# Andrey GritsunRussian Academy of Sciences | RAS · Institute of Numerical Mathematics

Andrey Gritsun

Doctor of Philosophy

## About

57

Publications

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923

Citations

Citations since 2016

Introduction

## Publications

Publications (57)

The problem of potential predictability of the temperature of the upper layer of the Arctic Ocean for the data of pre-industrial climate modelling run by the INM-CM5 Earth system model developed at the INM RAS is considered. The main attention is paid to the analysis of predictability of the phases of the dominant modes of low-frequency variability...

Unstable periodic orbits (UPOs) are a valuable tool for studying chaotic dynamical systems, as they allow one to distill their dynamical structure. We consider here the Lorenz 1963 model with the classic parameters’ value. We investigate how a chaotic trajectory can be approximated using a complete set of UPOs up to symbolic dynamics’ period 14. At...

In this paper we present first results on the use of Polar WRF model for regionalization of the atmospheric circulation in the Arctic region produced by the global climate model INM-CM48 developed in INM RAS. We demonstrate that Polar WRF does not show run off effects in the first year of integration, gives reasonable results with respect to the gl...

We use a simple yet Earth-like hemispheric atmospheric model to propose a new framework for the mathematical properties of blocking events. Using finite-time Lyapunov exponents, we show that the occurrence of blockings is associated with conditions featuring anomalously high instability. Longer-lived blockings are very rare and have typically highe...

The problem of modelling 2D isotropic turbulence in a periodic rectangular domain excited by the forcing pattern of prescribed spatial scale is considered. This setting could be viewed as the simplest analogue of the large scale quasi-2D circulation of the ocean and the atmosphere. Since the direct numerical simulation (DNS) of this problem is usua...

We use a simple yet Earth-like global atmospheric model to propose a new framework for the mathematical properties of blocking events. Using finite-time Lyapunov exponents, we show that the occurrence of blockings is associated to conditions featuring anomalously high instability, and that the lifetime of a blocking is positively correlated with su...

An attempt is made in this study to evaluate the potential predictability of the TEC field (its deviation from the weekly average) at hourly time scales based on observational data. The method is based on the calculation of the distance between the group of observations and its subsample (group of analogues) contaning pairs of points separated in t...

The structure of main modes of the decadal and multidecadal variability of the Atlantic meridional overturning circulation (AMOC) is analyzed for the climate models INM-CM5 (INM RAS), CCSM4 (NCAR), MPI-LR and MPI-MR (MPI). It is shown that oscillations with characteristic periods of 25–35 and 50–70 years are recognized in the models, and the corres...

We consider simulation of the present day climate with the use of the climate model INM-CM48 in comparison with the result of the previous model INMCM4.0 which used different parameterizations of many physical processes and also in comparison with the model INM-CM5 which uses the same parameterizations, but with better spatial resolution. It is sho...

The low-frequency variability of sea surface temperature and salinity in the Arctic is analyzed using the data of the 1200-year preindustrial experiment with the INM-CM5 climate model developed in the Marchuk Institute of Numerical Mathematics of Russian Academy of Sciences. It is shown that the leading variability pattern is a regular coupled osci...

The results of numerical experiments on the sensitivity of the INMCM48 Earth System model (Institute of Numerical Mathematics, Russian Academy of Science (INM RAS)) to the various parameterizations of convection induced by the formation of a new ice are presented and analyzed. It is shown that the response in temperature and salinity is observed no...

Climate changes observed in 1850–2014 are modeled and studied on the basis of seven historical runs with the climate model INM-CM5 under the scenario proposed for the Coupled Model Intercomparison Project Phase 6 (CMIP6). In all runs global mean surface temperature rises by 0.8K at the end of the experiment (2014) in agreement with the observations...

Variations in the temperature of the Earth’s surface over the period 1850–2014 are reproduced and analyzed using seven historical calculations in the INM-CM5 climate model following the scenarios suggested for the CMIP6 project of comparison of climate models. In all calculations, the mean surface temperature increased by 0.8 K to the date of final...

Many subgrid-scale (SGS) parameterizations in climate models contain empirical parameters and are thus data dependent. In particular, it is not guaranteed that the SGS parameterization still helps the model to produce the correct climate projection in the presence of an external perturbation (e.g., because of climate change). Therefore, a climate d...

Climate changes observed in 1850-2014 are modeled and studied on the basis of seven historical runs with the climate model INM-CM5 under the scenario proposed for Coupled Model Intercomparison Project, Phase 6 (CMIP6). In all runs global mean surface temperature rises by 0.8 K at the end of the experiment (2014) in agreement with the observations....

In this work we are considering the problem of modeling 2D isotropic turbulence in a periodic rectangular domain excited by the forcing pattern of prescribed spatial scale. This setting could be viewed as the simplest analog of the large scale quasi 2D circulation of the ocean and the atmosphere. Since the direct numerical simulation (DNS) of this...

In this paper we present the fifth generation of the INMCM climate model that is being developed at the Institute of Numerical Mathematics of the Russian Academy of Sciences (INMCM5). The most important changes with respect to the previous version (INMCM4) were made in the atmospheric component of the model. Its vertical resolution was increased to...

We study the response of a simple quasi-geostrophic barotropic model of the atmosphere to various classes of perturbations affecting its forcing and its dissipation using the formalism of the Ruelle response theory. We investigate the geometry of such perturbations using the covariant Lyapunov vectors on the unperturbed system and discover in one s...

The INMCM5.0 numerical model of the Earth’s climate system is presented, which is an evolution from the previous version, INMCM4.0. A higher vertical resolution for the stratosphere is applied in the atmospheric block. Also, we raised the upper boundary of the calculating area, added the aerosol block, modified parameterization of clouds and conden...

The fluctuation dissipation theorem (FDT), a classical result coming from statistical mechanics, suggests that, under certain conditions, the system response to external forcing can be obtained using the statistics of natural fluctuation of the system. Starting from (Leith, 1973) the use of the FDT to study the response of atmospheric systems has r...

The purpose of the authors of this collective monograph was to present some results of the work carried out at
the Institute of Numerical Mathematics RAS to create the numerical model of the Earth System that meets modern
requirements and is at the global forefront of scientific and technological activities in this direction. This model is used
to...

The results of simulations of the World Ocean sea surface hight (SSH) in by various versions of the Climate Model of the Institute of Numerical Mathematics, Russian Academy of Sciences, are compared with the CNES-CLS09 fields of the mean dynamic topography (deviation of the ocean level from the geoid). Three models with different ocean blocks are c...

Climate-system models use a multitude of parameterization schemes for small-scale processes. These should respond to externally forced climate variability in an appropriate manner so as to reflect the response of the parameterized process to a changing climate. The most attractive route to achieve such a behavior would certainly be provided by theo...

The theory of chaotic dynamical systems gives many tools that can be used in climate studies. The widely used ones are the Lyapunov exponents, the Kolmogorov entropy and the attractor dimension characterizing global quantities of a system. Another potentially useful tool from dynamical system theory arises from the fact that the local analysis of a...

Presently even, and perhaps especially, the most elaborate climate
system models use a multitude of parameterization schemes for
small-scale processes. These should respond to externally forced climate
variability in an appropriate manner so as to reflect the response of
the parameterized process to a changing climate. The most attractive
route to...

Many chaotic systems have an infinite number of periodic solutions
forming the skeleton of the system attractor. This allows one to
approximate the system trajectories and statistical characteristics
using periodic orbits of the system. The "lifetime" of the system
trajectory in the vicinity of the given orbit depends on the orbit
instability chara...

We have investigated the relationship between periodic trajectories of barotropic atmospheric model and the modes of the model
variability. In particular, we have studied the nature of “25 day” mode of variability (Branstator, 1987; Kushnir 1987). This
mode arises as a first complex empirical orthogonal function (or “Hilbert EOF” according to (H. v...

Fluctuation-dissipation relations make it possible to connect the response operators of system statistical characteristics
to small external perturbations with the statistical characteristics of the unperturbed system (providing statistical stationary
of the system). This gives a possibility to estimate the sensitivity of the system directly from m...

This paper is devoted to the problem of approximating an invariant measure and statistical characteristics of barotropic atmospheric
model with the help of its periodic trajectories. In this procedure orbits are taken into account according to their weights
defined by the orbit instability characteristics. The method comes from the dynamical system...

We consider the problem of estimation of the sensitivity of the barotropic atmosphere model to small external impacts, which consist in a change of the external forcing of the system. The general concept of the method is based on approximation of the point distribution density on the attractor of the system with the use of its unstable periodic tra...

It was shown recently (Gritsun, 2008) that an attractor of barotropic atmospheric system contains many unstable periodic orbits (UPOs). Orbits form a skeleton for the system attractor and approximate statistical characteristics of the system with high accuracy. Consequently, it is reasonable to expect that some of UPOs are somehow connected with mo...

Unstable periodic orbits (UPOs) are an important feature of chaotic dissipative systems(i.e. systems having positive Lyapunov exponents and contracting the phase space). For some of chaotic systems like Anosov or Axiom A systems UPOs are dense on the system attractor so that any trajectory of the system can be approximated by some orbit with any gi...

A generalization of the fluctuation-dissipation theorem (FDT) that allows generation of linear response operators that estimate the response of functionals of system state variables is tested for a system defined by an atmospheric general circulation model (AGCM). A sketch of the proof of this generalization is provided, followed by comparison of r...

Unstable periodic trajectories of a chaotic dissipative system belong to the attractor of the system and are its important characteristics. Many chaotic systems have an infinite number of periodic solutions forming the skeleton of the system attractor. This allows one to approximate the system trajectories and statistical characteristics by using p...

The fluctuation–dissipation theorem (FDT) states that for systems with certain properties it is possible to generate a linear operator that gives the response of the system to weak external forcing simply by using covariances and lag-covariances of fluctuations of the undisturbed system. This paper points out that the theorem can be shown to hold f...

This paper provides a consistent consideration of current problems in the mathematical theory of climate such as the solvability of the equations governing the climate system, the existence of an attractor and the possible estimation of its dimension, conditions for the attractor's stability to constantly acting perturbations, and some other proble...

In this paper, we give some results of an investigation into the climate system sensitivity to small external forcings. We analyse the response to increasing atmospheric carbon dioxide content in 18 climate models involved in the CMIP program. It is shown that of vital importance in the total response is its radiative component. Moreover, a signifi...

It is demonstrated in this study that a class of models for the large scale atmospheric dynamics satisfies to the so-called Lyapunov exponents symmetry property. Namely, the sums of i-th and (N - i + 1)-th Lyapunov exponent of a system are equal to the doubled Rayleigh friction coefficient taken with negative sign provided that the nonlinear part o...

We present a method for constructing an approximate response operator of the average state of an atmospheric general circulation model to small external forcing. The method is based on Kraichnan’s fluctuation-dissipation relationship under the assumption of ‘quasiregularity’ of the systems studied. Its advantage is that only the statistical charact...

In this paper we consider the theoretical results obtained for atmospheric models with chaotic dynamics. To define the notion of ‘climate’ for the real climate system we introduce the concept of ‘ideal climate model’. Starting from this concept we formulate problems that should be studied for the specific climate (or atmospheric) model under consid...

In this paper we discuss some theoretical results obtained for climate models (theorems for the existence of global attractors and inertial manifolds, estimates of attractor dimension and Lyapunov exponents, symmetry property of Lyapunov spectrum). We define the conditions for "quasi-regular behaviour" of a climate system. Under these conditions, t...

The pairing property of Lyapunov exponents for models describing large-scale atmospheric dynamics is considered. It is shown that, if the nonlinear part of the model operator can be reduced to the Hamiltonian form and if the model dissipation is of the Rayleigh type, then the Lyapunov exponents μi can be ordered so that μi + μN+1-i = -2α, where α i...

- This study deals with the numerical verification of the fluctuation-dissipation theorem (FDT) for atmospheric models. The theorem relates the impulse response operator of a system to its statistical characteristics (lag correlation coefficients). Consequently, the FDT can be used for the prediction of system sensitivity to small external perturba...

This work studies the response of a system of equations describing the dynamics of a baroclinic atmosphere to small external actions of an arbitrary form and considers the possibility of predicting the response on the basis of simplified models constructed from modeling data. With the aid of the Monte Carlo method, the operator of the model respons...

this paper we have considered the applicability of given approach on the example of barotropic atmosphere model. At rst, we directly calculate the operator of the model response to the small steady perturbations of external forcing with the help of Monte-Carlo technique. We show that this operator can be considered with good accuracy as linear for...

We investigate the dependence of the attractor characteristics on the space resolution for the Galerkin approximations of the barotropic vorticity equation on a sphere. We show that the Lyapunov indices and the attractor dimension of approximate systems do not depend on resolution beginning with truncation equal to 30. The attractor dimension is ma...

Extremely low-frequency variability of atmospheric circulation (with periods longer than 50 days) is studied by using a two-layer baroclinic model as an example. It is shown that, with a random forcing in the form of a white noise, a barotropic model linearized about the upper-level state describes 70% of this variability (the correlation coefficie...

## Projects

Project (1)

Construction of stochastic and climate-dependent subgrid-scale parameterizations to improve statistical and sensitivity properties of coarse grained atmospheric and oceanic coarse grained models