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Estimating climate response to observed and projected increases in atmospheric greenhouse gases usually requires averaging among multiple independent simulations of computationally expensive global climate models to filter out the spontaneous internal climate variability. Studies have shown that advanced pattern recognition methods allow one to obtain accurate estimates of the forced climate signal from just a handful of such climate realizations. The accuracy of these methods for a fixed ensemble size, however, decreases with an increasing magnitude of the low-frequency, decadal and longer internal climate variability. Here we generalize a previously developed Bayesian methodology of Linear Dynamical Mode (LDM) decomposition for spatially extended time series to enable joint identification and analysis of forced signal and internal variability in ensembles of climate simulations, a methodology dubbed here an ensemble LDM, or ELDM. The new ELDM method is shown to outperform its pattern-recognition competitors by more accurately isolating the forced signal in small ensembles of both toy- and state-of-the-art climate-model simulations. It is able to do so by explicitly recognizing a non-random structure of the internal variability, identified by the ELDM algorithm alongside the optimal forced-signal estimate, which allows one to study possible dynamical connections between the two types of variability. The optimal ELDM filtering provides a unique opportunity for objective intercomparison of decadal and longer climate variability across different global climate models --- a task that proved difficult due to uncertainties associated with the noisy character and limited length of historical climate simulations combined with parameter uncertainties of alternative signal-detection methods.

The paper presents the results of numerical simulation of three-dimensional turbulent flow around a hydraulic turbine guide vane at the angle of attack of 9° with the aspect ratio of the foil equal to 0.8. The influence of turbulence modeling variants on 3D flow effects is analyzed. The 3D boundary layer separation at the vane-sidewall junctions and the flow separation near the trailing edge influence the flow pattern. The study considered various approaches for modeling of a turbulent flow, such as the k-ω SST turbulent viscosity model and several variants of the differential and algebraic Reynolds stress models. At the given angle of attack, the k-ω SST model shows a significant separation zone in the corners between the wall and the vane, while no separation of the flow in the central plane is observed. Both differential and algebraic Reynolds stress models reproduce the secondary vortex flow at the corners and suppress the flow separation near the central cross section.

In this work the interval stability concept is used for study the stability of the Earth’s climate system during last 2.6 million years. For the study we used an empirical model of the Earth’s climate in the Pleistocene [1] which was constructed on the basis of LR04 stack data. By means of this model, we analysed dependence of the Pleistocene climate interval stability on time, and compare the results with the behavior of local linear stability. We find that the global climate resilience to any perturbations decreases throughout the Pleistocene and the nonlinearity plays significant role in this phenomenon. The work was carried out within the framework of the Program for the Development of the Regional Scientifc and Educational Mathematical Center "Mathematics of Future Technologies", project #075-02-2020-1483/1.1. Mukhin, D., Gavrilov, A., Loskutov, E. et al. Bayesian Data Analysis for Revealing Causes of the Middle Pleistocene Transition. Sci Rep 9, 7328 (2019). https://doi.org/10.1038/s41598-019-43867-3

In this work, we demonstrate the performance of a new data-driven method [1] for modeling cross-interacting processes with different time scales represented by time series with different sampling steps. The model is a generalization of a nonlinear stochastic model of evolution operator based on neural networks, designed for the case of time series with constant sampling step, and has complex structure. First, it describes each process by its own stochastic evolution operator with its own time step. Second, it considers possible nonlinear connections within each pair of processes in both directions. These connections are parameterized asymmetrically, depending on which process is faster and which process is slower. They make this model essentially different from the set of independent stochastic models constructed individually for each time scale. All evolution operators and connections are trained and optimized using Bayesian framework, forming a multi-scale stochastic model. We demonstrate the capabilities of the model using two climate data examples. The first example is a climate spatio-temporal data generated by a global climate model running in the middle 19th century external conditions. A second example is spatially distributed reanalysis data describing current climate evolution. In both examples we investigate first how correctly the multiscale model reconstructs the individual evolution of both subsystems, and second whether it reveals the connection between processes that is not captured by models built individually for each process.The work was supported by the Russian Science Foundation (Grant No. 20-62-46056).[1] Gavrilov et al. (2021). Data-driven stochastic model for cross-interacting processes with different time scales, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-4199.

The results of numerical simulation of cavitating flow around the experimental model of a guide vane of a water turbine are given. The possibilities of the detached eddy simulation (DES) method for calculating the flow dynamics around the hydrofoil in two regimes at 3° and 9° angles of attack are analyzed. The mean flow velocity inside the boundary layer is compared with the experimental data. The dimensions and shape of the three-dimensional vapor cavity are presented in various operating regimes. The cavity dynamics and induced pulsations are analyzed.

Two-dimensional flow around a semi-circular profile at the zero angle of attack and at Re = 50000 on the self-oscillatory period is extensively studied by the URANS method involving the standard semi-empirical SST turbulence models, the SST turbulence model with the correction for streamline curvature modified within the Rodi-Leschziner-Isaev and Smirnov-Menter approaches, as well as involving Hanjalic's four-parameter eddy viscosity elliptic relaxation model and its analog - eddy viscosity elliptic blending model proposed in the present work. This has been done with the use of different-structure grids (multiblock with structured overlapping and unstructured composite). Different numerical approximation methods realized in six codes (VP2/3, SigmaFlow, Fluent, CFX, OpenFOAM, and StarCCM+) are used. An underestimation (up to 30%) of time-averaged integral aerodynamic loads is revealed by means of the standard near-wall SST model. This is explained by the high vortex viscosity production in the profile wake. Wind tunnel tests show that the location of cutoff washers on the semi-circular profile provides a quasi-two-dimensional flow around it and allows applying measurement data to verify two-dimensional turbulent flow. The best agreement of experimental results and numerical predictions when comparing the Strouhal number and time-averaged surface pressure coefficient distributions is achieved using both the modified SST model with the correction for streamline curvature and the modified eddy viscosity elliptic blending model. When the SST model with the correction for streamline curvature, modified within the Rodi-Leschziner-Isaev, Smirnov-Menter and Durbin approaches, is used, all the above codes yield close predictions of a vertical aerodynamic load on the oscillation period.

Currently, causes of the middle Pleistocene transition (MPT) – the onset of large-amplitude glacial variability with 100 kyr time scale instead of regular 41 kyr cycles before – are a challenging puzzle in Paleoclimatology. Here we show how a Bayesian data analysis based on machine learning approaches can help to reveal the main mechanisms underlying the Pleistocene variability, which most likely explain proxy records and can be used for testing existing theories. We construct a Bayesian data-driven model from benthic δ 18O records (LR04 stack) accounting for the main factors which may potentially impact climate of the Pleistocene: internal climate dynamics, gradual trends, variations of insolation, and millennial variability. In contrast to some theories, we uncover that under long-term trends in climate, the strong glacial cycles have appeared due to internal nonlinear oscillations induced by millennial noise. We find that while the orbital Milankovitch forcing does not matter for the MPT onset, the obliquity oscillation phase-locks the climate cycles through the meridional gradient of insolation.

The paper presents the results of an investigation into drilling mud flow with cuttings in a vertical well. The drilling mud rheology was described with the Herschel-Bulkley model. The axial Reynolds number was around 1000, the flow regime changing together with drill pipe RPM. The investigation covered the flow’s structures, integral parameters and cuttings transport in relation to drill pipe RPM and rate of penetration (ROP). In the laminar flow, most of the particles were localized in the quasi-solid region to move together with the last; the integral parameters had little dependence on drill pipe RPM increase. Increasing drill pipe RPM resulted in formation of the Görtler vortices near the channel’s external and internal walls, whose interaction led to the formation of smaller eddies converting the flow into a turbulent one. Due to the turbulence dispersion, the region taken by the particles widened. Particles suppress the vortex intensity near the channel’s external wall. Under the conditions described, increasing drill pipe RPM and ROP resulted in higher pressure drops and lower transport efficiency.

The loss of autocorrelations of tropical sea surface temperatures (SST) during late spring, also called the spring predictability barrier (SPB), is a factor that strongly limits the predictability ...

We investigate the decadal-to-centennial ENSO variability based on nonlinear data-driven stochastic modeling. We construct data-driven model of yearly Niño-3.4 indices reconstructed from paleoclimate proxies based on three different sea-surface temperature (SST) databases at the time interval from 1150 to 1995 [1]. The data-driven model is forced by the solar activity and CO2 concentration signals. We find the persistent antiphasing relationship between the solar forcing and Niño-3.4 SST on the bicentennial time scale. The dynamical mechanism of such a response is discussed.The work was supported by the Russian Science Foundation (Grant No. 20-62-46056)1. Emile-Geay, J., Cobb, K. M., Mann, M. E., & Wittenberg, A. T. (2013). Estimating Central Equatorial Pacific SST Variability over the Past Millennium. Part II: Reconstructions and Implications, Journal of Climate, 26(7), 2329-2352.

Interseasonal forecasting of El Niño Southern Oscillation (ENSO), which is traditionally based on data of tropical sea surface temperatures (SST), is in high demand due to the impacts of ENSO on regional climatic conditions around the world as well as the global climate. Improvements in the quality of data in recent decades have led to the active use of statistical ENSO models, which compete with physical models in predictive power. The main disadvantage of statistical forecasts is the pronounced seasonal growth of uncertainty when predicting the upcoming summer-fall ENSO conditions from winter-spring months (so called the spring predictability barrier (SPB)). Recent studies show that Pacific atmospheric circulation anomalies in winter-spring may have a long-term impact on the summer tropical climate via the SST footprint. Here, we infer an index based on sea level pressure (SLP) data from February-March in a single area surrounding Hawaii, and show that this area is the most informative part of the large SLP pattern initiating the SST footprinting mechanism. We define the Hawaiian index (HI) as the mean SLP anomalies in the region (130N-190N, 1500W-1600W) averaged over February-March and demonstrate that the statistical AR model of the Niño 3.4 index taking the HI as a forcing is better in the Bayesian sense and delivers significantly better multimonth predictions. In fact, the HI forcing in the model substantially lowers the SPB and hence increases the predictability of the whole June-May ENSO cycle for forecasts starting in spring. Thus, we can recommend that modelers test the HI as an additional predictor in statistical ENSO models.This research was supported by the Russian Science Foundation (Contract 19-42-04121)

An analysis of the climate system is usually complicated by its very high dimensionality and its nonlinearity which impedes spatial and time scale separation. An even more difficult problem is to obtain separate estimates of the climate system’s response to external forcing (e.g. anthropogenic emissions of greenhouse gases and aerosols) and the contribution of the climate system’s internal variability into recent climate trends. Identification of spatiotemporal climatic patterns representing forced signals and internal variability in global climate models (GCMs) would make it possible to characterize these patterns in the observed data and to analyze dynamical relationships between these two types of climate variability.In contrast with real climate observations, many GCMs are able to provide ensembles of many climate realizations under the same external forcing, with relatively independent initial conditions (e.g. LENS [1], MPI-GE [2], CMIP ensembles of 20th century climate). In this report, a recently developed method of empirical spatio-temporal data decomposition into linear dynamical modes (LDMs) [3] based on Bayesian approach, is modified to address the problem of self-consistent separation of the climate system internal variability modes and the forced response signals in such ensembles. The LDM method provides the time series of principal components and corresponding spatial patterns; in application to an ensemble of realizations, it determines both time series of the internal variability modes of current realization and the time series of forced response (defined as signal shared by all realizations). The advantage of LDMs is the ability to take into account the time scales of the system evolution better than some other linear techniques, e.g. traditional empirical orthogonal function decomposition. Furthermore, the modified ensemble LDM (E-LDM) method is designed to determine the optimal number of principal components and to distinguish their time scales for both internal variability modes and forced response signals.The technique and results of applying LDM method to different GCM ensemble realizations will be presented and discussed. This research was supported by the Russian Science Foundation (Grant No. 18-12-00231).[1] Kay, J. E., Deser, C., Phillips, A., Mai, A., Hannay, C., Strand, G., Arblaster, J., Bates, S., Danabasoglu, G., Edwards, J., Holland, M. Kushner, P., Lamarque, J.-F., Lawrence, D., Lindsay, K., Middleton, A., Munoz, E., Neale, R., Oleson, K., Polvani, L., and M. Vertenstein (2015), The Community Earth System Model (CESM) Large Ensemble Project: A Community Resource for Studying Climate Change in the Presence of Internal Climate Variability, Bulletin of the American Meteorological Society, doi: 10.1175/BAMS-D-13-00255.1, 96, 1333-1349 [2] Maher, N., Milinski, S., Suarez-Gutierrez, L., Botzet, M., Dobrynin, M., Kornblueh, L., Kröger, J., Takano, Y., Ghosh, R., Hedemann, C., Li, C., Li, H., Manzini, E., Notz, N., Putrasahan, D., Boysen, L., Claussen, M., Ilyina, T., Olonscheck, D., Raddatz, T., Stevens, B. and Marotzke, J. (2019). The Max Planck Institute Grand Ensemble: Enabling the Exploration of Climate System Variability. Journal of Advances in Modeling Earth Systems, 11, 1-21. https://doi.org/10.1029/2019MS001639[3] Gavrilov, A., Kravtsov, S., Mukhin, D. (2020). Analysis of 20th century surface air temperature using linear dynamical modes. Chaos: An Interdisciplinary Journal of Nonlinear Science, 30(12), 123110. https://doi.org/10.1063/5.0028246

The problem of modeling interaction between processes with different time scales is very important in geoscience. In this report, we propose a new form of empirical evolution operator model based on the analysis of multiple time series representing processes with different time scales. We assume that the time series are given on the same time interval.To construct the model, we extend the previously developed general form of nonlinear stochastic model based on artificial neural networks and designed for the case of time series with constant sampling interval [1]. This sampling interval is related to the main time scale of the process under consideration, which is described by the deterministic component of the model, while the faster time scales are modeled by its stochastic component, possibly depending on the system’s state. This model also includes slower processes in the form of weak time-dependence, as well as external forcing. The structure of the model is optimized using Bayesian approach [1]. The model has proven its efficiency in a number of applications [2-4].The idea of modeling time series with different time scales is to formulate the above-described model individually for each time scale, and then to include the parameterized influence of the other time scales in it. Particularly, the influence of “slower” time series is included in the form of parameter trends, and the influence of “faster” time series is included by time-averaging their statistics. The algorithm and first results of comparison between the new model and the model without cross-interactions will be discussed.The work was supported by the Russian Science Foundation (Grant No. 20-62-46056).1. Gavrilov, A., Loskutov, E., & Mukhin, D. (2017). Bayesian optimization of empirical model with state-dependent stochastic forcing. Chaos, Solitons & Fractals, 104, 327–337. http://doi.org/10.1016/j.chaos.2017.08.0322. Mukhin, D., Kondrashov, D., Loskutov, E., Gavrilov, A., Feigin, A., & Ghil, M. (2015). Predicting Critical Transitions in ENSO models. Part II: Spatially Dependent Models. Journal of Climate, 28(5), 1962–1976. http://doi.org/10.1175/JCLI-D-14-00240.13. Gavrilov, A., Seleznev, A., Mukhin, D., Loskutov, E., Feigin, A., & Kurths, J. (2019). Linear dynamical modes as new variables for data-driven ENSO forecast. Climate Dynamics, 52(3–4), 2199–2216. http://doi.org/10.1007/s00382-018-4255-74. Mukhin, D., Gavrilov, A., Loskutov, E., Kurths, J., & Feigin, A. (2019). Bayesian Data Analysis for Revealing Causes of the Middle Pleistocene Transition. Scientific Reports, 9(1), 7328. http://doi.org/10.1038/s41598-019-43867-3

The global climate system is an aggregate of a huge number of interacting components, each having an intrinsic time scale. Such a complex dynamical system demonstrates nontrivial behavior and can exhibit a variety of possible modes of evolution. Gradual change of the parameters of the global climate system can lead to transitions (e.g., the Mid-Pleistocene Transition or to abrupt climate changes) from the observed to a new mode.In this work, we investigate the stability of the global climate system against strong sudden perturbations in the last 2.5 million years. This case is fundamentally different from the small perturbations case: in particularly, the system response cannot be described by a linearized evolution operator. To estimate the climate system’s nonlinear stability during the last 2.5 million years, we use a nonlinear data-driven model of climate dynamics in Pleistocene [1] and basin stability criterion [2]. Our results indicate that the stabilityof the Pleistocene climate to large perturbations decreases with time: past climates being much more stable compared to the present one.This work was supported by RFBR grant 19-02-00502.1. D. Mukhin, A. Gavrilov, E. Loskutov, J. Kurths, A. Feigin. “Bayesian Data Analysis for Revealing Causes of the Middle Pleistocene Transition”. ScientificReports, 9 7328 (2019).2. V. Klinshov, S. Kirillov, J. Kurths, V. Nekorkin. “Interval stability for complex systems”. New Journal of Physics, v. 20, p. 043040.

A Bayesian Linear Dynamical Mode (LDM) decomposition method is applied to isolate robust modes of climate variability in the observed surface air temperature (SAT) field. This decomposition finds the optimal number of internal modes characterized by their own time scales, which enter the cost function through a specific choice of prior probabilities. The forced climate response, with time dependence estimated from state-of-the-art climate-model simulations, is also incorporated in the present LDM decomposition and shown to increase its optimality from a Bayesian standpoint. On top of the forced signal, the decomposition identifies five distinct LDMs of internal climate variability. The first three modes exhibit multidecadal scales, while the remaining two modes are attributable to interannual-to-decadal variability associated with El Nino–Southern oscillation; all of these modes contribute to the secular climate signal—the so-called global stadium wave—missing in the climate-model simulations. One of the multidecadal LDMs is associated with Atlantic multidecadal oscillation. The two remaining slow modes have secular time scales and patterns exhibiting regional-to-global similarities to the forced-signal pattern. These patterns have a global scale and contribute significantly to SAT variability over the Southern and Pacific Oceans. In combination with low-frequency modulation of the fast LDMs, they explain the vast majority of the variability associated with interdecadal Pacific oscillation. The global teleconnectivity of the secular climate modes and their possible crucial role in shaping the forced climate response are the two key dynamical questions brought about by the present analysis.

Annual cycle events may be interlinked, influence following annual cycle stages, and may alter performance of individuals. Such links, called carry-over effects, can explain individual variation in timing or reproductive success in migratory species. Identifying the key links affecting fitness may reveal the mechanisms of species population dynamics but the current evidence for the strongest carry-over effects is equivocal. Here, we aim to assess the carry-over effects in great reed warblers Acrocephalus arundinaceus, a long-distance migratory songbird, using 103 full-annual tracks from three European and two Asian breeding populations. Our results showed strong positive relationships within autumn and spring migration periods and buffering capacity of the non-breeding period preventing events to carry over between these periods. Moreover, we found no profound relation between the non-breeding habitat quality or seasonality (quantified using stable isotopes and remote sensing data) and the timing of spring migration. The strongest carry-over effects occurred in individuals from the southern European breeding population compared to the northern and the central European populations. A moderate relationship between the habitat seasonality during moult and the spring migration timing indicates the importance of the complete moult. The overall weak carry-over effects of non-breeding habitat conditions found in this study contrast with previous results and imply between-species differences in these crucial relationships. Moreover, the population-specific carry-over effects highlight the importance of multi-population approach and advise caution in interpretation of results from single-population studies. Finally, the carry-over effect from the moulting period indicates the significance of a so-far neglected link in the species., + Publisher's Statement: This is a post-peer-review, pre-copyedit version of an article published in Behavioral Ecology and Sociobiology. The final authenticated version is available online at: https://doi.org/10.1007/s00265-020-02929-7.

Transient three-dimensional flow simulations of power–law fluid in a long axisymmetric annular channel considering 0.5 diameter ratio were performed. An in–house CFD code considering URANS (Unsteady Reynolds Averaged Navier–Stokes), 2D RANS (steady-state axially uniform 2D RANS) and LES (Large Eddy Simulation) approaches were compared to perform the simulations. Flow structure was analyzed. Numerical experiments showed that rotation of the inner cylinder (drill pipe) leads to two effects: decrease of apparent viscosity in the region close to the rotating cylinder, thus decreasing viscous shear stresses; development of secondary vorticity structures increasing energy loss. First mechanism decreases pressure losses and dominates when Re < 300. At Re ∼ 300 the mechanisms compete with each other and pressure losses depends on power–law index n. At Re > 300 mechanism of second vortex structured dominates and increases pressure loss with rotation. Pressure losses for two-dimensional steady-state and three-dimensional transient problems were compared. Pressure losses using a two-dimensional approach can be underestimated by up to 30%.

Development of vascular collaterals in a lesion area is one of the key factors that determine not only the choice of treatment for ischemic stroke (IS) patients, but also outcome and therapy effectiveness. The main method for examining the vessels' ramification is CT angiography (CTA). CTA analysis may be improved by incorporating filters designed to extract more features about vessels and quantify their level of development. This work suggests the usage of radiomics methods in the analysis of vesselness measure calculated from CTA images. Vesselness measurement is based on the analysis of the Hessian matrix with a few modifications dictated by practical aspects of this issue. The developed algorithm was implemented as a filter that generates a new 3D image, every voxel of which has the probability of belonging to a vessel-like structure. Further analysis of the distribution of vesselness in the lesion area and in the intact contralateral area was conducted with the methods from the open library PyRadiomics. A set of radiomics features was calculated. Preliminary analysis on a sample of 30 IS patients showed the presence of significant differences between afflicted and intact hemispheres.

According to recent study [1], the current state-of-the-art climate models lack the substantial part of internal multidecadal climate signal which is observed in the 20th century surface air temperature reanalysis data as a global stadium wave (GSW). In the presented work we further investigate this phenomenon using the recently developed method [2] of empirical spatio-temporal data decomposition into linear dynamical modes (LDMs). The important property of LDMs is their ability to take into account the time scales of the system evolution (they are extracted from observed dataset by the Bayesian optimization technique) better than some other linear techniques, e.g. traditional empirical orthogonal function decomposition. Like any linear decomposition, it provides the time series of principal components and corresponding spatial patterns.We modify the initially developed LDM decomposition to make it possible to take into account a prescribed external forcing (like CO2 emissions, sun activity etc.) and then find part of variability which may be considered as an internal climate dynamics decomposed into set of modes with different time scales, and hence may be helpful in GSW interpretation. The results of applying the method to the 20th century surface air temperature with different ways of forcing inclusion will be presented and discussed.1. Kravtsov, S., Grimm, C., & Gu, S. (2018). Global-scale multidecadal variability missing in state-of-the-art climate models. Npj Climate and Atmospheric Science, 1(1), 34. https://doi.org/10.1038/s41612-018-0044-62. Gavrilov, A., Seleznev, A., Mukhin, D., Loskutov, E., Feigin, A., & Kurths, J. (2018). Linear dynamical modes as new variables for data-driven ENSO forecast. Climate Dynamics. https://doi.org/10.1007/s00382-018-4255-7

We investigate the Middle Pleistocene Transition (MPT) - a rapid change in the periodicity of the Pleistocene glacial cycles from 41 kyr to about 100 kyr, which occurred about a million years ago - using the data-driven model [1]. Here we estimate stability of the model using a novel concept of interval stability [2-4], referring to the behavior of the perturbed model during a finite time interval. In a few words we define the class of 'safe' perturbations after which the system (our data-driven model) returns back to the initial dynamical regime and 'unsafe' perturbation of minimal amplitude needed to disrupt the system.We demonstrate that the MPT is likely associated with decreasing of the climate system's interval stability to rapid disturbances (millennial and shorter). This confirms the statement made in the paper [1] that the main factor in the onset of the long-period glacial cycles is strongly nonlinear oscillations induced by the short-scale variability.D. Mukhin, A. Gavrilov, E. Loskutov, J. Kurths, A. Feigin. Bayesian Data Analysis for Revealing Causes of the Middle Pleistocene Transition. Scientific Reports, 9 7328 (2019). P. Menck, J. Heitzig, N. Marwan, J. Kurths. How basin stability complements the linear-stability paradigm. Nature Phys, 9 89–92 (2013). V. Klinshov, V. Nekorkin, J. Kurths. Stability threshold approach for complex dynamical systems. New Journal Physics, 18 013004 (2016). V. Klinshov, S. Kirillov, J. Kurths, V. Nekorkin. Interval stability for complex systems. New Journal Physics, 18 013004 (2018).