Highly efficient methods for regional weather forecasting
A model and computational method is offered for the high performance forecasting regional meteorological processes. Relying on «unilateral influence» relationship of macro- and mesoscale models it suggests avoiding the Cauchy problem in the atmospheric model and replacing it by a boundary-value prob...
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| Цитувати: | Highly efficient methods for regional weather forecasting / A.Yu. Doroshenko, V.A. Prusov, Yu.M.Tyrchak // Систем. дослідж. та інформ. технології. — 2005. — № 4. — С. 24-31. — Бібліогр.: 8 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860223670917529600 |
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| author | Doroshenko, A.Yu. Prusov, V.A. Tyrchak, Yu.M. |
| author_facet | Doroshenko, A.Yu. Prusov, V.A. Tyrchak, Yu.M. |
| citation_txt | Highly efficient methods for regional weather forecasting / A.Yu. Doroshenko, V.A. Prusov, Yu.M.Tyrchak // Систем. дослідж. та інформ. технології. — 2005. — № 4. — С. 24-31. — Бібліогр.: 8 назв. — англ. |
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| description | A model and computational method is offered for the high performance forecasting regional meteorological processes. Relying on «unilateral influence» relationship of macro- and mesoscale models it suggests avoiding the Cauchy problem in the atmospheric model and replacing it by a boundary-value problem with specific interpolation technique that has a number of advantages of computational efficiency and good suitability for parallelization. The method and its parallel implementation on multiprocessor cluster architecture are considered.
Предлагаются модель и вычислительный метод для высокопроизводительного прогноза региональных метеорологических процессов. Метод основан на подходе «одностороннего влияния» макромасштабной модели на мезомасштабную, что позволяет решение проблемы Коши в модели атмосферы заменить ее краевой задачей с применением методов интерполяции, которая имеет преимущества в вычислительной эффективности и возможности распараллеливания. Рассматривается параллельная реализация модели на кластерной архитектуре многопроцессорной системы.
Пропонуються модель і обчислювальний метод для високопродуктивного прогнозу регіональних метеорологічних процесів. Метод засновано на підході «однобічного впливу» макромасштабної моделі на мезомасштабну, що дозволяє розв’язання задачі Коші в моделі атмосфери замінити її крайовою задачею із застосуванням методів інтерполяції, що має переваги в обчислювальній ефективності та можливості розпаралелювання. Розглядається паралельна реалізація моделі на кластерній архітектурі мультипроцесорної системи.
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| first_indexed | 2025-12-07T18:19:09Z |
| format | Article |
| fulltext |
A.Yu. Doroshenko, V.A. Prusov, Yu.M.Tyrchak, 2005
24 ISSN 1681–6048 System Research & Information Technologies, 2005, № 4
UDC 681.3
HIGHLY EFFICIENT METHODS FOR REGIONAL WEATHER
FORECASTING
A.YU. DOROSHENKO, V.A. PRUSOV, YU.M.TYRCHAK
A model and computational method is offered for the high performance forecasting
regional meteorological processes. Relying on «unilateral influence» relationship of
macro- and mesoscale models it suggests avoiding the Cauchy problem in the at-
mospheric model and replacing it by a boundary-value problem with specific inter-
polation technique that has a number of advantages of computational efficiency and
good suitability for parallelization. The method and its parallel implementation on
multiprocessor cluster architecture are considered.
INTRODUCTION
In recent years a great attention is taken by mesoscale weather events (floods, tor-
nadoes, strong winds and others) as they can cause many deaths and result in huge
economic losses [1]. Mitigating the impacts of such events would yield enormous
economic and societal benefits, so models and methods of high performance large
scale computation leading to regional forecasting regional atmospheric processes
are of great importance to provide accommodation the real time, on-demand, and
dynamically-adaptive needs of mesoscale weather research.
Regional atmospheric processes are influenced by macroscale atmospheric
circulation, so modeling meteorological values in restricted area is to be consid-
ered as a task with transitional boundary conditions. To achieve a prescribed level
of accuracy of the solutions for a model in places of heavy gradients of related
functions it is often necessary to apply a numerical method with variable grid
steps for restricted terrains. However the common techniques of mathematical
physics [2] cannot often satisfy these requirements because of low accuracy, slow
divergence and stability problems, so some dedicated numerical methods are
needed to make computation more time- and cost-effective.
Following «unilateral influence» approach to combine macro- and mesoscale
models [3,4] in this paper we describe our technique for modeling and forecasting
atmospheric processes over a region [5,6] that replaces the Cauchy problem in the
atmospheric model by a boundary-value problem and introduces a specific inter-
polation method that has advantages of computational efficiency and good paral-
lelization. The methodology is well tested and approved in complex regional eco-
logical-meteorological modeling in Ukraine [5, 6, 7].
REGIONAL WEATHER FORECASTING PROBLEM STATEMENT AND A
METHOD OF ITS NUMERICAL SOLUTION
For forecasting values of meteorological quantities (components 321 ,, vvv of ve-
locity V , pressure, temperature, specific humidity, specific liquid water content,
Highly efficient methods for regional weather forecasting
Системні дослідження та інформаційні технології, 2005, № 4 25
concentration of pollutants and others) in the atmosphere in a bounded territory
G we will follow the basics of the method of «unilateral influence» [3], where
results of analyses and forecasts received from a macroscale (hemisphere or
global) model are used as boundary conditions in a regional model.
Let the state of the atmosphere at spatial point ( )σϕλ ,,=r of the macro-
space area G be defined by a vector of meteorological quantities ( )tr,ℜ of
discrete values of the analysis and, similarly, forecast ( ) ( )rtr mm 11, ++ ℜ=ℜ re-
ceived from a macroscale model at time 1+= mtt ( )Mm ,...,1,0= with a step
mm tt −= +1τ .
Then for determining the atmospheric state in the bounded domain
( ) ( )rGrG ⊂ at [ ]1, +∈∀ mm ttt we will solve a task of the following kind in vec-
tor representation:
ℜ=
∂
ℜ∂ D
t
, [ ]1, +∈∀ mm ttt , Gr∈∀ , (1)
( ) )(, 11 rtr mm ++ ℜ=ℜ , Mm ,...,1,0= , where
−
ℜ
+
ℜ
+
ℜ
=ℜ
rrrrrr
D
∂
∂
ν
∂
∂
ϕ∂
∂ν
∂ϕ
∂
λ∂
∂
ϕ
ν
λ∂
∂
ϕ 3
21 1
coscos
1
F
r
v
r
v
r
v
+
ℜ
−
ℜ
−
ℜ
−
∂
∂
ϕ∂
∂
λ∂
∂
ϕ 3
21
cos
is the right-hand side function describing the momentum, heat and mass transmis-
sion in spherical coordinates with sink/source term F .
Now replace continuum G by a spatial grid of points gained by a spatial
grid of points obtained by discretization of the domain G with a set of 1−J
elements jλ∆ , 1−K elements kϕ∆ and 1−L elements lσ∆ . Let us construct a
vector { }jklr , defining the continuous variable r only in points ( )Jjj ≤≤1 ,
( )Kkk ≤≤1 , ( )Lll ≤≤1 . As a result we will have
∑
−
=
∆+=
1
2
1
J
J
µ
µλλλ ∑
−
=
∆+=
1
2
1
K
K
µ
µϕϕϕ ∑
−
=
∆+=
1
2
1
L
L
µ
µσσσ .
In the domain G instead of function ( )tr,ℜ defined on a macroscale grid,
we will construct below a function of discrete argument on a regional grid in the
nodes ( ) Rt m
lkj ∈,,, σϕλ , Jj ≤≤1 , Kk ≤≤1 , Ll ≤≤1 , Ll ≤≤1 . Our aim is
to put in correspondence the differential operator D in (1) and the grid operator
Λ (see the next section). After filling up function ( ) 11 ++ ℜ=ℜ m
jkl
m
jkl t in the
nodes of the regional grid and computing the right parts ( )=+1mtf
11 ++ ℜΛ== mmf , Mm ,...,2,1= , in all nodes of the grid, ( )lkj σϕλ ,, , Jj ≤≤1 ,
A.Yu. Doroshenko, V.A. Prusov, Yu.M.Tyrchak
ISSN 1681–6048 System Research & Information Technologies, 2005, № 4 26
Kk ≤≤1 , Ll ≤≤1 , we will search for a solution of the problem (1) for
[ ]1, +∈∀ mm ttt with the help of a Hermite polynomial like above for number of
points 3=M :
( ) ( )
−ℜ+ℜ−ℜ
−
+
−
+ℜ=ℜ −+ 11 24
4
mmm
m
m
m
m ttfttt
τ
τ
τ
( ) ( ) ( )
−++−ℜ−ℜ
−
+−− −+−+−+ 111111 85
4
mmmmm
m
mm fffttff τ
τ
τ
( ) ( )
+−−ℜ+ℜ−ℜ
−
− −+−+ 1111 22
4
mmmmm
m
fftt τ
τ
( ) ( )
++−ℜ−ℜ
−
+ −+−+ 1111 43
4
mmmmm
m
ffftt τ
τ
(2)
for each node of the grid ( )lkj σϕλ ,, , Jj ≤≤1 , Kk ≤≤1 , Ll ≤≤1 .
It is easy to check up that the scheme (2) has interpolation properties,
i.e. at mtt = or ( )0=−= mttτ and 1+= mtt or ( )01 =−= + tt mτ the equalities
( ) mmt ℜ=ℜ and ( ) 11 ++ ℜ=ℜ mmt hold, respectively. So the maximal error of the
solution of problem (1) with the help of (2) is inside the interval 1+≤≤ mm ttt and
it has an order of approximation ][ 4)(τO .
It was shown in [5] that constructed interpolation formulae involving a func-
tion and its derivative ( ) ( )if ηα , Ni ,...,2,1= , 1,0=α , have following advan-
tages:
• they have greater accuracy than any of the formulae using only function
values ( )if η ;
• no data are required on the right border of the interpolation interval, and
so the formulae can also be used for the rightmost interval;
• the values of function ( )if η and its derivatives ( ) ( )if ηα can be given
through unequal intervals.
APPROXIMATIONS OF DIFFERENTIAL OPERATORS
To provide a fourth-order approximation of a differential operator D in (1) by a
grid operatorΛ we need to guarantee the accuracy of the same order in the inter-
polation method for smooth filling up of the given discrete function in the nodes
of the regional grid. To this aim we propose in this section the following compu-
tational scheme.
Designate with η one of the horizontal axes of the system of coordinates
( )σϕλ ,,=r and with interval ba ≤≤η the linear size of the area of the
solutions of the macroscale model along this axis. Let any points
ba N <<<<< −121 ... ηηη , form a non-uniform macroscale grid [ ]bah ,ω
Highly efficient methods for regional weather forecasting
Системні дослідження та інформаційні технології, 2005, № 4 27
with grid step 11 −− −= iiih ηη . Let us enumerate all nodes in some order
Nηηηη ,...,,, 210 and consider the values of macroscale function ( )m
i t,ηℜ in the
nodes of a grid as components of a vector ( ){ }Nit m
i ,...,1,0, =ℜ=ℜ .
The task of filling up values of a function defined on a macroscale grid in
nodes of a regional grid on each interval [ ]1, +ii ηη will be performed with the
help of a polynomial of the fifth degree:
( ) ( ) ( ) +−+−+= 2
210 iii aaaQ ηηηηη
( ) ( ) ( )55
4
4
3
3 iii aaa ηηηηηη −+−+−+ , (3)
where
ia ℜ=0 , ( )
ℜ−ℜ
−−ℜ
+
= −
−−
+
−
−
12
1
2
2
1
2
1
1
1
1 1 i
i
i
i
i
i
i
iii
i
h
h
h
h
hhh
h
a ,
( )
ℜ+ℜ
+−ℜ
+
= −
−−
+
−
1
11
1
1
2 11
i
i
i
i
i
i
i
iii h
h
h
h
hhh
a ,
( )543 ahaha ii +−= , 54 2
5 aha i−= ,
( )
ℜ+ℜ
−−ℜ
+
−= +
+
+
+
++
i
i
i
i
i
i
i
iiii h
h
h
h
hhh
a
h
a 1
1
1
2
11
235 112 .
As for vertical changes of the meteorological values near the underlying sur-
face, where they have the heaviest gradients, it is needed to use grids with small
steps. On the other hand, to save computer memory and time it is expedient to
make use of a rough grid far from the land surface. So, irregular grids are needed
for solving mesoscale problems. However macroscale models are usually deter-
mined on the standard levels of pressure σ ( )hPa, ...,500,700,850,0z where 0z
stands for sea level. Evidently, there is no unique interpolating formula which
provides necessary accuracy of interpolation in the segment [ ]850,0z of the at-
mospheric boundary layer.
Let us divide the domain height H=σ into two pieces: h≤≤σ0 and
Hh ≤≤σ , where h is the 850 hPa pressure level. Values of the meteorological
quantities in the nodes of the vertical grid Hh ≤≤σ will be filled in with an
interpolation polynomial spline like (3) above, and values on another layer
h≤≤σ0 will be based on the commonly known theory of the turbulent atmos-
pheric boundary layer [7].
We will adopt the conditions of horizontal homogeneity of the
meteorological fields, the absence of heating or chilling effects and other factors
except turbulent exchange in the atmosphere. Then a system of equations for the
mesoscale processes in the layer h≤≤σ0 can be written as follows:
( )gT vv
z
v
zt
v
22
11 −+
=
∂
∂
ν
∂
∂
∂
∂
, (4)
A.Yu. Doroshenko, V.A. Prusov, Yu.M.Tyrchak
ISSN 1681–6048 System Research & Information Technologies, 2005, № 4 28
( )gT vv
z
v
zt
v
11
22 −−
=
∂
∂
ν
∂
∂
∂
∂
,
θ∂
θ∂ν
∂
∂
∂
θ∂ S
zzt
T +
=
Pr
,
q
T S
z
q
cSzt
q
+
=
∂
∂ν
∂
∂
∂
∂ ,
ρ
∂
∂ g
z
p
−= ,
( )qT 608.01+=θ ,
θ
ρ
R
p
= ,
where t is time, playing the role of the iteration parameter; 1v and 2v are the
components of the wind velocity; gv1 and gv2 are those at the height h=σ
(geostrophic wind); θS and qS the sources and outflows of enthalpy and humid-
ity, respectively; Tν is the turbulent viscosity; Pr is the Prandtl number; cS is
the Schmidt number, is a Coriolis parameter. The further designations are
commonly known.
We construct a vertical grid of M levels with uneven grid steps estimated as
( )[ ] ( )[ ]{ }
( ) ( )[ ]1/1ln
1/1ln1
−+
+−−+
−=
ββ
σβσβ hhz , (5)
where ∞<< β1 should hold and the closer parameter β to 1 the more nodes are
collected nearby the level 0=z .
The formulated nonlinear problem (4) has a numerical solution on the grid
(5) [7].
Equation system (4) concerns all internal points of the whole layer
Hz << σ0 . Particularly, for the sub-domain Hh <<σ , where the turbulence
viscosity coefficient can be considered as constant, system (4) has an analytical
solution [7]. Combining the numerical solution on the segment hz <<σ0 with
the analytical solution on the other segment Hh <<σ and imposing respective
boundary conditions one can define a divergent iterative process to reproduce the
vertical profiles of the meteorological fields based on their known values on the
standard levels ( )hPa ,...,500,700,850,0z .
The offered method of filling up the vertical grid allows us to take into ac-
count the heterogeneity of the underlying surface, which can disturb the macro-
scale flow.
Now the computation of the grid values of the partial derivatives of the first
order ( )ii ηψ ∂ℜ∂= and of the second order ( )ii
22 ηζ ∂ℜ∂= included in
m
jkl
m
jklf ℜΛ= , will be performed on the basis of the following relations:
Highly efficient methods for regional weather forecasting
Системні дослідження та інформаційні технології, 2005, № 4 29
=+
++ −
−−
+ 1
11
1 12 i
i
i
i
i
i
i h
h
h
h
ψψψ
4
42
1
2
1
2
1
2
1
1 1
24
13 1
η∂
ℜ∂
−−
ℜ
−ℜ
−−ℜ=
−
−
−−
+
−
i
ii
i
i
i
i
i
i
i
i h
hhh
h
h
h
h
h
i , (6)
+
+
+
++
+
− −−−
+
−−−
i
i
i
i
i
i
i
i
i
i
i
i
i
i
h
h
h
h
h
h
h
h
h
h
h
h
ξξ 13111 111
1
111
+
ℜ+ℜ
+−ℜ=
−
++ −
−
+
−
−
−−
1
1
1
1
21
11 11211 ii
i
i
i
i
i
i
i
i
i
i
i
h
h
h
h
hh
h
h
h
ξ
5
52
11
2
11
2
1251
360 η∂
ℜ∂
−+
−+ −−−−
i
i
i
i
i
iii
h
h
h
h
h
hhh
. (7)
It is obvious that the relations (6), (7) have the third order at 1−≠ ii hh and
the fourth order at 1−= ii hh . Derivatives ( )ii ηψ ∂ℜ∂= and ( )ii
22 ηξ ∂ℜ∂=
belong to (4), (5) implicitly. But these are systems of algebraic equations with
tridiagonal matrices, so solutions can be found effectively with the help of the
sweep method [8] with the boundary conditions
( ) [ ]4
1
1
12
2112
1 2
6
hO
h
h
+
ℜ−ℜ
=++−− ψψξξ , (8)
( ) [ ]4
1
1
1
11
1 2
6 −
−
−
−−
− +
ℜ−ℜ
=++−− N
N
NN
NNNN
N hO
h
h
ψψξξ . (9)
The main advantage of the offered method for the approximation of
derivatives is that the solution of the system of algebraic equations (6)–(7) at all
points depends on values at other points, i.e., it depends on iℜ globally, which
means smooth filling up and approximation of the differential operators by the
grid operators.
SOFTWARE IMPLEMENTATION AND EXPERIMENTS
A software package of the method considered above was implemented and ex-
perienced in short- and intermediate-term regional meteorological forecasting for
the territory of Ukraine and nearby areas. The meteorological functionality of the
package includes following options:
• setting up an area of the initial data and weather forecast;
• downloading and decoding initial meteorological data;
• adaptation of the initial meteorological data;
• weather forecast on required term;
• visualization of results of the forecast.
A.Yu. Doroshenko, V.A. Prusov, Yu.M.Tyrchak
ISSN 1681–6048 System Research & Information Technologies, 2005, № 4 30
The size of area and the parameters of a grid depend on parameters of model
of numerical weather forecast of hydrometeorological service DWD Offenbach
(Germany) from which the initial meteorological data are accepted.
Initial data are downloaded via Internet channels from Offenbach in GRIB
binary representation and then decoding is performed. This task is launched twice
per day after 5.00 and 17.00 at local time. The program of weather forecast on
required term (from 1 to 5 days with a step of 1 hour) can be started on demand
any times. The execution begins with the analysis of presence of files with the
initial data, and process is visually supervised.
Experiments on parallel implementation of the package were carried out on
cluster multiprocessor (2.6 MHz, 512Mb of main memory for each Intel Xeon
processor, Dolphin SCI interconnection) and exposed good suitability of the task
to parallelization. Below a diagram is depicted (see Figure) concerning interpola-
tion of data received from macroscale grid into points of mesoscale grid. The dia-
gram shows computation time (in sec, axis Z ) on various numbers of processors
(from 1 up to 8, axis Y ) at the various sizes mesoscale grid (axis X ).
CONCLUSION
We have presented a new computational method for the efficient solution of the
complex problem of forecasting regional meteorological processes. Our method
follows the approach of “unilateral influence” to combine macro- and mesoscale
models [3,4]. It gives opportunity to replace the Cauchy problem in the atmos-
pheric model (1) by a boundary-value problem and introduces a specific interpo-
lation method (2) that has a number of advantages:
• the time step in getting macroscale information for regional forecasting
can be significantly increased and reach 12=τ hours [6];
• as opposed to classical numerical methods for solving the equations of
mathematical physics, the offered method is deprived of instability problems;
1 2 4 6 8
1000x1000x10
1600x1600x10
2200x2200x10
0
5
10
15
20
25
30
35
40
45
1000x1000x10
1200x1200x10
1400x1400x10
1600x1600x10
1800x1800x10
2000x2000x10
2200x2200x10
Results of interpolation macroscale data into mesoscale grid
Highly efficient methods for regional weather forecasting
Системні дослідження та інформаційні технології, 2005, № 4 31
• the accuracy of the offered method has fourth order and is determined by
the same order of accuracy of the following constituent methods: smooth filling
up of macroscale values into mesoscale grid nodes (3), (
The model and method have been implemented in a software package and
tested by the Hydrometeorological Center of Ukraine. The comparison with actual
wheather cards has shown that the numerical forecasts qualitatively and
quantitatively well coordinate with real observed data. The model and method
have been successfully applied in regional short- and middle-term weather fore-
casting for districts of Ukraine.
Results of experiments in parallel implementation of the computational
scheme for solving problems in regional meteorological forecasting in Ukraine
show its good computational efficiency, scalability and applicability for parallel
computation.
4), approximating differ-
ential operators by grid ones (6)–(9) and interpolation method (2) for solving the
boundary-valued problem based on the approach of «unilateral influence».
Acknowledgement
The work is partially supported by NATO Collaborative Linkage Grant 980505.
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Received 20.07.2005
______________________________
From the Editorial Board: The article corresponds completely to submitted manu-
script.
Highly Efficient Methods for Regional Weather Forecasting
A.Yu. Doroshenko, V.A. Prusov, Yu.M.Tyrchak
Introduction
Regional Weather Forecasting Problem Statement and a Method of Its Numerical Solution
Approximations of Differential Operators
Software Implementation and Experiments
Conclusion
Acknowledgement
Results of interpolation macroscale data into mesoscale grid
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| id | nasplib_isofts_kiev_ua-123456789-13872 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1681–6048 |
| language | English |
| last_indexed | 2025-12-07T18:19:09Z |
| publishDate | 2005 |
| publisher | Навчально-науковий комплекс "Інститут прикладного системного аналізу" НТУУ "КПІ" МОН та НАН України |
| record_format | dspace |
| spelling | Doroshenko, A.Yu. Prusov, V.A. Tyrchak, Yu.M. 2010-12-06T11:18:45Z 2010-12-06T11:18:45Z 2005 Highly efficient methods for regional weather forecasting / A.Yu. Doroshenko, V.A. Prusov, Yu.M.Tyrchak // Систем. дослідж. та інформ. технології. — 2005. — № 4. — С. 24-31. — Бібліогр.: 8 назв. — англ. 1681–6048 https://nasplib.isofts.kiev.ua/handle/123456789/13872 681.3 A model and computational method is offered for the high performance forecasting regional meteorological processes. Relying on «unilateral influence» relationship of macro- and mesoscale models it suggests avoiding the Cauchy problem in the atmospheric model and replacing it by a boundary-value problem with specific interpolation technique that has a number of advantages of computational efficiency and good suitability for parallelization. The method and its parallel implementation on multiprocessor cluster architecture are considered. Предлагаются модель и вычислительный метод для высокопроизводительного прогноза региональных метеорологических процессов. Метод основан на подходе «одностороннего влияния» макромасштабной модели на мезомасштабную, что позволяет решение проблемы Коши в модели атмосферы заменить ее краевой задачей с применением методов интерполяции, которая имеет преимущества в вычислительной эффективности и возможности распараллеливания. Рассматривается параллельная реализация модели на кластерной архитектуре многопроцессорной системы. Пропонуються модель і обчислювальний метод для високопродуктивного прогнозу регіональних метеорологічних процесів. Метод засновано на підході «однобічного впливу» макромасштабної моделі на мезомасштабну, що дозволяє розв’язання задачі Коші в моделі атмосфери замінити її крайовою задачею із застосуванням методів інтерполяції, що має переваги в обчислювальній ефективності та можливості розпаралелювання. Розглядається паралельна реалізація моделі на кластерній архітектурі мультипроцесорної системи. en Навчально-науковий комплекс "Інститут прикладного системного аналізу" НТУУ "КПІ" МОН та НАН України Прогресивні інформаційні технології, високопродуктивні комп’ютерні системи Highly efficient methods for regional weather forecasting Высокоэффективные методы регионального прогнозирования погоды Високоефективні методи регіонального прогнозування погоди Article published earlier |
| spellingShingle | Highly efficient methods for regional weather forecasting Doroshenko, A.Yu. Prusov, V.A. Tyrchak, Yu.M. Прогресивні інформаційні технології, високопродуктивні комп’ютерні системи |
| title | Highly efficient methods for regional weather forecasting |
| title_alt | Высокоэффективные методы регионального прогнозирования погоды Високоефективні методи регіонального прогнозування погоди |
| title_full | Highly efficient methods for regional weather forecasting |
| title_fullStr | Highly efficient methods for regional weather forecasting |
| title_full_unstemmed | Highly efficient methods for regional weather forecasting |
| title_short | Highly efficient methods for regional weather forecasting |
| title_sort | highly efficient methods for regional weather forecasting |
| topic | Прогресивні інформаційні технології, високопродуктивні комп’ютерні системи |
| topic_facet | Прогресивні інформаційні технології, високопродуктивні комп’ютерні системи |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/13872 |
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