NGA > Office of Geomatics > GPS > Documentation
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 41term Yoder zonal tide model, with
periods from 5.64 days to 34.85 days 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 xp, yp, 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 WHICH
APPROXIMATES ZONAL TIDES IN THE UT1UTC PREDICTIONS ONLY.
Approximate solid Earth zonal tides
are restored to UT1UTC predictions (only) in the web file named
'EOPP####.TXT', where #### is the bulletin number. This is accomplished by using the unused
UT1UTC coefficients by fitting the two dominant periods, 27.56 days (lunar
cycle) and 13.66 days (semilunar cycle), of the zonal tides. Zonal tide approximation utilizes the unused
UT1UTC coefficients, K_{1}, K_{2}, L_{1}, L_{2}
(all formerly set = 0.000000), as specified in the NGA bulletin.
Zonal tide approximation requires no
change to existing EOPP users that do not restore zonal tides but may need
better prediction accuracy in UT1UTC.
Also, using this method, the first two periods (R1 and R2) are set to
27.56 days and 13.66 days (lunar and semilunar periods), respectively.
2) TOTAL RESTORATION TO THE POLAR
X, POLAR Y, AND UT1UTC PREDICTIONS.
The web tabular file named
'USAF####.DAT', again where #### is the bulletin number, has had the 41term Yoder
zonal tide model, representing periods from 5.64 days to 34.85 days, applied to
the UT1UTC predictions and the Ray diurnals/subdiurnals model applied to the
polar X, polar Y, and UT1UTC. If these
predictions are used, the K_{1}, K_{2}, L_{1}, and L_{2}
coefficients need to be ignored or reset (each) to zero.
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. They no longer use the
approximation method in 1) above.
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 
27.56 
R_{1} (set to 500 prior
to 2^{nd} week of 2005) 
Semilunar 
13.66 
R_{2} (set to 500 prior
to 2^{nd} week of 2005) 
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
·
Weekly file format (prior to 1 July 2009)
52958.00
.054272 .000000 .056994
.103402 .014470 .106800365.25
435.00
.348539 .000000 .011996
.106209 .049085 .106233365.25435.00
53370.00
.510015 .000337 .000615
.000667 .022000 .006000
.000829
.001090 .012000 .007000
27.5600 13.6600 365.2500 182.6250
32
502 53379 53376
·
Daily file format (starting 1 July 2009)
55756.00
.086462 .000000 .143942
.028860 .025332 .047571365.25
435.00
.338797 .000000 .021268
.049319 .123890 .018568365.25435.00
55926.00
.619928 .000991 .000623
.000636 .022000 .006000
.000400
.000006 .012000 .007000
27.5600 13.6600 365.2500 182.6250
35 2249 56175 56174
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 week/day) 

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

5 
17 
A18 
Generation Date (MJD) 

5 
35 
46X 
Blank 

All dates are given in Modified
Julian Date (MJD)
Document last modified April 2016