@phdthesis{Paganini2018,
  author    = {Paganini, Claudio Francesco},
  title     = {The role of trapping in black hole spacetimes},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-414686},
  school      = {Universit{\"a}t Potsdam},
  pages     = {v, 138},
  year      = {2018},
  abstract  = {In the here presented work we discuss a series of results that are all in one way or another connected to the phenomenon of trapping in black hole spacetimes. First we present a comprehensive review of the Kerr-Newman-Taub-NUT-de-Sitter family of black hole spacetimes and their most important properties. From there we go into a detailed analysis of the bahaviour of null geodesics in the exterior region of a sub-extremal Kerr spacetime. We show that most well known fundamental properties of null geodesics can be represented in one plot. In particular, one can see immediately that the ergoregion and trapping are separated in phase space. We then consider the sets of future/past trapped null geodesics in the exterior region of a sub-extremal Kerr-Newman-Taub-NUT spacetime. We show that from the point of view of any timelike observer outside of such a black hole, trapping can be understood as two smooth sets of spacelike directions on the celestial sphere of the observer. Therefore the topological structure of the trapped set on the celestial sphere of any observer is identical to that in Schwarzschild. We discuss how this is relevant to the black hole stability problem. In a further development of these observations we introduce the notion of what it means for the shadow of two observers to be degenerate. We show that, away from the axis of symmetry, no continuous degeneration exists between the shadows of observers at any point in the exterior region of any Kerr-Newman black hole spacetime of unit mass. Therefore, except possibly for discrete changes, an observer can, by measuring the black holes shadow, determine the angular momentum and the charge of the black hole under observation, as well as the observer's radial position and angle of elevation above the equatorial plane. Furthermore, his/her relative velocity compared to a standard observer can also be measured. On the other hand, the black hole shadow does not allow for a full parameter resolution in the case of a Kerr-Newman-Taub-NUT black hole, as a continuous degeneration relating specific angular momentum, electric charge, NUT charge and elevation angle exists in this case. We then use the celestial sphere to show that trapping is a generic feature of any black hole spacetime. In the last chapter we then prove a generalization of the mode stability result of Whiting (1989) for the Teukolsky equation for the case of real frequencies. The main result of the last chapter states that a separated solution of the Teukolsky equation governing massless test fields on the Kerr spacetime, which is purely outgoing at infinity, and purely ingoing at the horizon, must vanish. This has the consequence, that for real frequencies, there are linearly independent fundamental solutions of the radial Teukolsky equation which are purely ingoing at the horizon, and purely outgoing at infinity, respectively. This fact yields a representation formula for solutions of the inhomogenous Teukolsky equation, and was recently used by Shlapentokh-Rothman (2015) for the scalar wave equation.},
  language  = {en}
}
@phdthesis{Wendi2018,
  author    = {Wendi, Dadiyorto},
  title     = {Recurrence Plots and Quantification Analysis of Flood Runoff Dynamics},
  doi       = {10.25932/publishup-43191},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-431915},
  school      = {Universit{\"a}t Potsdam},
  pages     = {114},
  year      = {2018},
  abstract  = {This paper introduces a novel measure to assess similarity between event hydrographs. It is based on Cross Recurrence Plots and Recurrence Quantification Analysis which have recently gained attention in a range of disciplines when dealing with complex systems. The method attempts to quantify the event runoff dynamics and is based on the time delay embedded phase space representation of discharge hydrographs. A phase space trajectory is reconstructed from the event hydrograph, and pairs of hydrographs are compared to each other based on the distance of their phase space trajectories. Time delay embedding allows considering the multi-dimensional relationships between different points in time within the event. Hence, the temporal succession of discharge values is taken into account, such as the impact of the initial conditions on the runoff event. We provide an introduction to Cross Recurrence Plots and discuss their parameterization. An application example based on flood time series demonstrates how the method can be used to measure the similarity or dissimilarity of events, and how it can be used to detect events with rare runoff dynamics. It is argued that this methods provides a more comprehensive approach to quantify hydrograph similarity compared to conventional hydrological signatures.},
  language  = {en}
}
@phdthesis{Roezer2018,
  author    = {R{\"o}zer, Viktor},
  title     = {Pluvial flood loss to private households},
  doi       = {10.25932/publishup-42991},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-429910},
  school      = {Universit{\"a}t Potsdam},
  pages     = {XXII, 109},
  year      = {2018},
  abstract  = {Today, more than half of the world's population lives in urban areas. With a high density of population and assets, urban areas are not only the economic, cultural and social hubs of every society, they are also highly susceptible to natural disasters. As a consequence of rising sea levels and an expected increase in extreme weather events caused by a changing climate in combination with growing cities, flooding is an increasing threat to many urban agglomerations around the globe. To mitigate the destructive consequences of flooding, appropriate risk management and adaptation strategies are required. So far, flood risk management in urban areas is almost exclusively focused on managing river and coastal flooding. Often overlooked is the risk from small-scale rainfall-triggered flooding, where the rainfall intensity of rainstorms exceeds the capacity of urban drainage systems, leading to immediate flooding. Referred to as pluvial flooding, this flood type exclusive to urban areas has caused severe losses in cities around the world. Without further intervention, losses from pluvial flooding are expected to increase in many urban areas due to an increase of impervious surfaces compounded with an aging drainage infrastructure and a projected increase in heavy precipitation events. While this requires the integration of pluvial flood risk into risk management plans, so far little is known about the adverse consequences of pluvial flooding due to a lack of both detailed data sets and studies on pluvial flood impacts. As a consequence, methods for reliably estimating pluvial flood losses, needed for pluvial flood risk assessment, are still missing. Therefore, this thesis investigates how pluvial flood losses to private households can be reliably estimated, based on an improved understanding of the drivers of pluvial flood loss. For this purpose, detailed data from pluvial flood-affected households was collected through structured telephone- and web-surveys following pluvial flood events in Germany and the Netherlands. Pluvial flood losses to households are the result of complex interactions between impact characteristics such as the water depth and a household's resistance as determined by its risk awareness, preparedness, emergency response, building properties and other influencing factors. Both exploratory analysis and machine-learning approaches were used to analyze differences in resistance and impacts between households and their effects on the resulting losses. The comparison of case studies showed that the awareness around pluvial flooding among private households is quite low. Low awareness not only challenges the effective dissemination of early warnings, but was also found to influence the implementation of private precautionary measures. The latter were predominately implemented by households with previous experience of pluvial flooding. Even cases where previous flood events affected a different part of the same city did not lead to an increase in preparedness of the surveyed households, highlighting the need to account for small-scale variability in both impact and resistance parameters when assessing pluvial flood risk. While it was concluded that the combination of low awareness, ineffective early warning and the fact that only a minority of buildings were adapted to pluvial flooding impaired the coping capacities of private households, the often low water levels still enabled households to mitigate or even prevent losses through a timely and effective emergency response. These findings were confirmed by the detection of loss-influencing variables, showing that cases in which households were able to prevent any loss to the building structure are predominately explained by resistance variables such as the household's risk awareness, while the degree of loss is mainly explained by impact variables. Based on the important loss-influencing variables detected, different flood loss models were developed. Similar to flood loss models for river floods, the empirical data from the preceding data collection was used to train flood loss models describing the relationship between impact and resistance parameters and the resulting loss to building structures. Different approaches were adapted from river flood loss models using both models with the water depth as only predictor for building structure loss and models incorporating additional variables from the preceding variable detection routine. The high predictive errors of all compared models showed that point predictions are not suitable for estimating losses on the building level, as they severely impair the reliability of the estimates. For that reason, a new probabilistic framework based on Bayesian inference was introduced that is able to provide predictive distributions instead of single loss estimates. These distributions not only give a range of probable losses, they also provide information on how likely a specific loss value is, representing the uncertainty in the loss estimate. Using probabilistic loss models, it was found that the certainty and reliability of a loss estimate on the building level is not only determined by the use of additional predictors as shown in previous studies, but also by the choice of response distribution defining the shape of the predictive distribution. Here, a mix between a beta and a Bernoulli distribution to account for households that are able to prevent losses to their building's structure was found to provide significantly more certain and reliable estimates than previous approaches using Gaussian or non-parametric response distributions. The successful model transfer and post-event application to estimate building structure loss in Houston, TX, caused by pluvial flooding during Hurricane Harvey confirmed previous findings, and demonstrated the potential of the newly developed multi-variable beta model for future risk assessments. The highly detailed input data set constructed from openly available data sources containing over 304,000 affected buildings in Harris County further showed the potential of data-driven, building-level loss models for pluvial flood risk assessment. In conclusion, pluvial flood losses to private households are the result of complex interactions between impact and resistance variables, which should be represented in loss models. The local occurrence of pluvial floods requires loss estimates on high spatial resolutions, i.e. on the building level, where losses are variable and uncertainties are high. Therefore, probabilistic loss estimates describing the uncertainty of the estimate should be used instead of point predictions. While the performance of probabilistic models on the building level are mainly driven by the choice of response distribution, multi-variable models are recommended for two reasons: First, additional resistance variables improve the detection of cases in which households were able to prevent structural losses. Second, the added variability of additional predictors provides a better representation of the uncertainties when loss estimates from multiple buildings are aggregated. This leads to the conclusion that data-driven probabilistic loss models on the building level allow for a reliable loss estimation at an unprecedented level of detail, with a consistent quantification of uncertainties on all aggregation levels. This makes the presented approach suitable for a wide range of applications, from decision support in spatial planning to impact- based early warning systems.},
  language  = {en}
}
@phdthesis{Angermann2018,
  author    = {Angermann, Lisa},
  title     = {Hillslope-stream connectivity across scales},
  doi       = {10.25932/publishup-42454},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-424542},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xix, 193},
  year      = {2018},
  abstract  = {The concept of hydrologic connectivity summarizes all flow processes that link separate regions of a landscape. As such, it is a central theme in the field of catchment hydrology, with influence on neighboring disciplines such as ecology and geomorphology. It is widely acknowledged to be an important key in understanding the response behavior of a catchment and has at the same time inspired research on internal processes over a broad range of scales. From this process-hydrological point of view, hydrological connectivity is the conceptual framework to link local observations across space and scales. This is the context in which the four studies this thesis comprises of were conducted. The focus was on structures and their spatial organization as important control on preferential subsurface flow. Each experiment covered a part of the conceptualized flow path from hillslopes to the stream: soil profile, hillslope, riparian zone, and stream. For each study site, the most characteristic structures of the investigated domain and scale, such as slope deposits and peat layers were identified based on preliminary or previous investigations or literature reviews. Additionally, further structural data was collected and topographical analyses were carried out. Flow processes were observed either based on response observations (soil moisture changes or discharge patterns) or direct measurement (advective heat transport). Based on these data, the flow-relevance of the characteristic structures was evaluated, especially with regard to hillslope to stream connectivity. Results of the four studies revealed a clear relationship between characteristic spatial structures and the hydrological behavior of the catchment. Especially the spatial distribution of structures throughout the study domain and their interconnectedness were crucial for the establishment of preferential flow paths and their relevance for large-scale processes. Plot and hillslope-scale irrigation experiments showed that the macropores of a heterogeneous, skeletal soil enabled preferential flow paths at the scale of centimeters through the otherwise unsaturated soil. These flow paths connected throughout the soil column and across the hillslope and facilitated substantial amounts of vertical and lateral flow through periglacial slope deposits. In the riparian zone of the same headwater catchment, the connectivity between hillslopes and stream was controlled by topography and the dualism between characteristic subsurface structures and the geomorphological heterogeneity of the stream channel. At the small scale (1 m to 10 m) highest gains always occurred at steps along the longitudinal streambed profile, which also controlled discharge patterns at the large scale (100 m) during base flow conditions (number of steps per section). During medium and high flow conditions, however, the impact of topography and parafluvial flow through riparian zone structures prevailed and dominated the large-scale response patterns. In the streambed of a lowland river, low permeability peat layers affected the connectivity between surface water and groundwater, but also between surface water and the hyporheic zone. The crucial factor was not the permeability of the streambed itself, but rather the spatial arrangement of flow-impeding peat layers, causing increased vertical flow through narrow "windows" in contrast to predominantly lateral flow in extended areas of high hydraulic conductivity sediments. These results show that the spatial organization of structures was an important control for hydrological processes at all scales and study areas. In a final step, the observations from different scales and catchment elements were put in relation and compared. The main focus was on the theoretical analysis of the scale hierarchies of structures and processes and the direction of causal dependencies in this context. Based on the resulting hierarchical structure, a conceptual framework was developed which is capable of representing the system's complexity while allowing for adequate simplifications. The resulting concept of the parabolic scale series is based on the insight that flow processes in the terrestrial part of the catchment (soil and hillslopes) converge. This means that small-scale processes assemble and form large-scale processes and responses. Processes in the riparian zone and the streambed, however, are not well represented by the idea of convergence. Here, the large-scale catchment signal arrives and is modified by structures in the riparian zone, stream morphology, and the small-scale interactions between surface water and groundwater. Flow paths diverge and processes can better be represented by proceeding from large scales to smaller ones. The catchment-scale representation of processes and structures is thus the conceptual link between terrestrial hillslope processes and processes in the riparian corridor.},
  language  = {en}
}