2679

AAS 13-373

EARTH ORIENTATION PARAMETER AND SPACE WEATHER

DATA FOR FLIGHT OPERATIONS

David A. Vallado* and T. S. Kelso†

Earth Orientation Parameter and Space Weather data are critical data elementsfor numerical propagation and space operations. Since CSSI first began assem-bling consolidated files of EOP and space weather data, we have tracked theperformance of these data to better understand what operational users can ex-pect. We present detailed analysis and results over the last few years to assessthe best sources for this data, and recommend options for processing when nodata exists. Corrections to space weather data are shown where anomalies ex-ist. Finally, we investigate the implications of space weather prediction accu-racy and its effect on satellite lifetime.

INTRODUCTION

The Center for Space Standards and Innovation (CSSI) has provided combined EOP and space weather data files for several years now (Vallado and Kelso, 2005). Recently the EOP data from the International Earth Rotation Society (IERS) began incorporating predictions to their files. Space weather files have long included predictions, and we have reported periodically on those efforts. With the release of new EOP pre-dictions, we felt it worthwhile to reexamine the accuracy of the EOP and space weather predictions.

Introducing the topic, we show the historical values of the parameters for both EOP and space weather. Several comparisons are made between various sources of data. Over time, we have collected several pre-dictions of each data, and we compare the predictions to the actual data, recorded later. Implications of se-lecting one source over another are discussed, along with applications such as satellite lifetime.

EOP SOURCES AND VALUES

Earth Orientation Parameters (EOP) data is a cornerstone for accomplishing the inertial to fixed trans-formation of coordinates. Most numerical integrators integrate in an inertial frame, while the force models are applied in a fixed frame. The EOP information consists of ΔUT1, the difference between UT1 (Univer-sal time) and UTC (Coordinated Universal time), the length of day, polar motion coefficients (xp, yp) de-scribing the movement of the Earth’s rotation axis to the crust, and ΔAT, the number of leap seconds be-tween UTC and TAI (Atomic time). There are typically small differences between sources of EOP data (e.g., International Earth Rotation Service - IERS, National Geospatial Intelligence Agency - NGA, and US Naval Observatory - USNO), but the impact on overall satellite positional accuracy is usually small (a few meters or so). Figure 1 shows the various sources, time spans of data provided, and parameters included.

* Senior Research Astrodynamicist, Center for Space Standards and Innovation, Analytical Graphics Inc., 7150 Campus Dr., Suite 260, Colorado Springs, Colorado, 80920-6522. dvallado@agi.com† Senior Research Astrodynamicist, Center for Space Standards and Innovation, Analytical Graphics Inc., 7150 Campus Dr., Suite 260, Colorado Springs, Colorado, 80920-6522. TSKelso@agi.com

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Figure 1 Earth Orientation Parameter Data Availability. Various sources of EOP data are shown. The primary sources for EOP data are the USNO and IERS. NGA provides coefficients that are fit for a week.

Data sources for EOP are shown below, along with some comments about the particular information that is included. (See http://celestrak.com/SpaceData/EOP-format.asp)

1. NGA ftp://ftp.nga.mil/pub2/gps/eopp/yyyyeopp/EOPPyddd.TXTContains: NGA coefficients for the upcoming week Updated: Daily Each week a file of the form EOPPyddd.TXT is produced where y is the last digit of the year and ddd is the day of the year.

2. IERS a. ftp://hpiers.obspm.fr/eoppc/eop/eopc04/

eopc04.62-now Contains: Observed data (x, y, UT1, LOD, , )eopc04_dPsi dEps.62-now Contains: Observed data (x, y, UT1, LOD, , )eopc04_IAU2000.62-now Contains: Observed data (x, y, UT1, LOD, dX, dY)

Updated: Tuesday/Thursday per their documentation, the official solution Consistent with ITRF 2008. No predictions

b. ftp://hpiers.obspm.fr/iers/series/opa eopc04 Contains: Observed data (x, y, UT1, LOD, , )eopc04_IAU2000 Contains: Observed data (x, y, UT1, LOD, dX, dY)eopc04R Contains: Observed data (x, y, UT1R, LODR, , )eopc04R_IAU2000 Contains: Observed data (x, y, UT1R, LODR, dX, dY)

Updated: Tuesday/Thursday per their documentation, the official solution C04 solution +180 days prediction The “R” denotes use of UT1R/LODR (Yoder et al., 1981; McCarthy, 1996). UT1R is a corrected UT1 for tidal variations. It’s a little smoother than UT1. There are also files with a “daily” extension that do not have predictions. We note that EOPc04.62-now and EOPc04 (and also EOPc04_IAU2000.62-now and EOPc04_IAU2000_daily) should be the same, but they actually differ by a small amount after July 22, 2010. ftp://hpiers.obspm.fr/iers/series/prediction/

eopc04_extended.dat C04 solution +180 days prediction

3. USNO http://maia.usno.navy.mil/ser7/

Current Time, t

00:00Sunday

23:59Saturday

IERS EOPc04, EOPc04R

(ΔUT1, xp, yp,, LOD, δΔΨ1980, δΔε 1980, dX, dY)

NGA Current week

EOPPyddd.txt (ΔUT1, xp, yp)

USNOfinals.daily, finals2000a.daily

(ΔUT1, xp, yp,, δΔΨ 1980, δΔε 1980, dX, dY)+ 90 days

USNOfinals.all, finals2000a.all

(ΔUT1, xp, yp)+ 1 year

1962

-3 months

1973

FUTUREPAST

+ 180 days

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finals.daily Contains: Observed data (x, y, UT1, LOD, , )finals2000A.daily Contains: Observed data (x, y, UT1, LOD, dX, dY)

Contains: Predicted data (to +90 days) from Bulletin A Updated: Daily

finals.all Contains: Observed data (x, y, UT1, LOD, , )finals2000A.all Contains: Observed data (x, y, UT1, LOD, dX, dY)

Contains: Predicted Data (to +1 year) from Bulletin A Updated: Weekly The files finals.data and finals2000A.data contain the same information but they start on January 1, 1992 instead of January 1, 1973.

tai-utc.dat Contains: TAI-UTC data Updated: With new leap seconds There is a mirror backup site available at: http://toshi.nofs.navy.mil andftp://toshi.nofs.navy.mil

It’s instructive to examine the past behavior of the EOP parameters to better understand the compari-sons and differences shown later on. The main parameters (x, y, UT1) are shown for the last 50 years to establish a nominal understanding of their variations over time.

Figure 2 EOP Historical Parameters xp, yp, ΔUT1. Polar motion and UT1 deltas are shown for many years along with linear approximations. Units on the vertical axis are in arcsec and secs.

Notice how the linear approximations capture the general behavior of the parameters over long periods (years) of time. Using the complete interval from 1962-2012 results in the linear trends shown in Eq 1. Note that t = MJD date.

DUT1 = –1 × 10-5 t + 0.3139 xp = 5.0 × 10-5 t – 0.1183 (1)

yp = 5.0 × 10-5 t – 0.177

Be aware that the trend lines are useful only for long range predictions as they do not capture the short periodic variations in the terms. It may be possible to form a polynomial that could approximate the dy-

xp = 5E-06t - 0.1183

yp = 1E-05t - 0.0177

DUT1 = -1E-05t + 0.3139-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

Mar-60 Dec-73 Aug-87 Apr-01 Dec-14 Sep-28

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namic behavior (long and short periods) but the cycles are not precisely symmetric and the polynomial could easily become out of phase with the actual data.

The remaining EOP parameters consists of corrections generally applied during the transformation pro-cess, and using data calculated from observed differences to the theories in use.

Figure 3 Historical FK5 Nutation Corrections Dw, De. Corrections to the equinox approach are shown since 1962. Units are arcseconds.

Using the complete 50 year interval, we find the following trend lines for the FK5 nutation corrections. Dw = –8 × 10-6 t + 0.2506 (2)

De = –7 × 10-7 t + 0.022

Figure 4 Historical IAU 2000 Nutation Corrections dX, dY. Corrections to the CIO approach are shown since 1962. Units are arcseconds. Values are not relevant until after about 1984. Also note the relatively stable nature of the corrections compared to the equinox corrections in Fig 3.

These values are small enough, and close enough to zero that trend lines are not necessary.

Dw = -8E-06t + 0.2506

De = -7E-07t + 0.022

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

Mar-60 Dec-73 Aug-87 Apr-01 Dec-14

-0.0030

-0.0020

-0.0010

0.0000

0.0010

0.0020

0.0030

0.0040

Mar-60 Dec-73 Aug-87 Apr-01 Dec-14

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Table 1: Linear EOP Prediction Tests: Several tests were run to determine what mean values of EOP pa-rameters would exist in the future. All values use the trends derived from the complete existing data.

In perspective, we see actual daily variations of about 0.05” and 0.02 s in about half a year, yet in 120 years, the averages move substantially less, which makes sense.

SPACE WEATHER SOURCES AND VALUES

Space weather data is the primary input, other than satellite characteristics, for atmospheric drag mod-els. Even the smallest changes in space weather data can have large effects during propagation. Space weather data are available through the National Geophysical Data Center (NGDC) in the National Oceanic and Atmospheric Administration (NOAA), but there are several files necessary to piece together a complete data file. We can show a schematic for what data are available for propagation activities. Because 3-hourly data are available for the geomagnetic indices, a truly current file requires frequent retrieval and organiza-tion of the data. Figure 5 shows the available data and their time of applicability.

Figure 5 Space Weather Parameter Data Availability. Sources for space weather parameters are shown.

Space weather data is accumulated form a variety of sources. The following list shows the sources, pa-rameters, and frequency. (See http://www.celestrak.com/SpaceData/SpaceWx-format.asp)

1. Files:ftp://ftp.ngdc.noaa.gov/STP/GEOMAGNETIC_DATA/INDICES/KP_AP/yyyy.vm

Contains: BSRN, ND, 3-hourly Kp, 3-hourly Ap, Cp, C9, ISN, F10.7Adj, QUpdated: Monthly (a little over one month after end of the month) Each month a yyyy.vm file is produced, where yyyy is the year and m is the month. When

Current 9/19/2012 1 year 9/19/2013 5 year 9/19/2017 10 year 9/19/2022 120 year 9/19/2013MJD Date values MJD Date values MJD Date values MJD Date values MJD Date values

x p 41171 0.08756 41536 0.08938 42997 0.09669 44823 0.10582 85000 0.30670y p 41171 0.39401 41536 0.39766 42997 0.41227 44823 0.43053 85000 0.83230

DUT1 41171 -0.09781 41536 -0.10146 42997 -0.11607 44823 -0.13433 85000 -0.53610Ddw 41171 -0.07877 41536 -0.08169 42997 -0.09338 44823 -0.10798 85000 -0.42940Dde 41171 -0.00682 41536 -0.00708 42997 -0.00810 44823 -0.00938 85000 -0.03750

Average EOP values

Current Time, t

00:00-1 month

14:28

00:001 month

Quar_dgd.txt (3 hrly kp, daily ap)Quar_dsd.txt (daily F10.7)

Predict.txt(monthly F10.7) + 6 year

+ 45 days45df.txt

(daily F10.7, ap)

yyyy.vm (daily F10.7, daily and 3 hrly kp, ap)

Current Year

- 3 months

- 6 months

00:00

FUTUREPAST

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the year is complete, file becomes simply yyyy. The data is up to 30 days behind the cur-rent time and the F10.7 value is considered as Lenhart data.

2. Files:ftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA/SOLAR_RADIO/FLUX/Penticton_Obs

erved/daily/DAILYPLT.OBSContains: F10.7Obs from 1947 Jan 01 until end of previous month Updated: Monthly (end of month) The “.OBS” file F10.7 values are considered as DRAO data. There is also an “.ADJ” file that contains the adjusted F10.7 DRAO data.

3. Files:http://www.swpc.noaa.gov/ftpdir/indices/quar_DGD.txt

Contains: 3-hourly Kp for the current quarter to date (previous quarters also available) Updated: Every 3 hours The F10.7 values are considered as DRAO data.

4. Files:http://www.swpc.noaa.gov/ftpdir/indices/quar_DSD.txt

Contains: Daily F10.7Adj, ISN for the current quarter to date (previous quarters also availa-ble) Updated: Daily The F10.7 values are considered as DRAO data.

5. Files:http://www.swpc.noaa.gov/ftpdir/latest/45DF.txt

Contains: 45-day forecast of daily Ap and F10.7AdjUpdated: Daily

6. Files:http://www.swpc.noaa.gov/ftpdir/weekly/Predict.txt

Contains: Monthly ISN and F10.7Adj for approximately two years Updated: Monthly

Unlike the EOP parameters, the space weather parameters are much more chaotic in nature. There are long period trends associated with the solar cycle, but the individual variations are significantly more pro-nounced.

Figure 6 Space Weather Parameters. Variations in the space weather parameters are shown. The geomagnetic indices (ap) and solar flux (F10.7 and averages) show the solar cycles over time.

0.0

50.0

100.0

150.0

200.0

250.0

300.0

Jan-50 Jan-54 Jan-58 Jan-62 Jan-66 Jan-70 Jan-74 Jan-78 Jan-82 Jan-86 Jan-90 Jan-94 Jan-98 Jan-02 Jan-06 Jan-10

Solar Cycle 23Solar Cycle 22Solar Cycle 21Solar Cycle 20Solar Cycle 19

F10.7

center F10.7

avg ap

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We note that periodically solar flux values are not recorded. There are several Flux Qualifiers given.

FLUX QUALIFIER. "0" indicates flux required no adjustment; "1" indicates flux required adjustment for burst in progress at time of measurement; "2" indicates a flux approximated by either interpolation or extrapolation; and "3" indicates no observation. (ftp://ftp.ngdc.noaa.gov/STP/GEOMAGNETIC_DATA/INDICES/KP_AP/kp_ap.fmt)

However, we found that there are blank values and 0.0 values that appear occasionally for both “2” and “3” qualifiers (e.g. 2 – May 28, 1966 (0.00) and Aug 23, 2008 (109.3), and 3 – Jan 1, 2011 (blank) and Dec 25, 1957 (0.00)). Because there is solar output in each case, we have corrected all cases where zero and blank entries are listed with a simple interpolation from the surrounding dates, and placed a “4” qualifier code to indicate the change.

CONSOLIDATED FILES

CelesTrak files offer a consolidated real-time listing of the EOP and Space Weather data parameters. These files are space-delimited, continuously updated as new data is produced, and integrated with STK and ODTK. The space weather data is updated on CelesTrak every three hours at 35 minutes past the hour (e.g., 0035 UTC, 0335 UTC) because the 3-hourly data seem to come out at 30 minutes past the hour. The formats are given at the top of each file. Because the files are simple ASCII data, they may also be used with other applications. The files are located at

http://www.celestrak.com/SpaceData/

EOP COMPARISONS OF DATA SOURCES

Several comparisons are possible for the EOP parameters because they are supplied by two separate lo-cations. (we examined the basic parameters, and the corrections , , dX, dY)

• IERS – USNO (Bulletin A) eopc04.62-now with eopc04 • eopc04opa with actual (show IERS prediction accuracy) • finals.all with actual (shows USNO prediction accuracy) • IERS – USNO predictions eopc04 with finals.all (compare the prediction accuracy between two

approaches)

Start by comparing the parameters from IERS and the USNO.

-0.0020

-0.0015

-0.0010

-0.0005

0.0000

0.0005

0.0010

0.0015

0.0020

Jan-73 Jan-77 Jan-81 Jan-85 Jan-89 Jan-93 Jan-97 Jan-01 Jan-05 Jan-09 Jan-13

D xp "

D yp "

D Dut1 s

D lod s

Figure 7 IERS – USNO Comparison. Polar motion and ΔUT1 deltas are shown for many years. By the late 1990’s, procedures had improved and the two organization results became much closer. Notice that there are still occasional large data differences.

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Figure 8 FK5 Nutation Corrections Comparison IERS-USNO. The nutation correction parameters ( ,) between organizations are quite similar. Comparisons are shown for both Bulletin A and B.

Figure 9 IAU2000 Parameter Comparison. The CIO correction parameters (dX, dY) are about the same order of magnitude as the nutation parameters ( , ). Comparisons are shown for both Bulletin A and B.

There is a latency between the USNO Bulletin A and B with the latter being the final product. We plot a comparison of the two valued over time.

-0.010

-0.005

0.000

0.005

0.010

0.015

0.020

Jan-73 Jan-77 Jan-81 Jan-85 Jan-89 Jan-93 Jan-97 Jan-01 Jan-05 Jan-09 Jan-13

B D dpsi "

B D deps "

A D dpsi "

A D deps "

-0.004

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

Jan-92 Jan-96 Jan-00 Jan-04 Jan-08 Jan-12

B D dX "

B D dY "

A D dX "

A D dY "

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Figure 10 USNO Bulletin A and B Comparison. Within the USNO values, the preliminary (Bulletin A) and Bulletin B (final) values differ slightly. Bulletin B values are the final values and lag behind the Bulletin A values.

The differences between Bulletins A and B, and the IERS values are all within the same order of magni-tude, and are all very small. Their contribution to noticeable positional errors in satellite obits is minimal (at about 0.0005”, the positional difference on a GEO orbit is about 0.120 m).

EOP PREDICTION ACCURACY

The new prediction values for EOP began in early 2012. This let us collect the predicted portion of EOP files, and compare to actual data at later times. We plot both the IERS and USNO predictions on the same scale next to each other for easier comparisons. Note that the IERS predictions are for 180 days and the USNO predictions are for 365 days. Each center may use similar prediction techniques because the predict-ed values all exhibit smooth periodic behavior once the actual data for comparison is past.

-0.0020

-0.0015

-0.0010

-0.0005

0.0000

0.0005

0.0010

0.0015

0.0020

Jan-92 Jan-96 Jan-00 Jan-04 Jan-08 Jan-12

D dX "

D dY "

-0.050

-0.025

0.000

0.025

0.050

-100 0 100 200 300 400

D xp "

D yp "

D Dut1 s

ActualsPredicted

-0.050

-0.025

0.000

0.025

0.050

-100 0 100 200 300 400

D xp "

D yp "

D Dut1 s

Actuals Predicted

2688

Figure 11 IERS (left) and USNO (right) Prediction Comparison. The top two graphs show predictions for about a 2.5 month period, and the bottom two depict a 5.5 month period.

Figure 12 IERS (left) and USNO (right) Prediction Comparison. The two graphs show predictions for about a 10.5 month period.

Examining additional cases results in the following figure.

-0.050

-0.025

0.000

0.025

0.050

-100 0 100 200 300 400

D xp "

D yp "

D Dut1 s

ActualsPredicted

-0.050

-0.025

0.000

0.025

0.050

-100 0 100 200 300 400

D xp "

D yp "

D Dut1 s

Actuals Predicted

-0.050

-0.025

0.000

0.025

0.050

-100 0 100 200 300 400

D xp "

D yp "

D Dut1 s

ActualsPredicted

-0.050

-0.025

0.000

0.025

0.050

-100 0 100 200 300 400

D xp "

D yp "

D Dut1 s

Actuals Predicted

-0.050

-0.025

0.000

0.025

0.050

-100 0 100 200 300 400

D xp "

D yp "

D Dut1 s

ActualsPredicted

-0.050

-0.025

0.000

0.025

0.050

-100 0 100 200 300 400

D xp "

D yp "

D Dut1 s

Actuals Predicted

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Figure 13 IERS (left) and USNO (right) Prediction Comparison. The two graphs show predictions for about a 9, 8, and 6 month periods, from the top.

Examining the correction parameters, we obtain Fig. 14. A challenge here is that the predictions, even for Bulletin A values, start well before the current time. Thus, there are variations before the “zero” line in Fig. 14.

Figure 14 EOPC04 (left) and USNO (right) Prediction Comparison. Comparisons of subsequent EOP C04 opa predictions, with some data being actuals. The largest difference appear in the dX, dY correction terms. The remainder are somewhat constant, and small. Notice that the scale here is smaller than previous graphs to show the smaller numbers, but consistent between plots here.

-0.050

-0.025

0.000

0.025

0.050

-100 0 100 200 300 400

D xp "

D yp "

D Dut1 s

ActualsPredicted

-0.050

-0.025

0.000

0.025

0.050

-100 0 100 200 300 400

D xp "

D yp "

D Dut1 s

Actuals Predicted

-0.050

-0.025

0.000

0.025

0.050

-100 0 100 200 300 400

D xp "

D yp "

D Dut1 s

ActualsPredicted

-0.050

-0.025

0.000

0.025

0.050

-100 0 100 200 300 400

D xp "

D yp "

D Dut1 s

Actuals Predicted

-0.0015

-0.0010

-0.0005

0.0000

0.0005

0.0010

0.0015

-50 0 50 100 150 200

D lod s

D dpsi "

D deps "

D dX "

D dY "

ActualsPredicted

-0.0015

-0.0010

-0.0005

0.0000

0.0005

0.0010

0.0015

-50 0 50 100

D lod s

D dpsi " A

D deps " A

D dX " A

D dY " A

Actuals Predicted

2690

There are small variations and trends apparent, but they are so small and close enough to zero that cate-gorizing them would provide little gain.

Some observations on the EOP comparisons and predictions.

• There are sometimes differences in the historical values. These are primarily a result of period-ic re-evaluations of the parameters.

• The actual data does not always extend to the current date. In particular, , and dX, dYand LOD do not extend until the current time because there is a greater time lag to measure and calculate these parameters.

• USNO prediction and actual comparisons are complicated because the parameters end at dif-ferent times. Predicted values start about 1 to 2 weeks before the current date. Bulletin A and bulletin B values start before this time, and and stop at different times as well.

• The longer prediction period from the USNO data without the need to worry about a disconti-nuity near the current time makes this our recommendation.

What should we do for very long time period predictions? Some programs keep the last value as a con-stant. Others switch to 0.0 for all values. Others use various forms of linear fits. It seems prudent to have “some” value, rather than zero, for long (for say up to 100 years or so) propagations. Given the behavior over the last 50 years, going twice that amount isn’t unreasonable given the parameter behavior, so we pro-pose to use the linear relationships for this period (Eq 1). Longer intervals are possible, and re-evaluation at some point is wise, but probably not more often than every 10-20 years. Table 1 showed that with some parameters the UT1 variable might exceed ±1 which suggests that the leap second issue should be consid-ered. Proposals have existed to eliminate the leap second (Finkleman, Seidelman, and Seago, 2010). In the absence of any resolution, we assume the existing leap second paradigm will continue into the future.

The EOP parameters affect transformations more, with UT1 being the most important contributor. The prediction of IERS and USNO seem relatively close, with perhaps a slight edge to the UT1 predictions of IERS. While the differences are quite small, it might be prudent to adopt the IERS predictions However, another problem arises because the IERS prediction “seems” to be a little better than the USNO predictions, but is only half as long. Thus for users wishing to have dynamic predictions for a year, if the IERS predic-tions are spliced with the USNO values, a potential discontinuity may exist. Because the predicted values are relatively close, we recommend using the USNO predicted values, and then the linear interpolation for long time spans into the future.

The corrections ( , / dX, dY /lod) are very small and prediction becomes less important due to their tiny effect on transformations. In addition, for long term propagations, arcsecond accuracy is simply not necessary.

SPACE WEATHER COMPARISONS OF DATA SOURCES

Observed vs adjusted solar flux values are required for some programs. The overall shape should show the solar cycle variations. There are still large spikes in the data, indicating incorrect, multiple, or missed scaling of the values being reported, although the frequency has declined in previous years. We note that there are additional Internet sources where the observed and adjusted may be found.

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Figure 15 Observed and Adjusted Solar Flux Comparison. The cyclical nature shows the solar cycle effect. Spikes occur when corrections or values are incorrect. Note that the plot contains corrected (interpolated) solar flux entries where nothing was reported.

We examined these discrepancies and have resolved the differences for each point. The approach was to determine the differences between each of the 3 values (Lenhart adjusted, DRAO adjusted, and DRAO observed). The errors appear to be random between all 3 base values, but we were able to establish a meth-odology to correct the inconsistencies by looking at the differences. Two corrections are necessary:

1. If the abs(DRAO Adj – Lenhart Adj flux) is greater than 0.001, the Lenhart adjusted flux was cor-rected by adding the DRAO-Lenhart adjusted difference.

2. If the abs(DRAO Adj – DRAO obs/corr) > 0.5, then set the DRAO obs to DRAO adj + DRAO obs – DRAO obs/corr.

The corrected differences look as follows.

Figure 16 Fixed Observed and Adjusted Solar Flux Comparison. The cyclical nature shows the solar cycle effect. With the corrections added, there should be no extraneous spikes. The observed minus adjusted differences are now the same.

-40.0

-30.0

-20.0

-10.0

0.0

10.0

20.0

30.0

40.0

Jan-50 Jan-54 Jan-58 Jan-62 Jan-66 Jan-70 Jan-74 Jan-78 Jan-82 Jan-86 Jan-90 Jan-94 Jan-98 Jan-02 Jan-06 Jan-10 Jan-14

DRAO (obs) -Lenhart (adj)

data

DRAO (obs) -DRAO (adj)

data

DRAO (adj) -Lenhart (adj)

data

-20.0

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

Jan-50 Jan-54 Jan-58 Jan-62 Jan-66 Jan-70 Jan-74 Jan-78 Jan-82 Jan-86 Jan-90 Jan-94 Jan-98 Jan-02 Jan-06 Jan-10 Jan-14

DRAO (obs) -Lenhart (adj)

data

DRAO (obs) -DRAO (adj)

data

DRAO (adj) -Lenhart (adj)

data

2692

SPACE WEATHER PREDICTION ACCURACY

Space Weather is an extremely important component of atmospheric drag calculations, and thus of sat-ellite Orbit Determination and propagation accuracy. Thus, we examined the long and short range predic-tions, as well as inconsistencies we noted in space weather data products. The consolidated Celestrak files have been updated to implement these findings and should represent a consistent set of information both for past and future operations. We note that we look exclusively at F10.7 and geomagnetic indices and the re-sults are not terribly good. However, recognize there is considerable ongoing research into new indices, models (physics based for instance like GITM), and the future looks bright for significant improvements.

We begin by looking at the geomagnetic and solar flux predictions (3, 27, and 45 day). Because OD and propagations require an averaged 81-day F10.7 parameter, the 27 and 45 day predictions are preferred.

Figure 17 27 and 45 day Prediction Values. Notice the large swings in the predicted and actual indices. Solar storms can cause differences of more than ±40 SFU on any day.

A review of the 45-day forecasts of F10.7 and ap, which comes out daily, allowed us to evaluate the pre-diction accuracy. For both F10.7 and ap, we took the 45 day forecasts for each data type and compared to the actual data on those days. Figure 18 is for F10.7 and it shows the accuracy for each date’s 45 forecasts over the span of our archives (2007-present). As expected, the forecasts are generally good around solar mini-mum but show a lot of variability around solar maximum. Still, almost all of the data is within ±20-40 SFU.

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Figure 18 Accuracy of 45 day F10.7 Prediction Values. Predicted values are compared to actual values on each day. Notice that the predictions are better during solar minima around 2009.

Figure 19 shows the accuracy of the predictions plotted against the prediction interval as a contour plot. Most of the data predicts well, with the majority of the predictions within a couple of percent of the ob-served results. But there can be large outliers even for short prediction intervals. As expected, as the fore-cast interval increases the variance increases, as well, and the contours flatten out.

Figure 19 Accuracy of 45 day F10.7 Prediction Values. The percent accuracy of the predicted values are shown from the epoch time. Errors in the predicted values are less than about 1 SFU only about 5-10% of the time.

For the ap forecasts, Fig. 20 shows the spread of the 45 forecasts for each date over the period 2007-present. Here the results are presented as the difference between the average for that date and the forecast, measured in gammas. Somewhat surprisingly, there is not as much variability over time, but there is a clear bias (forecast values are greater than the actual observations).

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Figure 20 45 day ap Prediction Values. The accuracy of the predicted values are shown on each date. Errors in the predicted values are generally less than about 20 gammas. There is a slight negative bias.

The contour plot for the ap forecasts shows little variability in the quality of the forecasts with predic-tion interval and clearly shows the bias between predicted and observed values

Figure 21 45 day ap Prediction Values. The percent accuracy of the predicted values are shown from the epoch time. Errors in the predicted values are less than about 1 gamma only about 5-10% of the time. Also notice the slight negative bias of about 2 gammas in all the predicted values.

On a larger (time) scale, the solar cycle dominates the behavior of indices used for atmospheric drag computations. Estimating the occurrence of these cycles is extremely difficult. As such, several approaches exist. We focus on the Schatten predictions due to their general variability, and long use. The Schatten pre-dictions are widely regarded as a common prediction data base for many applications. Predictions come out 3-4 times per year. The behavior is shown below.

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Figure 22 Predicted Schatten solar cycles. A couple predictions are shown, about 10 years apart. Notice the magnitude and timing mis-matches. While various Schatten predictions exist to cover magnitude and timing, their accuracy seems to be limited to less than 1 solar cycle.

Notice the mis-match in timing – there are early, mid, and late estimates in addition to the low mid high estimates. An additional note is that predictions out about 10 years (or just 1 solar cycle), appear to be sig-nificantly off, both in time and magnitude. While the multiple options would generally seem to cover the discrepancies in Fig. 6, the overwhelming difficulty is which one to pick?

The NOAA predicted solar flux extends through the current solar cycle, and can be a few years in length. Figure 23 shows several examples. Notice that the prediction matches the current actual data, and does reasonably well for the remainder of the next cycle.

Figure 23 NOAA Predicted Solar Flux. A couple predictions are shown for the NOAA predictions. Notice the match at the start, but only the remainder of the current cycle being estimated.

Another interesting approach is given by Oltrogge and Chao (2007). Their method for extrapolating and interpolating atmospheric density is based on adjusting or modifying actual density values, not the proxies. The rationale is that the dependence of density on the proxies is nonlinear; hence averaging or interpolating proxies does not yield correct average or interpolated density. They were examining the effect of solar flux prediction estimates on satellite lifetimes and noted that most orbital lifetime prediction errors were caused by (1) the poor performance of current mean solar activity predictions as compared to actual activity varia-tions; (2) non-availability of predictions more than one solar cycle away; and (3) nonlinear density as a

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function of solar and geomagnetic activity. To circumvent these obstacles, they used the complete set of solar and geomagnetic data available (from February 1947). Thus, five solar cycles were used and com-bined into a single cycle of 10.82546 years (3954 days). Rather than attempting to produce a single mean solar cycle, they chose to directly use the solar flux and geomagnetic values from the previous cycles. Es-sentially, the technique creates a day of solar and geomagnetic data (a combined triad of values including the 81-day average) from one of the five cycles at random, and does so for each day of the simulation. Thus, the existing data is used to construct a future solar cycle, while retaining all the variability and inter-relations of the existing data. This technique is certainly worthy of additional analysis and use as it avoids the vagaries of other prediction techniques that often vary widely for estimates just a few years apart.

The European Space Agency has an approach which has been used since 1992 called PDFLAP (Predic-tion of Flux and Ap) (Thompson, 2001). The approach uses a variety of auto-regression techniques to fore-cast the space weather indices. The coefficients are calculated each day using 60-day data spans for F10.7and 30 day spans for ap (both derived experimentally). They are derived from 24 and 6 month intervals, respectively. Complete testing over a solar cycle has been completed, and alternate indices (e.g. E10.7) are considered. Additional, actual satellite data is used in the development of the results. Accuracy is claimed at or above 5% from existing index variations.

IMPLICATIONS

EOP files are routinely used, and sources like CelesTrak consolidate current values. However, not all systems use current EOP files, and the predicted values change continuously, although they are reasonably consistent. Bradley et al. (2011) discusses the need to interpolate EOP values in the same way atmospheric drag indices are interpolated (Vallado and Finkleman, 2008).

To assess the impact of time, consider an 800 km (LEO) and a 35780 km (GEO) altitude circular satel-lite. Several sensitivity tests were run to determine the effect of various methods employed, or envisioned in operational systems. In each case, the vectors were transformed from Earth fixed (ITRF) to Earth Inertial (GCRF) coordinates, permitting a positional difference determination at the end state.

The first set of options center mainly around the EOP values and how they are used. Much discussion has occurred with leap seconds (Finkleman, Seago and Seidelmann, 2010) it is possible that some systems may not use leap seconds, or may not update them. This would lead to errors of 1 or 2 seconds in TAI. Be-cause this is used only as an argument in the transformation, the difference is quite small. If the TT is off by a minute, perhaps because of assumptions or EOP values simply not being used, it is again used as an ar-gument in the transformation.

We know that the EOP files change periodically and are updated daily to include recent observational data. If old EOP files are used, the ΔUT1 value could differ by 0.01 sec. here we see additional effects be-cause the UT1 time is affected, along with GMST. If ΔUT1 is not used, the differences become larger in each transformation. If the UTC is off by a second, a clock could be off, or a script error could be present. Since UTC affects all the parameters and arguments, the differences are very large.

Finally, it’s conceivable that the time tags could be off by a second. This is very different from the pre-vious leap second and EOP errors because the argument is no longer an input into the transformation, but rather a simple offset. The results are significantly larger. Notice that for the case of a 1 sec error affecting the transformation, a vector closer to the earth will move less than a GEO satellite. For the case of a time tag error of 1 sec, the satellites will be off by the orbital velocity over that time interval.

Table 2: EOP Sensitivity Tests: Several tests were run to examine potential errors and the effect on satellite positions from various EOP discrepancies. The time tag error is not a transformation error and is therefore larger than the UTC time argument error of 1 second.

Test Possible Cause LEO GEO Notes TT is off by a min Not using TT 0.000 m 0.000 m TT is an argument ΔAT error of 1 sec Old EOP file 0.000 02 m 0.000 10 m Only TAI affected Correction sources off by 0.0001”

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ΔUT1 value differs by 0.01 sec

Truncation, old EOP 6.0 m 31.0 m

Ignoring ΔUT1, assume -0.25 sec ΔUT1

Not using EOP 145.0 m 800.0 m

UTC error of 1 sec Clock off 581.0 m 3075.0 m UTC is an argument Time tag is incorrect by 1 sec

Script error 7500.0 m 3075.0 m Bookkeeping error, (velocity × time)

For space weather, we created a Low Earth satellite using standard force models, including atmospheric drag. The baseline configuration was propagated for 4 days. Tests were conducted in which flux and geo-magnetic index errors were artificially inserted into the space weather tables. Notice that the results are not necessarily linear as the introduced error is changed.

Table 3: Space Weather Sensitivity Tests: Tests were run to examine potential errors and the effect on sat-ellite positions from various space weather discrepancies. In each case, a single days data (geomagnetic or flux) was changed by about 20 or 40. The differences in propagation are shown at the end of the day, and af-ter one additional day of propagation.

Satellite Lifetime discussion

Satellite lifetime is an important planning activity for many satellite owner operators. Satellites in all orbital regimes are affected. Notably, GEO satellites have 100 year disposal orbits to achieve while rela-tively low, LEO satellites generally have “splash” requirements. For satellites a little higher, satellite life-time is an important consideration for planners examining conjunctions. Several cases have demonstrated that satellite lifetime can actually result in years of difference in predictions. While these differences seem large, consider the effect of atmospheric drag over many years. From Fig. 19, if the July 2004 prediction is used and a satellite designed expecting a large solar max, and experiencing only 25% the maximum, the satellite lifetime will be considerably longer using the real data, than if drag were more pronounced during the interval the satellite was operational. Another factor with satellite lifetime is the actual program used for calculation. Using the same predicted solar flux with different models can produce vastly different results as well. The bottom line is that several techniques and approaches should be evaluated, weighed and con-sidered when assigning a range of satellite lifetimes to a particular mission.

RECOMMENDATIONS

• Use IERS for EOP actuals• Use USNO EOP predictions to 1 year • Use linear extrapolation for long term EOP values to 50 years, Eq 1. (small discontinuity) • Use NOAA products to dynamically assemble the latest actual space weather data • Use predicted values (45DF and Predict) for predictions to end of current solar cycle • Assess various approaches for long term lifetime studies – Schatten, sampling, etc.

CONCLUSIONS

We have examined the EOP and space weather parameters, sources, and predictions. Consolidated files have been available for several years now at CelesTrak. Our focus was to understand the prediction accura-cies, and to recommend approaches to combine the EOP and space weather parameters form a variety of courses. We found that for EOP, the IERS represents the best choice for obtaining values, but that the IERS prediction values are slightly better, but the USNO values are longer. For space weather, we noted several anomalies in the data (missing points, etc), that we correct in the formation of CelesTrak files. We also

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investigated various prediction approaches. The Schatten predictions are quite popular, and extend the NOAA NGDC predictions past 1 year into the future, but with significant uncertainty.

REFERENCES Bradley, Ben K., David A. Vallado, Aurore Sibois, and Penina Axelrad. 2011. Earth Orientation Parameter Considera-

tions for Precise Spacecraft Operations. Paper AAS 11-529 presented at the AAS/AIAA Astrodynamics Specialist Conference. July 31-August 4, Girdwood, AK.

Finkelman, David, K. Seidelmann, and J. Seago. 2010. The Debate over UTC and Leap Seconds. Paper AIAA 2010-8391 presented at the AAS/AIAA Astrodynamics Specialist Conference. August 2 - 5, Toronto, Ontario, Canada.

McCarthy, Dennis. 1996. IERS Technical Note #21. U.S. Naval Observatory. Oltrogge, Daniel L. and Chia-Chun Chao. 2007. Standardized Approaches for Estimating Orbit Lifetime after End-of-

Life. Paper AAS 07-261 presented at the AAS/AIAA Astrodynamics Specialist Conference. Mackinac Island, MI. Thompson, Alan W. P., et al. 2001. Improved Predictions of Solar and Geomagnetic Activity with Application to

ESA/LEO Satellite Operations. Paper presented at the Space Weather Workshop 17-19 December 2001. ESTEC, Noordwijk, The Netherlands.

Vallado, David A., and David Finkleman. 2008. A Critical Assessment of Satellite Drag and Atmospheric Density Modeling. Paper AGI-UTH-Vallado presented at the AGI Users Conference, October 7-9. Chicago, IL. (updated from AIAA 2008-6442).

Vallado, David A., and T. S. Kelso. 2005. Using EOP and Solar Weather Data for Real-time Operations. Paper USR 05-S7.3 presented at the US/Russian Space Surveillance Workshop, August 22-26. St Petersburg, Russia.

Yoder, C. F., J. G. Williams, and M. E. Parke. 1981. Tidal Variations of Earth Rotation. Journal of Geophysical Re-search. 86: 881-891.