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1

Medium- and long-term prediction of polar motion using weighted least squares extrapolation and vector autoregressive modeling

Lei Yu, Zhao Danning, Guo Min

Artificial Satellites : Journal of Planetary Geodesy

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2023

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Vol. 58, No. 2

42--55

EN

This article presents the application of weighted least squares (WLS) extrapolation and vector autoregressive (VAR) modeling in polar motion prediction. A piecewise weighting function is developed for the least squares (LS) adjustment in consideration of the effect of intervals between observation and prediction epochs on WLS extrapolation. Furthermore, the VAR technique is used to simultaneously model and predict the residuals of xp, yp pole coordinates for WLS misfit. The simultaneous predictions of xp, yp pole coordinates are subsequently computed by the combination of WLS extrapolation of harmonic models for the linear trend, Chandler and annual wobbles, and VAR stochastic prediction of the residuals (WLS+VAR). The 365-day-ahead xp, yp predictions are compared with those generated by LS extrapolation+univariate AR prediction and LS extrapolation+VAR modeling. It is shown that the xp, yp predictions based on WLS+VAR taking into consideration both the interval effect and correlation between xp and yp outperform those generated by two others. The accuracies of the xp predictions are 13.97 mas, 18.47 mas, and 20.52 mas, respectively for the 150-, 270-, and 365-day horizon in terms of the mean absolute error statistics, 36%, 24.8%, and 33.5% higher than LS+AR, respectively. For the yp predictions, the 150-, 270-, and 365-day accuracies are 15.41 mas, 21.17 mas, and 21.82 mas respectively, 27.4%, 11.9%, and 21.8% higher than LS+AR respectively. Moreover, the absolute differences of the WLS+VAR predictions and observations are smaller than the differences from LS+VAR and LS+AR, which is practically important to practical and scientific users, although the improvement in accuracies is no more than 10% relative to LS+VAR. The further comparison with the predictions submitted to the 1st Earth Orientation Parameters Prediction Comparison Campaign (1st EOP PCC) shows that while the accuracy of the predictions within 30 days is comparable with that by the most accurate prediction techniques including neural networks and LS+AR participating in the campaign for xp, yp pole coordinates, the accuracy of the predictions up to 365 days into the future are better than accuracies by the other techniques except best LS+AR used in the EOP PCC. It is therefore concluded that the medium- and long-term prediction accuracy of polar motion can be improved by modeling xp, yp pole coordinates together.

2

Prediction of Earth Rotation Parameters With the Use of Rapid Products From IGS, Code and GFZ Data Centres Using ARIMA and Kriging - A Comparison

Michalczak Maciej, Ligas Marcin, Kudrys Jacek

Artificial Satellites : Journal of Planetary Geodesy

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2022

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Vol. 57, Special Issue 1

275--289

EN

Real-time prediction of Earth Orientation Parameters is necessary for many advanced geodetic and astronomical tasks including positioning and navigation on Earth and in space. Earth Rotation Parameters (ERP) are a subset of EOP, consisting of coordinates of the Earth’s pole (PMx, PMy) and UT1-UTC (or Length of Day - LOD). This paper presents the ultra-short-term (up to 15 days into the future) and short-term (up to 30 days into the future) ERP prediction using geostatistical method of ordinary kriging and autoregressive integrated moving average (ARIMA) model. This contribution uses rapid GNSS products EOP 14 12h from IGS, CODE and GFZ and also IERS final products - IERS EOP 14 C04 12h (IAU2000A). The results indicate that the accuracy of ARIMA prediction for each ERP is better for ultra-short prediction. The maximum differences between methods for first few days of 15-day predictions are around 0.32 mas (PMx), 0.23 mas (PMy) and 0.004 ms (LOD) in favour of ARIMA model. The maximum differences of Mean Absolute Prediction Errors (MAPEs) on the last few days of 30-day predictions are 1.91 mas (PMx), 0.30 mas (PMy) and 0.026 ms (LOD) with advantage to kriging method. For all ERPs the differences of MAPEs for time series from various analysis centres are not significant and vary up to maximum value of around 0.05 mas (PMx), 0.04 mas (PMy) and 0.005 ms (LOD).

3

ESMGFZ Products for Earth Rotation Prediction

Dill Robert, Dobslaw Henryk, Thomas Maik

Artificial Satellites : Journal of Planetary Geodesy

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2022

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Vol. 57, Special Issue 1

254--261

EN

The Earth System Modelling Group of GeoForschungsZentrum Potsdam (ESMGFZ) provides geodetic products for gravity variations, Earth rotation excitations, and Earth surface deformations related to mass redistributions and mass loads in the atmosphere, ocean, and terrestrial water storage. Earth rotation excitation compiled as effective angular momentum (EAM) functions for each Earth subsystem (atmosphere, ocean, continental hydrology) are important for Earth rotation prediction. Especially the 6-day forecasts extending the model analysis runs offer essential information for the improvement of ultra-short-term Earth rotation predictions. In addition to the individual effective angular momentum function of each subsystem, ESMGFZ calculates a combined EAM prediction product. Adjusted to the official Earth orientation parameter (EOP) products IERS 14C04 and Bulletin A, this EAM prediction product allows to extrapolate the polar motion and Length-of-Day parameter time series for 90 days into the future via the Liouville equation. ESMGFZ submits such an EOP prediction to the 2nd EOPPCC campaign.

4

Geodesy: General theory and methodology 2015–2018

Borkowski Andrzej, Kosek Wiesław, Ligas Marcin

Geodesy and Cartography

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2019

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Vol. 68, no. 1

145--162

EN

The summary of research activities concerning general theory and methodology performed in Poland in the period of 2015–2018 is presented as a national report for the 27th IUGG (International Union of Geodesy and Geophysics) General Assembly. It contains the results of research on new or improved methods and variants of robust parameter estimation and their application, especially to control network analysis. Reliability analysis of the observation system and an integrated adjustment approach are also given. The identifiability (ID) index as a new measure for minimal detectable bias (MDB) in the observation system of a network, has been introduced. A new method of covariance function parameter estimation in the least squares collocation has been developed. The robustified version of the Shift-Msplit estimation, termed as Shift-M*split estimation, which enables estimation of parameter differences (robustly), without the need of prior estimation of the parameters, has been introduced. Results on the analysis of geodetic time series, particularly Earth orientation parameter time series, geocenter time series, permanent station coordinates and sea level variation time series are also provided in this review paper. The entire bibliography of related works is provided in the references.

5

Terrestrial water storage variations and their effect on polar motion

Śliwińska Justyna, Wińska Małgorzata, Nastula Jolanta

Acta Geophysica

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2019

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Vol. 67, no. 1

17--39

EN

The role of continental water in polar motion excitation can be illustrated by determining Hydrological Angular Momentum calculated from terrestrial water storage (TWS). In this paper we compare global and regional changes in TWS computed using Coupled Model Intercomparison Project Phase 5 climate models, Global Land Data Assimilation System (GLDAS) land hydrology models and observations from the Gravity Recovery and Climate Experiment (GRACE) satellite mission. We also compare hydrological excitation functions derived from models with those obtained from the GRACE mission and the hydrological signal in observed polar motion excitation (the so-called geodetic residuals). The results confirm that GLDAS models of seasonal and non-seasonal TWS change are more consistent with GRACE data than climate models; on the other hand, none of the considered models are fully consistent with GRACE data or geodetic residuals. In turn, GRACE observations are most consistent with the non-seasonal hydrological signal in observed excitation. A detailed study of the contribution of different TWS components to the hydrological excitation function shows that soil moisture dominates.

6

Hydrological excitations of polar motion derived from different variables of FGOALS - g2 climate model

Winska M.

Artificial Satellites : Journal of Planetary Geodesy

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2016

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Vol. 51, No. 4

107--122

EN

The hydrological contribution to decadal, inter-annual and multi-annual suppress polar motion derived from climate model as well as from GRACE (Gravity Recovery and Climate Experiment) data is discussed here for the period 2002.3-2016.0. The data set used here are Earth Orientation Parameters Combined 04 (EOP C04), Flexible Global Ocean-Atmosphere-Land System Model: Grid-point Version 2 (FGOALg2) and Global Land Data Assimilation System (GLDAS) climate models and GRACE CSR RL05 data for polar motion, hydrological and gravimetric excitation, respectively. Several Hydrological Angular Momentum (HAM) functions are calculated here from the selected variables: precipitation, evaporation, runoff, soil moisture, accumulated snow of the FGOALS and GLDAS climate models as well as from the global mass change fields from GRACE data provided by the International Earth Rotation and Reference System Service (IERS) Global Geophysical Fluids Center (GGFC). The contribution of different HAM excitation functions to achieve the full agreement between geodetic observations and geophysical excitation functions of polar motion is studied here.

7

Assessment of the Global and Regional Land Hydrosphere and Its Impact on the Balance of the Geophysical Excitation Function of Polar Motion

Wińska M., Nastula J., Kołaczek B.

Acta Geophysica

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2016

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Vol. 64, no. 1

270--292

EN

The impact of continental hydrological loading from land water, snow and ice on polar motion excitation, calculated as hydrological angular momentum (HAM), is difficult to estimate, and not as much is known about it as about atmospheric angular momentum (AAM) and oceanic angular momentum (OAM). In this paper, regional hydrological excitations to polar motion are investigated using monthly terrestrial water storage data derived from the Gravity Recovery and Climate Experiment (GRACE) mission and from the five models of land hydrology. The results show that the areas where the variance shows large variability are similar for the different models of land hydrology and for the GRACE data. Areas which have a small amplitude on the maps make an important contribution to the global hydrological excitation function of polar motion. The comparison of geodetic residuals and global hydrological excitation functions of polar motion shows that none of the hydrological excitation has enough energy to significantly improve the agreement between the observed geodetic excitation and geophysical ones.

8

Theoretical geodesy

Borkowski A., Kosek W.

Geodesy and Cartography

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2015

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Vol. 64, no. 2

261--279

EN

The paper presents a summary of research activities concerning theoretical geodesy performed in Poland in the period of 2011-2014. It contains the results of research on new methods of the parameter estimation, a study on robustness properties of the M-estimation, control network and deformation analysis, and geodetic time series analysis. The main achievements in the geodetic parameter estimation involve a new model of the M-estimation with probabilistic models of geodetic observations, a new Shift-Msplit estimation, which allows to estimate a vector of parameter differences and the Shift-Msplit(+) that is a generalisation of Shift-Msplit estimation if the design matrix A of a functional model has not a full column rank. The new algorithms of the coordinates conversion between the Cartesian and geodetic coordinates, both on the rotational and triaxial ellipsoid can be mentioned as a highlights of the research of the last four years. New parameter estimation models developed have been adopted and successfully applied to the control network and deformation analysis. New algorithms based on the wavelet, Fourier and Hilbert transforms were applied to find time-frequency characteristics of geodetic and geophysical time series as well as time-frequency relations between them. Statistical properties of these time series are also presented using different statistical tests as well as 2nd, 3rd and 4th moments about the mean. The new forecasts methods are presented which enable prediction of the considered time series in different frequency bands.

9

Comparison of the geophysical excitations of polar motion from the period: 1980.0-2009.0

Nastula J., Paśnicka M., Kołaczek B.

Acta Geophysica

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2011

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Vol. 59, no. 3

561-577

EN

In this study we compared contributions to polar motion excitation determined separately from each of three kinds of geophysical data: atmospheric pressure, equivalent water height estimated from hydrological models, and harmonic coefficients of the Earth gravity field obtained from Gravity Recovery and Climate Experiment (GRACE). Hydrological excitation function (Hydrological Angular Momentum - HAM) has been estimated from models of global hydrology, based on the observed distribution of surface water, snow, ice, and soil moisture. In our consideration we used several global models of land hydrosphere and models of Atmospheric Angular Momentum (AAM) and Oceanic Angular Momentum (OAM). All of them were compared with observed Geodetic Angular Momentum (GAM). The spectra of the following excitation functions of polar motion: GAM, AAM+OAM, AAM+OAM+HAM, GAM-AAM-OAM residual geodetic excitation function, and HAM were computed too. The time variable spectra of geodetic, gravimetric, and the sum of atmospheric, oceanic, and hydrological excitation functions are also presented. Phasor diagrams of the seasonal components of polar motion excitation functions of all HAM excitation functions as well as of two GRACE solutions: Center for Space Research (CSR), Centre National d'Etudes Spatiales/Groupe de Recherche en Geodesie Spatiale (CNES/GRGS) were determined and discussed.

10

Tide gauge records-derived variations of Baltic Sea level in terms of geodynamics

Kryński J., Zanimonskiy Y. M.

Geodezja i Kartografia

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2004

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T. 53, z. 2

85-98

EN

Sea level monitoring at tide gauges plays an important role in geodesy, geodynamics research and oceanography. It provides data for referencing vertical datum, for modelling geoid in coastal regions, for determination of vertical land movements and for studying ocean dynamics. Investigation of Baltic Sea level variations is considered an important component of geodynamics research in Central and Northern Europe. The analysis of tide gauge records from Baltic sites was conducted in the framework of the project on a cm geoid in Poland. Those records showed strong common features that were further used for deriving the model of Baltic Sea level variations. High level of correlations of the model with individual site data proved its adequacy. Regional characteristics of the model were investigated using regression and correlation analysis. It was shown that the model represents very well both global and regional features of Baltic Sea level variations. The use of the model as reference to investigate local features of tide gauge records that reflect site-specific variations of sea level was also discussed. Spectral analysis of the model of Baltic Sea level variations indicates the existence of distinguished term of Chandler period besides two major terms of annual and semi-annual periods. The existence ot polar motion component in Baltic Sea level variations was investigated using correlation analysis. Also the land vertical movement derived from Baltic tide gauge data was determined and compared with literature data.

PL

Monitorowanie poziomu morza w oparciu o dane mareograficzne jest istotnym elementem badań geodezyjnych, geodynamicznych i oceanograficznych. Dostarcza ono informacji wykorzystywanych do określania poziomu odniesienia systemów wysokościowych, modelowania geoidy w obszarach nadmorskich, badania ruchów skorupy ziemskiej oraz badania dynamiki oceanów. Badanie zmian poziomu Morza Bałtyckiego stanowi ważny element studiów geodynamicznych na obszarze Centralnej i Północnej Europy. W ramach projektu badawczego, dotyczącego wyznaczenia centymetrowej geoidy na obszarze Polski, przeprowadzono analizę ciągów czasowych obserwacji mareografich ze stacji w basenie Morza Bałtyckiego. W oparciu o wspólne cechy zaobserwowane w ciągach czasowych z różnych stacji mareograficznych opracowany został model zmienności poziomu Morza Bałtyckiego. 0 poprawności opracowanego modelu świadczy wysoki stopień jego skorelowania z danymi mareograficznymi z poszczególnych stacji. Regionalne charakterystyki modelu badano przy użyciu metod regresji i analizy korelacyjnej. Pokazano, że model odzwierciedla zarówno globalne jak i lokalne cechy zmienności poziomu Morza Bałtyckiego. Dyskutowane były rownież możliwości użycia opracowanego modelu jako odniesienia do badania w mareograficznych ciągach czasowych lokalnych cech, które odzwierciedlają specyficzne dla konkretnej stacji zmiany poziomu morza. Z analizy spektralnej modelu zmienności poziomu Morza Bałtyckiego wynika, iż w zmiennościach tych, obok zasadniczych wyrazów okresowych o okresach rocznym i półrocznym, występuje wyraźny wyraz o okresie Chandlera. Obecność w zmienności poziomu Morza Bałtyckiego składowej charakterystycznej dla nutacji swobodnej była badana przy użyciu analizy korelacyjnej. Na podstawie danych mareograficznych ze stacji z basenu Morza Bałtyckiego wyznaczono rownież parametry pionowego ruchu kontynentalnego, które są zgodne z odpowiednimi parametrami dostępnymi w literaturze.