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7New method for analytical continuation of the planetary potential fields and terrain topography
I. E. Stepanova1,2, A. V. Shchepetilov3, V. V. Pogorelov1,2, V. A. Timofeeva1,2
1Schmidt Institute of Physics of the Earth, Moscow
2Sirius University of Science and Technology, Sochi
3Lomonosov Moscow State University
Email: tet@ifz.ru
DOI 10.24412/cl-35065-2021-1-01-55
A new effective technique based on the modified S-approximation is proposed for constructing analytical
description and continuation of terrain topography and potential fields. The modern digital elevation models
are, most frequently, regular grids of cells of a given size or irregular triangular grids. Analytical topography
models are another type of representation of the terrestrial or planetary surface data [1]. In contrast to digital
models with a piecewise continuous dependence of elevation of the observation point on its projection coor-
dinates, analytical models imply a more complex relationship between the elevation of the observation point
above the surface and the geographical coordinates of the point. This lends the possibility to study structural
features of the Earth�s surface, smooth the relief data for different-scale mapping and also analytically contin-
ue the fields under investigation [2]. The approximation accuracy and degree of detail in the description of the
terrain features are very important in this research. This paper addresses the results of the mathematical ex-
periment using optical satellite data for a test region with urban elements and combining various continental
landforms (hill and mountain terrain, a plain, ravines, and river mouth).
The work was supported by Russian Fund for Basic Research (RFBR, project number 19-35-51014).
References
1. Stepanova, I.E., Kerimov, I.A., and Yagola, A.G., Approximation approach in various modifications of the method of
linear integral representations, Izv. Phys. Solid Earth, 2019, V. 55, no. 2, pp. 218�231.
2. Stepanova, I.E., Shchepetilov, A.V., Pogorelov, V.V., and Mikhailov, P. S., Using of structural-parametric approach
for constructing digital models of elevations and Earth�s gravity field using analytical S-approximations, Geofiz. Protsessy
Biosfera, 2020, V. 19, no. 2, pp. 107�116. https://doi.org/10.21455/gpb2020.2-8.
Non-isothermal problem of fluid filtration in a poroelastic medium
M. A. Tokareva, A. A. Papin, R. A. Virts
Altai State University, Barnaul
Email: tma25@mail.ru
DOI 10.24412/cl-35065-2021-1-01-56
The process of nonisothermal filtration of a viscous fluid in a deformable porous medium is considered.
The mathematical model is based on the equations of conservation of mass for liquid and solid phases, Darcy�s
law, rheological relation, the law of conservation of balance of forces and the equation for temperature [1, 2].
The viscosity of the porous skeleton is a function of temperature. In the isothermal case, the problem was in-
vestigated in [2�4]. This paper investigates the issues of justifying the model.
This work was completed within the framework of the state assignment of the Ministry of Science and Higher Educa-
tion of the Russian Federation on the topic "Modern methods of hydrodynamics for problems of nature management,
industrial systems and polar mechanics" (project FZMW-2020-0008).
References
1. Connolly J.A.D., Podladchikov Y.Y. Temperature dependent viscoelastic compaction and compartmentalization in
sedimentary // Tectonophysics. 2000. V. 324. (3). P. 137-168.
2. Papin A.A., Tokareva M.A. On local solvability of the system of the equations of one dimensional motion of magma
// J. Sib. Fed. Univ. Math. Phys. 2017. V. 10 (1). P. 385�395.
3. Koleva M. N., Vulkov L. G. Numerical analysis of one dimensional motion of magma without mass forces // J. of
Computational and Applied Mathematics. 2020. V. 366. P. 112338.
4. Tokareva M.A., Papin A.A. Global solvability of a system of equations of one-dimensional motion of a viscous fluid
in a deformable viscous porous medium // J. of Applied and Industrial Mathematics. 2019. V. 13. No. 2. P. 350-362.
Soil moisture analysis for the multilayer soil scheme of the global atmospheric model SLAV
S. V. Travova 1, M. A. Tolstykh 2,1
1Hydrometeorological Research Center of Russian Federation, Moscow
2Marchuk Institute of Numerical Mathematics RAS, Moscow
Email: makhnorylova@gmail.com, m.tolstykh@inm.ras.ru
DOI 10.24412/cl-35065-2021-1-01-58
The study presents a new soil analysis system for the SLAV global atmospheric model, based on a simpli-
fied point-wise Extended Kalman filter (SEKF). This analysis system was developed within the framework of the
offline version of the surface model ISBA and the multilayer soil scheme of the INM RAS for the initialization of
the soil fields in the numerical weather forecast model. This system is compared with the land assimilation
system that uses a full atmospheric model to compute Jacobians of the observation operators in finite differ-
ences. By comparing the Jacobians of both analysis schemes, it was shown that the assumption of the linearity
of these operators is better fulfilled in the offline version. Another advantage of the offline approach is the
reduction in computation time, which makes the SEKF method compatible with the operational requirements.
The elements of the Jacobi matrix of the observation operator for two soil layers and the spatial structure of
the analysis increments are presented. The interval from June to August 2014 was taken as the estimation pe-
riod. Comprehensive data assessments are presented regarding the screen-level temperature and relative
humidity observations, irregular observations of soil temperature and atmosphere. It was shown that using
the SEKF improves forecast quality of the SLAV model.
This work was partially (the part concerning long-range forecasts) supported by the Russian Science Foundation
(grant 21-17-00254).
New versions of models of hydrodynamics and distribution of impurities in Lake Baikal
E. A. Tsvetova
Institute of Computational Mathematics and Mathematical Geophysics SB RAS
Email: E.Tsvetova@ommgp.sscc.ru
DOI 10.24412/cl-35065-2021-1-01-59
New versions of the implementation of large-scale models of hydrothermodynamics and the distribution
of impurities in Lake Baikal are presented. One of the main goals was to improve the spatial resolution and,
consequently, effective implementation on parallel computers. In the framework of the variational approach,
the initial object of the numerical implementation of the models is the integral identity, in which all equations
with boundary and initial conditions participate. Further, based on this identity, using the ideas of the splitting
method for physical processes and for spatial variables, finite-difference approximations are constructed. The
