Modeling Errors in GPS Vertical Estimates

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Modeling Errors in GPS Vertical Estimates

• Signal propagation effects
• Signal scattering ( antenna phase
  center/multipath )
• Atmospheric delay ( parameterization, mapping
  functions )
• Unmodeled motions of the station
• Monument instability
• Loading of the crust by atmosphere, oceans, and
  surface water

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Modeling Errors in GPS Vertical Estimates

• Signal propagation effects
• Signal scattering ( antenna phase
  center/multipath )
• Atmospheric delay ( parameterization, mapping
  functions )
• Unmodeled motions of the station
• Monument instability
• Loading of the crust by atmosphere, oceans, and
  surface water

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Simple geometry for incidence of a direct and
reflected signal
Multipath contributions to observed phase for an
antenna at heights (a) 0.15 m, (b) 0.6 m, and (c
) 1 m. From Elosegui et al, 1995
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Antenna Phase Patterns
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Left Phase residuals versus elevation for
Westford pillar, without (top) and with (bottom)
microwave absorber. Right Change in height
estimate as a function of minimum elevation angle
of observations solid line is with the
unmodified pillar, dashed with microwave absorber
added
From Elosequi et al.,1995
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Top PBO station near Lind, Washington. Bottom
BARD station CMBB at Columbia College, California
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Modeling Errors in GPS Vertical Estimates

• Signal propagation effects
• Signal scattering ( antenna phase
  center/multipath )
• Atmospheric delay ( parameterization, mapping
  functions )
• Unmodeled motions of the station
• Monument instability
• Loading of the crust by atmosphere, oceans, and
  surface water

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GPS adjustments to atmospheric zenith delay for
29 June, 2003 southern Vancouver Island (ALBH)
and northern coastal California (ALEN). Estimates
at 2-hr intervals.
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Uncertainty in estimated height as function of
minimum elevation angle observed (VLBI, from
Davis 1986 dotted line with no zenith delay
estimated)
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Correlation between estimates of height and
zenith delay as function of minimum elevation
angle observed (VLBI, from Davis 1986)
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Percent difference (red) between hydrostatic and
wet mapping functions for a high latitude (dav1)
and mid-latitude site (nlib). Blue shows
percentage of observations at each elevation
angle. From Tregoning and Herring 2006.
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Difference between a) surface pressure derived
from standard sea level pressure and the mean
surface pressure derived from the GPT model. b)
station heights using the two sources of a priori
pressure. c) Relation between a priori pressure
differencesand height differences.
Elevation-dependent weighting was used in the GPS
analysis with a minimum elevation angle of 7 deg.
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Height (red simulated black estimated) and ZTD
(green simulated blue estimated) errors versus
latitude as a function of error in surface
pressure used to calculate the a priori ZHD.
Uniform 10 mm data weighting applied.
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Height (black/blue) and ZTD (red/green) errors at
Davis, Antarctica, for different elevation cutoff
angles as a function of error in surface pressure
used to calculate the a priori ZHD.. Results
shown for both elevation-dependent (blue and red
results) and constant data weighting (black and
green).
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Modeling Errors in GPS Vertical Estimates

• Signal propagation effects
• Signal scattering ( antenna phase
  center/multipath )
• Atmospheric delay ( parameterization, mapping
  functions )
• Unmodeled motions of the station
• Monument instability
• Loading of the crust by atmosphere, oceans, and
  surface water

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Modeling Errors in GPS Vertical Estimates

• Signal propagation effects
• Signal scattering ( antenna phase
  center/multipath )
• Atmospheric delay ( parameterization, mapping
  functions )
• Unmodeled motions of the station
• Monument instability
• Loading of the crust by atmosphere, oceans, and
  surface water

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Atmosphere (purple) 2-5 mm Snow/water (blue)
2-10 mm Nontidal ocean (red) 2-3 mm
Annual vertical loading effects on site
coordinates From Dong et al. J. Geophys. Res.,
107, 2075, 2002
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Vertical (a) and north (b) displacements from
pressure loading at a low-latitude site (S.
Africa). Bottom is power spectrum. From Petrov
and Boy (2004)
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Vertical (a) and north (b) displacements from
pressure loading at a mid-latitude site
(Germany). Bottom is power spectrum.
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Spatial and temporal autocorrelation of
atmospheric pressure loading
From Petrov and Boy, J. Geophys. Res., 109,
B03405, 2004
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Atmosphere (purple) 2-5 mm Snow/water (blue)
2-10 mm Nontidal ocean (red) 2-3 mm
Annual vertical loading effects on site
coordinates From Dong et al. J. Geophys. Res.,
107, 2075, 2002
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Differences in GPS estimates of ZTD at Algonquin,
Ny Alessund, Wettzell and Westford computed using
static or observed surface pressure to derive the
a priori. (Elevation-dependent weighting used).
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Station height estimates for Rio Grande,
Argentina, using pressure from height-corrected
STP, GPT and actual observations (MET). Dashed
black line shows observed surface pressure pink
line shows atmospheric pressure loading
deformation (corrected for in the GPS analyses) ,
offset by 2.07 m.