Technical description of solution usn2007b
1. Purpose of the solution:
a) obtain baseline length series;
b) provide intermediary information, such as covariance matrix,
matrix of constraints equaiton, decomposed normal matrix,
for individuals who are investigating in study of a feasibility
and usefulness of attempts to combine solutions from different
space geodesy techniques.
c) generate daily SINEX file output
2. Analysis center: USN ( U.S. Naval Observatory )
3. Short narrative description of solution:
Solution usn2007b estimates position of all stations, coordinates of some
unstable or infrequently observed sources, UT1, polar motion and their rates,
daily nutation offsets for each session independently. No-net-rotation,
no-net-translation constraints are imposed on the estimates of the station positions.
Clock function for all stations except the reference one and atmosphere zenith
path delay are modeled by a linear spline with the time span 60 and 20 minutes respectively.
Parameters of these spline are estimated as well together with other
parameters.
NB: although UT1 and pole coordinates are adjusted in the solution, these
estimates should not be used in scientific analysis, since they heavily depend
on apriori EOP values.
Mean site gradients were computed from the GSFC Data Assimilation Office
(DAO) model from met data from 1990-95. The atmospheric gradient delay is
modeled as
tau = m_grad(el) * [GN*cos(az)+GE*sin(az)],
where el and az are the elevation and azimuth of the observation and the
gradient mapping function is m_grad. The gradient vector has east and
north components GE and GN. Refer to [2] and [3].
4. Estimated parameters:
a. celestial frame: right ascension, declination of about 277 sources estimated
when they were observed. This includes all sources
NOT estimated as global parameters in TRF solutions usn2007b
(633 sources listed in control file). These were
estimated as local parameters for each individual sessions
independently in the usn2007b solution since they were
not observed very frequently.
b. terrestrial frame: X, Y, Z of all sites for each 24 hour session
independently.
c. Earth orientation: x, y, UT1-TAI, xdot, ydot, UT1dot, dpsi, deps.
d. zenith troposphere: linear spline 20-min interval; rate constraint
with reciprocal weights generally 50 ps/hr;
NMF wet partial derivative (segmented).
e. troposphere gradient: east and north gradients as well of the rate of
their change was estimated for all stations
offset and rate constraints with reciprocal
weights 0.5 mm and 2.0 mm/day were applied
(local).
f. station clocks: quadratic (local) +
linear spline with 1-hr interval (segmented);
rate constraint with reciprocal weights
generally 5.0E-14
g. baseline clocks: set in initial analysis - usually used (local)
5. Celestial reference frame:
a. a priori source positions: glo.src catalogue
b. source positions adjusted in solution: yes, positions for
infrequently observed sources were estimated.
If yes,
c. definition of orientation: no-net-rotation tie to the ICRF using
only the 212 ICRF defining sources
d. source position estimation: 277 local
6. Terrestrial reference frame:
a. a priori station positions: itrf2000.sit
b. a priori station velocities: itrf2000.vel
c. reference epoch: 1997.0
d. station positions/velocities adjusted in solution: yes, positions only
e. definition of origin, orientation, and their time evolution:
no-net-translation and no-net-rotation of position with respect to
itrf2000.sit. All stations participate in equations of constraints.
Equations of constraints are equally weighted.
f. station parameter estimation: X, Y, Z, locally for all stations
g. stations with constraints: NO!
h. stations with discontinuous positions and date of discontinuity: no
i. stations with nonlinear velocities: no
j. relativity scale: the terrestrial reference frame is defined using
the following metric tensor:
G_oo = -(1 - (2W/c^2 + W^2/c^4) + 2L_g )
G_oa = -4W^a/c^3
G_ab = \delta_ab (1 + 2W/c^2 - 2L_g) )
Specifically, the old formula 29 in IERS Conventions 1992, page 127-136
was used, although it is known to have a deficiency.
THIS METRIC TENSOR DOES NOT CONFORM IAU 2000 RESOLUTIONS!
k. permanent tide correction: yes
"Yes" means that both the permanent and the periodic tides have
been modeled, so that the output station position is for after the
removal of both the permanent and the periodic tidal effect.
The model used includes tide displacements for zero frequency with
Love numbers h2(freq=0) = 0.6074, l2(freq=0) = 0.0852
7. Earth orientation:
a. a priori precession/nutation model: IAU2000A nutation/precision model
using the non-rotating origin
b. a priori short-period tidal variations in x, y, UT1 were taken
into account in accordance with the model presented in Appendix A.
c. EOP estimation: X, Y, UT1, Xdot, Ydot, UT1dot, deps, dpsi each day with
a priori error of 45 mas for pole and 3 ms for UT1, 45 mas/day and
3 ms/day for pole rate and UT1 rate to allow estimation for
one-baseline sessions; deps and dpsi are relative to IAU 1976
precession and IAU 1980 nutation models. Time tag of EOP series is
the middle epoch of the observing session.
8. A priori geophysical models:
a. troposphere: NMF dry mapping function; Saastamoinen zenith delay
calculated using logged pressure, temperature;
a priori mean gradients from DAO weather model.
b. solid Earth tide: IERS Conventions 1996, p.56-65, step 1 and step 2,
anelasticity variant, including tides of the 3-rd order.
c. ocean loading: 3D ocean loading displacements computed by SPOTL
software by Leonid Petrov. Marmonic model 2007b_oclo.hps
d. atmosphere loading: 3D displacements computed by convolving global
surface pressure field on 2.5x2.5 degrees grid with 6 hour temporal
resolution using the NCEP Reanalysis model by Leonid Petrov.
9. Data type: group delays
10. Data editing: 5 deg elevation cutoff
11. Data weighting. Weights are defined as follows: 1/sqrt ( f**2 + a**2 )
where "f" is formal uncertainty of the ionosphere free linear combination
of group delays at X- and S-band obtained by fringe fitting on the base
of achieved signal to noise ratio. The station-dependent parameter "a"
was computed for each session by an iterative procedure such that the
ratio of the sum of squares of weighted residuals to the estimate of
their mathematical expectation is about unity.
12. Standard errors reported: all errors derived from least-squares
estimation propagated from the data weights and the constraints applied
to the estimated parameters.
13. Software: Calc 10.0, SOLVE revision date 2007.07.03
14. Other information:
Mean pole coordinates used for computation of pole tide deformation were
set to the mean pole expression given in the IERS2003 Conventions.
Axis offsets were fixed to either measured offsets or to offsets estimated
in a solution (2007c_axis) run by Leonid Petrov. The corresponding axis
offset file 2007c.axo was used.
References:
1. COORDINATES OF THE DEFINING SOURCES IN ICRF
http://hpiers.obspm.fr/webiers/results/icrf/icrfdef.html
2. MacMillan, D.S. and C. Ma, Atmospheric gradients from very
long baseline interferometry observations, Geophys. Res.
Lett., 22, 1041-1044, 1995.
3. MacMillan, D.S. and C. Ma, Atmospheric gradients and the
VLBI terrestrial and celestial reference frames, Geophys.
Res. Lett., 24, 453-456, 1997.
4. Petrov, L. and J.-P. Boy, "Study of the atmospheric pressure loading
signal in VLBI observations", J. Geophys. Res., 10.1029/2003JB002500,
vol. 109, No. B03405, 2004.
23-JULY-2007
----------------------------------------------------------------------------
Appendix A.
~~~~~~~~~~~
Expansion of short-period variations in polar motion and UT1.
UT1 tidal terms (microseconds)
l l' F D Om GST | Cos | Sin |
+pi | | |
-----------------------------------------
2 0 2 0 2 -1 -.13 -1.24
0 0 2 2 2 -1 .19 -.82
1 0 2 0 1 -1 -.50 -.92
1 0 2 0 2 -1 -2.64 -4.90
-1 0 2 2 2 -1 -1.10 -.77
0 0 2 0 1 -1 -2.51 -3.34
0 0 2 0 2 -1 -13.31 -17.72
-1 0 2 0 2 -1 .34 .63
1 0 0 0 0 -1 .48 .77
0 1 2 -2 2 -1 -.21 -.43
0 0 2 -2 2 -1 -3.20 -5.32
0 1 0 0 0 -1 .50 1.89
0 0 0 0 -1 -1 -.19 -.33
0 0 0 0 0 -1 9.83 16.45
0 0 0 0 1 -1 1.33 2.23
0 -1 0 0 0 -1 -.17 .41
0 0 -2 2 -2 -1 .08 -.04
-1 0 0 0 0 -1 .13 1.25
0 0 -2 0 -2 -1 .68 .33
0 0 -2 0 -1 -1 .44 .21
-1 0 -2 0 -2 -1 .18 .75
-1 0 -2 0 -1 -1 .12 .48
2 0 2 0 2 -2 -.30 .61
0 0 2 2 2 -2 -.83 .47
1 0 2 0 2 -2 -1.94 3.13
-1 0 2 2 2 -2 -.19 .67
0 0 2 0 1 -2 .37 -.57
0 0 2 0 2 -2 -9.88 15.37
-1 0 2 0 2 -2 .12 -.34
0 1 2 -2 2 -2 -.06 .17
0 0 2 -2 2 -2 -1.25 7.73
0 1 0 0 0 -2 .24 .27
0 0 0 0 0 -2 .28 2.48
0 0 0 0 1 -2 .08 .74
0 0 3 0 3 -3 .24 .03
0 0 0 4 1 -1 .26 .10
1 0 4 -2 2 -1 .43 -.52
0 0 0 1 0 -1 -.29 -.23
3 -1 2 0 2 -2 .14 .00
1 1 2 0 1 -2 -.26 -.40
0 0 0 -2 2 -2 .23 .09
-----------------------------------------
Polar motion tidal terms (microarcseconds)
l l' F D Om GST | Cos | Sin |
+pi | | |
-----------------------------------------
-2 0 -2 0 -2 1 -6.90 5.52
0 0 -2 -2 -2 1 -8.63 3.00
-1 0 -2 0 -1 1 -5.58 1.48
-1 0 -2 0 -2 1 -29.56 7.83
1 0 -2 -2 -2 1 -7.86 3.64
0 0 -2 0 -1 1 -25.03 8.53
0 0 -2 0 -2 1 -132.70 45.21
1 0 -2 0 -2 1 2.59 .60
-1 0 0 0 0 1 3.26 -8.76
0 -1 -2 2 -2 1 1.25 9.68
0 0 -2 2 -2 1 -49.40 19.23
0 -1 0 0 0 1 25.06 6.71
0 0 0 0 1 1 -3.09 1.76
0 0 0 0 0 1 156.21 -88.75
0 0 0 0 -1 1 21.18 -12.04
0 1 0 0 0 1 4.99 .50
0 0 2 -2 2 1 3.25 2.62
1 0 0 0 0 1 .51 -4.99
0 0 2 0 2 1 5.93 -10.38
0 0 2 0 1 1 3.80 -6.65
1 0 2 0 2 1 .46 .59
1 0 2 0 1 1 .30 .37
-2 0 -2 0 -2 2 4.13 -.28
0 0 -2 -2 -2 2 -1.37 .40
-1 0 -2 0 -2 2 10.48 -12.69
1 0 -2 -2 -2 2 4.33 1.81
0 0 -2 0 -1 2 -1.06 2.12
0 0 -2 0 -2 2 28.34 -56.83
1 0 -2 0 -2 2 1.92 .54
0 -1 -2 2 -2 2 5.42 -4.28
0 0 -2 2 -2 2 -.48 -20.16
0 -1 0 0 0 2 2.61 1.85
0 0 0 0 0 2 -.83 -18.26
0 0 0 0 -1 2 -.25 -5.44
0 0 -3 0 -3 3 1.92 -1.16
0 0 0 -4 -1 1 5.23 -1.47
-1 0 -4 2 -2 1 -1.28 -3.62
0 0 0 -1 0 1 2.33 -2.61
-3 1 -2 0 -2 2 -.88 -1.13
-1 -1 -2 0 -1 2 .24 .00
0 0 0 2 -2 2 .05 -1.31
2 0 2 0 2 -2 2.33 7.19
0 0 2 2 2 -2 2.87 7.66
1 0 2 0 2 -2 .59 43.62
-1 0 2 2 2 -2 -3.07 8.30
0 0 2 0 1 -2 .50 -9.59
0 0 2 0 2 -2 -13.37 257.07
-1 0 2 0 2 -2 1.83 -7.67
0 1 2 -2 2 -2 -7.08 .33
0 0 2 -2 2 -2 -72.53 106.95
0 1 0 0 0 -2 .34 -4.29
0 0 0 0 0 -2 -18.74 12.64
0 0 0 0 1 -2 -5.59 3.77
0 0 3 0 3 -3 -.56 -1.57
3 -1 2 0 2 -2 -.98 4.60
1 1 2 0 1 -2 -.62 4.28
0 0 0 -2 2 -2 -.83 2.72
-----------------------------------------