Abstract

The International Earth Rotation and Reference Systems Service (IERS) has established a Working Group on Prediction to investigate what IERS prediction products are useful to the user community in addition to making a detailed examination of the fundamental properties of the different input data sets and algorithms. The major goals and objectives of the WG are to determine the desired Earth orientation prediction products, the importance of the observational accuracy, which types of input data create an optimal prediction, the strengths and weaknesses of the various prediction algorithms, and the interactions between input series and algorithms that are beneficial or harmful. The plans and activities of the working group are summarized.

Introduction

Earth orientation parameters (EOP), which provide the time-varying alignment of the Earth’s terrestrial reference frame with respect to the celestial reference frame, are critical to modern navigation and space applications. EOP predictions are a necessity for real-time space applications such as GPS. The Working Group was established to determine what can be done to improve the IERS prediction of Earth orientation. There are two areas of investigation: the input data (geodetic and geophysical information) and the algorithms used to process the data.

Goals and Objectives

1) Determine the desired EOP products – What is needed by the user community?2) Determine the importance of the input data – What new data sets are available? Are data sets interchangeable? Are some inherently better?3) Determine which types of input data create an optimal prediction – What is the noise of the series? What smoothing is best? What geophysical phenomena are being measured?4) Determine the strengths and weaknesses of the prediction algorithms – Which algorithms perform best under what circumstances? How can problems be mitigated?5) Determine the interactions between series and algorithms that are beneficial or harmful – What qualities of certain data sets make them well suited or poorly suited for certain algorithms?

EOP User Survey

1) Are the current IERS EOP prediction products, which were implemented more than 15 years ago, meeting the needs of the EOP user community2) Given the multitude of modern high accuracy applications, what characteristics of EOP predictions (type, accuracy, data spacing, data span, form, etc.) are required3) To understand the needs of current and potential users of EOP predictions and focus its effort, the Working Group has developed a short user survey.4) The IERS Rapid Service/Prediction Center has implemented this user survey on its web site at the following URL: http://maia.usno.navy.mil/Prediction_Survey.html5) The link to the survey is being distributed by the IERS Central Bureau and the IERS Rapid Service/ Prediction Center with the request that it be completed by January 15, 2007

Prediction Algorithms

The EOP time series data generally consist of both deterministic and stochastic components. The deterministic component gives rise to trends, seasonal variations, and tidal variations, while the stochastic component causes statistical fluctuations which have a short term correlation structure. The best prediction results of the EOP are obtained when the deterministic components are predicted by the deterministic method and a stochastic prediction technique is applied to forecast the stochastic component. Combination of deterministic and stochastic predictions improves the prediction accuracy in low and high frequency components. It should be noted that a good approximation does not guarantee a good prediction.

EOP Prediction Methods

1. Least-squares (LS) extrapolation (deterministic prediction method) 2. Least-squares collocation (LSC) 3. Kalman Filter (KF)4. Autoregressive (AR)5. Autoregressive (integrated) moving-average (ARIMA)6. Auto covariance (AC)7. Neural networks (NN)8. Fuzzy Logic 9. Multidimensional (MD)

IERS Working Group on Prediction: Plans and Activities William Wooden1, Tonie van Dam2, Wieslaw Kosek3

1U. S. Naval Observatory, Washington DC, USA (whw@ usno.navy.mil)2European Center for Geodynamics and Seismology, L-7256 Walferdange, Luxembourg3Space Research Center, Polish Academy of Sciences, Warsaw, Poland

EOP prediction methods - problems

Least-squares (LS) extrapolation - prediction error depends mostly on the LS model adequacy. Due to variations of amplitudes and phases of oscillations as well as the trend, the optimum length of the EOP data should be found to get the minimum prediction error of the extrapolation model. The LS is the most appropriate to resolve the Chandler and annual oscillations even from a short data record (> 1 year). The LS extrapolation model differs from the last observed EOP datum, so this difference must be used to adjust the extrapolated curve by an amount that decreases with the length of the forecast.

Least-squares collocation – technique used to combine geophysical excitation functions correlated with the EOP to determine their predictions. The relevant problems are similar as in the LS method + problem of modelling the covariance function of the signal.

Kalman Filter – can combine different EOP data sets together with atmospheric/ oceanic/ hydrologic angular momentum data to extrapolate the EOP.

Autoregressive prediction – the prediction error depends on the autoregressive coefficients but mostly on the autoregressive order. The optimum autoregressive model depends on the frequency band of the most

energetic oscillations. Autoregressive (integrated) moving-average (ARIMA) – prediction error depends on the

autoregressive and moving average coefficients but mostly on the autoregressive and moving average model orders.

Neural networks (NN) – the main problem is to design the optimal topology of the network and effectiveness of the training algorithm. If the number of neurons is too big the training would take too much time, but too few neurons would allow only a poor representation of time series.

Multidimensional (MD) – can combine different data sets to predict each of them. The multivariate autoregressive model is fit to the multivariate time series and this model is used to forecast them. The problem is to estimate the autoregressive coefficient matrices and the autoregressive order.

Input Data Considerations

1) Exploit methods to minimize data latency; minimize extrapolation to current time 2) Determine loss of information if all data sets have a common epoch 3) Examine potential geophysical data sets from the IERS Global Geophysical Fluids Center 4) Examine the geodetic technique services’ combination data sets resulting from the IERS Combination Pilot

Project 5) Determine sensitivities of missing data sets to the prediction process 6) Examine pathological data sets from Chandler and annual destructive interference time frame 7) Determine the optimum combination of geophysical signals to create the best predictions 8) Determine where research is needed to make future improvements in EOP prediction

Future Plans

1) Determine the optimum parameters for the combination prediction algorithms2) Include the AAM, OAM, and HAM excitation functions, if available, in the Kalman filter or multidimensional

prediction of x, y, and UT1-UTC data in order to improve their prediction accuracy for a few days in the future3) Investigate the geophysical causes of EOP prediction errors4) Investigate new forecast methods and algorithms for the EOP prediction

References

IERS Working Group on Prediction details on IERS web site at http://www.iers.org/MainDisp.csl?pid=167-1100082

Stochastic prediction methods

•Irregular amplitudes and phases of broadband semiannual oscil-lation and other oscillations with periods of less than one year

•Amplitude and phase variations of the Chandler oscillation in the case of x, y pole coordinate data only•Irregular phase and amplitude variations of the broadband annual oscillation•Irregular decadal and secular variations

Accuracy of EOP Prediction depends on:Short-term prediction medium-term prediction

Two ways to predict polar motion

In Cartesian coordinate system - Prediction is applied directly to x, y pole coordinate data. Before the prediction is applied, the linear trend is removed and the trend extrapolation model is added to the computed forecast.

In polar coordinate system - Prediction is applied to the polar motion radius and angular velocity and then their forecasts are transformed to the pole coordinate prediction using linear intersection. The radius and its prediction must be referred to the mean pole and its forecast. This transformation to polar coordinates helps solve the problem of the resolution of the Chandler and annual terms.

Combined Prediction Algorithms

1) Combination of the Least-squares (LS) extrapolation and the stochastic prediction - in the combination of the LS extrapolation and the stochastic prediction, the LS residuals of the EOP data are determined as the difference between these data and their corresponding LS models. Next, the stochastic prediction method is applied to the LS residuals of EOP data. The final prediction of EOP data is the sum of the LS extrapolation model and the stochastic prediction of the LS residuals. 2) Combination of the Discrete Wavelet Transform (DWT) decomposition and prediction of frequency components - in the combination of the DWT and stochastic prediction, the time series is decomposed into frequency components using Shannon or Meyer discrete wavelet functions in such a way that the sum of all the frequency components reconstructs the input time series. Each frequency component is predicted separately and the final prediction is the sum of the predictions of all the components.

AGU Fall Meeting 10-15 December 2006 San Francisco