Analyzing and modeling environmental loading induced displacements with GPS and GRACE

The redistribution of atmospheric, oceanic and hydrological masses on the Earth's surface varies in time and this in turn loads and deforms the surface of the solid Earth. Analyzing such environmental loading signal and modeling its induced elastic displacements are of great importance for explaining geophysical phenomena. Based on the well-established loading theory, this thesis makes use of two different space-borne measurements, i.e. GPS and GRACE, along with other environmental loading data to investigate three different aspects of environmental loading and its induced elastic deformations: Firstly, an increasing concern is observed recently over time variable seasonal signals in geodesy. Several model based approaches were applied to extract amplitude and phase modulated annual and semiannual signals. In view of this phenomenon, this thesis introduces an alternative approach, namely, singular spectrum analysis (SSA). With respect to these model-dependent approaches, the advantage of SSA lies in data-driven and model-independence. Several aspects regarding the application of SSA, e.g. optimal choice of window size, are investigated before showing its abilities. Through applying SSA to the lake level time series of Lake Urmia (Iran) and the basin averaged equivalent water height time series of the Congo basin, the capabilities of SSA in separating time varying seasonal signals are demonstrated. In addition, we find that SSA is also able to extract the non-linear trend as well as long-term oscillations from geodetic time series. Secondly, we look into the comparison between GPS and GRACE with an emphasis on GRACE data filtering. Three types of deterministic filters and two types of stochastic filters are studied and compared over GPS sites from two regions, i.e. the Europe area and the Amazon area. The comparisons indicate that no single filtering scheme could provide consistently better performance over other considered filters. However, we find that the stochastic filters generally show better performance than the deterministic filters. The DDK 1 filter outperforms other filters in the Europe area and the regularization filter of parameter lambda=4, which follows the concept of the DDK filters, shows optimal performance in the Amazon area. The combination of the isotropic Gaussian filter of a low smoothing radius, e.g. around 300 km with the destriping filter is proved to be optimal filter choice if only the deterministic filters are considered. Thirdly, based on an overview of displacements modeling at various spatial scales, we evaluate three methods, i.e. two types of half-space approaches and the classic Green function approach, by using a high spatial resolution local load data along the lower Mississippi river when a severe flood happened in 2011. The equivalence between the two half-space approaches, i.e. point load approach and surface load approach, are demonstrated with the local load data. However, the point load approach is recommended for practical use in terms of computational efficiency. In addition, within such a limited spatial extent, we investigate the differences between the half-space approach and the Green function approach. It is shown that the half-space approach predicts larger displacements than the Green function approach and agrees better with the observed deformations at 11 considered GPS sites. Meanwhile, strong global environmental loading effects are found via two global hydrological models, i.e. GLDAS and MERRA. Thus, a reduction of these far-field loading effects beforehand is suggested before probing the local crustal structure using the half-space approach. Last but not least, based on the local load data, the effects of site-dependent Green functions are studied with two types of site-dependent Green functions, which were generated by modifying the local crustal structure of the REF Earth model using the CRUST 1.0 and CRUST 2.0 models. A relative RMS of differences of more than 5% in vertical component and 25% in horizontal components are found with respect to the PREM Earth model based Green functions. It indicates that the Green functions could contribute more uncertainties in loading induced displacements modeling than reported in the literature. Die Massenumverteilungen zwischen Atmosphare, Ozeanen und Hydrologie der Erdoberflache variieren stetig und fuhren im Gegenzug zu Auflasten und Deformationen der festen Erde. Die Untersuchung dieser Auflastsignale und die Modellierung der induzierten elastischen Verformungen sind von enormer Bedeutung fur die Erklarungen geophysikalischer Phanomene. Basierend auf gangigen Theorien werden in dieser Dissertation die beiden Satellitenverfahren GPS und GRACE zusammen mit anderen Auflastdaten genutzt, um drei Aspekte von Auflasten und die von diesen verursachte elastischen Deformationen naher zu untersuchen: Zunachst lasst sich in der Geodasie eine wachsende Tendenz erkennen, auch zeitlich variable, saisonale Signale besser zu untersuchen. Zahlreiche, auf Modellen basierende Verfahren werden angewendet, um Amplituden und Phasen aus jahrlichen und halbjahrlichen Signalen zu erfassen. Fur diese Aufgabe wird in dieser Arbeit die "singular spectrum analysis" (SSA) als alternative Methode dargestellt. Im Gegensatz zu den ublichen modellbasierten Verfahren arbeitet die SSA modellunabhangig nur auf Grundlage der Daten. Verschiedene Freiheitsgrade in der SSA, wie zum Beispiel die Wahl der optimalen Fenstergrose, werden vor der Verwendung untersucht. Die Fahigkeit der SSA, saisonale Signale zu trennen, wird sowohl an der Bestimmung des Wasserstandes fur den Urmia-See (Iran) als auch anhand der Zeitreihe der uber dem Kongo-Becken gemittelten Massenanderungen demonstriert. Zusatzlich konnen mit SSA auch nichtlineare Trends und langfristige Oszillationen aus geodatischen Zeitreihen extrahiert werden. Zweitens werden die Daten von GPS und GRACE unter besonderer Berucksichtigung der Filterung von GRACE-Daten verglichen. Drei Arten deterministischer Filter sowie zwei Arten stochastischer Filter werden untersucht und fur die GPS-Stationen von zwei ausgewahlten Regionen in Mitteleuropa und dem Amazonasgebiet gegenubergestellt. Der Vergleich bestatigt, dass keiner der Filter grundsatzlich den Anderen uberlegen ist. Jedoch kann gezeigt werden, dass die stochastischen Filter im Allgemeinen besser abschneiden als die deterministischen Ansatze. Der DDK 1 Filter fuhrt in Europa zu den besten Ergebnissen, wahrend ein "Regularisierungsfilter", der dem Konzept der DDK Filter nachempfunden ist, mit einem Regularisierungsparameter lambda = 4 die besten Ergebnisse in fur das Amazonasbecken liefert. Die Kombination aus einem isotropen Gausfilter mit kleinem Glattungsradius, z.B. 300 km, und einem "De-striping"-Filter konnte als optimaler Filter bestatigt werden, solange nur deterministische Filter verwendet werden Drittens werden nach einer Zusammenfassung der Deformationsmodelle auf verschiedenen raumlichen Skalen drei Methoden -- zwei Arten von "half-space"-Ansatzen und die klassische Methode der Greenfunktionen -- auf die raumlich hochauflosenden Daten der Uberflutungen im Mississippi-Becken (2011) angewendet. Die Gleichwertigkeit der beiden "half-space"-Ansatze, einerseits der "point load approach" und andererseits der "surface load approach" werden fur lokale Auflastdaten bestatigt. Aus Grunden der numerischen Effizienz ist jedoch der "point load approach" zu bevorzugen. Auserdem werden innerhalb des raumlich begrenzten Gebietes auch die Unterschiede zwischen den "half-space"-Ansatzen und die Methode der Greenfunktionen gegenubergestellt. Es wird gezeigt, dass die "half-space"-Ansatze grosere Deformationen vorhersagen als die Greenfunktionen, wobei die Ergebnisse besser zu den Beobachtungen der 11 GPS-Stationen passen. Inzwischen konnen auch grosere globale Auflasteffekte in den globalen hydrologischen Modellen, wie z.B. GLDAS und MERRA, gefunden werden. Daher wird eine vorherige Reduktion der Fernwirkung von Auflasteffekten empfohlen, ehe man eine lokale Krustenstruktur mit den "half-space"-Ansatzen erforscht. Nicht zuletzt werden auch die Effekte der ortsabhangigen Greenfunktionen fur die lokalen Auflastdaten studiert, wobei die beiden ortsabhangen Varianten der Greenfunktionen aus der lokalen Krustenstruktrur des REF Erdmodells mit den Modellen CRUST 1.0 bzw. CRUST 2.0 erzeugt werden. Im Vergleich zu den Greenfunktionen aus dem PERM Erdmodell wird ein relativer RMS der Differenzen von mehr als 5% in der Vertikalkomponente und 25% in der Horizonalkomponente beobachtet. Daraus kann man ablesen, dass die Greenfunktionen deutlich mehr Unsicherheiten zu den auflastinduzierten Deformationen beitragen, als dies bisher in der Literatur wahrgenommen wird.

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