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6References
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
most time-consuming are the splitting stages, when it is necessary to solve two-dimensional problems for the
level surface and three-dimensional problems for pressure fields. Finally, iterative methods with incomplete
factorization are applied to solve systems of linear algebraic equations. The OpenMP standard is used to build
parallel versions. The results of comparative experiments on the efficiency of implementation and examples of
solving continuation problems related to the modeling of large-scale hydrodynamic processes and the propa-
gation of impurities in the lake are given.
The work was carried out within the framework of the State Task of the ICMMG SB RAS code 0251-2021-0003 in
terms of the development of basic models of the lake and with the financial support of the Russian Foundation for Basic
Research (project code 20-01-00560) in solving the problems of continuation.
Meteorological effects of forest canopy under the conditions of steep orography
M. S. Yudin
Institute of Computational Mathematics and Mathematical Geophysics SB RAS (ICMMG)
E-mail: m.yudin@ommgp.sscc.ru
DOI 10.24412/cl-35065-2021-1-01-60
It is often difficult to perform observations within areas covered by various kinds of vegetation, especially
under conditions of steep underlying surface. The lack of data can often be compensated by using an appro-
priate mathematical model to describe the effects of canopy on the structure of the atmospheric boundary
layer. Specifically, in this study a simulation is carried out with a numerical mathematical model of a compress-
ible atmosphere based on finite elements [1, 2] to estimate the effects of some parameterization schemes of
forest canopy on distributions of meteorological variables in a domain covered by tall forests over a steep
terrain.
The simulation results appropriately reproduce well-known meteorological phenomena in forest areas, for
example, stable thermal stratification near the surface during the day, neutral or slightly unstable state at
night and, in general, a reduced wind speed in the forest cover.
This work was supported by ICMMG SB RAS under state contract 0251-2021-0003 (the numerical simulation) and the
Russian Foundation for Basic Research under grant 17-01-00137 (the formulation and development of the numerical algo-
rithms).
References
1. Yudin M.S., Calculation of stratification effects and parameters of atmospheric currents over steep surface
obstacles Proc. SPIE 11560, 26th International Symposium on Atmospheric and Ocean Optics, Atmospheric Physics,
1156070 (12 November 2020); doi: 10.1117/12.2575567.
2. Yudin, M.S., Wilderotter, K., Simulating atmospheric flows in the vicinity of a water basin // Computational
Technologies. 2006. V. 11, N.3. P. 128�134.
