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Earth Orientation Parameter Prediction (EOPP)
Description
The
National GeospatialIntelligence Agency provides Earth Orientation Parameter
Prediction (EOPP) coefficients and predictions daily. Using NGA’s EOPP coefficients
allows a user to generate polar X, polar Y, and UT1UTC predictions for any
number of days in the future through the summation equations given below. The
coefficients are recomputed every day at NGA and sent to the users after a
quality control check. They are labeled
to go into effect on the following day.
The
coefficients are computed daily by using updated Polar x, Polar y, and UT1UTC
values from the International Earth Rotation and Reference Systems Service
(IERS) at the United State Naval Observatory.
These updated values are fit, in a least squares manner, to the math
models below. Prior to the leastsquares fit, NGA removes a 62term Gross zonal
tide model, with periods from 5.64 days to ~18.6 years from the UT1UTC data
prior to computing the coefficients. The resulting coefficients, constants and
variables used in the math models are output in a five (5) line (80 columns per
line) format. By simply substituting the
output values back into the math model it is possible to get parameter
predictions for any day in the future.
One must know the Modified Julian Day (MJD) of your day of
interest.
The
following equations are the math models used in x_{p},
y_{p}, and UT1UTC coefficient
generation:
NGA
analysis shows that the weekly RMS difference between NGA predictions and final
IERS values is under 0.003 arcsec (10 cm. at the
equator) for Polar X and Y and under 0.8 msec for
UT1UTC. The accuracy of NGA’s EOPP coefficients and model degrades with time. Always
use the most recent set of NGA coefficients.
The EOP predictions calculated from NGA coefficients and equations may
not necessarily reproduce the NGA predicted EOP values (also provided on the
NGA web site). This is primarily due to differences
in machine precision and the restoration of zonal and diurnal solid Earth tides.
1)
NGA EOPP BULLETIN DOES NOT CONTAIN APPROXIMATE ZONAL TIDES.
The
use of the 62term Gross zonal tide model eliminates the need for approximate
zonal tide coefficients. Thus, the zonal tide coefficients K_{1}, K_{2}, L_{1}, and L_{2} are set to 0. The
corresponding lunar and semilunar periods, R_{1}
and R_{2}, are set to
500.
2)
TOTAL RESTORATION TO THE POLAR X, POLAR Y, AND UT1UTC PREDICTIONS.
In both
EOPP output files (`EOPP####.TXT` and 'USAF####.DAT', again where #### is the
bulletin number), the 62term Gross zonal tide model, representing periods from
5.64 days to~18.6 years, is added to the UT1UTC value as calculated above.
Similarly, the diurnal/semidiurnal ocean tide model is added to the polar X,
polar Y, and UT1UTC. This method gives
the best accuracy of all three components when compared to the IERS Finals. The
Air Force GPS Master Control Station uses these coefficients and predictions in
their process.
Solid Earth Tide Phases Used
Quantity 
Period
(days) 
EOPP
Model Parameters 
Annual 
365.25 
P_{1}, Q_{1}, and R_{3} 
Chandler
cycle 
435 
P_{2}
and Q_{2} 
Lunar 
500.0
(no longer used) 
R_{1}

Semilunar 
500.0
(no longer used) 
R_{2}

Semiannual 
182.625 
R_{4} 
Seasonal variation coefficients
assumed to be constant
EOPP Model Parameter 
Coefficient (sec) 
K_{3} 
0.022 
K_{4} 
0.006 
L_{3} 
0.012 
L_{4} 
0.007 
These
constants were computed by I. I. Mueller in the 1960's (Moritz, H. and I.I.
Mueller, Earth Rotation: Theory and Observations, 1987, Ungar,
New York).
Sample EOPP 5line Products
57134.00
.096535 .000000 .079560 .001056 .094888
.011426365.25
435.00
.360340 .000000 .110327 .043663 .056139
.001909365.25435.00
57387.00 .037772 .001042 .000000
.000000 .022000 .006000
.000000 .000000 .012000 .007000 500.0000 500.0000 365.2500
182.6250
36
6166 57553 57552
00000 1.041778
57553 .11412908 .49412727 .20154468
57554 .11622101 .49396709 .20219709
57555 .11832966 .49378092 .20277489
57556 .12045747 .49355565 .20326385
57557 .12260569 .49327790 .20365996
57558 .12477375 .49293417 .20397038
57559 .12695799 .49251222 .20421432
Line Number 
Column Start 
Format 
Value 
Variable 
1 
1 
F10.2 
Start
Date of the Polar XY Motion Model (MJD) 
t_{a}

1 
11 
F10.6 
Polar
X offset (arcsec) 
A 
1 
21 
F10.6 
Polar
X linear drift (arcsec/day) 
B 
1 
31 
F10.6 
Sine
Coefficient of the Annual Variations in Polar X (arcsec) 
C_{1
} 
1 
41 
F10.6 
Sine
Coefficient of the Chandler Variations in Polar X (arcsec) 
C_{2}

1 
51 
F10.6 
Cosine
Coefficient of the Annual Variations in Polar X (arcsec) 
D_{1}

1 
61 
F10.6 
Cosine Coefficient of the Chandler Variations in Polar X (arcsec)_{} 
D_{2 } 
1 
71 
F6.2 
Annual
Period (days) 
P_{1}

1 
77 
4X 
Blank 

2 
1 
F6.2 
Chandler
Period (days) 
P_{2}

2 
7 
F10.6 
Polar
Y offset (arcsec) 
E 
2 
17 
F10.6 
Polar
Y linear drift (arcsec/day) 
F 
2 
27 
F10.6 
Sine
Coefficient of the Annual Variation in Polar Y (arcsec) 
G_{1}

2 
37 
F10.6 
Sine
Coefficient of the Chandler Variations in Polar Y (arcsec) 
G_{2}

2 
47 
F10.6 
Cosine
Coefficient of the Annual Variation in Polar Y (arcsec) 
H_{1}

2 
57 
F10.6 
Cosine
Coefficient of the Chandler Variations in Polar Y (arcsec) 
H_{2}

2 
67 
F6.2 
Annual
Period (days) 
Q_{1} 
2 
73 
F6.2 
Chandler
Period (days) 
Q_{2} 
2 
79 
2X 
Blank 

3 
1 
F10.2 
Start
Date of the UT1UTC Model (MJD) 
t_{b} 
3 
11 
F10.6 
UT1UTC
offset (sec) 
I 
3 
21 
F10.6 
UT1UTC
linear drift (sec/day) 
J 
3 
31 
F10.6 
Sine
Coefficient of the Lunar Variations in UT1UTC (sec) 
K_{1}

3 
41 
F10.6 
Sine
Coefficient of the Semilunar Variations in UT1UTC (sec) 
K_{2}

3 
51 
F10.6 
Sine
Coefficient of the Annual Variations in UT1UTC (sec) 
K_{3}

3 
61 
F10.6 
Sine
Coefficient of the Semiannual Variations in UT1UTC (sec) 
K_{4}

3 
71 
10X 
Blank 

4 
1 
F10.6 
Cosine
Coefficient of the Lunar Variations in UT1UTC (sec) 
L_{1}

4 
11 
F10.6 
Cosine
Coefficient of the Semilunar Variations in UT1UTC (sec) 
L_{2}

4 
21 
F10.6 
Cosine
Coefficient of the Annual Variations in UT1UTC (sec) 
L_{3}

4 
31 
F10.6 
Cosine
Coefficient of the Semiannual Variations in UT1UTC (sec) 
L_{4}

4 
41 
F9.4 
Lunar Period (days)_{} 
R_{1} 
4 
50 
F9.4 
Semilunar Period (days)_{} 
R_{2} 
4 
59 
F9.4 
Annual Period (days)_{} 
R_{3} 
4 
68 
F9.4 
Semiannual Period (days)_{} 
R_{4} 
4 
77 
4X 
Blank 

5 
1 
I4 
Number
of Leap Seconds since the beginning of GPS time 
TAIUTC 
5 
5 
I5 
Bulletin
Number (EOPP year/day) 

5 
10 
I6 
Effectivity
Date (MJD) 
t 
5 
16 
1X 
Blank 

5 
17 
A18 
Generation
Date (MJD) 

5 
23 
1X 
Blank 

5 
24 
I5 
Time
of Effectivity (sec) 
ToE 
5 
29 
1X 
Blank 

5 
30 
F11.6 
UT1UTC
linear drift (msec/day) 
rJ 
612 
1 
16X 
Blank 

612 
17 
I5 
MJD
of predictions 

612 
18 
1X 
Blank 

612 
19 
F13.8 
Polar
X (arcseconds) 

612 
32 
1X 
Blank 

612 
33 
F13.8 
Polar
Y (arcseconds) 

612 
46 
1X 
Blank 

612 
47 
F13.8 
UT1UTC
(arcseconds) 

All
dates are given in Modified Julian Date (MJD)
Internal comparison of EOPP
calculations with IERS Final values produce a weekly RMS difference of ~0.003 arcsec (10 cm. at the equator) in Polar X and Y and ~0.8 ms in UT1UTC. The accuracy of NGA’s EOPP coefficients
degrade with time, and the most recent coefficients should always be used.
Document last modified June 2017
Point
of Contact: NGA Public Affairs
Phone Numbers:
Com. (571)5575400
DSN 8469140
publicaffairs@nga.mil