Modeling Errors in GPS Vertical Estimates
description
Transcript of Modeling Errors in GPS Vertical Estimates
![Page 1: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/1.jpg)
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
![Page 2: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/2.jpg)
![Page 3: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/3.jpg)
![Page 4: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/4.jpg)
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
![Page 5: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/5.jpg)
Antenna Phase Patterns
![Page 6: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/6.jpg)
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
![Page 7: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/7.jpg)
Top: PBO station near Lind, Washington.
Bottom: BARD station CMBB at Columbia College, California
![Page 8: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/8.jpg)
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]
![Page 9: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/9.jpg)
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
![Page 10: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/10.jpg)
![Page 11: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/11.jpg)
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
![Page 12: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/12.jpg)
![Page 13: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/13.jpg)
GPS adjustments to atmospheric zenith delay for 29 June, 2003; southern Vancouver Island (ALBH) and northern coastal California (ALEN). Estimates at 2-hr intervals.
![Page 14: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/14.jpg)
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)
.
![Page 15: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/15.jpg)
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].
![Page 16: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/16.jpg)
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.
![Page 17: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/17.jpg)
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).
![Page 18: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/18.jpg)
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
![Page 19: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/19.jpg)
![Page 20: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/20.jpg)
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
![Page 21: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/21.jpg)
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
![Page 22: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/22.jpg)
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)
![Page 23: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/23.jpg)
Vertical (a) and north (b) displacements from pressure loading at a mid-latitude site (Germany). Bottom is power spectrum.
![Page 24: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/24.jpg)
Spatial and temporal autocorrelation of atmospheric pressure loading
From Petrov and Boy, J. Geophys. Res., 109, B03405, 2004
![Page 25: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/25.jpg)
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
![Page 26: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/26.jpg)
![Page 27: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/27.jpg)
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.
![Page 28: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/28.jpg)
![Page 29: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/29.jpg)
Correlation between estimates of height and zenith delay as function of minimum elevation angle observed (VLBI, from Davis [1986])
![Page 30: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/30.jpg)
Uncertainty in estimated height as function of minimum elevation angle observed (VLBI, from Davis [1986]; dotted line with no zenith delay estimated)
![Page 31: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/31.jpg)
![Page 32: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/32.jpg)
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.
![Page 33: Modeling Errors in GPS Vertical Estimates](https://reader036.fdocuments.net/reader036/viewer/2022062310/56815da3550346895dcbce81/html5/thumbnails/33.jpg)
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).