G1.1

Water mass changes at and below the surface of the Earth cause changes in the Earth’s gravity field which can be observed by at least three geodetic observation techniques: ground-based point measurements using terrestrial gravimeters, space-borne gravimetric satellite missions (GRACE and GRACE-FO) and geometrical deformations of the Earth’s crust observed by GNSS. Combining these techniques promises the opportunity to compute the most accurate (regional) water mass change time series with the highest possible spatial and temporal resolution, which is the goal of a joint project with the interdisciplinary DFG Collaborative Research Centre (SFB 1464) "TerraQ – Relativistic and Quantum-based Geodesy".

A method well suited for data combination of time-variable quantities is the Kalman filter algorithm, which sequentially updates water storage changes by combining a prediction step with observations from the next time step. As opposed to the standard way of describing gravity field variations by global spherical harmonics, we will introduce space-localizing radial basis functions as a more suitable parameterization of high-resolution regional water storage change. A closed-loop simulation environment has been set up to allow the testing of the setup and the tuning of the algorithm. In a first step only simulated GRACE data together with realistic correlated observation errors will be used in the Kalman filter to sequentially update the parameters of a regional gravity field model. However, the implementation was designed to flexibly include further observation techniques (GNSS, terrestrial gravimetry) at a later stage. This presentation will outline the Kalman filter framework, introduce the regional parameterization approach, and address challenges related to, e.g., ill-conditioned matrices and the proper choice of the radial basis function parameterization.

How to cite: Wöhnke, V., Eicker, A., Jensen, L., and Weigelt, M.: Regional modeling of water storage variations in a Kalman filter framework, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-2447, https://doi.org/10.5194/egusphere-egu22-2447, 2022.

The approximation of the gravitational potential is still of interest in geodesy as it is utilized, e.g., for the mass transport of the Earth. The Inverse Problem Matching Pursuits (IPMPs) were proposed as alternative solvers for these kind of problems. They were successfully tested on diverse applications, including the downward continuation of the gravitational potential.

It is well-known that, for such linear inverse problems on the sphere, there exist a variety of global as well as local basis systems, e.g. spherical harmonics, Slepian functions as well as radial basis functions and wavelets. Each type has its specific pros and cons. Nonetheless, approximations are often represented in only one of them. On the contrary, the IPMPs enable an approximation as a mixture of diverse trial functions. They are chosen iteratively from an intentionally overcomplete dictionary such that the Tikhonov functional is reduced. However, an a-priori defined, finite dictionary has its own drawbacks, in particular with respect to efficiency.

Thus, we developed a learning add-on which uses an infinite dictionary instead while simultaneously reducing the computational cost. The add-on is implemented as constrained non-linear optimization problems with respect to the characteristic parameters of the different basis systems. In this talk, we give details on the matching pursuits and, in particular, the learning add-on and show recent numerical results with respect to the downward continuation of the gravitational potential.

How to cite: Schneider, N. and Michel, V.: Experimenting with automatized numerical methods, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-2963, https://doi.org/10.5194/egusphere-egu22-2963, 2022.

We establish a theoretical framework, an algorithmic basis, and a computational workflow for the statistical analysis of multi-variate multi-dimensional random fields - sampled (possibly irregularly, with missing data) and finite (possibly bounded irregularly). Our research is practically motivated by geodetic and scientific problems of topography and gravity analysis in geophysics and planetary physics, but our solutions fulfill the more general need for sophisticated methods of inference that can be applied to massive remote-sensing data sets, and as such, our mathematical, statistical, and computational solutions transcend any particular application. The generic problem that we are addressing is: two (or more) spatial fields are observed, e.g., by passive or active sensing, and we desire a parsimonious statistical description of them, individually and in their relation to one another. We consider the fields to be realizations of a random process, parameterized as a Matern covariance structure, a very flexible description that includes, as special cases, many of the known models in popular use (e.g. exponential, autoregressive, von Karman, Gaussian, Whittle, ...) Our fundamental question is how to find estimates of the parameters of a Matern process, and the distribution of those estimates for uncertainty quantification. Our answer is, fundamentally: via maximum-likelihood estimation.  We now provide a computationally and statistically efficient method for estimating the parameters of a stochastic covariance model observed on a regular spatial grid in any number of dimensions. Our proposed method, which we call the Debiased Spatial Whittle likelihood, makes important corrections to the well-known Whittle likelihood to account for large sources of bias caused by boundary effects and aliasing. We generalise the approach to flexibly allow for significant volumes of missing data including those with lower-dimensional substructure, and for irregular sampling boundaries. We build a theoretical framework under relatively weak assumptions which ensures consistency and asymptotic normality in numerous practical settings including missing data and non-Gaussian processes. We also extend our consistency results to multivariate processes. We provide detailed implementation guidelines which ensure the estimation procedure can still be conducted in O(n log n) operations, where n is the number of points of the encapsulating rectangular grid, thus keeping the computational scalability of Fourier and Whittle-based methods for large data sets. We validate our procedure over a range of simulated and real world settings, and compare with state-of-the-art alternatives, demonstrating the enduring practical appeal of Fourier-based methods, provided they are corrected and augmented by the procedures that we developed.

How to cite: Simons, F. J., Guillaumin, A. P., Sykulski, A. M., and Olhede, S. C.: Efficient Parameter Estimation of Sampled Random Fields Using the Debiased Spatial Whittle Likelihood, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-10879, https://doi.org/10.5194/egusphere-egu22-10879, 2022.

In this study, the effects of seasonal variation on the vertical position accuracy of GPS calculated by time series analysis of continuous GPS stations were investigated. Weather changes, water vapor in the atmosphere affect the position accuracy of GPS and cause fluctuations in GPS height values. It is also known that the height component has more air passage changes. Since it is easier to interpret the effects of the height component due to its topographic features and seasonal changes are more effective than the rest of the country, four continuous GPS stations, covering the 2014-2019 date range, from the Turkish National Permanent GNSS Network (TUSAGA-Aktif) were used in the East of Turkey were chosen. The daily coordinates of the stations were obtained as a result of GAMIT/GLOBK software solution. By applying time series analysis to the daily coordinate values of the stations, statistically significant trend, periodic and stochastic components of the stations were determined. As a result of the analysis, the vertical annual velocities of the stations and the standard deviations of the velocities were determined.

For the stations determined according to the ellipsoid heights, the velocity and standard deviation values of the height component were calculated for each month, season and year. As the ellipsoid height increases, the velocity and its standard deviation values decrease. While the minimum velocity values are observed for the station with the lowest ellipsoidal height in winter, for the station with the highest ellipsoidal height in autumn, the minimum their standard deviation values are determined in winter for the station with the lowest ellipsoidal height, and in summer for the station with the highest ellipsoidal height. According to the results obtained, the coordinate displacements caused by seasonal variation may be important and their effects should be considered especially in high precision geodetic surveys.

In addition, the velocity values of the stations were calculated for different years, and a decrease was observed in the height component depending on the observation duration. As the observation duration for the height component increases, both the velocity values and their standard deviation values decrease. In order to avoid velocity estimation error completely, the data length should be more than 4.5 years.

Keywords: GPS height compenent, GPS time series, Seasonal effect, Velocity estimation

How to cite: Tekin Ünlütürk, N. and Doğan, U.: The Effects of Seasonal Variation on GPS Height Component, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-1590, https://doi.org/10.5194/egusphere-egu22-1590, 2022.

Understanding and modelling the properties of the stochastic variability -- often referred to as noise -- in geodetic time series is crucial to obtain realistic uncertainties for deterministic parameters, e.g., long-term velocities, and helpful in characterizing non-modelled processes. With the ever-increasing span of geodetic time series, it is expected that additional observations would help better understanding the low-frequency properties of the stochastic variability. In the meantime, recent studies evidenced that the choice of the functional model for the time series may bias the assessment of these low-frequency stochastic properties. In particular, the presence of frequent offsets, or step discontinuities, in position time series tends to systematically flatten the periodogram of position residuals at low frequencies and prevents the detection of possible random-walk-type variability.

In this study, we investigate the ability of frequently-used statistical tools, namely the Lomb-Scargle periodogram and Maximum Likelihood Estimation (MLE) method, to correctly retrieve low-frequency stochastic properties of geodetic time series in the presence of frequent offsets. By evaluating the biases of each method for several functional models, we demonstrate that neither of these tools is reliable for low-frequency investigation. By assessing alternative approaches, we show that using  Least-Squares Harmonic Estimation and Restricted Maximum Likelihood Estimation (RMLE) solves part of the problems reported by previous works. However, we evidence that, even when using those optimal methods, the presence of frequent offsets inevitably blurs the estimated low-frequency properties of geodetic time series by increasing low-frequency stochastic parameter uncertainties more than that of other stochastic parameters.

How to cite: Gobron, K., Rebischung, P., de Viron, O., Demoulin, A., and Van Camp, M.: Impact of Offsets on Assessing the Low-Frequency Stochastic Properties of Geodetic Time Series, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-3605, https://doi.org/10.5194/egusphere-egu22-3605, 2022.

Considering that the precise orbit and clock products provided by international GNSS service (IGS) were of a magnitude different from those required by the global geodetic observing system (GGOS) in accuracy of 1 mm, the Lomb-Scargle periodogram was used to analyze the systematic deviation and the periodical deviation between the precise products of GNSS analysis centers (ACs) and the IGS final precision products. On this basis, a deviation correction model was established based on the least square method for the correction of precision parameters. The deviation correction results show that the standard deviation of the precise clock decreases by 15.4% on average, the standard deviation of the radial orbit decreases by 33.3% on average, and the standard deviation of the ensemble effects of radial orbit and clock decreases by 24.0% on average. The signal-in-space user ranging error (SISURE) also significantly decreases from the level of centimeters to millimeters. The positioning verification results of the 15 stations show that the consistency between the positioning results of the precision products using single AC and the positioning results of IGS final precision products is also improved after deviation correction, and the average improvement ratio of three ACs is 14.3%. It is proved that the deviation correction model can effectively improve the consistency between the precision products of ACs and the final products of IGS.

How to cite: Hou, Y., Chen, J., and Zhang, Y.: Characteristics analysis and correction of GPS precise products in analysis centers based on Lomb-Scargle periodogram, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-6864, https://doi.org/10.5194/egusphere-egu22-6864, 2022.