Ensemble Prediction for Earth Orientation Parameters

1. Figure 5. Scatter plot between absolute residuals and formal errors. Figure 1. Prediction errors in PM-x. Figure 2. Prediction errors in PM-y. Figure 6. Distribution of 1-day prediction residuals in PM-x. Figure 3. Prediction errors in UT1-UTC. Figure 4. Correlations between absolute residuals and formal errors. Ensemble Prediction for Earth Orientation Parameters B. Luzum (1), W. Wooden (1), D. McCarthy (1), H. Schuh (2), W. Kosek (3), and M. Kalarus (3) (1) U.S. Naval Observatory, US, (2) TU Vienna, Austria, (3) Space Research Centre, Poland luzum.brian@maia.usno.navy.mil A scatter plot of the 1-day absolute prediction residuals versus the formal errors in UT1-UTC is shown in Figure 5. While the correlation for these data is high, the relationship between the variables is not totally apparent. Visually, it appears that a significant amount of the correlation derives from the fact that 1-day predictions have small formal errors (i.e. most 1-day predictions agree fairly well). It is not clear that this correlation is an indication that small formal errors imply small residuals and large formal errors imply large residuals. Abstract. Ensemble prediction, a technique gaining prominence in the meteorological and hydrological communities, offers the possibility of improved prediction accuracy and robustness. As part of the International Earth Rotation and Reference Systems Service (IERS) Working Group on Prediction (WGP), the IERS Rapid Service/Prediction Center has made a preliminary investigation into the efficacy of ensemble prediction for Earth orientation parameters (EOP), specifically, polar motion and UT1-UTC. Initial results, based on roughly a year’s worth of data collected by the EOP Prediction Comparison Campaign, indicate that ensemble prediction produces results similar to the best prediction methods over a given data span. These results and their implications for the prediction process, in general, and for the IERS WGp, in particular, are presented. • Results. To determine the error of the ensemble predictions, first the residuals in the sense of [ensemble prediction - 97C04] were created. The errors of the predictions were then computed by taking the root mean square (rms) of the residuals. Plots of the errors of the input prediction series and the ensemble series (labeled 9999) are shown in Figures 1, 2, and 3. Ensemble Prediction – The Technique. Ensemble prediction is a technique that combines a set of predicted time series to produce one time series. The strength of this technique is that by combining information from different algorithms and from using different initial conditions or parameterizations, a better estimate of future conditions can be obtained than can be obtained from a single algorithm. To evaluate the possible application of the ensemble predictions, a histogram of the 1-day prediction residuals in the polar motion x component of all input series was plotted. The data are reasonably Gaussian. This indicates that the usefulness of the ensemble predictions may be due to the averaging process reducing the effect of the random error of each individual prediction series. The result is noteworthy because a single set of prediction residuals can be highly non-Gaussian. The ensemble predictions errors compare favorably with the errors of the individual series. In all three components, the ensemble errors are approximately the second best scheme. Note that even though the ensemble prediction is a mean of the input predictions, the ensemble prediction error is better than the mean of the prediction errors. Data. The input prediction series were taken from the first year of the Earth orientation parameter (EOP) Prediction Comparison Campaign (PCC) (ref.). The series that were used in the creation of the ensemble polar motion prediction were chosen because they produced short-term predictions and provided data for at least half of the test period. Some of these series also provided UT1-UTC predictions, so only these series were used in the ensemble UT1-UTC predictions. To ensure homogenization of the input series, only the first 49 weeks of data were used in this analysis. One series was produced for only 28 weeks so only those data are included in the ensemble. The data were not adjusted to ensure that the first prediction in each file was a 1-day prediction. Conclusions. The initial effort at ensemble EOP prediction has shown promising results. By taking the mean of the input predictions, the ensemble prediction error is better than most of the input series. The formal errors of the ensemble prediction do not appear to be correlated with the absolute value of the residuals. Ensemble Creation. To test the concept for this initial ensemble, a simple mean of the input prediction series for each day was created. The prediction series were not weighted using prior knowledge of the prediction accuracy. They were also not edited to eliminate spurious predictions. The formal error of the predictions was estimated by computing the standard deviation of the input predictions for each ensemble prediction. The suitability of this estimate as a proxy for the true error of each prediction is discussed in the Results section. • Implications for the IERS Working Group on Prediction (WGP). There are several things that the IERS WGP should consider investigating as part of their ongoing work. • What is the exact mechanism responsible for the improvement in the ensemble prediction? • What are optimal methods for creating ensemble predictions? • What effect do the variety of input prediction methods have on the creation of the ensemble? • Are there effective ways to estimate the likely error of the ensemble predictions? In an effort to understand the cause of this improvement, correlations between the absolute value of the residuals and the calculated formal errors were computed. These correlations are plotted in Figure 4. Only the 1- and 2-day UT1-UTC prediction correlations are significant at the 99% confidence level. Acknowledgements. The authors would like to thank the contributors to the EOP PCC for their work in creating the input series for this analysis. References: EOP PCC reference?