ALBERT

Description: Spectral diagonal ensemble Kalman filters Nonlinear Processes in Geophysics, 22, 485-497, 2015 Author(s): I. Kasanický, J. Mandel, and M. Vejmelka A new type of ensemble Kalman filter is developed, which is based on replacing the sample covariance in the analysis step by its diagonal in a spectral basis. It is proved that this technique improves the approximation of the covariance when the covariance itself is diagonal in the spectral basis, as is the case, e.g., for a second-order stationary random field and the Fourier basis. The method is extended by wavelets to the case when the state variables are random fields which are not spatially homogeneous. Efficient implementations by the fast Fourier transform (FFT) and discrete wavelet transform (DWT) are presented for several types of observations, including high-dimensional data given on a part of the domain, such as radar and satellite images. Computational experiments confirm that the method performs well on the Lorenz 96 problem and the shallow water equations with very small ensembles and over multiple analysis cycles.

Description: Search for the 531-day-period wobble signal in the polar motion based on EEMD Nonlinear Processes in Geophysics, 22, 473-484, 2015 Author(s): H. Ding and W. Shen In this study, we use a nonlinear and non-stationary time series analysis method, the ensemble empirical mode decomposition method (EEMD), to analyze the polar motion (PM) time series (EOP C04 series from 1962 to 2013) to find a 531-day-period wobble (531 dW) signal. The 531 dW signal has been found in the early PM series (1962–1977), but cannot be found in the recent PM series (1978–2013) using conventional analysis approaches. By virtue of the demodulation feature of EEMD, the 531 dW can be confirmed to be present in PM based on the differences of the amplitudes and phases between different intrinsic mode functions. Results from three sub-series divided from the EOP C04 series show that the period of the 531 dW is subject to variations, in the range of 530.9–524 days, and its amplitude is also time-dependent (about 2–11 mas). Synthetic tests are carried out to explain why the 531 dW can only be observed in recent 30-year PM time series after using EEMD. The 531 dW is also detected in the two longest available superconducting gravimeter (SG) records, which further confirms the presence of the 531 dW. The confirmation of the 531 dW existence could be significant in establishing a more reasonable Earth rotation model and may effectively contribute to the prediction of the PM and its mechanism interpretation.

Description: Dynamics of turbulence under the effect of stratification and internal waves Nonlinear Processes in Geophysics, 22, 337-348, 2015 Author(s): O. A. Druzhinin and L. A. Ostrovsky The objective of this paper is to study the dynamics of small-scale turbulence near a pycnocline, both in the free regime and under the action of an internal gravity wave (IW) propagating along a pycnocline, using direct numerical simulation (DNS). Turbulence is initially induced in a horizontal layer at some distance above the pycnocline. The velocity and density fields of IWs propagating in the pycnocline are also prescribed as an initial condition. The IW wavelength is considered to be larger by the order of magnitude as compared to the initial turbulence integral length scale. Stratification in the pycnocline is considered to be sufficiently strong so that the effects of turbulent mixing remain negligible. The dynamics of turbulence is studied both with and without an initially induced IW. The DNS results show that, in the absence of an IW, turbulence decays, but its decay rate is reduced in the vicinity of the pycnocline, where stratification effects are significant. In this case, at sufficiently late times, most of the turbulent energy is located in a layer close to the pycnocline center. Here, turbulent eddies are collapsed in the vertical direction and acquire the "pancake" shape. IW modifies turbulence dynamics, in that the turbulence kinetic energy (TKE) is significantly enhanced as compared to the TKE in the absence of IW. As in the case without IW, most of the turbulent energy is localized in the vicinity of the pycnocline center. Here, the TKE spectrum is considerably enhanced in the entire wave-number range as compared to the TKE spectrum in the absence of IW.

Description: The transient variation in the complexes of the low-latitude ionosphere within the equatorial ionization anomaly region of Nigeria Nonlinear Processes in Geophysics, 22, 527-543, 2015 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 five GPS receiver stations in Nigeria, which lies within the equatorial ionization anomaly region. The non-linear aspects of the TEC time series were obtained by detrending the data. The detrended TEC time series were subjected to various analyses to obtain the phase space reconstruction and to compute the chaotic quantifiers, which are Lyapunov exponents LE, correlation dimension, and Tsallis entropy, for the study of dynamical complexity. 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 exponents for the entire year show a wavelike semiannual variation pattern with lower values around March, April, September and October. 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 a similar variation pattern to that of the Lyapunov exponent, with both quantifiers correlating within the range of 0.79 to 0.82. These results show that both quantifiers can be further 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 in 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 the Lyapunov exponent and Tsallis entropy during storms. The dynamical behaviour of the ionosphere throughout the year, as described by these quantifiers, was discussed in this work.

Description: A dynamical systems approach to the surface search for debris associated with the disappearance of flight MH370 Nonlinear Processes in Geophysics, 22, 701-712, 2015 Author(s): V. J. García-Garrido, A. M. Mancho, S. Wiggins, and C. Mendoza The disappearance of Malaysia Airlines flight MH370 on the morning of 8 March 2014 is one of the great mysteries of our time. Perhaps the most relevant aspect of this mystery is that not a single piece of debris from the aircraft was found during the intensive surface search carried out for roughly 2 months following the crash. Difficulties in the search efforts, due to the uncertainty of the plane's final impact point and the time that had passed since the accident, bring the question on how the debris scattered in an always moving ocean, for which there are multiple data sets that do not uniquely determine its state. Our approach to this problem is based on the use of Lagrangian descriptors (LD), a novel mathematical tool coming from dynamical systems theory that identifies dynamic barriers and coherent structures governing transport. By combining publicly available information supplied by different ocean data sources with these mathematical techniques, we are able to assess the spatio-temporal state of the ocean in the priority search area at the time of impact and the following weeks. Using this information we propose a revised search strategy by showing why one might not have expected to find debris in some large search areas targeted by the Australian Maritime Safety Authority (AMSA), and determining regions where one might have expected impact debris to be located, which were not subjected to any exploration.

Description: Evaluation of a spectral line width for the Phillips spectrum by means of numerical simulation Nonlinear Processes in Geophysics, 22, 325-335, 2015 Author(s): A. O. Korotkevich and V. E. Zakharov The work aims to check one of the assumptions under which the kinetic equation for water waves was derived in order to understand whether it can be applied to the situations described by the Phillips spectrum. We evaluate a spectral line width of the spectrum from the simulations in the framework of primordial dynamical equations at different levels of nonlinearity in the system, corresponding to the weakly turbulent Kolmogorov–Zakharov spectra ω −4 , Phillips spectra ω −5 , and intermediate cases. The original motivation of the work was to check one of the assumptions under which the kinetic equation for water waves was derived in order to understand whether it can be applied to the Phillips spectrum. It is shown that, even in the case of relatively high average steepness, when the Phillips spectrum is present in the system, the spectral lines are still very narrow, at least in the region of the direct cascade spectrum. It allows us to state that, even in the case of the Phillips spectrum, one of the assumptions used for the derivation of the Hasselmann kinetic equation is still valid, at least in the case of moderate whitecapping.

Description: Comparison of box counting and correlation dimension methods in well logging data analysis associate with the texture of volcanic rocks D. Mou and Z. W. Wang Nonlin. Processes Geophys. Discuss., doi:10.5194/npg-2014-85,2016 Manuscript under review for NPG (discussion: open, 0 comments) We have developed a fractal analysis method to estimate the dimension of well logging curves in Liaohe oil field, China. The box counting and correlation dimension are methods that can be applied to predict the texture of volcanic rocks with calculation the fractal dimension of well logging curves. The well logging curves are composed of gamma ray (GR), compensated neutron logs (CNL), acoustic (AC), density (DEN), Resistivity lateral log deep ( R LLD ), every curve contains a total of 6000 logging data. The dimension of well logging curves are calculated using box counting and correlation algorithms respectively. It is shown that two types of dimension of CNL, DEN and AC have the same average value. The box counting dimension of volcanic lava is lower than the pyroclastic rock obviously. The majority of correlation dimension of volcanic lava is lower than the pyroclastic rock, but a small amount of correlation dimension of volcanic lava is equal to the pyroclastic rock. It is demonstrated that the box counting dimension is more suitable for predicting the texture of volcanic rocks. Applications to logging data, A well show the relationship between the fractal dimension and the texture of volcanic rock in certain depth.

Description: Multifractal behaviour of the soil water content of a vineyard in northwest Spain during two growing seasons José Manuel Mirás-Avalos, Emiliano Trigo-Córdoba, Rosane da Silva-Dias, Irene Varela-Vila, and Aitor García-Tomillo Nonlin. Processes Geophys., 23, 205-213, doi:10.5194/npg-23-205-2016, 2016 The current study aimed to describe the dynamics of soil water content at three depths in a vineyard under rain-fed and irrigation conditions and to assess the multifractality of these time data series. Soil water content data series obeyed power laws and tended to behave as multifractals. Our results suggest that singularity spectra were useful for characterising temporal variability of soil water content, distinguishing patterns among series registered under rain-fed and irrigation treatments.

Description: Spectral characteristics of high-latitude raw 40 MHz cosmic noise signals Chris M. Hall Nonlin. Processes Geophys., 23, 215-222, doi:10.5194/npg-23-215-2016, 2016 The relative ionospheric opacity meter ("riometer") is a traditional instrument for measuring the degree to which cosmic noise is absorbed by the ionosphere and therefore how energetic the particles – electrons, protons etc. – are that cause the ionisation. We identify the same signatures in the "hour-to-days" timescale variability as reported in solar and geomagnetic disturbances. The result demonstrates the relationship between riometer data and the underlying physics for different timescales.

Description: Recent seismic activity at Cephalonia (Greece): a study through candidate electromagnetic precursors in terms of non-linear dynamics Stelios M. Potirakis, Yiannis Contoyiannis, Nikolaos S. Melis, John Kopanas, George Antonopoulos, Georgios Balasis, Charalampos Kontoes, Constantinos Nomicos, and Konstantinos Eftaxias Nonlin. Processes Geophys., 23, 223-240, doi:10.5194/npg-23-223-2016, 2016 Based on the methods of critical fluctuations and natural time, we have shown that the fracture-induced MHz electromagnetic emissions recorded by two stations in our network prior to two recent significant earthquakes that occurred in Cephalonia present criticality characteristics, implying that they emerge from a system in critical state.

Description: Spatial and radiometric characterization of multi-spectrum satellite images through multifractal analysis Carmelo Alonso, Ana M. Tarquis, Ignacio Zuñiga, and Rosa M. Benito Nonlin. Processes Geophys. Discuss., doi:10.5194/npg-2016-33,2016 Manuscript under review for NPG (discussion: open, 0 comments) Vegetation indexes, estimated from satellites images, can been used to estimate root zone soil moisture. However, depending on the spatial and radiometric resolution of the sensors used estimations could change. In this work, images taken by satellites IKONOS-2 and LANDSAT-7 of the same location are compared on the four bands involved in these vegetation indexes. The results showed that spatial resolution has a similar scaling effect in the four bands, but not radiometric resolution.

Description: Scale and space dependencies of soil Nitrogen variability Ana M. Tarquis, María Teresa Castellanos, Maria Carmen Cartagena, Augusto Arce, Francisco Ribas, María José Cabello, Juan López de Herrera, and Nigel R. A. Bird Nonlin. Processes Geophys. Discuss., doi:10.5194/npg-2016-32,2016 Manuscript under review for NPG (discussion: open, 0 comments) Melon crop got different level of N that constituted a contribution to the variation of soil N at mainly larger scales. During its development a proportion of the N was taken up adding a second factor of variability at smaller scales. After the melons harvest, the wheat was sown across the plots and harvested at the end of the season. Wheat was used as a N sink crop and allowed us to evaluate the soil N residual. Multiscale and relative entropy were applied to study N scale dependencies.

Description: Parametrization of stochastic multiscale triads Jeroen Wouters, Stamen I. Dolaptchiev, Valerio Lucarini, and Ulrich Achatz Nonlin. Processes Geophys. Discuss., doi:10.5194/npg-2016-37,2016 Manuscript under review for NPG (discussion: open, 0 comments) We discuss applications of a recently developed method for model reduction based on linear response theory of weakly coupled dynamical systems. We apply the weak coupling method to simple stochastic differential equations with slow and fast degrees of freedom. The weak coupling model reduction method results in general in a non-Markovian system, we therefore discuss the Markovianization of the system to allow for straightforward numerical integration. We compare the applied method to the equations obtained through homogenization in the limit of large time scale separation between slow and fast degrees of freedom. We numerically compare the ensemble spread from a fixed initial condition, correlation functions and exit times from a domain. The weak coupling method gives more accurate results in all test cases, albeit with a higher numerical cost.

Description: An improved global zenith tropospheric delay model GZTD2 considering diurnal variations Yibin Yao, Yufeng Hu, Chen Yu, Bao Zhang, and Jianjian Guo Nonlin. Processes Geophys., 23, 127-136, doi:10.5194/npg-23-127-2016, 2016 By considering the diurnal variations in zenith tropospheric delay (ZTD) and modifying the model expansion function, we developed an improved global empirical ZTD model GZTD2 with higher temporal and spatial resolutions compared to our previous GZTD model. The external validation testing with IGS ZTD data shows the bias and rms for GZTD2 are −0.3 and 3.9 cm respectively, indicating higher accuracy and reliability for geodesy technology compared to GZTD and other commonly used ZTD models.

Description: Hierarchical scale dependence associated with the extension of the nonlinear feedback loop in a seven-dimensional Lorenz model Bo-Wen Shen Nonlin. Processes Geophys., 23, 189-203, doi:10.5194/npg-23-189-2016, 2016 We construct a seven-dimensional Lorenz model (7DLM) to discuss the impact of an extended nonlinear feedback loop on solutions' stability and illustrate the hierarchical scale dependence of chaotic solutions. The 7DLM requires a much larger critical value for the Rayleigh parameter ( r c  ∼ 116.9) for the onset of chaos. For chaotic solutions with r  = 120, high correlation coefficients among the modes at different scales indicate hierarchical scale dependence.

Description: Multi-scale statistical analysis of coronal solar activity Diana Gamborino, Diego del-Castillo-Negrete, and Julio J. Martinell Nonlin. Processes Geophys., 23, 175-188, doi:10.5194/npg-23-175-2016, 2016 We use temperature maps of the solar corona for three regions and use a technique that separates multiple timescales and space scales to show that the small-scale temperature fluctuations appear more frequently prior to the occurrence of a solar flare, in comparison with the same region after the flare and with a quiet region. We find that, during the flare, energy flows from large to small scales and heat transport associated with a heat front is convective along and diffusive across the front.

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

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

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

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

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

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

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

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

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

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

Description: Two-dimensional numerical simulations of shoaling internal solitary waves at the ASIAEX site in the South China Sea Nonlinear Processes in Geophysics, 22, 289-312, 2015 Author(s): K. G. Lamb and A. Warn-Varnas The interaction of barotropic tides with Luzon Strait topography generates some of the world's largest internal solitary waves which eventually shoal and dissipate on the western side of the northern South China Sea. Two-dimensional numerical simulations of the shoaling of a single internal solitary wave 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. The bulk of the simulations are inviscid; however, exploratory simulations using a vertical eddy-viscosity confined to a near bottom layer, along with a no-slip boundary condition, suggest that viscous effects may become important in water shallower than about 200 m. A shoaling solitary wave fissions into several waves. At depths of 200–300 m the front of the leading waves become nearly parallel to the bottom and develop a very steep back as has been observed. The leading waves are followed by waves of elevation (pedestals) that are conjugate to the waves of depression ahead and behind them. Horizontal resolutions of at least 50 m are required to simulate these well. Wave breaking was found to occur behind the second or third of the leading solitary waves, never at the back of the leading wave. Comparisons of the shoaling of waves started at depths of 1000 and 3000 m show significant differences and the shoaling waves can be significantly non-adiabatic even at depths greater than 2000 m. When waves reach a depth of 200 m, their amplitudes can be more than 50% larger than the largest possible solitary wave at that depth. The shoaling behaviour is sensitive to the presence of small-scale features in the bathymetry: a 200 m high bump at 700 m depth can result in the generation of many mode-two waves and of higher mode waves. Sensitivity to the stratification is considered by using three stratifications based on summer observations. They primarily differ in the depth of the thermocline. The generation of mode-two waves and the behaviour of the waves in shallow water is sensitive to this depth. Rotation affects the shoaling waves by reducing the amplitude of the leading waves via the radiation of long trailing inertia-gravity waves. The nonlinear-dispersive evolution of these inertia-gravity waves results in the formation of secondary mode-one wave packets.

Description: A novel method for analyzing the process of abrupt climate change Nonlinear Processes in Geophysics, 22, 249-258, 2015 Author(s): P. C. Yan, G. L. Feng, and W. Hou A climate system which is transitioning from one state to another is known as an abrupt climate change. Most of the recent studies regarding abrupt climate change have focused on the changes occurring before and after the abrupt change point, while little attention has been given to the "transition process" which occurs when the system breaks away from the original state to a new state. In this study, a novel method for analyzing the process of abrupt climate change was presented. By using the mathematical model based on the logistic model, the process of the abrupt change could be analyzed and divided into different phases which include start moment, end moment, stable state, and unstable transition state. Meanwhile, the method was confirmed to be effective by testing in a study of Pacific decadal oscillation (PDO) time sequence, and the results of this study specify that this abrupt change process (ACP) of PDO has a relationship with global warming.

Description: Incidence and reflection of internal waves and wave-induced currents at a jump in buoyancy frequency Nonlinear Processes in Geophysics, 22, 259-274, 2015 Author(s): J. P. McHugh 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 buoyancy frequency approximately modeling 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 that can contaminate the wave envelope and has a vertical wavelength that decreases as the wave packet interacts with the interface.

Description: Oscillations in a simple climate–vegetation model Nonlinear Processes in Geophysics, 22, 275-288, 2015 Author(s): J. Rombouts and M. Ghil We formulate and analyze a simple dynamical systems model for climate–vegetation interaction. The planet we consider consists of a large ocean and a land surface on which vegetation can grow. The temperature affects vegetation growth on land and the amount of sea ice on the ocean. Conversely, vegetation and sea ice change the albedo of the planet, which in turn changes its energy balance and hence the temperature evolution. Our highly idealized, conceptual model is governed by two nonlinear, coupled ordinary differential equations, one for global temperature, the other for vegetation cover. The model exhibits either bistability between a vegetated and a desert state or oscillatory behavior. The oscillations arise through a Hopf bifurcation off the vegetated state, when the death rate of vegetation is low enough. These oscillations are anharmonic and exhibit a sawtooth shape that is characteristic of relaxation oscillations, as well as suggestive of the sharp deglaciations of the Quaternary. Our model's behavior can be compared, on the one hand, with the bistability of even simpler, Daisyworld-style climate–vegetation models. On the other hand, it can be integrated into the hierarchy of models trying to simulate and explain oscillatory behavior in the climate system. Rigorous mathematical results are obtained that link the nature of the feedbacks with the nature and the stability of the solutions. The relevance of model results to climate variability on various timescales is discussed.

Description: Estimation of the total magnetization direction of approximately spherical bodies Nonlinear Processes in Geophysics, 22, 215-232, 2015 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 shapes and known centres. Our method is an overdetermined inverse problem that can be applied to interpret multiple sources with different but homogeneous magnetization directions. It requires neither 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 geologically meaningful magnetization directions. The results obtained for a region of the GAP, near to 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 to the alkaline complex of Diorama have almost the same magnetization direction of those ones in the alkaline complex of Montes Claros de Goiás, strongly suggesting that these sources have been emplaced in the crust within almost the same geological time interval.

Description: Statistical optimization for passive scalar transport: maximum entropy production versus maximum Kolmogorov–Sinai entropy Nonlinear Processes in Geophysics, 22, 187-196, 2015 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 for 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 a parameter f connected to the jump probability, admit a unique maximum denoted f max EP and f max KS . The behaviour of these two maxima is explored as a function of the system disequilibrium and the system resolution N . The main result of this paper is that f max EP and f max KS have the same Taylor expansion at first order in the deviation from 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 those adopted by Paltridge and climatologists working on maximum entropy production ( 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: Intermittent heat instabilities in an air plume Jean-Louis Le Mouël, Vladimir G. Kossobokov, Frederic Perrier, and Pierre Morat Nonlin. Processes Geophys. Discuss., doi:10.5194/npg-2016-23,2016 Manuscript under review for NPG (discussion: open, 0 comments) The heating experiments carried in a limestone quarry close to Paris have shown a classical shape of temperature distribution in steady state plumes in averages over 24 hours, along with a rich dynamics of heat flow with intermittent trains of oscillations, spatially coherent, of large amplitudes and ~ 400 s period, separated by relative quiescence whose duration can reach several hours. The observed behavior could be a universal feature of some turbulent plumes in real geophysical environments.

Description: Brief communication: Possible explanation of the values of Hack's drainage basin, river length scaling exponent Allen G. Hunt Nonlin. Processes Geophys., 23, 91-93, doi:10.5194/npg-23-91-2016, 2016 Percolation theory can be used to find flow paths of least resistance. Applying percolation theory to drainage networks apparently allows identification of the range of exponent values describing the tortuosity of rivers in real networks, thus generating observed scaling between drainage basin area and channel length, a relationship known as Hack's law. Such a theoretical basis for Hack's law may allow interpretation of the range of exponent values based on assessment of substrate heterogeneity.

Description: Constraining ecosystem model with Adaptive Metropolis algorithm using boreal forest site eddy covariance measurements Jarmo Mäkelä, Jouni Susiluoto, Tiina Markkanen, Mika Aurela, Ivan Mammarella, Stefan Hagemann, and Tuula Aalto Nonlin. Processes Geophys. Discuss., doi:10.5194/npg-2016-21,2016 Manuscript under review for NPG (discussion: open, 0 comments) The land based hydrological cycle is one of the key processes controlling the growth and wilting of plants and the amount of carbon vegetation can assimilate. Recent studies have shown that many land surface models have biases in this area. We optimized parameters in one such model (JSBACH) and were able to enhance the model performance in many respects, but the response to drought remained unaffected. Further studies into this aspect should include alternative stomatal conductance formulations.

Description: Estimating the State of a Geophysical System with Sparse Observations: Time Delay Methods to Achieve Accurate Initial States for Prediction Zhe An, Daniel Rey, Jing Xin Ye, and Henry D. I. Abarbanel Nonlin. Processes Geophys. Discuss., doi:10.5194/npg-2016-22,2016 Manuscript under review for NPG (discussion: open, 0 comments) The data assimilation process, in which observational data is used to estimate the states and parameters of a dynamical model, becomes seriously impeded when the model expresses chaotic behavior and the number of measurements is below a critical threshold, L s . Since this problem of insufficient measurements is typical across many fields, including numerical weather prediction, we analyze a method introduced in Rey et al. (2014a, b) to remedy this matter, in the context of the nonlinear shallow water equations on a β -plane. This approach generalizes standard nudging methods by utilizing time delayed measurements to augment the transfer of information from the data to the model. We will show it provides a sizable reduction in the number of observations required to construct accurate estimates and high-quality predictions. For instance, in Whartenby et al. (2013) we found that to achieve this goal, standard nudging requires observing approximately 70 % of the full set of state variables. Using time delays, this number can be reduced to about 33 %, and even further if Lagrangian drifter information is also incorporated.

Description: Multi-scale analysis of the Asian Monsoon change in the last millennium TingGui Jiang, JiaJia Lin, ZhenShan Lin, and YuXia Li Nonlin. Processes Geophys. Discuss., doi:10.5194/npg-2015-75,2016 Manuscript under review for NPG (discussion: open, 0 comments) This paper is mainly about the change rule and the driving mechanism of the Asian monsoon in the last millennial. We obtain the main cycles of the Asian monsoon changes, drought and wet periods in the history, and can predict the precipitation trend at the local site in the future. It also shows that solar activity and average Northern Hemisphere Temperature can influence the intensity of the Asian monsoon in the different degree in the last 1000 years.

Description: 〈b〉Statistical Hypothesis Testing in Wavelet Analysis: Theoretical Developments and Applications to India Rainfall〈/b〉〈br〉 Justin A. Schulte〈br〉 Nonlin. Processes Geophys. Discuss., https//doi.org/10.5194/npg-2018-55,2018〈br〉 〈b〉Manuscript under review for NPG〈/b〉 (discussion: open, 1 comment)〈br〉 Statistical hypothesis tests in wavelet analysis are used to asses the likelihood that time series features are noise. The choice of test will determine what features emerge as a signal. Tests based on area do poorly at distinguishing abrupt fluctuations from periodic behavior unlike tests based on arc length that do better. The application of the tests suggests that there are features in India rainfall time series that emerge from background noise.

Description: 〈b〉Can the Nucleation Phase be Generated on a Sub-fault Linked to the Main Fault of an Earthquake?〈/b〉〈br〉 Jeen-Hwa Wang〈br〉 Nonlin. Processes Geophys. Discuss., https//doi.org/10.5194/npg-2018-49,2018〈br〉 〈b〉Manuscript under review for NPG〈/b〉 (discussion: open, 0 comments)〈br〉 〈p〉We study the effects of seismic coupling, friction, viscous, and inertia on earthquake nucleation based on a two-body spring-slider model in the presence of thermal-pressurized slip-dependent friction and viscosity. The stiffness ratio of the system to represent seismic coupling is the ratio of coil spring 〈i〉K〈/i〉 between two sliders and the leaf spring 〈i〉L〈/i〉 between a slider and the background plate and denoted by 〈i〉s〈/i〉 = 〈i〉K/L〈/i〉. The 〈i〉s〈/i〉 is not a significant factor in generating the nucleation phase. The masses of the two sliders are 〈i〉m〈/i〉〈sub〉1〈/sub〉 and 〈i〉m〈/i〉〈sub〉2〈/sub〉, respectively. The frictional and viscous effects are specified by the static friction force, 〈i〉f〈/i〉〈sub〉o〈/sub〉, the characteristic displacement, 〈i〉U〈/i〉〈sub〉c〈/sub〉, and viscosity coefficient, 〈i〉h〈/i〉, respectively. Numerical simulations show that friction and viscosity can both lengthen the natural period of the system and viscosity increases the duration time of motion of the slider. Higher viscosity causes lower particle velocities than lower viscosity. The ratios γ = 〈i〉h〈/i〉〈sub〉2〈/sub〉/〈i〉h〈/i〉〈sub〉1〈/sub〉, φ = 〈i〉f〈/i〉〈sub〉o2〈/sub〉/〈i〉f〈/i〉〈sub〉o1〈/sub〉, ψ = 〈i〉U〈/i〉〈sub〉c2〈/sub〉/〈i〉U〈/i〉〈sub〉cl〈/sub〉, and μ = 〈i〉m〈/i〉〈sub〉2〈/sub〉/〈i〉m〈/i〉〈sub〉1〈/sub〉 are four important factors in influencing the generation of a nucleation phase. When 〈i〉s〈/i〉 〉 0.17, γ 〉 1, 1.15 〉 φ 〉 1, ψ P wave on slider 2. The results are consistent with the observations and suggest the possibility of generation of nucleation phase on a sub-fault.〈/p〉

Description: 〈b〉Characterization of the South Atlantic Anomaly〈/b〉〈br〉 Khairul Afifi Nasuddin, Mardina Abdullah, and Nurul Shazana Abdul Hamid〈br〉 Nonlin. Processes Geophys. Discuss., https//doi.org/10.5194/npg-2018-51,2018〈br〉 〈b〉Manuscript under review for NPG〈/b〉 (discussion: final response, 4 comments)〈br〉 This research intends to characterize the South Atlantic Anomaly (SAA) by applying power spectrum analysis approach. The outcomes of the research revealed that the SAA region had a tendency to be persistent during active period and normal periods. It can be said, it experiences this characteristic because of the Earth’s magnetic field strength. It is very important for spacecraft when entering the SAA take safety precaution in order to minimize the damage.

Description: 〈b〉Estimating vertically averaged energy dissipation rate〈/b〉〈br〉 Nozomi Sugiura, Shinya Kouketsu, Shuhei Masuda, Satoshi Osafune, and Ichiro Yasuda〈br〉 Nonlin. Processes Geophys. Discuss., https//doi.org/10.5194/npg-2018-48,2018〈br〉 〈b〉Manuscript under review for NPG〈/b〉 (discussion: final response, 2 comments)〈br〉 The observed profiles of the turbulent energy dissipation rate look so erratic that we can hardly identify them as continuous curves. However, we found that each sequence has the striking feature of self-similarity. Using this, we can efficiently take ensemble statistics of the vertically averaged energy dissipation rate from a single observation profile, by scaling up and promoting the observed value at each depth to one that corresponds to the whole profile.

Description: 〈b〉On the localization in strongly coupled ensemble data assimilation using a two-scale Lorenz model〈/b〉〈br〉 Zheqi Shen, Youmin Tang, Xiaojing Li, Yanqiu Gao, and Junde Li〈br〉 Nonlin. Processes Geophys. Discuss., https//doi.org/10.5194/npg-2018-50,2018〈br〉 〈b〉Manuscript under review for NPG〈/b〉 (discussion: final response, 2 comments)〈br〉 In this work, we conduct the strongly coupled data assimilation (SCDA) experiments using a two-scale Lorenz '96 model with the ensemble adjustment Kalman filter. This is a coupled system composed by two models with different scales. We have developed a new localization strategy for the cross-domain error covariances, which is crucial for the quality of SCDA. The results show that the SCDA with localization could provide much more accurate estimation of the states than the WCDA.

Description: Brief Communication: Earthquake sequencing: analysis of time series constructed from the Markov chain model Nonlinear Processes in Geophysics, 22, 589-599, 2015 Author(s): M. S. Cavers and K. Vasudevan Directed graph representation of a Markov chain model to study global earthquake sequencing leads to a time series of state-to-state transition probabilities that includes the spatio-temporally linked recurrent events in the record-breaking sense. A state refers to a configuration comprised of zones with either the occurrence or non-occurrence of an earthquake in each zone in a pre-determined time interval. Since the time series is derived from non-linear and non-stationary earthquake sequencing, we use known analysis methods to glean new information. We apply decomposition procedures such as ensemble empirical mode decomposition (EEMD) to study the state-to-state fluctuations in each of the intrinsic mode functions. We subject the intrinsic mode functions, derived from the time series using the EEMD, to a detailed analysis to draw information content of the time series. Also, we investigate the influence of random noise on the data-driven state-to-state transition probabilities. We consider a second aspect of earthquake sequencing that is closely tied to its time-correlative behaviour. Here, we extend the Fano factor and Allan factor analysis to the time series of state-to-state transition frequencies of a Markov chain. Our results support not only the usefulness of the intrinsic mode functions in understanding the time series but also the presence of power-law behaviour exemplified by the Fano factor and the Allan factor.

Description: A framework for variational data assimilation with superparameterization Nonlinear Processes in Geophysics, 22, 601-611, 2015 Author(s): I. Grooms and Y. Lee Superparameterization (SP) is a multiscale computational approach wherein a large scale atmosphere or ocean model is coupled to an array of simulations of small scale dynamics on periodic domains embedded into the computational grid of the large scale model. SP has been successfully developed in global atmosphere and climate models, and is a promising approach for new applications, but there is currently no practical data assimilation framework that can be used with these models. The authors develop a 3D-Var variational data assimilation framework for use with SP; the relatively low cost and simplicity of 3D-Var in comparison with ensemble approaches makes it a natural fit for relatively expensive multiscale SP models. To demonstrate the assimilation framework in a simple model, the authors develop a new system of ordinary differential equations similar to the two-scale Lorenz-'96 model. The system has one set of variables denoted { Y i }, with large and small scale parts, and the SP approximation to the system is straightforward. With the new assimilation framework the SP model approximates the large scale dynamics of the true system accurately.

Description: Nonstationary time series prediction combined with slow feature analysis Nonlinear Processes in Geophysics, 22, 377-382, 2015 Author(s): G. Wang and X. Chen Almost all climate time series have some degree of nonstationarity due to external driving forces perturbing the observed system. Therefore, these external driving forces should be taken into account when constructing the climate dynamics. This paper presents a new technique of obtaining the driving forces of a time series from the slow feature analysis (SFA) approach, and then introduces them into a predictive model to predict nonstationary time series. The basic theory of the technique is to consider the driving forces as state variables and to incorporate them into the predictive model. Experiments using a modified logistic time series and winter ozone data in Arosa, Switzerland, were conducted to test the model. The results showed improved prediction skills.

Description: Data assimilation experiments using diffusive back-and-forth nudging for the NEMO ocean model Nonlinear Processes in Geophysics, 22, 233-248, 2015 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 of 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 behaviour 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 modelled by diffusion operators which dissipate energy that cascade from large to small scales. Thus, in this article, the DBFN approximations and their consequences for the data assimilation system set-up are analysed. 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. The conducted sensitivity tests show that the 4Dvar profits of long assimilation windows to propagate surface information downwards, and that for the DBFN, it is worth using short assimilation windows to reduce the impact of diffusion-induced errors. Moreover, the DBFN is less sensitive to the first guess than the 4Dvar.

Description: Detecting and tracking eddies in oceanic flow fields: a Lagrangian descriptor based on the modulus of vorticity Rahel Vortmeyer-Kley, Ulf Gräwe, and Ulrike Feudel Nonlin. Processes Geophys., 23, 159-173, doi:10.5194/npg-23-159-2016, 2016 Since eddies play a major role in the dynamics of oceanic flows, it is of great interest to gain information about their tracks, lifetimes and shapes. We develop an eddy tracking tool based on structures in the flow with collecting (attracting) or separating (repelling) properties. In test cases mimicking oceanic flows it yields eddy lifetimes close to the analytical ones. It even provides a detailed view of the dynamics that can be useful to gain more insight into eddy dynamics in oceanic flows.

Description: Fractal behavior of soil water storage at multiple depths Wenjun Ji, Mi Lin, Asim Biswas, Bing C. Si, Henry W. Chau, and Hamish P. Cresswell Nonlin. Processes Geophys., 23, 269-284, doi:10.5194/npg-23-269-2016, 2016 We measure soil water at points (point scale) and try to understand how they vary over the landscape. Previous studies identified a statistical relationship between these scales only at the surface and not at depths. This study found that the relationship stands at different depths. The relationship was very similar at different depths in drier season or in late summer and fall. A less similar relationship was observed between surface and subsurface layers in spring or in wetter seasons.

Description: Limiting amplitudes of fully nonlinear interfacial tides and solitons Borja Aguiar-González and Theo Gerkema Nonlin. Processes Geophys., 23, 285-305, doi:10.5194/npg-23-285-2016, 2016 We derive a new two-fluid layer model consisting of forced rotation-modified Boussinesq equations for studying the limiting amplitudes of tidally generated fully nonlinear, weakly nonhydrostatic dispersive interfacial tides and solitons. Numerical solutions show that solitons attain in some cases a limiting table-shaped form, but may also be limited well below that state by saturation of the underlying quasi-linear internal tide under increasing barotropic forcing.

Description: A new estimator of heat periods for decadal climate predictions – a complex network approach Michael Weimer, Sebastian Mieruch, Gerd Schädler, and Christoph Kottmeier Nonlin. Processes Geophys., 23, 307-317, doi:10.5194/npg-23-307-2016, 2016 This paper is the first time that a complex network approach has been used for analysis of decadal climate predictions. We have developed an alternative estimator of heat periods based on network statistics, which turns out to be superior for parts of Europe. This paper opens the perspective that network measures have the potential to improve decadal predictions.

Description: Intermittent heat instabilities in an air plume Jean-Louis Le Mouël, Vladimir G. Kossobokov, Frederic Perrier, and Pierre Morat Nonlin. Processes Geophys., 23, 319-330, doi:10.5194/npg-23-319-2016, 2016 Heating experiments carried out in a limestone quarry close to Paris have shown a classical shape of temperature distribution in steady-state plumes in averages over 24 h, along with rich dynamics of heat flow with intermittent trains of oscillations, spatially coherent, of large amplitudes and a ~ 400 s period, separated by relative quiescence whose duration can reach several hours. The observed behavior could be a universal feature of some turbulent plumes in real geophysical environments.

Description: The Stochastic Calculus Reformulation of Data Assimilation: on Scale Feng Liu and Xin Li Nonlin. Processes Geophys. Discuss., doi:10.5194/npg-2016-35,2016 Manuscript under review for NPG (discussion: open, 0 comments) This is the first mathematical definitions of the spatial scale and its change. A definition of variable with respect to scale was also provided by considering the variation of geographical parameters. The stochastic calculus for data assimilation discovered the formulation of error caused by spatial scale. The results improve the ability to understand the uncertainty and scale problem in Earth observation, modeling and data assimilation.

Description: Wavelet analysis for non-stationary, nonlinear time series Justin A. Schulte Nonlin. Processes Geophys., 23, 257-267, doi:10.5194/npg-23-257-2016, 2016 Methods for detecting and quantifying nonlinearities in nonstationary time series are introduced and developed. In particular, higher-order wavelet analysis was applied to an ideal time series and the quasi-biennial oscillation (QBO) time series. Multiple-testing problems inherent in wavelet analysis were addressed by controlling the false discovery rate. A new local autobicoherence spectrum facilitated the detection of local nonlinearities and the quantification of cycle geometry. The local autobicoherence spectrum of the QBO time series showed that the QBO time series contained a mode with a period of 28 months that was phase coupled to a harmonic with a period of 14 months. An additional nonlinearly interacting triad was found among modes with periods of 10, 16 and 26 months. Local biphase spectra determined that the nonlinear interactions were not quadratic and that the effect of the nonlinearities was to produce non-smoothly varying oscillations. The oscillations were found to be skewed so that negative QBO regimes were preferred, and also asymmetric in the sense that phase transitions between the easterly and westerly phases occurred more rapidly than those from westerly to easterly regimes.

Description: Foreshocks and short-term hazard assessment of large earthquakes using complex networks: the case of the 2009 L'Aquila earthquake Eleni Daskalaki, Konstantinos Spiliotis, Constantinos Siettos, Georgios Minadakis, and Gerassimos A. Papadopoulos Nonlin. Processes Geophys., 23, 241-256, doi:10.5194/npg-23-241-2016, 2016 The monitoring of statistical network properties could be useful for short-term hazard assessment of the occurrence of mainshocks in the presence of foreshocks. Using successive connections between events acquired from the earthquake catalog of INGV for the case of the L’Aquila (Italy) mainshock ( M w  = 6.3) of 6 April 2009, we provide evidence that network measures, both global (average clustering coefficient, small-world index) and local (betweenness centrality) ones, could potentially be used.

Description: Using sparse regularization for multi-resolution tomography of the ionosphere Nonlinear Processes in Geophysics, 22, 613-624, 2015 Author(s): T. Panicciari, N. D. Smith, C. N. Mitchell, F. Da Dalt, and P. S. J. Spencer Computerized ionospheric tomography (CIT) is a technique that allows reconstructing the state of the ionosphere in terms of electron content from a set of slant total electron content (STEC) measurements. It is usually denoted as an inverse problem. In this experiment, the measurements are considered coming from the phase of the GPS signal and, therefore, affected by bias. For this reason the STEC cannot be considered in absolute terms but rather in relative terms. Measurements are collected from receivers not evenly distributed in space and together with limitations such as angle and density of the observations, they are the cause of instability in the operation of inversion. Furthermore, the ionosphere is a dynamic medium whose processes are continuously changing in time and space. This can affect CIT by limiting the accuracy in resolving structures and the processes that describe the ionosphere. Some inversion techniques are based on ℓ 2 minimization algorithms (i.e. Tikhonov regularization) and a standard approach is implemented here using spherical harmonics as a reference to compare the new method. A new approach is proposed for CIT that aims to permit sparsity in the reconstruction coefficients by using wavelet basis functions. It is based on the ℓ 1 minimization technique and wavelet basis functions due to their properties of compact representation. The ℓ 1 minimization is selected because it can optimize the result with an uneven distribution of observations by exploiting the localization property of wavelets. Also illustrated is how the inter-frequency biases on the STEC are calibrated within the operation of inversion, and this is used as a way for evaluating the accuracy of the method. The technique is demonstrated using a simulation, showing the advantage of ℓ 1 minimization to estimate the coefficients over the ℓ 2 minimization. This is in particular true for an uneven observation geometry and especially for multi-resolution CIT.

Description: Intermittent particle dynamics in marine coastal waters Nonlinear Processes in Geophysics, 22, 633-643, 2015 Author(s): P. R. Renosh, F. G. Schmitt, and H. Loisel Marine coastal processes are highly variable over different space scales and timescales. In this paper we analyse the intermittency properties of particle size distribution (PSD) recorded every second using a LISST instrument (Laser In-Situ Scattering and Transmissometry). The particle concentrations have been recorded over 32 size classes from 2.5 to 500 μm, at 1 Hz resolution. Such information is used to estimate at each time step the hyperbolic slope of the particle size distribution, and to consider its dynamics. Shannon entropy, as an indicator of the randomness, is estimated at each time step and its dynamics is analysed. Furthermore, particles are separated into four classes according to their size, and the intermittent properties of these classes are considered. The empirical mode decomposition (EMD) is used, associated with arbitrary-order Hilbert spectral analysis (AHSA), in order to retrieve scaling multifractal moment functions, for scales from 10 s to 8 min. The intermittent properties of two other indicators of particle concentration are also considered in the same range of scales: the total volume concentration C vol-total and the particulate beam attenuation coefficient c p (670). Both show quite similar intermittent dynamics and are characterised by the same exponents. Globally we find here negative Hurst exponents (meaning the small scales show larger fluctuation than large scales) for each time series considered, and nonlinear moment functions.

Description: Earthquake source parameters that display the first digit phenomenon Nonlinear Processes in Geophysics, 22, 625-632, 2015 Author(s): P. A. Toledo, S. R. Riquelme, and J. A. Campos We study the main parameters of earthquakes from the perspective of the first digit phenomenon: the nonuniform probability of the lower first digit different from 0 compared to the higher ones. We found that source parameters like coseismic slip distributions at the fault and coseismic inland displacements show first digit anomaly. We also found the tsunami runups measured after the earthquake to display the phenomenon. Other parameters found to obey first digit anomaly are related to the aftershocks: we show that seismic moment liberation and seismic waiting times also display an anomaly. We explain this finding by invoking a self-organized criticality framework. We demonstrate that critically organized automata show the first digit signature and we interpret this as a possible explanation of the behavior of the studied parameters of the Tohoku earthquake.

Description: Nonlinear feedback in a six-dimensional Lorenz model: impact of an additional heating term Nonlinear Processes in Geophysics, 22, 749-764, 2015 Author(s): B.-W. Shen In this study, a six-dimensional Lorenz model (6DLM) is derived, based on a recent study using a five-dimensional (5-D) Lorenz model (LM), in order to examine the impact of an additional mode and its accompanying heating term on solution stability. The new mode added to improve the representation of the streamfunction is referred to as a secondary streamfunction mode, while the two additional modes, which appear in both the 6DLM and 5DLM but not in the original LM, are referred to as secondary temperature modes. Two energy conservation relationships of the 6DLM are first derived in the dissipationless limit. The impact of three additional modes on solution stability is examined by comparing numerical solutions and ensemble Lyapunov exponents of the 6DLM and 5DLM as well as the original LM. For the onset of chaos, the critical value of the normalized Rayleigh number ( r c ) is determined to be 41.1. The critical value is larger than that in the 3DLM ( r c ~ 24.74), but slightly smaller than the one in the 5DLM ( r c ~ 42.9). A stability analysis and numerical experiments obtained using generalized LMs, with or without simplifications, suggest the following: (1) negative nonlinear feedback in association with the secondary temperature modes, as first identified using the 5DLM, plays a dominant role in providing feedback for improving the solution's stability of the 6DLM, (2) the additional heating term in association with the secondary streamfunction mode may destabilize the solution, and (3) overall feedback due to the secondary streamfunction mode is much smaller than the feedback due to the secondary temperature modes; therefore, the critical Rayleigh number of the 6DLM is comparable to that of the 5DLM. The 5DLM and 6DLM collectively suggest different roles for small-scale processes (i.e., stabilization vs. destabilization), consistent with the following statement by Lorenz (1972): "If the flap of a butterfly's wings can be instrumental in generating a tornado, it can equally well be instrumental in preventing a tornado." The implications of this and previous work, as well as future work, are also discussed.

Description: Brief Communication: Breeding vectors in the phase space reconstructed from time series data Erin Lynch, Daniel Kaufman, A. Surjalal Sharma, Eugenia Kalnay, and Kayo Ide Nonlin. Processes Geophys., 23, 137-141, doi:10.5194/npg-23-137-2016, 2016 In this article, bred vectors are computed from a single time series data using time-delay embedding, with a new technique, nearest-neighbor breeding. Since the dynamical properties of the nearest-neighbor bred vectors are shown to be similar to bred vectors computed using evolution equations, this provides a new and novel way to model and predict sudden transitions in systems represented by time series data alone.

Description: Ocean–atmosphere–wave characterisation of a wind jet (Ebro shelf, NW Mediterranean Sea) Manel Grifoll, Jorge Navarro, Elena Pallares, Laura Ràfols, Manuel Espino, and Ana Palomares Nonlin. Processes Geophys., 23, 143-158, doi:10.5194/npg-23-143-2016, 2016 In this contribution the wind jet dynamics in the northern margin of the Ebro River shelf (NW Mediterranean Sea) are investigated using coupled numerical models. The study area is characterized by persistent and energetic offshore winds during autumn and winter. However, the coupling effect in the wind resource assessment may be relevant due to the cubic relation between the wind intensity and power.

Description: Trend analysis by a piecewise linear regression model applied to surface air temperatures in Southeastern Spain (1973–2014) Pablo Campra and Maria Morales Nonlin. Processes Geophys. Discuss., doi:10.5194/npg-2016-29,2016 Manuscript under review for NPG (discussion: open, 0 comments) Simple linear trend analysis constitutes the most straightforward assessment of the long-term behavior of time series in climate change. Here we have applied an alternative nonlinear fitting model of flexible regression developed to characterize climatic trends in surface air temperature series in SE Spain, a key region to study impacts of climate change. This model offers a better fit to the observational records than conventional simple linear trends analyses.

Description: Sandpile-based model for capturing magnitude distributions and spatiotemporal clustering and separation in regional earthquakes Rene C. Batac, Antonino A. Paguirigan Jr., Anjali B. Tarun, and Anthony G. Longjas Nonlin. Processes Geophys. Discuss., doi:10.5194/npg-2016-28,2016 Manuscript under review for NPG (discussion: open, 0 comments) The sandpile-based model is the paradigm model of self-organized criticality (SOC), a mechanism believed to be responsible for the occurrence of scale-free (power-law) distributions in nature. One particular SOC system that is rife with power-law distributions is that of earthquakes, the most widely-known of which is the Gutenberg–Richter (GR) law of earthquake energies. Here, we modify the sandpile to be of use in capturing the energy, space, and time statistics of earthquakes simultaneously.

Description: Sparsity-based compressive reservoir characterization and modeling by applying ILS-DLA sparse approximation with LARS on DisPat-generated MPS models using seismic, well log, and reservoir data Mohammad Hosseini and Mohammad Ali Riahi Nonlin. Processes Geophys. Discuss., doi:10.5194/npg-2016-46,2016 Manuscript under review for NPG (discussion: open, 0 comments) Observations of an unknown property is very limited but manipulation of the limited observations are possible in order to characterize different aspects of the unknown property based on which, it is desired to get the closest approximation to the unknown property. This closest approximation possess 90 % characteristics of the observations by 90 % probability. This workflow is already used in image processing and can be further applied in remote sensing, mining, hydrology and petroleum science.

Description: Data assimilation for moving mesh methods with an application to ice sheet modelling Bertrand Bonan, Nancy K. Nichols, Michael J. Baines, and Dale Partridge Nonlin. Processes Geophys. Discuss., doi:10.5194/npg-2016-45,2016 Manuscript under review for NPG (discussion: open, 0 comments) We develop data assimilation techniques for numerical models using moving mesh methods. Moving meshes are valuable for explicitly tracking interfaces and boundaries in evolving systems. The application of the techniques is demonstrated on a one-dimensional model of an ice sheet. It is shown, using various types of observations, that the techniques predict the evolution of the edges of the ice sheet and its height accurately and efficiently.

Description: Inverting Rayleigh surface wave velocities for eastern Tibet and western Yangtze craton crustal thickness based on deep learning neural networks Xian-Qiong Cheng, Qi-He Liu, and Ping Ping Li Nonlin. Processes Geophys. Discuss., doi:10.5194/npg-2016-39,2016 Manuscript under review for NPG (discussion: open, 0 comments) In this paper we resolve classic geophysical problem based on newly developed computer and information science. Since many classic geophysical problems are nonlinear, researches treating them as linearity are approximate. When we treat inverting moho depth as full nonlinearity we attain more satisfactory results with lower costs and higher accuracy. Results we have attained can provide important data for discussing origin and development of earthquake, also for distribution of mineral resources.

Description: Comparison of the multifractal characteristics of heavy metals in soils within two areas of contrasting economic activities in China Xiaohui Li, Xiangling Li, Feng Yuan, Simon M. Jowitt, Taofa Zhou, Kui Yang, Jie Zhou, Xunyu Hu, and Yang Li Nonlin. Processes Geophys., 23, 331-339, doi:10.5194/npg-23-331-2016, 2016 In this paper, we present the results of a heavy metal soil geochemical survey in Hefei city and use three multifractal parameters to indicate the overall amount of multifractality within the soil geochemical data. The results show all of the elements barring Hg have larger multifractal parameters in the Daxing area compared to the Yicheng area. The degree of multifractality suggests that the differing economic activities in Daxing and Yicheng generate very different heavy metal pollution loads.

Description: Corrigendum to "Breeding and predictability in the baroclinic rotating annulus using a perfect model" published in Nonlin. Processes Geophys., 15, 469–487, 2008 Nonlinear Processes in Geophysics, 18, 359-359, 2011 Author(s): R. M. B. Young and P. L. Read No abstract available.

Description: Strategies for coupling global and limited-area ensemble Kalman filter assimilation Nonlinear Processes in Geophysics, 18, 415-430, 2011 Author(s): D. Merkova, I. Szunyogh, and E. Ott This paper compares the forecast performance of four strategies for coupling global and limited area data assimilation: three strategies propagate information from the global to the limited area process, while the fourth strategy feeds back information from the limited area to the global process. All four strategies are formulated in the Local Ensemble Transform Kalman Filter (LETKF) framework. Numerical experiments are carried out with the model component of the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS) and the NCEP Regional Spectral Model (RSM). The limited area domain is an extended North-America region that includes part of the north-east Pacific. The GFS is integrated at horizontal resolution T62 (about 150 km in the mid-latitudes), while the RSM is integrated at horizontal resolution 48 km. Experiments are carried out both under the perfect model hypothesis and in a realistic setting. The coupling strategies are evaluated by comparing their deterministic forecast performance at 12-h and 48-h lead times. The results suggest that the limited area data assimilation system has the potential to enhance the forecasts at 12-h lead time in the limited area domain at the synoptic and sub-synoptic scales (in the global wave number range of about 10 to 40). There is a clear indication that between the forecast performance of the different coupling strategies those that cycle the limited area assimilation process produce the most accurate forecasts. In the realistic setting, at 12-h forecast time the limited area systems produce more modest improvements compared to the global system than under the perfect model hypothesis, and at 48-h forecast time the global forecasts are more accurate than the limited area forecasts.

Description: Spectral methods for internal waves: indistinguishable density profiles and double-humped solitary waves Nonlinear Processes in Geophysics, 18, 351-358, 2011 Author(s): M. Dunphy, C. Subich, and M. Stastna Internal solitary waves are widely observed in both the oceans and large lakes. They can be described by a variety of mathematical theories, covering the full spectrum from first order asymptotic theory (i.e. Korteweg-de Vries, or KdV, theory), through higher order extensions of weakly nonlinear-weakly nonhydrostatic theory, to fully nonlinear-weakly nonhydrostatic theories and finally exact theory based on the Dubreil-Jacotin-Long (DJL) equation that is formally equivalent to the full set of Euler equations. We discuss how spectral and pseudospectral methods allow for the computation of novel phenomena in both approximate and exact theories. In particular we construct markedly different density profiles for which the coefficients in the KdV theory are very nearly identical. These two density profiles yield qualitatively different behaviour for both exact, or fully nonlinear, waves computed using the DJL equation and in dynamic simulations of the time dependent Euler equations. For exact, DJL, theory we compute exact solitary waves with two-scales, or so-called double-humped waves.

Description: A nonlinear method of removing harmonic noise in geophysical data Nonlinear Processes in Geophysics, 18, 367-379, 2011 Author(s): Y. Jeng and C.-S. Chen A nonlinear, adaptive method to remove the harmonic noise that commonly resides in geophysical data is proposed in this study. This filtering method is based on the ensemble empirical mode decomposition algorithm in conjunction with the logarithmic transform. We present a synthetic model study to investigate the capability of signal reconstruction from the decomposed data, and compare the results with those derived from other 2-D adaptive filters. Applications to the real seismic data acquired by using an ocean bottom seismograph and to a shot gather of the ground penetrating radar demonstrate the robustness of this method. Our work proposes a concept that instead of Fourier-based approaches, the harmonic noise removal in geophysical data can be achieved effectively by using an alternative nonlinear adaptive data analysis method, which has been applied extensively in other scientific studies.

Description: Comparison of correlation analysis techniques for irregularly sampled time series Nonlinear Processes in Geophysics, 18, 389-404, 2011 Author(s): K. Rehfeld, N. Marwan, J. Heitzig, and J. Kurths Geoscientific measurements often provide time series with irregular time sampling, requiring either data reconstruction (interpolation) or sophisticated methods to handle irregular sampling. We compare the linear interpolation technique and different approaches for analyzing the correlation functions and persistence of irregularly sampled time series, as Lomb-Scargle Fourier transformation and kernel-based methods. In a thorough benchmark test we investigate the performance of these techniques. All methods have comparable root mean square errors (RMSEs) for low skewness of the inter-observation time distribution. For high skewness, very irregular data, interpolation bias and RMSE increase strongly. We find a 40 % lower RMSE for the lag-1 autocorrelation function (ACF) for the Gaussian kernel method vs. the linear interpolation scheme,in the analysis of highly irregular time series. For the cross correlation function (CCF) the RMSE is then lower by 60 %. The application of the Lomb-Scargle technique gave results comparable to the kernel methods for the univariate, but poorer results in the bivariate case. Especially the high-frequency components of the signal, where classical methods show a strong bias in ACF and CCF magnitude, are preserved when using the kernel methods. We illustrate the performances of interpolation vs. Gaussian kernel method by applying both to paleo-data from four locations, reflecting late Holocene Asian monsoon variability as derived from speleothem δ 18 O measurements. Cross correlation results are similar for both methods, which we attribute to the long time scales of the common variability. The persistence time (memory) is strongly overestimated when using the standard, interpolation-based, approach. Hence, the Gaussian kernel is a reliable and more robust estimator with significant advantages compared to other techniques and suitable for large scale application to paleo-data.

Description: Brief communication "On one mechanism of low frequency variability of the Antarctic Circumpolar Current" Nonlinear Processes in Geophysics, 18, 361-365, 2011 Author(s): O. G. Derzho and B. de Young In this paper we present a simple analytical model for low frequency and large scale variability of the Antarctic Circumpolar Current (ACC). The physical mechanism of the variability is related to temporal and spatial variations of the cyclonic mean flow (ACC) due to circularly propagating nonlinear barotropic Rossby wave trains. It is shown that the Rossby wave train is a fundamental mode, trapped between the major fronts in the ACC. The Rossby waves are predicted to rotate with a particular angular velocity that depends on the magnitude and width of the mean current. The spatial structure of the rotating pattern, including its zonal wave number, is defined by the specific form of the stream function-vorticity relation. The similarity between the simulated patterns and the Antarctic Circumpolar Wave (ACW) is highlighted. The model can predict the observed sequence of warm and cold patches in the ACW as well as its zonal number.

Description: A semi-phenomenological approach to explain the event-size distribution of the Drossel-Schwabl forest-fire model Nonlinear Processes in Geophysics, 18, 381-388, 2011 Author(s): S. Hergarten and R. Krenn We present a novel approach to explain the complex scaling behavior of the Drossel-Schwabl forest-fire model in two dimensions. Clusters of trees are characterized by their size and perimeter only, whereas spatial correlations are neglected. Coalescence of clusters is restricted to clusters of similar sizes. Our approach derives the value of the scaling exponent τ of the event size distribution directly from the scaling of the accessible perimeter of percolation clusters. We obtain τ = 1.19 in the limit of infinite growth rate, in perfect agreement with numerical results. Furthermore, our approach predicts the unusual transition from a power law to an exponential decay even quantitatively, while the exponential decay at large event sizes itself is reproduced only qualitatively.

Description: Double rank-ordering technique of ROMA (Rank-Ordered Multifractal Analysis) for multifractal fluctuations featuring multiple regimes of scales Nonlinear Processes in Geophysics, 18, 405-414, 2011 Author(s): S. W. Y. Tam and T. Chang Rank-Ordered Multifractal Analysis (ROMA), a technique capable of deciphering the multifractal characteristics of intermittent fluctuations, was originally applied to the results of a magnetohydrodynamic (MHD) simulation. Application of ROMA to measured fluctuations in the auroral zone, due to the dominant physical effects changing from kinetic to MHD as the scale increases, requires an additional level of rank-ordering in order to divide the domain of scales into regimes. An algorithm for the additional step in this double rank-ordering technique is discussed, and is demonstrated in the application to the electric field fluctuations in the auroral zone as an example. As a result of the double rank-ordering, ROMA is able to take into account the nonlinear crossover behavior characterized by the multiple regimes of time scales by providing a scaling variable and a scaling function that are global to all the time scales.

Description: Improved variational methods in statistical data assimilation Nonlinear Processes in Geophysics, 22, 205-213, 2015 Author(s): J. Ye, N. Kadakia, P. J. Rozdeba, H. D. I. Abarbanel, and J. C. Quinn Data assimilation transfers information from an observed system to a physically based model system with state variables x (t) . The observations are typically noisy, the model has errors, and the initial state x (t 0 ) is uncertain: the data assimilation is statistical. One can ask about expected values of functions ⟨ G( X )⟩ on the path X = { x (t 0 ), ..., x (t m ) } of the model state through the observation window t n = { t 0 , ..., t m }. The conditional (on the measurements) probability distribution P( X ) = exp[− A 0 ( X )] determines these expected values. Variational methods using saddle points of the "action" A 0 ( X ), known as 4DVar (Talagrand and Courtier, 1987; Evensen, 2009), are utilized for estimating ⟨ G( X ) ⟩. In a path integral formulation of statistical data assimilation, we consider variational approximations in a realization of the action where measurement errors and model errors are Gaussian. We (a) discuss an annealing method for locating the path X 0 giving a consistent minimum of the action A 0 ( X 0 ), (b) consider the explicit role of the number of measurements at each t n 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: Analysis of stochastic model for nonlinear volcanic dynamics Nonlinear Processes in Geophysics, 22, 197-204, 2015 Author(s): D. V. Alexandrov, I. A. Bashkirtseva, and L. B. 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 a 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 by increasing the noise intensity. The plug velocity, pressure and displacement are highly dependent of noise intensity as well. These new stochastic phenomena are related to 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: An analytical model of the evolution of a Stokes wave and its two Benjamin–Feir sidebands on nonuniform unidirectional current Nonlinear Processes in Geophysics, 22, 313-324, 2015 Author(s): I. V. Shugan, H. H. Hwung, and R. Y. Yang An analytical weakly nonlinear model of the Benjamin–Feir instability of a Stokes wave on nonuniform unidirectional current is presented. The model describes evolution of a Stokes wave and its two main sidebands propagating on a slowly varying steady current. In contrast to the models based on versions of the cubic Schrödinger equation, the current variations could be strong, which allows us to examine the blockage and consider substantial variations of the wave numbers and frequencies of interacting waves. The spatial scale of the current variation is assumed to have the same order as the spatial scale of the Benjamin–Feir (BF) instability. The model includes wave action conservation law and nonlinear dispersion relation for each of the wave's triad. The effect of nonuniform current, apart from linear transformation, is in the detuning of the resonant interactions, which strongly affects the nonlinear evolution of the system. 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, resulting 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 waves accompanied by energy income from sufficiently strong opposing current. We employ the model for the estimation of the maximum amplification of wave amplitudes as a function of opposing current value and compare the result obtained with recently published experimental results and modeling results obtained with the nonlinear Schrödinger equation.

Description: Inferring origin of mercury inclusions in quartz by multifractal analysis Nonlinear Processes in Geophysics, 22, 47-52, 2015 Author(s): T. Shibata, T. Maruoka, and T. Echigo In order to refine our understanding of 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 geological settings, the resultant fractal dimensions were 1.70 and 1.71 for the San Benito and Itomuka samples, respectively. The fractal dimensions were also close to those predicted by diffusion-limited aggregation models and percolation theory, which are controlled by the irreversible kinetics. Given the fractal dimension and its implied mechanism, we conclude that the mercury-bearing fluids were not primary fluid inclusions, but migrated into the pre-existing cracks of quartz crystals by diffusion processes.

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

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

Description: Site effect classification based on microtremor data analysis using a concentration–area fractal model Nonlinear Processes in Geophysics, 22, 53-63, 2015 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 modelling reveal that proper soil types are located around the central city. The results derived via the fractal modelling were utilized to improve the Nogoshi and Igarashi (1970, 1971) classification results in the Meybod city. The resulting 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: Estimation of flow velocity for a debris flow via the two-phase fluid model Nonlinear Processes in Geophysics, 22, 109-116, 2015 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 the velocity for a debris flow.

Description: Non-Gaussian interaction information: estimation, optimization and diagnostic application of triadic wave resonance Nonlinear Processes in Geophysics, 22, 87-108, 2015 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: Fluctuations in a quasi-stationary shallow cumulus cloud ensemble Nonlinear Processes in Geophysics, 22, 65-85, 2015 Author(s): M. Sakradzija, A. Seifert, and T. Heus We propose an approach to stochastic parameterisation of shallow cumulus clouds to represent the convective variability and its dependence on the model resolution. To collect information about the individual cloud lifecycles and the cloud ensemble as a whole, we employ a large eddy simulation (LES) model 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, active and passive clouds. Each distribution mode can be approximated using a Weibull distribution, which is a generalisation of exponential distribution by accounting for the change in distribution shape due to the diversity of cloud lifecycles. The exponential distribution of cloud mass flux previously suggested for deep convection parameterisation 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: Instability and change detection in exponential families and generalized linear models, with a study of Atlantic tropical storms Nonlinear Processes in Geophysics, 21, 1133-1143, 2014 Author(s): Y. Lu and S. Chatterjee Exponential family statistical distributions, including the well-known normal, binomial, Poisson, and exponential distributions, are overwhelmingly used in data analysis. In the presence of covariates, an exponential family distributional assumption for the response random variables results in a generalized linear model. However, it is rarely ensured that the parameters of the assumed distributions are stable through the entire duration of the data collection process. A failure of stability leads to nonsmoothness and nonlinearity in the physical processes that result in the data. In this paper, we propose testing for stability of parameters of exponential family distributions and generalized linear models. A rejection of the hypothesis of stable parameters leads to change detection. We derive the related likelihood ratio test statistic. We compare the performance of this test statistic to the popular normal distributional assumption dependent cumulative sum (Gaussian CUSUM) statistic in change detection problems. We study Atlantic tropical storms using the techniques developed here, so to understand whether the nature of these tropical storms has remained stable over the last few decades.

Description: Spatial random downscaling of rainfall signals in Andean heterogeneous terrain Nonlinear Processes in Geophysics, 22, 383-402, 2015 Author(s): A. Posadas, L. A. Duffaut Espinosa, C. Yarlequé, M. Carbajal, H. Heidinger, L. Carvalho, C. Jones, and R. Quiroz Remotely sensed data are often used as proxies for indirect precipitation measures over data-scarce and complex-terrain areas such as the Peruvian Andes. Although this information might be appropriate for some research requirements, the extent at which local sites could be related to such information is very limited because of the resolution of the available satellite data. Downscaling techniques are used to bridge the gap between what climate modelers (global and regional) are able to provide and what decision-makers require (local). Precipitation downscaling improves the poor local representation of satellite data and helps end-users acquire more accurate estimates of water availability. Thus, a multifractal downscaling technique complemented by a heterogeneity filter was applied to TRMM (Tropical Rainfall Measuring Mission) 3B42 gridded data (spatial resolution ~ 28 km) from the Peruvian Andean high plateau or \textit{Altiplano} to generate downscaled rainfall fields that are relevant at an agricultural scale (spatial resolution ~ 1 km).

Description: Improved singular spectrum analysis for time series with missing data Nonlinear Processes in Geophysics, 22, 371-376, 2015 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 develops an improved SSA (ISSA) for processing the incomplete time series and the modified SSA (SSAM) of Schoellhamer (2001) is its special case. The approach is 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. Both the mean absolute error and mean root mean squared error of the reconstructed time series by ISSA are also 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 standard deviation (SD) derived by ISSA is 12.27 mg L −1 , smaller than the 13.48 mg L −1 derived by SSAM.

Description: Reversals in the large-scale αΩ-dynamo with memory Nonlinear Processes in Geophysics, 22, 361-369, 2015 Author(s): L. K. Feschenko and G. M. Vodinchar Inversion of the magnetic field in a model of large-scale αΩ-dynamo with α-effect with stochastic memory is under 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 timescale is fractal. Its dimension is consistent with the dimension of the real geomagnetic polarity timescale.

Description: Rank ordering multifractal analysis of the auroral electrojet index Nonlinear Processes in Geophysics, 18, 277-285, 2011 Author(s): G. Consolini and P. De Michelis In the second half of the 90s interest grew on the complex features of the magnetospheric dynamics in response to solar wind changes. An important series of papers were published on the occurrence of chaos, turbulence and complexity. Among them, particularly interesting was the study of the bursty and fractal/multifractal character of the high latitude energy release during geomagnetic storms, which was evidenced by analyzing the features of the Auroral Electrojet (AE) indices. Recently, the multifractal features of the small time-scale increments of AE-indices have been criticized in favor of a more simple fractal behavior. This is particularly true for the scaling features of the probability density functions (PDFs) of the AE index increments. Here, after a brief review of the nature of the fractal/multifractal features of the magnetospheric response to solar wind changes, we investigate the multifractal nature of the scaling features of the AE index increments PDFs using the Rank Ordering Multifractal Analysis (ROMA) technique. The ROMA results clearly demonstrate the existence of a hierarchy of scaling indices, depending on the increment amplitude, for the data collapsing of PDFs relative to increments at different time scales. Our results confirm the previous results by Consolini et al. (1996) and the more recent results by Rypdal and Rypdal (2010).

Description: Preface Large amplitude internal waves in the coastal ocean Nonlinear Processes in Geophysics, 18, 653-655, 2011 Author(s): R. Grimshaw, K. Helfrich, and A. Scotti No Abstract available.

Description: Size distribution and structure of Barchan dune fields Nonlinear Processes in Geophysics, 18, 455-467, 2011 Author(s): O. Durán, V. Schwämmle, P. G. Lind, and H. J. Herrmann Barchans are isolated mobile dunes often organized in large dune fields. Dune fields seem to present a characteristic dune size and spacing, which suggests a cooperative behavior based on dune interaction. In Duran et al. (2009), we propose that the redistribution of sand by collisions between dunes is a key element for the stability and size selection of barchan dune fields. This approach was based on a mean-field model ignoring the spatial distribution of dune fields. Here, we present a simplified dune field model that includes the spatial evolution of individual dunes as well as their interaction through sand exchange and binary collisions. As a result, the dune field evolves towards a steady state that depends on the boundary conditions. Comparing our results with measurements of Moroccan dune fields, we find that the simulated fields have the same dune size distribution as in real fields but fail to reproduce their homogeneity along the wind direction.

Description: Combining 2-m temperature nowcasting and short range ensemble forecasting Nonlinear Processes in Geophysics, 18, 903-910, 2011 Author(s): A. Kann, T. Haiden, and C. Wittmann During recent years, numerical ensemble prediction systems have become an important tool for estimating the uncertainties of dynamical and physical processes as represented in numerical weather models. The latest generation of limited area ensemble prediction systems (LAM-EPSs) allows for probabilistic forecasts at high resolution in both space and time. However, these systems still suffer from systematic deficiencies. Especially for nowcasting (0–6 h) applications the ensemble spread is smaller than the actual forecast error. This paper tries to generate probabilistic short range 2-m temperature forecasts by combining a state-of-the-art nowcasting method and a limited area ensemble system, and compares the results with statistical methods. The Integrated Nowcasting Through Comprehensive Analysis (INCA) system, which has been in operation at the Central Institute for Meteorology and Geodynamics (ZAMG) since 2006 (Haiden et al., 2011), provides short range deterministic forecasts at high temporal (15 min–60 min) and spatial (1 km) resolution. An INCA Ensemble (INCA-EPS) of 2-m temperature forecasts is constructed by applying a dynamical approach, a statistical approach, and a combined dynamic-statistical method. The dynamical method takes uncertainty information (i.e. ensemble variance) from the operational limited area ensemble system ALADIN-LAEF (Aire Limitée Adaptation Dynamique Développement InterNational Limited Area Ensemble Forecasting) which is running operationally at ZAMG (Wang et al., 2011). The purely statistical method assumes a well-calibrated spread-skill relation and applies ensemble spread according to the skill of the INCA forecast of the most recent past. The combined dynamic-statistical approach adapts the ensemble variance gained from ALADIN-LAEF with non-homogeneous Gaussian regression (NGR) which yields a statistical \mbox{correction} of the first and second moment (mean bias and dispersion) for Gaussian distributed continuous variables. Validation results indicate that all three methods produce sharp and reliable probabilistic 2-m temperature forecasts. However, the statistical and combined dynamic-statistical methods slightly outperform the pure dynamical approach, mainly due to the under-dispersive behavior of ALADIN-LAEF outside the nowcasting range. The training length does not have a pronounced impact on forecast skill, but a spread re-scaling improves the forecast skill substantially. Refinements of the statistical methods yield a slight further improvement.

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

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

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

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

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

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

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

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