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 / local groundwater
• Loading of the crust by atmosphere, oceans, and
  surface water
• One-sided geometry increases vertical
  uncertainties relative to horizontal and makes
  the vertical more sensitive to session length

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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 / local groundwater
• Loading of the crust by atmosphere, oceans, and
  surface water

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Antenna Phase Patterns
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Modeling Antenna Phase-center Variations (PCVs)

• Ground antennas
• Relative calibrations by comparison with a
  standard antenna (NGS, used by the IGS prior to
  November 2006)
• Absolute calibrations with mechanical arm (GEO)
  or anechoic chamber
• May be depend on elevation angle only or
  elevation and azimuth
• Current models are radome-dependent
• Errors for some antennas can be several cm in
  height estimates
• Satellite antennas (absolute)
• Estimated from global observations (T U Munich)
• Differences with evolution of SV constellation
  mimic and scale change
• Recommendation for GAMIT Use latest IGS
  absolute ANTEX file (absolute) with AZ/EL for
  ground antennas and ELEV (nadir angle) for SV
  antennas

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Top PBO station near Lind, Washington. Bottom
BARD station CMBB at Columbia College, California
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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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Antenna Ht
0.15 m
0.6 m
Simple geometry for incidence of a direct and
reflected signal
1 m
Multipath contributions to observed phase for
three different antenna heights From Elosegui
et al, 1995
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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 / local groundwater
• 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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Effect of Neutral Atmosphere on GPS
Measurements Slant delay (Zenith Hydrostatic
Delay) (Dry Mapping Function)
(Zenith Wet Delay) (Wet Mapping
Function) ZHD well modeled by pressure (local
sensors or global model, GPT) Analytical
mapping functions (GMF) work well to 10 degrees
ZWD cannot be modeled with local temperature
and humidity - must estimate using the wet
mapping function as partial derivatives  Because
the wet and dry mapping functions are different,
errors in ZHD can cause errors in estimating
the wet delay (and hence total delay) .
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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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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. Height differences will be about twice
as large. (Elevation-dependent weighting used).
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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 / local groundwater
• 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 / local ground water
• 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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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.
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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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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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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).