atmospheric and oceanic excitation of earth...
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Journées 2011, ViennaSession 3
Atmospheric and oceanic excitation of
Earth rotationEarth rotation
d hSigrid BöhmTobias Nilsson
Michael Schindelegger
Harald SchuhHarald Schuh
Earth rotation – fundamental terms 2
Direction of rotation axisPolar motion (PM)
Spin variationsUniversal time (UT1) Polar motion (PM)
(Precession/Nutation)
Universal time (UT1)
Length of day (LOD)
f lConservation of angular momentum
Angular momentum approach 3
Mass displacementaffects inertia tensor
Relative motionCauses relative angularaffects inertia tensor
mass/pressure term
Causes relative angular momentum
motion/wind term/
Periodic LOD – composition 4
ocean tidesocean tides librationlibration
ocean non‐tidalocean non‐tidal
librationlibration
h id lh id l
atmosphere tidesatmosphere tides
body tidesbody tides
atmosphere non‐tidalatmosphere non‐tidal
core mantle couplingcore mantle coupling
body tidesbody tides
core‐mantle couplingcore‐mantle coupling
Periodic polar motion – composition 5
ocean tidesocean tideslibrationlibration
ocean non‐tidalocean non‐tidal
t h tidt h tid
decadal variationsdecadal variations
atmosphere non‐tidalatmosphere non‐tidal
atmosphere tidesatmosphere tides
pp
Chandler wobbleChandler wobble
Observation of Earth rotation variations 6
Earth orientation parameters (EOP)Pole coordinates (terrestrial coordinates of CIP)U i l ti (UT1) L th f D (LOD)Universal time (UT1), Length of Day (LOD)Nutation (celestial coordinates of CIP)
(Space) geodetic techniques:VLBI
GPSGLONASSGALILEO
Ringlaser
DORIS
SLRSatellite Laser Ranging
LLRLunar Laser Ranging
Observation/modelling of atmospheric excitation 7
Numerical weather modelsPressure, surface and different levels
Wind, east and north velocities,
t h i
∫∫∫
atmospheric excitation
atmospheric angular ∫∫∫ momentum (functions)AAM(F)
Observation/modelling of oceanic excitation 8
Circulation modelsOcean bottom pressure
Ocean tide modelsTidal heights
(+) p
Current velocities
g
Tidal current velocities
∫∫∫
oceanic excitation ocean tidal excitationoceanic excitation oceanic angular momentum
OAM
ocean tidal excitationocean tidal angular momentum
OTAM
Observed vs. modeled Earth rotation variation / excitation 9
Earth rotation observationPolar motion of the CIP
Geophysical ExcitationEquatorial effective angular
PM of the rotation pole
momentum function (EAMF)
( ) ( )motionmass
ACh
ACc χχχ ˆˆ
'
ˆ608.1'ˆ100.1ˆ +=
Ω⋅
+⋅
=
( ) ( ) ( )tptptp yx iˆ −=
Excess length of day
Axial EAMF
( ) ( )ACAC '' −⋅Ω−
h
( ) ( )dt
tpdtptmˆi)(ˆˆ
Ω−=
Excess length of day
Geophysical excitation in terms of
motionmass
mm Ch
Cc
33333
3 998.0748.0 χχχ +=Ω
+=( )3
0)(1 mtdUT
dtd
LODtLOD
−=−=δ
Geodetic excitation ERP
( ) ( ) ( )dt
tpditptcw
ˆˆ
ˆˆσ
χ += ( ) ⎟⎠⎞
⎜⎝⎛ −= ∫
t tcw
t depetp cwcw
0
ˆi-ˆi )(ˆˆi)0(ˆˆ ττχσ σσ
cw
( ) ( ) 03 LODttLOD ⋅= χδ
⎠⎝ 0
( ) ( )0
3 LODtLODt δχ =
Observed vs. modeled Earth rotation variation / excitation 10
ERP from convolution f AAMFof AAMF
observed polar motion
Excitation
Atmospheric and oceanic effects ‐ classification 11
Non‐tidalSeasonal: annual semiannual terannualSeasonal: annual, semiannual, terannualIntraseasonal: 4 days – 1 year, except seasonalInterannual: 1 year – 10 years except annualInterannual: 1 year – 10 years, except annual
TidalSh i d di l d bdi lShort period: diurnal and subdiurnal Long period: 5 days – 18.6 years
Free oscillations, special phenomenaChandler wobble, Free Core Nutation
El Niño Southern Oscillation (ENSO)
Effects of atmosphere and oceans on LOD 12
Seasonal
450
300350400
μs]
Observed
150200250
mplitu
de[
WindsSurface pressureCurrents
050100150a Currents
Ocean bottom pressureTotal atm. + ocean
0Annual Semiannual Terannual
Seasonal LOD variations during 1980‐2000 (Gross et al., 2004), [NCEP/ECCO]
Effects of atmosphere and oceans on LOD 13
Intraseasonal
100100
89 1
80
10083,6
89,1
ned[%
]
Observed
40
60
nceexplain
WindsSurface pressureCurrents
20
40
4,2 3,4 2 2
Varia
n CurrentsOcean bottom pressureTotal atm. + ocean
0
, 2,2
Intraseasonal LOD variations during 1980‐2000 (Gross et al., 2004)
Effects of atmosphere and oceans on LOD 14
Interannualwinds explain ~86% of obs. variance
surf. press., oceansurf. press., ocean currents and bottom press. → i ifi t→ no significant correlation
El Niño: correlation SOI/zonal winds ~ ‐0,72. No sign. corr with ocb and
InterannualLOD variationsduring 1980corr. with ocb and
currentsduring 1980‐2000 (Gross et al., 2004)
Effects of atmosphere and oceans on PM 15
Seasonal
15 Observedprograde
5
10 WindsSurface pressureCurrentsas
]
prograde
(Seitz & Schuh, 2010)
0Annual Semiannual Terannual
Ocean bottom pressure
15ObservedWindspl
itude
[ma
retrograde
0
5
10 Surface pressureCurrentsOcean bottom pressure
amp
Seasonal polar motion variations during 1980‐2000 (Gross et al., 2003), [NCEP/ECCO]
0Annual Semiannual Terannual
Ocean bottom pressureTotal atm. + ocean
Effects of atmosphere and oceans on PM 16
Intraseasonal
100
708090
61,366,9 65,3
ned[%
]
Observed
30405060
nceexplain
WindsSurface pressureCurrents
0102030
Varia
n CurrentsOcean bottom pressureTotal atm. + ocean
0X Y X+iY
Intraseasonal polar motion variations during 1980‐2000 (Gross et al., 2003)
Effects of atmosphere and oceans on PM 17
Interannualatmospheric processes are not effective in exciting interannual wobblesinterannual wobbles
ocean bottom pressure variations are most effective in exciting especially Y‐component
total A+O cannot explain X
variance explained in X+iY b t t l A+O ~40%by total A+O. ~40%
Interannual PM variations during 1980‐2000 (Gross et al., 2003)
Additional comments on seasonal PM 18
Brzezinski et al. (2009), [NCEP/ECCO]: inclusion of HAM (hydrologic angular momentum):inclusion of HAM (hydrologic angular momentum): controversial, estimates from hydrology models differ considerablyocean model with data assimilation improves closurecombination GRACE + AAM/OAM(motion) is better than A+O alone for annual terms and retrograde semiannual termalone for annual terms and retrograde semiannual term
Dobslaw et al. (2010), [ECMWF/OMCT/LSDM]contributions from individual subsystems differ, but thecontributions from individual subsystems differ, but the differences geodetic – geophysical excitation are similar to previous studies.
(relative angular momentum due to HAM motion terms (river flow) has been found negligible.
Atmosphere and ocean tidal effects 19
Gravitational tides: caused by attraction of sun and moon (and planets)
d l/ h l dRadiational/thermal tides: caused by solar heating
Diurnal and subdiurnal ocean tidal effects 20
Still discrepancies between models and observation in high‐frequency UT1 and PM (apart from atmospherehigh frequency UT1 and PM (apart from atmosphere tides)Currently no alternative to IERS Conventions modelStudy from EGU 2011
probing performance of new ocean tide models:compared tidal terms / time series from ...
IERS2010 conventions model, IERS2010
l l d f id d lTPXO7.2 calculated from TPXO7.2 ocean tide model
HAM11a calculated from HAMTIDE11a ocean tide model
VLBI time series (26 years) derived with Vienna VLBI software VieVS
GPS normal equations (13 years) derived with Bernese GPS software (provided by Natalia Panafidina, ETH Zürich)
Residual amplitudes w.r.t. IERS2010 21
Diurnal and subdiurnal ocean tidal effects 22
ERP variations based on TPXO7 2 fit best
RMS differences in terms of time seriesModell IERS2010 TPXO7.2 HAM11a GPS VLBI ERP on TPXO7.2 fit best
to the GPS and VLBI values (except for GPS DUT1)
IERS2010 29,4 26,0 30,0 36,0
Δx(t)
TPXO7.2 34,2 20,6 24,3 34,2HAM11a 27,9 27,0 28,4 41,6GPS 33 4 25 3 34 6 35 4 GPS DUT1)
overall the resulting RMS differences do
GPS 33,4 25,3 34,6 35,4VLBI 42,4 39,8 50,0 41,1
ERP Δy(t)
not differ notablyRMS differences in terms of time seriesModell IERS2010 TPXO7.2 HAM11a GPS VLBI ERP
IERS2010TPXO7 2 2 3TPXO7.2 2,3HAM11a 3,1 2,1GPS 2,7 2,9 3,8VLBI 3,1 2,8 3,1 3,2
Project proposal to
FWFERP ΔUT1(t) FWF
Concluding remarks 23
Most recent ocean tide models should be used to derive high‐frequency ERP variations in combinationderive high frequency ERP variations, in combination with advanced modeling approaches.
Observed LOD variations can be explained considerably better with present geophysical modelsconsiderably better with present geophysical models than PM (at the time scales discussed here), but the excitation budget is closed in neither case.excitation budget is closed in neither case.Improvement can be expected from more sophisticated models for land hydrology and/or longersophisticated models for land hydrology and/or longer time series of mass variations from GRACE.
Appendix
)obsvar()modelobsvar()obsvar(%100explained variance −−
×=)(
Appendix
⎟⎞
⎜⎛ + 131211
BcccA
I⎟⎟⎟
⎠⎜⎜⎜
⎝ ++=
332313
232212cCcc
ccBcI⎠⎝ 332313
⎟⎞
⎜⎛ 1hh
h ⎟⎞
⎜⎛ 1m
⎟⎟⎟
⎠⎜⎜⎜
⎝=
3
2hhh
⎟⎟⎟
⎠⎜⎜⎜
⎝ +⋅Ω=
3
21 m
mω
( ) ( ) LhIωωhIω =+×++∂
⎠⎝ 3 ⎠⎝ + 31 m
( ) ( )HH
∂ 4342143421t