# JSG T.33

**JSG T.33: Time series in geodesy and geodynamics**

Chair: *: Wieslaw Kosek (Poland)*

Affiliation:*Commissions 1, 3 and 4, GGOS*

### Introduction

Observations of the space geodesy techniques enable measuring Earth’s gravity variations caused by mass displacement, the change in the Earth’s shape, and the change in the Earth’s rotation. The Earth’s rotation represented by the Earth Orientation Parameters (EOP) should be observed with possibly the smallest latency to provide real-time transformation between the International Terrestrial and Celestial Reference Frames (ITRF and ICRF). Observed by GRACE missions, redistribution of mass within the fluid layers relative to the solid Earth induces exchange of angular momentum between these layers and solid Earth, changes in the Earth’s inertia tensor.

Redistribution of masses induce temporal variations of Earth's gravity field where 1 degree spherical harmonics correspond to the Earth’s centre of mass variations (long term mean of them determines the ITRF origin) and 2 degree spherical harmonics correspond to Earth rotation changes. Satellite altimetry enables observation of changes in geometry of sea level and space geodesy techniques enable observations of changes in geometry of the Earth's crust by monitoring horizontal and vertical deformations of site positions. Sea surface height varies due to thermal expansion of sea water and changes in ocean water mass arising from melting polar ice cap, mountain glacier ice, as well as due to groundwater storage. The site positions which are determined together with satellite orbit parameters (in the case of SLR, GNSS and DORIS) or radio source coordinates (in the case of VLBI) and Earth orientation parameters (x, y pole coordinates, UT1-UTC/LOD and precession-nutation corrections dX, dY) are then used to build the global ITRF which changes due to e.g. plate tectonics, postglacial rebound, atmospheric, hydrology and ocean loading and earthquakes. In these three components of geodesy which should be integrated into one unique physical and mathematical model there are changes that are described by spatial and temporal geodetic time series.

Different time series analysis methods have been applied to analyze all elements of the Earth’s system for better understanding the mutual relationship between them. The nature of considered signals in the geodetic time series is mostly wideband, irregular and non-stationary. Thus, it is recommended to apply spectra-temporal analyzes methods to analyze and compare these series to explain the mutual interaction between them in different time and different frequency bands. The main problems to deal with is to estimate the deterministic (including trend and periodic variations) and stochastic (non-periodic variations and random changes described by different noise characters) components in these geodetic time series as well as to apply the appropriate methods of spectra-temporal comparison of these series. The multiple methods of time series analysis may be encouraged to be applied to the preprocessing of raw data from various geodetic measurements in order to promote the quality level of enhancement of signals existing in these data. The topic on the improvement of the edge effects in time series analysis should be also considered, since they may affect the reliability of long-range tendency (trends) estimated from data series as well as the real-time data processing and prediction. For coping with small geodetic samples one can apply simulation-based methods and if the data are sparse, Monte-Carlo simulation or bootstrap technique may be useful.

Measurements by space geodetic techniques provide an important contribution to the understanding of climate change. The analysis of Earth rotation and geophysical time series as well as global sea level variations shows that there is a mutual relationship between them for oscillations with periods from a few days to decades. The thermal annual cycle caused by the Earth's orbital motion modified by variable solar activity induces seasonal variations the Earth’s fluid layers, thus in the Earth rotation, sea level variations as well as in the changes of the Earth's gravity field and centre of mass. The interrelationships between the geodetic time series and changes of global troposphere temperature show that they provide very important information about the Earth's climate change (for example global sea level increases faster during El Nino events associated with the increase of global temperature and in this time the increase of length of day can be also noticed). Thus, the spectra-temporal analysis and comparison of geodetic time series should also include time series associated with solar activity.

### Objectives

- Study of the nature of geodetic time series to choose optimum time series analysis methods for filtering, spectral analysis, time frequency analysis and prediction.
- Study of Earth's geometry, rotation and gravity field variations and their geophysical causes in different frequency bands.
- Evaluation of appropriate covariance matrices for the time series by applying the law of error propagation to the original measurements, including weighting schemes, regularization, etc.
- Determination of the statistical significance levels of the results obtained by different time series analysis methods and algorithms applied to geodetic time series.
- Comparison of different time series analysis methods in order to point out their advantages and disadvantages.
- Application and development of time frequency analysis methods to detect the relationship between geodetic time series and time series associated with the solar activity in order to solve the problems related to the climate change.
- Recommendations of different time series analysis methods for solving problems concerning specific geodetic time series.
- Detection of reliable station velocities and their uncertainties with taking into account their non-linear motion and environmental loadings and identification of site clusters with similar velocities
- Deterministic and stochastic modelling and prediction of troposphere and ionosphere parameters for real time precise GNSS positioning.
- Better Earth Orientation Parameters short-term prediction using the extrapolation models of the fluid excitation functions.

### Program of activities

- Organization of a session on time series analysis in geodesy at the Hotine-Marussi Symposium in 2022.
- Co-organization of the PICO sessions "Mathematical methods for the analysis of potential field data and geodetic time series" at the European Geosciences Union General Assemblies in Vienna, Austria.

### Membership

* Wieslaw Kosek (Poland), chair Orhan Akyilmaz (Turkey) Johannes Boehm (Austria) Xavier Collilieux (France) Olivier de Viron (France) Laura Fernandez (Argentina) Richard Gross (USA) Mahmut O. Karslioglu (Turkey) Anna Kłos (Poland) Hans Neuner (Germany) Tomasz Niedzielski (Poland) Sergei Petrov (Russia) Waldemar Popiński (Poland) Michael Schmidt (Germany) Michel Van Camp (Belgium) Jan Vondrák (Czech Republic) Dawei Zheng (China) Yonghong Zhou (China) *