On determination of mean values of observed quantities according to O. Ya. Orlov
The definition of O.Ya.Orlov for mean values of observed quantities for any epoch suits for application not only in astronomy, and in geophysics, geodesy, meteorology. The method of seasonal decomposition and adjustment Census X-11 for realization of Orlov’s definition in various areas of researches...
Збережено в:
| Опубліковано в: : | Кинематика и физика небесных тел |
|---|---|
| Дата: | 2005 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Головна астрономічна обсерваторія НАН України
2005
|
| Теми: | |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/79679 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On determination of mean values of observed quantities according to O. Ya. Orlov / M. Tyshchuk, A. Gozhy // Кинематика и физика небесных тел. — 2005. — Т. 21, № 5-додаток. — С. 372-375. — Бібліогр.: 3 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859911537385275392 |
|---|---|
| author | Tyshchuk, M. Gozhy, A. |
| author_facet | Tyshchuk, M. Gozhy, A. |
| citation_txt | On determination of mean values of observed quantities according to O. Ya. Orlov / M. Tyshchuk, A. Gozhy // Кинематика и физика небесных тел. — 2005. — Т. 21, № 5-додаток. — С. 372-375. — Бібліогр.: 3 назв. — англ. |
| collection | DSpace DC |
| container_title | Кинематика и физика небесных тел |
| description | The definition of O.Ya.Orlov for mean values of observed quantities for any epoch suits for application not only in astronomy, and in geophysics, geodesy, meteorology. The method of seasonal decomposition and adjustment Census X-11 for realization of Orlov’s definition in various areas of researches is used.
|
| first_indexed | 2025-12-07T16:02:47Z |
| format | Article |
| fulltext |
ON DETERMINATION OF MEAN VALUES
OF OBSERVED QUANTITIES ACCORDING TO O. Ya. ORLOV
M. Tyshchuk, A. Gozhy
Poltava Gravimetrical Observatory, NAS of Ukraine
27/29 Myasoedova Str., 36029 Poltava, Ukraine
e-mail: pgo@poltava.ukrtel.net
The definition of O.Ya. Orlov for mean values of observed quantities for any epoch suits for appli-
cation not only in astronomy, and in geophysics, geodesy, meteorology. The method of seasonal
decomposition and adjustment Census X-11 for realization of Orlov’s definition in various areas of
researches is used.
INTRODUCTION
In the scientific work [1] O. Ya.Orlov wrote: “In astronomy such definition is accepted: if any quantity has
secular and periodic changes, its “mean” value for the given moment is equal to such its value, which this
quantity would have, if there were no its periodic changes. This clear standard concept should use to define,
what is “mean latitude” at the given moment: it is such value of latitude, which it would have at this moment,
if there were no its periodic changes... Similarly told, “mean pole” at the given moment is named such position
of pole, which it would occupy at the moment, if there were no its periodic fluctuations”.
PURPOSE
It is necessary to note that O. Ya. Orlov’s definition of “mean latitude” and “mean pole” is possible to generalize
on any other observable quantities. Then it can be used not only in astronomy, and in other areas of researches,
such as geodesy, geophysics, meteorology, etc. In particular, it can be applied for calculation of mean values
of coordinates, gravity, atmospheric pressure, external temperature, levels of reservoirs, and other spatial,
geophysical, and meteorological parameters for any given point and epoch of observation.
The determination of mean value of parameters for various epoch is very important to study of different
evolutionary processes. It is also necessary for precision reductions of observations to basic points of various
spatial, geophysical and other networks. If there are stations of complex diverse observations (for example
astronomical, geodetic, geophysical), the knowledge of mean values of measured quantities is necessary very
much for reduction of these observations to the certain geometrical centres in each epoch of observations and
for common using and interpretation of results of observations.
O. Ya. Orlov’s definition can be used not only in natural sciences, but in socio-economic sphere also.
METHOD
O.Ya. Orlov has developed the formulas for calculation of values of “mean latitudes” of points and positions
of “mean pole” for any epoch of observations. These formulas (filters) were subsequently advanced by other
authors. For discovering and exception of periodic fluctuations of the polar motion and other phenomena,
the spectral analysis is also widely applied. But to take into account time variability of some fluctuations
parameters is very difficult.
For calculation of the mean values of observable quantities we have applied a known method of seasonal
decomposition and adjustment Census II (version X-11) [2]. Its program realization is in the STATISTICA 6
package [3]. The basic idea of seasonal decomposition is simple. In general, a time series can be thought of as
consisting of four different components:
1. a seasonal component St, where t stands for the particular point in time;
2. a trend component Tt;
3. a cyclical component Ct;
4. an irregular component It.
c© M. F. Tyshchuk, A. V. Gozhy, 2004
372
���� ���� ���� ���� ���� ����
�� �
��
�� �
�� �
�� �
��
�� �
latitude, trend-cycle comp., trend comp.
F1 j
TCv
T v
T1 j T2 v, T2 v,
���� ���� ���� ���� ���� ����
� �
� �
� �
�
� �
� �
� �
seasonal and irregular comp., resid.
Sv
Iv
Irv
T2 v
���� ���� ���� ���� ���� ����
�� �
��
�� �
�� �
�� �
��
�� �
latitude, mean latitude
F1 j
MLat v
T1 j T2 v,
���� ���� ���� ���� ���� ����
��
�
�
�
��
��
��
��
temperature, trend-cycle and trend comp.
F1 j
TCv
T v
T1 j T2 v, T2 v,
���� ���� ���� ���� ���� ����
��
��
�
�
�
�
��
��
seasonal and irregular comp., resid.
Sv
Iv
Irv
T2 v
���� ���� ���� ���� ���� ����
��
�
�
�
��
��
��
��
temperature, mean temperature
F1 j
MTem v
T1 j T2 v,
latitude (arcsec) temperature (◦C)
Figure 1. Results of the analysis of the astrometric and meteorological data
The difference between a cyclical and a seasonal component is that the latter occurs at regular (seasonal)
intervals, while cyclical factors usually have a longer duration that varies from cycle to cycle. The trend and
cyclical components are combined into a trend-cycle component (TCt) in this realization of Census II method.
An irregular component represents residual movement and errors of observations. The specific functional rela-
tionship between these components can assume different forms. However, two straightforward possibilities are
that they combine in an additive or a multiplicative fashion. We used additive model:
Xt = TCt + St + It, (1)
where Xt designates value of a time series at the moment of time t.
Proceeding from definition, that the mean value is such value, in which there are no periodic fluctuations,
the formula (1) can be written down in the following kind:
Xmeant = Tt + Irt, (2)
where Xmeant is the mean value of quantity of a time series at the moment of time t, Irt is the residual
movement in an irregular component.
To select trend component from trend-cycle component we used Gaussian smoothing method. It is difficult
to separate residual movement from errors of observations, therefore, we have entered an additional condi-
tion, having admitted, that the smoothed irregular component is a residual movement. The same method of
smoothing in this case was used.
373
���� ���� ���� ���� ����
�� �
�� �
�� �
��
�� �
elevation, trend-cycle comp., trend
F1 j
TCv
T v
T1 j T2 v, T2 v,
���� ���� ���� ���� ����
� �
� �
�
� �
� �
seasonal and irregular comp., resid.
Sv
Iv
Irv
T2 v
���� ���� ���� ���� ����
�� �
�� �
�� �
��
�� �
elevation, mean elevation
F1 j
MHeiv
T1 j T2 v,
���� ���� ���� ���� ���� ���� ���� ����
�
�
�
��
�
��
inclination, trend-cycle and trend comp.
F1 j
TCv
T v
T1 j T2 v, T2 v,
���� ���� ���� ���� ���� ���� ���� ����
��
�
�
��
seasonal and irregular comp., resid.
Sv
Iv
Irv
T2 v
���� ���� ���� ���� ���� ���� ���� ����
�
�
�
��
�
��
inclination, mean inclination
F1 j
MInc v
T1 j T2 v,
elevation (mm) inclination (arcsec)
Figure 2. Results of the analysis of the geodetic and geophysical data
DATA FOR THE ANALYSIS
To illustrate calculation of mean values of observable quantities, we used time series of observations of various
length and from different fields of knowledge. In accordance with the rules of processing of time series by
the STATISTICA 6 package we used not individual values of the measured quantities, but their monthly
average values. These time series are following:
1. astrometric (7723 latitude observations of bright zenith stars α Per and η UMa with the ZTL-180 zenith-
telescope for the 30 years period (1972.0–2002.0) in Poltava (360 monthly average values));
2. geodetic (152 precision determinations of the elevation between two deep bench mark A1 and A4 (depth
of laying is 6.0 m) by a geometrical levelling method for the 3.1 years period (4.05.2001–30.06.2004) in
Poltava (38 monthly average values));
3. geophysical (2372 daily determinations of inclination of a terrestrial surface with pitchmeter in a direction
“north–south” for the 6.5 years period (1.01.1977–30.06.1983) in excavation of 6 m depth near the field of
hydrochloric mine in Soledar (78 monthly average values));
4. meteorological (3878 determinations of air temperature during the latitude observations of bright zenith
star α Per with the ZTL-180 for the 30 years period (1972.0–2002.0) in Poltava (360 monthly average
values)).
374
RESULTS
After seasonal decomposition of time series for each kind of observations the trend-cycle, seasonal and irregular
components are received. Thus, the trend-cycle and seasonal components have complex structure and well
reflect changes of observed quantities. To select trend component from trend-cycle component and residual
movement from irregular component we used Gaussian smoothing method. Width of a smoothing window was
selected individually for each time series to exclude its long-period fluctuations.
After analysis three diagrams are constructed for each kind of observations (Figs. 1 and 2). There are curves
of monthly average values of observable quantity (dotted line), trend-cycle component (solid line) and trend
(dashed heavy line) on the first diagram. Seasonal component (dotted line), irregular component (solid line),
residual movement (dashed heavy line) are submitted on the second diagram. Curves of monthly average values
(dotted line) and mean values of observable quantity (solid heavy line) are shown on the third diagram.
As it is seen from results of calculations and diagrams the seasonal decomposition method is quite suitable for
determination of mean values of various spatial, geophysical and meteorological parameters. It has the following
advantages in comparison with other ways. It is not necessary in this case to know beforehand , what components
make general change of quantity, and so is not necessary to know their characteristics. Besides, in this method
a changeability of the characteristics of the basic periodic components (seasonal and cyclical) are taken into
account. It allows rather precisely to exclude them.
The defects of the Census X-11 method in its program realization STATISTICA 6 are following. The irregular
component is not separated into residual movement and errors of observations, trend is not selected separately,
long-period component is not determined. But last two obstacles can easily be bypassed, for example, how it is
shown above.
Acknowledgements. The authors are grateful to the colleagues Ph. Drs V. G. Pavlyk and A. M. Kutnyj for
the kindly given geodetic and geophysical data, which were used in this research.
[1] Orlov A. Ya. Service des latitudes.–Moscou, 1958.–126 p. (in Russian).
[2] Shiskin J., Young A. H., Musgrave J. C. The X-11 variant of the Census Method II seasonal adjustment program //
U.S. Dept. of Commerce, Bureau of the Census, Technical Paper.–1967.–N 15.
[3] STATISTICA 6.–StatSoft Inc., 2001.
375
|
| id | nasplib_isofts_kiev_ua-123456789-79679 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0233-7665 |
| language | English |
| last_indexed | 2025-12-07T16:02:47Z |
| publishDate | 2005 |
| publisher | Головна астрономічна обсерваторія НАН України |
| record_format | dspace |
| spelling | Tyshchuk, M. Gozhy, A. 2015-04-03T18:40:15Z 2015-04-03T18:40:15Z 2005 On determination of mean values of observed quantities according to O. Ya. Orlov / M. Tyshchuk, A. Gozhy // Кинематика и физика небесных тел. — 2005. — Т. 21, № 5-додаток. — С. 372-375. — Бібліогр.: 3 назв. — англ. 0233-7665 https://nasplib.isofts.kiev.ua/handle/123456789/79679 The definition of O.Ya.Orlov for mean values of observed quantities for any epoch suits for application not only in astronomy, and in geophysics, geodesy, meteorology. The method of seasonal decomposition and adjustment Census X-11 for realization of Orlov’s definition in various areas of researches is used. The authors are grateful to the colleagues Ph.Drs V. G. Pavlyk and A. M. Kutnyj for the kindly given geodetic and geophysical data, which were used in this research. en Головна астрономічна обсерваторія НАН України Кинематика и физика небесных тел MS4: Positional Astronomy and Global Geodynamics On determination of mean values of observed quantities according to O. Ya. Orlov Article published earlier |
| spellingShingle | On determination of mean values of observed quantities according to O. Ya. Orlov Tyshchuk, M. Gozhy, A. MS4: Positional Astronomy and Global Geodynamics |
| title | On determination of mean values of observed quantities according to O. Ya. Orlov |
| title_full | On determination of mean values of observed quantities according to O. Ya. Orlov |
| title_fullStr | On determination of mean values of observed quantities according to O. Ya. Orlov |
| title_full_unstemmed | On determination of mean values of observed quantities according to O. Ya. Orlov |
| title_short | On determination of mean values of observed quantities according to O. Ya. Orlov |
| title_sort | on determination of mean values of observed quantities according to o. ya. orlov |
| topic | MS4: Positional Astronomy and Global Geodynamics |
| topic_facet | MS4: Positional Astronomy and Global Geodynamics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/79679 |
| work_keys_str_mv | AT tyshchukm ondeterminationofmeanvaluesofobservedquantitiesaccordingtooyaorlov AT gozhya ondeterminationofmeanvaluesofobservedquantitiesaccordingtooyaorlov |