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6Section 4
MATHEMATICAL MODELS OF ATMOSPHERIC PHYSICS, OCEAN AND ENVIRONMENT
Application of the methods of direct and inverse modeling for processing airborne measurements results
of air composition
P. N. Antokhin1, O. Yu. Antokhina1, M.Yu. Arshinov1, B. D. Belan1, A. V. Penenko2,3, D. V. Simonenkov1
1V.E. Zuev Institute of Atmospheric Optics SB RAS
2Institute of Computational Mathematics and Mathematical Geophysics SB RAS
3Novosibirsk State University
Email: apn@iao.ru
DOI 10.24412/cl-35065-2021-1-01-17
The report presents an approach to processing the results of aircraft measurements using the results of
direct and inverse modeling. For direct modeling, the WRF-Chem v.4.2 model was used. The resulting mete-
orological fields were used for inverse modeling. For inverse modeling, the IMDAF [1] model was used. As a
result of the approach used, it became possible not only to estimate the total contribution of local sources to
the measured values, but also to highlight the influence of a particular source.
This work was supported RFBR grant No. 19-05-50024, 18-45-700020 (modeling are carried out), and the studies of
small gaseous constituents of the atmosphere and aerosols were carried out with the support of the Ministry of Educa-
tion and Science of the Russian Federation.
References
1. A. V. Gochakov, A. V. Penenko, P. N. Antokhin, A. B. Kolker Air pollution modelling in urban environment based on
a priori and reconstructed data // IOP Conf. Ser.: Earth Environ. Sci. 2018, 211, 012050.
Modelling of multiphase multi-velocity unsteady flows in pipes with elevation difference
V. P. Bashurin, A. V. Shvedov, A. A. Kibkalo, A. S. Myshkin, A. V. Vankov, Al-dr. A. Kibkalo, N. N. Degtyarenko,
A. G. Danilov, I. G. Rogozhkin, M. M. Khabibulin, M. S. Kulikov, L. V. Ktitorov, V. I. Zhigalov
FSUE �Russian Federal Nuclear Center � All-Russian Research Institute of Experimental Physics�, Sarov, Nizhny
Novgorod Region
Email: Andrey.shvedov@sarov-itc.ru
DOI 10.24412/cl-35065-2021-1-01-18
This research aims at studying the behaviour of flows of multiphase mixtures in pipes, when there is a dif-
ference in elevations. The study method is based on computer modelling using a simulator of multiphase flows
created by the authors [1]. The simulator is appropriate for describing the flow of multiphase mixtures in com-
plex systems, with implementation of two-velocity motion model of various phases. In liquid-gas mixture, it
results in different velocities of phases motion [3]. The analysis results demonstrate that velocities differ sub-
stantially. The presence of gravitational component greatly affects the nature of flow, and, in some cases,
leads to a change in flow regimes [2]. The work shows that regimes can also be implemented without reaching
steady-state conditions.
References
1. State registration certificate of a programm for a computer ("Tube Hydro Simulation 1.0" software package)
No. 2020614768 dated 24.04.2020 (Authors: Zhigalov V.I., Kibkalo Al.A., Bashurin V.P., Kibkalo Al-dr A., Myshkin A.S.,
Degtyarenko N.N., Vankov A.V., Ktitorov L.V., Danilov A.G., Shvedov A.V., Rogozhkin I.G., Kulikov M.S., Khabibulin M.M.).
2. A Study Of Terrain-Induced Slugging In Two-Phase Flow Pipelines V. De Henaut and G. D. Raithby Department of
Mechanical Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3GI (Received 28 April 1994; in revised
form 4 November 1994).
3. Badie S., Hale C.P., Lawrence C.J., Hewitt G.F. Pressure gradient and holdup in horizontal two-phase gas�liquid
flows with low liquid loading. // Int. J. Multiphase Flow 2000. - 26, 1525�1543.
The problem of retrieval the methane profiles in the Earth�s atmosphere from high-resolution IR spectra
P. A. Chistyakov1,2, I. V. Zadvornykh2, K. G. Gribanov2
1Krasovskii Institute of Mathematics and Mechanics UB RAS
2Ural Federal University, Ekaterinburg
Email: pavel.chistyakov@urfu.ru, ilia.zadvornyh@urfu.ru, kgribanov@remotesensing.ru
DOI 10.24412/cl-35065-2021-1-01-21
Here we present some results of modified Levenberg-Marquardt method [1] applicability for solving inverse
problems of greenhouse gases remote sensing in Earth�s atmosphere. The computational experiments were per-
formed to retrieve the vertical profile of the main methane isotopologue from the thermal IR synthetic spectra of
IASI/MetOp spectrometer. The noise parameters were set equivalent to sensor characteristics. The optimal esti-
mation method implemented in FIRE-ARMS software [2] was used for solving the inverse problem. The data of
the retrospective climate analysis CAMS GHG Flux Inversions [3] were used as an initial guess and a statistical set
of profiles. The computational experiment showed convergence and accuracy of the proposed method, which,
however, turned out to be more computationally expensive than Gauss � Newton method.
This work is supported by the Russian Science Foundation grant � 18-11-00024-�.
References
1. Vasin, V.V., Perestoronina, G.Y. �The Levenberg-Marquardt method and its modified versions for solving nonlinear
equations with application to the inverse gravimetry problem�, Proc. Steklov Inst. Math. 280, 174�182 (2013) .
2. Gribanov, K.G., Zakharov, V.I., Tashkun, S.A., Tyuterev, Vl.G., �A New Software Tool for Radiative Transfer
Calculations and its application to IMG/ADEOS data�, JQSRT 68(4), 435-451, (2001).
3. �CAMS Green House Gases Flux Inversions,� https://apps.ecmwf.int/datasets/data/cams-ghg-inversions/
(20 December 2020).
Modelling of internal solitary waves in a multilayer stratified fluid
V. E. Ermishina1,2, V. Yu. Liapidevskii1,2, A. A. Chesnokov1,2
1Lavrentyev Institute of Hydrodynamics
2Novosibirsk State University
Email: eveyrg@gmail.com
DOI 10.24412/cl-35065-2021-1-01-22
We present a hyperbolic model describing the propagation of internal waves in a stratified shallow water
with a non-hydrostatic pressure distribution in two external layers and an arbitrary number of internal hydro-
static layers, which is an extension of the models from [1, 2]. The construction of the hyperbolic model is
based on the use of additional instantaneous variables. This allows the reduction of the dispersive multi-layer
Green�Naghdi model to a first-order system of evolution equations.
Stationary solutions of the motion equations are investigated and conditions for the formation of the soli-
tary waves are formulated. The model was verified by comparison with the results of field observations and
calculations using two-dimensional equations. Numerical simulation of the propagation of non-stationary non-
linear wave packets in a multilayer fluid has been performed.
