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Yavor Chapanov 1, Jan Vondrák 2, Cyril Ron 21National Institute of Geophysics, Geodesy and Geografy – Bulgarian Academy of Sciences2Astronomical Institute – Academy of Sciences of Czech Republic
OBJECTIVESDetermination of centennial oscillations of Earth rotation, solar indices, climatic parameters and
mean sea level
Investigation of possible connection between these oscillations and centennial cycles of the
solar activity
USED DATAUT1-TT for the period 1623-2005
Smoothed Wolf’s numbers for the period 1700-2010
Total solar Irradiance TSI: (1610-2010); (843-1961); 9Kyr series
Local temperature and precipitation variations: 1-2Kyr series
Mean sea level at Stockholm for the period 1770-2001
METHODSFourier approximation + Method of Least Squares
Averaging and Vondrak’s filtration
Cubic spline interpolation
FFT spectrograms
RESULTSThe best model of centennial cycles of the solar activity and Earth rotation is based on 210a
oscillations
The appropriative model of centennial cycles should combine 180a, 210a and 230a oscillations
and their harmonics
UT1 and LOD variations for 1623 - 2005
1650 1700 1750 1800 1850 1900 1950 2000Epoch-60-40-20
0204060
UT
1-T
T [
s]
-10
-5
0
5
LOD
[m
s]
1650 1700 1750 1800 1850 1900 1950 2000
UT1-TT
Polynomial part
LOD
Linear trend
DATA
Mean Sea Level variations at Stockholm
1770-2001
DATA
1750 1800 1850 1900 1950 2000Epoch-50.0-40.0-30.0-20.0-10.0
0.010.020.030.040.050.060.0
MS
L [c
m]
1750 1800 1850 1900 1950 2000Epoch-10.0
-5.0
0.0
5.0
10.0
MS
L [c
m]
Raw detrended data
Long term variations > 5a
Solar IndicesDATA
1700 1750 1800 1850 1900 1950 2000Epoch0.0
50.0
100.0
150.0
200.0
250.0
Wn
Smoothed Wolf’s numbers
1600 1650 1700 1750 1800 1850 1900 1950 2000Epoch1364.01365.01366.01367.01368.01369.0
TS
I [W
/m**
2]
TSI variations
800 1000 1200 1400 1600 1800 2000Epoch-3.0-2.0-1.00.01.02.0
TS
I [W
/m**
2]
(Lean)
(Bard)
Climatic Indices
DATA
-400 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000Epoch13.0
14.0
15.0
16.0
17.0
18.0
T [d
egre
e]
Local temperature variations – N. Am.
400 600 800 1000 1200 1400 1600 1800 2000Epoch10.0
20.0
30.0
40.0
50.0
60.0
P [c
m]
Local precipitation variations – N. Am.
TIME SERIES SPECTRA
2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3
10 100 1000Periods [a]
0.00
0.05
0.10A
m. T
SI [
W/m
**2]
2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 310 100 1000
4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5
100 1000Periods [a]
0.0
0.1
0.2
0.3
Am
pl. P
[cm
]
4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5100 1000
Harmonics of the
Hallstatt cycle
Signature of 2300a
Hallstatt cycle
TIME SERIES SPECTRA
100 120 140 160 180 200 220 240 260 280 300Periods [a]
0.00
0.05
0.10
Am
. TS
I W/m
**2]
100 120 140 160 180 200 220 240 260 280 300
0.00
0.10
0.20
Am
pl. P
[cm
]
Hallstatt cycle harmonics:No 10 – 230a period (Suess cycle);No 11 – 210a period (de Vries cycle);
Planetary periods:178.8a period (Jose cycle, Jupiter/Saturn syn. p.);171.4a period (Uranus/Neptune synodic period).
170a-180a MODELS
1600 1650 1700 1750 1800 1850 1900 1950 2000Epoch-20.0
0.0
20.0
UT
1
-0.4
0.0
0.4
TS
I [w
/m**
2]
1600 1650 1700 1750 1800 1850 1900 1950 2000
1600 1650 1700 1750 1800 1850 1900 1950 2000Epoch-10.0
-5.0
0.0
5.0
10.0
UT
1
-0.4
-0.2
0.0
0.2
0.4
TS
I [w
/m**
2]
1600 1650 1700 1750 1800 1850 1900 1950 2000
PARTIAL NEGATIVE CORRELATON
Partial agreement
Poor agreement
170a
178.8a
210a-230a MODELs
1600 1650 1700 1750 1800 1850 1900 1950 2000Epoch-10
0
10
20
UT
1-T
T [s
]
-1.0
-0.5
0.0
0.5
1.0
TS
I [w
/m**
2]
1600 1650 1700 1750 1800 1850 1900 1950 2000
210aBest agreement
NEGATIVE CORRELATON
PHASE DISCREPANCY
1600 1650 1700 1750 1800 1850 1900 1950 2000Epoch-20.0
-10.0
0.0
10.0
20.0
UT
1 [s
]
-1.0
-0.5
0.0
0.5
1.0
TS
I [w
/m**
2]
1600 1650 1700 1750 1800 1850 1900 1950 2000
230a
Similar behavior,
but -20a or +40a lag
UT1, MSL and icethickness variations
1600 1650 1700 1750 1800 1850 1900 1950 2000Epoch-15.0-10.0-5.00.05.0
10.015.0
UT
1
-3.0
-2.0
-1.0
0.0
1.0
2.0
MS
L [c
m]
1600 1650 1700 1750 1800 1850 1900 1950 2000
-0.2
-0.1
0.0
0.1
0.2
ICE
[m]
Relatively good agreement between thecentennial cycles of UT1, MSL and icethickness
230a
1600 1650 1700 1750 1800 1850 1900 1950 2000Epoch-10.0
-5.00.05.0
10.015.020.0
UT
1
-4.0
-2.0
0.0
2.0
MS
L [c
m]
1600 1650 1700 1750 1800 1850 1900 1950 2000
-0.2
0.0
0.2
ICE
[m]210a
CONCLUSIONSThe best agreement between the centennial cycles of the TSI and UT1 is achieved by 210a model.Partial correlation exists between the 180- and 230- year cycles of the time series of solar and climatic ind ices, UT1 and LOD, so the appropriative model the centenn ial cycles of the Earth rotation should combine 180a, 2 10a, 230a oscillations and their harmonics.The dependence between the TSI and UT1 centennial variations is negative, so the Earth rotation accel eration is connected with the decrease of the MSL, due to cooling effects of solar grand minima and corresponding increasing of the polar ice thickness .