Estimation of Terrestrial Water Storage Variations in Sichuan-Yunnan Region from GPS Observations Using Independent Component Analysis

GPS can be used to measure land motions induced by mass loading variations on the Earth’s surface. This paper presents an independent component analysis (ICA)-based inversion method that uses vertical GPS coordinate time series to estimate the change of terrestrial water storage (TWS) in the Sichuan-Yunnan region in China. The ICA method was applied to extract the hydrological deformation signals from the vertical coordinate time series of GPS stations in the Sichuan-Yunnan region from the Crustal Movement Observation Network of China (CMONC). These vertical deformation signals were then inverted to TWS variations. Comparative experiments were conducted based on Gravity Recovery and Climate Experiment (GRACE) data and a hydrological model for validation. The results demonstrate that the TWS changes estimated from GPS(ICA) deformations are highly correlated with the water variations derived from the GRACE data and hydrological model in Sichuan-Yunnan region. The TWS variations are overestimated by the vertical GPS observations the northwestern Sichuan-Yunnan region. The anomalies are likely caused by inaccurate atmospheric loading correction models or residual tropospheric errors in the region with high topographic variability and can be reduced by ICA preprocessing.

Predictive Temporal Analytics Method in Situational Modeling of the Evolution of Complex Systems

The article discusses the main characteristics of complex systems, as well as the structures, domains and interactions occurring in the course of evolution. The main properties of complex systems are defined to include openness, non-ergodicity, disequilibrium, activity and multiplicity of goals. The classification attributes are defined to include free energy, anthropic factor, incomplete observability, computational irreducibility, dominant coded interactions, dynamic structure and transformable environments. A variety of primary entities, which form complex systems, are represented by two classes, possible individuals and abstract individuals. The space-time structure as a 6D continuum is formulated; spatial and temporal vacuums and quanta of interaction are defined. The three-dimensional time is presented in terms of three orthogonal components: coordinate time, structural time and discrete time. The coordinate time corresponds to the variability of a system when individuals move in space; the structural time corresponds to the variability of a system when the structure of individuals changes; the discrete time corresponds to the variability of the system caused by informational interaction between or within individuals. A model of a one-time ideal event and a continuous event is defined. The interaction between individuals is presented through a two-way reflexive model of cyclic interaction of an actor and an acceptor. The occurrence of post-causes and post-effects of physical interactions is shown to result in unpredictable chains of effects. The essence of the predictive temporal analytics method is presented. The use of the method involves the construction of a six-dimensional hypergraph of cause-and-effect relations with subsequent analysis of a body of causes and effects. The optimal way of evolution of a system is considered a way that maximizes diversity (in terms of liberty of actions, states, goals achieved) and minimizes the energy costs in a certain time perspective.

Potential Contributors to Common Mode Error in Array GPS Displacement Fields in Taiwan Island

The existence of the common mode error (CME) in the continuous global navigation satellite system (GNSS) coordinate time series affects geophysical studies that use GNSS observations. To understand the potential contributors of CME in GNSS networks in Taiwan and their effect on velocity estimations, we used the principal component analysis (PCA) and independent component analysis (ICA) to filter the vertical coordinate time series from 44 high-quality GNSS stations in Taiwan island in China, with a span of 10 years. The filtering effects have been evaluated and the potential causes of the CME are analyzed. The root-mean-square values decreased by approximately 14% and 17% after spatio-temporal filtering using PCA and ICA, respectively. We then discuss the relationship between the CME sources obtained by ICA and the environmental loads. The results reveal that the independent displacements extracted by ICA correlate with the atmospheric mass loading (ATML) and land water storage mass loading (LWS) of Taiwan in terms of both its amplitude and phase. We then use the white noise plus power law noise model to quantitatively estimate the noise characteristics of the pre- and post-filtered coordinate time series based on the maximum likelihood estimation criterion. The results indicate that spatio-temporal filtering reduces the amplitude of the PL and the periodic terms in the GPS time series.

Stability analysis of circular orbits around a charged BTZ black hole spacetime in a nonlinear electrodynamics model via Lyapunov exponents

We investigate the existence and stability of both the timelike and null circular orbits for a (2 + 1)-dimensional charged BTZ black hole in Einstein-nonlinear Maxwell gravity with a negative cosmological constant. The stability analysis of orbits is performed to study the possibility of chaos in geodesic motion for a special case of black hole so-called conformally invariant Maxwell spacetime. The computations of both proper time Lyapunov exponent [Formula: see text] and coordinate time Lyapunov exponent [Formula: see text] are useful to determine the stability of these circular orbits. We observe the behavior of the ratio [Formula: see text] as a function of radius of circular orbits for the timelike case in view of different values of charge parameter. However, for the null case, we calculate only the coordinate time Lyapunov exponent [Formula: see text] as there is no proper time for massless test particles. More specifically, we further analyze the behavior of the ratio of [Formula: see text] to angular frequency [Formula: see text], so-called instability exponent as a function of charge [Formula: see text] and parameter related to cosmological constant [Formula: see text] for the particular values of other parameters.

Discontinuity Detection in GNSS Station Coordinate Time Series Using Machine Learning

Global navigation satellite systems (GNSS) provide globally distributed station coordinate time series that can be used for a variety of applications such as the definition of a terrestrial reference frame. A reliable estimation of the coordinate time series trends gives valuable information about station movements during the measured time period. Detecting discontinuities of various origins in such time series is crucial for accurate and robust velocity estimation. At present, there is no fully automated standard method for detecting discontinuities. Instead, discontinuity-catalogues are frequently used, which provide information about when a device was changed or an earthquake occurred. However, it is known that these catalogues suffer from incompleteness. This study investigates the suitability of machine learning classification algorithms that are fully data-driven to detect discontinuities caused by earthquakes in station coordinate time series without the need for external information. For this study, Japan was selected as a testing area. Ten different machine learning algorithms have been tested. It is found that Random Forest achieves the best performance with an F1 score of 0.77, a recall of 0.78, and a precision of 0.76. Overall, 525 of 565 recorded earthquakes in the test data were correctly classified. It is further highlighted that splitting the time series into chunks of 21 days leads to the best performance. Furthermore, it is beneficial to combine the three (normalized) components of the GNSS solution into one sample, and that adding the value range as an additional feature improves the result. Thus, this work demonstrates how it is possible to use machine learning algorithms to detect discontinuities in GNSS time series.

Comparative Analysis of The Correction Effect of Different Environmental Loading Products On Global GNSS Coordinate Time Series

The global navigation satellite system (GNSS) coordinate time series is affected by the environmental loading (including atmospheric loading (ATML), hydrological loading (HYDL), non-tidal oceanic loading (NTOL), etc.) and many organizations now provide grid products of these loadings. The temporal and spatial resolutions of these products, the loading models and data sources used are not the same, so the effect of correcting the nonlinear deformation of the GNSS coordinate time series is obviously different. This study mainly selects the three agencies, namely, School and Observatory of Earth Sciences (EOST) in France, German Research Center for Geosciences (GFZ) in Germany, and International Mass Loading Service (IMLS) in the United States, including 6 types of ATML models, 7 types of HYDL models and 5 NTOL models. The classification of these 18 environmental loading models was discussed, and the root mean square (RMS) reduction rate of the GNSS coordinate time series after environmental loading corrections (ELCs) was used to evaluate the performance differences of various models. Our results show that both the different models provided by the same organization and the same model provided by different organizations have different correction effects. Regardless of the models, it has a significant impact on the vertical coordinate time series. In order to correct the nonlinear deformation of the GNSS stations to the greatest extent, based on the above analysis, this study selects the optimal model combination of three environmental loadings as ECMWF_IB+MERRA2+ECCO1, and then explores its influence on the periodic signals in the GNSS coordinate time series. Research suggests that environmental loadings have a significant impact on the amplitude and phase of GNSS time series. Especially in the vertical direction, the largest RMS value can reach 8.42 mm. Before and after ELCs, the maximal difference of the annual amplitude and the half-annual amplitude at global 631 stations can reach 8.96 mm and 1.51 mm, respectively. Among them, 84.60% of the stations were corrected by the optimal environmental loading combination model, thus the nonlinear deformation was weakened.

Determination of the correlation degree between GNSS stations of Ukraine based on time series

Using GNSS for many years is the most common technology for the collection, processing, and interpretation of Earth observation data, in particular for the high-precision study of plate tectonics. The results of GNSS observations, such as coordinate time series, allow us to do continuous monitoring of stations, and modern methods of satellite observation processing provide high-precision results for geodynamic interpretation. The aim of our study is to process the results of observations by DD and PPP methods and determine the degree of correlation between GNSS stations based on coordinate time series. For our study, we selected 10 GNSS stations, which merged into two networks - Lviv (SAMB, STOY, STRY, SULP та ZLRS) and Ukrainian (BCRV, CHTK, CNIV, CRNI, GLSV та SULP). The duration of observations on each of them is about 1.5 years (2019-2020). The downloaded observation files were processed in two software packages: Gamit and GipsyX. After applying the «cleaned» procedures based on the iGPS software package, the residual time series were obtained and the coefficients of the interstation correlation matrices were calculated. After the procedure of "cleaning" the time series, we obtained the RMS value decrease for all components of the coordinates by an average of 7-30%, and some stations by 55%. Based on the obtained RMS values, we can conclude that the influence of unextracted or incorrectly modeled errors can significantly affect the results of satellite observations. The obtained interstation correlation coefficients for both networks show different results depending on the used method for processing satellite observations. The larger correlation values of the DD method can be explained by the fact that the effect of errors is distributed evenly to all network stations, whereas in the PPP method errors for each station are individual. The obtained graphs of the common-mode errors values, after their removal from the residual time series, confirm the more uniform nature of the DD method. The results of our study indicate the feasibility of using the PPP method, as the autonomous processing of stations allows you to see the real geodynamic picture of the studied region.

Imputation of GPS Coordinate Time Series Using MissForest

The global positioning system (GPS) can provide the daily coordinate time series to help geodesy and geophysical studies. However, due to logistics and malfunctioning, missing values are often “seen” in GPS time series, especially in polar regions. Acquiring a consistent and complete time series is the prerequisite for accurate and reliable statical analysis. Previous imputation studies focused on the temporal relationship of time series, and only a few studies used spatial relationships and/or were based on machine learning methods. In this study, we impute 20 Greenland GPS time series using missForest, which is a new machine learning method for data imputation. The imputation performance of missForest and that of four traditional methods are assessed, and the methods’ impacts on principal component analysis (PCA) are investigated. Results show that missForest can impute more than a 30-day gap, and its imputed time series has the least influence on PCA. When the gap size is 30 days, the mean absolute value of the imputed and true values for missForest is 2.71 mm. The normalized root mean squared error is 0.065, and the distance of the first principal component is 0.013. MissForest outperforms the other compared methods. MissForest can effectively restore the information of GPS time series and improve the results of related statistical processes, such as PCA analysis.