Earth Orientation Parameter Prediction (EOPP) Description
Effective date 09 January 2005
The National Geospatial-Intelligence Agency (NGA) is required to provide Earth Orientation Parameter Prediction (EOPP) coefficients to the Air Force GPS Master Control Station at Schriever Air Force Base and defense related customers on a weekly basis. The coefficients are unclassified and thus also available to non-military users. They can be used to generate polar x (xp), polar y (yp), and UT1(R)-UTC prediction values for any number of days in the future. The NGA coefficients can be valuable in high precision satellite tracking in any Earth Centered-Earth fixed reference system (eg. WGS84). Please note here that the UT1R, above, refers to the UT1 system that has an earth tide model removed. The coefficients are computed by using updated xp, yp, and UT1-UTC values retrieved by NGA through the International Earth Rotation Service (IERS) at USNO. These updated values are then fit, in a least squares manner, to specified math models. 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.) PLEASE NOTE HERE, that using the weekly coefficients, provided on the NGA web site, in the following equations may not reproduce the exact prediction values, also provided on the NGA web site. This is due to the precision values used by NGA when computing the predictions (double precision) versus the formatted requirements of the listed web site coefficients. UPDATE: USING REVISED NGA EOPP BULLETIN WHICH APPROXIMATES ZONAL TIDES IN UT1-UTC. Starting with EOPP bulletin 502, NGA has restored zonal tides into the EOPP bulletin using 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. For existing EOPP users that apply the 41-term zonal tide model, they need to ignore the coefficients, K1, K2, L1, and L2 (or reset each to zero). Please note below. The following equations are the math models used in xp, yp, and UT1-UTC coefficient generation: A) 2 2 x(t) = A + B(t-ta) + Sum(Cj sin[(2pi(t-ta)/Pj]) + Sum(Dj cos[(2pi(t-ta)/Pj]) j=1 j=1 B) 2 2 y(t) = E + F(t-ta) + Sum(Gk sin[(2pi(t-ta)/Qk]) + Sum(Hk cos[(2pi(t-ta)/Qk]) k=1 K=1 C) 4 4 UT1-UTC(t) = I + J(t-tb) + Sum(Km sin[(2pi(t-tb)/Rm]) + Sum(Lm cos[(2pi(t-tb)/Rm]) m=1 m=1 The following is a list of the constants in the equations above: P1 and Q1 = 365.25 days (annual period) P2 and Q2 = 435 days (Chandler period) ----> R1, R2 = formerly set to 500.0 days...prior to EOPP502 <---- R1 = 27.56 days (lunar period) R2 = 13.66 days (semi-lunar period) R3 = 365.25 days (annual period) R4 = 182.625 days (semi-annual period) ----> K1, K2, L1, L2 = formerly set to zero (0)...prior to EOPP502 <---- K1, K2, L1, L2 = computed variables fitted to the two dominant (new) R1 and R2 periods (note above)...values are in seconds K3 = -0.022 seconds K3, K4, L3, and L4 are seasonal K4 = 0.006 seconds variation coefficients found L3 = 0.012 seconds through astronomical observations. L4 = -0.007 seconds (They are assumed to be constant.) B, F = 0 (assumed) pi = 3.14159265... The following is a list of the variables in the equations above: A, E - offset terms (in arcseconds) Cj, Dj, Gk, Hk - polar position coefficients (in arcseconds) I - offset term (in seconds) J - time drift coefficient (in seconds per day) The following is a list of the time variables in the equations above: t - the MJD of the day that predictions are desired (prediction or effectivity dates) ta - the MJD of the first day of data used as input (435 days, Chandler Period, prior to the generation date) tb - the MJD of the day before January 1st of the current year...this is the MJD of December 31st of the previous year...the UT1-UTC equation needs this date along with the seasonal variation coefficients to account for a 'correct phase' of the seasonal effects during the current year. eg. Jan. 1st, 2005 = MJD 53371 Dec. 31st, 2004 = MJD 53370 A) The following is an example of the five record output prior to EOPP502, i.e., EOPP501 (with no changes to K1, K2, L1, L2, R1, and R2): 52951.00 .048890 .000000 -.054723 -.088378 .028945 .109437365.25 435.00 .347596 .000000 -.017649 -.116192 -.046661 -.095657365.25435.00 53370.00 -.510031 -.000276 .000000 .000000 -.022000 .006000 .000000 .000000 .012000 -.007000 500.0000 500.0000 365.2500 182.6250 32 501 53372 53368 B) The following is an example of the five record output starting with EOPP502 (with changes to K1, K2, L1, L2, R1, and R2): 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 The record output format is: RECORD NUMBER COLUMN START FORMAT VALUE 1 1 F10.2 ta 11 F10.6 A 21 F10.6 B 31 F10.6 C1 41 F10.6 C2 51 F10.6 D1 61 F10.6 D2 71 F6.2 P1 77 4X Fill 2 1 F6.2 P2 7 F10.6 E 17 F10.6 F 27 F10.6 G1 37 F10.6 G2 47 F10.6 H1 57 F10.6 H2 67 F6.2 Q1 73 F6.2 Q2 79 2X Fill 3 1 F10.2 tb 11 F10.6 I 21 F10.6 J 31 F10.6 K1 41 F10.6 K2 51 F10.6 K3 (*) 61 F10.6 K4 (*) 71 10X Fill 4 1 F10.6 L1 11 F10.6 L2 21 F10.6 L3 (*) 31 F10.6 L4 (*) 41 F9.4 R1 50 F9.4 R2 59 F9.4 R3 68 F9.4 R4 77 4X Fill 5 1 I4 TAI-UTC 5 I5 Serial Number (EOPP week) 10 I6 t - Effectivity Date 16 1X Fill 17 A18 Generation Date / Info 35 46X Fill (*) - values computed by I. I. Mueller, at Ohio State University, in the 1960's ... note the text by Moritz, H. and I.I. Mueller, Earth Rotation: Theory and Observations, 1987, Ungar, New York. An analysis of NGA's polar parameter predictions show that over the week the coefficients are in effect, xp should have an RMS error of under 0.003 arcseconds (10 cm. at the equator) with the IERS Final Values. The RMS error for yp should be under 0.003 arcseconds (10 cm. at the equator) with the Final Values. The RMS error for UT1-UTC should be found to be below 0.8 milliseconds with the Final Values. It is important to realize that the accuracy of the coefficients degrade with time. Therefore, the person using the NGA coefficients should always use the most recent set available. The coefficients are recomputed every week by Friday at NGA and sent to the users after a quality control check. They are labeled to go into effect on the following Sunday. A FINAL NOTE: In UT1(R), mentioned above, prior to EOPP 502, the effects of zonal tides with periods shorter than 35 days are removed. UT1-UT1(R) (zonal tides) smaller than 0.0025s in absolute value should be restored after the interpolation of UT1R.
Point of Contact: GPS Division
Phone Numbers:
Com. (314)676-9142
DSN 846-9142
