VARIABILITY OF TOTAL ELECTRON CONTENT AT EUROPEAN LATITUDES A. Krankowski(1), L. W. Baran(1), W....
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VARIABILITY OF TOTAL ELECTRON CONTENT VARIABILITY OF TOTAL ELECTRON CONTENT AT EUROPEAN LATITUDES AT EUROPEAN LATITUDES wski(1), L. W. Baran(1), W. Kosek (2), I. I. Shagimuratov(3), M. Kal ute of Geodesy, University of Warmia and Mazury in Olsztyn YN, POLAND, [email protected]; Fax:+48-89-5234768 Research Centre, Polish Academy of Sciences, POLAND epartment of the IZMIRAN of the Russian Academy of Sciences NINGRAD, RUSSIA Annual Seminar of Commission of Satellite Geodesy, Committee Space Research PAS Section of Geodetic Networks, Committee of Geodesy PAS Section of Geodynamics, Committee of Geodesy PAS Space Research Centre PAS „EARTH ROTATION AND SATELLITE GEODESY FROM ASTROMETRY TO GNSS” Warsaw, 18-19 September 2003
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Transcript of VARIABILITY OF TOTAL ELECTRON CONTENT AT EUROPEAN LATITUDES A. Krankowski(1), L. W. Baran(1), W....
VARIABILITY OF TOTAL ELECTRON VARIABILITY OF TOTAL ELECTRON CONTENTCONTENT AT EUROPEAN LATITUDESAT EUROPEAN LATITUDES
A. Krankowski(1), L. W. Baran(1), W. Kosek (2), I. I. Shagimuratov(3), M. Kalarus (2)
(1) Institute of Geodesy, University of Warmia and Mazury in Olsztyn OLSZTYN, POLAND, [email protected]; Fax:+48-89-5234768
(2) Space Research Centre, Polish Academy of Sciences, POLAND (3) West Department of the IZMIRAN of the Russian Academy of Sciences KALININGRAD, RUSSIA
Annual Seminar of Commission of Satellite Geodesy, Committee Space Research PASSection of Geodetic Networks, Committee of Geodesy PAS
Section of Geodynamics, Committee of Geodesy PAS Space Research Centre PAS
„EARTH ROTATION AND SATELLITE GEODESY FROM ASTROMETRY TO GNSS”
Warsaw, 18-19 September 2003
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1. Introduction1. Introduction
Nowadays, GPS measurements are commonly used to investigate the structure and dynamic of the ionosphere. The ionosphere is a significant error source for telecommunication activity, space geodesy, navigation. Precise GPS positioning, even using dual-frequency technique, cannot ignore the ionosphere effects. It is concerned, for example, in resolving of phase ambiguity in relative positioning. The ionosphere limits the area of using the ionospheric correction for Differential GPS.
GPS measurements from 100 European EPN/IGS permanent stations were used to monitor the ionospheric effects of geomagnetic storms. The dense network of GPS stations in Europe allows to obtain high spatial and temporal resolution of TEC.
In this paper TEC date from six IGS/EPN European stations for ionospheric quiet and disturbed conditions from years 1995 (minimum solar activity) to 2001 (maximum solar activity) were studied.
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2.2. ESTIMATION TECHNIQUE OF TEC
While estimating TEC from GPS observations the ionosphere was approximated by a spherical shell at fixed height of 350 km above the Earth’s
surface.
The absolute TEC and the instrumental bias were estimated using the single site algorithm:
The biases were determined for every individual station using the GPS
measurements and for all satellite passes over a site during 24-hour period.
ppAzTECMmP cos/][ AzTECMm cos/][
We used a simple geometric factor to convert slant TEC into vertical one. High precision GPS phase measurements were used while processing. Phase ambiguities were removed by fitting phase measurements to the code data collected along individual satellite pass. After the pre-processing phase measurements contained an instrumental bias only.
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The measurements were fitted to a surface harmonic expansion in and in order to obtain the spatial and temporal variations of TEC and to produce TEC maps Chosen coordinate system is the geographic latitude () and longitude ().
Only GPS observations with elevation angles above 200 were used in the calculations. TEC was modelled with a spherical harmonic expansion to degree 16 and order 16:
VTEC = a1 +a2 + a3cos(s) + a4sin(s) + a5cos(2s) + a6sin(2s) +
+...a13cos(6s) + a14sin(6s) + a152s ;
s = ( LT – 14 )/12 .
Diurnal variations of TEC over a site and the biases for all satellites were estimated simultaneously. We used this technique to process all observations from all stations, so instrumental biases were removed. Using this procedure we calculated an absolute line of sight TEC for all satellite-receiver paths.
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2.2. VARIABILITY OF TOTAL ELECTRON CONTENT
• The TEC measurements obtained using GPS signals received at six IGS/EPN permanent stations: Onsala, Metsahovi, Hailsham, Lamkowko, Borowa Gora, Borowiec and Matera are used to study day-to-day the behaviour of the ionospheric variable.
• Latitude of selected stations range from 40N to 60N.
• The TEC date for ionospheric quiet and disturbed conditions from years 1995 (minimum solar activity) to 2001 (maximum solar activity) were studied.
• Variability of TEC is presented on example of the two stations (Borowiec and Matera). These results from this stations are compared to the others analyzed ones.
•To specify variability the following coefficients are considered:
V = (SD / mean) x 100VQ = [(QU – QL) / median] x 100
VU = [(QU – median) / median] x 100VL = [(median – QL) / median] x 100
where QU and QL are the upper and lower quartile, respectively.
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Borowiec, January, 1996 (minimum solar activity)
Fig.1 VTEC over Borowiec, January 1996, (TECU=1x1016m-2). a) Mean of standard deviation (SD), b) coefficient of variability V: standard deviation (in % of mean), c) Median, lower and upper quartiles, d) coefficient of variability VQ: difference from lower to upper quartile (in % of median), e) coefficient of
variability VU: difference from median to upper quartile (in % of median), f) coefficient of variability VL: difference from median to lower quartile (in % of median)
VQ[%]=((QU-QL)/median)*100
020406080
100
0 2 4 6 8 10 12 14 16 18 20 22 UT
VQ[%
]
d)
Vu[%]=((QU-median)/median)*100
020406080
100
0 2 4 6 8 10 12 14 16 18 20 22 UT
VU[%
]
e)
VL[%]=((median-QL)/median)*100
020406080
100
0 2 4 6 8 10 12 14 16 18 20 22 UT
VL[%
]
f)V[%]=(SD/mean)*100
020406080
100
0 2 4 6 8 10 12 14 16 18 20 22 UT
V[%
]
b)
VTEC
0
5
10
15
20
0 2 4 6 8 10 12 14 16 18 20 22 UT
TE
CU
mean mean+SD mean-SD
a) VTEC (median, upper quartill - QU, lower quartill - QL)
0
5
10
15
20
0 2 4 6 8 10 12 14 16 18 20 22 UT
TE
CU
median QU QL
c)
7
Borowiec, January, 1999 (increasing solar activity)
Fig.2 VTEC over Borowiec, January 1999, (TECU=1x1016m-2). a) Mean of standard deviation (SD), b) coefficient of variability V: standard deviation (in % of mean), c) Median, lower and upper quartiles, d) coefficient of variability VQ: difference from lower to upper quartile (in % of median), e) coefficient of
variability VU: difference from median to upper quartile (in % of median), f) coefficient of variability VL: difference from median to lower quartile (in % of median)
VQ[%]=((QU-QL)/median)*100
020406080
100
0 2 4 6 8 10 12 14 16 18 20 22 UT
VQ[%
]
d)
Vu[%]=((QU-median)/median)*100
020406080
100
0 2 4 6 8 10 12 14 16 18 20 22 UT
VU[%
]
e)
VL[%]=((median-QL)/median)*100
020406080
100
0 2 4 6 8 10 12 14 16 18 20 22 UT
VL[%
]
f)V[%]=(SD/mean)*100
020406080
100
0 2 4 6 8 10 12 14 16 18 20 22 UT
V[%
]
b)
VTEC
01020304050
0 2 4 6 8 10 12 14 16 18 20 22 UT
TE
CU
mean mean+SD mean-SD
a) VTEC (median, upper quartill - QU, lower quartill - QL)
01020304050
0 2 4 6 8 10 12 14 16 18 20 22 UT
TE
CU
median QU QL
c)
8
Borowiec, January, 2000 (maximum solar activity)
Fig.3 VTEC over Borowiec, January 2000, (TECU=1x1016m-2). a) Mean of standard deviation (SD), b) coefficient of variability V: standard deviation (in % of mean), c) Median, lower and upper quartiles, d) coefficient of variability VQ: difference from lower to upper quartile (in % of median), e) coefficient of
variability VU: difference from median to upper quartile (in % of median), f) coefficient of variability VL: difference from median to lower quartile (in % of median)
VQ[%]=((QU-QL)/median)*100
020406080
100
0 2 4 6 8 10 12 14 16 18 20 22 UT
VQ[%
]
d)
Vu[%]=((QU-median)/median)*100
020406080
100
0 2 4 6 8 10 12 14 16 18 20 22 UT
VU[%
]
e)
VL[%]=((median-QL)/median)*100
020406080
100
0 2 4 6 8 10 12 14 16 18 20 22 UT
VL[%
]
f)V[%]=(SD/mean)*100
020406080
100
0 2 4 6 8 10 12 14 16 18 20 22 UT
V[%
]
b)
VTEC
010203040506070
0 2 4 6 8 10 12 14 16 18 20 22 UT
TE
CU
mean mean+SD mean-SD
a) VTEC (median, upper quartill - QU, lower quartill - QL)
010203040506070
0 2 4 6 8 10 12 14 16 18 20 22 UT
TE
CU
median QU QL
c)
9
Matera, April, 1996 (minimum solar activity)
Fig.4 VTEC over Matera, April 1996, (TECU=1x1016m-2). a) Mean of standard deviation (SD), b) coefficient of variability V: standard deviation (in % of mean), c) Median, lower and upper quartiles, d) coefficient of variability VQ: difference from lower to upper quartile (in % of median), e) coefficient of
variability VU: difference from median to upper quartile (in % of median), f) coefficient of variability VL: difference from median to lower quartile (in % of median)
VQ[%]=((QU-QL)/median)*100
020406080
100
0 2 4 6 8 10 12 14 16 18 20 22 UT
VQ[%
]
d)
Vu[%]=((QU-median)/median)*100
020406080
100
0 2 4 6 8 10 12 14 16 18 20 22 UT
VU[%
]
e)
VL[%]=((median-QL)/median)*100
020406080
100
0 2 4 6 8 10 12 14 16 18 20 22 UT
VL[%
]
f)V[%]=(SD/mean)*100
020406080
100
0 2 4 6 8 10 12 14 16 18 20 22 UT
V[%
]
b)
VTEC
0
5
10
15
20
0 2 4 6 8 10 12 14 16 18 20 22 UT
TE
CU
mean mean+SD mean-SD
a) VTEC (median, upper quartill - QU, lower quartill - QL)
0
5
10
15
20
0 2 4 6 8 10 12 14 16 18 20 22 UT
TE
CU
median QU QL
c)
10
Matera, April, 1999 (increasing solar activity)
Fig.5 VTEC over Matera, April 1999, (TECU=1x1016m-2). a) Mean of standard deviation (SD), b) coefficient of variability V: standard deviation (in % of mean), c) Median, lower and upper quartiles, d) coefficient of variability VQ: difference from lower to upper quartile (in % of median), e) coefficient of
variability VU: difference from median to upper quartile (in % of median), f) coefficient of variability VL: difference from median to lower quartile (in % of median)
VQ[%]=((QU-QL)/median)*100
020406080
100
0 2 4 6 8 10 12 14 16 18 20 22 UT
VQ[%
]
Vu[%]=((QU-median)/median)*100
020406080
100
0 2 4 6 8 10 12 14 16 18 20 22 UT
VU[%
]
VL[%]=((median-QL)/median)*100
020406080
100
0 2 4 6 8 10 12 14 16 18 20 22 UT
VL[%
]
V[%]=(SD/mean)*100
020406080
100
0 2 4 6 8 10 12 14 16 18 20 22 UT
V[%
]
VTEC
01020304050
0 2 4 6 8 10 12 14 16 18 20 22 UT
TE
CU
mean mean+SD mean-SD
VTEC (median, upper quartill - QU, lower quartill - QL)
01020304050
0 2 4 6 8 10 12 14 16 18 20 22 UT
TE
CU
median QU QL
11
Matera, April, 2000 (maximum solar activity)
Fig.6 VTEC over Matera, April 2000, (TECU=1x1016m-2). a) Mean of standard deviation (SD), b) coefficient of variability V: standard deviation (in % of mean), c) Median, lower and upper quartiles, d) coefficient of variability VQ: difference from lower to upper quartile (in % of median), e) coefficient of
variability VU: difference from median to upper quartile (in % of median), f) coefficient of variability VL: difference from median to lower quartile (in % of median)
VQ[%]=((QU-QL)/median)*100
020406080
100
0 2 4 6 8 10 12 14 16 18 20 22 UT
VQ[%
]d)
Vu[%]=((QU-median)/median)*100
020406080
100
0 2 4 6 8 10 12 14 16 18 20 22 UT
VU[%
]
e)
VL[%]=((median-QL)/median)*100
020406080
100
0 2 4 6 8 10 12 14 16 18 20 22 UT
VL[%
]
f)V[%]=(SD/mean)*100
020406080
100
0 2 4 6 8 10 12 14 16 18 20 22 UT
V[%
]
b)
VTEC
01020304050607080
0 2 4 6 8 10 12 14 16 18 20 22 UT
TE
CU
mean mean+SD mean-SD
a) VTEC (median, upper quartill - QU, lower quartill - QL)
01020304050607080
0 2 4 6 8 10 12 14 16 18 20 22 UT
TE
CU
median QU QL
c)
12
3. Similar pattern prediction of real-valued time series
Let ntforxt ,...,2,1 be an equidistant stochastic process. The forecast is based on
fitting the final time series part 1jnx (Last Pattern LP) to the similar pattern
kSPof the same time series found in the past.
Therefore, the first points directly beyond the kSP pattern which is the mostsimilar to LP are assumed as the forecast points. The last pattern in the time
series tx is given by:
njnjn xxxLP,...,, 21 n - number of input data, j – length of the pattern.
For a number of pattern jnk 2,...,2,1 the following set of patterns can begenerated: 11,...,, jkkkk xxxSP which are compared to the last pattern LP
as follows: kjnk
SPLPK 2,...,2,1
minarg
The forecast points P are obtained in the following way: 11,...,, qmmm xxxP ,
jKm , q – the number of prediction points and K - is the number of pattern forwhich kSP is the most similar to theLP.
13
51240.00 51242.00 51244.00 51246.00 51248.00
MJD
a) 03-10.03.1999
0.00
0.05
0.10
0.15
Par
t o
f d
ay in
th
e fu
ture
0 .00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
18.00
20.00
TECU
hours
1
2
3
0.00 0.05 0.10 0.15Part of day in the future
0.00
4.00
8.00
TE
CU
a)
51240.00 51242.00 51244.00 51246.00 51248.00M JD
0.00
10.00
20.00
30.00
40.00
50.00
TECU
a) 03-10.03.1999
Fig. Similar pattern prediction errors of the TEC data as a function of data time span and prediction length for March 03-10 1999 Fig. The mean prediction errors of
the TEC data of the autocovariance prediction for March 03-10, 1999
Fig. Four-hour ahead forecast of TEC (in TECU) for March 03-10, 1999. For comparison, real data are shown.
Similar pattern prediction
14
hours
1
2
3
TECU
51605.00 51607.00 51609.00 51611.00 51613.00
MJD
a) 01-10.03.2000
0.00
0.05
0.10
0.15
Par
t o
f d
ay in
th
e fu
ture
0 .00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
0.00 0.05 0.10 0.15Part of day in the future
0.00
4.00
8.00
12.00
TE
CU
a)
51604.00 51606.00 51608.00 51610.00 51612.00 51614.00M JD
0.00
20.00
40.00
60.00
80.00
TECU
a) 01-10.03.2000
Fig. Similar pattern prediction errors of the TEC data as a function of data time span and prediction length for March 01-10 2000 Fig. The mean prediction errors of
the TEC data of the autocovariance prediction for March 01-10, 2000
Fig. Four-hour ahead forecast of TEC (in TECU) for March 01-10, 2000. For comparison, real data are shown.
Similar pattern prediction
15
4.4. Conclusion
• Absolute variability is generally greater at high than low solar activity.
• Relative variability is higher at night than during the daytime at both
high and low solar activity periods. • Difference (Max. VTEC – Min VTEC) is greater at low latitudes
(Matera) then at high latitudes (Metsahovi).
• This forecasting method is very simple and don’t need any information a-priori about the process as well as additional inputs
such as the solar or magnetic activity indices.
• The values corresponding to equinoxes are greater then corresponding
to solstices.
• In the case the similar pattern method the amount of past TEC data used for forecasting is very important. The best results are obtained for all the time series with the length of 1880 days (16-18 - December 2000).
