Transcript Document

Estimating Heights and Atmospheric Delays
• “One-sided” geometry increases vertical uncertainties relative to
horizontal and makes the vertical more sensitive to session
length
• Height and zenith delays are highly correlated, with separation
achieved by observing to low elevation angles, increasing
signal-scattering/multipath errors
• Dominant effects of error / interest are signal scattering, water
vapor, and loading of the crust by atmosphere, oceans, and
surface water
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)
Time series for
continuous station in
(dry) eastern Oregon
Vertical wrms 5.5 mm,
higher than the best stations.
Systematics of 25 mm peakto-peak may be atmospheric
or hydrological loading.
This variation will maps
into ZTD errors of ~10 mm
if heights are held fixed.
Modeling Errors in GPS Vertical Estimates
• Unmodeled motions of the station
– Monument instability / local groundwater
– Loading of the crust by atmosphere, oceans, and surface water
• Signal propagation effects
– Signal scattering ( antenna phase center/multipath )
– Atmospheric delay ( parameterization, mapping functions )
Monuments Anchored to Bedrock are Critical for Tectonic Studies
(not so much for atmospheric studies)
Good anchoring:
Pin in solid rock
Drill-braced (left) in
fractured rock
Low building with deep
foundation
Not-so-good anchoring:
Vertical rods
Buildings with shallow
foundation
Towers or tall building
(thermal effects)
Modeling Errors in GPS Vertical Estimates
• Unmodeled motions of the station
– Monument instability / local ground water
– Loading of the crust by atmosphere, oceans, and surface water
• Signal propagation effects
– Signal scattering ( antenna phase center/multipath )
– Atmospheric delay ( parameterization, mapping functions )
Annual Component of Vertical Loading
Atmosphere (purple)
2-5 mm
Snow/water (blue)
2-10 mm
Nontidal ocean (red)
2-3 mm
From Dong et al. J. Geophys. Res., 107, 2075, 2002
Atmospheric pressure loading near equator
Vertical (a) and north (b) displacements from pressure loading at a site
in South Africa. Bottom is power spectrum. Dominant signal is annual.
From Petrov and Boy (2004)
Atmospheric pressure loading at mid-latitudes
Vertical (a) and north (b) displacements from pressure loading at a site
in Germany. Bottom is power spectrum. Dominant signal is shortperiod.
Spatial and temporal
autocorrelation of
atmospheric pressure
loading
Implies that for networks less
than 1500 km, we get 80%
cancellation of pressure
loading ( < 1 mm in height, <
0.5 mm in ZTD)
From Petrov and Boy, J. Geophys. Res., 109, B03405, 2004
Modeling Errors for Height and Atmosphere
• Unmodeled motions of the station
– Monument instability / local groundwater
– Loading of the crust by atmosphere, oceans, and surface water
• Signal propagation effects
– Signal scattering ( antenna phase center/multipath )
– Atmospheric delay ( parameterization, mapping functions )
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 depend on elevation angle only or elevation and azimuth
– Adding a radome changes the model
– 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 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
(MIT file augmented with NGS values for antennas missing from IGS)
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]
Antenna Ht
0.15 m
0.6 m
Simple geometry for incidence
of a direct and reflected signal
1m
Multipath contributions to observed phase for three different antenna
heights [From Elosegui et al, 1995]
Modeling Errors for Height and Atmosphere
• Unmodeled motions of the station
– Monument instability / local groundwater
– Loading of the crust by atmosphere, oceans, and surface water
• Signal propagation effects
– Signal scattering ( antenna phase center/multipath )
– Atmospheric delay ( parameterization, mapping functions )
Modeling the Neutral Atmosphere in GPS Analysis
Slant delay = (Zenith Hydrostatic Delay) * (“Dry” Mapping Function) +
(Zenith Wet Delay) * (Wet Mapping Function)
• ZHD well modeled by pressure (local sensors or numerical weather model)
• Analytical mapping functions (NMF, 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)
.
Effect of errors in a priori ZHD
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].
Effect of error in a priori ZHD
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.
Tregoning and Herring [2006]
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. (Elevationdependent weighting used).
Tregoning and Herring [2006]
GAMIT Piecewise-linear Model for ZTD
GPS adjustments to atmospheric zenith delay for 29 June, 2003;
southern Vancouver Island (ALBH) and northern coastal California
(ALEN). Estimates at 2-hr intervals. Linear spline model allows
stochastic constraints on point-to-point estimates.
Estimating ZWD from GAMIT
1. Supply GAMIT with a priori ZHD accurate enough to avoid error from using
the wet MF as partial derivative
Error in ZTD (mm) = ~ 0.1 error in a priori ZHD (mb)
--> 20 mb error (e.g GPT) = 2 mm error in ZTD (or ZWD)
( compare with a typical estimation error of ~5 mm )
2. Read ZTD estimates from linear spline in o-file
Error depends on rapidity of change of ZHD and ZWD and spacing of knots
3. Calculate ZWD = ZTD - ZHD where ZHD now must have the same accuracy
you expect for ZWD, ~ 5 mm = 2 mb, best obtained from surface met, but
closely matched by VMF1
Should you constrain coordinates (mainly heights) when
estimating ZTD for PW studies ?
Probably…
Yes, if the noise noise is less than the uncertainties
No, if there are significant unmodeled errors in the height
variations
Slant ZWD for PW Studies
Residuals from
autcln (DPH files)
are mostly water
vapor and signalscattering/multipath
Multipath can be
removed by
averaging the
residuals over days
to weeks. (Program
to do this is in
preparation at MIT.)
References
Bevis, M., S. Businger, S. Chriswell, T. A. Herring, R. A. Anthes, C. Rocken, and R. Ware,
GPS meteorology: Mapping zenith wet delys onto precipitable water, J. Appl. Met., 33, 379,
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Boehm, J., B. Werl, and H. Schuh, Tropospheric mapping functions for GPS and very long
baseline interferometry from European Centre for Medium Range Weather Forecasts
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Boehm, J., R. Heinkelmann, and H. Schuh, Short Note: A global model of pressure and
temperature for geodetic applications, J Geod, 81, 679, doi: 10.1007/s00190-007-0135-3,
2007.
Boehm, J. A. Neill, P. Tregoning, and H. Schuh, Global Mapping Function (GMF): A new
empirical mapping function based on numerical weather model data, Geophys. Res. Lett., 33,
L07304, doi:10.1029/2005GL025546, 2006.
Dong, D., P. Fang, Y. Bock, M. K.. Cheng, and S. Miyazaki, Anatomy of apparent seasonal
vairation from GPS-derived site position time series, J. Geophys. Res., 107, 2075,
doi:10.1029/2001JB000573, 2002.
Elosegui, P., J. L., Davis, R. T. K. Jadlehag, J. M. Johansson, A. E. Niell, and I. I. Shapiro,
Geodesy using the Global Positioning Sysems: The effects of signal scattering on estimates of
site position, J. Geophys. Res., 100, 9921, 1995.
References (continued)
Fratepietro, F., T. F. Baker, S. D. P. Williams, and M. Van Camp, Ocean loading deformations
caused by storm surges on the northwest European shelf, Geophys. Res. Lett., 33, l06317,
doi:10.1029/2005GL025475, 2006.
Hagemann, S., L. Bengtsson, and G. Gendt, On the determination of atmospheric wter vapor
from GPS measurements, J. Geophys. Res., 108, 4678, doi:10.1029/2002JD003235, 2003.
Jade, S., and M. S. M. Vijayan, GPS-based atmospheric precipitable water vapor estimation
using meteorological parameters interpolated from NCEP global reanalysis data, G. Geophys.
Res., 113, D03106, doi: 10.1029/2007JD008758, 2008.
Penna, N. T., M. A. King, and M. P. Stewart, GPS height time series: Short period origins of
spurious long period signals, J. Geophys. Res., 111 doi:10.1029/2005JB0004047, 2006.
Petrov and Boy, Study of the atmospheric pressure loading signal in very long baseline
interferometry observations, J. Geophys. Res., 109, B03405, doi:10.1029/2003JB000250, 2004
Tregoning, P., and T. A. Herring, Impact of a priori zenith hydrostatic delay errors on GPS estimtes of
station heights and zenith total delays, Geophys. Res. Lett., 33, L23303, doi:10.1029/2006GL027706,
2006.
Watson, C., P. Tregoning, and R. Coleman, Impact of solid Earth tide models on GPS coordinate and
tropospheric time series, Geophys. Res. Lett., 33, L08306, doi:10.1029/2005GL025538, 2006.