Wieslaw Kosek

Comparison of two wavelet transform coherence and cross-covariance functions applied on polar motion and atmospheric excitation

The wavelet transform techniques were applied to compute time-frequency spectra, coherence and cross-covariance functions between complex-valued polar motion and atmospheric excitation functions. These wavelet transform approaches are based on the classical wavelet transform with Morlet wavelet and the harmonic wavelet transform. The computed coherence and cross-covariance functions enable comparison of polar motion and atmospheric excitation functions data in the chosen frequency band. In the study we concentrate on short period oscillations with periods ranging from several to about 250 days. The time lag functions show frequency dependent time lags corresponding to maxima of the modules of cross-covariance functions between the polar motion and atmospheric excitation functions.

El Niño Impact on Polar Motion Prediction Errors

The polar motion prediction is computed as a least-squares extrapolation of the polar motion data. The least-squares model consists of a Chandler circle with constant or variable amplitude, annual and semiannual ellipses, and a bias. The model with constant amplitude of the Chandler oscillation is fit to the last three years of polar motion data and the model with variable amplitude of the Chandler oscillation is fit to the whole time series ranging from 1973.0 to 2001.1. The variable amplitude of the Chandler oscillation is modeled from the envelope of the Chandler oscillation filtered by the Fourier transform band pass filter from the long-term IERS EOPC01 polar motion series. The accuracy of the polar motion prediction depends mostly on the phase variation of the annual oscillation, which is treated as a constant in the least-squares adjustment. There were two significant changes of the annual oscillation phase of the order of 30° before the two El Niño events in 1982/83 and 1997/98.

Does circumnutation follow tidal plumb line variations

The Morlet wavelet coherences and spectro-temporal coherences were applied to detect common oscillations in sunflower autonomic movements (circumnutations) and variations of the direction of the gravity vector. The mean coherence between time series of sunflower coordinates and the theoretical plumb line model was of the order of 0.6–0.8 for oscillations with periods greater than two days. We also detected weak common oscillations with periods of 0.5 and 1.0 days, which may correspond to semidiurnal and diurnal tides, respectively. Computing the common signal in the time series of sunflowers used in the experiment revealed a low, but statistically significant coherence for semidiurnal and diurnal oscillations. Although we cannot determine if plumb line variations indeed influence circumnutation in sunflower, we prove that there is a significant correlation between these two phenomena.

Prediction Analysis of UT1-UTC Time Series by Combination of the Least-Squares and Multivariate Autoregressive Method

The objective of this paper is to extensively discuss the theory behind the multivariate autoregressive prediction technique used elsewhere for forecasting Universal Time (UT1-UTC) and to characterise its performance depending on input geodetic and geophysical data. This method uses the bivariate time series comprising length-of-day and the axial component of atmospheric angular momentum data and needs to be combined with a least-squares extrapolation of a polynomial-harmonic model. Two daily length-of-day time series, i.e. EOPC04 and EOPC04_05 spanning the time interval from 04.01.1962 to 02.05.2007, are utilised. These time series are corrected for tidal effects following the IERS Conventions model. The data on the axial component of atmospheric angular momentum are processed to gain the 1-day sampling interval and cover the time span listed above. The superior performance of the multivariate autoregressive prediction in comparison to autoregressive forecasting is noticed, in particular during El Nino and La Nina events. However, the accuracy of the multivariate predictions depends on a particular solution of input length-of-day time series. Indeed, for EOPC04-based analysis the multivariate autoregressive predictions are more accurate than for EOPC04_05-based one. This finding can be interpreted as the meaningful influence of smoothing on forecasting performance.

Analysis of Pole Coordinate Data Predictions in the Earth Orientation Parameters Combination of Prediction Pilot Project

Analysis of Pole Coordinate Data Predictions in the Earth Orientation Parameters Combination of Prediction Pilot Project In October 2010 the US Naval Observatory together with the Space Research Centre in Warsaw initiated the Earth Orientation Parameters Combination of Prediction Pilot Project, which was accepted by the IERS Directing Board. The goal of this project is to determine the feasibility of combining Earth Orientation Parameters (EOP) predictions on an operational basis. The ensemble predictions of EOPs are more accurate than the results from individual predictions. The pole coordinate data predictions from different prediction contributors and ensemble predictions computed by the U.S. Naval Observatory are studied to determine the statistical properties of polar motion forecasts by looking at second, third and fourth moments about the mean. The increase of prediction errors in pole coordinate data can be due to the change of phase of the annual oscillation in the joint atmospheric-ocean excitation function.

An Application of Low-Order Arma and Garch Models for Sea Level Fluctuations

An Application of Low-Order Arma and Garch Models for Sea Level Fluctuations The paper presents the analysis of geographically-dependent irregular sea level fluctuations, often referred to as residual terms around deterministic signals, carried out by means of stochastic low-order autoregressive moving average (ARMA) and generalised autoregressive conditional heteroscedastic (GARCH) models. The gridded sea level anomaly (SLA) time series from TOPEX/Poseidon (T/P) and Jason-1 (J-1) satellite altimetry, commencing on 10th January 1993 and finishing on 14th July 2003, has been examined. The aforementioned models, limited to low-orders being combinations of 0,1 and 2, have been fitted to the SLA data. The root mean square and the Shapiro-Wilk test for the normal distribution have been used to calculate statistics of the residuals from these models. It has been found that autoregressive (AR) models as well as ARMA ones serve well the purpose of adequate modelling irregular sea level fluctuations, with a successful fit in some patchy bits of the equatorial Pacific. In contrast, GARCH models have been shown to be rather inaccurate, specifically in the vicinity of the tropical Pacific, in the North Pacific and in the equatorial Indian Ocean. The pattern of the Tropical Instability Waves (TIWs) has been noticed in the statistics of AR and ARMA model residuals indicating that the dynamics of these waves cannot be captured by the aforementioned linear stochastic processes.

The common short periodic oscillations in the Earth's rate of rotation, atmospheric angular momentum and solar activity

In order to find short periodic oscillations in the Earths rate of rotation, atmospheric angular momentum, solar activity the Maximum Entropy Spectral Analysis — MESA (Burg, 1967) has been applied. The MESA with moving autoregressive order has been introduced in order to detect more accurately periods of very weak short periodic variations. Oscillations with periods of about 75, 50, 27 and 18 days have been found in length of day — LOD, from which tidal oscillations were removed up to 35 days — LODR computed by the Center for Space Research — CSR from Lageos Laser Ranging data, in the axial component of atmospheric angular momentum —χ3 determined by the U.S. National Meteorological Center — NMC and in the geomagnetic activity represented by the geomagnetic index —Ap (Lincoln, 1967). These oscillations computed by Ormsby band pass filter (Ormsby, 1961) are in a very good phase agreement in the case of oscillations with periods of 50 and 18 days in these 3 series. The MESA of the cross covariance estimations between LODR-χ3,χ3-Ap,Ap-LODR, LODR-FLUX,χ3-FLUX, andAp-FLUX has confirmed the existence of common oscillations with periods of 70, 50, 27 and 18 days. This indicates a possible relationship between solar activity and the short periodic exchange of angular momentum between the atmosphere and the solid Earth.

Geodynamic Research at the Department of Planetary Geodesy, SRC PAS

Abstract The Department of Planetary Geodesy of the Space Research Centre PAS has been conducting research on a broad spectrum of problems within a field of global dynamics of the Earth. In this report we describe the investigations on selected subjects concerning polar motion (modeling and geophysical interpretation of the Chandler wobble, hydrological excitation of seasonal signals, search for optimal prediction methods), tectonic activity in the region of the Książ Geodynamic Laboratory of the SRC, and finally the new joint Polish-Italian project GalAc analyzing feasibility and usefulness of equipping second-generation Galileo satellites with accelerometers.

Variable Seasonal and Subseasonal Oscillations in Sea Level Anomaly Data and Their Impact on Prediction Accuracy

Weekly sea level anomaly (SLA) maps are now available courtesy of the Archiving, Validation and Interpretation of Satellite Oceanographic (AVISO) data. Using the Fourier Transform Band Pass Filter (FTBPF) variable broadband seasonal and subseasonal oscillations were computed as a function of geographic location. Irregular amplitude and phase variations in these oscillations cause the increase of prediction errors of the SLA data for a few weeks in the future. The amplitude and phase variations of the broadband annual oscillation were computed by a combination of the FTBPF and the Hilbert transform. In order to detect the impact of irregular amplitude or/and phase variations of the annual oscillation on the SLA prediction errors, standard deviations maps of amplitude time differences as well as of the products of phase time differences and amplitudes were examined. The SLA data prediction errors in certain geographic regions of the ocean seem to be caused mainly by nonlinear behaviour of the broadband annual oscillation. The nonlinearities are probably driven by mesoscale eddies, and the significant impact on SLA prediction errors was observed in the vicinity of the western boundary currents.