change in pattern which demonstrates the self-organized critical phenomenon of the system. This can be seen from the correlation dimension with values between 2.7 and 3.2 with lower values occurring mostly during storm periods demonstrating a phase transition from higher dimension during the quiet periods to lower dimension during storms for most of the stations. The values of Tsallis entropy show similar variation pattern with that of Lyapunov exponent with a lot of agreement in their comparison, with all computed values of Lyapunov exponent correlating with values of Tsallis entropy within the range of 0.79 to 0.82. These results show that Lyapunov quantifiers can be used together as indices in the study of the variations of the dynamical complexity of the ionosphere. The presence of chaos and high variations in the dynamical complexity, even at quiet periods in the ionosphere may be due to the internal dynamics and inherent irregularities of the ionosphere which exhibit non-linear properties. However, this inherent dynamics may be complicated by external factors like geomagnetic storms. This may be the main reason for the drop in the values of Lyapunov exponent and Tsallis entropy during storms. The results also show a strong interplay between determinism and stochasticity, as the ionosphere shows its response to changes in solar activities and in its internal dynamics. The dynamical behavior of the ionosphere throughout the year as described by these quantifiers, were discussed in this work.

Description: Evaluation of empirical mode decomposition for quantifying multi-decadal variations in sea level records Nonlinear Processes in Geophysics Discussions, 1, 1833-1854, 2014 Author(s): D. P. Chambers The ability of empirical mode decomposition (EMD) to extract multidecadal variability from sea level records is tested using three simulations: one based on a series of purely sinusoidal modes, one based on scaled climate indices of El Niño and the Pacific Decadal Oscillation (PDO), and the final one including a single month with an extreme sea level event. All simulations include random noise of similar variance to high-frequency variability in the San Francisco tide gauge record. The intrinsic mode functions (IMFs) computed using EMD were compared to the prescribed oscillations. In all cases, the longest-period modes are significantly distorted, with incorrect amplitudes and phases. This affects the estimated acceleration computed from the longest periodic IMF. In these simulations, the acceleration was underestimated in the case with purely sinusoidal modes, and overestimated by nearly 100% in the case with prescribed climate modes. Additionally, in all cases, extra low-frequency modes uncorrelated with the prescribed variability are found. These experiments suggest that using EMD to identify multidecadal variability and accelerations in sea level records should be used with caution.

Description: Benjamin–Feir instability of waves in the presence of current Nonlinear Processes in Geophysics Discussions, 1, 1803-1832, 2014 Author(s): I. V. Shugan, H. H. Hwung, and R. Y. Yang The development of Benjamin–Feir instability of Stokes waves in the presence of variable current is presented. We employ a model of a resonance system having three coexisting nonlinear waves and nonuniform current. The model is free from the narrow-band approximation for surface waves and relatively weak adverse current. The modulation instability of Stokes waves in nonuniform moving media has special properties. Interaction with countercurrent accelerates the growth of sideband modes on a short spatial scale. An increase in initial wave steepness intensifies the wave energy exchange accompanied by wave breaking dissipation, results in asymmetry of sideband modes and a frequency downshift with an energy transfer jump to the lower sideband mode, and depresses the higher sideband and carrier wave. Nonlinear waves may even overpass the blocking barrier produced by strong adverse current. The frequency downshift of the energy peak is permanent and the system does not revert to its initial state. We find reasonable correspondence between the results of model simulations and available experimental results for wave interaction with blocking opposing current. Large transient or freak waves with amplitude and steepness several times those of normal waves may form during temporal nonlinear focusing of the resonant waves accompanied by energy income from sufficiently strong opposing current. We employ the resonance model for the estimation of the maximum amplification of wave amplitudes as a function of gradually increasing opposing current and compare the result obtained with recently published experimental results and modeling results obtained with the nonlinear Schrödinger equation.

Description: Non-Gaussian interaction information: estimation, optimization and diagnostic application of triadic wave resonance Nonlinear Processes in Geophysics Discussions, 1, 1539-1602, 2014 Author(s): C. A. L. Pires and R. A. P. Perdigão Non-Gaussian multivariate probability distributions, derived from climate and geofluid statistics, allow for nonlinear correlations between linearly uncorrelated components, due to joint Shannon negentropies. Triadic statistical dependence under pair-wise (total or partial) independence is thus possible. Synergy or interaction information among triads is estimated. We formulate an optimization method of triads in the space of orthogonal rotations of normalized principal components, relying on the maximization of third-order cross cumulants. Its application to a minimal one-dimensional, periodic, advective model, leads to enhanced triads that occur between oscillating components of circular or locally confined wave-trains satisfying the triadic wave resonance condition.

Description: Self-organization of ULF electromagnetic wave structures in the shear flow driven dissipative ionosphere Nonlinear Processes in Geophysics Discussions, 1, 1431-1464, 2014 Author(s): G. Aburjania, K. Chargazia, O. Kharshiladze, and G. Zimbardo This work is devoted to investigation of nonlinear dynamics of planetary electromagnetic (EM) ultra-low-frequency wave (ULFW) structures in the rotating dissipative ionosphere in the presence of inhomogeneous zonal wind (shear flow). Planetary EM ULFW appears as a result of interaction of the ionospheric medium with the spatially inhomogeneous geomagnetic field. The shear flow driven wave perturbations effectively extract energy of the shear flow increasing own amplitude and energy. These perturbations undergo self organization in the form of the nonlinear solitary vortex structures due to nonlinear twisting of the perturbation's front. Depending on the features of the velocity profiles of the shear flows the nonlinear vortex structures can be either monopole vortices, or dipole vortex, or vortex streets and vortex chains. From analytical calculation and plots we note that the formation of stationary nonlinear vortex structure requires some threshold value of translation velocity for both non-dissipation and dissipation complex ionospheric plasma. The space and time attenuation specification of the vortices is studied. The characteristic time of vortex longevity in dissipative ionosphere is estimated. The long-lived vortices transfer the trapped medium particles, energy and heat. Thus they represent structural elements of turbulence in the ionosphere.

Description: Analysis of stochastic model for non-linear volcanic dynamics Nonlinear Processes in Geophysics Discussions, 1, 1735-1755, 2014 Author(s): D. Alexandrov, I. Bashkirtseva, and L. Ryashko Motivated by important geophysical applications we consider a dynamic model of the magma-plug system previously derived by Iverson et al. (2006) under the influence of stochastic forcing. Due to strong nonlinearity of the friction force for solid plug along its margins, the initial deterministic system exhibits impulsive oscillations. Two types of dynamic behavior of the system under the influence of the parametric stochastic forcing have been found: random trajectories are scattered on both sides of the deterministic cycle or grouped on its internal side only. It is shown that dispersions are highly inhomogeneous along cycles in the presence of noises. The effects of noise-induced shifts, pressure stabilization and localization of random trajectories have been revealed with increasing the noise intensity. The plug velocity, pressure and displacement are highly dependent of noise intensity as well. These new stochastic phenomena are related with the nonlinear peculiarities of the deterministic phase portrait. It is demonstrated that the repetitive stick-slip motions of the magma-plug system in the case of stochastic forcing can be connected with drumbeat earthquakes.

Description: Estimation of the total magnetization direction of approximately spherical bodies Nonlinear Processes in Geophysics Discussions, 1, 1465-1507, 2014 Author(s): V. C. Oliveira Jr., D. P. Sales, V. C. F. Barbosa, and L. Uieda We have developed a fast total-field anomaly inversion to estimate the magnetization direction of multiple sources with approximately spherical shape and known centres. Our method can be applied to interpret multiple sources with different magnetization directions. It neither requires the prior computation of any transformation like reduction to the pole nor the use of regularly spaced data on a horizontal grid. The method contains flexibility to be implemented as a linear or non-linear inverse problem, which results, respectively, in a least-squares or robust estimate of the components of the magnetization vector of the sources. Applications to synthetic data show the robustness of our method against interfering anomalies and errors in the location of the sources' centre. Besides, we show the feasibility of applying the upward continuation to interpret non-spherical sources. Applications to field data over the Goiás Alkaline Province (GAP), Brazil, show the good performance of our method in estimating geological meaningful magnetization directions. The results obtained for a region of the GAP, near from the alkaline complex of Diorama, suggest the presence of non-outcropping sources marked by strong remanent magnetization with inclination and declination close to -70.35° and -19.81°, respectively. This estimated magnetization direction leads to predominantly positive reduced-to-the-pole anomalies, even for other region of the GAP, in the alkaline complex of Montes Claros de Goiás. These results show that the non-outcropping sources near from the alkaline complex of Diorama have almost the same magnetization direction of that ones in the alkaline complex of Montes Claros de Goiás, strongly suggesting that these sources have emplaced the crust almost within the same geological time interval.

Description: Self-breeding: a new method to estimate local Lyapunov structures Nonlinear Processes in Geophysics Discussions, 1, 1509-1537, 2014 Author(s): J. D. Keller and A. Hense We present a new approach to estimate local Lyapunov vectors. The so called self-breeding method is based on the breeding of growing modes technique from medium range weather forecasting and consists of a continuous forecasting and rescaling cycle. Using the Lorenz96 model we test and characterize the behavior of the algorithm regarding error growth, spatial perturbation structure estimates and orthogonalization. The results indicate that the method can be used to generate error growing modes optimized for a certain rescaling interval, thus enabling the user to target specific scales of error growth. When an additional orthogonalization procedure is applied, the method is able to produce structures representing the error growth subspace spanned by the largest Lyapunov vectors.

Description: Transient behavior in the Lorenz model Nonlinear Processes in Geophysics Discussions, 1, 1905-1917, 2014 Author(s): S. Kravtsov, N. Sugiyama, and A. A. Tsonis Dynamical systems like the one described by the three-variable Lorenz model may serve as metaphors for complexity in nature. When natural systems are perturbed by external forcing factors, they tend to relax back to their equilibrium conditions after the forcing has shut off. Here we investigate the behavior of such transients in the Lorenz model by studying its trajectories initialized far away from the asymptotic attractor. Perhaps somewhat surprisingly, these transient trajectories exhibit complex routes and, among other things, sensitivity to initial conditions akin to that of the asymptotic behavior on the attractor. Thus, similar extreme events may lead to widely different variations before the perturbed system returns back to its statistical equilibrium.

Description: Precision variational approximations in statistical data assimilation Nonlinear Processes in Geophysics Discussions, 1, 1603-1620, 2014 Author(s): J. Ye, N. Kadakia, P. J. Rozdeba, H. D. I. Abarbanel, and J. C. Quinn Data assimilation transfers information from observations of a complex system to physically-based system models with state variables x ( t ). Typically, the observations are noisy, the model has errors, and the initial state of the model is uncertain, so the data assimilation is statistical. One can thus ask questions about expected values of functions ⟨ G ( X )⟩ on the path X = { x ( t 0 ), ..., x ( t m )} of the model as it moves through an observation window where measurements are made at times { t 0 , ..., t m }. The probability distribution on the path P ( X ) = exp[− A 0 ( X )] determines these expected values. Variational methods seeking extrema of the "action" A 0 ( X ), widely known as 4DVar (Talagrand and Courtier, 1987; Evensen, 2009),, are widespread for estimating ⟨ G ( X ) ⟩ in many fields of science. In a path integral formulation of statistical data assimilation, we consider variational approximations in a standard realization of the action where measurement and model errors are Gaussian. We (a) discuss an annealing method for locating the path X 0 giving a consistent global minimum of the action A 0 ( X 0 ), (b) consider the explicit role of the number of measurements at each measurement time in determining A 0 ( X 0 ), and (c) identify a parameter regime for the scale of model errors which allows X 0 to give a precise estimate of ⟨ G ( X 0 )⟩ with computable, small higher order corrections.

Description: Data assimilation experiments using the diffusive back and forth nudging for the NEMO ocean model Nonlinear Processes in Geophysics Discussions, 1, 1073-1131, 2014 Author(s): G. A. Ruggiero, Y. Ourmières, E. Cosme, J. Blum, D. Auroux, and J. Verron The Diffusive Back and Forth Nudging (DBFN) is an easy-to-implement iterative data assimilation method based on the well-known Nudging method. It consists in a sequence of forward and backward model integrations, within a given time window, both of them using a feedback term to the observations. Therefore in the DBFN, the Nudging asymptotic behavior is translated into an infinite number of iterations within a bounded time domain. In this method, the backward integration is carried out thanks to what is called backward model, which is basically the forward model with reversed time step sign. To maintain numeral stability the diffusion terms also have their sign reversed, giving a diffusive character to the algorithm. In this article the DBFN performance to control a primitive equation ocean model is investigated. In this kind of model non-resolved scales are modeled by diffusion operators which dissipate energy that cascade from large to small scales. Thus, in this article the DBFN approximations and their consequences on the data assimilation system set-up are analyzed. Our main result is that the DBFN may provide results which are comparable to those produced by a 4Dvar implementation with a much simpler implementation and a shorter CPU time for convergence.

Description: Estimation of flow velocity for a debris flow via the two-phase fluid model Nonlinear Processes in Geophysics Discussions, 1, 999-1021, 2014 Author(s): S. Guo, P. Xu, Z. Zheng, and Y. Gao The two-phase fluid model is applied in this study to calculate the steady velocity of a debris flow along a channel bed. By using the momentum equations of the solid and liquid phases in the debris flow together with an empirical formula to describe the interaction between two phases, the steady velocities of the solid and liquid phases are obtained theoretically. The comparison of those velocities obtained by the proposed method with the observed velocities of two real-world debris flows shows that the proposed method can estimate accurately the velocity for a debris flow.

Description: Time dependent Long's equation Nonlinear Processes in Geophysics Discussions, 1, 1673-1690, 2014 Author(s): M. Humi Long's equation describes steady-state two-dimensional stratified flow over terrain. Its numerical solutions under various approximations were investigated by many authors. Special attention was paid to the properties of the gravity waves that are predicted to be generated as a result. In this paper we derive a time-dependent generalization of this equation and investigate analytically its solutions under some simplifications. These results might be useful in the experimental analysis of gravity waves over topography and their impact on atmospheric modeling.

Description: Reversal in the nonlocal large-scale αΩ-dynamo Nonlinear Processes in Geophysics Discussions, 1, 1715-1734, 2014 Author(s): L. K. Feschenko and G. M. Vodinchar Inversion of the magnetic field in a large-scale model of αΩ-dynamo with nonlocal α-effect is under the investigation. The model allows us to reproduce the main features of the geomagnetic field reversals. It was established that the polarity intervals in the model are distributed according to the power law. Model magnetic polarity time scale is fractal. Its dimension is consistent with the dimension of the real geomagnetic polarity time scale.

Description: Statistical optimization for passive scalar transport: maximum entropy production vs. maximum Kolmogorov–Sinay entropy Nonlinear Processes in Geophysics Discussions, 1, 1691-1713, 2014 Author(s): M. Mihelich, D. Faranda, B. Dubrulle, and D. Paillard We derive rigorous results on the link between the principle of maximum entropy production and the principle of maximum Kolmogorov–Sinai entropy using a Markov model of the passive scalar diffusion called the Zero Range Process. We show analytically that both the entropy production and the Kolmogorov–Sinai entropy seen as functions of f admit a unique maximum denoted f max EP and f max KS . The behavior of these two maxima is explored as a function of the system disequilibrium and the system resolution N . The main result of this article is that f max EP and f max KS have the same Taylor expansion at first order in the deviation of equilibrium. We find that f max EP hardly depends on N whereas f max KS depends strongly on N . In particular, for a fixed difference of potential between the reservoirs, f max EP ( N ) tends towards a non-zero value, while f max KS ( N ) tends to 0 when N goes to infinity. For values of N typical of that adopted by Paltridge and climatologists ( N ≈ 10 ~ 100), we show that f max EP and f max KS coincide even far from equilibrium. Finally, we show that one can find an optimal resolution N * such that f max EP and f max KS coincide, at least up to a second order parameter proportional to the non-equilibrium fluxes imposed to the boundaries. We find that the optimal resolution N * depends on the non equilibrium fluxes, so that deeper convection should be represented on finer grids. This result points to the inadequacy of using a single grid for representing convection in climate and weather models. Moreover, the application of this principle to passive scalar transport parametrization is therefore expected to provide both the value of the optimal flux, and of the optimal number of degrees of freedom (resolution) to describe the system.

Description: Features of fluid flows in strongly nonlinear internal solitary waves Nonlinear Processes in Geophysics Discussions, 1, 1919-1946, 2014 Author(s): S. Semin, O. Kurkina, A. Kurkin, T. Talipova, E. Pelinovsky, and E. Churaev The characteristics of highly nonlinear solitary internal waves (solitons) are calculated within the fully nonlinear numerical model of the Massachusetts Institute of Technology. The verification and adaptation of the model is based on the data from laboratory experiments. The present paper also compares the results of our calculations with the calculations performed in the framework of the fully nonlinear Bergen Ocean Model. The comparison of the computed soliton parameters with the predictions of the weakly nonlinear theory based on the Gardner equation is given. The occurrence of reverse flow in the bottom layer directly behind the soliton is confirmed in the numerical simulations. The trajectories of Lagrangian particles in the internal soliton on the surface, on the pycnocline and near the bottom are computed.

Description: Geometric and topological approaches to significance testing in wavelet analysis Nonlinear Processes in Geophysics Discussions, 1, 1331-1363, 2014 Author(s): J. A. Schulte, C. Duffy, and R. G. Najjar Geometric and topological methods are applied to significance testing in the wavelet domain. A geometric test was developed for assigning significance to pointwise significance patches in local wavelet spectra, contiguous regions of significant wavelet coefficients with respect to some noise model. This geometric significance test was found to produce results similar to an existing areawise significance test, while being more computationally flexible and efficient. The geometric significance test can be readily applied to pointwise significance patches at various pointwise significance levels in wavelet power and coherence spectra. A topological analysis of pointwise significance patches determined that holes, deficits in pointwise significance embedded in significance patches, are capable of identifying important structures, some of which are undetected by the geometric and areawise tests. The application of the new and existing significance tests to ideal time series and to the time series of the Niño 3.4 and North Atlantic Oscillation showed that the areawise and geometric tests perform similarly in ideal and geophysical settings, while the topological methods showed that the Niño 3.4 time series contains numerous phase-coherent oscillations.

Description: Multifractal analysis of mercury inclusions in quartz by X-ray computed tomography Nonlinear Processes in Geophysics Discussions, 1, 1365-1379, 2014 Author(s): T. Shibata, T. Maruoka, and T. Echigo In order to refine our understanding how fluid inclusions were trapped in the host minerals, we non-destructively observed mercury inclusions (liquid Hg 0 ) in quartz samples using X-ray computed tomography (CT) technique. The X-ray CT apparatus can observe internal structures of the samples and give cross-sectional images from the transmission of the X-rays through the samples. From the cross-sectional images, we obtained three-dimensional spatial distributions of mercury inclusions, and quantitatively analyzed them using fractal and multifractal methods. Although the samples were from different mines, the resultant fractal dimensions were about 1.7 for the samples. The fractal dimensions were also close to those predicted by diffusion-limited aggregation models and percolation theory, which are controlled by the irreversible kinetics. Then, the mercury-bearing fluids were not primary fluid inclusions, but migrated into the pre-existing cracks of quartz crystals by diffusion processes.

Description: Toward the assimilation of images Nonlinear Processes in Geophysics Discussions, 1, 1381-1430, 2014 Author(s): F.-X. Le Dimet, I. Souopgui, O. Titaud, and V. Shutyaev The equations that govern geophysical fluids (namely atmosphere, ocean and rivers) are well known but their use for prediction requires the knowledge of the initial condition. In many practical cases, this initial condition is poorly known and the use of an imprecise initial guess is not sufficient to perform accurate forecasts because of the high sensitivity of these systems to small perturbations. As every situation is unique, the only additional information than can help to retrieve the initial condition are observations and statistics. The set of methods that combine these sources of heterogeneous information to construct such an initial condition are referred to as data assimilation. More and more images and sequences of images, of increasing resolution, are produced for scientific or technical studies. This is particularly true in the case of geophysical fluids that are permanently observed by remote sensors. However, the structured information contained in images or image sequences is not assimilated as regular observations: images are still (under)utilized to produce qualitative analysis by experts. This paper deals with the quantitative assimilation of information provided in an image form into a numerical model of a dynamical system. We describe several possibilities for such assimilation and identify associated difficulties. Results from our ongoing research are used to illustrate the methods. The assimilation of image is a very general framework that can be transposed in several scientific domains.

Description: Isotropy restoration toward high-beta space plasmas Nonlinear Processes in Geophysics Discussions, 1, 1313-1330, 2014 Author(s): H. Comişel, Y. Narita, and U. Motschmann Wavevector anisotropy of ion-scale plasma turbulence is studied at various values of 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. The both methods provide evidence of wavevector anisotropy as a function of beta such that isotropy is gradually restored toward higher values of beta. Furthermore, the numerical simulation study demonstrates the existence of scaling law between plasma beta and wavevector anisotropy. This fact can be used to construct a diagnostic tool to determine or to constrain plasma beta using multi-point magnetic field measurements in space.

Description: Bayesian optimization for tuning chaotic systems Nonlinear Processes in Geophysics Discussions, 1, 1283-1312, 2014 Author(s): M. Abbas, A. Ilin, A. Solonen, J. Hakkarainen, E. Oja, and H. Järvinen In this work, we consider the Bayesian optimization (BO) approach for tuning parameters of complex chaotic systems. Such problems arise, for instance, in tuning the sub-grid scale parameterizations in weather and climate models. For such problems, the tuning procedure is generally based on a performance metric which measures how well the tuned model fits the data. This tuning is often a computationally expensive task. We show that BO, as a tool for finding the extrema of computationally expensive objective functions, is suitable for such tuning tasks. In the experiments, we consider tuning parameters of two systems: a simplified atmospheric model and a low-dimensional chaotic system. We show that BO is able to tune parameters of both the systems with a low number of objective function evaluations and without the need of any gradient information.

Description: Fluctuations in a quasi-stationary shallow cumulus cloud ensemble Nonlinear Processes in Geophysics Discussions, 1, 1223-1282, 2014 Author(s): M. Sakradzija, A. Seifert, and T. Heus We propose an approach to stochastic parameterization of shallow cumulus clouds to represent the convective variability and its dependence on the model resolution. To collect the information about the individual cloud lifecycles and the cloud ensemble as a whole, we employ a Large-Eddy Simulation model (LES) and a cloud tracking algorithm, followed by conditional sampling of clouds at the cloud-base level. In the case of a shallow cumulus ensemble, the cloud-base mass flux distribution is bimodal due to the different shallow cloud subtypes. Each distribution mode can be approximated with a Weibull distribution, explaining the deviation from a single-parameter exponential shape through the diversity in cloud lifecycles. The exponential distribution of cloud mass flux previously suggested for deep convection parameterization is a special case of the Weibull distribution, which opens a way towards unification of the statistical convective ensemble formalism of shallow and deep cumulus clouds. Based on the empirical and theoretical findings, a stochastic model has been developed to simulate a shallow convective cloud ensemble. It is formulated as a compound random process, with the number of convective elements drawn from a Poisson distribution, and the cloud mass flux sampled from a mixed Weibull distribution. Convective memory is accounted for through the explicit cloud lifecycles, making the model formulation consistent with the choice of the Weibull cloud mass flux distribution function. The memory of individual shallow clouds is required to capture the correct convective variability. The resulting distribution of the subgrid convective states in the considered shallow cumulus case is scale-adaptive – the smaller the grid size, the broader the distribution.

Description: Site effect classification based on microtremor data analysis using concentration–area fractal model Nonlinear Processes in Geophysics Discussions, 1, 1133-1161, 2014 Author(s): A. Adib, P. Afzal, and K. Heydarzadeh The aim of this study is to classify the site effect using concentration–area ( C – A ) fractal model in Meybod city, Central Iran, based on microtremor data analysis. Log–log plots of the frequency, amplification and vulnerability index (k-g) indicate a multifractal nature for the parameters in the area. The results obtained from the C – A fractal modeling reveal that proper soil types are located around the central city. The results derived via the fractal modeling were utilized to improve the Nogoshi's classification results in the Meybod city. The resulted categories are: (1) hard soil and weak rock with frequency of 6.2 to 8 Hz, (2) stiff soil with frequency of about 4.9 to 6.2 Hz, (3) moderately soft soil with the frequency of 2.4 to 4.9 Hz, and (4) soft soil with the frequency lower than 2.4 Hz.

Description: Shoaling of internal solitary waves at the ASIAEX site in the South China Sea Nonlinear Processes in Geophysics Discussions, 1, 1163-1222, 2014 Author(s): K. G. Lamb and A. Warn-Varnas The interaction of barotropic tides with Luzon Strait topography generates westward propagating internal bores and solitary waves trains which eventually shoal and dissipate on the western side of the South China Sea. Two-dimensional numerical simulations of this shoaling process at the site of the Asian Seas International Acoustic Experiment (ASIAEX) have been undertaken in order to investigate the sensitivity of the shoaling process to the stratification and the underlying bathymetry, and to explore the influence of rotation. A range of wave amplitudes are considered. Comparisons with adiabatic shoaling waves are also made and the potential impact of a non-slip boundary condition are briefly explored. On the slope secondary solitary waves and mode-two wave packets are generated which propagate towards the shelf. Comparisons with observations made during the ASIAEX experiment are made.

Description: Estimation of sedimentary proxy records together with associated uncertainty Nonlinear Processes in Geophysics Discussions, 1, 1023-1071, 2014 Author(s): B. Goswami, J. Heitzig, K. Rehfeld, N. Marwan, A. Ambili, S. Prasad, and J. Kurths Sedimentary proxy records constitute a significant portion of the recorded evidence that allow 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 inter-comparisons. While there are various age-modeling approaches to improve the estimation of the age-depth relations of archives, relatively less focus has been given to 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 datasets 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 proxy 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 time scale that makes further time series analyses and inter-comparison of proxies relatively simpler and clearer. 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: Improved singular spectrum analysis for time series with missing data Nonlinear Processes in Geophysics Discussions, 1, 1947-1966, 2014 Author(s): Y. Shen, F. Peng, and B. Li Singular spectrum analysis (SSA) is a powerful technique for time series analysis. Based on the property that the original time series can be reproduced from its principal components, this contribution will develop an improved SSA (ISSA) for processing the incomplete time series and the modified SSA (SSAM) of Schoellhamer (2001) is its special case. The approach was evaluated with the synthetic and real incomplete time series data of suspended-sediment concentration from San Francisco Bay. The result from the synthetic time series with missing data shows that the relative errors of the principal components reconstructed by ISSA are much smaller than those reconstructed by SSAM. Moreover, when the percentage of the missing data over the whole time series reaches 60%, the improvements of relative errors are up to 19.64, 41.34, 23.27 and 50.30% for the first four principal components, respectively. Besides, both the mean absolute errors and mean root mean squared errors of the reconstructed time series by ISSA are also much smaller than those by SSAM. The respective improvements are 34.45 and 33.91% when the missing data accounts for 60%. The results from real incomplete time series also show that the SD derived by ISSA is 12.27 mg L −1 , smaller than 13.48 mg L −1 derived by SSAM.

Description: The ability of empirical mode decomposition (EMD) to extract multidecadal variability from sea level records is tested using three simulations: one based on a series of purely sinusoidal modes, one based on scaled climate indices of El Niño and the Pacific Decadal Oscillation (PDO), and the final one including a single month with an extreme sea level event. All simulations include random noise of similar variance to high-frequency variability in the San Francisco tide gauge record. The intrinsic mode functions (IMFs) computed using EMD were compared to the prescribed oscillations. In all cases, the longest-period modes are significantly distorted, with incorrect amplitudes and phases. This affects the estimated acceleration computed from the longest periodic IMF. In these simulations, the acceleration was underestimated in the case with purely sinusoidal modes, and overestimated by nearly 100% in the case with prescribed climate modes. Additionally, in all cases, extra low-frequency modes uncorrelated with the prescribed variability are found. These experiments suggest that using EMD to identify multidecadal variability and accelerations in sea level records should be used with caution.

Description: The development of Benjamin–Feir instability of Stokes waves in the presence of variable current is presented. We employ a model of a resonance system having three coexisting nonlinear waves and nonuniform current. The model is free from the narrow-band approximation for surface waves and relatively weak adverse current. The modulation instability of Stokes waves in nonuniform moving media has special properties. Interaction with countercurrent accelerates the growth of sideband modes on a short spatial scale. An increase in initial wave steepness intensifies the wave energy exchange accompanied by wave breaking dissipation, results in asymmetry of sideband modes and a frequency downshift with an energy transfer jump to the lower sideband mode, and depresses the higher sideband and carrier wave. Nonlinear waves may even overpass the blocking barrier produced by strong adverse current. The frequency downshift of the energy peak is permanent and the system does not revert to its initial state. We find reasonable correspondence between the results of model simulations and available experimental results for wave interaction with blocking opposing current. Large transient or freak waves with amplitude and steepness several times those of normal waves may form during temporal nonlinear focusing of the resonant waves accompanied by energy income from sufficiently strong opposing current. We employ the resonance model for the estimation of the maximum amplification of wave amplitudes as a function of gradually increasing opposing current and compare the result obtained with recently published experimental results and modeling results obtained with the nonlinear Schrödinger equation.

Description: Low frequency is a key issue to reduce the nonlinearity of elastic full waveform inversion. Hence, the lack of low frequency in recorded seismic data is one of the most challenging problems in elastic full waveform inversion. Theoretical derivations and numerical analysis are presented in this paper to show that envelope operator can retrieve strong low frequency modulation signal demodulated in multicomponent data, no matter what the frequency bands of the data is. With the benefit of such low frequency information, we use elastic envelope of multicomponent data to construct the objective function and present an elastic envelope inversion method to recover the long-wavelength components of the subsurface model, especially for the S-wave velocity model. Numerical tests using synthetic data for the Marmousi-II model prove the effectiveness of the proposed elastic envelope inversion method, especially when low frequency is missing in multicomponent data and when initial model is far from the true model. The elastic envelope can reduce the nonlinearity of inversion and can provide an excellent starting model.

Description: The quest to find an index for proper characterization and description of the dynamical response of the ionosphere to external influences and its various internal irregularities has led to the study of the day to day variations of the chaoticity and dynamical complexity of the ionosphere. This study was conducted using Global Positioning System (GPS) Total Electron Content (TEC) time series, measured in the year 2011, from 5 GPS receiver stations in Nigeria which lies within the Equatorial Ionization Anomaly region. The nonlinear aspect of the TEC time series were 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 which are Lyapunov exponents LE, correlation dimension, and Tsallis entropy for the study of dynamical complexity. The results show positive Lyapunov exponents for all days which indicate chaoticity of the ionosphere with no definite pattern for both quiet and disturbed days. However values of LE were lower for the storm period compared to its nearest relative quiet periods for all the stations. Considering all the days of the year the daily/transient variations show no definite pattern for each month but day to day values of Lyapunov exponent for the entire year show a wavelike semiannual variation pattern with lower values around March, April, September and October, a change in pattern which demonstrates the self-organized critical phenomenon of the system. This can be seen from the correlation dimension with values between 2.7 and 3.2 with lower values occurring mostly during storm periods demonstrating a phase transition from higher dimension during the quiet periods to lower dimension during storms for most of the stations. The values of Tsallis entropy show similar variation pattern with that of Lyapunov exponent with a lot of agreement in their comparison, with all computed values of Lyapunov exponent correlating with values of Tsallis entropy within the range of 0.79 to 0.82. These results show that Lyapunov quantifiers can be used together as indices in the study of the variations of the dynamical complexity of the ionosphere. The presence of chaos and high variations in the dynamical complexity, even at quiet periods in the ionosphere may be due to the internal dynamics and inherent irregularities of the ionosphere which exhibit non-linear properties. However, this inherent dynamics may be complicated by external factors like geomagnetic storms. This may be the main reason for the drop in the values of Lyapunov exponent and Tsallis entropy during storms. The results also show a strong interplay between determinism and stochasticity, as the ionosphere shows its response to changes in solar activities and in its internal dynamics. The dynamical behavior of the ionosphere throughout the year as described by these quantifiers, were discussed in this work.

Description: Inversion of the magnetic field in a large-scale model of αΩ-dynamo with nonlocal α-effect is under the investigation. The model allows us to reproduce the main features of the geomagnetic field reversals. It was established that the polarity intervals in the model are distributed according to the power law. Model magnetic polarity time scale is fractal. Its dimension is consistent with the dimension of the real geomagnetic polarity time scale.

Description: The two-phase fluid model is applied in this study to calculate the steady velocity of a debris flow along a channel bed. By using the momentum equations of the solid and liquid phases in the debris flow together with an empirical formula to describe the interaction between two phases, the steady velocities of the solid and liquid phases are obtained theoretically. The comparison of those velocities obtained by the proposed method with the observed velocities of two real-world debris flows shows that the proposed method can estimate accurately the velocity for a debris flow.

Description: Very Low Frequency (VLF) disturbances in the ionospheric electric field observed by DEMETER satellite prior to three different earthquakes that occurred during the years 2008–2009 have been presented. The electromagnetic wave data has been analyzed for few days before the earthquake with special attention to the variation in spectral characteristics and non-linear effects using the statistical and wavelet based techniques. Results indicate that the earthquake preparation process may disturb the ionospheric plasma and these disturbances can reach the non-linear stage leading to the strong variations in the electromagnetic field and plasma parameters. The enhancement in statistical parameters shows the coherent structure and intermittent phenomenon which is the signature of turbulence. The characteristics features of VLF disturbances have further been studied using the wavelet and bispectral analysis tools which provide useful information on the plasma turbulence.

Description: In this work, we consider the Bayesian optimization (BO) approach for tuning parameters of complex chaotic systems. Such problems arise, for instance, in tuning the sub-grid scale parameterizations in weather and climate models. For such problems, the tuning procedure is generally based on a performance metric which measures how well the tuned model fits the data. This tuning is often a computationally expensive task. We show that BO, as a tool for finding the extrema of computationally expensive objective functions, is suitable for such tuning tasks. In the experiments, we consider tuning parameters of two systems: a simplified atmospheric model and a low-dimensional chaotic system. We show that BO is able to tune parameters of both the systems with a low number of objective function evaluations and without the need of any gradient information.

Description: Lightning measurements from the Geostationary Lightning Mapper (GLM) that will be aboard the Goestationary 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), improving initial conditions, and partially improving WRF-NMM forecasts during several data assimilation cycles.

Description: The aim of this study is to classify the site effect using concentration–area (C–A) fractal model in Meybod city, Central Iran, based on microtremor data analysis. Log–log plots of the frequency, amplification and vulnerability index (k-g) indicate a multifractal nature for the parameters in the area. The results obtained from the C–A fractal modeling reveal that proper soil types are located around the central city. The results derived via the fractal modeling were utilized to improve the Nogoshi's classification results in the Meybod city. The resulted categories are: (1) hard soil and weak rock with frequency of 6.2 to 8 Hz, (2) stiff soil with frequency of about 4.9 to 6.2 Hz, (3) moderately soft soil with the frequency of 2.4 to 4.9 Hz, and (4) soft soil with the frequency lower than 2.4 Hz.

Description: The interaction of barotropic tides with Luzon Strait topography generates westward propagating internal bores and solitary waves trains which eventually shoal and dissipate on the western side of the South China Sea. Two-dimensional numerical simulations of this shoaling process at the site of the Asian Seas International Acoustic Experiment (ASIAEX) have been undertaken in order to investigate the sensitivity of the shoaling process to the stratification and the underlying bathymetry, and to explore the influence of rotation. A range of wave amplitudes are considered. Comparisons with adiabatic shoaling waves are also made and the potential impact of a non-slip boundary condition are briefly explored. On the slope secondary solitary waves and mode-two wave packets are generated which propagate towards the shelf. Comparisons with observations made during the ASIAEX experiment are made.

Description: 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 along the years. Here we investigate the temperature network of North America region and show that two network characteristics, namely degree and clustering, have markedly differences between the Eastern and Western regions. We show that such differences are a reflection of the presence of a large network community in the western side of the continent. Moreover, we provide evidences that this large community is a consequence of the peculiar characteristics of the western relief of North America.

Description: Recurrence plot based recurrence networks are an approach to analyze time series using 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 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: This paper investigates the controls on the transformation mechanism among different channel patterns. A 2-D depth-averaged numerical model is applied to produce the evolution of channel patterns with complex interactions among water flow, sediment transport, and bank erosion. Changes of the variables as discharge, sediment supply, and vegetation are considered in the numerical experiments, leading to the transformation from a braided pattern into a meandering one. What controls the transformation is discussed with the numerical results: vegetation helps stabilize the cut bank and bar surface, but is not a key in the transition; a decrease in discharge and sediment supply could lead a braided pattern to a meandering one. The conclusion is in agreement with various previous field work, confirming the two dimensional model's potential in predicting the transition between different rivers and improving understanding of patterning processes.

Description: Auto Regressive Integrated Moving Average (ARIMA) model is often used to calculate time series data formed by inter-annual variations of monthly data. However, the influence brought about by inter-monthly variations within each year is ignored. Based on the monthly data classified by clustering analysis, the characteristics of time series data are extracted. An improved ARIMA model is developed accounting for both the inter-annual and inter-monthly variation. The correlation between characteristic quantity and monthly data within each year is constructed by regression analysis first. The model can be used for predicting characteristic quantity followed by the stationary treatment for characteristic quantity time series by difference. A case study is conducted to predict the precipitation in Lanzhou precipitation station, 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: Solar activity is characterized by complex dynamics superimposed to an almost periodic, about 11 years cycle. One of its main features is the presence of a marked, time-varying hemispheric asymmetry, the deeper reasons of 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 potentials 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: In this study, we discuss the role of the nonlinear terms and linear (heating) term in the energy cycle of the three-dimensional (X–Y–Z) non-dissipative Lorenz model (3D-NLM). (X, Y, Z) represent the solutions in the phase space. We first present the closed-form solution to the nonlinear equation d2 X/dτ2+ (X2/2)X = 0, τ is a non-dimensional time, which was never documented in the literature. As the solution is oscillatory (wave-like) and the nonlinear term (X2) is associated with the nonlinear feedback loop, it is suggested that the nonlinear feedback loop may act as a restoring force. We then show that the competing impact of nonlinear restoring force and linear (heating) force determines the partitions of the averaged available potential energy from Y and Z modes, respectively, denoted as APEY and APEZ. Based on the energy analysis, an energy cycle with four different regimes is identified with the following four points: A(X, Y) = (0,0), B = (Xt, Yt), C = (Xm, Ym), and D = (Xt, -Yt). Point A is a saddle point. The initial perturbation (X, Y, Z) = (0, 1, 0) gives (Xt, Yt) = ( √ 2σr , r) and (Xm, Ym) = (2√  σr , 0). σ is the Prandtl number, and r is the normalized Rayleigh number. The energy cycle starts at (near) point A, A+ = (0, 0+) to be specific, goes through B, C, and D, and returns back to A, i.e., A- = (0,0-). From point A to point B, denoted as Leg A–B, where the linear (heating) force dominates, the solution X grows gradually with { KE↑, APEY↓, APEZ↓}. KE is the averaged kinetic energy. We use the upper arrow (↑) and down arrow (↓) to indicate an increase and decrease, respectively. In Leg B–C (or C–D) where nonlinear restoring force becomes dominant, the solution X increases (or decreases) rapidly with {KE↑, APEY↑, APEZ↓} (or {KE↓, APEY↓, APEZ↑}). In Leg D–A, the solution X decreases slowly with {KE↓, APEY↑, APEZ↑ }. As point A is a saddle point, the aforementioned cycle may be only half of a "big" cycle, displaying the wing pattern of a glasswinged butterfly, and the other half cycle is antisymmetric with respect to the origin, namely B = (-Xt, -Yt), C = (-Xm, 0), and D = (-Xt, Yt).

Description: The properties of the multiple scale instabilities present in a non-hydrostatic forecast model are investigated. The model simulates intense convection episodes occurring in Northern Italy. A breeding technique is used to construct ensembles of perturbations of the model trajectories aimed to represent the instabilities that are responsible for error growth at various time and space scales. It is found that for initial errors of the order of present-day analysis error, error growth is mainly determined by intermediate scale instabilities, and that a non-negligible fraction of the forecast error can be explained by an ensemble of bred vectors of reasonable size. In contrast, when the initial error is much smaller, the spectrum of bred vectors representing the fast convective-scale instabilities becomes flat and the number of ensemble members needed to explain even a small fraction of the forecast error becomes extremely large. The conclusion is that as the analysis error is decreased, it becomes more and more computationally demanding to construct an ensemble that can describe the high-dimensional subspace of convective instabilities and that can thus be potentially useful for controlling the error growth.

Description: The Variational Ensemble Kalman Filter (VEnKF), a recent data assimilation method that combines a variational assimilation of the Bayesian estimation problem with an ensemble of forecasts, is demonstrated in two-dimensional geophysical flows using a Quasi-Geostrophic (QG) model and a shallow water model. Using a synthetic experiment, a two layer QG model with model bias is solved on a cylindrical 40 x 20 domain. The performance of VEnKF on the QG model with increasing ensemble size is compared with the classical Extended Kalman Filter (EKF). It is shown that although convergence can be achieved with just 20 ensemble members, increasing the number of members results in a better estimate that approaches the one produced by EKF. In the second test case, a 2-D shallow water model is described using a real dam-break experiment. The VEnKF algorithm was used to assimilate observations obtained from a modified laboratory dam-break experiment with a two-dimensional setup of sensors at the downstream end. The wave meters are placed parallel to the direction of the flow alongside the flume walls to capture both cross flow and stream flow. In both test cases, VEnKF was able to predict genuinely two-dimensional flow patterns when the sensors had a two-dimensional geometry and was stable against model bias in the first test case. In the second test case, the experiments are complemented with an empirical study of the impact of observation interpolation on the stability of the VEnKF filter. In this study, a novel Courant–Friedrichs–Lewy type filter stability condition is observed that relates ensemble variance to the time interpolation distance between observations. The results of the two experiments shows that VEnKF is a good candidate for data assimilation problems and can be implemented in higher dimensional nonlinear models.

Description: Principal Component Analysis (PCA) is one of the popular statistical methods for feature extraction. The neural network model has been performed on the PCA to obtain nonlinear principal component analysis (NLPCA), which allows the extraction of nonlinear features in the dataset missed by the PCA. NLPCA is applied to the monthly Sea Surface Temperature (SST) data from the eastern tropical Atlantic Ocean (29° W–21° E, 25° S–7° N) for the period 1982–2005. The focus is on the differences between SST inter-annual variability patterns; either extracted through traditional PCA or the NLPCA methods.The first mode of NLPCA explains 45.5% of the total variance of SST anomaly compared to 42% explained by the first PCA. Results from previous studies that detected the Atlantic cold tongue (ACT) as the main mode are confirmed. It is observed that the maximum signal in the Gulf of Guinea (GOG) is located along coastal Angola. In agreement with composite analysis, NLPCA exhibits two types of ACT, referred to as weak and strong Atlantic cold tongues. These two events are not totally symmetrical. NLPCA thus explains the results given by both PCA and composite analysis. A particular area observed along the northern boundary between 13 and 5° W vanishes in the strong ACT case and reaches maximum extension to the west in the weak ACT case. It is also observed that the original SST data correlates well with NLPCA and PCA, but with a stronger correlation on ACT area for NLPCA and southwest in the case of PCA.

Description: The seismic reflection data processing to identify thin coal beds and intrinsic fault structure associated with coalmines suffers from the coherent noise that arises due to interference and diffraction of seismic signals from adjacent horizontal boundaries on either sides of the fault structure. The amplitudes of the interfering reflections mislead the interpretation of geological features like faults, curved reflectors, etc. In particular, correlated and erratic noise create more severe problem than the random noise in the interpretation of such complex geological structures. Here, we employed Space Lagged Singular Spectral Analysis (SLSSA) algorithm, which decomposes the amplitudes from a constant time/depth to determine the original signal amplitude based on eigen properties of the signal. Thus, we can de-noise seismic signal to delineate the concealed discontinuities and to map the fault structures. Initially, we tested the algorithm on the synthetic data of fault structure embedded with complex mixed noise (random and colored) of known percentage. Finally, the method was employed on high-resolution seismic reflection observations recorded from Singareni coalfield, India. The SLSSA method reveals some significant kinematic fault structures in the coal-bearing zone, which agreed with regional fault structures in the PG basin and correlates well with available geological information in the area.

Description: Describing the nature and variability of Indian monsoon rainfall extremes 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. Several GLMM algorithms are described and simulations are performed to vet these algorithms before applying them to the Indian precipitation data procured from the National Climatic Data Center. The logit-normal model was applied with fixed covariates of latitude, longitude, elevation, daily minimum and maximum temperatures with a random intercept by weather station. In general, the estimation methods concurred in their suggestion of a relationship between the El Niño Southern Oscillation (ENSO) and extreme rainfall variability estimates. This work provides a valuable starting point for extending GLMM to incorporate the intricate dependencies in extreme climate events.

Description: 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 data collection process. A failure of stability leads to nonsmoothness and nonlinearity in the physical processes that drive the data under. 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, to understand whether the nature of these tropical storms has remained stable over the last few decades.

Description: 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: 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 it 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 the persistence analysis has been used to study IMF time series. We use data from the IMF GSM-components with time resolution of 16 s. Time intervals corresponding to distinct processes around 41 MCs in the period between March 1998 and December 2003 were selected. In this exploratory study the purpose with 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 select the following threshold values: 〈α(j)〉 =1.392; 〈Ha(j)〉 = 0.327; 〈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 exponents 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: The large scale atmospheric vortices (tropical cyclones, tornadoes) are complex physical systems combining thermodynamics and fluid-mechanical processes. The late phase of the evolution towards stationarity consists of the vorticity concentration, a well known tendency to self-organization , an universal property of the two-dimensional fluids. It may then be expected that the stationary state of the tropical cyclone has the same nature as the vortices of many other systems in nature: ideal (Euler) fluids, superconductors, Bose–Einsetin condensate, cosmic strings, etc. Indeed it was found that there is a description of the atmospheric vortex in terms of a classical field theory. It is compatible with the more conventional treatment based on conservation laws, but the field theoretical model reveals properties that are almost inaccessible to the conventional formulation: it identifies the stationary states as being close to self-duality. This is of highest importance: the self-duality is known to be the origin of all coherent structures known in natural systems. Therefore the field theoretical (FT) formulation finds that the cuasi-coherent form of the atmospheric vortex (tropical cyclone) at stationarity is an expression of this particular property. In the present work we examine a strong property of the tropical cyclone, which arises in the FT formulation in a natural way: the equality of the masses of the particles associated to the matter field and respectively to the gauge field in the FT model is translated into the equality between the maximum radial extension of the tropical cyclone and the Rossby radius. For the cases where the FT model is a good approximation we calculate characteristic quantities of the tropical cyclone and find good comparison with observational data.

Description: Long's equation describes steady-state two-dimensional stratified flow over terrain. Its numerical solutions under various approximations were investigated by many authors. Special attention was paid to the properties of the gravity waves that are predicted to be generated as a result. In this paper we derive a time-dependent generalization of this equation and investigate analytically its solutions under some simplifications. These results might be useful in the experimental analysis of gravity waves over topography and their impact on atmospheric modeling.

Description: Motivated by important geophysical applications we consider a dynamic model of the magma-plug system previously derived by Iverson et al. (2006) under the influence of stochastic forcing. Due to strong nonlinearity of the friction force for solid plug along its margins, the initial deterministic system exhibits impulsive oscillations. Two types of dynamic behavior of the system under the influence of the parametric stochastic forcing have been found: random trajectories are scattered on both sides of the deterministic cycle or grouped on its internal side only. It is shown that dispersions are highly inhomogeneous along cycles in the presence of noises. The effects of noise-induced shifts, pressure stabilization and localization of random trajectories have been revealed with increasing the noise intensity. The plug velocity, pressure and displacement are highly dependent of noise intensity as well. These new stochastic phenomena are related with the nonlinear peculiarities of the deterministic phase portrait. It is demonstrated that the repetitive stick-slip motions of the magma-plug system in the case of stochastic forcing can be connected with drumbeat earthquakes.

Description: We have developed a fast total-field anomaly inversion to estimate the magnetization direction of multiple sources with approximately spherical shape and known centres. Our method can be applied to interpret multiple sources with different magnetization directions. It neither requires the prior computation of any transformation like reduction to the pole nor the use of regularly spaced data on a horizontal grid. The method contains flexibility to be implemented as a linear or non-linear inverse problem, which results, respectively, in a least-squares or robust estimate of the components of the magnetization vector of the sources. Applications to synthetic data show the robustness of our method against interfering anomalies and errors in the location of the sources' centre. Besides, we show the feasibility of applying the upward continuation to interpret non-spherical sources. Applications to field data over the Goiás Alkaline Province (GAP), Brazil, show the good performance of our method in estimating geological meaningful magnetization directions. The results obtained for a region of the GAP, near from the alkaline complex of Diorama, suggest the presence of non-outcropping sources marked by strong remanent magnetization with inclination and declination close to -70.35° and -19.81°, respectively. This estimated magnetization direction leads to predominantly positive reduced-to-the-pole anomalies, even for other region of the GAP, in the alkaline complex of Montes Claros de Goiás. These results show that the non-outcropping sources near from the alkaline complex of Diorama have almost the same magnetization direction of that ones in the alkaline complex of Montes Claros de Goiás, strongly suggesting that these sources have emplaced the crust almost within the same geological time interval.

Description: We present a new approach to estimate local Lyapunov vectors. The so called self-breeding method is based on the breeding of growing modes technique from medium range weather forecasting and consists of a continuous forecasting and rescaling cycle. Using the Lorenz96 model we test and characterize the behavior of the algorithm regarding error growth, spatial perturbation structure estimates and orthogonalization. The results indicate that the method can be used to generate error growing modes optimized for a certain rescaling interval, thus enabling the user to target specific scales of error growth. When an additional orthogonalization procedure is applied, the method is able to produce structures representing the error growth subspace spanned by the largest Lyapunov vectors.

Description: Wavevector anisotropy of ion-scale plasma turbulence is studied at various values of 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. The both methods provide evidence of wavevector anisotropy as a function of beta such that isotropy is gradually restored toward higher values of beta. Furthermore, the numerical simulation study demonstrates the existence of scaling law between plasma beta and wavevector anisotropy. This fact can be used to construct a diagnostic tool to determine or to constrain plasma beta using multi-point magnetic field measurements in space.

Description: Sedimentary proxy records constitute a significant portion of the recorded evidence that allow 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 inter-comparisons. While there are various age-modeling approaches to improve the estimation of the age-depth relations of archives, relatively less focus has been given to 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 datasets 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 proxy 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 time scale that makes further time series analyses and inter-comparison of proxies relatively simpler and clearer. 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: The Diffusive Back and Forth Nudging (DBFN) is an easy-to-implement iterative data assimilation method based on the well-known Nudging method. It consists in a sequence of forward and backward model integrations, within a given time window, both of them using a feedback term to the observations. Therefore in the DBFN, the Nudging asymptotic behavior is translated into an infinite number of iterations within a bounded time domain. In this method, the backward integration is carried out thanks to what is called backward model, which is basically the forward model with reversed time step sign. To maintain numeral stability the diffusion terms also have their sign reversed, giving a diffusive character to the algorithm. In this article the DBFN performance to control a primitive equation ocean model is investigated. In this kind of model non-resolved scales are modeled by diffusion operators which dissipate energy that cascade from large to small scales. Thus, in this article the DBFN approximations and their consequences on the data assimilation system set-up are analyzed. Our main result is that the DBFN may provide results which are comparable to those produced by a 4Dvar implementation with a much simpler implementation and a shorter CPU time for convergence.

Description: 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 is that the nonlinear operator and its tangent-linear operator are iteratively calculated in the minimization of a nonlinear objective function similar to 4DVAR, which 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 seeks a way to avoid these problems. First, we apply the second-order Taylor approximation of the nonlinear observation operator to avoid iteratively calculating the operator and its tangent-linear operator. 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 of the analysis error compared with the traditional linear approximation. Similarly, the proposed inflation scheme leads to a reduction of the analysis error compared with the procedure using the traditional inflation scheme.

Description: Decades of hypothesis-driven and/or first-principles research have been applied towards the discovery and explanation of the mechanisms that drive climate phenomena, such as western African Sahel summer rainfall variability. Although connections between various climate factors have been theorized, not all of the key relationships are fully understood. We propose a data-driven approach to identify candidate players in this climate system, which can help explain underlying mechanisms and/or even suggest new relationships, to facilitate building a more comprehensive and predictive model of the modulatory relationships influencing a climate phenomenon of interest. We applied coupled heterogeneous association rule mining (CHARM), Lasso multivariate regression, and Dynamic Bayesian networks to find relationships within a complex system, and explored means with which to obtain a consensus result from the application of such varied methodologies. Using this fusion of approaches, we identified relationships among climate factors that modulate Sahel rainfall, including well-known associations from prior climate knowledge, as well as promising discoveries that invite further research by the climate science community.

Description: An effective boundary condition (EBC) is introduced as a novel technique to predict tsunami wave run-up along the coast and offshore wave reflections. Numerical modeling of tsunami propagation at the coastal zone has been a daunting task since high accuracy is needed to capture aspects of wave propagation in the more shallow 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 sloping bathymetry. 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: Climate projections simulated by Global Climate Models (GCM) are often used for assessing the impacts of climate change. However, the relatively coarse resolutions of GCM outputs often precludes their application towards 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 are 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 which 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 relatively more generalizable than non-sparse alternatives, and lends 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 shows our method can lead to new insights.

Description: Weakly nonlinear internal gravity waves are treated in a two-layer fluid with a set of nonlinear Schrodinger equations. The layers have a sharp interface with a jump in buoyance frequency approximately modelling the tropopause. The waves are periodic in the horizontal but modulated in the vertical and Boussinesq flow is assumed. The equation governing the incident wave packet is directly coupled to the equation for the reflected packet, while the equation governing transmitted waves is only coupled at the interface. Solutions are obtained numerically. The results indicate that the waves create a mean flow that is strong near and underneath the interface, and discontinuous at the interface. Furthermore, the mean flow has an oscillatory component with a vertical wavelength that decreases as the wave packet interacts with the interface.

Description: Earthquake network describes the complexity of seismicity both qualitatively and quantitatively. The procedure of constructing an earthquake network contains as a single parameter the size of the cells, into which a geographical region under consideration is divided. Then, the characteristics of the network depend on the cell size, in general. Here, the dependency of the clustering coefficient, C, of network on the cell size is studied. Remarkably, C of the earthquake networks constructed from the seismic data taken from California, Japan, and Iran well coincide for each value of the scaled dimensionless cell size. It is found that the networks in California and Japan are three-dimensional, whereas the one in Iran is rather two-dimensional. In addition, the values of C of all these three networks monotonically converge to C ≈ 0.85 as the scaled dimensionless cell size increases, highlighting a universal aspect of the concept of earthquake network.

Description: SSH altimetry observations for 1992 to 2009 off Central and Southern 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 bi-annual oscillations and quasi-zonal jets. The total number of quartets induced off California was approximately 10 times larger than the number of existing triads, and quartet amplitudes in general were larger than triad amplitudes. The spectral centroid regularly shifted into the domain of low-order modes. Local "negative" viscosity probably did not generate a classical inverse cascade because the spectrum of SSHs did not demonstrate power behavior. Two types of quartets were identified: (a) quasi-zonal jets, annual and semi-annual Rossby waves and eddies, and (b) bi-annual oscillations, semi-annual Rossby waves and eddies. For a case with bottom friction, quartet instability required the existence of a certain level of dissipativity in the flow.

Description: We define, calculate and analyze irregularity indices λWN and λaa of daily series of sunspot number WN and geomagnetic index aa 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. λWN and λaa display Schwabe cycles with sharp peaks not only at cycle maxima but also at minima: we call the resulting ~5.5 year variations "half Schwabe variations" (HSV). The mean of λWN 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 T1 and T2 (T1 = 11 years, and intermediate T2 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 T2 variations. When m = 2, Q1 occurs when T2 variations are present, whereas Q2 occurs when T2 variations are suppressed. We propose that the HSV behavior of the irregularity index of WN 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: Singular spectrum analysis (SSA) is a powerful technique for time series analysis. Based on the property that the original time series can be reproduced from its principal components, this contribution will develop an improved SSA (ISSA) for processing the incomplete time series and the modified SSA (SSAM) of Schoellhamer (2001) is its special case. The approach was evaluated with the synthetic and real incomplete time series data of suspended-sediment concentration from San Francisco Bay. The result from the synthetic time series with missing data shows that the relative errors of the principal components reconstructed by ISSA are much smaller than those reconstructed by SSAM. Moreover, when the percentage of the missing data over the whole time series reaches 60%, the improvements of relative errors are up to 19.64, 41.34, 23.27 and 50.30% for the first four principal components, respectively. Besides, both the mean absolute errors and mean root mean squared errors of the reconstructed time series by ISSA are also much smaller than those by SSAM. The respective improvements are 34.45 and 33.91% when the missing data accounts for 60%. The results from real incomplete time series also show that the SD derived by ISSA is 12.27 mg L−1, smaller than 13.48 mg L−1 derived by SSAM.

Description: The characteristics of highly nonlinear solitary internal waves (solitons) are calculated within the fully nonlinear numerical model of the Massachusetts Institute of Technology. The verification and adaptation of the model is based on the data from laboratory experiments. The present paper also compares the results of our calculations with the calculations performed in the framework of the fully nonlinear Bergen Ocean Model. The comparison of the computed soliton parameters with the predictions of the weakly nonlinear theory based on the Gardner equation is given. The occurrence of reverse flow in the bottom layer directly behind the soliton is confirmed in the numerical simulations. The trajectories of Lagrangian particles in the internal soliton on the surface, on the pycnocline and near the bottom are computed.

Description: Dynamical systems like the one described by the three-variable Lorenz model may serve as metaphors for complexity in nature. When natural systems are perturbed by external forcing factors, they tend to relax back to their equilibrium conditions after the forcing has shut off. Here we investigate the behavior of such transients in the Lorenz model by studying its trajectories initialized far away from the asymptotic attractor. Perhaps somewhat surprisingly, these transient trajectories exhibit complex routes and, among other things, sensitivity to initial conditions akin to that of the asymptotic behavior on the attractor. Thus, similar extreme events may lead to widely different variations before the perturbed system returns back to its statistical equilibrium.

Description: We studied the evolutions of double layers which appear after the magnetic reconnection through two-dimensional electromagnetic particle-in-cell simulation. The simulation results show that the double layers are formed in the plasma sheet boundary layer after magnetic reconnection. At first, the double layers which have unipolar structures are formed. And then the double layers turn into bipolar structures, which will couple with another new weak bipolar structure. Thus a new double layer or tripolar structure comes into being. The double layers found in our work are about several ten Debye lengths, which accords with the observation results. It is suggested that the electron beam formed during the magnetic reconnection is responsible for the production of the double layers.

Description: In order to refine our understanding how fluid inclusions were trapped in the host minerals, we non-destructively observed mercury inclusions (liquid Hg0) in quartz samples using X-ray computed tomography (CT) technique. The X-ray CT apparatus can observe internal structures of the samples and give cross-sectional images from the transmission of the X-rays through the samples. From the cross-sectional images, we obtained three-dimensional spatial distributions of mercury inclusions, and quantitatively analyzed them using fractal and multifractal methods. Although the samples were from different mines, the resultant fractal dimensions were about 1.7 for the samples. The fractal dimensions were also close to those predicted by diffusion-limited aggregation models and percolation theory, which are controlled by the irreversible kinetics. Then, the mercury-bearing fluids were not primary fluid inclusions, but migrated into the pre-existing cracks of quartz crystals by diffusion processes.

Description: We propose an approach to stochastic parameterization of shallow cumulus clouds to represent the convective variability and its dependence on the model resolution. To collect the information about the individual cloud lifecycles and the cloud ensemble as a whole, we employ a Large-Eddy Simulation model (LES) and a cloud tracking algorithm, followed by conditional sampling of clouds at the cloud-base level. In the case of a shallow cumulus ensemble, the cloud-base mass flux distribution is bimodal due to the different shallow cloud subtypes. Each distribution mode can be approximated with a Weibull distribution, explaining the deviation from a single-parameter exponential shape through the diversity in cloud lifecycles. The exponential distribution of cloud mass flux previously suggested for deep convection parameterization is a special case of the Weibull distribution, which opens a way towards unification of the statistical convective ensemble formalism of shallow and deep cumulus clouds. Based on the empirical and theoretical findings, a stochastic model has been developed to simulate a shallow convective cloud ensemble. It is formulated as a compound random process, with the number of convective elements drawn from a Poisson distribution, and the cloud mass flux sampled from a mixed Weibull distribution. Convective memory is accounted for through the explicit cloud lifecycles, making the model formulation consistent with the choice of the Weibull cloud mass flux distribution function. The memory of individual shallow clouds is required to capture the correct convective variability. The resulting distribution of the subgrid convective states in the considered shallow cumulus case is scale-adaptive – the smaller the grid size, the broader the distribution.

Description: Geometric and topological methods are applied to significance testing in the wavelet domain. A geometric test was developed for assigning significance to pointwise significance patches in local wavelet spectra, contiguous regions of significant wavelet coefficients with respect to some noise model. This geometric significance test was found to produce results similar to an existing areawise significance test, while being more computationally flexible and efficient. The geometric significance test can be readily applied to pointwise significance patches at various pointwise significance levels in wavelet power and coherence spectra. A topological analysis of pointwise significance patches determined that holes, deficits in pointwise significance embedded in significance patches, are capable of identifying important structures, some of which are undetected by the geometric and areawise tests. The application of the new and existing significance tests to ideal time series and to the time series of the Niño 3.4 and North Atlantic Oscillation showed that the areawise and geometric tests perform similarly in ideal and geophysical settings, while the topological methods showed that the Niño 3.4 time series contains numerous phase-coherent oscillations.

Description: The equations that govern geophysical fluids (namely atmosphere, ocean and rivers) are well known but their use for prediction requires the knowledge of the initial condition. In many practical cases, this initial condition is poorly known and the use of an imprecise initial guess is not sufficient to perform accurate forecasts because of the high sensitivity of these systems to small perturbations. As every situation is unique, the only additional information than can help to retrieve the initial condition are observations and statistics. The set of methods that combine these sources of heterogeneous information to construct such an initial condition are referred to as data assimilation. More and more images and sequences of images, of increasing resolution, are produced for scientific or technical studies. This is particularly true in the case of geophysical fluids that are permanently observed by remote sensors. However, the structured information contained in images or image sequences is not assimilated as regular observations: images are still (under)utilized to produce qualitative analysis by experts. This paper deals with the quantitative assimilation of information provided in an image form into a numerical model of a dynamical system. We describe several possibilities for such assimilation and identify associated difficulties. Results from our ongoing research are used to illustrate the methods. The assimilation of image is a very general framework that can be transposed in several scientific domains.

Description: We employ 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 corresponds 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 among well logs with the differences among DFA-exponents of geophysical quantities using spatial correlation function and Mantel test. Our data analysis suggests that sonic profile is a good candidate to represent 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 correlation among DFA-exponents of geophysical quantities.

Description: 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. 25 year-long 10 s resolution datasets are analysed, but for fluctuations with timescales less than 1 day. Quantile-quantile (Q-Q) plots are employed first, revealing 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 reveals that timescales between 1 h and 1 d 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. This is consistent with changes in the position of the auroral electrojet that can be considered rapid during the course of an evening, whereas from minute-to-minute the electrojet moves more persistently in geomagnetic latitude.

Description: 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, models of sediment transport as sophisticated as the present coupled model 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: The impact of the temperature distribution on the Hadley circulation simulated by an axisymmetric model is studied. The temperature distributions that drive the model are modulated here by two parameters, n and k, the former controlling the horizontal broadness and the latter defining change in the vertical lapse rate. In the present study, the changes of the temperature distribution mimic changes of the energy input of the atmospheric system leaving as an invariant the equator-poles difference. Both equinoctial and time-dependent Hadley circulations are simulated and results compared. The results give evidence that concentrated temperature distributions enhance the meridional circulation and jet wind speed intensities even with a lower energy input. The meridional circulation and the subtropical jet stream widths are controlled by the broadness of horizontal temperature rather than the vertical lapse rate k, which is important only when the temperature distribution is concentrated at the equator. The jet stream position does not show any dependence with n and k, except when the temperature distribution is very wide and in such a case the jet is located at the mid-latitude. Using n = 2 and k = 1 we have the formulation of the potential temperature adopted in classical literature. A comparison with other works is performed and our results show that the model running in different configurations (equinoctial, solstitial and time-dependent) yields results similar to one another.

Description: Non-Gaussian multivariate probability distributions, derived from climate and geofluid statistics, allow for nonlinear correlations between linearly uncorrelated components, due to joint Shannon negentropies. Triadic statistical dependence under pair-wise (total or partial) independence is thus possible. Synergy or interaction information among triads is estimated. We formulate an optimization method of triads in the space of orthogonal rotations of normalized principal components, relying on the maximization of third-order cross cumulants. Its application to a minimal one-dimensional, periodic, advective model, leads to enhanced triads that occur between oscillating components of circular or locally confined wave-trains satisfying the triadic wave resonance condition.

Description: Data assimilation transfers information from observations of a complex system to physically-based system models with state variables x(t). Typically, the observations are noisy, the model has errors, and the initial state of the model is uncertain, so the data assimilation is statistical. One can thus ask questions about expected values of functions ⟨G(X)⟩ on the path X = {x(t0), ..., x(tm)} of the model as it moves through an observation window where measurements are made at times {t0, ..., tm}. The probability distribution on the path P(X) = exp[−A0(X)] determines these expected values. Variational methods seeking extrema of the "action" A0(X), widely known as 4DVar (Talagrand and Courtier, 1987; Evensen, 2009),, are widespread for estimating ⟨G(X) ⟩ in many fields of science. In a path integral formulation of statistical data assimilation, we consider variational approximations in a standard realization of the action where measurement and model errors are Gaussian. We (a) discuss an annealing method for locating the path X0 giving a consistent global minimum of the action A0(X0), (b) consider the explicit role of the number of measurements at each measurement time in determining A0(X0), and (c) identify a parameter regime for the scale of model errors which allows X0 to give a precise estimate of ⟨G(X0)⟩ with computable, small higher order corrections.

Description: We derive rigorous results on the link between the principle of maximum entropy production and the principle of maximum Kolmogorov–Sinai entropy using a Markov model of the passive scalar diffusion called the Zero Range Process. We show analytically that both the entropy production and the Kolmogorov–Sinai entropy seen as functions of f admit a unique maximum denoted fmaxEP and fmaxKS. The behavior of these two maxima is explored as a function of the system disequilibrium and the system resolution N. The main result of this article is that fmaxEP and fmaxKS have the same Taylor expansion at first order in the deviation of equilibrium. We find that fmaxEP hardly depends on N whereas fmaxKS depends strongly on N. In particular, for a fixed difference of potential between the reservoirs, fmaxEP(N) tends towards a non-zero value, while fmaxKS(N) tends to 0 when N goes to infinity. For values of N typical of that adopted by Paltridge and climatologists (N ≈ 10 ~ 100), we show that fmaxEP and fmaxKS coincide even far from equilibrium. Finally, we show that one can find an optimal resolution N* such that fmaxEP and fmaxKS coincide, at least up to a second order parameter proportional to the non-equilibrium fluxes imposed to the boundaries. We find that the optimal resolution N* depends on the non equilibrium fluxes, so that deeper convection should be represented on finer grids. This result points to the inadequacy of using a single grid for representing convection in climate and weather models. Moreover, the application of this principle to passive scalar transport parametrization is therefore expected to provide both the value of the optimal flux, and of the optimal number of degrees of freedom (resolution) to describe the system.

Description: This work is devoted to investigation of nonlinear dynamics of planetary electromagnetic (EM) ultra-low-frequency wave (ULFW) structures in the rotating dissipative ionosphere in the presence of inhomogeneous zonal wind (shear flow). Planetary EM ULFW appears as a result of interaction of the ionospheric medium with the spatially inhomogeneous geomagnetic field. The shear flow driven wave perturbations effectively extract energy of the shear flow increasing own amplitude and energy. These perturbations undergo self organization in the form of the nonlinear solitary vortex structures due to nonlinear twisting of the perturbation's front. Depending on the features of the velocity profiles of the shear flows the nonlinear vortex structures can be either monopole vortices, or dipole vortex, or vortex streets and vortex chains. From analytical calculation and plots we note that the formation of stationary nonlinear vortex structure requires some threshold value of translation velocity for both non-dissipation and dissipation complex ionospheric plasma. The space and time attenuation specification of the vortices is studied. The characteristic time of vortex longevity in dissipative ionosphere is estimated. The long-lived vortices transfer the trapped medium particles, energy and heat. Thus they represent structural elements of turbulence in the ionosphere.

Description: An analytical theory is presented to predict Horton laws for five Hydraulic-Geometric (H-G) variables (stream discharge Q, width W, depth D, velocity U, slope S, and friction n'). The theory builds on the concept of dimensional analysis, and identifies six independent dimensionless River-Basin numbers. We consider self-similar Tokunaga networks and derive a mass conservation equation in the limit of large network order in terms of Horton bifurcation and discharge ratios. It is applied to obtain self-similar solutions of type-1 (SS-1), and predict Horton laws for width, depth and velocity as asymptotic relationships. Exponents of width and the Reynold's number are predicted. Assuming that SS-1 is valid for slope, depth and velocity, corresponding Horton laws and the H-G exponents are derived. The exponent values agree with that for the Optimal Channel Network (OCN) model, but do not agree with values from three field experiments. The deviations are substantial, suggesting that H-G in network does not obey optimality or 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 in self-similar solutions of Type-2 (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's friction. The Manning's friction exponent, y, is predicted and tested against observed exponents from three field studies. 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: Numerical climate models constitute the best available tools to tackle the problem of climate prediction. Two assumptions lie at the heart of their suitability: (1) a climate attractor exists, and (2) the numerical climate model's attractor lies on the actual climate attractor, or at least on the projection of the climate attractor on the model's phase space. In this contribution, the Lorenz '63 system is used both as a prototype system and as an imperfect model to investigate the implications of the second assumption. By comparing results drawn from the Lorenz '63 system and from numerical weather and climate models, the implications of using imperfect models for the prediction of weather and climate are discussed. It is shown that the imperfect model's orbit and the system's orbit are essentially different, purely due to model error and not to sensitivity to initial conditions. Furthermore, if a model is a perfect model, then the attractor, reconstructed by sampling a collection of initialised model orbits (forecast orbits), will be invariant to forecast lead time. This conclusion provides an alternative method for the assessment of climate models.