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

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

Antenna Phase Patterns

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

Top: PBO station near Lind, Washington.

Bottom: BARD station CMBB at Columbia College, California

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]

Simple geometry for incidence

of a direct and reflected signal

Multipath contributions to observed phase for three different antenna heights [From Elosegui et al, 1995]

0.15 m

Antenna Ht

0.6 m

1 m

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

GPS adjustments to atmospheric zenith delay for 29 June, 2003; southern Vancouver Island (ALBH) and northern coastal California (ALEN). Estimates at 2-hr intervals.

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)

.

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].

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 differences

and height differences. Elevation-dependent

weighting was used in the GPS analysis with a

minimum elevation angle of 7 deg.

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).

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

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

Annual vertical loading effects on site coordinates

From Dong et al. J. Geophys. Res., 107, 2075, 2002

Atmosphere (purple) 2-5 mm

Snow/water (blue) 2-10 mm

Nontidal ocean (red) 2-3 mm

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)

Vertical (a) and north (b) displacements from pressure loading at a mid-latitude site (Germany). Bottom is power spectrum.

Spatial and temporal autocorrelation of atmospheric pressure loading

From Petrov and Boy, J. Geophys. Res., 109, B03405, 2004

Annual vertical loading effects on site coordinates

From Dong et al. J. Geophys. Res., 107, 2075, 2002

Atmosphere (purple) 2-5 mm

Snow/water (blue) 2-10 mm

Nontidal ocean (red) 2-3 mm

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.

Correlation between estimates of height and zenith delay as function of minimum elevation angle observed (VLBI, from Davis [1986])

Uncertainty in estimated height as function of minimum elevation angle observed (VLBI, from Davis [1986]; dotted line with no zenith delay estimated)

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.

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).