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Scientific inquiry requires that we formulate not only what we know, but also what we do not know and by how much. In climate data analysis, this involves an accurate specification of measured quantities and a consequent analysis that consciously propagates the measurement errors at each step. The dissertation presents a thorough analytical method to quantify errors of measurement inherent in paleoclimate data. An additional focus are the uncertainties in assessing the coupling between different factors that influence the global mean temperature (GMT).
Paleoclimate studies critically rely on `proxy variables' that record climatic signals in natural archives. However, such proxy records inherently involve uncertainties in determining the age of the signal. We present a generic Bayesian approach to analytically determine the proxy record along with its associated uncertainty, resulting in a time-ordered sequence of correlated probability distributions rather than a precise time series. We further develop a recurrence based method to detect dynamical events from the proxy probability distributions. The methods are validated with synthetic examples and
demonstrated with real-world proxy records. The proxy estimation step reveals the interrelations between proxy variability and uncertainty. The recurrence analysis of the East Asian Summer Monsoon during the last 9000 years confirms the well-known `dry' events at 8200 and 4400 BP, plus an additional significantly dry event at 6900 BP.
We also analyze the network of dependencies surrounding GMT. We find an intricate, directed network with multiple links between the different factors at multiple time delays. We further uncover a significant feedback from the GMT to the El Niño Southern Oscillation at quasi-biennial timescales. The analysis highlights the need of a more nuanced formulation of influences between different climatic factors, as well as the limitations in trying to estimate such dependencies.

Pulsar wind nebulae (PWNe) are the most abundant TeV gamma-ray emitters in the Milky Way. The radiative emission of these objects is powered by fast-rotating pulsars, which donate parts of their rotational energy into winds of relativistic particles. This thesis presents an in-depth study of the detected population of PWNe at high energies. To outline general trends regarding their evolutionary behaviour, a time-dependent model is introduced and compared to the available data. In particular, this work presents two exceptional PWNe which protrude from the rest of the population, namely the Crab Nebula and N 157B. Both objects are driven by pulsars with extremely high rotational energy loss rates. Accordingly, they are often referred to as energetic twins. Modelling the non-thermal multi-wavelength emission of N157B gives access to specific properties of this object, like the magnetic field inside the nebula. Comparing the derived parameters to those of the Crab Nebula reveals large intrinsic differences between the two PWNe. Possible origins of these differences are discussed in context of the resembling pulsars.
Compared to the TeV gamma-ray regime, the number of detected PWNe is much smaller in the MeV-GeV gamma-ray range. In the latter range, the Crab Nebula stands out by the recent detection of gamma-ray flares. In general, the measured flux enhancements on short time scales of days to weeks were not expected in the theoretical understanding of PWNe. In this thesis, the variability of the Crab Nebula is analysed using data from the Fermi Large Area Telescope (Fermi-LAT). For the presented analysis, a new gamma-ray reconstruction method is used, providing a higher sensitivity and a lower energy threshold compared to previous analyses. The derived gamma-ray light curve of the Crab Nebula is investigated for flares and periodicity. The detected flares are analysed regarding their energy spectra, and their variety and commonalities are discussed. In addition, a dedicated analysis of the flare which occurred in March 2013 is performed. The derived short-term variability time scale is roughly 6h, implying a small region inside the Crab Nebula to be responsible for the enigmatic flares. The most promising theories explaining the origins of the flux eruptions and gamma-ray variability are discussed in detail.
In the technical part of this work, a new analysis framework is presented. The introduced software, called gammalib/ctools, is currently being developed for the future CTA observa- tory. The analysis framework is extensively tested using data from the H. E. S. S. experiment. To conduct proper data analysis in the likelihood framework of gammalib/ctools, a model describing the distribution of background events in H.E.S.S. data is presented. The software provides the infrastructure to combine data from several instruments in one analysis. To study the gamma-ray emitting PWN population, data from Fermi-LAT and H. E. S. S. are combined in the likelihood framework of gammalib/ctools. In particular, the spectral peak, which usually lies in the overlap energy regime between these two instruments, is determined with the presented analysis framework. The derived measurements are compared to the predictions from the time-dependent model. The combined analysis supports the conclusion of a diverse population of gamma-ray emitting PWNe.

The H.E.S.S. array is a third generation Imaging Atmospheric Cherenkov Telescope (IACT) array. It is located in the Khomas Highland in Namibia, and measures very high energy (VHE) gamma-rays. In Phase I, the array started data taking in 2004 with its four identical 13 m telescopes. Since then, H.E.S.S. has emerged as the most successful IACT experiment to date. Among the almost 150 sources of VHE gamma-ray radiation found so far, even the oldest detection, the Crab Nebula, keeps surprising the scientific community with unexplained phenomena such as the recently discovered very energetic flares of high energy gamma-ray radiation. During its most recent flare, which was detected by the Fermi satellite in March 2013, the Crab Nebula was simultaneously observed with the H.E.S.S. array for six nights. The results of the observations will be discussed in detail during the course of this work. During the nights of the flare, the new 24 m × 32 m H.E.S.S. II telescope was still being commissioned, but participated in the data taking for one night. To be able to reconstruct and analyze the data of the H.E.S.S. Phase II array, the algorithms and software used by the H.E.S.S. Phase I array had to be adapted. The most prominent advanced shower reconstruction technique developed by de Naurois and Rolland, the template-based model analysis, compares real shower images taken by the Cherenkov telescope cameras with shower templates obtained using a semi-analytical model. To find the best fitting image, and, therefore, the relevant parameters that describe the air shower best, a pixel-wise log-likelihood fit is done. The adaptation of this advanced shower reconstruction technique to the heterogeneous H.E.S.S. Phase II array for stereo events (i.e. air showers seen by at least two telescopes of any kind), its performance using MonteCarlo simulations as well as its application to real data will be described.

In the presented thesis, the most advanced photon reconstruction technique of ground-based γ-ray astronomy is adapted to the H.E.S.S. 28 m telescope. The method is based on a semi-analytical model of electromagnetic particle showers in the atmosphere. The properties of cosmic γ-rays are reconstructed by comparing the camera image of the telescope with the Cherenkov emission that is expected from the shower model. To suppress the dominant background from charged cosmic rays, events are selected based on several criteria. The performance of the analysis is evaluated with simulated events. The method is then applied to two sources that are known to emit γ-rays. The first of these is the Crab Nebula, the standard candle of ground-based γ-ray astronomy. The results of this source confirm the expected performance of the reconstruction method, where the much lower energy threshold compared to H.E.S.S. I is of particular importance. A second analysis is performed on the region around the Galactic Centre. The analysis results emphasise the capabilities of the new telescope to measure γ-rays in an energy range that is interesting for both theoretical and experimental astrophysics. The presented analysis features the lowest energy threshold that has ever been reached in ground-based γ-ray astronomy, opening a new window to the precise measurement of the physical properties of time-variable sources at energies of several tens of GeV.

Water management and environmental protection is vulnerable to extreme low flows during streamflow droughts. During the last decades, in most rivers of Central Europe summer runoff and low flows have decreased. Discharge projections agree that future decrease in runoff is likely for catchments in Brandenburg, Germany. Depending on the first-order controls on low flows, different adaption measures are expected to be appropriate. Small catchments were analyzed because they are expected to be more vulnerable to a changing climate than larger rivers. They are mainly headwater catchments with smaller ground water storage. Local characteristics are more important at this scale and can increase vulnerability. This thesis mutually evaluates potential adaption measures to sustain minimum runoff in small catchments of Brandenburg, Germany, and similarities of these catchments regarding low flows. The following guiding questions are addressed: (i) Which first-order controls on low flows and related time scales exist? (ii) Which are the differences between small catchments regarding low flow vulnerability? (iii) Which adaption measures to sustain minimum runoff in small catchments of Brandenburg are appropriate considering regional low flow patterns? Potential adaption measures to sustain minimum runoff during periods of low flows can be classified into three categories: (i) increase of groundwater recharge and subsequent baseflow by land use change, land management and artificial ground water recharge, (ii) increase of water storage with regulated outflow by reservoirs, lakes and wetland water management and (iii) regional low flow patterns have to be considered during planning of measures with multiple purposes (urban water management, waste water recycling and inter-basin water transfer). The question remained whether water management of areas with shallow groundwater tables can efficiently sustain minimum runoff. Exemplary, water management scenarios of a ditch irrigated area were evaluated using the model Hydrus-2D. Increasing antecedent water levels and stopping ditch irrigation during periods of low flows increased fluxes from the pasture to the stream, but storage was depleted faster during the summer months due to higher evapotranspiration. Fluxes from this approx. 1 km long pasture with an area of approx. 13 ha ranged from 0.3 to 0.7 l\s depending on scenario. This demonstrates that numerous of such small decentralized measures are necessary to sustain minimum runoff in meso-scale catchments. Differences in the low flow risk of catchments and meteorological low flow predictors were analyzed. A principal component analysis was applied on daily discharge of 37 catchments between 1991 and 2006. Flows decreased more in Southeast Brandenburg according to meteorological forcing. Low flow risk was highest in a region east of Berlin because of intersection of a more continental climate and the specific geohydrology. In these catchments, flows decreased faster during summer and the low flow period was prolonged. A non-linear support vector machine regression was applied to iteratively select meteorological predictors for annual 30-day minimum runoff in 16 catchments between 1965 and 2006. The potential evapotranspiration sum of the previous 48 months was the most important predictor (r²=0.28). The potential evapotranspiration of the previous 3 months and the precipitation of the previous 3 months and last year increased model performance (r²=0.49, including all four predictors). Model performance was higher for catchments with low yield and more damped runoff. In catchments with high low flow risk, explanatory power of long term potential evapotranspiration was high. Catchments with a high low flow risk as well as catchments with a considerable decrease in flows in southeast Brandenburg have the highest demand for adaption. Measures increasing groundwater recharge are to be preferred. Catchments with high low flow risk showed relatively deep and decreasing groundwater heads allowing increased groundwater recharge at recharge areas with higher altitude away from the streams. Low flows are expected to stay low or decrease even further because long term potential evapotranspiration was the most important low flow predictor and is projected to increase during climate change. Differences in low flow risk and runoff dynamics between catchments have to be considered for management and planning of measures which do not only have the task to sustain minimum runoff.

One of the most exciting predictions of Einstein's theory of gravitation that have not yet been proven experimentally by a direct detection are gravitational waves. These are tiny distortions of the spacetime itself, and a world-wide effort to directly measure them for the first time with a network of large-scale laser interferometers is currently ongoing and expected to provide positive results within this decade. One potential source of measurable gravitational waves is the inspiral and merger of two compact objects, such as binary black holes. Successfully finding their signature in the noise-dominated data of the detectors crucially relies on accurate predictions of what we are looking for. In this thesis, we present a detailed study of how the most complete waveform templates can be constructed by combining the results from (A) analytical expansions within the post-Newtonian framework and (B) numerical simulations of the full relativistic dynamics. We analyze various strategies to construct complete hybrid waveforms that consist of a post-Newtonian inspiral part matched to numerical-relativity data. We elaborate on exsisting approaches for nonspinning systems by extending the accessible parameter space and introducing an alternative scheme based in the Fourier domain. Our methods can now be readily applied to multiple spherical-harmonic modes and precessing systems. In addition to that, we analyze in detail the accuracy of hybrid waveforms with the goal to quantify how numerous sources of error in the approximation techniques affect the application of such templates in real gravitational-wave searches. This is of major importance for the future construction of improved models, but also for the correct interpretation of gravitational-wave observations that are made utilizing any complete waveform family. In particular, we comprehensively discuss how long the numerical-relativity contribution to the signal has to be in order to make the resulting hybrids accurate enough, and for currently feasible simulation lengths we assess the physics one can potentially do with template-based searches.

In the present work synchronization phenomena in complex dynamical systems exhibiting multiple time scales have been analyzed. Multiple time scales can be active in different manners. Three different systems have been analyzed with different methods from data analysis. The first system studied is a large heterogenous network of bursting neurons, that is a system with two predominant time scales, the fast firing of action potentials (spikes) and the burst of repetitive spikes followed by a quiescent phase. This system has been integrated numerically and analyzed with methods based on recurrence in phase space. An interesting result are the different transitions to synchrony found in the two distinct time scales. Moreover, an anomalous synchronization effect can be observed in the fast time scale, i.e. there is range of the coupling strength where desynchronization occurs. The second system analyzed, numerically as well as experimentally, is a pair of coupled CO₂ lasers in a chaotic bursting regime. This system is interesting due to its similarity with epidemic models. We explain the bursts by different time scales generated from unstable periodic orbits embedded in the chaotic attractor and perform a synchronization analysis of these different orbits utilizing the continuous wavelet transform. We find a diverse route to synchrony of these different observed time scales. The last system studied is a small network motif of limit cycle oscillators. Precisely, we have studied a hub motif, which serves as elementary building block for scale-free networks, a type of network found in many real world applications. These hubs are of special importance for communication and information transfer in complex networks. Here, a detailed study on the mechanism of synchronization in oscillatory networks with a broad frequency distribution has been carried out. In particular, we find a remote synchronization of nodes in the network which are not directly coupled. We also explain the responsible mechanism and its limitations and constraints. Further we derive an analytic expression for it and show that information transmission in pure phase oscillators, such as the Kuramoto type, is limited. In addition to the numerical and analytic analysis an experiment consisting of electrical circuits has been designed. The obtained results confirm the former findings.

This thesis describes two main projects; the first one is the optimization of a hierarchical search strategy to search for unknown pulsars. This project is divided into two parts; the first part (and the main part) is the semi-coherent hierarchical optimization strategy. The second part is a coherent hierarchical optimization strategy which can be used in a project like Einstein@Home. In both strategies we have found that the 3-stages search is the optimum strategy to search for unknown pulsars. For the second project we have developed a computer software for a coherent Multi-IFO (Interferometer Observatory) search. To validate our software, we have worked on simulated data as well as hardware injected signals of pulsars in the fourth LIGO science run (S4). While with the current sensitivity of our detectors we do not expect to detect any true Gravitational Wave signals in our data, we can still set upper limits on the strength of the gravitational waves signals. These upper limits, in fact, tell us how weak a signal strength we would detect. We have also used our software to set upper limits on the signal strength of known isolated pulsars using LIGO fifth science run (S5) data.

Recurrence plots, a rather promising tool of data analysis, have been introduced by Eckman et al. in 1987. They visualise recurrences in phase space and give an overview about the system's dynamics. Two features have made the method rather popular. Firstly they are rather simple to compute and secondly they are putatively easy to interpret. However, the straightforward interpretation of recurrence plots for some systems yields rather surprising results. For example indications of low dimensional chaos have been reported for stock marked data, based on recurrence plots. In this work we exploit recurrences or ``naturally occurring analogues'' as they were termed by E. Lorenz, to obtain three key results. One of which is that the most striking structures which are found in recurrence plots are hinged to the correlation entropy and the correlation dimension of the underlying system. Even though an eventual embedding changes the structures in recurrence plots considerably these dynamical invariants can be estimated independently of the special parameters used for the computation. The second key result is that the attractor can be reconstructed from the recurrence plot. This means that it contains all topological information of the system under question in the limit of long time series. The graphical representation of the recurrences can also help to develop new algorithms and exploit specific structures. This feature has helped to obtain the third key result of this study. Based on recurrences to points which have the same ``recurrence structure'', it is possible to generate surrogates of the system which capture all relevant dynamical characteristics, such as entropies, dimensions and characteristic frequencies of the system. These so generated surrogates are shadowed by a trajectory of the system which starts at different initial conditions than the time series in question. They can be used then to test for complex synchronisation.