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52. Marchuk G. I., Lebedev V. I. Numerical methods of the theory of neutron transport. M. Atomizdat, 1981.
3. Vladimirov V. S. Mathematical problems of the one-velocity theory of particle transport// Trudy Mat. Inst. Steklov.
1961. V. 61. P. 3-158.
4. Sushkevich T. A. Mathematical models of radiation transfer. M.: BINOM, 2006.
5. Kalinin A. V., Morozov S. F. A mixed problem for a nonstationary system of nonlinear inregro-differential equations
// Sib. Math. J. 1999. V. 40, N. 5. P. 887-900.
Local ensemble optimal nonlinear filtering algorithm
E. G. Klimova
Federal Research Center for Information and Computational Technologies
Novosibirsk State University
Email: klimova@ict.nsc.ru
DOI 10.24412/cl-35065-2021-1-01-30
A shortcoming of the classical particle filter method is that observation data are used only to calculate the
weight coefficients with which the elements (particles) of an ensemble are summed. An approach to solving
the nonlinear filtering problem based on a representation of the distribution density as a sum of Gaussian
functions has been used. If the distribution density is represented as a sum of Gaussian functions, a sum with
weights of estimates obtained in Kalman filters corresponding to Gaussian distribution densities is the optimal
estimate. In the report, an approach to solving the nonlinear filtering problem with the distribution density
represented as a sum of Gaussian functions is considered. The ensemble .-algorithm, which was proposed
earlier by the author, is used to implement the algorithm [1, 2]. The algorithm is local and can be implemented
in separate subdomains. This allows its implementation in high-dimensional geophysical models. The results of
numerical experiments with a 1-dimensional nonlinear model are presented.
References
1. Klimova, E. A suboptimal data assimilation algorithm based on the ensemble Kalman filter // Quarterly J. of the
Royal Meteorological Society. 2012. V.138. P. 2079-2085.
2. Klimova, E.G. The Kalman stochastic ensemble filter with transformation of perturbation ensemble // Numerical
Analysis and Applications. 2019. V.12 (1). P. 26�36.
Data assimilation problems for production-destruction models with parameter identification
V. S. Konopleva1,2, A. V. Penenko1
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS
2Novosibirsk State University
Email: v.konopleva@g.nsu.ru
DOI 10.24412/cl-35065-2021-1-01-31
To predict and assess the state of rapidly changing processes, stable data assimilation algorithms are
widely used. An example is the process of changing the chemical composition of atmospheric air. To study the
dynamics of pollutants in urban conditions, methods of mathematical modeling are used with the assimilation
of measurement data of the pollution level obtained at monitoring posts. Data assimilation algorithms restore
the missing information about the parameters of the mathematical model in the process of modeling with the
input measurement data for the past and current values of the model state functions. We will understand the
data assimilation problem as a sequence of related inverse problems [1, 2]. As a basic inverse problem, let us
consider the problem of evaluating the initial data and parameters of the product-destruction model from the
data of point measurements of the state function. Optimization algorithms are used to solve it.
The results of the operation of data assimilation algorithms, when the measurement data become availa-
ble in some portions in time, and algorithms for solving the inverse problem, when all data are available at the
time of the start of calculations, are numerically compared. The computation time and accuracy are analyzed.
This work was supported by the Russian Foundation for Basic Research 20-01-00560 in terms of comparing the data
assimilation problem and the inverse problem and RFBR 19-07-01135 in terms of solving the inverse coefficient problem.
References
1. Penenko V. V. Methods of numerical modeling of atmospheric processes // Gidrometeoizdat, 1981.
2. Nakamura G. and Potthast R. Inverse Modeling An introduction to the theory and methods of inverse problems
and data assimilation // IOP Publishing, 2015.
Analysis of the annual water balance of the Lena river basin and variability of river flow
A. I. Krylova1, N. A. Lapteva2
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS
2FBRI �State Research Center of Virology and Biotechnology �Vector� Rospotrebnadzor, Koltsovo, Novosibirsk
region
Email: alla@climate.sscc.ru
DOI 10.24412/cl-35065-2021-1-01-32
It is known that the hydrological system of the Arctic is especially sensitive to an increase in temperature,
and it is also influenced by precipitation, evapotranspiration, processes on the land surface: the development
and distribution of taliks, the dynamics of the depth of the seasonally thawed layer [1]. Analysis of fluctuations
in water balance components in a changing climate based on MERRA reanalysis data for the period
1980�2020. [2] makes it possible to identify the most important factor controlling the increase in river
flow.
The purpose of this work is to analyze changes in meteorological processes and their influence on the var-
iability of river flow.
This work is supported by the Russian Foundation for Basic Research (grant �20-05-00241�) and within the frame-
work of the State Assignment for the ICMMG SB RAS (project �0215-2021-003).
References
1. Sazonova, T.S., Romanovsky, V.E., Walsh, J.E., Sergueev, D.O. Permafrost dynamics in 20th and 21st centuries
along the East-Siberian Transect // J. Geophys. Res. 2004. V.109 (D1, D01108).
2. Shiklomanov, A.I., Holmes, R.M., McClelland, J.W., Tank, S.E., Spenser R.G.M. ArcticGRO Discharge Dataset
[Electron. resource]. URL:https:////www.arcticrivers.org/data/ (2021).
