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4first and only academician among cosmonauts-researchers V.Savinykh celebrated his 80th anniversary. The
first and only Doctor of physical and mathematical sciences among the cosmonauts-researchers G.Grechko
would have celebrated his 90th birthday. Soviet achievements in space research were ahead of the rest thanks
to manned space exploration. Theoretical and computational research was provided by three scientific schools
on the radiation transfer theory and mathematical modeling � in Moscow, Leningrad and Novosibirsk. The
huge theoretical and applied scientific potential created by Russian scientists at the dawn of the space age al-
lows us to maintain a leading position in the world in the implementation of "Earth Future" Program. Studies
of the Earth's radiation field are large-scale tasks that never have completion, since the atmosphere-land-
ocean is constantly changing and never repeating � it is a dynamic system with an unpredictable state. The
role of mathematicians, "computer sciences" and space for the implementation of the Program is increasing,
since natural experiments are impossible to study the evolution of the natural environment and the planet's
climate. At the initiative of T.A.Sushkevich, the radiation field was recognized as an "immaterial" component of
the Earth's climate system. The priority is related direct and inverse tasks � computer modeling of radiation
processes, predictive calculations of radiation characteristics and processing of huge data sets of global moni-
toring and remote sensing of the Earth from space.
This research was supported by Task 0017-2019-0002 of KIAM RAS.
Recent developments of SL-AV numerical weather prediction model
M. A. Tolstykh1,2, R. Yu. Fadeev1,2, V. V. Shashkin1,2, G. S. Goyman1, S. V. Travova2, K. A. Alipova2
1Marchuk Institute of Numerical Mathematics RAS, Moscow
2Hydrometcentre of Russia, Moscow
Email: m.tolstykh@inm.ras.ru
DOI 10.24412/cl-35065-2021-1-01-57
The global atmosphere model SL-AV [1] is applied for medium-range weather forecasts and subseasonal
and seasonal probabilistic prediction. The same code is used for all the applications.
The medium-range ensemble prediction system based on this model is described. It consists of LETKF-
based data assimilation system with ensemble centering into Hydrometcentre operational analysis [2], and the
model incorporating stochastic parameter perturbations (SPP) [2] and stochastic perturbations of parameterti-
zation tendencies SPPT [3] (for temperature and vorticity only). The results of quasioperational runs are
shown.
The development of the medium-range version of the model (10 km horizontal resolution) is presented.
Parallel and I/O optimizations have allowed to accelerate the SL-AV code significantly.
The new long-range prediction system is depicted. Some results of seasonal forecasts starting from rea-
nalysis data (hindcasts) are shown.
This work was partially (the part concerning long-range forecasts) supported by the Russian Science Foundation
(grant 21-17-00254).
References
1. Tolstykh M.A., Fadeev R.Yu., Shlyaeva A.V., Mizyak V.G., Rogutov V.S., Bogoslovsky N.N., Goiman G.S., Makhnorylova
S.V., Yurova A.Yu. Atmosphere modelling system for seamless prediction. M: Triada, 2017 166 p. (in Russian).
2. Mizyak V., Rogutov V., Alipova K. Development of the new ensemble weather prediction system at the
Hydrometcentre of Russia // J. Phys.: Conf. Ser. 2021. V. 1740. 012072.
3. Ollinaho P. et al. Towards process-level representation of model uncertainties: stochastically perturbed
parametrizations in the ECMWF ensemble // Q. J. R. Meteorol. Soc. 2017. V. 143, N. 702. P. 408-422. 2017.
4. Buizza R., Miller M., Palmer T. Stochastic representation of model uncertainties in the ECMWF Ensemble
Prediction System. ECMWF Tech. Memo. V. 279. 1999.
Alternative designs of high load queuing systems with small queue
G. Sh. Tsitsiashvili
Institute for Applied Mathematics FEB RAS
Email: guram@iam.dvo.ru
DOI 10.24412/cl-35065-2021-1-02-35
In this paper, two alternative designs are constructing for queuing systems with a large load and a small
queue. These modes are convenient from an economic point of view, since the service device is almost fully
loaded. On the other hand, this mode is also convenient for users who will not be idle in the queue for a long
time. The first design is an aggregation of a large number of single-channel systems into a multi-channel sys-
tem. The second design is basing on the model of a single-channel system, in which random fluctuations are
defining as the degree of tending to zero difference between the unit and the load factor. The exponent of this
degree has a critical value, above which the stationary waiting time tends to zero, and below which it tends to
infinity. A similar phase transition is founding in the multi-channel queuing system. The methods of the
sources [1-4] are using.
References
1. Borovkov A.A. Asymptotic methods in queueing theory. M.: Nauka, 1980.
2. Borovkov A.A. Stochastic processes in queuing theory. M.: Nauka, 1972.
3. Tsitsiashvili G.Sh., Osipova M.A. Phase Transitions in Multiserver Queuing Systems // Information Technologies
and Mathematical Modelling. Queueing Theory and Applications. 2016. V. 638. P. 341-353.
4. Boxma O.J., Cohen, J.W. Heavy-traffic analysis for the GI/G/l queue with heavy-tailed distributions // Queueing
Systems. 1999. V. 33. P. 177-204.
Taking into account a priori information is the most important stage in solving ill-posed problems
V. V. Vasin, A. L. Ageev
1Institute of Mathematics and Mechanics UB RAS
Ural Federal University, Ekaterinburg
Email: vasin@imm.uran.ru
DOI 10.24412/cl-35065-2021-1-02-18
What is a problem with a priori information? It is a problem, in which together with the basic statement
there is an additional information on a solution (namely, constraints) that is absent in the original statement.
But this information might contain important data on some properties of a solution. It should be noted that in
the case of a non-uniqueness solution, (when a priori information is not used in the algorithm of the problem
to be solved), the approximate solutions could not satisfy to physical reality. In the case of uniqueness of solu-
tion, attraction of the additional constraints permits to localize the desired solution and to raise its stability
w.r.t. the errors in the input data. Majority of a priori constraints that arise in the applied problems can be
presented in the form of the linear relations or systems of the linear and convex inequalities. We investigate
various methods of taking into account a priori constraints, in particular, the most general and economical
method on the basis of the Fejer mappings. Also, we consider the ill-posed problems, for which the solutions
are found by the high-precision algorithms using a priori information [1�3].
