ALBERT

Description: Recently, various models have been developed, including the fractional Brownian motion (fBm), to analyse the stochastic properties of geodetic time series together with the estimated geophysical signals. The noise spectrum of these time series is generally modelled as a mixed spectrum, with a sum of white and coloured noise. Here, we are interested in modelling the residual time series after deterministically subtracting geophysical signals from the observations. This residual time series is then assumed to be a sum of three stochastic processes, including the family of Lévy processes. The introduction of a third stochastic term models the remaining residual signals and other correlated processes. Via simulations and real time series, we identify three classes of Lévy processes, namely Gaussian, fractional and stable. In the first case, residuals are predominantly constituted of short-memory processes. The fractional Lévy process can be an alternative model to the fBm in the presence of long-term correlations and self-similarity properties. The stable process is here restrained to the special case of infinite variance, which can be only satisfied in the case of heavy-tailed distributions in the application to geodetic time series. Therefore, the model implies potential anxiety in the functional model selection, where missing geophysical information can generate such residual time series.

Description: The behavior of the iterative ensemble-based data assimilation algorithm is discussed. The ensemble-based method for variational data assimilation problems, referred to as the 4D ensemble variational method (4DEnVar), is a useful tool for data assimilation problems. Although the 4DEnVar is derived based on a linear approximation, highly uncertain problems, in which system nonlinearity is significant, are solved by applying this method iteratively. However, the ensemble-based methods basically seek the solution within a lower-dimensional subspace spanned by the ensemble members. It is not necessarily trivial how high-dimensional problems can be solved with the ensemble-based algorithm which employs the lower-dimensional approximation based on the ensemble. In the present study, an ensemble-based iterative algorithm is reformulated to allow us to analyze its behavior in high-dimensional nonlinear problems. The conditions for monotonic convergence to a local maximum of the objective function are discussed in a high-dimensional context. It is shown that the ensemble-based algorithm can solve high-dimensional problems by distributing the ensemble in different subspace at each iteration. The findings as the results of the present study were also experimentally supported.

Description: In previous work, it was shown that the preservation of physical properties in the data assimilation framework can significantly reduce forecast errors. Proposed data assimilation methods, such as the quadratic programming ensemble (QPEns) that can impose such constraints on the calculation of the analysis, are computationally more expensive, severely limiting their application to high-dimensional prediction systems as found in Earth sciences. We, therefore, propose using a convolutional neural network (CNN) trained on the difference between the analysis produced by a standard ensemble Kalman filter (EnKF) and the QPEns to correct any violations of imposed constraints. In this paper, we focus on the conservation of mass and show that, in an idealised set-up, the hybrid of a CNN and the EnKF is capable of reducing analysis and background errors to the same level as the QPEns.

Description: A method for objectively extracting the displacement signals associated with coherent eddies from Lagrangian trajectories is presented, refined, and applied to a large dataset of 3770 surface drifters from the Gulf of Mexico. The method, wavelet ridge analysis, is a general method for the analysis of modulated oscillations, here modified to be more suitable to the eddy-detection problem. A means for formally assessing statistical significance is introduced, addressing the issue of false positives arising by chance from an unstructured turbulent background and opening the door to confident application of the method to very large datasets. Significance is measured through a frequency-dependent comparison with a stochastic dataset having statistical and spectral properties that match the original, but lacking organized oscillations due to eddies or waves. The application to the Gulf of Mexico reveals major asymmetries between cyclones and anticyclones, with anticyclones dominating at radii larger than about 50 km, but an unexpectedly rich population of highly nonlinear cyclones dominating at smaller radii. Both the method and the Gulf of Mexico eddy dataset are made freely available to the community for noncommercial use in future research.

Description: The Ms 8.0 Wenchuan earthquake in 2008 and Ms 7.0 Lushan earthquake in 2013 produced thousands of landslides in the southern region of the Longmen Mountains in China. We conducted field investigations and analyzed remote sensing data to determine the distribution law of earthquake-triggered landslides. The results show a strong negative power law relationship between the size and frequency of landslides in VII, VIII, and IX seismic intensity zones, a weak power law in the X seismic intensity zone, and a lognormal distribution in the XI seismic intensity zone. Landslide density increases with increasing seismic intensity. A sandpile cellular automata model was built under the conceptual framework of self-organized criticality theory to simulate earthquake-induced landslides. Data from the simulations demonstrate that, with increasing disturbance intensity, the dynamical mechanism of the sandpile model changes from a strong power law to a weak power law and then to a lognormal distribution. Results from shaking table experiments of a one-sided slope sandpile show that, for peak ground acceleration (PGA) in the range of 0.075–0.125 g, the relation between the amount and frequency of sand follows a negative power law. For PGA between 0.15 and 0.25 g, the relation obeys a lognormal distribution. This verifies that the abovementioned distribution of earthquake-induced landslides should be a universal law from a physical viewpoint and may apply to other areas. This new perspective may be used to guide the development of an inventory of earthquake-triggered landslides and provide a scientific basis for their prediction.

Description: The Trajectory-Adaptive Multilevel Sampling (TAMS) is a promising method to determine probabilities of noise-induced transition in multi-stable high-dimensional dynamical systems. In this paper, we focus on two improvements of the current algorithm related to (i) the choice of the target set and (ii) the formulation of the score function. In particular, we use confidence ellipsoids determined from linearised dynamics in the choice of the target set. Furthermore, we define a score function based on empirical transition paths computed at relatively high noise levels. The suggested new TAMS method is applied to two typical problems illustrating the benefits of the modifications.

Description: Earthquake precursors and earthquake monitoring are always important in the earthquake research field, even if there is still debate about the existence of earthquake precursors. However, it is extremely difficult to observe the seismogenic environment of earthquakes directly. Laboratory rupture experiment is a useful technique to simulate and gain an insight into the complex mechanisms of earthquakes. Five marble samples with prefabricated cracks are used for uniaxial loading experiments to investigate whether there is a precursory signal before rock fracture and to simulate the rupture process of strike-slip fault. The existence of a precursory signal is confirmed by the coefficient of variation (CV) results, from which we can see two patterns which are known as seismicity acceleration and quiescence before an earthquake. Moreover, these CV findings are applied to determine the locations of large deformation sampling points on the rock surface at different loading stages. Similar results are obtained when we consider actual seismicity at the northern end of the San Andreas Fault in California, which provides crucial evidence to prove the existence of precursor characteristics. In this case, three kinds of seismic monitoring models are designed to find out how to monitor these characteristics more effectively.

Description: We give a simple description of the blessing of dimensionality with the main focus on the concentration phenomena. These phenomena imply that in high dimensions the lengths of independent random vectors from the same distribution have almost the same length and that independent vectors are almost orthogonal. In the climate and atmospheric sciences we rely increasingly on ensemble modelling and face the challenge of analysing large samples of long time series and spatially extended fields. We show how the properties of high dimensions allow us to obtain analytical results for e.g. correlations between sample members and the behaviour of the sample mean when the size of the sample grows. We find that the properties of high dimensionality with reasonable success can be applied to climate data. This is the case although most climate data show strong anisotropy and both spatial and temporal dependence, resulting in effective dimensions around 25–100.

Description: Recent advances in statistical and machine learning have opened the possibility of forecasting the behaviour of chaotic systems using recurrent neural networks. In this article we investigate the applicability of such a framework to geophysical flows, known to involve multiple scales in length, time and energy and to feature intermittency. We show that both multiscale dynamics and intermittency introduce severe limitations to the applicability of recurrent neural networks, both for short-term forecasts as well as for the reconstruction of the underlying attractor. We suggest that possible strategies to overcome such limitations should be based on separating the smooth large-scale dynamics from the intermittent/small-scale features. We test these ideas on global sea-level pressure data for the past 40 years, a proxy of the atmospheric circulation dynamics. Better short- and long-term forecasts of sea-level pressure data can be obtained with an optimal choice of spatial coarse graining and time filtering.

Description: Shoaling internal solitary waves near the Dongsha Atoll in the South China Sea dissipate their energy and enhance diapycnal mixing, which have an important impact on the oceanic environment and primary productivity. The enhanced diapycnal mixing is patchy and instantaneous. Evaluating its spatiotemporal distribution requires comprehensive observation data. Fortunately, seismic oceanography meets the requirements, thanks to its high spatial resolution and large spatial coverage. In this paper, we studied three internal solitary waves in reversing polarity near the Dongsha Atoll and calculated their spatial distribution of diapycnal diffusivity. Our results show that the average diffusivities along three survey lines are 2 orders of magnitude larger than the open-ocean value. The average diffusivity in internal solitary waves with reversing polarity is 3 times that of the non-polarity reversal region. The diapycnal diffusivity is higher at the front of one internal solitary wave and gradually decreases from shallow to deep water in the vertical direction. Our results also indicate that (1) the enhanced diapycnal diffusivity is related to reflection seismic events, (2) convective instability and shear instability may both contribute to the enhanced diapycnal mixing in the polarity-reversing process, and (3) the difference between our results and Richardson-number-dependent turbulence parameterizations is about 2–3 orders of magnitude, but its vertical distribution is almost the same.

Description: Localization is widely used in data assimilation schemes to mitigate the impact of sampling errors on ensemble-derived background error covariance matrices. Strongly coupled data assimilation allows observations in one component of a coupled model to directly impact another component through the inclusion of cross-domain terms in the background error covariance matrix. When different components have disparate dominant spatial scales, localization between model domains must properly account for the multiple length scales at play. In this work, we develop two new multivariate localization functions, one of which is a multivariate extension of the fifth-order piecewise rational Gaspari–Cohn localization function; the within-component localization functions are standard Gaspari–Cohn with different localization radii, while the cross-localization function is newly constructed. The functions produce positive semidefinite localization matrices which are suitable for use in both Kalman filters and variational data assimilation schemes. We compare the performance of our two new multivariate localization functions to two other multivariate localization functions and to the univariate and weakly coupled analogs of all four functions in a simple experiment with the bivariate Lorenz 96 system. In our experiments, the multivariate Gaspari–Cohn function leads to better performance than any of the other multivariate localization functions.

Description: We revisit three variants of the well-known Stommel diagrams that have been used to summarize knowledge of characteristic scales in time and space of some important hydrologic phenomena and modified these diagrams focusing on spatiotemporal scaling analyses of the underlying hydrologic processes. In the present paper we focus on soil formation, vegetation growth, and drainage network organization. We use existing scaling relationships for vegetation growth and soil formation, both of which refer to the same fundamental length and timescales defining flow rates at the pore scale but different powers of the power law relating time and space. The principle of a hierarchical organization of optimal subsurface flow paths could underlie both root lateral spread (RLS) of vegetation and drainage basin organization. To assess the applicability of scaling, and to extend the Stommel diagrams, data for soil depth, vegetation root lateral spread, and drainage basin length have been accessed. The new data considered here include timescales out to 150 Myr that correspond to depths of up to 240 m and horizontal length scales up to 6400 km and probe the limits of drainage basin development in time, depth, and horizontal extent.

Description: Non-Gaussian forecast error is a challenge for ensemble-based data assimilation (DA), particularly for more nonlinear convective dynamics. In this study, we investigate the degree of the non-Gaussianity of forecast error distributions at 1 km resolution using a 1000-member ensemble Kalman filter, and how it is affected by the DA update frequency and observation number. Regional numerical weather prediction experiments are performed with the SCALE (Scalable Computing for Advanced Library and Environment) model and the LETKF (local ensemble transform Kalman filter) assimilating phased array radar observations every 30 s. The results show that non-Gaussianity develops rapidly within convective clouds and is sensitive to the DA frequency and the number of assimilated observations. The non-Gaussianity is reduced by up to 40 % when the assimilation window is shortened from 5 min to 30 s, particularly for vertical velocity and radar reflectivity.

Description: Most available verification metrics for ensemble forecasts focus on univariate quantities. That is, they assess whether the ensemble provides an adequate representation of the forecast uncertainty about the quantity of interest at a particular location and time. For spatially indexed ensemble forecasts, however, it is also important that forecast fields reproduce the spatial structure of the observed field and represent the uncertainty about spatial properties such as the size of the area for which heavy precipitation, high winds, critical fire weather conditions, etc., are expected. In this article we study the properties of the fraction of threshold exceedance (FTE) histogram, a new diagnostic tool designed for spatially indexed ensemble forecast fields. Defined as the fraction of grid points where a prescribed threshold is exceeded, the FTE is calculated for the verification field and separately for each ensemble member. It yields a projection of a – possibly high-dimensional – multivariate quantity onto a univariate quantity that can be studied with standard tools like verification rank histograms. This projection is appealing since it reflects a spatial property that is intuitive and directly relevant in applications, though it is not obvious whether the FTE is sufficiently sensitive to misrepresentation of spatial structure in the ensemble. In a comprehensive simulation study we find that departures from uniformity of the FTE histograms can indeed be related to forecast ensembles with biased spatial variability and that these histograms detect shortcomings in the spatial structure of ensemble forecast fields that are not obvious by eye. For demonstration, FTE histograms are applied in the context of spatially downscaled ensemble precipitation forecast fields from NOAA's Global Ensemble Forecast System.

Description: In this paper, the performance of three machine-learning methods for predicting short-term evolution and for reproducing the long-term statistics of a multiscale spatiotemporal Lorenz 96 system is examined. The methods are an echo state network (ESN, which is a type of reservoir computing; hereafter RC–ESN), a deep feed-forward artificial neural network (ANN), and a recurrent neural network (RNN) with long short-term memory (LSTM; hereafter RNN–LSTM). This Lorenz 96 system has three tiers of nonlinearly interacting variables representing slow/large-scale (X), intermediate (Y), and fast/small-scale (Z) processes. For training or testing, only X is available; Y and Z are never known or used. We show that RC–ESN substantially outperforms ANN and RNN–LSTM for short-term predictions, e.g., accurately forecasting the chaotic trajectories for hundreds of numerical solver's time steps equivalent to several Lyapunov timescales. The RNN–LSTM outperforms ANN, and both methods show some prediction skills too. Furthermore, even after losing the trajectory, data predicted by RC–ESN and RNN–LSTM have probability density functions (pdf's) that closely match the true pdf – even at the tails. The pdf of the data predicted using ANN, however, deviates from the true pdf. Implications, caveats, and applications to data-driven and data-assisted surrogate modeling of complex nonlinear dynamical systems, such as weather and climate, are discussed.

Description: This article presents the results of a bifurcation analysis of a simple energy balance model (EBM) for the future climate of the Earth. The main focus is on the following question: can the nonlinear processes intrinsic to atmospheric physics, including natural positive feedback mechanisms, cause a mathematical bifurcation of the climate state, as a consequence of continued anthropogenic forcing by rising greenhouse gas emissions? Our analysis shows that such a bifurcation could cause an abrupt change to a drastically different climate state in the EBM, which is warmer and more equable than any climate existing on Earth since the Pliocene epoch. In previous papers, with this EBM adapted to paleoclimate conditions, it was shown to exhibit saddle-node and cusp bifurcations, as well as hysteresis. The EBM was validated by the agreement of its predicted bifurcations with the abrupt climate changes that are known to have occurred in the paleoclimate record, in the Antarctic at the Eocene–Oligocene transition (EOT) and in the Arctic at the Pliocene–Paleocene transition (PPT). In this paper, the EBM is adapted to fit Anthropocene climate conditions, with emphasis on the Arctic and Antarctic climates. The four Representative Concentration Pathways (RCP) considered by the IPCC (Intergovernmental Panel on Climate Change) are used to model future CO2 concentrations, corresponding to different scenarios of anthropogenic activity. In addition, the EBM investigates four naturally occurring nonlinear feedback processes which magnify the warming that would be caused by anthropogenic CO2 emissions alone. These four feedback mechanisms are ice–albedo feedback, water vapour feedback, ocean heat transport feedback, and atmospheric heat transport feedback. The EBM predicts that a bifurcation resulting in a catastrophic climate change, to a pre-Pliocene-like climate state, will occur in coming centuries for an RCP with unabated anthropogenic forcing, amplified by these positive feedbacks. However, the EBM also predicts that appropriate reductions in carbon emissions may limit climate change to a more tolerable continuation of what is observed today. The globally averaged version of this EBM has an equilibrium climate sensitivity (ECS) of 4.34 K, near the high end of the likely range reported by the IPCC.

Description: The seismic section image contains a wealth of texture detail information, which is important for the interpretation of the formation profile information. In order to enhance the texture detail of the image while keeping the structural information of the image intact, a multi-scale enhancement method based on wavelet transform is proposed. Firstly, the image is wavelet decomposed to obtain a low-frequency structural component and a series of high-frequency texture detail components. Secondly, bilateral texture filtering is performed on the low-frequency structural components to filter out high-frequency noise while maintaining the edges of the image; adaptive enhancement is performed on the high-frequency detail components to filter out low-frequency noise while enhancing detail. Finally, the processed high- and low-frequency components reconstructed by wavelets can obtain a seismic section image with enhanced detail. The method of this paper enhances the texture detail information in the image while preserving the edge of the image.

Description: Many applications require wind gust estimates at very different atmospheric height levels. For example, the renewable energy sector is interested in wind and gust predictions at the hub height of a wind power plant. However, numerical weather prediction models typically only derive estimates for wind gusts at the standard measurement height of 10 m above the land surface. Here, we present a statistical post-processing method to derive a conditional distribution for hourly peak wind speed as a function of height. The conditioning variables are taken from the COSMO-REA6 regional reanalysis. The post-processing method was trained using peak wind speed observations at five vertical levels between 10 and 250 m from the Hamburg Weather Mast. The statistical post-processing method is based on a censored generalized extreme value (cGEV) distribution with non-homogeneous parameters. We use a least absolute shrinkage and selection operator to select the most informative variables. Vertical variations of the cGEV parameters are approximated using Legendre polynomials, such that predictions may be derived at any desired vertical height. Further, the Pickands dependence function is used to assess dependencies between gusts at different heights. The most important predictors are the 10 m gust diagnostic, the barotropic and the baroclinic mode of absolute horizontal wind speed, the mean absolute horizontal wind at 700 hPa, the surface pressure tendency, and the lifted index. Proper scores show improvements of up to 60 % with respect to climatology, especially at higher vertical levels. The post-processing model with a Legendre approximation is able to provide reliable predictions of gusts' statistics at non-observed intermediate levels. The strength of dependency between gusts at different levels is non-homogeneous and strongly modulated by the vertical stability of the atmosphere.

Description: Analysing palaeoclimate proxy time series using windowed recurrence network analysis (wRNA) has been shown to provide valuable information on past climate variability. In turn, it has also been found that the robustness of the obtained results differs among proxies from different palaeoclimate archives. To systematically test the suitability of wRNA for studying different types of palaeoclimate proxy time series, we use the framework of forward proxy modelling. For this, we create artificial input time series with different properties and compare the areawise significant anomalies detected using wRNA of the input and the model output time series. Also, taking into account results for general filtering of different time series, we find that the variability of the network transitivity is altered for stochastic input time series while being rather robust for deterministic input. In terms of significant anomalies of the network transitivity, we observe that these anomalies may be missed by proxies from tree and lake archives after the non-linear filtering by the corresponding proxy system models. For proxies from speleothems, we additionally observe falsely identified significant anomalies that are not present in the input time series. Finally, for proxies from ice cores, the wRNA results show the best correspondence to those for the input data. Our results contribute to improve the interpretation of windowed recurrence network analysis results obtained from real-world palaeoclimate time series.

Description: Statistical post-processing of ensemble forecasts, from simple linear regressions to more sophisticated techniques, is now a well-known procedure for correcting biased and poorly dispersed ensemble weather predictions. However, practical applications in national weather services are still in their infancy compared to deterministic post-processing. This paper presents two different applications of ensemble post-processing using machine learning at an industrial scale. The first is a station-based post-processing of surface temperature and subsequent interpolation to a grid in a medium-resolution ensemble system. The second is a gridded post-processing of hourly rainfall amounts in a high-resolution ensemble prediction system. The techniques used rely on quantile regression forests (QRFs) and ensemble copula coupling (ECC), chosen for their robustness and simplicity of training regardless of the variable subject to calibration. Moreover, some variants of classical techniques used, such as QRF and ECC, were developed in order to adjust to operational constraints. A forecast anomaly-based QRF is used for temperature for a better prediction of cold and heat waves. A variant of ECC for hourly rainfall was built, accounting for more realistic longer rainfall accumulations. We show that both forecast quality and forecast value are improved compared to the raw ensemble. Finally, comments about model size and computation time are made.

Description: Baroclinic and barotropic instabilities are well known as the mechanisms responsible for the production of the dominant energy-containing eddies in the atmospheres of Earth and several other planets, as well as Earth's oceans. Here we consider insights provided by both linear and nonlinear instability theories into the conditions under which such instabilities may occur, with reference to forced and dissipative flows obtainable in the laboratory, in simplified numerical atmospheric circulation models and in the planets of our solar system. The equilibration of such instabilities is also of great importance in understanding the structure and energetics of the observable circulation of atmospheres and oceans. Various ideas have been proposed concerning the ways in which baroclinic and barotropic instabilities grow to a large amplitude and saturate whilst also modifying their background flow and environment. This remains an area that continues to challenge theoreticians and observers, though some progress has been made. The notion that such instabilities may act under some conditions to adjust the background flow towards a critical state is explored here in the context of both laboratory systems and planetary atmospheres. Evidence for such adjustment processes is found relating to baroclinic instabilities under a range of conditions where the efficiency of eddy and zonal-mean heat transport may mutually compensate in maintaining a nearly invariant thermal structure in the zonal mean. In other systems, barotropic instabilities may efficiently mix potential vorticity to result in a flow configuration that is found to approach a marginally unstable state with respect to Arnol'd's second stability theorem. We discuss the implications of these findings and identify some outstanding open questions.

Description: The description of the relationship between interplanetary plasma and geomagnetic activity requires complex models. Drastically reducing the ambition of describing this detailed complex interaction and, if we are interested only in the fractality properties of the time series of its characteristic parameters, a magnetohydrodynamic (MHD) shell model forced using solar wind data might provide a possible novel approach. In this paper we study the relation between the activity of the magnetic energy dissipation rate obtained in one such model, which may describe geomagnetic activity, and the fractal dimension of the forcing. In different shell model simulations, the forcing is provided by the solution of a Langevin equation where a white noise is implemented. This forcing, however, has been shown to be unsuitable for describing the solar wind action on the model. Thus, we propose to consider the fluctuations of the product between the velocity and the magnetic field solar wind data as the noise in the Langevin equation, the solution of which provides the forcing in the magnetic field equation. We compare the fractal dimension of the magnetic energy dissipation rate obtained, of the magnetic forcing term, and of the fluctuations of v⋅bz, with the activity of the magnetic energy dissipation rate. We examine the dependence of these fractal dimensions on the solar cycle. We show that all measures of activity have a peak near solar maximum. Moreover, both the fractal dimension computed for the fluctuations of v⋅bz time series and the fractal dimension of the magnetic forcing have a minimum near solar maximum. This suggests that the complexity of the noise term in the Langevin equation may have a strong effect on the activity of the magnetic energy dissipation rate.

Description: For most statistical postprocessing schemes used to correct weather forecasts, changes to the forecast model induce a considerable reforecasting effort. We present a new approach based on response theory to cope with slight model changes. In this framework, the model change is seen as a perturbation of the original forecast model. The response theory allows us then to evaluate the variation induced on the parameters involved in the statistical postprocessing, provided that the magnitude of this perturbation is not too large. This approach is studied in the context of a simple Ornstein–Uhlenbeck model and then on a more realistic, yet simple, quasi-geostrophic model. The analytical results for the former case help to pose the problem, while the application to the latter provides a proof of concept and assesses the potential performance of response theory in a chaotic system. In both cases, the parameters of the statistical postprocessing used – the Error-in-Variables Model Output Statistics (EVMOS) method – are appropriately corrected when facing a model change. The potential application in an operational environment is also discussed.

Description: There is much observational evidence of different fine structures in the ionosphere and magnetosphere of the Earth. Such structures are created and evolve as a perturbation of the ionosphere's parameters. Instead of dealing with a number of linear waves, we propose to investigate and follow up the perturbations in the ionosphere by dynamics of soliton structure. Apart from the fact that this is a more accurate solution, the advantage of soliton solution is its localization in space and time as a consequence of the balance between nonlinearity and dispersion. The existence of such a structure is driven by the properties of the medium. We derive the necessary condition for having a nonlinear soliton wave, taking the vortex shape as a description of the ionosphere parameter perturbation. We employ a magnetohydrodynamical description for the ionosphere in plane geometry, including rotational effects, magnetic field effects via ponderomotive force, and pressure and gravitational potential effects, treating the problem self-consistently and nonlinearly. In addition, we consider compressible perturbation. As a result, we have found that Coriolis force and magnetic force on the one hand and pressure and gravity on the other hand determine dispersive properties. Dispersion at higher latitudes is mainly driven by rotation, while near the Equator, within the E and F layers of the ionosphere, the magnetic field modifies the soliton solution. Also, a very general description of the ionosphere results in the conclusion that the unperturbed thickness of the ionosphere layer cannot be taken as an ad hoc assumption: it is rather a consequence of equilibrium property, which is shown in this calculation.

Description: Stochastic subgrid parameterizations enable ensemble forecasts of fluid dynamic systems and ultimately accurate data assimilation (DA). Stochastic advection by Lie transport (SALT) and models under location uncertainty (LU) are recent and similar physically based stochastic schemes. SALT dynamics conserve helicity, whereas LU models conserve kinetic energy (KE). After highlighting general similarities between LU and SALT frameworks, this paper focuses on their common challenge: the parameterization choice. We compare uncertainty quantification skills of a stationary heterogeneous data-driven parameterization and a non-stationary homogeneous self-similar parameterization. For stationary, homogeneous surface quasi-geostrophic (SQG; QG) turbulence, both parameterizations lead to high-quality ensemble forecasts. This paper also discusses a heterogeneous adaptation of the homogeneous parameterization targeted at a better simulation of strong straight buoyancy fronts.

Description: In atmospheric chemistry, a parameter called residence time is defined for each gas as T=M/F, where M represents the mass of the gas in the atmosphere and F is the total average influx or outflux, which in time averages are equal. In this brief communication, we extend this concept from matter to energy which is also a conservative quantity and estimate the average residence time of energy in the atmosphere, which amounts to about 58 d. A similar estimation for the residence time of energy in the Sun is of the order of 107 years, which agrees with the Kelvin–Helmholtz timescale.

Description: Ideally, perturbation schemes in ensemble forecasts should be based on the statistical properties of the model errors. Often, however, the statistical properties of these model errors are unknown. In practice, the perturbations are pragmatically modelled and tuned to maximize the skill of the ensemble forecast. In this paper a general methodology is developed to diagnose the model error, linked to a specific physical process, based on a comparison between a target and a reference model. Here, the reference model is a configuration of the ALADIN (Aire Limitée Adaptation Dynamique Développement International) model with a parameterization of deep convection. This configuration is also run with the deep-convection parameterization scheme switched off, degrading the forecast skill. The model error is then defined as the difference of the energy and mass fluxes between the reference model with scale-aware deep-convection parameterization and the target model without deep-convection parameterization. In the second part of the paper, the diagnosed model-error characteristics are used to stochastically perturb the fluxes of the target model by sampling the model errors from a training period in such a way that the distribution and the vertical and multivariate correlation within a grid column are preserved. By perturbing the fluxes it is guaranteed that the total mass, heat and momentum are conserved. The tests, performed over the period 11–20 April 2009, show that the ensemble system with the stochastic flux perturbations combined with the initial condition perturbations not only outperforms the target ensemble, where deep convection is not parameterized, but for many variables it even performs better than the reference ensemble (with scale-aware deep-convection scheme). The introduction of the stochastic flux perturbations reduces the small-scale erroneous spread while increasing the overall spread, leading to a more skillful ensemble. The impact is largest in the upper troposphere with substantial improvements compared to other state-of-the-art stochastic perturbation schemes. At lower levels the improvements are smaller or neutral, except for temperature where the forecast skill is degraded.

Description: We apply a coupled modelling system composed of a state-of-the-art hydrodynamical model and a low-complexity biogeochemical model to an idealized Iberian Peninsula upwelling system to identify the main drivers of dissolved-oxygen variability and to study its response to changes in the duration of the upwelling season and in the phytoplankton growth regime. We find that the export of oxygenated waters by upwelling front turbulence is a major sink for nearshore dissolved oxygen. In our simulations of summer upwelling, when the phytoplankton population is generally dominated by diatoms whose growth is boosted by nutrient input, net primary production and air–sea exchange compensate dissolved-oxygen depletion by offshore export over the shelf. A shorter upwelling duration causes a relaxation of upwelling winds and a decrease in offshore export, resulting in a slight increase of net dissolved-oxygen enrichment in the coastal region as compared to longer upwelling durations. When phytoplankton is dominated by groups less sensitive to nutrient inputs, growth rates decrease, and the coastal region becomes net heterotrophic. Together with the physical sink, this lowers the net oxygenation rate of coastal waters, which remains positive only because of air–sea exchange. These findings help in disentangling the physical and biogeochemical controls of dissolved oxygen in upwelling systems and, together with projections of increased duration of upwelling seasons and phytoplankton community changes, suggest that the Iberian coastal upwelling region may become more vulnerable to hypoxia and deoxygenation.

Description: Many practical applications of statistical post-processing methods for ensemble weather forecasts require accurate modeling of spatial, temporal, and inter-variable dependencies. Over the past years, a variety of approaches has been proposed to address this need. We provide a comprehensive review and comparison of state-of-the-art methods for multivariate ensemble post-processing. We focus on generally applicable two-step approaches where ensemble predictions are first post-processed separately in each margin and multivariate dependencies are restored via copula functions in a second step. The comparisons are based on simulation studies tailored to mimic challenges occurring in practical applications and allow ready interpretation of the effects of different types of misspecifications in the mean, variance, and covariance structure of the ensemble forecasts on the performance of the post-processing methods. Overall, we find that the Schaake shuffle provides a compelling benchmark that is difficult to outperform, whereas the forecast quality of parametric copula approaches and variants of ensemble copula coupling strongly depend on the misspecifications at hand.

Description: Climate change is expressed as a climate system transiting from the initial state to a new state in a short time. The period between the initial state and the new state is defined as the transition process, which is the key part for connecting the two states. By using a piece-wise function, the transition process is stated approximately (Mudelsee, 2000). However, the dynamic processes are not included in the piece-wise function. Thus, we proposed a method (Yan et al., 2015, 2016) to fit the transition process by using a continuous function. In this paper, this method is further developed for predicting the uncompleted transition process based on the dynamic characteristics of the continuous function. We introduce this prediction method in detail and apply it to three ideal time sequences and the Pacific Decadal Oscillation (PDO). The PDO is a long-lasting El Niño-like pattern of Pacific climate variability (Barnett et al., 1999; Newman et al., 2016). A new quantitative relationship during the transition process has been revealed, and it explores a nonlinear relationship between the linear trend and the amplitude (difference) between the initial state and the end state. As the transition process begins, the initial state and the linear trend are estimated. Then, according to the relationship, the end state and end moment of the uncompleted transition process are predicted.

Description: An initial dimension reduction forms an integral part of many analyses in climate science. Different methods yield low-dimensional representations that are based on differing aspects of the data. Depending on the features of the data that are relevant for a given study, certain methods may be more suitable than others, for instance yielding bases that can be more easily identified with physically meaningful modes. To illustrate the distinction between particular methods and identify circumstances in which a given method might be preferred, in this paper we present a set of case studies comparing the results obtained using the traditional approaches of empirical orthogonal function analysis and k-means clustering with the more recently introduced methods such as archetypal analysis and convex coding. For data such as global sea surface temperature anomalies, in which there is a clear, dominant mode of variability, all of the methods considered yield rather similar bases with which to represent the data while differing in reconstruction accuracy for a given basis size. However, in the absence of such a clear scale separation, as in the case of daily geopotential height anomalies, the extracted bases differ much more significantly between the methods. We highlight the importance in such cases of carefully considering the relevant features of interest and of choosing the method that best targets precisely those features so as to obtain more easily interpretable results.

Description: The scientific problems posed by the Earth's atmosphere, oceans, cryosphere – along with the land surface and biota that interact with them – are central to major socioeconomic and political concerns in the 21st century. It is natural, therefore, that a certain impatience should prevail in attempting to solve these problems. The point of a review paper published in this journal in 2001 was that one should proceed with all diligence but not excessive haste, namely “festina lente”, i.e., “to hurry in a measured way”. The earlier paper traced the necessary progress through the solutions of 10 problems, starting with “What can we predict beyond 1 week, for how long, and by what methods?” and ending with “Can we achieve enlightened climate control of our planet by the end of the century?” A unified framework was proposed to deal with these problems in succession, from the shortest to the longest timescale, i.e., from weeks to centuries and millennia. The framework is that of dynamical systems theory, with an emphasis on successive bifurcations and the ergodic theory of nonlinear systems, on the one hand, and on pursuing this approach across a hierarchy of climate models, from the simplest, highly idealized ones to the most detailed ones. Here, we revisit some of these problems, 20 years later,1 and extend the framework to coupled climate–economy modeling.

Description: This paper gives an overview of Deutscher Wetterdienst's (DWD's) postprocessing system called Ensemble-MOS together with its motivation and the design consequences for probabilistic forecasts of extreme events based on ensemble data. Forecasts of the ensemble systems COSMO-D2-EPS and ECMWF-ENS are statistically optimised and calibrated by Ensemble-MOS with a focus on severe weather in order to support the warning decision management at DWD. Ensemble mean and spread are used as predictors for linear and logistic multiple regressions to correct for conditional biases. The predictands are derived from synoptic observations and include temperature, precipitation amounts, wind gusts and many more and are statistically estimated in a comprehensive model output statistics (MOS) approach. Long time series and collections of stations are used as training data that capture a sufficient number of observed events, as required for robust statistical modelling. Logistic regressions are applied to probabilities that predefined meteorological events occur. Details of the implementation including the selection of predictors with testing for significance are presented. For probabilities of severe wind gusts global logistic parameterisations are developed that depend on local estimations of wind speed. In this way, robust probability forecasts for extreme events are obtained while local characteristics are preserved. The problems of Ensemble-MOS, such as model changes and consistency requirements, which occur with the operative MOS systems of the DWD are addressed.

Description: With numerical weather prediction ensembles unable to produce sufficiently calibrated forecasts, statistical post-processing is needed to correct deterministic and probabilistic biases. Over the past decades, a number of methods addressing this issue have been proposed, with ensemble model output statistics (EMOS) and Bayesian model averaging (BMA) among the most popular. They are able to produce skillful deterministic and probabilistic forecasts for a wide range of applications. These methods are usually applied to the newest model run as soon as it has finished, before the entire forecast trajectory is issued. RAFT (rapid adjustment of forecast trajectories), a recently proposed novel approach, aims to improve these forecasts even further, utilizing the error correlation patterns between lead times. As soon as the first forecasts are verified, we start updating the remainder of the trajectory based on the newly gathered error information. As RAFT works particularly well in conjunction with other post-processing methods like EMOS and techniques designed to reconstruct the multivariate dependency structure like ensemble copula coupling (ECC), we look to identify the optimal combination of these methods. In our study, we apply multi-stage post-processing to wind speed forecasts from the UK Met Office's convective-scale MOGREPS-UK ensemble and analyze results for short-range forecasts at a number of sites in the UK and the Republic of Ireland.

Description: Non-homogeneous regression is a frequently used post-processing method for increasing the predictive skill of probabilistic ensemble weather forecasts. To adjust for seasonally varying error characteristics between ensemble forecasts and corresponding observations, different time-adaptive training schemes, including the classical sliding training window, have been developed for non-homogeneous regression. This study compares three such training approaches with the sliding-window approach for the application of post-processing near-surface air temperature forecasts across central Europe. The predictive performance is evaluated conditional on three different groups of stations located in plains, in mountain foreland, and within mountainous terrain, as well as on a specific change in the ensemble forecast system of the European Centre for Medium-Range Weather Forecasts (ECMWF) used as input for the post-processing. The results show that time-adaptive training schemes using data over multiple years stabilize the temporal evolution of the coefficient estimates, yielding an increased predictive performance for all station types tested compared to the classical sliding-window approach based on the most recent days only. While this may not be surprising under fully stable model conditions, it is shown that “remembering the past” from multiple years of training data is typically also superior to the classical sliding-window approach when the ensemble prediction system is affected by certain model changes. Thus, reducing the variance of the non-homogeneous regression estimates due to increased training data appears to be more important than reducing its bias by adapting rapidly to the most current training data only.

Description: Universal multifractals (UMs) have been widely used to simulate and characterize, with the help of only two physically meaningful parameters, geophysical fields that are extremely variable across a wide range of scales. Such a framework relies on the assumption that the underlying field is generated through a multiplicative cascade process. Derived analysis techniques have been extended to study correlations between two fields not only at a single scale and for a single statistical moment as with the covariance, but across scales and for all moments. Such a framework of joint multifractal analysis is used here as a starting point to develop and test an approach enabling correlations between UM fields to be analysed and approximately simulated. First, the behaviour of two fields consisting of renormalized multiplicative power law combinations of two UM fields is studied. It appears that in the general case the resulting fields can be well approximated by UM fields with known parameters. Limits of this approximation will be quantified and discussed. Techniques to retrieve the UM parameters of the underlying fields as well as the exponents of the combination have been developed and successfully tested on numerical simulations. In a second step tentative correlation indicators are suggested. Finally the suggested approach is implemented to study correlation across scales of detailed rainfall data collected with the help of disdrometers of the Fresnel platform of Ecole des Ponts ParisTech (see available data at https://hmco.enpc.fr/portfolio-archive/taranis-observatory/, last access: 12 March 2020). More precisely, four quantities are used: the rain rate (R), the liquid water content (LWC) and the total drop concentration (Nt) along with the mass weighed diameter (Dm), which are commonly used to characterize the drop size distribution. Correlations across scales are quantified. Their relative strength (very strong between R and LWC, strong between DSD features and R or LWC, almost null between Nt and Dm) is discussed.

Description: The auroral oval boundary represents an important physical process with implications for the ionosphere and magnetosphere. An automatic auroral oval boundary prediction method based on deep learning in this paper is applied to study the variation of the auroral oval boundary associated with different space physical parameters. We construct an auroral oval boundary dataset to train our proposed model, which consists of 184 416 auroral oval boundary points extracted from 3842 images captured by the Ultraviolet Imager (UVI) of the Polar satellite and its corresponding 18 space physical parameters selected from the OMNI dataset from December 1996 to March 1997. Furthermore, several statistical experiments and correlation analysis experiments are performed based on our dataset to explore the relationship between space physical parameters and the location of the auroral oval boundary. The experiment results show that the prediction model based on the deep learning method can estimate the auroral oval boundary efficiently, and different space physical parameters have different effects on the auroral oval boundary, especially the interplanetary magnetic field (IMF), geomagnetic indexes, and solar wind parameters.

Description: Crucial to the development of earthquake forecasting schemes is the manifestation of spatiotemporal correlations between earthquakes as highlighted, for example, by the notion of aftershocks. Here, we present an analysis of the statistical relation between subsequent magnitudes of a recently proposed self-similar aftershock rates model of seismicity, whose main distinguishing feature is that of interdependence between trigger and triggered events in terms of a time-varying frequency–magnitude distribution. By means of a particular statistical measure, we study the level of magnitude correlations under specific types of time conditioning, explain their provenance within the model framework and show that the type of null model chosen in the analysis plays a pivotal role in the type and strength of observed correlations. Specifically, we show that while the variations in the magnitude distribution can give rise to large trivial correlations between subsequent magnitudes, the non-trivial magnitude correlations are rather minimal. Simulations mimicking southern California (SC) show that these non-trivial correlations cannot be observed at the 3σ level using real-world catalogs for the magnitude of completeness as a reference. We conclude that only the time variations in the frequency–magnitude distribution might lead to significant improvements in earthquake forecasting.

Description: Major geomagnetic storms are caused by unusually intense solar wind southward magnetic fields that impinge upon the Earth's magnetosphere (Dungey, 1961). How can we predict the occurrence of future interplanetary events? Do we currently know enough of the underlying physics and do we have sufficient observations of solar wind phenomena that will impinge upon the Earth's magnetosphere? We view this as the most important challenge in space weather. We discuss the case for magnetic clouds (MCs), interplanetary sheaths upstream of interplanetary coronal mass ejections (ICMEs), corotating interaction regions (CIRs) and solar wind high-speed streams (HSSs). The sheath- and CIR-related magnetic storms will be difficult to predict and will require better knowledge of the slow solar wind and modeling to solve. For interplanetary space weather, there are challenges for understanding the fluences and spectra of solar energetic particles (SEPs). This will require better knowledge of interplanetary shock properties as they propagate and evolve going from the Sun to 1 AU (and beyond), the upstream slow solar wind and energetic “seed” particles. Dayside aurora, triggering of nightside substorms, and formation of new radiation belts can all be caused by shock and interplanetary ram pressure impingements onto the Earth's magnetosphere. The acceleration and loss of relativistic magnetospheric “killer” electrons and prompt penetrating electric fields in terms of causing positive and negative ionospheric storms are reasonably well understood, but refinements are still needed. The forecasting of extreme events (extreme shocks, extreme solar energetic particle events, and extreme geomagnetic storms (Carrington events or greater)) are also discussed. Energetic particle precipitation into the atmosphere and ozone destruction are briefly discussed. For many of the studies, the Parker Solar Probe, Solar Orbiter, Magnetospheric Multiscale Mission (MMS), Arase, and SWARM data will be useful.

Description: The basis and challenge of strongly coupled data assimilation (CDA) is the accurate representation of cross-domain covariances between various coupled subsystems with disparate spatio-temporal scales, where often one or more subsystems are unobserved. In this study, we explore strong CDA using ensemble Kalman filtering methods applied to a conceptual multiscale chaotic model consisting of three coupled Lorenz attractors. We introduce the use of the local attractor dimension (i.e. the Kaplan–Yorke dimension, dimKY) to prescribe the rank of the background covariance matrix which we construct using a variable number of weighted covariant Lyapunov vectors (CLVs). Specifically, we consider the ability to track the nonlinear trajectory of each of the subsystems with different variants of sparse observations, relying only on the cross-domain covariance to determine an accurate analysis for tracking the trajectory of the unobserved subdomain. We find that spanning the global unstable and neutral subspaces is not sufficient at times where the nonlinear dynamics and intermittent linear error growth along a stable direction combine. At such times a subset of the local stable subspace is also needed to be represented in the ensemble. In this regard the local dimKY provides an accurate estimate of the required rank. Additionally, we show that spanning the full space does not improve performance significantly relative to spanning only the subspace determined by the local dimension. Where weak coupling between subsystems leads to covariance collapse in one or more of the unobserved subsystems, we apply a novel modified Kalman gain where the background covariances are scaled by their Frobenius norm. This modified gain increases the magnitude of the innovations and the effective dimension of the unobserved domains relative to the strength of the coupling and timescale separation. We conclude with a discussion on the implications for higher-dimensional systems.

Description: The basin-wide surface transport of tracers such as heat, nutrients and plastic in the North Atlantic Ocean is organized into large-scale flow structures such as the Western Boundary Current and the Subtropical and Subpolar gyres. Being able to identify these features from drifter data is important for studying tracer dispersal but also for detecting changes in the large-scale surface flow due to climate change. We propose a new and conceptually simple method to detect groups of trajectories with similar dynamical behaviour from drifter data using network theory and normalized cut spectral clustering. Our network is constructed from conditional bin-drifter probability distributions and naturally handles drifter trajectories with data gaps and different lifetimes. The eigenvalue problem of the respective Laplacian can be replaced by a singular value decomposition of a related sparse data matrix. The construction of this matrix scales with O(NM+Nτ), where N is the number of particles, M the number of bins and τ the number of time steps. The concept behind our network construction is rooted in a particle's symbolic itinerary derived from its trajectory and a state space partition, which we incorporate in its most basic form by replacing a particle's itinerary by a probability distribution over symbols. We represent these distributions as the links of a bipartite graph, connecting particles and symbols. We apply our method to the periodically driven double-gyre flow and successfully identify well-known features. Exploiting the duality between particles and symbols defined by the bipartite graph, we demonstrate how a direct low-dimensional coarse definition of the clustering problem can still lead to relatively accurate results for the most dominant structures and resolve features down to scales much below the coarse graining scale. Our method also performs well in detecting structures with incomplete trajectory data, which we demonstrate for the double-gyre flow by randomly removing data points. We finally apply our method to a set of ocean drifter trajectories and present the first network-based clustering of the North Atlantic surface transport based on surface drifters, successfully detecting well-known regions such as the Subpolar and Subtropical gyres, the Western Boundary Current region and the Caribbean Sea.

Description: The special issue on advances in post-processing and blending of deterministic and ensemble forecasts is the outcome of several successful successive sessions organized at the General Assembly of the European Geosciences Union. Statistical post-processing and blending of forecasts are currently topics of important attention and development in many countries to produce optimal forecasts. Ten contributions have been received, covering key aspects of current concerns on statistical post-processing, namely the restoration of inter-variable dependences, the impact of model changes on the statistical relationships and how to cope with it, the operational implementation at forecasting centers, the development of appropriate metrics for forecast verification, and finally two specific applications to snow forecasts and seasonal forecasts of the North Atlantic Oscillation.

Description: Dynamical models of various centres have shown in recent years seasonal prediction skill of the North Atlantic Oscillation (NAO). By filtering the ensemble members on the basis of statistical predictors, known as subsampling, it is possible to achieve even higher prediction skill. In this study the aim is to design a generalisation of the subsampling approach and establish it as a post-processing procedure. Instead of selecting discrete ensemble members for each year, as the subsampling approach does, the distributions of ensembles and statistical predictors are combined to create a probabilistic prediction of the winter NAO. By comparing the combined statistical–dynamical prediction with the predictions of its single components, it can be shown that it achieves similar results to the statistical prediction. At the same time it can be shown that, unlike the statistical prediction, the combined prediction has fewer years where it performs worse than the dynamical prediction. By applying the gained distributions to other meteorological variables, like geopotential height, precipitation and surface temperature, it can be shown that evaluating prediction skill depends highly on the chosen metric. Besides the common anomaly correlation (ACC) this study also presents scores based on the Earth mover's distance (EMD) and the integrated quadratic distance (IQD), which are designed to evaluate skills of probabilistic predictions. It shows that by evaluating the predictions for each year separately compared to applying a metric to all years at the same time, like correlation-based metrics, leads to different interpretations of the analysis.

Description: 〈b〉Precision Annealing Monte Carlo Methods for Statistical Data Assimilation: Metropolis-Hastings Procedures〈/b〉〈br〉 Adrian S. Wong, Kangbo Hao, Zheng Fang, and Henry D. I. Abarbanel〈br〉 Nonlin. Processes Geophys. Discuss., https//doi.org/10.5194/npg-2019-1,2019〈br〉 〈b〉Manuscript under review for NPG〈/b〉 (discussion: open, 0 comments)〈br〉 Our paper deals with data assimilation methods for chaotic systems and how one can make predictions from incomplete data of such systems. The method that we chose to explore in detail is a Monte Carlo method with an annealing heuristic. Our results show that Monte Carlo methods are a viable alternatives to the standard set of derivative-based methods. We verify the method using the Lorenz 96 system due to the simplicity of that system.

Description: 〈b〉Mahalanobis distance based recognition of changes in the dynamics of seismic process〈/b〉〈br〉 Teimuraz Matcharashvili, Zbigniew Czechowski, and Natalia Zhukova〈br〉 Nonlin. Processes Geophys. Discuss., https//doi.org/10.5194/npg-2018-57,2019〈br〉 〈b〉Manuscript under review for NPG〈/b〉 (discussion: open, 0 comments)〈br〉 〈p〉In present work we aimed to analyze regularity of seismic process based on all its spatial, temporal and energetic characteristics. Increments of cumulative times, increments of cumulative distances and increments of cumulative seismic energies, have been calculated from southern California earthquake catalogue, 1975 to 2017.〈/p〉 〈p〉Used method of analysis represented combination of multivariate Mahalanobis distance calculation with the surrogate data testing. Prior to proceed to the analysis of dynamical features of seismic process we have tested used approach for two different 3 dimensional models in which dynamical features were changed from more regular to the more randomized conditions by adding some extent of noises.〈/p〉 〈p〉Analysis of variability in the extent of regularity of seismic process have been accomplished for different representative threshold values.〈/p〉 〈p〉According to results of our analysis about third part of considered 50 data windows, the original seismic process is indistinguishable from random process by its features of temporal, spatial and energetic variability. It was shown that prior to strong earthquake occurrences, in periods of relatively small earthquakes generation, percentage of windows in which seismic process is indistinguishable from random process essentially increases (to 60–80 %). At the same time, in periods of aftershock activity in all considered windows the process of small earthquake generation become regular and thus is strongly different from randomized catalogues.〈/p〉 〈p〉 〈/p〉 〈p〉In some periods of catalogue time span seismic process looks closer to randomness while in other cases it becomes closer to regular behavior. Exactly, in periods of relatively decreased earthquake generation activity (at smaller energy release), seismic process looks random-like while in periods of occurrence of strong events, followed by series of aftershocks, it reveal significant deviation from randomness – the extent of regularity essentially increases. The period, for which such deviation from the random behavior can last, depends on the amount of seismic energy released by the strong earthquake.〈/p〉

Description: The dynamics of three local models, for momentum transfer at the air–sea interface, is compared. The models differ by whether or not the ocean velocity is included in the shear calculation applied to the ocean and the atmosphere. All three cases are employed in climate or ocean simulations. Analytic calculations for the models with deterministic and random forcing (white and coloured) are presented. The short-term behaviour is similar in all models, with only small quantitative differences, while the long-term behaviour differs qualitatively between the models. The fluctuation–dissipation relation, which connects the fast atmospheric motion to the slow oceanic dynamics, is established for all models with random forcing. The fluctuation–dissipation theorem, which compares the response to an external forcing to internal fluctuations, is established for a white-noise forcing and a coloured forcing when the phase space is augmented by the forcing variable. Using results from numerical integrations of stochastic differential equations, we show that the fluctuation theorem, which compares the probability of positive to negative fluxes of the same magnitude, averaged over time intervals of varying lengths, holds for the energy gained by the ocean from the atmosphere.

Description: Ever since its inception, the ensemble Kalman filter (EnKF) has elicited many heuristic approaches that sought to improve it. One such method is covariance localization, which alleviates spurious correlations due to finite ensemble sizes by using relevant spatial correlation information. Adaptive localization techniques account for how correlations change in time and space, in order to obtain improved covariance estimates. This work develops a Bayesian approach to adaptive Schur-product localization for the deterministic ensemble Kalman filter (DEnKF) and extends it to support multiple radii of influence. We test the proposed adaptive localization using the toy Lorenz'96 problem and a more realistic 1.5-layer quasi-geostrophic model. Results with the toy problem show that the multivariate approach informs us that strongly observed variables can tolerate larger localization radii. The univariate approach leads to markedly improved filter performance for the realistic geophysical model, with a reduction in error by as much as 33 %.

Description: The importance of chaotic advection relative to turbulent diffusion is investigated in an idealized model of a 3-D swirling and overturning ocean eddy. Various measures of stirring and mixing are examined in order to determine when and where chaotic advection is relevant. Turbulent diffusion is alternatively represented by (1) an explicit, observation-based, scale-dependent diffusivity, (2) stochastic noise, added to a deterministic velocity field, or (3) explicit and implicit diffusion in a spectral numerical model of the Navier–Stokes equations. Lagrangian chaos in our model occurs only within distinct regions of the eddy, including a large chaotic “sea” that fills much of the volume near the perimeter and central axis of the eddy and much smaller “resonant” bands. The size and distribution of these regions depend on factors such as the degree of axial asymmetry of the eddy and the Ekman number. The relative importance of chaotic advection and turbulent diffusion within the chaotic regions is quantified using three measures: the Lagrangian Batchelor scale, the rate of dispersal of closely spaced fluid parcels, and the Nakamura effective diffusivity. The role of chaotic advection in the stirring of a passive tracer is generally found to be most important within the larger chaotic seas, at intermediate times, with small diffusivities, and for eddies with strong asymmetry. In contrast, in thin chaotic regions, turbulent diffusion at oceanographically relevant rates is at least as important as chaotic advection. Future work should address anisotropic and spatially varying representations of turbulent diffusion for more realistic models.

Description: The transient electromagnetic method (TEM) is extremely important in geophysics. However, the secondary field signal (SFS) in the TEM received by coil is easily disturbed by random noise, sensor noise and man-made noise, which results in the difficulty in detecting deep geological information. To reduce the noise interference and detect deep geological information, we apply autoencoders, which make up an unsupervised learning model in deep learning, on the basis of the analysis of the characteristics of the SFS to denoise the SFS. We introduce the SFSDSA (secondary field signal denoising stacked autoencoders) model based on deep neural networks of feature extraction and denoising. SFSDSA maps the signal points of the noise interference to the high-probability points with a clean signal as reference according to the deep characteristics of the signal, so as to realize the signal denoising and reduce noise interference. The method is validated by the measured data comparison, and the comparison results show that the noise reduction method can (i) effectively reduce the noise of the SFS in contrast with the Kalman, principal component analysis (PCA) and wavelet transform methods and (ii) strongly support the speculation of deeper underground features.

Description: This research intends to characterize the South Atlantic Anomaly (SAA) by applying the power spectrum analysis approach. The motivation to study the SAA region is due to its nature. A comparison was made between the stations in the SAA region and outside the SAA region during the geomagnetic storm occurrence (active period) and the normal period where no geomagnetic storm occurred. The horizontal component of the data of the Earth's magnetic field for the occurrence of the active period was taken on 11 March 2011 while for the normal period it was taken on 3 February 2011. The data sample rate used is 1 min. The outcome of the research revealed that the SAA region had a tendency to be persistent during both periods. It can be said that the region experiences these characteristics because of the Earth's magnetic field strength. Through the research, it is found that as the Earth's magnetic field increases, it is likely to show an antipersistent value. This is found in the high-latitude region. The lower the Earth's magnetic field, the more it shows the persistent value as in the middle latitude region. In the region where the Earth's magnetic field is very low like the SAA region it shows a tendency to be persistent.

Description: We investigate the geometrical structure of instabilities in the two-scale Lorenz 96 model through the prism of Lyapunov analysis. Our detailed study of the full spectrum of covariant Lyapunov vectors reveals the presence of a slow bundle in tangent space, composed by a set of vectors with a significant projection onto the slow degrees of freedom; they correspond to the smallest (in absolute value) Lyapunov exponents and thereby to the longer timescales. We show that the dimension of the slow bundle is extensive in the number of both slow and fast degrees of freedom and discuss its relationship with the results of a finite-size analysis of instabilities, supporting the conjecture that the slow-variable behavior is effectively determined by a nontrivial subset of degrees of freedom. More precisely, we show that the slow bundle corresponds to the Lyapunov spectrum region where fast and slow instability rates overlap, “mixing” their evolution into a set of vectors which simultaneously carry information on both scales. We suggest that these results may pave the way for future applications to ensemble forecasting and data assimilations in weather and climate models.

Description: Crustal thickness is an important factor affecting lithospheric structure and deep geodynamics. In this paper, a deep learning neural network based on a stacked sparse auto-encoder is proposed for the inversion of crustal thickness in eastern Tibet and the western Yangtze craton. First, with the phase velocity of the Rayleigh surface wave as input and the theoretical crustal thickness as output, 12 deep-sSAE neural networks are constructed, which are trained by 380 000 and tested by 120 000 theoretical models. We then invert the observed phase velocities through these 12 neural networks. According to the test error and misfit of other crustal thickness models, the optimal crustal thickness model is selected as the crustal thickness of the study area. Compared with other ways to detect crustal thickness such as seismic wave reflection and receiver function, we adopt a new way for inversion of earth model parameters, and realize that a deep learning neural network based on data driven with the highly non-linear mapping ability can be widely used by geophysicists, and our result has good agreement with high-resolution crustal thickness models. Compared with other methods, our experimental results based on a deep learning neural network and a new Rayleigh wave phase velocity model reveal some details: there is a northward-dipping Moho gradient zone in the Qiangtang block and a relatively shallow north-west–south-east oriented crust at the Songpan–Ganzi block. Crustal thickness around Xi'an and the Ordos basin is shallow, about 35 km. The change in crustal thickness in the Sichuan–Yunnan block is sharp, where crustal thickness is 60 km north-west and 35 km south-east. We conclude that the deep learning neural network is a promising, efficient, and believable geophysical inversion tool.

Description: Statistical hypothesis tests in wavelet analysis are methods that assess the degree to which a wavelet quantity (e.g., power and coherence) exceeds background noise. Commonly, a point-wise approach is adopted in which a wavelet quantity at every point in a wavelet spectrum is individually compared to the critical level of the point-wise test. However, because adjacent wavelet coefficients are correlated and wavelet spectra often contain many wavelet quantities, the point-wise test can produce many false positive results that occur in clusters or patches. To circumvent the point-wise test drawbacks, it is necessary to implement the recently developed area-wise, geometric, cumulative area-wise, and topological significance tests, which are reviewed and developed in this paper. To improve the computational efficiency of the cumulative area-wise test, a simplified version of the testing procedure is created based on the idea that its output is the mean of individual estimates of statistical significance calculated from the geometric test applied at a set of point-wise significance levels. Ideal examples are used to show that the geometric and cumulative area-wise tests are unable to differentiate wavelet spectral features arising from singularity-like structures from those associated with periodicities. A cumulative arc-wise test is therefore developed to strictly test for periodicities by using normalized arclength, which is defined as the number of points composing a cross section of a patch divided by the wavelet scale in question. A previously proposed topological significance test is formalized using persistent homology profiles (PHPs) measuring the number of patches and holes corresponding to the set of all point-wise significance values. Ideal examples show that the PHPs can be used to distinguish time series containing signal components from those that are purely noise. To demonstrate the practical uses of the existing and newly developed statistical methodologies, a first comprehensive wavelet analysis of Indian rainfall is also provided. An R software package has been written by the author to implement the various testing procedures.

Description: Climate and weather conditions in the mid-latitudes are strongly driven by the large-scale atmosphere circulation. Observational data indicate that important components of the large-scale circulation have changed in recent decades, including the strength and the width of the Hadley cell, jets, storm tracks and planetary waves. Here, we use a new statistical–dynamical atmosphere model (SDAM) to test the individual sensitivities of the large-scale atmospheric circulation to changes in the zonal temperature gradient, meridional temperature gradient and global-mean temperature. We analyze the Northern Hemisphere Hadley circulation, jet streams, storm tracks and planetary waves by systematically altering the zonal temperature asymmetry, the meridional temperature gradient and the global-mean temperature. Our results show that the strength of the Hadley cell, storm tracks and jet streams depend, in terms of relative changes, almost linearly on both the global-mean temperature and the meridional temperature gradient, whereas the zonal temperature asymmetry has little or no influence. The magnitude of planetary waves is affected by all three temperature components, as expected from theoretical dynamical considerations. The width of the Hadley cell behaves nonlinearly with respect to all three temperature components in the SDAM. Moreover, some of these observed large-scale atmospheric changes are expected from dynamical equations and are therefore an important part of model validation.

Description: Forecasting the height of new snow (HN) is crucial for avalanche hazard forecasting, road viability, ski resort management and tourism attractiveness. Météo-France operates the PEARP-S2M probabilistic forecasting system, including 35 members of the PEARP Numerical Weather Prediction system, where the SAFRAN downscaling tool refines the elevation resolution and the Crocus snowpack model represents the main physical processes in the snowpack. It provides better HN forecasts than direct NWP diagnostics but exhibits significant biases and underdispersion. We applied a statistical post-processing to these ensemble forecasts, based on non-homogeneous regression with a censored shifted Gamma distribution. Observations come from manual measurements of 24 h HN in the French Alps and Pyrenees. The calibration is tested at the station scale and the massif scale (i.e. aggregating different stations over areas of 1000 km2). Compared to the raw forecasts, similar improvements are obtained for both spatial scales. Therefore, the post-processing can be applied at any point of the massifs. Two training datasets are tested: (1) a 22-year homogeneous reforecast for which the NWP model resolution and physical options are identical to the operational system but without the same initial perturbations; (2) 3-year real-time forecasts with a heterogeneous model configuration but the same perturbation methods. The impact of the training dataset depends on lead time and on the evaluation criteria. The long-term reforecast improves the reliability of severe snowfall but leads to overdispersion due to the discrepancy in real-time perturbations. Thus, the development of reliable automatic forecasting products of HN needs long reforecasts as homogeneous as possible with the operational systems.

Description: Recent research has demonstrated that hidden Markov model (HMM) analysis is an effective tool to classify atmospheric observations of the stably stratified nocturnal boundary layer (SBL) into weakly stable (wSBL) and very stable (vSBL) regimes. Here we consider the development of explicitly stochastic representations of SBL regime dynamics. First, we analyze whether HMM-based SBL regime statistics (the occurrence of regime transitions, subsequent transitions after the first, and very persistent nights) can be accurately represented by “freely running” stationary Markov chains (FSMCs). Our results show that despite the HMM-estimated regime statistics being relatively insensitive to the HMM transition probabilities, these statistics cannot all simultaneously be captured by a FSMC. Furthermore, by construction a FSMC cannot capture the observed non-Markov regime duration distributions. Using the HMM classification of data into wSBL and vSBL regimes, state-dependent transition probabilities conditioned on the bulk Richardson number (RiB) or the stratification are investigated. We find that conditioning on stratification produces more robust results than conditioning on RiB. A prototype explicitly stochastic parameterization is developed based on stratification-dependent transition probabilities, in which turbulence pulses (representing intermittent turbulence events) are added during vSBL conditions. Experiments using an idealized single-column model demonstrate that such an approach can simulate realistic-looking SBL regime dynamics.

Description: Using the solar-wind-driven magnetosphere–ionosphere–thermosphere system, a methodology is developed to reduce a state-vector description of a time-dependent driven system to a composite scalar picture of the activity in the system. The technique uses canonical correlation analysis to reduce the time-dependent system and driver state vectors to time-dependent system and driver scalars, with the scalars describing the response in the system that is most-closely related to the driver. This reduced description has advantages: low noise, high prediction efficiency, linearity in the described system response to the driver, and compactness. The methodology identifies independent modes of reaction of a system to its driver. The analysis of the magnetospheric system is demonstrated. Using autocorrelation analysis, Jensen–Shannon complexity analysis, and permutation-entropy analysis the properties of the derived aggregate scalars are assessed and a new mode of reaction of the magnetosphere to the solar wind is found. This state-vector-reduction technique may be useful for other multivariable systems driven by multiple inputs.

Description: As one of the most active nonlinear inversion methods in transient electromagnetic (TEM) inversion, the back propagation (BP) neural network has high efficiency because the complicated forward model calculation is unnecessary in iteration. The global optimization ability of the particle swarm optimization (PSO) is adopted for amending the BP's sensitivity to its initial parameters, which avoids it falling into a local optimum. A chaotic-oscillation inertia weight PSO (COPSO) is proposed for accelerating convergence. The COPSO-BP algorithm performance is validated by two typical testing functions, two geoelectric models inversions and a field example. The results show that the COPSO-BP method is more accurate, stable and needs relatively less training time. The proposed algorithm has a higher fitting degree for the data inversion, and it is feasible to use it in geophysical inverse applications.

Description: Neural networks are able to approximate chaotic dynamical systems when provided with training data that cover all relevant regions of the system's phase space. However, many practical applications diverge from this idealized scenario. Here, we investigate the ability of feed-forward neural networks to (1) learn the behavior of dynamical systems from incomplete training data and (2) learn the influence of an external forcing on the dynamics. Climate science is a real-world example where these questions may be relevant: it is concerned with a non-stationary chaotic system subject to external forcing and whose behavior is known only through comparatively short data series. Our analysis is performed on the Lorenz63 and Lorenz95 models. We show that for the Lorenz63 system, neural networks trained on data covering only part of the system's phase space struggle to make skillful short-term forecasts in the regions excluded from the training. Additionally, when making long series of consecutive forecasts, the networks struggle to reproduce trajectories exploring regions beyond those seen in the training data, except for cases where only small parts are left out during training. We find this is due to the neural network learning a localized mapping for each region of phase space in the training data rather than a global mapping. This manifests itself in that parts of the networks learn only particular parts of the phase space. In contrast, for the Lorenz95 system the networks succeed in generalizing to new parts of the phase space not seen in the training data. We also find that the networks are able to learn the influence of an external forcing, but only when given relatively large ranges of the forcing in the training. These results point to potential limitations of feed-forward neural networks in generalizing a system's behavior given limited initial information. Much attention must therefore be given to designing appropriate train-test splits for real-world applications.

Description: In this special issue contribution, I provide a personal view on the role of bifurcation analysis of climate models in the development of a theory of climate system variability. The state of the art of the methodology is shortly outlined, and the main part of the paper deals with examples of what has been done and what has been learned. In addressing these issues, I will discuss the role of a hierarchy of climate models, concentrate on results for spatially extended (stochastic) models (having many degrees of freedom) and evaluate the importance of these results for a theory of climate system variability.

Description: Ensemble randomized maximum likelihood (EnRML) is an iterative (stochastic) ensemble smoother, used for large and nonlinear inverse problems, such as history matching and data assimilation. Its current formulation is overly complicated and has issues with computational costs, noise, and covariance localization, even causing some practitioners to omit crucial prior information. This paper resolves these difficulties and streamlines the algorithm without changing its output. These simplifications are achieved through the careful treatment of the linearizations and subspaces. For example, it is shown (a) how ensemble linearizations relate to average sensitivity and (b) that the ensemble does not lose rank during updates. The paper also draws significantly on the theory of the (deterministic) iterative ensemble Kalman smoother (IEnKS). Comparative benchmarks are obtained with the Lorenz 96 model with these two smoothers and the ensemble smoother using multiple data assimilation (ES-MDA).

Description: The Eulerian point of view is the traditional theoretical and numerical tool to describe fluid mechanics. Some modern computational fluid dynamics codes allow for the efficient simulation of particles, in turn facilitating a Lagrangian description of the flow. The existence and persistence of Lagrangian coherent structures in fluid flow has been a topic of considerable study. Here we focus on the ability of Lagrangian methods to characterize mixing in geophysical flows. We study the instability of a strongly non-linear double-jet flow, initially in geostrophic balance, which forms quasi-coherent vortices when subjected to ageostrophic perturbations. Particle clustering techniques are applied to study the behavior of the particles in the vicinity of coherent vortices. Changes in inter-particle distance play a key role in establishing the patterns in particle trajectories. This paper exploits graph theory in finding particle clusters and regions of dense interactions (also known as subclusters). The methods discussed and results presented in this paper can be used to identify mixing in a flow and extract information about particle behavior in coherent structures from a Lagrangian point of view.

Description: In this paper, we study Bragg resonance, i.e., the triad interaction between surface and/or interfacial waves with a bottom ripple, in the presence of background velocity. We show that when one of the constituent waves of the triad has negative energy, the amplitudes of all the waves grow exponentially. This is very different from classic Bragg resonance in which one wave decays to cause the growth of the other. The instabilities we observe are “explosive” and are different from normal mode shear instabilities since our velocity profiles are linearly stable. Our work may explain the existence of large-amplitude internal waves over periodic bottom ripples in the presence of tidal flow observed in oceans and estuaries.

Description: In the present work, we aim to analyse the regularity of a seismic process based on its spatial, temporal, and energetic characteristics. Increments of cumulative times, increments of cumulative distances, and increments of cumulative seismic energies are calculated from an earthquake catalogue for southern California from 1975 to 2017. As the method of analysis, we use the multivariate Mahalanobis distance calculation, combined with a surrogate data testing procedure that is often used for the testing of non-linear structures in complex data sets. Before analysing the dynamical features of the seismic process, we tested the used approach for two different 3-D models in which the dynamical features were changed from more regular to more randomised conditions by adding a certain degree of noise. An analysis of the variability in the extent of regularity of the seismic process was carried out for different completeness magnitude thresholds. The results of our analysis show that in about a third of all the 50-data windows the original seismic process was indistinguishable from a random process based on its features of temporal, spatial, and energetic variability. It was shown that prior to the occurrence of strong earthquakes, mostly in periods of generation of relatively small earthquakes, the percentage of windows in which the seismic process is indistinguishable from a random process increases (to 60 %–80 %). During periods of aftershock activity, the process of small earthquake generation became regular in all of the windows considered, and thus was markedly different from the randomised catalogues. In some periods within the catalogue, the seismic process appeared to be closer to randomness, while in other cases it became closer to a regular behaviour. More specifically, in periods of relatively decreased earthquake generation activity (with low energy release), the seismic process appears to be random, while during periods of occurrence of strong events, followed by series of aftershocks, significant deviation from randomness is shown, i.e. the extent of regularity markedly increases. The period for which such deviation from random behaviour lasts depends on the amount of seismic energy released by the strong earthquake.

Description: The aim of this study is to delineate and identify various mineralized zones and barren host rocks based on surface and subsurface lithogeochemical data from the Pulang porphyry copper deposit, southwestern China, utilizing the number–size (N-S), concentration–volume (C-V) and power-spectrum–volume (S-V) fractal models. The N-S model reveals three mineralized zones characterized by Cu thresholds of 0.28 % and 1.45 %:  1.45 % Cu represents highly mineralized zones. The results obtained by the C-V model depict four geochemical zones defined by Cu thresholds of 0.25 %, 1.48 % and 1.88 %, representing nonmineralized wall rocks (Cu1.88 %). The S-V model is used by performing a 3-D fast Fourier transformation of assay data in the frequency domain. The S-V model reveals three mineralized zones characterized by Cu thresholds of 0.23 % and 1.33 %: 1.33 % Cu represents supergene enrichment zones. All the multifractal models indicate that high-grade mineralization occurs in the central and southern parts of the ore deposit. Their results are compared with the alteration and mineralogical models resulting from the 3-D geological model using a log-ratio matrix. The results show that the S-V model is best at identifying highly mineralized zones in the deposit. However, the results of the C-V model for moderately and weakly mineralized zones are also more accurate than those obtained from the N-S and S-V models.

Description: The stability properties as characterized by the fluctuations of finite-time Lyapunov exponents around their mean values are investigated in a three-level quasi-geostrophic atmospheric model with realistic mean state and variability. Firstly, the covariance structure of the fluctuation field is examined. In order to identify dominant patterns of collective excitation, an empirical orthogonal function (EOF) analysis of the fluctuation field of all of the finite-time Lyapunov exponents is performed. The three leading modes are patterns where the most unstable Lyapunov exponents fluctuate in phase. These modes are virtually independent of the integration time of the finite-time Lyapunov exponents. Secondly, large-deviation rate functions are estimated from time series of finite-time Lyapunov exponents based on the probability density functions and using the Legendre transform method. Serial correlation in the time series is properly accounted for. A large-deviation principle can be established for all of the Lyapunov exponents. Convergence is rather slow for the most unstable exponent, becomes faster when going further down in the Lyapunov spectrum, is very fast for the near-neutral and weakly dissipative modes, and becomes slow again for the strongly dissipative modes at the end of the Lyapunov spectrum. The curvature of the rate functions at the minimum is linked to the corresponding elements of the diffusion matrix. Also, the joint large-deviation rate function for the first and the second Lyapunov exponent is estimated.

Description: We previously performed local ensemble transform Kalman filter (LETKF) experiments with up to 10 240 ensemble members using an intermediate atmospheric general circulation model (AGCM). While the previous study focused on the impact of localization on the analysis accuracy, the present study focuses on the probability density functions (PDFs) represented by the 10 240-member ensemble. The 10 240-member ensemble can resolve the detailed structures of the PDFs and indicates that non-Gaussianity is caused in those PDFs by multimodality and outliers. The results show that the spatial patterns of the analysis errors are similar to those of non-Gaussianity. While the outliers appear randomly, large multimodality corresponds well with large analysis error, mainly in the tropical regions and storm track regions where highly nonlinear processes appear frequently. Therefore, we further investigate the life cycle of multimodal PDFs, and show that they are mainly generated by the on–off switch of convective parameterization in the tropical regions and by the instability associated with advection in the storm track regions. Sensitivity to the ensemble size suggests that approximately 1000 ensemble members are necessary in the intermediate AGCM-LETKF system to represent the detailed structures of non-Gaussian PDFs such as skewness and kurtosis; the higher-order non-Gaussian statistics are more vulnerable to the sampling errors due to a smaller ensemble size.

Description: While nonlinear stochastic partial differential equations arise naturally in spatiotemporal modeling, inference for such systems often faces two major challenges: sparse noisy data and ill-posedness of the inverse problem of parameter estimation. To overcome the challenges, we introduce a strongly regularized posterior by normalizing the likelihood and by imposing physical constraints through priors of the parameters and states. We investigate joint parameter-state estimation by the regularized posterior in a physically motivated nonlinear stochastic energy balance model (SEBM) for paleoclimate reconstruction. The high-dimensional posterior is sampled by a particle Gibbs sampler that combines a Markov chain Monte Carlo (MCMC) method with an optimal particle filter exploiting the structure of the SEBM. In tests using either Gaussian or uniform priors based on the physical range of parameters, the regularized posteriors overcome the ill-posedness and lead to samples within physical ranges, quantifying the uncertainty in estimation. Due to the ill-posedness and the regularization, the posterior of parameters presents a relatively large uncertainty, and consequently, the maximum of the posterior, which is the minimizer in a variational approach, can have a large variation. In contrast, the posterior of states generally concentrates near the truth, substantially filtering out observation noise and reducing uncertainty in the unconstrained SEBM.

Description: A better understanding of precipitation dynamics in the Indian subcontinent is required since India's society depends heavily on reliable monsoon forecasts. We introduce a non-linear, multiscale approach, based on wavelets and event synchronization, for unravelling teleconnection influences on precipitation. We consider those climate patterns with the highest relevance for Indian precipitation. Our results suggest significant influences which are not well captured by only the wavelet coherence analysis, the state-of-the-art method in understanding linkages at multiple timescales. We find substantial variation across India and across timescales. In particular, El Niño–Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD) mainly influence precipitation in the south-east at interannual and decadal scales, respectively, whereas the North Atlantic Oscillation (NAO) has a strong connection to precipitation, particularly in the northern regions. The effect of the Pacific Decadal Oscillation (PDO) stretches across the whole country, whereas the Atlantic Multidecadal Oscillation (AMO) influences precipitation particularly in the central arid and semi-arid regions. The proposed method provides a powerful approach for capturing the dynamics of precipitation and, hence, helps improve precipitation forecasting.

Description: A large earthquake of 8.0 magnitude occurred on 12 May 2008, 14:28 UTC, with the epicentre in Wenchuan. To investigate the pre-earthquake anomalous strain changes, negentropy is introduced to borehole strain data for three locations, approximated by skewness and kurtosis, revealing the non-Gaussianity of recorded fluctuations. We separate the negentropy anomalies from the background by Otsu's method and accumulate the anomaly frequency on different scales. The results show that the long-term cumulative frequency of negentropy anomalies follows a sigmoid behaviour, while the inflection point of the fitting curve is close to the occurrence of the earthquake. For the short-term analysis before the earthquake, there are two cumulative acceleration phases. To further verify the correlation with the earthquake, we compare our findings for different time periods and stations and rule out the possible influence of meteorological factors. We consider the negentropy analysis to exhibit potential for studying pre-earthquake anomalies.

Description: We consider a stochastic differential equation model for Earth's axial magnetic dipole field. Our goal is to estimate the model's parameters using diverse and independent data sources that had previously been treated separately, so that the model is a valid representation of an expanded paleomagnetic record on kyr to Myr timescales. We formulate the estimation problem within the Bayesian framework and define a feature-based posterior distribution that describes probabilities of model parameters given a set of features derived from the data. Numerically, we use Markov chain Monte Carlo (MCMC) to obtain a sample-based representation of the posterior distribution. The Bayesian problem formulation and its MCMC solution allow us to study the model's limitations and remaining posterior uncertainties. Another important aspect of our overall approach is that it reveals inconsistencies between model and data or within the various data sets. Identifying these shortcomings is a first and necessary step towards building more sophisticated models or towards resolving inconsistencies within the data. The stochastic model we derive represents selected aspects of the long-term behavior of the geomagnetic dipole field with limitations and errors that are well defined. We believe that such a model is useful (besides its limitations) for hypothesis testing and give a few examples of how the model can be used in this context.

Description: Recent progress in machine learning has shown how to forecast and, to some extent, learn the dynamics of a model from its output, resorting in particular to neural networks and deep learning techniques. We will show how the same goal can be directly achieved using data assimilation techniques without leveraging on machine learning software libraries, with a view to high-dimensional models. The dynamics of a model are learned from its observation and an ordinary differential equation (ODE) representation of this model is inferred using a recursive nonlinear regression. Because the method is embedded in a Bayesian data assimilation framework, it can learn from partial and noisy observations of a state trajectory of the physical model. Moreover, a space-wise local representation of the ODE system is introduced and is key to coping with high-dimensional models. It has recently been suggested that neural network architectures could be interpreted as dynamical systems. Reciprocally, we show that our ODE representations are reminiscent of deep learning architectures. Furthermore, numerical analysis considerations of stability shed light on the assets and limitations of the method. The method is illustrated on several chaotic discrete and continuous models of various dimensions, with or without noisy observations, with the goal of identifying or improving the model dynamics, building a surrogate or reduced model, or producing forecasts solely from observations of the physical model.

Description: Numerical models solved on adaptive moving meshes have become increasingly prevalent in recent years. Motivating problems include the study of fluids in a Lagrangian frame and the presence of highly localized structures such as shock waves or interfaces. In the former case, Lagrangian solvers move the nodes of the mesh with the dynamical flow; in the latter, mesh resolution is increased in the proximity of the localized structure. Mesh adaptation can include remeshing, a procedure that adds or removes mesh nodes according to specific rules reflecting constraints in the numerical solver. In this case, the number of mesh nodes will change during the integration and, as a result, the dimension of the model's state vector will not be conserved. This work presents a novel approach to the formulation of ensemble data assimilation (DA) for models with this underlying computational structure. The challenge lies in the fact that remeshing entails a different state space dimension across members of the ensemble, thus impeding the usual computation of consistent ensemble-based statistics. Our methodology adds one forward and one backward mapping step before and after the ensemble Kalman filter (EnKF) analysis, respectively. This mapping takes all the ensemble members onto a fixed, uniform reference mesh where the EnKF analysis can be performed. We consider a high-resolution (HR) and a low-resolution (LR) fixed uniform reference mesh, whose resolutions are determined by the remeshing tolerances. This way the reference meshes embed the model numerical constraints and are also upper and lower uniform meshes bounding the resolutions of the individual ensemble meshes. Numerical experiments are carried out using 1-D prototypical models: Burgers and Kuramoto–Sivashinsky equations and both Eulerian and Lagrangian synthetic observations. While the HR strategy generally outperforms that of LR, their skill difference can be reduced substantially by an optimal tuning of the data assimilation parameters. The LR case is appealing in high dimensions because of its lower computational burden. Lagrangian observations are shown to be very effective in that fewer of them are able to keep the analysis error at a level comparable to the more numerous observers for the Eulerian case. This study is motivated by the development of suitable EnKF strategies for 2-D models of the sea ice that are numerically solved on a Lagrangian mesh with remeshing.

Description: An intelligent method is presented for locating a microseismic source based on the particle swarm optimization (PSO) concept. It eliminates microseismic source locating errors caused by the inaccurate velocity model of the earth medium. The method uses, as the target of PSO, a global minimum of the sum of squared discrepancies between differences of modeled arrival times and differences of measured arrival times. The discrepancies are calculated for all pairs of detectors of a seismic monitoring system. Then, the adaptive PSO algorithm is applied to locate the microseismic source and obtain optimal value of the P-wave velocity. The PSO algorithm adjusts inertia weight, accelerating constants, the maximum flight velocity of particles, and other parameters to avoid the PSO algorithm trapping by local optima during the solution process. The origin time of the microseismic event is estimated by minimizing the sum of squared discrepancies between the modeled arrival times and the measured arrival times. This sum is calculated using the obtained estimates of the microseismic source coordinates and P-wave velocity. The effectiveness of the PSO algorithm was verified through inversion of a theoretical model and two analyses of actual data from mine blasts in different locations. Compared with the classic least squares method (LSM), the PSO algorithm displays faster convergence and higher accuracy of microseismic source location. Moreover, there is no need to measure the microseismic wave velocity in advance: the PSO algorithm eliminates the adverse effects caused by error in the P-wave velocity when locating a microseismic source using traditional methods.

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: 〈b〉A Bayesian Approach to Multivariate Adaptive Localization in Ensemble-Based Data Assimilation with Time-Dependent Extensions〈/b〉〈br〉 Andrey A. Popov and Adrian Sandu〈br〉 Nonlin. Processes Geophys. Discuss., https//doi.org/10.5194/npg-2018-45,2018〈br〉 〈b〉Manuscript under review for NPG〈/b〉 (discussion: final response, 3 comments)〈br〉 This work has to do with a small part of existing algorithms that are used in applications such as predicting the weather. We provide empirical evidence that our new technique works well on small, but representative models. This might lead to creating a better weather forecast and potentially saving lives as in the case of hurricane prediction.

Description: 〈b〉Characterising regime behaviour in the stably stratified nocturnal boundary layer on the basis of stationary Markov chains〈/b〉〈br〉 Carsten Abraham and Adam H. Monahan〈br〉 Nonlin. Processes Geophys. Discuss., https//doi.org/10.5194/npg-2018-44,2018〈br〉 〈b〉Manuscript under review for NPG〈/b〉 (discussion: final response, 3 comments)〈br〉 〈p〉Recent research has demonstrated that hidden Markov model (HMM) analysis is an effective tool to classify regimes of the stratified nocturnal boundary layer (SBL) at different tower sites. Here we analyse if SBL regime statistics (the occurrence of regime transitions, subsequent transitions after the first, and very persistent nights) in observations match theoretical calculations obtained from a stationary Markov chain with the goal of developing the foundations of novel Markov-chain-based boundary layer schemes which capture the effects of SBL regime dynamics. The regime statistics of a stationary Markov chain using the best estimate transition probabilities from the HMM analyses generally overestimate occurrence probabilities of regime transitions, resulting in an underestimation of persistent nights. Across the locations considered, sensitivity analyses of transition probability matrices in the HMM and the stationary Markov chain reveal that regimes are generally required to be more persistent in the stationary Markov chain in order to simulate observations accurately. A range of transition probability matrices allowing for a relatively accurate description of the occurrence of at least one transition within a night, multiple transitions, and the mean event durations is identified. The occurrence of very persistent nights (nights without regime transitions) is found to depend highly on the season. Therefore, for better representations of very persistent nights a nonstationary Markov chain linked to external drivers is likely appropriate. The observed transition probability maximum between one and two hours after a previous transition cannot be accounted for by two-state Markov processes (stationary or not). The use of these results in the development of SBL turbulence parameterisations is discussed.〈/p〉

Description: 〈b〉Lyapunov analysis of multiscale dynamics: The slow manifold of the two-scale Lorenz '96 model〈/b〉〈br〉 Mallory Carlu, Francesco Ginelli, Valerio Lucarini, and Antonio Politi〈br〉 Nonlin. Processes Geophys. Discuss., https//doi.org/10.5194/npg-2018-41,2018〈br〉 〈b〉Revised manuscript under review for NPG〈/b〉 (discussion: final response, 4 comments)〈br〉 We explore the nature of instabilities in a well-known meteorological 〈q〉toy〈/q〉 model, the Lorenz 96, to unravel key mechanisms of interaction between scales of different resolutions and time scales. To do so, we use a mathematical machinery known as Lyapunov analysis, allowing us to capture the degrees of chaoticity associated with fundamental directions of instability. We find a non-trivial group of such directions projecting significantly on slow variables, associated with long term dynamics.

Description: 〈b〉Ion acceleration at dipolarization fronts associated with interchange instability in the magnetotail〈/b〉〈br〉 Chao Sun, Yasong Ge, and Haoyu Lu〈br〉 Nonlin. Processes Geophys. Discuss., https//doi.org/10.5194/npg-2018-43,2018〈br〉 〈b〉Revised manuscript under review for NPG〈/b〉 (discussion: final response, 4 comments)〈br〉 In this paper, we used a test particle simulation to investigate ion acceleration at dipolarization fronts (DFs) produced by interchange instability in the magnetotail, by performing a Hall MHD simulation. Test particles were settled in both the pre-DF and post-DF region, most of them exhibited earthward and dawnward drift and then diverted tailward. Numerical simulation results indicate that the ions initially settled behind the front may obtain higher energization.

Description: 〈b〉A denoising stacked autoencoders for transient electromagnetic signal denoising〈/b〉〈br〉 Fanqiang Lin, Kecheng Chen, Xuben Wang, Hui Cao, Danlei Chen, and Fanzeng Chen〈br〉 Nonlin. Processes Geophys. Discuss., https//doi.org/10.5194/npg-2018-39,2018〈br〉 〈b〉Revised manuscript accepted for NPG〈/b〉 (discussion: closed, 6 comments)〈br〉 The deep-seated information is reflected in the late-stage data of the second field. By introducing the deep learning algorithm integrated with the characteristics of the secondary field data, it can map the contaminated data in late track data to a high probability position. By comparing several filtering algorithms, the stack noise reduction from the encoder method can reduce the MAE, it is conducive to the subsequent pumping processing to further improve the effective detection depth.

Description: 〈b〉Exploring the effects of missing data on the estimation of fractal and multifractal parameters based on bootstrap method〈/b〉〈br〉 Xin Gao and Xuan Wang〈br〉 Nonlin. Processes Geophys. Discuss., https//doi.org/10.5194/npg-2018-38,2018〈br〉 〈b〉Manuscript under review for NPG〈/b〉 (discussion: final response, 3 comments)〈br〉 An observation series obtained in the natural world is often incomplete and contains many missing values, however, many natural phenomena are concerned with fractals or multifractals, therefore, the fractal modeling of a time series with missing values has certain uncertainties, In this study, the simulation and actual data were used to statistically infer the estimation accuracy of the time series containing missing values and four kinds of interpolated series.

Description: 〈b〉Nonlinear effects in 4D-Var〈/b〉〈br〉 Massimo Bonavita, Peter Lean, and Elias Holm〈br〉 Nonlin. Processes Geophys., 25, 713-729, https://doi.org/10.5194/npg-25-713-2018, 2018〈br〉 This paper deals with the effects of nonlinearity in a state-of-the-art atmospheric global data assimilation system. It is shown that these effects have become increasingly important over the years due to increased model resolution and use of nonlinear observations. The ability to deal with nonlinearities has thus become a crucial asset of data assimilation algorithms. At ECMWF this is done in a perturbative fashion. Advantages and limitations of this technique are discussed.

Description: 〈b〉A comprehensive model for the kyr and Myr time scales of Earth's axial magnetic dipole field〈/b〉〈br〉 Matthias Morzfeld and Bruce A. Buffett〈br〉 Nonlin. Processes Geophys. Discuss., https//doi.org/10.5194/npg-2018-42,2018〈br〉 〈b〉Manuscript under review for NPG〈/b〉 (discussion: final response, 2 comments)〈br〉 We discuss how to calibrate simplified models of the geomagnetic dipole field to data collected over the past 2 Myrs over two different time scales.

Description: 〈b〉The onset of chaos in nonautonomous dissipative dynamical systems: a low-order ocean-model case study〈/b〉〈br〉 Stefano Pierini, Mickaël D. Chekroun, and Michael Ghil〈br〉 Nonlin. Processes Geophys., 25, 671-692, https://doi.org/10.5194/npg-25-671-2018, 2018〈br〉 A four-dimensional nonlinear spectral ocean model is used to study the transition to chaos induced by periodic forcing in systems that are nonchaotic in the autonomous limit. The analysis makes use of ensemble simulations and of the system's pullback attractors. A new diagnostic method characterizes the transition to chaos: this is found to occur abruptly at a critical value and begins with the intermittent emergence of periodic oscillations with distinct phases.

Description: 〈b〉Chaotic dynamics and the role of covariance inflation for reduced rank Kalman filters with model error〈/b〉〈br〉 Colin Grudzien, Alberto Carrassi, and Marc Bocquet〈br〉 Nonlin. Processes Geophys., 25, 633-648, https://doi.org/10.5194/npg-25-633-2018, 2018〈br〉 Using the framework Lyapunov vectors, we analyze the asymptotic properties of ensemble based Kalman filters and how these are influenced by dynamical chaos, especially in the context of random model errors and small ensemble sizes. Particularly, we show a novel derivation of the evolution of forecast uncertainty for ensemble-based Kalman filters with weakly-nonlinear error growth, and discuss its impact for filter design in geophysical models.

Description: 〈b〉Comparison of stochastic parameterizations in the framework of a coupled ocean–atmosphere model〈/b〉〈br〉 Jonathan Demaeyer and Stéphane Vannitsem〈br〉 Nonlin. Processes Geophys., 25, 605-631, https://doi.org/10.5194/npg-25-605-2018, 2018〈br〉 We investigate the modeling of the effects of the unresolved scales on the large scales of the coupled ocean–atmosphere model MAOOAM. Two different physically based stochastic methods are considered and compared, in various configurations of the model. Both methods show remarkable performances and are able to model fundamental changes in the model dynamics. Ways to improve the parameterizations' implementation are also proposed.

Description: 〈b〉Climatic responses to systematic time variations of parameters: a dynamical approach〈/b〉〈br〉 Catherine Nicolis〈br〉 Nonlin. Processes Geophys., 25, 649-658, https://doi.org/10.5194/npg-25-649-2018, 2018〈br〉 Ordinarily the climatic impact of systematic variations of parameters arising from anthropogenic effects is addressed on the basis of large numerical models, where parameters are set to a prescribed level and the system is subsequently left to relax. We have revisited the problem from a nonlinear dynamics perspective in which the time variation of parameters is fully incorporated into the evolution laws. Some universal trends of the response have been identified.

Description: 〈b〉Role of nonlinear interaction between water and plant in stability analysis of nonspatial plants〈/b〉〈br〉 Guodong Sun and Xiaodong Zeng〈br〉 Nonlin. Processes Geophys. Discuss., https//doi.org/10.5194/npg-2018-36,2018〈br〉 〈b〉Publication in NPG not foreseen〈/b〉 (discussion: closed, 4 comments)〈br〉 In this study, a theoretical ecosystem model is applied to discuss a stability of plant using linear and nonlinear methods. Through analyzing the nonlinear dynamics of the theoretical model, it is found that the nonlinear interaction between plant and water play more important role to a transitions between two equilibriums states than the evaporation and the plant losses expressed by linear terms in the theoretical model.

Description: 〈b〉Cascade processes in rapidly rotating turbulence〈/b〉〈br〉 Maxim Reshetnyak and Oleg Pokhotelov〈br〉 Nonlin. Processes Geophys. Discuss., https//doi.org/10.5194/npg-2018-37,2018〈br〉 〈b〉Manuscript under review for NPG〈/b〉 (discussion: final response, 2 comments)〈br〉 The interaction of waves can lead to inverse cascades, when energy is transferred from small scales to large ones. In dynamo theory, this corresponds to the alpha-effect, where turbulence generates large-scale magnetic field, in two-dimensional hydrodynamic turbulence transfer of kinetic energy from small scales to large ones is observed. We suggest simple analytical model that explains existence of inverse cascades of kinetic energy in rapidly rotating turbulence.

Description: 〈b〉Ensemble variational assimilation as a probabilistic estimator – Part 1: The linear and weak non-linear case〈/b〉〈br〉 Mohamed Jardak and Olivier Talagrand〈br〉 Nonlin. Processes Geophys., 25, 565-587, https://doi.org/10.5194/npg-25-565-2018, 2018〈br〉 Ensemble variational assimilation (EnsVAR) has been implemented on two small-dimension non-linear chaotic toy models, as well as on a linearized version of those models. In the linear case, EnsVAR is exactly Bayesian and produced highly reliable ensembles. In the non-linear case, EnsVAR, implemented on temporal windows on the order of magnitude of the predictability time of the systems, shows as good performance as in the exactly linear case. EnsVar is as good an estimator as EnKF and PF.

Description: 〈b〉Internal waves in marginally stable abyssal stratified flows〈/b〉〈br〉 Nikolay Makarenko, Janna Maltseva, Eugene Morozov, Roman Tarakanov, and Kseniya Ivanova〈br〉 Nonlin. Processes Geophys., 25, 659-669, https://doi.org/10.5194/npg-25-659-2018, 2018〈br〉 The problem on internal waves in a weakly stratified two-layered fluid is studied semi-analytically. We discuss the 2.5-layer fluid flows with exponential stratification of both layers. The long-wave model describing travelling waves is constructed by means of a scaling procedure with a small Boussinesq parameter. It is demonstrated that solitary-wave regimes can be affected by the Kelvin–Helmholtz instability arising due to interfacial velocity shear in upstream flow.

Description: 〈b〉A novel approach for solving CNOPs and its application in identifying sensitive regions of tropical cyclone adaptive observations〈/b〉〈br〉 Linlin Zhang, Bin Mu, Shijin Yuan, and Feifan Zhou〈br〉 Nonlin. Processes Geophys., 25, 693-712, https://doi.org/10.5194/npg-25-693-2018, 2018〈br〉 We propose a novel approach to solve conditional nonlinear optimal perturbation for identifying sensitive areas for tropical cyclone adaptive observations. This method is free of adjoint models and overcomes two obstacles, not having adjoint models and having dimensions higher than the problem space. All experimental results prove that it is a meaningful and effective method for solving CNOP and provides a new way for such research. This work aims to solve CNOP and identify sensitive areas.

Description: 〈b〉Ensemble variational assimilation as a probabilistic estimator – Part 2: The fully non-linear case〈/b〉〈br〉 Mohamed Jardak and Olivier Talagrand〈br〉 Nonlin. Processes Geophys., 25, 589-604, https://doi.org/10.5194/npg-25-589-2018, 2018〈br〉 EnsVAR is fundamentally successful in that, even in conditions where Bayesianity cannot be expected, it produces ensembles which possess a high degree of statistical reliability. In non-linear strong-constraint cases, EnsVAR has been successful here only through the use of quasi-static variational assimilation. In the weak-constraint case, without QSVA, EnsVAR provided new evidence as to the favourable effect.

Description: 〈b〉On the phase dependence of the soliton collisions in the Dyachenko–Zakharov envelope equation〈/b〉〈br〉 Dmitry Kachulin and Andrey Gelash〈br〉 Nonlin. Processes Geophys., 25, 553-563, https://doi.org/10.5194/npg-25-553-2018, 2018〈br〉 We consider the nonlinear model well known in geophysics for deep water surface gravity waves – the envelope version of the Dyachenko–Zakharov equation. This model predicts that waves can propagate as a stable localized groups – solitons. We study numerically in detail the soliton collisions and find fundamentally different effects when compared to the previously known results. We demonstrate the formation of extreme amplitude waves that may cause serious damage appearing in seas and oceans.

Description: 〈b〉Asymptotes of the nonlinear transfer and wave spectrum in the frame of the kinetic equation solution〈/b〉〈br〉 Vladislav G. Polnikov, Fangli Qiao, and Yong Teng〈br〉 Nonlin. Processes Geophys. Discuss., https//doi.org/10.5194/npg-2018-35,2018〈br〉 〈b〉Revised manuscript not accepted〈/b〉 (discussion: closed, 7 comments)〈br〉 The Hasselmann kinetic equation for gravity waves (describing wave turbulence) was solved numerically with the aim of searching for features of the Kolmogorov turbulence. Two versions of the numerical algorithm are used, preserving values of total wave action and energy, because both of them are not preserved. In every case, the solutions result in formation of the same self-similar spectrum shape, with the frequency tail 〈i〉S(ω) ~ ω〈/i〉〈sup〉−4〈/sup〉, what contradicts to applicability the Kolmogorov approach.