Berlin, Techn. Univ., Diss., 2001.

Techn. Universiẗat, Diss., 2001--Berlin.

Hillslopes are one of the basic units that mainly control water movement and flow pathways within catchments. The structure of their shallow subsurface affects water balance, e.g. infiltration, retention, and runoff. Nevertheless, there is still a gap of knowledge of the hydrological dynamics on hillslopes, notably due to the lack of generalization and transferability. To improve the knowledge of hydrological responses on hillslopes with periglacial cover beds, hydrometrical measurements have been carried out on a small spring catchment in the eastern Ore Mountains since November 2007. In addition, surface ERT measurements of several profiles were applied to enhance resolution of punctual hydrometric data. From May to December 2008 geoelectrical monitoring in nearly weekly intervals was implemented to trace seasonal moisture dynamics on the hillslope scale. To obtain the link between water content and resistivity, the parameters of Archie's law were determined using different core samples. To optimize inversion parameters and methods, the derived spatial and temporal water content distribution was compared to tensiometer data and resulting in remarkable coincidence. The measured resistivity shows a close correlation with precipitation. Depending on the amount and intensity of rain, different depths were affected by seepage water. Three different types of response to different amounts of precipitation (small, medium, high), could be differentiated. A period with a small amount causes a short interruption of the drying pattern at the surface in summer, whereas a medium amount induces a distinctive reaction at shallow depth (<0.9 m), and a high amount results in a strong response reaching down to 2 m.

Hillslopes are one of the basic units that mainly control water movement and flow pathways within catchments. The structure of their shallow subsurface affects water balance, e.g. infiltration, retention, and runoff. Nevertheless, there is still a gap of knowledge of the hydrological dynamics on hillslopes, notably due to the lack of generalization and transferability. To improve the knowledge of hydrological responses on hillslopes with periglacial cover beds, hydrometrical measurements have been carried out on a small spring catchment in the eastern Ore Mountains since November 2007. In addition, surface ERT measurements of several profiles were applied to enhance resolution of punctual hydrometric data. From May to December 2008 geoelectrical monitoring in nearly weekly intervals was implemented to trace seasonal moisture dynamics on the hillslope scale. To obtain the link between water content and resistivity, the parameters of Archie's law were determined using different core samples. To optimize inversion parameters and methods, the derived spatial and temporal water content distribution was compared to tensiometer data and resulting in remarkable coincidence. The measured resistivity shows a close correlation with precipitation. Depending on the amount and intensity of rain, different depths were affected by seepage water. Three different types of response to different amounts of precipitation (small, medium, high), could be differentiated. A period with a small amount causes a short interruption of the drying pattern at the surface in summer, whereas a medium amount induces a distinctive reaction at shallow depth (<0.9 m), and a high amount results in a strong response reaching down to 2 m.

Die vorliegende Arbeit befasst sich mit der Fragestellung, inwiefern sich gegebene Verfahren zur Approximation von rationalen Krylow-Räumen zur Berechnung von Matrixfunktionen eignen. Als Modellproblem wird dazu eine 2.5D-Formulierung eines Problems aus der Gleichstrom-Geoelektrik mit finiten Elementen formuliert und dann mittels Matrixfunktionen auf rationalen Krylow-Unterräumen gelöst. Ein weiterer Teil beschäftigt sich mit dem Vergleich zweier Verfahren zur Transformation bestehender rationaler Krylow-Räume. Bei beiden Varianten werden die zugrunde liegenden Pole getauscht ohne dass ein explizites Invertieren von Matrizen notwendig ist. In dieser Arbeit werden die über mehrere Publikationen verteilten Grundlagen einheitlich zusammengetragen und fehlende Zusammenhänge ergänzt. Beide Verfahren eignen sich prinzipiell um rationale Krylow-Räume zu approximieren. Dies wird anhand mehrerer Beispiele gezeigt. Anhand des Modellproblems werden Beschränkungen der Methoden verdeutlicht.