Wavelet analysis in TEC measurements obtained using dual-frequency space and satellite techniques A. Krankowski (1), W. Kosek, (2), Th. Hobiger (3), H. Schuh (3) (1) Institute of Geodesy, Warmia and Mazury University in Olsztyn, POLAND (2) Space Research Centre, Polish Academy of Sciences, POLAND (3) Institute of Geodesy and Geophysics, Vienna University of Technology, AUSTRIA Journées 25 Systèmes de Référence Spatio-Temporels Earth dynamics and reference systems: five years after the adoption of the IAU 2 Resolutions Warsaw, 19-22 September 25 1
CONTENTS 1. DATA SOURCE AND ESTIMATION TECHNIQUE OF TEC USING GPS AND VLBI MEASUREMENTS 2. DIURNAL VARIATIONS OF TEC ( and ) 3. THE MORLET WAVELET TIME-FREQUENCY SPECTRA OF TEC DATA 4. THE WAVELET TIME-FREQUENCY COHERENCES OF TEC DATA 5. CONCLUSION 2
GPS DATA SOURCE AND ESTIMATION TECHNIQUE GPS measurements of European IGS stations for 1996 24 were used to obtain TEC data. The range of solar activity during the years coveraged from low (1996) to high (21) levels. For TEC estimation we used the single site algorithm. The TEC was approximated as a function of the local time (LT) and difference between the receiver latitude and the latitude of the subionospheric point (sp) along satellite passes. 7 6 5 4-2 -1 1 2 3 4 Fig. Geographic map of GPS stations used for retrieving TEC over Europe The diurnal variation of TEC: 6 6 2 TEC= a + a cosis+ b sinis+ c1 ϕ+ c2 ϕ s+ c3 ϕ i i= 1 i= 1 i 3
VLBI DATA SOURCE AND ESTIMATION TECHNIQUE VLBI provides only baseline (=differential) measurements estimation method developed at Vienna University of Technology - station dependent VTEC values modelled by piece-wise linear functions - longitudinal rotation of datapoints equivalent to sun-fixed reference system - north-south variations described by linear gradients - adjustment algorithm prohibits negative TEC values Fig. Geographic map of VLBI stations used for retrieving TEC over Europe data from International VLBI Service for Geodesy & Astrometry period: : 1984 25, depending on antenna involvement 4
DIURNAL VARIATIONS OF TEC (GPS and VLBI) WETTZELL (1984-24) 1 8 WETTZELL 12 6 4 2 45 47 49 51 53 MATERA (199-24) 1 8 MATERA 12 6 4 2 45 47 49 51 53 and observed over Wettzell (top panel) and Matera (lower panel) for 1984-24. 5
COMPARISON OF DIURNAL VARIATIONS OF TEC (GPS and VLBI) WETTZELL maximum solar activity - 2 January April October 3 6 6 2 1 CU TE 4 2 4 2 3 2 1 6 12 18 24 6 12 18 24 6 12 18 24 26 January 2 12 April 2 4 October 2 maximum solar activity - 21 6 4 2 6 4 2 6 12 18 24 1 January 21 6 12 18 24 4 April 21 6 12 18 24 3 October 21 6
COMPARISON OF DIURNAL VARIATIONS OF TEC (GPS and VLBI) 3 2 1 January MATERA maximum solar activity - 2 April 8 6 4 2 8 6 4 2 October 6 12 18 24 26 January 2 6 12 18 24 12 April 2 6 12 18 24 31 October 2 4 3 2 1 maximum solar activity - 21 6 4 2 8 6 4 2 6 12 18 24 1 January 21 6 12 18 24 17 April 21 6 12 18 24 5 October 21 7
THE MORLET WAVELET TIME-FREQUENCY SPECTRA AND COHERENCE OF TEC DATA The Wavelet transform coefficients: + 1 ( 1 2 ( X ( b, a) = a x( ω) ϕ( aω)exp( ibω) dω 2π The CFT of the Morlet wavelet: 2 2 2 2 ( ω 2π ) σ ( ω 2π ) σ 2 2 exp exp( π ) ( ϕ ( ω) = σ exp σ 2 4 x ( ( ω) - CFT of x( t) σ parameter which controls the decay of the Morlet wavelet Time-frequency spectrum: Time-frequency coherence: ( b a) X, ( b, a) Cxy γ xy ( b, a) =, C xx ( b, a) C ( b, a) yy C M ( b, a) X ( b + k, a) Y ( b k, a) == xy + k = M 8
THE MORLET WAVELET TIME-FREQUENCY SPECTRA OF TEC DATA WETTZELL diurnal oscillations 11.3.21 19.6.21 Wavelet time-frequency spectrum of the data Wettzell - TEC mesurements obtained by VLBI Wavelet time-frequency spectrum of the data Wettzell - TEC mesurements obtained by GPS perio d (d ays) 1.5 perio d (d ays) 1.5 5198 52 522 524 526 528 5198 52 522 524 526 528 Wavelet time-frequency spectrum of the TEC data obtained using VLBI (left panel) and GPS (right panel) measurements over Wettzell during the period of March to June 21. 9
THE WAVELET TIME-FREQUENCY COHERENCE BETWEEN AND OVER WETTZEL WETTZELL diurnal oscillations 11.3.21 19.6.21 coherence (VLBI-Wettzell and GPS-Wettzell) 1.5 5198 52 522 524 526 528.8.6.4.2 Wavelet time-frequency coherence between TEC data obtained using VLBI and GPS measurements over Wettzell during the period of March to June 21. 1. coh (s=1, Morlet), =5198-528 coherence.8.6.4.2 white noise coherence The wavelet transform coherence (s=1, M=1, Morlet) between TEC data together with the empirical coherence for white noise data (dashed lines)..2.4.6.8 1. 1.2 1.4 1
THE MEAN AMPLITUDE SPECTRA OF TEC OBTAINED USING GPS AND VLBI MEASUREMENTS OVER WETTZELL AND MATERA 3 WETTZELL WETTZELL 3 MATERA MATERA 2 2 1 TEC - VLBI TEC - GPS 1 TEC - VLBI TEC - GPS 1 2 3 4 5 1 2 3 4 5 The mean amplitude spectra of TEC obtained using GPS and VLBI measurements over Wettzell and Matera during one (TEC from GPS) and two solar cycles (TEC from VLBI) 11
THE MORLET WAVELET TIME-FREQUENCY SPECTRA OF TEC DATA Wavelet time-frequency spectrum of the data WETTZELL (1984-24) Wettzell - TEC mesurements obtained by VLBI 4 2 46 47 48 49 5 51 52 53 MATERA (199-24) Matera- TEC mesurements obtained by VLBI 4 2 485 49 495 5 55 51 515 52 525 Wavelet time-frequency spectrum of the TEC data obtained using VLBI measurements over Wettzell and Matera during two solar cycles. 12
THE MORLET WAVELET TIME-FREQUENCY SPECTRA OF TEC DATA Wavelet time-frequency spectrum of the data annual and semiannual oscillations WETTZELL (1996-22) MATERA (1996-22) Wettzell - TEC mesurements obtained by GPS Matera - TEC mesurements obtained by GPS 4 2 4 2 55 51 515 52 525 55 51 515 52 525 Wavelet time-frequency spectrum of the data Wettzell - TEC mesurements obtained by VLBI Matera - TEC mesurements obtained by VLBI 4 2 4 2 55 51 515 52 525 55 51 515 52 525 Wavelet time-frequency spectrum of the TEC data obtained using GPS (top panel) and VLBI (lower panel) measurements over WettzelL and Matera for 1996-22. 13
THE WAVELET TIME-FREQUENCY COHERENCE FUNCTION BETWEEN AND annual and semiannual oscillations WETTZELL 1997-22 4 2 coherence (GPS-Wettzell and GPS-Wettzell) 56 58 51 512 514 516 518 52 MATERA 1997-22 4 2 coherence (VLBI-Matera and GPS-Matera) 56 58 51 512 514 516 518 52 Wavelet time-frequency coherence function between TEC data obtained using VLBI and GPS measurements over Wettzell and Matera during the period of 1996 to 22..9.7.5.3.1.9.7.5.3.1 coh (Wettzell - - ) coh (Matera - - ) coherence 1..8.6.4.2. 5 15 25 35 45 The wavelet transform coherence (σ=1, Morlet) between TEC data (solid lines) together with the empirical coherence for white noise data (dashed lines) 14
Conclusions (1) TEC time series of quiet and disturbed ionospheric conditions above different European collocation stations (GPS and VLBI): Wettzell, Matera and Onsala were compared in this study, covering one (GPS) and two solar cycles (VLBI). Our research has led to the following conclusions: - Both estimation methods of TEC: from GPS and VLBI permanent measurements provide an acceptable accuracy (about 1 3 ). - A very good agreement between diurnal variations of TEC obtained using GPS and VLBI observations was obtained. The differences between diurnal variations of and data, even during maximum solar activity in 21, amounted to 3-4. During increasing and low solar activity these differences were significant lower and reached 1-1.5. - The MWT time-frequency spectra of and data over two collocation stations Wettzell and Matera from a half period of solar activity (between 1996 22) present the same pattern for semidiurnal and diurnal oscillations. 15
Conclusions (2) - Time-frequency coherence map between and data over Wettzell and Matera reveals two maxim (of the order of.85.97) for the diurnal and semidiurnal oscillations. - Results for semiannual and annual oscillations obtained using GPS and VLBI TEC measurements agree also very well. Time-frequency coherence map reveals also two maxim (of the order of.95) for semiannual and annual oscillations. - Today the IGS / EPN and IVS networks are broader and denser than the ionosonde one. Joint GPS and VLBI TEC measurement will be used in the further investigations aiming at creating the predicted TEC maps over Europe, especially at the high latitude ionosphere. 16
Thank you for your attention e-mail: kand@uwm.edu.pl 17