Estimating Heights and Atmospheric Delays

1
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/mul
  tipath errors
• Dominant effects of error / interest are signal
  scattering, water vapor, and loading of the
  crust by atmosphere, oceans, and surface water

2
Correlation between estimates of height and
zenith delay as function of minimum elevation
angle observed (VLBI, from Davis 1986)?
3
Uncertainty in estimated height as function of
minimum elevation angle observed (VLBI, from
Davis 1986 dotted line with no zenith delay
estimated)?
4
Time series for continuous station in (dry)
eastern Oregon Vertical wrms 5.5 mm, higher than
the best stations. Systematics of 25 mm
peak-to-peak may be atmospheric or hydrological
loading. This variation will maps into ZTD
errors of 10 mm if heights are held fixed.
5
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 )?

6
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)
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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 )?

8
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
9
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)?
10
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 short-period.

11
Spatial and temporal autocorrelation of
atmospheric pressure loading Implies that for
networks less than 1500 km, we get 80
cancellation of pressure loading ( lt 1 mm in
height, lt 0.5 mm in ZTD)?
From Petrov and Boy, J. Geophys. Res., 109,
B03405, 2004
12
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 )?

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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 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)?

15
Top PBO station near Lind, Washington. Bottom
BARD station CMBB at Columbia College, California
16
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 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 )?

19
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)? .
20
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 errors in a priori ZHD
21
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
Effect of error in a priori ZHD
22
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).
Tregoning and Herring 2006
23
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.
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• 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)?
• --gt 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

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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
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Slant ZWD for PW Studies
Residuals from autcln (DPH files) are mostly
water vapor and signal-scattering/multipath Multi
path can be removed by averaging the residuals
over days to weeks. (Program to do this is in
preparation at MIT.)?
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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,
1994 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 operational
data analysis, J. Geophys. Res, 111, B02406,
doi10.1029/2005JB03629, 2006. 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, doi10.1029/2005GL025546,
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,
doi10.1029/2001JB000573, 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.
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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,
doi10.1029/2005GL025475, 2006. Hagemann, S., L.
Bengtsson, and G. Gendt, On the determination of
atmospheric wter vapor from GPS measurements, J.
Geophys. Res., 108, 4678, doi10.1029/2002JD003235
, 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 doi10.1029/2005JB0
004047, 2006. Petrov and Boy, Study of the
atmospheric pressure loading signal in very long
baseline interferometry observations, J. Geophys.
Res., 109, B03405, doi10.1029/2003JB000250,
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,
doi10.1029/2006GL027706, 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,
doi10.1029/2005GL025538, 2006.