GNSS Observations of Earth Orientation

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GNSS Observations of Earth Orientation

• 1. Polar motion observability using GNSS
• concepts, complications, error sources
• subdaily considerations
• 2. Performance of IGS polar motion series
• compare Final, Rapid, Ultra-rapid products
• assess random systematic errors
• 3. Utility of IGS length-of-day (LOD)
• assess value for combinations with VLBI UT1
• 4. Impact of errors in subdaily EOP tide model
• effects on orbits, EOPs, other IGS products

Jim Ray, NOAA/NGS
Wuhan University, May 2013
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Earth Orientation Parameters (EOPs)

• EOPs are the five angles used to
• relate points in the Terrestrial
• Celestial Reference Frames
• CRF P N(?, e) R(UT1) W(xp , yp)
  TRF
• Precession-Nutation describes the motion
• of the Earths rotation axis in inertial
  space
• Rotation about axis given by UT1 angle
• Wobble of pole in TRF given by terrestrial
• coordinates of polar motion (xp , yp)
• But only three angles, not five, are independent
• this conventional form is used to distinguish
  excitation sources
• Nutation ? driven by gravitational
  potentials outside Earth system
• Polar Motion ? driven by internal
  redistributions of mass/momentum
• separation of Nutation Polar Motion estimates
  given by convention

(xp, yp)
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Separation of Nutation Polar Motion

• Motions defined in frequency domain
• note that diurnal retrograde motion in TRF is
  fixed in CRF
• -1.0 cycle per sidereal day (TRF) 0.0
  cycles per sidereal day (CRF)
• Because GNSS cannot observe CRF (quasar frame),
  it does not measure precession-nutation or UT1
• but GNSS can sense nutation-rate UT1-rate (LOD)
  changes
• GNSS is superb for Polar Motion due to robust
  global tracking network
• pole position is essentially an unmarked point in
  the TRF

frequency in Terrestrial Frame
? polar motion
polar motion ?
frequency in Celestial Frame
precession nutation
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Observability of Polar Motion (PM)

• Suppose a priori pole position has some unknown
  error
• Due to diurnal Earth spin, PM error causes
  sinusoidal apparent motion for all TRF points as
  viewed from GNSS satellite frame
• (xp , yp) partials are simple
• diurnal sine waves
• amplitude phase depend
• only on station XYZ location
• quality of PM estimates
• depends mostly on Earth
• coverage by GNSS stations
• IGS formal errors sx,y 5 µas

actual pole position
assumed pole position
Signature of PM error in GNSS Observations
? 1 solar day ?
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Some Observability Complications

• GPS satellites have period of 0.5 sidereal day
• ground tracks repeat every 1 sidereal day
• differs from 1 solar day by only 4 minutes
• other GNSS constellations have longer or shorter
  periods
• any common-mode near-diurnal orbit errors can
  alias into PM estimates
• Any other net diurnal sinusoidal error in GNSS
  orbits will also alias into PM estimates
• main error comes from model for 12h/24h EOP tides
• mostly caused by EOP effect of ocean tidal
  motions
• current IERS model has errors at lt 20
• Other common mode effects could also be
  important
• diurnal temperature effects (e.g., heights of
  GNSS stations)
• diurnal troposphere modeling errors
• various other tidal modeling errors
• local station multipath signatures due to ground
  repeat period

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On Subdaily" Polar Motion

• First, subdaily polar motion is not a
  well-defined concept
• overlaps with nutation band in retrograde sense
• inseparable from a global rotation of satellite
  frame
• so constraint normally applied to block diurnal
  retrograde frequencies
• this is effectively a filter with poor response
  for GNSS arcs of 1 day
• D. Thaller et al., J. Geodesy, 2007
• Second, observability is reduced for intervals lt1
  solar day
• partial diurnal sinusoidal cannot be separated
  from other parameters
• so parameter continuity is required for direct
  subdaily estimates
• most common approach (Bern group) is to use 1 hr
  continuous segments
• this operates as another filter, but with other
  disadvantages (next slides)
• So subdaily results are easily affected by
  spurious effects

subdaily prograde PM ?
? subdaily retrograde PM
frequency in Terrestrial Frame
? polar motion
polar motion ?
precession nutation
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Effects of Continuity Filter (1/3)

• Compare offset rate to continuous linear
  segments (CLS)
• IGS requests daily PM estimates as mid-day
  offsets rates
• but some Analysis Centers prefer CLS approach
• results are not equivalent near Nyquist frequency
• CLS results are non-physical at high freqs
• Consider cosine wave at Nyquist freq
• f p
• CLS offset rate give exactly same
• estimates for this phase
• Now shift cosine by -90
• f p/2
• CLS estimates are all 0.0
• but offset rate estimates are not
• zero not constant

CLS estimation
Offset rate estimation
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Effects of Continuity Filter (2/3)

• CLS attenuates Nyquist signal amplitudes by
  factor of 2
• power reduced by factor of 4 at Nyquist frequency
• power starts dropping at 0.6 x Nyquist frequency
  higher
• Filter effect clearly seen in IGS PM results
• most Analysis Centers follow f-4 power law for
  sub-seasonal periods,
• e.g., GFZ (below right, during 11 Mar 2005
  29 Dec 2007)
• but CODE used CLS parameters had strong
  high-freq smoothing

Smoothed PSD for Reprocessed CODE PM
Smoothed PSD for Reprocessed GFZ PM
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Effects of Continuity Filter (3/3)

• CLS method is not a simple smoothing filter
• it distorts signal content by attenuating certain
  phases over others
• causes all parameters to be strongly correlated
  at all times
• should not be used when signals of interest are
  near Nyquist sampling
• Unfiltered IGS daily PM can be extrapolated to
  estimate subdaily PM variance (non-tidal)
• sub-seasonal PSD follows f-4 power law
  (integrated random walk process)
• fits to GFZ PSD over 0.1 to 0.5 cpd
• PSDx(f) (48.11 µas2/cpd) (f/cpd)-4.55     
• PSDy(f) (64.21 µas2/cpd) (f/cpd)-4.10
• if valid at f gt 0.5 cpd, then
• integrate over 1 cpd ? infinity
• s2x(subdaily) 13.55 µas2     
• s2y(subdaily) 20.73 µas2
• much too small to be detectable

Smoothed PSD for Reprocessed GFZ PM
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Estimating Subdaily" PM

• Three methods probably feasible
• Kalman filter
• use normal deterministic PM parameters for daily
  offset rate
• add stochastic model (f-4 integrated random walk)
  to estimate deviations
• probably can be done with JPLs GIPSY, but I know
  of no results
• CLS
• only method used till now
• but problems noted above are serious probably
  gives unreliable results
• invert from overlapping daily fits
• in principle, probably could invert normal daily
  offset rate fits
• but use overlapping data arcs (highly correlated
  estimates)
• would probably need to add f-4 integrated random
  walk model to inversion
• not known to be tried
• could be tested using IGS Ultra-rapid PM series
  (24 hr arcs with 6 hr time steps)
• Subdaily PM (non-tidal) power is so small, no
  clear reason to try to measure

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