=Paper=
{{Paper
|id=Vol-3066/paper11
|storemode=property
|title=Further Development of Atmosphere Pressure Field Research in the Arctic Region of Russia
|pdfUrl=https://ceur-ws.org/Vol-3066/paper11.pdf
|volume=Vol-3066
|authors=Natalia Tuchkova,Konstantin Belyaev,Gury Mikhaylov,Alexey Salnikov
|dblpUrl=https://dblp.org/rec/conf/ssi/TuchkovaBMS21
}}
==Further Development of Atmosphere Pressure Field Research in the Arctic Region of Russia==
https://ceur-ws.org/Vol-3066/paper11.pdf
Further Development of Atmosphere Pressure Field Research
in the Arctic Region of Russia
Natalia P. Tuchkova1, Konstantin P. Belyaev2, Gury M. Mikhaylov3, Alexey N. Salnikov4
1,2,3,4
Dorodnicyn Computing Center FRC CSC of RAS, Vavilov str., 40, Moscow, 119333, Russia
2
Shirshov Institute of Oceanology of RAS, Nahimovskiy pr., 36, Moscow, 117218, Russia
4
Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow, 11999, Russia
Abstract
The results of studies of atmospheric pressure in the Arctic region of Russia for the period from
1948 to 2008 presented. The analysis of the climatic seasonal variation of the atmospheric
pressure fields has been carried out. As the main research method, the probabilistic and statis-
tical analysis of the time series of the pressure field during 60 years at fixed points in the region
of the Arctic zone of Russia was used. In total, about 90,000 daily (with a six-hour interval)
pressure values were studied. Based on these data, the climatic seasonal variability was con-
structed as an averaging of the values of a given time series at each point in space and for a
fixed date. The characteristics of the seasonal cycle, its amplitude and phase have been ana-
lyzed. Those characteristics were studied and their geophysical interpretation was carried out.
In particular, the minimum and maximum values of the series were determined for the entire
region and the time series of these characteristics were constructed. It is shown that the devia-
tion is asymmetrical in nature; this is an unobvious result of research. For the maximum and
minimum, the best approximations were proposed, and these approximations were tested by
known methods of statistical analysis, including maximum likelihood, least squares and good-
ness of fit methods (tests), in particular, the χ2 test. The performed study has applications both
purely physical (allows to explain the nature, genesis and distribution of large-scale atmos-
pheric formations in a climatic year) and prognostic (allows to understand and track trends in
climate, as well as to quantitatively estimate the scale and variability of large-scale atmospheric
processes). Numerical calculations were performed on the Lomonosov-2 supercomputer of the
Moscow State University named after M.V. Lomonosov.
Keywords 1
Time series analysis, climatic seasonal variability, maximum and minimum pressure values
within a climatic annual cycle
1. Introduction
The work utilized the methods of time series analysis, in particular, the separation of the time series
into periodic and non-periodic components. Such methods are successfully used in the analysis of the
financial market [1] and long-term variability of geophysical characteristics, such as the temperature of
air or water [2], as well as in more complex models and schemes [3]. In geophysical schemes and
models, the concept of climatic seasonal variability is frequently used, when the average values of the
entire time series are plotted for each date of the year and at each fixed point in space. For example, all
the values on January 1 at a specific point in space for the entire observation period are averaged, and
as a result, the average value of the series for January 1 is plotted, which is considered as a climatic
value. This procedure is carried out for each day within the year. Such a way, the climatic seasonal
SSI-2021: Scientific Services & Internet, September 20–23, 2021, Moscow (online)
EMAIL: natalia_tuchkova@mail.ru (N.P. Tuchkova); kosbel55@gmail.com (K.P. Belyaev); gmickail@ccas.ru (G.M. Mikhaylov);
salnikov@angel.cs.msu.ru (A.N. Salnikov)
ORCID: 0000-0001-6518-5817 (N.P. Tuchkova), 0000-0003-2111-2709 (K.P. Belyaev), 0000-0002-4535-7180 (G.M. Mikhaylov),
0000-0001-8669-9905 (A.N. Salnikov)
© 2021 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
variability of a specific physical characteristic is built. This method is described in detail, for example,
in [4]. Further in the studies, it is possible to analyze in more detail the obtained series of observations,
for example, to select the maximum and (or) minimum values of this physical characteristic over a
given area and to study the variability of only these maximum or minimum. Note the importance of
these characteristics, since, for example, in the field of atmospheric pressure. These extrema are asso-
ciated with such physical processes as cyclones and anti-cyclones, their localization and variability.
Plenty of modern works have been devoted to the study of the Arctic region, since the climate of
this region has been especially subject to changes due to global warming in recent decades, which has
led to a significant decrease in snow and ice cover [5–8]. For example, paper [8] presents the results of
the analysis of the pressure fields of the Arctic region in the “early instrumental” period 1801–1920.
These data refer to the time when the collection of meteorological data from the network of regular
stations has started. The data array of observations [9] over 20 years is insufficient to assess the climatic
seasonal variation, but their analysis allowed the authors to get an idea of the state of pressure in the
Arctic and find out that, in general, it was lower than the current one.
Many works are also devoted to the study of anomalies, deviations from the corresponding mean
[10, 11]. Anomaly indices [12] made it possible to combine series with similar characteristics. It was
found that below zero anomalies of the mean annual air temperature and positive anomalies in the total
ice extent of the seas of the Siberian shelf prevailed from the mid-1950s to the end of the 1980s and
were accompanied by weaker high-latitude zonal transport in the troposphere, strengthening of the Arc-
tic High, and other features [13].
This work continues the studies published earlier in [14, 15]. Just as in those ones, here the atmos-
pheric pressure field was used in the area bounded by the coordinates of 62°N–80°N and 15°E–60°E.
On the one hand, this area is wide enough to ignore the local features of atmospheric processes, on the
other, it is sufficiently uniform, since the sizes of large atmospheric formations are comparable to the
dimensions of the entire area. By time, pressure data were recorded from January 1, 1948 to December
31, 2008, daily in a one-degree grid. These data were obtained at the Hydro-meteorological Center of
Russia and were used earlier in several works, for example, [16].
This article presents the results of a probabilistic analysis of atmospheric pressure fields, carried out
on the basis of separating of the entire series into periodic and non-periodic components. Such an anal-
ysis was carried out for the maximum and minimum values of the pressure fields in the region and
within the climatic year. It is shown that the studied processes can be represented as a sum, where one
term characterizes a regular periodic signal, and the other is a random process independent of the first
one. The characteristics of this random process can be determined from the obtained sample. In this
case, both the periodic signal and the characteristics of the random process for the maximum and min-
imum pressure is different, have their own fundamental features and require additional study.
For the considered atmospheric pressure fields in the region the maxima and minima values differ
markedly. If the minima in space change from 980 hPa to 995 hPa, then the maxima change from
1010 hPa to 1025 hPa, and these values “migrate” within the region during the year. This is due to the
behavior of cyclones and anticyclones, their movement, deepening and restructuring. In the Arctic re-
gion of Russia, there are noticeably more cyclones during the climatic year than anticyclones. There-
fore, the distributions of their characteristics are different. Note that the size of the cyclonic atmospheric
formation, which mainly forms the pressure field, is comparable to the size of the entire area under
consideration. In other words, we are dealing with one, maximum, two cyclones and anticyclones at the
same time.
The following research was done in the work:
built a climatic seasonal process for the field of atmospheric pressure in the Arctic region of
Russia, described its features for maximum and minimum values in the area;
time dependence of these characteristics were built, their analysis was carried out;
the division of these processes into periodic and aperiodic components was carried out, the
amplitudes and phases of the periodic components were estimated;
for the aperiodic components, the approximations of the observed values that are optimal in
terms of the minimum variances are selected, their agreement with the approximating distribu-
tions is shown.
113
2. Observational data for pressure fields
Consider the field of atmospheric pressure in the area bounded by coordinates 62°–80°N and 15°–
60°E, that is, the European part of the Arctic zone of Russia, including the Baltic coast, the waters of
the White and Barents Seas to the Kara Sea and the Yamal Peninsula. This is a sufficiently wide area
to neglect the local features of atmospheric processes, and also fairly uniform, since the sizes of large
atmospheric formations are comparable to the sizes of this area. Pressure observational data were rec-
orded in the period from 01.01.1948 to 31.12.2008 every day with an interval of 6 hours in a one-degree
grid.
For clarity, we will present the pressure fields themselves, which are typical for this region. In Fig-
ure 1 shows the average pressure field for each point of the European part of the Arctic zone of the
Russian Federation for 60 years from 1948 to 2008. It can be seen that the field is a rather smooth
surface in space, although if the values themselves are presented in the form of a curve (Figure 2), then
jumps and anomalies within the annual seasonal variation become noticeable.
1014,0Pa (hPa)
1012,0-1014,0
1012,0
1010,0 1010,0-1012,0
1008,0 1008,0-1010,0
1006,0
1006,0-1008,0
1004,0
15,020,0 1004,0-1006,0
77,5
25,0
30,0
35,0 70,0
40,0
45,0
50,0 62,5
55,0
60,0
Figure 1: Average values field of pressure over 60 years for each point of the area bounded by coordi-
nates 62°–80°N and 15°–60°E
Figure 2 shows the curve of changes in the average values for the entire time period of observations
for each day. One can see that there are no visible lows, but there are periods of the largest jumps in
values, for example, in 1958 and 1968–1988. Since 1975, according to the Hydro-meteorological Cen-
ter of the Russian Federation, there has been a trend towards an increase in temperature jumps, which
is shown in [17] on the picture of anomalies in the mean annual air temperature in the Arctic region.
The difference in the anomalies of mean values for the period 1948–2008 over the European part of
the Arctic zone of Russia is 8.04 hPa, and for the period 1882–1990 over the entire Arctic region,
regarding to studies [9, Table VII] – 1.4 hPa. This comparison gives an indication of the change in the
trend of the observed values.
114
1016
1014
1012
1010
1008
1006
1004
1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003 2008
Figure 2: The curve of average pressure values for each day for 60 years from 01.01.1948
to 12.31.2008 in the Arctic zone of the Russian Federation
3. Results of analysis of field pressure
In the considered fields, areas of minimum and maximum pressure for each day were identified and
graphs of their behavior were plotted for annual climate cycle values.
Pa (hPa)
1024
1020
1016
1012
1008
1-Jan 20-Feb 10-Apr 30-May 19-Jul 7-Sep 27-Oct 16-Dec
Figure 3: Behavior of the average annual pressure maximum – red line; approximation – blue dotted
line
Figure 3 shows the graphs of the average maximum of the climatic annual cycle for the period under
consideration and the approximating function. The behavior of the average annual pressure maximum
Pa (yr) over the entire region for the period from 1948 to 2008 and over the space of 62.5°–80°N and
15°–60°E is shown versus to the trigonometric function averaged over the observational data set. In
Figure 3 it is very clear that the behavior of the maximum can be represented as a sum of a trigonometric
function and a random remain.
115
ΔP
2,5
2
1,5
1
0,5
0
-0,5
-1
-1,5
-2
-2,5
17-Feb 7-Apr 27-May 16-Jul 4-Sep 24-Oct 13-Dec
Figure 4: Difference between the observed and approximating curves for the mean annual maximum
pressur
The least squares method can be used to find the parameters of this trigonometric function, which
turns out to be equal, where A=1016.5 (hPa), B=6 (hPa), ω=0.01 (year-1). After subtracting its approx-
imation from the “red line”, the curve (ΔPa) is shown in Figure 4 (the initial of coordinates has been
moved for better presentation).
50
40
30
20
10
0
-2,3 -2,0 -1,8 -1,5 -1,3 -1,0 -0,8 -0,5 -0,3 0,0 0,2 0,5 0,8 1,0 1,3 1,5 1,8 2,0 2,3
Figure 5: Hystogramm of maxima for ΔPa annual seasonal cycle
This histogram quite well, with the required degree of probability with respect to the χ 2 criterion,
agrees with two distributions: Gaussian (Pd1) and Maxwell (Pd2), which is shown in Figure 6 (a, b).
116
0,6 Pd
Pd
0,6
0,5
0,5
0,4
0,4
0,3
0,3
0,2
0,2
0,1 0,1
0 0
-1,30 -0,80 -0,30 0,20 0,70 1,20 1,70 2,20 -1,00 -0,50 0,00 0,50 1,00 1,50 2,00
-0,1 (a) ΔP -0,1 (b) ΔP
a
Figure 6: Approximation of the random rest of maxima (blue line) by (a) Gaussian distribution; (b) Max-
well distribution (red line)
1 ( x )2
For the Gaussian distribution, F1 ( x) exp[ ] the optimal parameters are
2 2 2
α=0.277, σ=0.5, β=0.78. In this case, the approximation occurs uniformly over the entire region, but
not very well in the region of low probabilities (“tails” of the distribution). The Maxwell distribution
(x ) ( x ) 2 with the parameters α=1, σ=0.8 approximates the “tails” much better, but
F2 ( x) exp[ ]
2 2 2
poorly approximates the region of small negative pressure values.
A similar study was carried out for the pressure minima. The behavior of climatic seasonal minima
is shown in Figure 7 (year to year averaged over the observational data set).
1000
995
990
985
980
1-Jan 20-Feb 10-Apr 30-May 19-Jul 7-Sep 27-Oct 16-Dec
Figure 7: Curve of averaged year to year minima (red line) and its approximation line (blue dashed
line)
117
40
35
30
25
20
15
10
5
0
984,75 985,75 986,76 987,76 988,77 989,77 990,78 991,78 992,79 993,79 994,80
Figure 8: Hystogram of averaged annual cycle
The curve of averaged minima (1948–2008 yr over entire region) and its approximation
fi A B sin xi , A=984,2, B=15, ω=0,01 (xi=0,9*k, k=0, 1, ..., 368) presented in Figure 7. The
histogram is shown in Figure 8.
According to an applied method the corresponding probability function is approximated by Maxwell
distribution F2 ( x) ( x 2 ) exp[ ( x 2 ) ] , where α=0, σ=1 (Figure 9).
2
2
Pd
0,4
0,35
0,3
0,25
0,2
0,15
0,1
0,05
984,00 986,00 988,00 990,00 992,00 994,00
Figure 9: Approximation of the rest of minima by Maxwell distibution (red line shows
an the approximation and blue line shows the origin function)
From this figure (Figure 9) it can be seen that the Maxwell distribution with the above parameters
constructed by the method of maximum likelihood and tested by the χ2 criterion with 12 degrees of
freedom (the division of the pressure interval into 14 subintervals and 2 parameters was estimated by
sample) agrees very well with observations (with a confidence level of 95%). It can be noted that for
the minima the model of the sum of the fixed trigonometric functions plus the random remainder is in
better agreement with the observations than for the maxima. This can be explained by the fact that for
the polar zone of Russia cyclones, their physical features are more characteristic than anticyclones and
their variability.
118
4. The upper boundaries determination for the pressure fields
Analyzing the variability of the pressure field, we used its representation in the form of a stochastic
differential equation, namely
(1)
dX a(t , X )dt b(t , X )dW .
In (1) it is denoted dX X (t dt ) X (t ) . That is the variability of the pressure at the fixed spatial
point, a(t , X ), b(t , X ) are coefficients of drift and diffusion, respectively. They defined by (2) according
to [12]
( y x)dP( y / x);
1
a(t , x) (dt )
(2)
b 2 (t , x) (dt ) 1 ( y x)2 dP( y / x) dta2 (t , x),
where P( y / x) is a conditional probability of the transition of the process X (t ) from state x into state
y , that is P( y / x) P( X (t dt ) y / X (t ) x) , dW stands for the standard notation of the Gaussian
“white noise” with zero mean and uniquely variation. The calculation methods of those variables are
defined in [17, 18].
t t
Form, the expression (1) will be written as X (t ) X (0) a( , x( ))d b( , x( ))d W . Then
0 0
breaking down the entire interval [0,t] into subintervals i 1 i , and then, replacing the integral by
integral sum we yield,
t т
b( , x( ))d W S (t ) b( i )(W ( i 1 ) W ( i )).
ш 0
(3)
0
From (3) one can see that we deal with the sum of independent random variables with zero mean
т т
and variance equaled B b 2 ( i ) . That means, the variance B b 2 ( i ) n min
2
approx-
i 0 i 0
imately equaled, B ~ tC , where С is some positive. From the latter representation and also from the
assumption that the pressure values are bounded the statement of the Petrov’s theorem [19] follows and
the equality (4) holds
(4)
S (t )
lim 1(almostsure).
B(t ) ln ln B(t )
This gives to assess the upper boundaries for the process X (t ) , as follows
t
| X (t ) || X (0) | | a( , x( ))d | 2 B ln ln B
0
(with the probability 1) when t .
In Figures 10 and 11 one can see that the coefficient b2 (t , x) quite well corresponds to the coefficient
a(t , x) , with some differences. So, from Figure 10 that the seasonal variation for the coefficient b2 (t , x)
is less pronounced, for example, it is almost invisible in April or July, and the interannual variation
reflects the 11-year cycle worse (although it also exists) and the quasi-biannual cycle is better than the
coefficient a(t , x) . Neither coefficient a(t , x) nor b2 (t , x) contain any linear trends.
119
14,00
a (15 Jan)
12,00
10,00
8,00
6,00
4,00
2,00
0,00
1948 1958 1968 1978 1988 1998 2008
-2,00
Figure 10: Graph for coefficient a(t , x) from 1948 until 2008 years (measured at 0 o'clock Jan 15)
200,00
b(15 Jan)
160,00
120,00
80,00
40,00
0,00
1948 1958 1968 1978 1988 1998 2008
Figure 11: Graph for coefficient b2 (t , x) from 1948 until 2008 years (measured at 0 o'clock Jan 15)
5. Conclusions
The paper proposes and implements methods of probabilistic analysis of the time series of atmos-
pheric pressure over 60 years. It is shown that the climatic seasonal variability constructed according
to such a series and the maximum and minimum are well approximated by the sum of the regular and
stochastic terms. At the same time, a quantitative assessment of the deviation of the real pressure from
the seasonal variation in the form of the probability density distribution is given. It is shown that the
deviation is asymmetric, which is an unobvious research result. For the maximum and minimum, the
best approximations were constructed, and these approximations were tested by known methods of
statistical analysis, including the maximum likelihood method, the least squares method and methods
(tests) of goodness, in particular, the χ2 test.
Such a study has both a purely physical application, that is, it allows explaining the nature, genesis
and distribution of large-scale atmospheric formations in a climatic year, and a prognostic one, that is,
it allows to understand and track trends in the climate, and also quantify the scale and variability of
large-scale atmospheric processes.
120
6. Acknowledgements
The work was carried out within the framework of the themes of the Ministry of Education and
Science of the Russian Federation 0128-2021-0002 IO RAS and “Mathematical Methods for Data Anal-
ysis and Forecasting” of the Federal Research Center of CSC RAS.
7. References
[1] M. Kendall, A. Stuart, J. K. Ord, The Advanced Theory of Statistics. Volume 3: Design and Anal-
ysis, and Time-Series. Fourth edition Hardcover, 1983.
[2] J. Murphy, Technical analysis of the futures markets. A Comprehensive Guide to Trading Methods
and Applications. New York Institute of Finance, 1986.
[3] V. E. Prival'skij, Statisticheskaya predskazuemost' srednej godovoj temperatury vozduha
severnogo polushariya, Dokl. AN SSSR 257, 6 (1981) 1342–1345.
[4] I. I. Zveryaev, I. M. Yashayaev, Sezonnaya izmenchivost' polej davleniya, temperatury vody i
vozduha v Severnoj Atlantike po dannym COADS, Izvestiya AN SSSR. Fizika atmosfery i okeana
2 (1996) 222-239.
[5] I. E. Frolov, Z. M. Gudkovich, V. P. Karklin, E. G. Kovalev, V. M. Smolyanickij, Klimaticheskie
izmeneniya ledovyh uslovij v arkticheskih moryah evrazijskogo shel'fa, Problemy Arktiki i
Antarktiki 75 (2007) 149–160.
[6] I. Frolov, Z. Gudkovich, V. Karklin, E. Kovalev, V. Smolyanitsky, Climate Change in Eurasian
Arctic Shelf Seas. Centennial Ice Cover Observations: Praxis Publishing Ltd, Chichester, UK,
2009.
[7] F. Fetterer, V. F. Radionov (eds), Environmental Working Group Arctic Meteorology and Climate
Atlas, Version 1. NSIDC, Colorado, USA. 2000. https://doi.org/10.7265/N5MS3QNJ.
[8] Y. Zhao, A. K. Liu, Arctic sea-ice motion and its relation to pressure field. J. Oceanography 63,
505–515 (2007). https://doi.org/10.1007/s10872-007-0045-2.
[9] R. Przybylak, P. Wyszyński, Z. Vízi, J. Jankowska, Atmospheric pressure changes in the Arctic
from 1801 to 1920, The International Journal of Climatology 33 (2013) 1730–1760.
https://doi.org/10.1002/joc.3546.
[10] Longterm Changes In Atmospheric Pressure Fields And Atmospheric Circulation Indices URL:
https://www.climate-policy-watcher.org/arctic-seas/longterm-changes-in-atmospheric-pressure-
fields-and-atmospheric-circulation-indices.html.
[11] O. Humlum, Climate 4you. 2012. URL: http://www.climate4you.com/index.htm.
[12] E. G. Kovalev, A. V. Yulin, Automated prognostic system for scientific-operational support of
navigation in the Arctic. AARI Proc. 438 (1998) 73–82.
[13] Z. M. Gudkovich, Ye. G. Kovalev, Conformity of large-scale processes in the atmosphere, ocean
and ice cover of the northern polar area. AARI Proc. 437 (1997) 17–29.
[14] K. Belyaev, G. Mikhaylov, A. Salnikov, N. Tuchkova, Seasonal and Decadal Variability of At-
mosphere Pressure in Arctic, its Statistical and Temporal Analysis, CEUR Workshop Proceedings
2784 (2020) 51–61. URL:http://ceur-ws.org/Vol-2784/rpaper05.pdf.
[15] K. Belyaev, G. Mikhaylov, A. Salnikov, N. Tuchkova, Sezonnaya i mnogoletnyaya izmenchivost'
atmosfernogo davleniya v Arktike, statisticheskij i vremennoj analiz, Russian Digital Libraries
Journal. 2021. V. 24. No. 1. S. 57–73.
https://doi.org/10.26907/1562-5419-2021-24-1-57-73.
[16] S. K. Popov, Influence of sea ice on the harmonic tidal oscillations of sea level and currents in the
Barents and White seas, Trudy Gidrometcentra RF, Gidrometeorologicheskie issledovaniya i
prognozy 4, 370 (2018) 137–155.
[17] B. A. Birman, T. V. Berezhnaya, A. D. Golubev, Osnovnye pogodno-klimaticheskie osobennosti,
nablyudavshiesya na Severnom polusharii Zemli v 2017 g. Analiticheskij obzor. FGBU
‘Gidrometcentr Rossii’, Moscow. 2017.
URL:http://www.meteorf.ru/upload/iblock/dc0/Бирман%20Климат_2017.pdf.
[18] I. Gihman, A. Skorohod, Vvedenie v teoriyu sluchajnyh processov. Nauka, Moscow, 1965.
[19] V. V. Petrov, O zakone povtornogo logarifma, UMN 15, 2 (1960) 189–194.
121