Polar Motion Prediction with Derivative Information

Our study introduces a hybrid model that combines least-squares (LS) extrapolation of a linear trend and periodic components with a vector autoregression applied to LS residuals in an attempt of enhancing polar motion (x, y) predictions through incorporating its rates (derivatives; x^', y^'). We used the historical daily sampled final IERS EOP 20 C04 time series available on https://www.iers.org as a reference for all computations. The prediction experiment covers 10 years, 01.03.2013 – 01.03.2023. Within this period, 1000 random samples with a length of one year were generated, with the starting modified Julian date (MJD) of each yearly sample randomized. Within each sample, a 30-day forecast was performed every 7 days, resulting in a total of 48 forecasts in each random trial. Polar motion rates were incorporated to the prediction procedure in various combinations, i.e., {x, x^'}, {y, y^'}, {x, y, x^'}, {x, y, y^'}, {x, y, x^', y^'} and the prediction results based on them were compared to the predictions obtained from the reference data combination {x, y}, which does not include derivative information. As a basic measure of prediction accuracy, we used the mean absolute prediction error (MAPE) as well as a number of measures indicating improvement through incorporating rates into the prediction procedure. The results indicate a noticeable gain in prediction accuracy with the use of derivatives, although not substantial, it is systematic. This improvement is particularly apparent for the first few days of the forecast, which might indicate its potential use in ultra-short-term prediction. This promising data combination (and prediction method) is worth further analysis and an attempt of adapting it for operational settings (real time forecast).