The Earth orientation parameters (EOP) is a set of parameters that describe the direction of rotating axis of the solid Earth in both the terrestrial reference frame (TRF) and the celestial reference frame (CRF) and the rotation angle of the TRF relative to the CRF. Determination and prediction of EOP is of importance for deep space and near Earth missions, including lunar and Mars exploration, satellite navigation, positioning of celestial objects, and geophysical applications (Petit and Luzum 2010).
Variations of the polar motion (PM) and the length of day (△LOD/△UTl) can be attributted to both the external forces (tidal torques from the Sun and Moon) and internal forces that cause mass redistributions and angular momentum exchanges among the solid Earth (crust and mantle), the fluidal atmospheric, oceanic and hydrospheric components, the liquid outer core and solid inner core (Gross 2007). Once the tidal excited variations of EOP are determined and removed, the fluidal correlated features will dominate (~ 90%) in the remaining tidal free EOP series (Dobslaw et al. 2010, Dill et al. 2013).
Dill et al. (2019) demonstrated the effective angular momentum (EAM) functions, derived from numerical geophysical models of the Earth’s fluidal components, are powerful data sets for the predictions of PM and ΔUT1. The EAM components
In the 2nd Earth Orientation Parameters Prediction Comparison Campaign (2nd EOP PCC), we used a method evolved from Dill2019’s method; here we call piecewise parameterization which predict PM and ΔUT1 with specified parameters at different time spans. The motivation of piecewise parameterization is that there may exist better LS and AR parameters for predictions at different time stages. In Section 2, we present the technical details of the method. In Section 3, we evaluate our predictions by comparing them with both the EOP 14 C04 series and Bulletin A predictions. Summary and Conclusions are presented in Section 4.
In Dill2019, the predictions of PM and ΔUT1 are processed in several step, as shown in Figure 1. First, the EOP series is transfered to geodetic angular momentum function (GAM) through Liouville equation. Then, the differences between GAM and EAM, are calculated and extrapolated to the next 6 days with least squares fit and autoregression (LS+AR). Third, the 6 days extrapolation of (GAM-EAM) and 6 days forcast of EAM are summed up to generate a 6-day prediction of GAM. Fourth, a 90-day GAM series is predicted with LS+AR. Finally, the 90-day prediction of PMX/PYM/UT1 is recovered from the 90-day GAM series.
Flowchart for EOP prediction of Dill2019 method
Our prediction methods are evolved from Dill2019 method. In this section, we first present the discrete formulas used for GAM and EOP transformation which are not presented in Dill2019 paper. Then, the technical details of piecewise parameterization in LS and AR are presented. In this paper, we focus on the prediction method of the polar motion.
The linearized Liouville equations that describe the relations between the EOP and GAM are presented in Equations 1 and 2
Given the coupling between
The transformation of GAM and EOP in the
Figure 2 shows the transformed
The transformed X (left panel) and Y (right panel) components of GAM, ESMGFZ EAM, and differences between GAM and EAM
In Figure 3, we present plots of GAM versus EAM to show such phenomenon. The magnitude of GAM and the correlation between GAM and EAM are higher for the
Correlation between GAM and EAM. Left panel: the X component; right panel: the Y component.
As shown in Figure 1, there are two steps of LS+AR. The first LS+AR is used to predict the 6 days GAM-EAM series and the second LS+AR is used to predict the 90 days GAM series. The strategy of LS is same for the two steps, we fit the
Piecewise continusous least squares fit of GAM-EAM (upper panels), and full GAM series (lower panels), with left panels for
Up to now, the techniques we used are all identical to Dill2019. Here we present the major technical differences of our method.
For a stationary random sequence
Practically,
In our prediction, we aussmed there exists a best
The effect of the new
Figure 5 shows exmaples of prediction for polar motions
Mean absolute error (MAE) of prediction of polar motion
Asumming there exists best (
Best autoregressive parameters for prediction of PMX
Future day | ||||
---|---|---|---|---|
1-2 | 60 | 60 | 5 | 15 |
3-6 | 60 | 60 | 1 | 15 |
7-10 | 18 | 18 | 16 | 16 |
11-13, 37-38, 41-42 | 8 | 8 | 2 | 2 |
14 | 5 | 3 | 1 | 1 |
15-20, 24, 28-29 | 2 | 3 | 1 | 1 |
21-23, 25-27, 30 | 4 | 4 | 2 | 2 |
31-34 | 5 | 19 | 1 | 1 |
35-36,39-40 | 6 | 6 | 2 | 2 |
43-57, 65-75 | 8 | 8 | 3 | 3 |
58, 62-64 | 20 | 20 | 18 | 18 |
59-61 | 19 | 19 | 17 | 17 |
75-90 | 10 | 10 | 6 | 6 |
Best autoregressive parameters for prediction of PMY
Future day | ||||
---|---|---|---|---|
1-6 | 19 | 19 | 1 | 1 |
7 | 19 | 19 | 17 | 17 |
8-11 | 20 | 20 | 18 | 18 |
12 | 6 | 6 | 2 | 2 |
13-14,16-67,73-90 | 4 | 4 | 2 | 2 |
15 | 3 | 2 | 1 | 1 |
68-72 | 8 | 8 | 2 | 2 |
In Figure 6, shown are the prediction errors for all the 441 predictions from Sep. 2019 to Feb. 2021. Within 90 days, the maximum prediction error of PMX is 36 mas, the maximum prediction error of PMX is 16 mas; within 10 days, the maximum prediction errors of PMX and PMY are 4.5 and 2 mas. On an average, the prediction of PMY is around 2 times better than that of PMX. In addition, we found that the prediciton errors of PMX are much higher in 2020 than 2019. In 2019 September, the prediction errors of both PMX and PMY are lower than 10 mas, whereas in 2020 August and September, the 30-90 days prediction errors are around 2 or even 3 times higher than that of 2019. We suspect that such phenomenon might be due to the pandemic of coronavirus COVID-19, which result in a decrease in global airline by more than 60%. As the air-borne meteorological radar data are very important for numerical weather model, a decrease of flight number finally results in worse weather and AAM forecast, and then worse EOP prediction. A future study on evaluation of whether and/or how much the AAM data might be influenced by the lack of air-borne meteorological data can be helpful to verify or deny such hypothesis.
Absolute difference between polar motions series of IERS EOP C04 and our predition up to 90 days
To compare with IERS bulletin A prediction, in Figure 7, we show the MAE of both our prediction and IERS bulletin A prediction. Our prediction of PMY is better (~20%) than bulletin A prediction in all timescale. Especially, on the 5th day and 90th day, the MAE is reduced by 49.0% and 28.9%, respectively. For the prediciton of PMX, within 30 days, our predictions are slightly better (2% - 8%) than bulletin A, but become worse (−7%~ −19%) than bulletin A within 30-90 days. In Table 3, we present the prediction errors (MAE) at different future days.
Comparing the MAE of our 90-day prediction with the MAE of IERS bulletin A 90-day prediction
PM prediction errors (MAE) at different future days
1 days | 5 days | 10 days | 20 days | 40 days | 60 days | 90 days | |
---|---|---|---|---|---|---|---|
PMX forecast of this paper (milli arcsec) | 0.30 | 1.04 | 2.74 | 4.57 | 7.62 | 10.58 | 13.78 |
PMX forecast of IERS (milli arcsec) | 0.31 | 1.56 | 2.93 | 4.95 | 7.08 | 9.51 | 11.57 |
PMX forecast error reduction (%) | 2.62 | 32.98 | 6.59 | 7.74 | −7.67 | −11.23 | −19.07 |
PMY forecast of this paper (milli arcsec) | 0.19 | 0.54 | 1.46 | 2.10 | 3.31 | 3.97 | 5.60 |
PMY forecast of IERS (milli arcsec) | 0.24 | 1.07 | 1.76 | 2.62 | 4.42 | 5.28 | 7.89 |
PMY forecast error Reduction (%) | 20.77 | 48.98 | 17.53 | 20.05 | 25.13 | 24.97 | 28.93 |
In the 2nd EOP PCC, we developed Dill2019 method for prediciton of polar motion by adopting different autoagressive parameters at different prediction stages. In steps of AR extrapolation, we introduced a