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The 5

th

IVS General Meeting Proceedings, 2008, p. 302­306

Interpretation of VLBI Results in Geodesy, Astrometry and Geophysics

Using the Singular Sp ectrum Analysis for Investigation of Trop osphere Parameters
Natalia Miller, Zinovy Malkin
Central Astronomical Observatory at Pulkovo of Russian Academy of Sciences Contact author: Natalia Mil ler, e-mail: natm@gao.spb.ru

Abstract. In this paper, the method of Singular Spectrum Analysis (SSA) is applied for investigation of the zenith troposphere delay time-series derived from VLBI observations. With the help of this method we can analyze the structure of time-series and separate the harmonic and irregular (trend) components. Combined IVS time-series of zenith wet and total trop osphere delays obtained in IGG were used for analysis. For this study, several VLBI stations with the most long time series of troposphere zenith delays were selected, also taking into consideration the geographic region where the station is located. The investigations were carried out using SSA mode. As a result, trends and seasonal components (with annual and semiannual periods) were obtained for all the stations. Using of SSA enabled us to determine nonlinear trends in zenith delay, and also to study variations in the amplitude and the phase of the seasonal comp onents with time.

1. SSA Metho d
In this research, we have investigated the combined IVS troposphere zenith delay (TZD) series and focused on behavior trends and seasonal components with the help of Singular Spectrum Analysis (SSA) [1]. Additional information on SSA method, its abilities and the corresponding software can be found on the site http://www.gistatgroup.com/cat/. With the help of this method we can: ­ Recognize certain components in the equally spaced time series, which have been obtained from observations. The result of such procedure is decomposition of time series into components that usually can be identified as trends, periodical or oscillatory and noise components; ­ Extract components with the well-known period and estimate value of phase shift and variation of amplitude of pseudo-harmonic signals; ­ Find periodicities that are not known in advance; ­ Extract trends of different resolutions. Natural decomposition of the time 302


series is constructed on the base of the unique parameter (the window length). Grouping different subsets of the decomposition components one can obtain both the tendency and accurate trend; ­ On the basis of the chosen components smooth out the initial data. Contrast to the standard spectral analysis, where the basic functions are given a priory as the sines and cosines of the Fourier method, in SSA they are determined from the very data to form orthogonal basis.

2. Analysis of Zenith Delay Time Series
The zenith total delay (ZTD) is the sum of the zenith hydrostatic (ZHD) and zenith wet delays (ZWD). The SSA method gives the opportunity to detect features of main ZTD and ZWD (ZD) trends and to compare them with the main trends of other time series, such as hydrostatic zenith delay, wet zenith delay, pressure at the site, temperature at the site, water vapor pressure at site, which were taken from the VMF1 files provided by the IGG. Combined IVS time-series of ZD,obtained at IGG, were used for analysis [2]. Six VLBI stations (Gilcreek, Kashima, Kokee-Kauai, Onsala, Westford, Wettzell) with the longest time series of troposphere zenith delays were selected for studying. Linear interpolation of data was carried out to get equally spaced series with the step of 0.01 year which was used for SSA. For all time series we used the same time interval 1984.88 ­ 2004.87, series length N=2000 points (20 years), and the maximum window length M=N/2=1000. After decomposing with SSA method in all series the trends hereafter referred to as trend SSA, annual and semiannual components were found. Figures 1 and 2 show ZD trends as obtained by SSA from the combined IVS series and their linear approximation. The fact that the stations located in the same geographic region (Onsala and Wettzell) reveal similar trend features is of a special interest. Moreover, all trends have the same small curving about year 1995. Original series obtained by analysis centers BKG, GSFC, IAA, MAO show the same properties, which are shown in Fig. 3 for Wettzell as an example. It is interesting to compare non-linear trends found in the ZD with those in the meteorological parameters. For this purpose, decomposition of the meteorological parameters for Wettzell and Gilcreek has been made using SSA. Figure 4 shows the trends for the hydrostatic zenith delay, pressure at the site from the VMF1 and ZTD-ZWD computed from the IVS combined series. The coincidence of all these curves is obvious for Wettzell. For Gilcreek one can see the difference in shape of the curves. Figure 5 shows the trends for wet zenith delay, temperature at the site, water vapor pressure at the site from the VMF1 and ZWD. The ZWD trend is very close to trend of water vapor pressure for the Wettzell. But for the Gilcreek the similar curves do not show such an agreement. The Gilcreek is the only station where we failed to extract the trend of the site temperature series. Figures 6 and 7 show the annual and semi-annual components ZWD for researched stations. The components have a steady phase but variations of 303


Gilcreek
2460 2272 2454 2448 2268 2442 2436 2264 1985 1990 1995 2000 2005 2390 2388 2386 2384 1985 1990 1995 2000 2005

Kashima

2132 2128 2124 2120 2116

Kokee-Kauai

1985 1990 1995 2000 2005 2390 2388 2386 2384 1985 1990 1995 2000 2005

1985 1990 1995 2000 2005

Onsala

Westford
2240 2238 2236

Wettzell

1985 1990 1995 2000 2005

Figure 1. SSA trends of ZTD (solid line) and their linear approximation (dashed line). Unit: mm.
Gilcreek
60 59 58 57 56 1985 1990 1995 2000 2005 165 160 155 150 145 140 135 1985 1990 1995 2000 2005 108 106 104 102 100 98 96 94

Kashima

110 105 100 95 90 85 80

Kokee-Kauai

1985 1990 1995 2000 2005 88 87 86 85 84 83

Onsala
85 84 83 82 1985 1990 1995 2000 2005

Westford

Wettzell

1985 1990 1995 2000 2005

1985 1990 1995 2000 2005

Figure 2. SSA trends of ZTD (solid line) and their linear approximation (dashed line). Unit: mm.

2246 2244 2242 2240 2238 2236 2234 1985 1990 1995 2000 2005

BKG GSF IAA MAO IVS

Figure 3. SSA trends in ZTD for individual series for Wettzell. Unit: mm.

304


ZTD-ZWD

ZHD

WETTZELL
ZHD [mm] P - pressure at the site [hPa] ZTD-ZWD [mm]

ZTD-ZWD
P

ZHD

GILKREEK

P

972.0 2214 2210 971.8 2213 971.6 2209 971.4 971.2 2208 971.0 1990 1995 2000 2005

2154 2153 2152

2149

943.0 942.8

2212
2148 2151 2150 2149 2147 1985 1990 1995 2000 2005 942.6

2211
942.4 942.2 942.0

2210 2209 2208 1985

Figure 4. SSA trends of hydrostatic zenith delay, pressure at the site and ZTD­ZWD.
WETTZELL
ZWDw ZWD

ZWDw from the VMF1 [mm] T - temperature at the site [C ] P - water vapour pressure [hPa] ZWD from the observation [mm]
o

p

t

94 88 93 87 92 86 91 90 89 83 88 1985 1990 85

8.5

8.8 8.7 8.6

8.4 8.5 8.4

84

8.3 8.3 8.2 1995 2000 2005

Figure 5. SSA trends of wet zenith delay, temperature at the site, water vapor pressure and ZWD.

mm
100 0 -100

Gilcreek

Kashima
100 0 -100 100 0 -100 100 0 -100

Kokee-Kauai

Onsala

Westford
100 0 -100

Wettzell
100 0 -100 1985 1990 1995 2000 2005

Figure 6. The annual components in reconstructed ZWD series.

305


mm
60 0 -60

Gilcreek

Kashima
60 0 -60

Onsala
60 0 -60

Westford
60 0 -60

Wettzell
60 0 -60 1985 1990 1995 2000 2005

Figure 7. The semiannual components in reconstructed ZWD series.

amplitude. It should be mentioned that the contribution of the semiannual component is comparatively small, near noise level, and therefore this component needs more careful study. For Kokee-Kauai semiannual component was not found, and so for ZTD at Onsala. For Kashima, the amplitude of the semiannual component is larger in the beginning of the time interval than at the rest of interval.

3. Conclusions
In this paper, we have examined an ability of the SSA method in analysis of the zenith troposphere delay. Non-linear trends and variations of the amplitude of seasonal components have been detected. Some interesting peculiarities in their behavior have individual character for every stations of site. Comparison of the trends with meteorological parameters also is presented to show possible similarities that deserve further investigations.

References
[1] N. Golyandina, V. Nekrutkin, A. Zhigljavsky. Analysis of Time Series Structure: SSA and Related Techniques, New York: Chapman and Hall/CRC, 2001. [2] R. Heinkelmann, J. BЁ ohm, H. Schuh. Combination of Long-term Time Series of Tropospheric Parameters Observed by VLBI In: IVS 2006 General Meeting Proceedings, Concepciґ Chile, January 9-11, D.Behrend, K.D.Baver (eds.), on, NASA/CP-2006-214140, p. 341-343, 2006.

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