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Earth Orientation Parameter Prediction (EOPP) Description

 

The National Geospatial-Intelligence 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 UT1-UTC 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 UT1-UTC 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 least-squares fit, NGA removes a 62-term Gross zonal tide model, with periods from 5.64 days to ~18.6 years from the UT1-UTC 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 UT1-UTC 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 UT1-UTC. 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 62-term Gross zonal tide model eliminates the need for approximate zonal tide coefficients. Thus, the zonal tide coefficients K1, K2, L1, and L2 are set to 0. The corresponding lunar and semi-lunar periods, R1 and R2, are set to 500.

 

2) TOTAL RESTORATION TO THE POLAR X, POLAR Y, AND UT1-UTC PREDICTIONS. 

In both EOPP output files (`EOPP####.TXT` and 'USAF####.DAT', again where #### is the bulletin number), the 62-term Gross zonal tide model, representing periods from 5.64 days to~18.6 years, is added to the UT1-UTC value as calculated above. Similarly, the diurnal/semi-diurnal ocean tide model is added to the polar X, polar Y, and UT1-UTC.  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

P1, Q1, and R3

Chandler cycle

435

P2 and Q2

Lunar

500.0 (no longer used)

R1

Semilunar

500.0 (no longer used)

R2

Semiannual

182.625

R4

 

 

Seasonal variation coefficients assumed to be constant

EOPP Model Parameter

Coefficient (sec)

K3

-0.022

K4

0.006

L3

0.012

L4

-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 5-line 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

The record output format is:

Line Number

Column Start

Format

Value

Variable

1

1

F10.2

Start Date of the Polar X-Y Motion Model (MJD)

ta

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)

C1

1

41

F10.6

Sine Coefficient of the Chandler Variations in Polar X (arcsec)

C2

1

51

F10.6

Cosine Coefficient of the Annual Variations in Polar X  (arcsec)

D1

1

61

F10.6

Cosine Coefficient of the Chandler Variations in Polar X (arcsec)

D2

1

71

F6.2

Annual Period (days)

P1

1

77

4X

Blank

 

2

1

F6.2

Chandler Period (days)

P2

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)

G1

2

37

F10.6

Sine Coefficient of the Chandler Variations in Polar Y (arcsec)

G2

2

47

F10.6

Cosine Coefficient of the Annual Variation in Polar Y (arcsec)

H1

2

57

F10.6

Cosine Coefficient of the Chandler Variations in Polar Y (arcsec)

H2

2

67

F6.2

Annual Period (days)

Q1

2

73

F6.2

Chandler Period (days)

Q2

2

79

2X

Blank

 

3

1

F10.2

Start Date of the UT1-UTC Model (MJD)

tb

3

11

F10.6

UT1-UTC offset (sec)

I

3

21

F10.6

UT1-UTC linear drift (sec/day)

J

3

31

F10.6

Sine Coefficient of the Lunar Variations in UT1-UTC (sec)

K1

3

41

F10.6

Sine Coefficient of the Semilunar Variations in UT1-UTC (sec)

K2

3

51

F10.6

Sine Coefficient of the Annual Variations in UT1-UTC (sec)

K3

3

61

F10.6

Sine Coefficient of the Semiannual Variations in UT1-UTC (sec)

K4

3

71

10X

Blank

 

4

1

F10.6

Cosine Coefficient of the Lunar Variations in UT1-UTC (sec)

L1

4

11

F10.6

Cosine Coefficient of the Semilunar Variations in UT1-UTC (sec)

L2

4

21

F10.6

Cosine Coefficient of the Annual Variations in UT1-UTC (sec)

L3

4

31

F10.6

Cosine Coefficient of the Semiannual Variations in UT1-UTC (sec)

L4

4

41

F9.4

Lunar Period (days)

R1

4

50

F9.4

Semilunar Period (days)

R2

4

59

F9.4

Annual Period (days)

R3

4

68

F9.4

Semiannual Period (days)

R4

4

77

4X

Blank

 

5

1

I4

Number of Leap Seconds since the beginning of GPS time

TAI-UTC

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

UT1-UTC linear drift (msec/day)

rJ

6-12

1

16X

Blank

 

6-12

17

I5

MJD of predictions

 

6-12

18

1X

Blank

 

6-12

19

F13.8

Polar X (arcseconds)

 

6-12

32

1X

Blank

 

6-12

33

F13.8

Polar Y (arcseconds)

 

6-12

46

1X

Blank

 

6-12

47

F13.8

UT1-UTC (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 UT1-UTC. The accuracy of NGA’s EOPP coefficients degrade with time, and the most recent coefficients should always be used.

 

 

Document last modified June 2017


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