A new approach to improve the Earth's polar motion prediction: on the deconvolution and convolution methods

Combining the Liouville equations for polar motion (PM) with forecasted geophysical effective angular momentum (EAM) functions can significantly improve the accuracy of Earth's PM predictions. These predictions rely on deconvolution and convolution methods. Deconvolution derives the geodetic EAM function from the PM observations, while convolution uses both the geodetic and geophysical EAM functions to reproduce and predict the PM values. However, there are limitations in existing numerical realisations of deconvolution and convolution that must be addressed. These limitations include low-frequency biases, high-frequency errors, and edge errors, which can negatively impact the accuracy of PM prediction. To overcome these concerns, we develop the Convolution Least Squares (Conv-LS) scheme through a multi-perspective analysis in the frequency domain, PM domain, and EAM domain. By comparing representative approaches for reproducing three different PM series (IERS C01, IERS C04, and IGS) with varying sampling intervals (18.25 days, daily, and 6 h), we demonstrate that the Conv-LS scheme can effectively eliminate the usually present spurious signals and also integrate high-accuracy deconvolution algorithms to reduce reproduced errors further. Compared to the traditional approacsh (using a low-accuracy discrete PM equation for deconvolution and numerical integration for convolution), our new approach (utilising a high-accuracy deconvolution algorithm along with the Conv-LS scheme for convolution) reduces the standard deviations of the residuals' x-component by 31.0%, 60.1%, and 13.7% for C01, C04, and IGS PM series, respectively, while also reducing the y-component by 17.3%, 47.0%, and 14.0%, respectively. These results highlight the superiority of the Conv-LS scheme, leading us to recommend it for practical applications.