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Contract number
Time span of the project

As of 01.11.2022

Number of staff members
scientific publications
Objects of intellectual property
General information

Name of the project: New approaches to research of climatic processes and forecasting extreme phenomena

Goals and objectives

Research directions: Modeling climatic processes

Project objective: Applying and enhancing methods of researching dynamics of complex systems for studying climatic systems of the Earth and related problems including forecasting extreme phenomena

The practical value of the study

Scientific results:

  • The Laboratory has created a method for the extraction principal nonlinear mode s of climate variability from data. An analysis of ocean surface temperature series allows to pinpoint low-dimensional modes that are responsible for the interannual and interdecadal variability of the climate.
  • We have developed a method for building empirical models based on the spatiotemporal decomposition of data and the neural network representation of the system evolution operator. By the example of an interannual forecast of the key climate indices we have demonstrated that the prognostic capability of models build using the new method is not inferior to the best of the existing counterparts.
  • A method has been developed that allows to identify repeating atmospheric variability modes in the middle latitudes from data of observations in a single procedure and to reconstruct the phase space that ensures the separation of these modes. The method combines two approaches to nonlinear data analysis: building and analysis of a network (graph) of recurrent states and the nonlinear analysis of principal components. The method has been tested using data generated by a quasigeostrophic model of the atmosphere and then applied to the analysis of data of the geopotential heights of the atmosphere in the middle latitudes of the Northern hemisphere in the winter seasons from 1981 to today. We have determined a set of recurrent atmospheric circulation modes at the planetary scale, researched their dynamic properties and demonstrated their relation to large-scale weather anomalies that determined, in particular, the abnormal winters over Eurasia and North America. The developed method opens new prospects for the modernization of  of the empirical modeling and long-term forecasting of large-scale atmospheric circulation modes in the middle latitudes.
  • A new method of research of stability against strong excitations has been used for the first time for the study of the properties of the real natural system: for the analysis of  change of the stability of the climate system of the Earth over the last 2,6 million years  (the Pleistocene period). On the basis of the new method and the empirical reconstruction of the evolution operator of the climate of the Earth has demonstrated that the stability of the global climate against any disturbances was reducing over the whole Pleistocene, thus strengthening its reaction to fast (at the scale of thousand of years and less) climate variations. It is this factor, caused by the nonlinearity of the climate system of the Earth, that lead to the qualitative rearrangement of the evolution of the global climate about a million years ago: the duration of glacial cycles, changed drastically (from 41 thousand years to 100-120 thousand years) and their structure (the ratio of the duration of the cold phase tp the warm phase in every cycle changed by an order of magnitude).

Implemented results of research:

We have developed algorithms used in the modeling of physical processes, big data processing and machine learning.  11 useful computer programs have been included in the state register:

  • «A program for computing the spatiotemporal mode from a one-dimensional time series»
  • «A program for computing the nonlinear dynamic mode and its justification from a multi-dimensional time series (version 1)»
  • «A program for computing the nonlinear dynamic mode and its justification from a multi-dimensional time series with optimization for dimensionality»
  • «A program for computing the stochastic model of the evolution operator on the basis of artificial neural networks, its justification and forecasting behavior from a scalar time series»
  • «A program for calibrating numerical schemes of climate models based on Bayesian averaging in a regular latitude-longitude grid»
  • «A program for computing statistical moments and cumulants of anomalies from a predefined interval of time scales on a latitude-longitude grid»
  • «A program for computing a predictive model of the evolution operator in the form of  a complex-valued artificial neural network»
  • «A program for computing the empirical predictive model of the evolution operator with the search for the optimal structure of embedding from a multi-dimensional time series»
  • «A program for computing the Bayesian justification of a model of the evolution operator in the form of a complex-valued artificial neural network»
  • «A program for computing the empirical predictive model of the evolution operator from a multi-dimensional time series accounting for its smoothness»

  • «A program for computing the complex-valued spatiotemporal mode from a multi-dimensional time series» 

Education and career development:

  • The international Conference on Mathematical Geophysics CMG 2018 has been organized (Russia, 2018).
  • Sections have been organized at internatioanl conferences: EGU General Assembly (Austria, 2015-2018), Topical problems of nonlinear wave physics (Russia, 2014, 2017), Frontiers of nonlinear physics (Russia, 2016), at the international youth schools «Nonlinear waves» (Russia, 2016, 2018).
  • We have organized the All-Russian School-conference for Young Scientists «Composition of the atmosphere. Atmospheric electricity. Climate effects» (Russia, 2016).
  • The Laboratory has organized the work groups «Network analysis and data driven modeling of the climate» (Germany, 2014) and «Analysis of Dynamic Networks and Data Driven Modeling of the Climate» (Germany, 2015).
  • Three specialists of the Laboratory have completed internships in empirical modeling of distributed systems.
  • Employees of the Laboratory have participated in delivering lecture courses  «Mechanics», «Molecular physics», «Theory of oscillations and waves», «General atmospheric circulation and its mathematical modeling», «Basics of the climate theory», «Control theory», «Information neurodynamics». 

Organizational and structural changes:

  • The Laboratory possesses a high-performance computing cluster (more than 500 современных computing cores, operating at a frequency of 2,4 GHz). This cluster is integrated with the infrastructure of the institute and is the core of the computation system of the Institute Applied Physics of the Russian Academy of Sciences.
  • The youth laboratory «Development and testing of climate models» has been created on the basis of our Laboratory under the supervision of Andrey S. Gavrilov, Candidate of Science, who prepared his dissertation in the process of the implementation of the mega-grant and defended it in 2019. 


  • Potsdam Institute for Climate Impact Research (Germany): joint research and scientific events, developing new methods of detecting interactions and the directions of connections in complex systems, developing a common concept of basin stability of dynamic systems and its application to researching the stability of climate modes detected both in regional climate systems and in the global climate system of the Earth.
  • University of California, Los Angeles (USA): joint research, creation of forecasting empirical models of the dynamics of Arctic marine ice and changes in the level of the ocean in the Arctic that describe the evolution at the seasonal, interannual and decade scales. 

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Gavrilov A., Seleznev A., Mukhin D., Loskutov E., Feigin A., & Kurths J.
Linear dynamical modes as new variables for data-driven ENSO forecast. Climate Dynamics 16 May: 1-18 (2018).
Mukhin D., Gavrilov A., Loskutov E., Feigin A., & Kurths, J.
Nonlinear reconstruction of global climate leading modes on decadal scales. Climate Dynamics September: 2301-2310 (2018).
Klinshov V., Kirillov S., Kurths J., Nekorkin V.
Interval stability for complex systems. New Journal of Physics 20 (2018).
Boers N., Chekroun M.D., Liu H., Kondrashov D., Rousseau D.D., Svensson A., … Ghil M.
Inverse stochastic–dynamic models for high-resolution Greenland ice core records. Earth System Dynamics 15 December: 1171–1190 (2017).
Volodin E. M., Mortikov E. V., Kostrykin S. V., Galin V. Y., Lykosov V. N., Gritsun A. S., … Yakovlev N. G.
Simulation of modern climate with the new version of the INM RAS climate model. Izvestiya, Atmospheric and Oceanic Physics 53(2): 142–155 (2017).
a. gavrilov, e. loskutov, and a. feigin.
Data-driven stochastic model for cross-interacting processes with different time scales. — Chaos 32, 023111 (2022); https://doi.org/10.1063/5.0077302 Статья отмечена как «editors-pick».
e. loskutov, v. vdovin, v. klinshov, a. gavrilov, d. mukhin, and a. feigin.
Applying interval stability concept to empirical model of middle Pleistocene transition. — Chaos : An Interdisciplinary Journal of Nonlinear Science, 32, 021103, (2022) https://doi.org/10.1063/5.0079963
dmitry mukhin, abdel hannachi, tobias braun, and norbert marwan
"Revealing recurrent regimes of mid-latitude atmospheric variability using novel machine learning method", Chaos: An Interdisciplinary Journal of Nonlinear Science, 32, 113105 (2022) https://doi.org/10.1063/5.0109889 Статья отобрана для включения в Scilight (Обзоры избранных статей из журналов AIP https://aip.scitation.org/journal/sci )
s. kravtsov, a. gavrilov , m. buyanova , e. loskutov , and a. feigin,
“Forced Signal and Predictability in a Prototype Climate Model: Implications for Fingerprinting Based Detection in the Presence of Multidecadal Natural Variability”, принята для публикации в декабрьском выпуске Chaos: An Interdisciplinary Journal of Nonlinear Science.
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