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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 41-term Yoder zonal tide model, with periods from 5.64 days to 34.85 days 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 WHICH APPROXIMATES ZONAL TIDES IN THE UT1-UTC PREDICTIONS ONLY.

Approximate solid Earth zonal tides are restored to UT1-UTC predictions (only) in the web file named 'EOPP####.TXT', where #### is the bulletin number.  This is accomplished by using the unused UT1-UTC coefficients by fitting the two dominant periods, 27.56 days (lunar cycle) and 13.66 days (semi-lunar cycle), of the zonal tides.  Zonal tide approximation utilizes the unused UT1-UTC coefficients, K1, K2, L1, L2 (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 UT1-UTC.  Also, using this method, the first two periods (R1 and R2) are set to 27.56 days and 13.66 days (lunar and semi-lunar periods), respectively.

 

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

The web tabular file named 'USAF####.DAT', again where #### is the bulletin number, has had the 41-term Yoder zonal tide model, representing periods from 5.64 days to 34.85 days, applied to the UT1-UTC predictions and the Ray diurnals/sub-diurnals model applied to the polar X, polar Y, and UT1-UTC.  If these predictions are used, the K1, K2, L1, and L2 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

P1, Q1, and R3

Chandler cycle

435

P2 and Q2

Lunar

27.56

R1 (set to 500 prior to 2nd week of 2005)

Semilunar

13.66

R2 (set to 500 prior to 2nd week of 2005)

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

·         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

 

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 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